development of polymer composite materials for ......abs acrylonitrile butadiene styrene terpolymer...

Development of Polymer

Composite Materials For

Packaging And Storage Of

Liquid Food Products

Krishnamurthy Prasad

A thesis submitted in fulfillment of the requirement for the degree of

Doctor of Philosophy

Mechanical and Product Design Engineering

Faculty of Science, Engineering and Technology

Swinburne University of Technology

Melbourne, Australia

July 2020

Abstract

ii

ABSTRACT

Linear Low-Density Polyethylene (LLDPE) is widely used in the manufacture of

packaging films, containers and tanks. Knowing and controlling the extent of permeant

(gas/vapour/liquid) transport through the matrix polymer is critical in packaging applications.

This involves exerting control on the extent of porosity observed through the bulk of the system.

This can be achieved by changing the chemical and physical nature of the polymer, blending

the polymer with another, dispersing particulate, fibrillar or lamellar fillers, converting the

microstructure of the polymer to a cellular one, creating a laminate type structure or using an

effective combination of all these processes. Amongst these, the dispersion of hydrophilic fillers

(specifically, natural fibres) in combination with the right processing technique was found to

be the most economical way of tuning the porosity of a hydrophobic polymer such as LLDPE.

In this thesis, we have studied the effect of two processing techniques- the high pressure,

high shear compression molding and the low pressure, low shear rotational molding/

rotomolding on the porosity, mechanical and morphological properties of LLDPE wood flour

composites. From the trends in the measured properties, we have created a better understanding

of the effect of the processing method on the porosities and transport characteristics at different

scales (free volume, microscopic and macroscopic) in the polymer microstructure. Three types

of probes have been used for this purpose viz., a positronium (a bound state between an electron

and a positron that can resolve free volume level porosity), gaseous oxygen and liquid ethanol.

The gas and liquid transport phenomena studied in this thesis provide information for potential

application of these manufactured composites in storage applications. As the raw materials used

are food contact approved, the composites can be used also for food storage and packaging

applications. With this in mind, a detailed analysis of the mechanical performance of the

manufactured composites post ethanol sorption is also discussed. The observed porosity in the

rotomolded composites was then correlated to a suitable intensive property i.e. density. The VP

parameter that was consequently developed based on density trends was found to be extremely

effective in modelling gas (oxygen) permeability for both types of LLDPE natural fibre

composites we studied during the course of this thesis. Thus, the overall gas permeability of the

system could be directly correlated to an easily measurable intensive parameter. In addition, as

Abstract

iii

the composite material produced reincorporates waste products (wood flour) from the furniture

industry back into the supply chain it is also an economical and environment friendly solution.

We have also achieved a molecular understanding of the transport phenomena in a semi-

crystalline polymer system. We have used Molecular Dynamics (MD) based simulations run

on the High-Performance Computing systems g2 and OzStar. Specifically, during the course of

this thesis, various phenomena of interest are simulated in individual phases of a composite

material separately and the results of those simulations are combined to provide a

comprehensive view of the phenomenon through the composite. The systems simulated and

analysed during the course of this work are purely amorphous and purely crystalline

polyethylene, in addition to, lignin, cellulose and hemicellulose in wood. The simulated

observations are then verified using several intensive properties as a benchmark such as density

and free volume pore sizes. Once, the veracity of the simulated systems has been established,

the observed properties are input into several multi-phase semi-empirical models and

predictions on the trends in the properties of interest are made. Using data available in literature

and by generating our own experimental data, a rigorous test of the efficacy of the combined

MD- semi-empirical modelling approach is carried out. The phenomena tested include diffusion

(gaseous and liquid) and mechanical response (elastic moduli) as a function of temperature and

composition. Overall, a concerted effort is made to establish the importance of this approach

for realizing bottom up design.

Acknowledgement

iv

ACKNOWLEDGEMENT

This thesis is the culmination of a 16-year journey through a Bachelors and two Masters

degrees. A PhD is an investment and as such, is not a smooth road. Therefore, the people who

guide your journey are the most vital and I state my eternal gratitude to A. Prof. Igor Sbarski

and Dr. Mostafa Nikzad.

Igor, thank for your wisdom and care and indulgence. I will forever cherish our conversations

on history, football and diffusion. Thank you for making me fall in love with diffusion as much

as I am in with the other two.

Mostafa, without your drive, and your vision this thesis would not exist. Thank you for the

hours upon hours of science talk. Thank you for your honesty, forthrightness and dedication.

Thank you also to Peter Steer and Flexcube Pty. Ltd. for providing the raw materials and their

facilities for conducting preliminary product research.

This thesis is also dedicated to the memory of Prof. Pio Iovenitti. Pio thank you for all the help

you gave me during the various PhD progress reviews.

I am also very thankful to everyone in AD 206, ATC 801 and 802. You all made these years

fly by.

To my Amma and Appa, this is all for you. You believe in me more than I do myself. I do not

know what I would do without you.

To the JG, yesterday, today and tomorrow. You know who you are.

To Mumbai and Melbourne, my homes.

To Futbol Club Barcelona, thank you for bringing so much joy into my weekends.

And finally, to spoken word poetry, you found me. You found me.

Hey Chris, there’s a shadow on my sun.

நானும் ஒர ்கனவ ா ?

இந்த ஞாலமும் ப ாய் தாவனா ?

- ாரதியார ்

Declaration

v

DECLARATION I declare that this thesis contains no material which has been accepted for the award of any

other degree or diploma, except where due reference is made in the text. To the best of my

knowledge, this thesis contains no material previously published or written by another person,

except where due reference is made in the text.

KRISHNAMURTHY PRASAD 25th JULY 2020

vi

TABLE OF CONTENTS Chapter Page

Abstract ii

Acknowledgement iv

Declaration v

Table of contents vi

List of Nomenclature viii

List of Figures xv

List of Tables xxiii

1. Introduction 1

2. Literature Survey 11

2.1 Polymer Blends 15

2.2 Polymer Composites and Nanocomposites 24

2.2.1 Polymer Nanocomposites 24

2.2.2 Polymer Composites 29

2.3 Foamed Polymers 38

2.4 Polymer Laminates 46

2.5 Molecular Dynamics (MD) Based Simulations 55

3. Materials and Methods 90

3.1 Materials and Processing 90

3.2 Testing Material Properties 94

3.3 Molecular Dynamics (MD) Based Simulations and Semi-empirical Modelling 104

4. Results and Discussion 117

4.1 Influence of Material Composition and Processing Technique on the

Microstructural, Mechanical and Gas Transport Properties of LLDPE Wood

Flour Composites

117

4.2 Correlating Processing Technique to Permeant Transport Phenomena 145

4.2.1 Combining Molecular Dynamics and Semi-empirical Modelling for

Predicting Gas Diffusion. 145

Table of Contents

vii

4.2.2 Combining Molecular Dynamics and Semi-empirical Modelling for

Predicting Liquid Diffusion. 160

4.2.3 Using Molecular Dynamics in conjunction with Semi-empirical Models

for Predicting Trends in Elastic Moduli. 175

4.3 Ethanol Uptake and Influence on Long- and Short-term Mechanical Properties 183

5. Conclusions and Future Work 210

References 215

List of Publications and Presentations 232

viii

LIST OF NOMENCLATURE

ABS Acrylonitrile Butadiene Styrene terpolymer

ADC Azodicarbonamide

aH Semi-empirical parameter which represents the stress transfer between the fibre

and matrix

AMBER Assisted Model Building and Energy Refinement

bck Cox Krenchel fibre length distribution parameter

C Ethanol uptakes at any time t

C1 molar fraction of permeant in continuous phase

C2 molar fraction of permeant in dispersed phase

C∞ Ethanol uptakes at equilibrium

CFF Consistent Force Fields

CHARMM Chemistry at HARvard Molecular Mechanics

ci Atomic charge on atom ‘i’

cif Crystallographic Information File

CNT Carbon Nanotubes

CS Cellulose Stearate

D Diffusion/ Diffusion Coefficient

d' Distance that the permeant molecule must travel to diffuse through the

unmodified polymer

D0 Diffusion coefficient of the pure polymer

Dc Diffusion coefficient of continuous phase

DD Diffusion coefficient of dispersed phase

dD Diameter of wood flour dispersed phase particle

deff Effective molecular diameter

DFT Density Functional Theory

DMA Dynamic Mechanical Analyzer/Analysis

DSC Differential Scanning Calorimeter

List of Nomenclature

ix

E Elastic modulus

E Total energy

E11 Tsai Pagano longitudinal direction modulus

E22 Tsai Pagano transverse direction modulus

EAA Ethylene acrylic acid copolymer

EC Cohesive Energy Density

EC Elastic modulus of the continuous phase

ED Elastic modulus of the dispersed phase

Eeq Equilibrium modulus value

EIP Empirical Interatomic Potentials

Elfm Longitudinal single particle modulus of wood flour dispersed phase particle

EM Elastic modulus obtained using the Rule of Mixtures

EP Elastic modulus obtained using the Laminate Model

Elfm Transverse single particle modulus of wood flour dispersed phase particle

EPDM Ethylene-propylene-diene monomer copolymeric elastomer

EVA Ethylene Vinyl Acetate copolymer

f1 Free volume of continuous phase

f2 Free volume of dispersed phase

fA Free volume of amorphous phase

fC Free volume of crystalline phase

FDA Food and Drug Administration

FF Force field

g Proper bond dihedral angle

g0 Proper equilibrium bond dihedral angle

GAMESS General Atomic and Molecular Electronic Structure System

GNP Graphite Nanoplatelets

GO Graphene Oxide

GROMOS GROningen MOlecular Simulation

h Sample thickness in cm

HDPE High Density PE

HDPE-g-MA HDPE grafted with Maleic Anhydride

HIPS High Impact Polystyrene

HPC High Performance Computing


x

j Characteristic jump distance for a single permeant molecule

Jeq Equilibrium creep compliance values

k Ratio of the average pore radius (s) to the average crystalline lamellar thickness

(lC)

kd Force constant for bond length

kg Force constant for proper bond dihedral angles

kN Kilo Newton

kθ Force constant for bond angle

kϕ Force constant for improper bond dihedrals

l Length of wood flour dispersed phase particle

L' Distance that the permeant molecule must travel to diffuse through the modified

polymer

LDPE Low Density PE

LLDPE Linear Low Density PE

LMDPE Linear Medium density PE

MAPS Materials and Process Simulation

MD Molecular Dynamics

MDPE Medium density PE

mi Mass of atom ‘i'

MM Molecular Mechanics

MMT Montmorillonite

MPa Mega Pascal

MSD Mean Squared Displacement

MW Molecular Weight

MWNT Multiwall carbon Nanotubes

n0 Cox Krenchel fibre orientation parameter

n1 Cox Krenchel fibre length distribution parameter

nHTL Halpin Tsai model parameter longitudinal direction

nHTT Halpin Tsai model parameter transverse direction

N Number of atoms in a MD simulation

NA Avogadro’s number

NMR Nuclear Magnetic Resonance Spectroscopy

NPT Number, Pressure, Temperature ensemble


xi

NVE Number, Volume, Energy ensemble

NVT Number, Volume, Temperature ensemble

o Average jump distance between neighbouring cavities or free volume pores

OM Optical Microscope

OPLS Optimized Potentials for Liquid Simulations

P Pressure

p Pearson’s coefficient of correlation

PA Polyamide

PALS Positron Annihilation Lifetime Spectroscopy

PAO Poly (alklylene oxide)

PBT Poly (butylene terephthalate)

Pc Permeability coefficient of the pure polymer/ continuous phase

PC Poly (carbonate)

PCFF Polymer Consistent Force Field

PCL Poly (caprolactone)

PE Polyethylene

PECVD Plasma Enhanced Chemical Vapour Deposition

PE-g-MA Maleic anhydride grafted PE

PEN Poly (ethylene naphthalate)

PET Poly (ethylene terephthalate)

PHBV Poly (hydroxybutyrate-co-valerate)

PHEE Poly (hydroxyester ether)

PLA Poly (lactic acid)

PMMA Poly (methyl methacrylate)

PPC Poly (propylene carbonate)

PPRED Predicted permeability using the Alter model.

Ps Positronium

PS Poly (styrene)

PTFE Poly (tetrafluouroethylene)

PVDF Poly (vinylidene fluoride)

q Improper bond dihedral angle

q0 Improper equilibrium bond dihedral angle

QM Quantum Mechanical


xii

r Actual bond length

R Pore size

r0 Equilibrium bond length

RF Radio Frequency

RGO Reduced Graphene Oxide

RH Relative Humidity

Ri Position of atom ‘i’

rij Distance between the two non-bonded atoms i and j

Rn Nanoplatelet radius in the Frederickson and Bicerano model

RP Probe radius in a MD environment

RPM Rotations per minute of the molding unit during the rotomolding operation.

Rrf Cut off radius in a MD environment

RT Room Temperature

RTM Resin Transfer Moulding

S Solubility/ Solubility Coefficient

S0 Solubility coefficient of the pure polymer

SBR Styrene-Acrylonitrile copolymers with Butadiene

SciPCFF Scienomics’ Polymer Consistent Force Field

SEBS Styrene Ethylene Butadiene Styrene block copolymer

SEM Scanning Electron Microscopy

STP Standard Temperature and Pressure

T Temperature in absolute (K)

tc Residence time of the permeant molecule within the cavity

Tg Glass transition temperature

TRAPPE Transferable Potentials for Phase Equilibria Force Field

Ubend Potential energy associated with angular bending interactions in a MD

environment

Ubond Potential energy associated with bonding interactions in a MD environment

Ubondbend Cross term defining coupling between bond stretching and bond flexing in a MD

environment

Ubondbond Cross term defining coupling two separate Ubond interactions in a MD

environment

UFF Universal Force Field


xiii

UHBonding Potential energy associated with hydrogen bonding interactions in a MD

environment

Uimp Potential energy associated with improper bond dihedral interactions in a MD

environment

Unon-bond Potential energy associated with electrostatic, hydrogen bonding and van der

Waal’s interactions in a MD environment.

Upot Overall Potential Energy

Uvib Potential energy associated with bond vibrational interactions in a MD

environment

V Volume of simulation box

VARTM Vacuum Assisted Resin Transfer Molding

Vi Velocity of atom ‘i’

Vp Overall porosity of composite based on deviation of density from ρTH

Wn Nanoplatelet thickness in the Frederickson and Bicerano model

xck Cox Krenchel fibre volume dispersion parameter

α Dispersed phase aspect ratio

β Chain immobilization factor

δ % Average absolute relative error

ΔL/L Fractional change in length of composite specimen after ethanol uptake

ΔM/M Fractional change in mass of composite specimen after ethanol uptake

ε Effective dielectric constant of the medium

ε0 Vacuum permittivity (8.854 × 1012 F/m)

εij Well depth of the Lennard Jones potential between atoms ‘i' and ‘j’

θ Bond angle

θ0 Equilibrium bond angle

λ Improper angle corresponding to the deviation from planarity

λ0 Improper angle corresponding to the deviation from planarity at equilibrium

ρTH Theoretical density of composite obtained using Rule of Mixtures

σij Contact radius of the Lennard Jones potential between atoms ‘i' and ‘j’

σPR Poisson’s ratio

σx Stress in x direction

σy Stress in y direction

σz Stress in z direction


xiv

τ Tortuosity

τ1, τ2 and τ3 Decay lifetimes associated with PALS measurements

ϕ Dispersed phase volume fraction

ϕCr Crystalline volume fraction of dispersed phase

ϕC Cellulose crystalline volume fraction in wood flour dispersed phase

xv

LIST OF FIGURES Figure Page

number

Figure 1.1: Steps involved in the Rotomolding Process. From Crawford [12] 4

Figure 1.2: Methods of controlling polymer permeability and mechanical

properties

5

Figure 2.1: Schematic of Permeation. 1: Adsorption, 2: Diffusion/Dissolution

through the polymer, 3. Desorption into stored material.

11

Figure 2.2: O2 permeability of PLA-MMT (○) and PLA-PCL-MMT (●)

systems with varying MMT content. From Urquijo et al. [57].

17

Figure 2.3: Variation in permeability of O2 and N2 in HDPE-EVA with

varying volume fraction of EVA. From John et al. [59].

18

Figure 2.4: Different morphologies and corresponding tortuous path exhibited

in HDPE-EVA blend. From John et al. [59]

18

Figure 2.5: Scheme for manufacturing microfibrillar LLDPE-PET blends.

Matrix polymer = LLDPE, Reinforcing polymer = PET microfibrills. From

Shields et al. [1].

20

Figure 2.6: (a): O2 permeability and (b): CO2 permeability of LDPE-EVA-

GO (■) and LDPE-EVA-RGO (▲) nanocomposites. From Tayebi et al. [72].

25

Figure 2.7: Model for Tortuous pathway of gas through PPC/OLDH

composites. From Li et al. [75]

27

Figure 2.8: Effect of moisture uptake on the hardness (GPa) of vinyl ester

clay nanocomposites. From Alatayeh et al. [77]

28

Figure 2.9: Liquid water uptake for rotomolded LMDPE-15% fibre

composites. From Cisneros-López et al. [85]

31

Figure 2.10: SEM micrographs of LLDPE- flax fibre composites (a):

(LLDPE: 12.5% fibre content, 75, 110, 120, 130, and 140°C barrel

temperature profile, and 150 rpm screw speed; (b): LLDPE: 12.5% fibre

content, 75, 120, 130, 140, and 150°C barrel temperature profile, and 110 rpm

screw speed). From Siaotong et al. [86]

32

List of Figures

xvi

Figure 2.11: Effect of water desorption on the Young’s modulus in the vinyl

ester based material up to an equilibrium state at around 3% of weight loss.

From Singer et al. [89].

34

Figure 2.12: O2 permeability for quenched and slow cooled HDPE-cellulose

fibre composites. From Fendler et al. [7]

36

Figure 2.13: Structure of azodicarbonamide (ADC). 39

Figure 2.14: Liquid Water absorption characteristics of HDPE-Wood straw

flour composites at various proportions of foaming agent and nano-clay. From

Babaei et al. [97]

41

Figure 2.15: Schematic for sol-gel deposition of TiOx films on PEN substrate.

Pre heating step makes the film denser by inducing solvent evaporation. Post

heating promotes polycondensation. From Park et al. [118].

50

Figure 2.16: SEM images of Nylon/carbon fibre laminates after contact with

water. From Pillay et al. [49]

52

Figure 2.17: (a): NVE ensemble (closed system), (b): NVT ensemble (closed

system but not heat isolated), (c): NPT ensemble (isobaric-isothermal)

70

Figure 2.18: Logarithm of the diffusion coefficients as a function of square

effective diameters. From Mozaffari et al. [139]

72

Figure 2.19: PE matrix containing six polymer chains, each having 200 C

atoms. The ball-and-stick model represents the PE chains with their centre of

mass in the unit cell and the thin-line model represents their periodic replicas.

From Börjesson et al. [140]

73

Figure 2.20: Three typical MSDs of an oxygen molecule in PE at 308 K. The

average MSD, shown in black, reveals a linear increase in MSD with time.

From Börjesson et al. [140]

73

Figure 2.21: Equilibrated structures of (a): PE–graphene and (b): PE–CNT

nanocomposites. From Erdtman et al. [141]

75

Figure 2.22: Layering in (a): PE–graphene and (b): PE–CNT (right) systems.

From Erdtman et al. [141].

75

Figure 2.23: Simulated (a): SiO2 and (b): PVDF-SiO2 composites. From Bai

et al. [142]

76

List of Figures

xvii

Figure 2.24: The graphs of MSD vs. time after MD, representing the fitting

line relation. From Deghani et al. [144].

77

Figure 2.25: Oxygen permeability along the z axis for simulated PET/PEN

blends (a): without transesterification and (b): with transesterification. From

Fermeglia et al. [145]

78

Figure 2.26: Simulating effect of branch length effect on PE strength for

different branch moieties (black: methyl, red: ethyl, brown: butyl) and

comparing with available experimental data (blue). 2n is the number of C

atoms in the PE backbone chain (50). From Liao et al. [146]

79

Figure 2.27: CNT (brown) delaminates from PE chains (Green). From Jia and

Qingsheng [147]

80

Figure 2.28: Trends in mechanical properties of PMMA as a function of

temperature using different MD forcefields. From Sahputra et al. [148]

81

Figure 3.1: (a): Compression Molding machine, (b): Chilling unit of

compression molding machine.

91

Figure 3.2: (a): Rotomolding machine, (b): Control unit of Rotomolding

machine 92

Figure 3.3: (a): Compression molded with pine flour L-R: 0%, 5%, 10% and

20% by weight pine flour, (b) Rotomolded specimens with pine flour L-R:

0%, 5%, 10% and 20% by weight pine flour (c): Rotomolded specimens 5%

and 10% by weight of oak flour.

93

Figure 3.4: Zwick Z010 Universal Testing Machine with (a): tensile grips,

(b): flexural grips, (c): Samples for tensile and flexural testing. 94

Figure 3.5: (a): CEAST Impact Testing machine, (b): Samples for impact

testing. 95

Figure 3.6: Olympus BX61 Optical Microscope (OM) 95

Figure 3.7: Zeiss Supra 40 Vp Scanning Electron Microscope (SEM) 96

Figure 3.8: Emitech K975X sputtering unit 96

Figure 3.9: Oven where solvent uptake experiments are conducted.

Maintained at an average temperature of 30 ±1ºC 97

Figure 3.10: Refrigerator where solvent uptake experiments are conducted.

Maintained at an average temperature of 6±2 ºC 98

List of Figures

xviii

Figure 3.11: (a): Differential Scanning Calorimeter, (b): Chiller Unit attached

to DSC machine. 98

Figure 3.12: (a): TA DMA 2980 Dynamic Mechanical Analyzer, (b):

Specimens for creep and storage modulus measurement 99

Figure 3.13: Hysitron TI Premier Nanoindenter 100

Figure 3.14: MOCON OxTran 2/21 Oxygen Permeability Tester 100

Figure 3.15: Disc samples for Oxygen Permeability testing 101

Figure 3.16: Pycnometer with water filled up to mark. 102

Figure 3.17: (a): Positron source of PALS machine, (b): Sample chamber for

PALS analysis 103

Figure 3.18: Crystalline Unit cell of PE constructed using the partial

coordinates suggested by Bruno et. al. [162] 104

Figure 3.19: Crystalline supercell of PE with C atoms shown in blue and H

atoms in green made up of several individual units of Figure 3.2.1. 105

Figure 3.20: Amorphous simulation box of PE with C atoms shown in blue

and H atoms in green. 105

Figure 3.21: Constructing the semi crystalline simulation cell. 110

Figure 3.22: Simulated molecules of (a): Cellulose, (b): Lignin, (c):

Hemicellulose, (d): Water, (e): Cellulose polymers, (f): Hemicellulose

polymer, (g): Lignin polymer, (h): Simulated wood flour with cellulose in

brown, water in yellow, hemi cellulose in green and lignin in blue.

111

Figure 3.23: γ vs crystalline volume fraction ϕCr for different sized

permeants through LLDPE. From Compan et al. [37] 113

Figure 4.1: SEM images of the raw materials (a): LLDPE, (b): Pine flour, (c):

Oak flour. 118

Figure 4.2: Evolution of microstructure in the LLDPE raw material as a

function of time at 200 °C: (a): 5 min, (b): 10 min, (c): 15 min, (d): 30 min.

(e): 240 °C at 12 min.

119

Figure 4.3: Evolution of microstructure in LLDPE raw material with 5% pine

flour as a function of time (a): 200°C, 5 min, (b): 200°C, 10 min, (c): 240 °C

at 12 min.

120

List of Figures

xix

Figure 4.4: Evolution of microstructure in LLDPE raw material with 10%

pine flour as a function of time: (a): 200°C, 5 min, (b): 200°C, 10 min, (c):

240 °C at 12 min.

120

Figure 4.5: Evolution of microstructure in LLDPE raw material with 20%

pine flour as a function of time at (a): 200°C, 5 min, (b): 200°C, 10 min, (c):

240 °C at 12 min.

121

Figure 4.6: Evolution of microstructure in LLDPE raw material with 5% oak

flour as a function of time at (a): 200°C, 5 min, (b): 200°C, 10 min, (c): 240

°C at 12 min.

121

Figure 4.7: Evolution of microstructure in LLDPE raw material with 10% oak

flour as a function of time at (a): 200°C, 5 min, (b): 200°C, 10 min, (c): 240

°C at 12 min.

122

Figure 4.8: VP of all the pine flour composite samples as determined by Eq

(3.2.5). 124

Figure 4.9: SEM images of samples with no pine flour incorporation. (a):

CM0, (b): Smooth surface of RM0; (c): Rough surface of RM0. 124-125

Figure 4.10: SEM images of samples with wood flour incorporation. (a):

CM5, (b): CM5_O, (c): CM 10, (d): CM 20, (e): RM5 smooth surface, (f):

RM10 smooth surface, (g): RM20 smooth surface, (h): RM5 rough surface,

(i): RM10 rough surface, (j): RM20 rough surface

126-127

Figure 4.11: SEM images of microstructure of compression molded samples.

(a): CM0, (b): CM5, (c): CM10, (d): CM20. 128

Figure 4.12: SEM images of microstructure of rotomolded samples (a): RM0,

(b): RM5, (c): RM10, (d): RM20. 128-129

Figure 4.13: Rotomolded RM20 specimen with physical holes indicated by

the red circle. 129

Figure 4.14: Estimating pore sizes through microstructural SEM of a RM5

sample. 130

Figure 4.15: Rough pore size distribution estimates of all composites. 130

Figure 4.16: Absolute and Relative Tensile strengths of (a), (b): Rotomolded

and (c), (d): Compression Molded composites 131-132

List of Figures

xx

Figure 4.17: Absolute and Relative Flexural strengths of (a), (b): Rotomolded


Figure 4.18: Absolute and Relative Impact strengths of (a), (b): Rotomolded


Figure 4.19: Absolute and Relative Storage Modulus in Single Cantilever

mode of (a), (b): Rotomolded and (c), (d): Compression Molded composites 137-138

Figure 4.20: Absolute and Relative Storage Modulus in Tensile mode of (a),

(b): Rotomolded and (c), (d): Compression Molded composites 139-140

Figure 4.21: Oxygen Permeability of all rotomolded composites 142

Figure 4.22: Pore size distribution of the simulated amorphous and crystalline

polyethylene molecules. 146

Figure 4.23: (a): Amorphous and (b): Crystalline PE simulation boxes with a

single oxygen molecule in red. 147

Figure 4.24: PALS spectrum of Compression Molded LLDPE specimen

where the yellow, blue, grey and black lines correspond to τ1, τ2, τ3 and the

source component.

149

Figure 4.25: Comparison of MSD of O2 molecule averaged over 30 runs

observed in Amorphous (A) and Crystalline (C) PE with the linear fit over a

temperature range of 293-308 K with a 5 K temperature step.

150

Figure 4.26: Evolution of the total energies of the simulated Amorphous and

the Crystalline PE systems with inserted oxygen molecule. 151

Figure 4.27: Comparison of D (cm2/s) between reported values obtained from

[38, 163-166] and simulated PE molecules (crystalline and amorphous). 152

Figure 4.28: Predicted D values compared to the reported data. 153

Figure 4.29: Visualising the crystallite and amorphous segments of

Polyethylene with increasing crystallinity. 158

Figure 4.30: Pore size distribution of the simulated wood molecule shown in

Section 3.2, Figure 3.22h. 161

Figure 4.31: Amorphous PE molecules in red. Ethanol in green. 162

Figure 4.32: Cellulose in brown, water in yellow, hemi cellulose in green and

lignin in blue. Ratio is 40:30:30 by weight cellulose: lignin: hemicellulose. 8%

by weight of water. 1 molecule of Ethanol in black.

162

List of Figures

xxi

Figure 4.33: Mean square displacement (MSD) of the ethanol molecules in

the Polyethylene simulation box with trajectory segment showing MSD α t.

Averaged over 30 simulations and a period of 10 ns.

163

Figure 4.34: Uptake of Ethanol of all samples at 6°C 164

Figure 4.35: Uptake of Ethanol of all samples at 30°C 164

Figure 4.36: Ethanol diffusion coefficients for the compression and

rotomolded composites at 6°C 165

Figure 4.37: Ethanol diffusion coefficients for the compression and

rotomolded composites at 30°C 166

Figure 4.38: Swelling of all composites at 6°C 167

Figure 4.39: Swelling of all composites at 30°C 167

Figure 4.40: Visualising tortuosity where s: average pore radius, lC: average

crystalline lamellar thickness and aspect ratio α = 2d/lC 171

Figure 4.41: Predictive abilities of the models listed in Table 2.10 for ethanol

diffusion at 6°C. 172

Figure 4.42: Predictive abilities of the models listed in Table 2.10 for ethanol

diffusion at 30°C. 172

Figure 4.43: Simulated stress vs strain curves in tensile mode for (a): semi-

crystalline PE at 30°C, 60°C and 90 °C and (b) simulated wood flour at 30°C,

60°C and 90 °C, (c): Relative drop in modulus value (E) as compared to

modulus value at the start (Ei) for the simulated PE vs experimental values.

176-177

Figure 4.44: Comparisons with experimental value; (a): Absolute and (b):

Relative composite elastic modulus 179

Figure 4.45: Tensile strength vs ethanol uptake % for all compression molded

samples 184

Figure 4.46: Tensile strength vs ethanol uptake % for all rotomolded samples 185

Figure 4.47: Flexural strength vs ethanol uptake % for all compression

molded samples 186

Figure 4.48: Flexural strength vs ethanol uptake % for all rotomolded samples 187

Figure 4.49: Impact strength vs ethanol uptake % for all compression molded

samples 188

Figure 4.50: Impact strength vs ethanol uptake % for all rotomolded samples 189

List of Figures

xxii

Figure 4.51: Storage Modulus (Tensile mode) vs ethanol uptake % for all

compression molded samples 190

Figure 4.52: Storage Modulus (Tensile mode) vs ethanol uptake % for all

rotomolded samples 191

Figure 4.53: Storage Modulus (Cantilever mode) vs ethanol uptake % for all

compression molded samples 192

Figure 4.54: Storage Modulus (Cantilever mode) vs ethanol uptake % for all

rotomolded samples 193

Figure 4.55: Burger’s representation of a viscoelastic material. 194

Figure 4.56: Creep compliance of all compression molded composites before

ethanol contact. 195

Figure 4.57: Creep compliance of all rotomolded composites before ethanol

contact 196

Figure 4.58: Creep compliance of all compression molded composites after

sustained ethanol contact at (a) 6°C, (b): 30°C. 197-198

Figure 4.59: Creep compliance of all rotomolded composites after sustained

ethanol contact at (a): 6°C, (b): 30°C. 199

Figure 4.60: Equilibrium Modulus vs ethanol uptake of the compression

molded samples. 200

Figure 4.61: Equilibrium Modulus vs ethanol uptake of the rotomolded

samples. 201

Figure 4.62: tr for all compression molded composites 208

Figure 4.63: tr for all rotomolded composites 208

xxiii

LIST OF TABLES

Table Page

number

Table 2.1: Permeabilities of compatibilized and uncompatibilized LDPE/PA

blends. From Mistretta et al. [61] 19

Table 2.2: Tensile strength (MPa) of polyurethane polysulfide blends with

varying polysulfide content and different soaking times. From Zhang et al. [66]. 22

Table 2.3: XC and O2 permeabilities of PET and PET/GNP nanocomposites.

From Al-Jabareen et al. [74] 26

Table 2.4: Tensile Strength and O2 permeabilities of rotomolded PE blend nano-

clay composites. From Pavani et al. [76] 27

Table 2.5: Tensile strength, Impact strength and water vapour permeability of

PP/PS-Sisal nanofibrils composite. From Krishnan et al. [87]. 33

Table 2.6: Water vapour permeabilities and elastic modulus of LDPE-Pineapple

fibre (of different surface treatments) composites. From George et al. [88] 33

Table 2.7: Mechanical and permeability properties of pristine epoxy and

mesostructured silica-epoxy nanocomposite. From Park et al. [99] 42

Table 2.8: O2 Transmission rates of the composite films before and after bending

tests. (U: Undercoat, NC= No change). From Shim et al. [114] 48

Table 2.9: Functional forms of several Class I and Class II forcefields. 61

Table 2.10: Semi-empirical models for estimating D 84

Table 2.11: Semi-empirical models for predicting elastic moduli of composites

with randomly oriented dispersed phase. 87

Table 3.1: Process cycle time and other parameters of the compression molding

technique 91

Table 3.2: Process cycle time and other parameters of the rotomolding technique 91

Table 3.3: Samples made from each molding method with wood flour content. 92

Table 4.1: Densities of all the specimens obtained from pycnometry 123

List of Tables

xxiv

Table 4.2: Heat of fusion (ΔHM; J/g) and % Crystallinities of all samples at 3

different heating rates 141

Table 4.3: Experimental (Pexp) vs predicted (Ppred) oxygen permeability values of

rotomolded composites 143

Table 4.4: Experimental and simulated densities 146

Table 4.5: PALS data indicating average pore size (R; in Å) compression molded

and rotomolded composites and the raw material 148

Table 4.6: δ for the various models listed in Table 2.10 154

Table 4.7: Experimental and simulated densities 160

Table 4.8: Slopes of MSD plot and simulated D from Eq (3.2.1) 163

Table 4.9: Pearson coefficient (p) between the D (cm2/s; shown in Figure 4.36

and 4.37) and VP (Figure 4.8) for both compression and rotomolding techniques

at two temperatures.

166

Table 4.10: Thickness and Swelling coefficient for all samples. 168

Table 4.11: Diffusion Coefficients obtained using several tortuosity models and

comparing to experimental values. 169

Table 4.12: δ values for all the models used in this thesis for ethanol diffusion 173

Table 4.13: Storage modulus from tensile mode DMA of compression molded

and rotomolded plain Polyethylene 178

Table 4.14: δ values for the models when compared to the experimental modulus

values of the compression and rotomolded sample. 180

Table 4.15: EM and ηM for the compression molded composites 203-204

Table 4.16: EM and ηM for the rotomolded composites 205-206

Table 4.17: EK for the compression molded composites 206

Table 4.18: EK for the rotomolded composites 207

1

CHAPTER 1

INTRODUCTION

In the packaging and storage industry, an extremely large range of products ranging

from food items to computer parts are enclosed and protected from the environment and other

factors by the use of effective packaging [1-5]. The polymer manufacturing sector is a massive

supplier of raw materials for the packaging and storage industry [6] . Food items such as fruits,

vegetables, meat, poultry and grains are only some of the items that are protected from

interacting with the environment using polymer based packaging [4]. As much as 42% of all

polymeric material manufactured globally is used in one form or the other in the packaging

industry [6]. In addition, almost half of the polymer consumed by the packaging industry is

food packaging in the form of films, sheets, bottles, etc. [6].

Amongst the polymers used for packaging and storage applications, it is the polyolefins

that are by and large, the most consumed [4, 6]. These include Polyethylene (PE) in its various

forms such as Low-Density PE (LDPE), High Density PE (HDPE) and linear low-density PE

(LLDPE). LLDPE happens to combine the main features of both LDPE and HDPE i.e. it has

improved chemical resistance, improved performance at both high and low temperatures, higher

strength at a given density and increased flexibility [6]. Thus, LLDPE has been used quite

extensively for the manufacture of polymeric storage units or tanks and forms the main raw

material that will be used throughout the scope of this thesis.

Now, for the storage of food items it is known that the control of permeant transport

through the packaging system, is of critical importance. Therefore, extensive research has been

carried out on the prediction and modelling of the transport of several permeants through

polymers and their composites [1, 7, 8]. However, in this project, the packaging of specific

liquid-based food products viz., high alcohol content foods such as wine and spirits will be

considered. Therefore, it is necessary for the developed packaging systems to address three very

important requirements.

Introduction

2

1. Food contact approval,

2. Required permeation/transport characteristics

3. Retention of mechanical properties.

First and foremost, the raw material (LLDPE) and all additives used as part of the raw

material formulation and the chosen dispersed phase all should pass Food and Drug

Administration (FDA) approval. As far as permeation is concerned, exerting control on the

permeability is immensely important for the physical, chemical and microbiological safety of

the stored material. Controlling the permeability characteristics of a polymer can be achieved

in many ways (and will be discussed in more detail in Sections 2.1 to 2.4). The formulation

designed must also possess predictable permeation characteristics for the wine/spirit type

material that will be stored in it. Therefore, an equation must be developed by which the

permeability of the molded system can be predicted based on an intensive property of the

system. In this work, density has been chosen as the intensive parameter, but it may be another

parameter such as volume crystallinity. It must be noted that both the extent and mechanism of

penetration/permeation of a permeant molecule (typically low molecular weight gases and

liquids) through a polymer has a massive effect on the service performance of the polymer

product. Hence, the third aspect of this project is understanding the effect of permeant uptake

on the mechanical performance of the product.

The generation of interfaces in a polymeric system due to the presence of a dispersed

phase creates routes for permeant transport and uptake and thus, avenues for control on

permeation [9-11]. However, the uptake of such materials into the polymer matrix through

either the static or dynamic free volume holes, has a massive influence is on the mechanical

performance of the polymer. Therefore, a composition that can retain its mechanical strength is

necessary. Also, as it is possible that the application of the storage unit can be at both low and

high temperatures, the molded compositions must be tested for their mechanical properties in

contact with the food product at various temperatures. Overall, a drop of around 10% in

mechanical performance (as compared to molded specimens that are dry) is a benchmark that

will be set. Specifically, the mechanical properties studied will be quasi static properties such

as tensile and flexural strength, storage moduli and equilibrium moduli (from creep analysis).

These properties will be measured before and after the uptake of the stored material. Also, the

temperature of storage will be varied so that both temperature and concentration effects are

Introduction

3

considered when studying the behavior of the composite material that will be used to design a

storage unit.

Storage units for storing wine/spirits can be manufactured in a variety of ways but

Rotational Molding or Rotomolding has certain characteristics that make it the most attractive

prospect for manufacturing large volume units. Rotomolding is one of the fastest growing

polymer processing techniques. Products fabricated using rotomolding find application in a

wide spectrum of industries ranging from agriculture to the automotive sector [12-15]. It is a

very low shear process and therefore the polymers chosen must have the requisite flow

properties. The process of rotomolding consists of 4 basic steps as shown in Figure 1.1:

1. Charging: In the first step of the rotomolding operation, the raw materials (polymer

powder or liquid as per requirement) are introduced into the shell-like mold.

2. Rotation and Heating: It is important to understand that rotomolding does not rely

on centrifugal forces to throw the plastic against the mold wall. The speeds of

rotation are slow, and the powder undergoes a regular tumbling and mixing action

[12]. Thus, after charging and closing the mold, it is slowly rotated on two axes

perpendicular to each other to ensure that the powder/liquid pool at the bottom of

the mold contacts with the entire inner surface of the mold. Using a combination of

biaxial rotation and heating over a period, the powder melts and forms a coating on

the inner surface of the mold.

3. Cooling: When all the raw material has adhered itself to the inner surface of the

mold, the external surface of the mold is cooled while continuing the rotation so that

the plastic raw material solidifies and attains the desired shape.

4. De-molding: Once the desired shape has been achieved, the mold is opened, and the

product is removed.

Introduction

4

Figure 1.1: Steps involved in the rotomolding Process. From Crawford [12]

The various kinds of articles that may be produced using rotomolding include tanks (

septic tanks to storage), door armrests, instrument panels, wheel arches, traffic and road signs,

shipping and airline containers, lightweight aerospace components, refrigerated boxes, pallets,

fish bins, paramedic cases, furniture, toys, bins and trash containers, road cones, helmets, boats

and kayaks, tool boxes, agricultural/gardening equipment, etc. Due to the simplicity of the

process, rotomolding has very few competitors for the production of large (> 2 m3) hollow

objects in one piece [12]. The polymers that may be rotomolded consists of polyolefins

(polyethylene- specifically LLDPE is currently the largest consumed polymer for this

manufacturing technique [12-15]), polycarbonate, polyamides, polyurethanes, polyvinyl

chloride, Acrylonitrile-Butadiene-Styrene (ABS) terpolymer, High Impact Polystyrene (HIPS),

various fluoropolymers, liquids such as liquid Nylon block copolymer, liquid polyurethanes,

and recently, biodegradable plastics like PLA, foamed plastic analogues of the polymers already

mentioned, etc. [12-15].

However, when rotomolding is compared to conventional polymer processing methods

such as compression molding, injection molding or blow molding, there are some major

differences. One of them is that there are complete phase changes followed by structure

consolidation in the conventional processing techniques while complete phase changes are

often not observed in the rotomolding process. In fact, in the rotomolding process, the

Introduction

5

polymeric raw material undergoes a sintering process, and this is then followed by structural

consolidation. Therefore, to benchmark all the results in this thesis, all compositions

manufactured by rotomolding were also made using compression molding. Using this, the

effects of process shear/pressure on the mechanical and transport properties of multi-phase

polymeric systems will be understood and knowledge gained that could be useful for the

packaging and storage industry, at large.

As mentioned earlier, there are three major requirements that the designed storage unit

must fulfill, and a comprehensive literature search was done for materials and methodologies

that could possibly do that and they are shown in Figure 1.2. More details on the literature

search are shown in Section 2.1 through Section 2.4 but briefly, the major ways include the

development of polymer blends, polymer composites or nanocomposites (depending on the

dimensions of the dispersed phase), creating laminates by coating or depositing thin layers of

high barrier materials on the polymer surface or converting the microstructure into a cellular

form via the incorporation of foaming agents [16].

Figure 1.2: Methods of controlling polymer permeability and mechanical properties

Introduction

6

The most suitable technique amongst these, for this thesis, was found to be the

development of polymer natural fibre composites. Traditionally, wines and spirits are stored in

wooden barrels and developing a polymer composite based on wood flour would have aesthetic

and functional properties that the other techniques could not offer. The mechanical and transport

properties of the developed composition were then comprehensively measured and modelled.

While this concluded the experimental section of the project, a further aspect of this study

involved developing a more fundamental understanding of the multi-phase polymer system and

to that effect, the use of Molecular Dynamics (MD) and semi-empirical modelling was

employed.

The application of MD is to act as a conduit between the macroscopic laboratory

environment and the microscopic length and time scales of transport processes in polymeric

systems. Basically, using MD allows the prediction of the static and dynamic properties of

molecules directly from the underlying interactions between the molecules. Thus, exact values

of bulk properties (or within experimental error) can be obtained and also an understanding of

the atomic/molecular scale processes occurring concurrently with these macroscopic

observations be gained. The earliest MD simulation was in the year 1957 by Alder and

Wainwright [17] wherein perfectly elastic collisions were considered to be the only way in

which the atoms of the simulated system can interact. This was later improved upon by Rahman

[18] who applied a smooth, continuous potential to mimic real atomic interactions. The first

complex MD simulation was done for a protein [19] by developing an empirical energy function

constructed using first-principles assumptions. In the case of multi-phase polymeric systems

like the polymer natural fibre composites that will be developed in this thesis, the overall

modelling of any physical phenomenon can be done much more efficiently by using MD in

combination with either Empirical, Deterministic or Semi-Empirical mathematical models.

Empirical modelling refers to methods that characterize the system through techniques

such as polynomial regression. These techniques have the advantage of being fast to implement,

calibrate and simulate but do not offer any knowledge about the physics of the process [20].

Deterministic models, on the other hand, implement equations that describe all the physico-

chemical processes that comprise that particular phenomenon. Such models are more accurate

than empirical models and provide exhaustive information about the phenomenon itself but are

computationally intensive and time consuming [21]. The third option of semi-empirical

modelling helps combine the advantages of the empirical and deterministic techniques while

Introduction

7

minimizing the inherent drawbacks. Semi-empirical modelling is a versatile technique used

successfully in several engineering fields ranging from the sizing and the simulation of heat

exchangers, pumps and expanders [22], fluidized [23] and packed bed reactors [24], modelling

phenomena such as adsorption [25], combustion [26], diffusion [27], sorption [28] and viscosity

[29] and predicting physical properties such as elastic moduli [30]. In this project, the

observations from MD in combination with semi-empirical modelling were utilised to

effectively to predict trends in both transport and mechanical properties.

Thus, this project aims to contribute to the overall scientific view of transport through

multi-phase polymer systems and the corresponding effect on the mechanical performance. The

way to achieve that is two-fold:

1. Develop a semi-empirical model that takes into account the effect of processing on both

the mechanical performance and on the permeation characteristics of the designed

multi-phase polymeric system.

2. Use MD based simulations to develop representative models of all materials involved

viz., the polymer, the dispersed phase and the permeant and correlate the simulated

models with experimental results and improve the level of agreement between the two

results.

These models, and the ones developed during the course of this thesis and the various

properties of multi-phase polymeric systems, especially those that influence their mechanical

and transport properties, exerting control on these transport phenomena (diffusion, solubility

and permeability), the overall method of MD based simulations and the contributions made by

this thesis to this sphere are all detailed in Chapter 2.

The overall thesis structure is as follows:

In Chapter 1, a brief introduction of the thesis and the research question is provided.

In Chapter 2, a review of the relevant literature for transport property modification of

multi-phase polymer systems, semi-empirical modelling approaches for predicting transport

properties and the simulation of macromolecules through MD is provided.

In Chapter 3, the materials used during the course of this thesis and all of the

experimental and simulation methodologies are laid out. A thorough description of each

individual method is provided along with several parameters used in the MD simulations

throughout this thesis.

In Chapter 4 Section 1, the processing technique used is correlated to microstructural,

morphological and gas transport features of LLDPE wood flour composites. An intensive

Introduction

8

parameter (density) is used to model the overall gas transport properties of the fabricated

composites.

In Chapter 4 Section 2.1, a proof of concept for demonstrating the efficacy of combining

MD with semi-empirical modelling is shown. Here, an experimental property i.e. the diffusion

coefficient of O2, an essential permeant for consideration in food packaging applications, is

predicted as a function of temperature in LLDPE. A novel approach involving the separate

simulation of O2 diffusion in amorphous and crystalline LLDPE and then the semi-empirical

combination of these two results to predict overall diffusion is laid out. The amorphous and

crystalline LLDPE models are validated using density and free volume pore size data obtained

experimentally. The most efficacious model based on overall deviation of predicted data from

experimental data is suggested.

In Chapter 4 Section 2.2, the results obtained from Chapter 4 Section 2.1 are used to

model liquid (ethanol) diffusion coefficients in the fabricated composites. Following on from

the simulation of amorphous and crystalline LLDPE, a MD model of the dispersed phase i.e.

wood flour is developed and validated. Similar to Chapter 4 Section 2.1, the MD model of the

wood flour is validated using density and free volume pore size data and the semi-empirical

models used in Chapter 4 Section 2.1, are then tested for their efficacy in modelling liquid

diffusion. Once again, the most efficacious model based on overall deviation of predicted data

from experimental data is suggested.

In Chapter 4, Section 2.3, after the successful prediction and modelling of diffusion

phenomena in the fabricated composites, the MD approach is used to predict the mechanical

properties (specifically the elastic modulus of the fabricated composites). Semi-empirical

approaches are used to fit the simulated data to the experimental values obtained and once again

the best fit model is discussed.

In Chapter 4 Section 3, the effect of ethanol uptake on the mechanical properties of the

compression and rotomolded composites are investigated. In addition, a critical property for

storage application i.e. the creep compliance trends of our fabricated composites are studied in

three separate conditions, dry, after ethanol sorption at a relatively low temperature (6°C) and

after ethanol sorption at a relatively high temperature (30°C). Viscoelastic modelling is carried

out using the four element Burger’s model and intrinsic properties of the fabricated composites

including the Maxwell moduli and viscosities, Kelvin Voigt moduli and overall relaxation times

are analysed. The most viable composition of wood flour (pine and oak) based on retention of

overall stiffness is suggested.

Introduction

9

In Chapter 5, the overall conclusions of the entire thesis are presented and possible

future work based on the conclusions of this thesis are suggested.

Attached to the end of Chapter 5 is all the research that has been referred to and cited in

this entire thesis.

Finally, a list of all the publications and presentations made during the course of this

thesis are shown.

To conclude this section, the main objectives in terms of research and engineering

output of this project are listed out as follows:

1. The design of a LLDPE (composite or otherwise) storage unit for organic liquid storage.

Study the effect of the microstructures for its viability for organic liquid storage. Model

the permeation characteristics of the material used as a function of some intensive

property characteristic of the system.

2. Analyze the effect of composition on overall mechanical, morphological and transport

properties. The main property that affects all these properties is the overall porosity.

This project will be aimed that the process of creating porosity does not adversely affect

the mechanical properties of the proposed composition.

3. Optimise dispersed phase concentration in manufacturing rotomolding technique and

the benchmarking compression molding method. Compare and contrast the two values.

4. In depth first principles study of the transport process of relevant low molecular weight

permeants through PE and through the chosen dispersed phase using MD. Correlation

of simulated results with experimental results.

5. Isolate the mechanism of transport in the amorphous and crystalline regions of the semi-

crystalline LLDPE.

6. Analyse porosity (free volume level, micro and macro porosity) that can exist in a multi-

phase polymer composite system. Use of probes of different sizes and states to study

the overall pore size distribution in the system. This will also help correlate results from

widely disparate characterization methods and help analyse the relationship between the

nature of the probe and the measurement of porosity. Here again, MD will be used to

correlate the simulated data to experimental results.

7. Predict trends in transport and mechanical properties of the composites using a

combination of MD based simulations and semi-empirical modelling. Demonstrate

versatility and effectiveness of this approach. Also, discuss the current limitations and

ways to improve the approach.

Introduction

10

Based on these objectives the following scientific and engineering contributions can be

made

1. An in-depth analysis of the trends in static and dynamic mechanical properties of

composites made by a sintering-based processing technique (Rotomolding) vs those of

a conventional phase change and consolidation-based processing technique

(Compression Molding).

2. Correlating the trends in gas and liquid transport phenomena to an intensive parameter

characteristic of the processing method and the polymeric system.

3. Developing a Molecular Dynamics (MD) based methodology or algorithm that can help

predict trends in both transport and mechanical properties of multi-phase polymeric

systems with high accuracy.

11

CHAPTER 2

LITERATURE SURVEY

Fundamentally speaking, transport processes like permeation occur in a polymer in three

steps. A schematic of the process is shown in Figure 2.1 and is comprised of:

1. Adsorption of the penetrant molecule on one surface of the polymer

2. Sorption (dissolution) into and diffusion of the penetrant through the polymer.

3. Desorption from the other surface of the polymer.

Figure 2.1: Schematic of Permeation. 1: Adsorption, 2: Diffusion/Dissolution through the

polymer, 3. Desorption into stored material.

Permeation also occurs through pores, pinholes or microscopic cracks present in the

polymer. This is called the pore effect or Knudsen flux and is inversely proportional to the

square root of the molecular weight of the permeant [11]. In addition, the presence of free

volume holes (created by Brownian motions of the chains or by thermal perturbations) also play

an important role [11]. Thus, the overall transport of permeants through a polymer is a

combination of transport through the scheme in Figure 2.1, the influence of free volume holes-

both static and dynamic, and the presence and distribution of pores throughout the volume of

the polymer [11].

Literature Survey

12

Now, the static free volume is essentially independent of the thermal motions of the

polymer chains and is related to gas solubility or the solubility coefficient- S. Dynamic free

volume, on the other hand, derives from accessible conformational changes and segmental

motions of the polymer chains and is related to gas diffusivity or the diffusion coefficient-D. In

addition, S is a thermodynamic factor while D is more of a kinetic factor that reflects the

mobility of the permeant molecules in the polymer phase [10, 11, 31]. The overall permeability

(P) is the product of these two coefficients and is given by:

P = D × S (2.1)

The major factors that determine the nature and extent of permeant transport through a

polymeric system are the characteristics of the materials involved (polymer and permeant),

environmental factors (temperature and humidity), porosity factors (density, crystallinity,

nature of the dispersed phase and the corresponding interfacial tension) and geometry [9-11,

32-34]. In this thesis, we will be concentrating on the influences of microstructure and dispersed

phases and to that end, a quantity known as ‘Tortuosity’ (τ) needs to be defined. Physically

speaking τ can be defined using Eq (2.2) and the overall diffusion coefficient, D can then be

defined using Eq (2.3). Thus, τ is a measure by which the diffusion and permeability of a

permeant through a polymer matrix is affected. Various models for τ have been developed and

these been detailed in several reviews [10, 11, 35, 36]. An increased tortuosity indicates that

the permeant will take a longer time to permeate through the polymer while conversely a

reduced tortuosity will increase the permeant transport through the polymer matrix.

τ = L′

d′ (2.2)

where L’ and d’, are the distances that the permeant molecule must travel to diffuse

through the modified polymer matrix and the pure polymer respectively.

D = D0

τ (2.3)

where D0 is the diffusion coefficient of the pure polymer

Literature Survey

13

τ depends upon the aspect ratio, the shape, orientation and the extent of dispersion of

the dispersed phase in the matrix. The solubility coefficient is also affected by the dispersed

phase and becomes,

S = S0 (1 − Φ) (2.4)

where S0 = solubility coefficient of the pure polymer matrix and ϕ = volume fraction of

the dispersed phase within the system. This is the case if and only if the densities of the

crystalline phase are much higher than the density of the amorphous phase. In fact, for semi

crystalline polymers it has been observed that the S value even at 100% crystallinity is not zero

but rather a finite non-zero value [37]. In some specific cases, the S value for completely

crystalline polymer was found to be as much as 30% of the S value for the completely

amorphous version of the same polymer. In general, this indicates that the relationship of S with

ϕ is exponential in nature rather than linear [37-39].

Combining Eq (2.3) and Eq (2.4), the overall permeability P can be expressed as,

P = D0 S0 (1−Φ)

τ (2.5)

P = PC1−Φ

τ (2.6)

where the permeability of the continuous phase (Pc) is given by:

PC = D0 × S0 (2.7)

Eq (2.6) is just one of the major models used for defining the permeation in multi-phase

polymeric systems. There are several other mathematical models available in literature that

relate P to τ or PC. The models have been detailed in reviews by George and Thomas [9] ,

Hiltner et al. [10], Choudalakis and Gotsis [11], Tan and Thomas [35], Cui et al. [36], etc. These

models have limitations (for instance, some can only be used for low dispersed phase

concentrations (ϕ lower than 20% by volume) but provide a useful way to measure transport

properties in different multi-phase polymeric systems.

Literature Survey

14

The ways in which the transport properties of a polymeric system can be controlled are

by the development of multi-phase systems such as polymeric blends [40-42], incorporating

fillers to generate polymeric composites or nanocomposites [43-45], coating the polymer

surface with high barrier materials [46] or the incorporation of foaming agents to form a cellular

structure [47, 48]. All of these operations have effects on the porosity, fractional free volume,

segmental mobility, internal microstructure, crystallinity, and density of the system. While the

equations laid out in Eq (2.1) to Eq (2.7) are, for the most part, valid for all permeants

independent of the phase it must be noted that for liquid permeants, the sorption step is of added

importance. As the materials studied in this thesis will be multi-phase in nature, the sorption of

liquid permeants is of specific relevance. Therefore, extensive studies have been done on the

nature of sorption in single phase and multi-phase polymeric systems such as the studies of

Pillay et al. [49], Shen and Springer [50] and Ishak and Berry [51]. Based on their results, it has

been established that the sorption of liquid permeants in multi-phase polymeric systems

proceeds via the pathway of Fickian diffusion [49-51]. While it is common knowledge that the

dispersion of a filler into the polymer matrix or tuning the microstructure of a polymer can also

have substantial effects on the mechanical properties of the polymer, if an efficient packaging

system is to be designed mere exertion of control on the transport characteristics is not enough.

The effect of permeant sorption on the mechanical properties of a multi-phase polymeric system

also need to be analysed. In fact, exertion of control on the transport properties should not gain

precedence over the mechanical properties of the designed storage unit.

For the permeants of gaseous or vapour form, the corresponding effect on the

mechanical properties of a multi-phase polymeric system is limited. While some minor

plasticization may be seen (resulting in a slightly lowered modulus value) in general, the uptake

would have limited effects on the overall stiffness and so the mechanical properties post uptake

would be similar to those before uptake. However, for liquid permeants this is markedly

different. The diffusion of the liquid molecules through the microstructure of the multi-phase

polymeric system will indeed influence the mechanical properties a lot more than gaseous or

vapor form permeants. For the potential industrial application of the materials studied in this

thesis it is essential that an understanding is obtained of the transport mechanism of permeants

of gaseous and liquid form and the corresponding influence of the liquid permeant on the

mechanical properties of the material studied. Therefore, for each type of multi-phase polymeric

system studied in this chapter, the influence of the type of dispersion or the microstructure

generated on the mechanical properties of the polymer are also taken into account.

15

2.1 POLYMER BLENDS

Most synthetic homopolymers may be defined as a blend of a well-defined and ordered

polymer (crystalline region) within a matrix of disordered amorphous region. They are, hence,

referred to as semi crystalline materials [11]. A polymer blend, concurrently, is defined as a

system where domains rich in one polymer species are distributed in a matrix comprised largely

of a second polymer species with differing crystalline or amorphous and rubbery or glassy

natures. If a rubbery polymer (elastomer) is dispersed in a plastic phase, then the blend obtained

has a significantly improved impact strength (an example of this is HIPS [52]). If a plastic type

material is dispersed in an elastomeric phase, then reinforcement of the elastomer is observed

as a consequence [53]. Historically important polymer blends include cross-linked phenol-

formaldehyde with natural rubber, styrene and styrene-acrylonitrile copolymers with butadiene

(SBR and ABS, respectively), ABS with polycarbonate (PC) and PVC, Linear Low Density PE

(LLDPE) with Low Density PE (LDPE), Polypropylene oxide-HIPS-Nylon, Polysulfone-ABS,

PET or Polybutylene terephthalate (PBT) with PC, etc. [52]

In general, polymeric blends are either of a miscible or immiscible (large proportion of

all blends) nature. In both cases, the overall blend properties are mainly defined by the

interaction between the polymeric phases, degree of heterogeneity, the extents of crystallinity

and rubbery/glassy characteristics [9-11]. In addition, the internal structure of the blend post

formation should either have increased or reduced tortuosity as compared to the virgin polymers

(explained in Chapter 1). In addition, the viscosity ratio i.e. the ratio of the dispersed phase

viscosity to that of the matrix/continuous phase is another important parameter to be considered

in blend formulation. Easier deformation of the dispersed phase leads to the formation of well-

extended ellipsoidal morphology and increased tortuosity within the blend. Choosing the right

polymers with the right viscosity ratio can help exert rigorous control on the permeability of

the blend [9-11]. Incompatible blends often have interfacial pores between the continuous and

dispersed phases and these pores can also have a detrimental effect on the mechanical properties

such as lowered stiffness and also create areas of stress concertation that can lead to poor impact

properties.

Geerts et al. [54], blended EPDM (an ethylene-propylene-diene copolymeric elastomer)

with different dimethylsiloxanes to form an immiscible polymer blend. They discovered that

even a small incorporation of the siloxane results in a major change in the overall permeability

Literature Survey: Polymer Blends

16

of the polymer (20 times increase with 25% volume fraction of siloxane). Marcandalli et al.

[55] carried out the melt based blending of PP with hydrogenated oligocyclopentadiene

resulting in a system with permeability characteristics that could be controlled with post

fabrication annealing. They stated that with controlled annealing they were able to create a

porous (cellular) microstructure which contributed to increased permeability. Polymers with

such microstructure will be covered in more detail in Section 2.3. Passador et al. [56] studied

blends of High Density PE (HDPE) with LLDPE and concluded that the incorporation of

LLDPE into a HDPE matrix (without any compatibilizing agent) had a significant effect on the

water and oxygen barrier properties. As LLDPE is lower in crystallinity than HDPE, the formed

blend allowed for an increased transport of oxygen while the non-polar nature of the blend

reduced the transport of water vapour. Thus, selectivity of gas permeation through the blend

depending on blend composition (permeselectivity) was achieved by only a simple melt based

blending [56]. All these blends show high potential for scale up as no major changes in the

overall processability are observed i.e. both the blend and the primary polymer can be processed

under the same conditions using the same machine design. No analysis was done however of

the mechanical properties of the blend in Geerts et al. [54] or in Marcandalli et al. [55] but

Passador et al. [56] carried out a systematic analysis of the blend crystallinity which could later

be correlated to the stiffness.

A more comprehensive study on both transport and mechanical properties of a

polymeric blend was done by Urquijo et al. [57]. While in Passador et al. [56] the crystallinity

of the blends were measured (which could be correlated to elastic modulus values), in [57]

direct measurements of modulus values were carried out in addition to oxygen permeability.

Specifically, Urquijo et al. [57] observed that when blending two biopolymers viz., Poly (lactic

acid)- PLA and Poly (caprolactone)- PCL [57], due to the relatively lower crystallinity of PCL

than PLA, the dispersion of PCL into the PLA matrix via melt blending has the effect of

increasing the oxygen transport (Figure 2.2). In addition, no significant reduction in the

mechanical properties were observed. In fact, Urquijo et al. [57] went further by improving the

mechanical properties of the blend by adding a nano-clay filler. They also observed a sharp rise

in the complex viscosity of the blend (up to 100 times increase in PLA-7 weight%

montmorillonite (MMT) as compared to plain PLA and up to 1000 times increase in PLA-PCL

as compared to PLA-PCL-7 weight% MMT). Polymeric systems of this type will be addressed

in more detail in the polymer nanocomposite section (Section 2.4).


17

Figure 2.2: O2 permeability of PLA-MMT (○) and PLA-PCL-MMT (●) systems with varying

MMT content. From Urquijo et al. [57].

According to Lange and Wyser [58], for an engineering polymer such as PET (which

has excellent solvent resistance), permeability is reduced between 2 and 10 times on an average

with respect to the base PET for about 5–30 % barrier polymer in the blend. Incorporation of

an aromatic polyester or a liquid crystalline polymer will increase the tortuosity to such an

extent that the obtained oxygen permeability is 50-100 times lower than that of base PET.

Conversely, John et al. [59] discovered that when Ethylene Vinyl Acetate copolymer (EVA) is

dispersed in a HDPE matrix, the overall permeability of the blend was higher than that of the

base HDPE. However, at high weight fractions of EVA (30 volume% and higher), the increase

in permeability with EVA incorporation is not as marked. Here, the blend morphology shifts

from a dispersed phase-continuous phase system to a co-continuous morphology (similar to an

interpenetrating polymer network, increasing the tortuosity and consequently, the extent of

increase in permeability is reduced). The variation in O2 and N2 permeabilities as a function of

EVA concentration is shown in Figure 2.3 and the mechanism for this is shown in Figure 2.4.

With the use of compatibilizers like Maleic anhydride grafted PE (PE-g-MA) it is observed that

there is better adhesion amongst the two phases and the overall permeability reduces but

remains higher than the base HDPE. This is due to the stabilizing effect of the compatibilizer

(increased interfacial adhesion) during the processing of the blend. Thus, control on the

permeability characteristics can be exerted by choosing whether to use a compatibilizer or not.


18

Figure 2.3: Variation in permeability of O2 and N2 in HDPE-EVA with varying volume fraction

of EVA. From John et al. [59].

Figure 2.4: Different morphologies and corresponding tortuous path exhibited in HDPE-EVA

blend. From John et al. [59]

Santamaria et al. [60] fabricated an engineering polymer blend films of PC and

amorphous Polyamide (PA). They discovered that despite the biphasic nature of the blend (no

compatibilizer was used), the permeability of the blend to oxygen was reduced by 31% at a

25% weight ratio of amorphous polyamide. This was further accompanied by an improvement

by ~10% in the elastic modulus. They also studied the effect of differing draw ratios on the

mechanical and barrier properties and found that the permeability of the blends decreased

(around 36%) with increasing the draw ratio from 5 to 15. These decreases were attributed to

the higher fibrillation at high draw ratios which increased the aspect ratio of the dispersed phase

and the tortuosity of the oxygen path. Mistretta et al. [61] blended PA with LDPE (25 weight%


19

PA, 75 weight% LDPE) and found that the incorporation of the engineering polymer PA

resulted in improved mechanical properties even under photo-oxidative conditions. The

improvement seen was also attributed to the use of maleic anhydride grafted SEBS (Styrene

Ethylene Butadiene Styrene) block copolymers as compatibilizers. However, the use of the

compatibilizer in this case resulted in lowered crystallinity leading to increased oxygen

permeability (Table 2.1). The actual mechanism for reduction in crystallinity with

compatibilization was not well defined but it showed how influential the crystallinity of the

fabricated blend is on the mechanical and barrier properties.

Table 2.1: Permeabilities of compatibilized and uncompatibilized LDPE/PA blends. From

Mistretta et al. [61]

Sample O2 Permeability [cm3 (STP) cm/cm2/s/atm]

LDPE/PA 6.82 × 10-9 ± 4 × 10-10

LDPE/PA/SEBS 2.95 × 10-8 ± 2 × 10-9

The major advantages of using polymeric blends is that it is possible to tailor the barrier

properties to the specific requirements of the manufacturer/application with little or no

modification of the existing processing equipment required [9]. However, some polymer blends

have been reported to undergo phase separation or spinodal decomposition after processing due

to temperature changes, applied shear force or pressure change [62]. Therefore, stabilizing

polymer blends at the interface becomes important. One way around this quandary is improving

the dispersion of the secondary phase into the primary polymer via the utilization of ultrasound

during processing as observed in the work by Hong and Lee [63]. However, the much-improved

impact strength of the synthesized blend cannot negate the significant increase in processing

cost that the use of a specialised ultrasonic transducer would entail. Another method is the use

of compatibilizing agents like maleic anhydride grafted polymers, silanes, etc. This limits the

application of the polymeric blend in food contact/storage or related applications as the toxicity

of the compatibilizer becomes an issue. This issue may be resolved using a dispersed phase

which is biologically benign. For instance, Krasnou et al., [64] synthesized a PP- Cellulose

Stearate (CS) blend. The use of CS had a two-fold advantage. Firstly, it was possible for melt-

based processing of the blend material (unmodified base cellulose is non-melting behaviour and

hence, high processing temperatures are required). Secondly, the water vapour permeability of


20

the blend can be controlled due to the increased hydrophobic nature of the dispersed CS phase

as compared to base cellulose [64].

It is also possible to manage the morphology of the manufactured blend by using

specialised processing techniques. For instance, PET in a microfibrillar form was dispersed in

a Linear Medium density PE (LMDPE) phase by Lin et al. [65] (who also dispersed Poly

(ethylene naphthalate); PEN) and in LLDPE by Shields et al. [1]. Lin et al. [65] used

rotomolding to achieve this dispersion. First, they produced a PE-PET or PE-PEN master-batch

using single screw extrusion, drew the formed blend to achieve a microfibrillar morphology

and dispersed the microfibrils in PE by rotomolding. Unlike PET microfibrils, which lost their

fibrillar structure after rotomolding, PEN could retain the microfibrils even after processing,

attributed to higher melting temperature.

Figure 2.5: Scheme for manufacturing microfibrillar LLDPE-PET blends. Matrix polymer =

LLDPE, Reinforcing polymer = PET microfibrills. From Shields et al. [1].


21

However, the mechanical properties of the rotomolded blend were not as good as those

observed by Shields et al. [1] who used a three step processing system culminating in a blown

film co-extrusion process. They were able to disperse PET in sheet and microfibrillar form

within the LLDPE matrix leading to an increased contact area and thus, better reinforcement

between the two phases (Schematic in Figure 2.5). They studied the effects of multiple

processing parameters, concentrating specifically on film drawing. They stated that the drawing

process did not have a significant effect on the overall barrier properties but played a huge role

in the improvement of the mechanical properties of the blend. For a 30% by weight

incorporation of PET microfibrils in a LLDPE matrix, the permeability to O2 was reduced by

40% with ~200% improvement in the tensile modulus. They suggested that if improvements in

mechanical properties were not of paramount importance then the drawing step could be

eliminated from the technique provided microfibrillar morphology was developed during co-

extrusion.

Therefore, by utilising rigorously selected polymers, ensuring efficient dispersion and

managing dispersed phase morphology, it is possible to control the permeability and mechanical

properties of a polymer blend. It is also required to address the class of polymers (commodity,

engineering or bio based, or a combination of all three) required, whether compatibilization of

the dispersed phase with the continuous phase is needed using an external aide (ultrasound/

chemical agent) or if the processing technique can produce an effective dispersion on its own.

If the use of an external aide is required, the production cost or toxicity regulations (if used in

a food contact environment) make the process untenable. Also, when considering the use of a

polymer blend for controlling permeability in a large-scale manufacturing application, the

viscoelastic, thermal and mechanical properties of the blend material chosen must be analysed

systematically to ensure that it fits the needs of the processing technique and the final

application.

However, this does not address situations wherein the permeant itself mechanically

adheres to or plasticizes the polymer through which the transport phenomenon is occurring. To

address this, the mechanical effects of liquid permeant uptake on the mechanical properties of

polymer blends need to be addressed. An example of this is provided by Zhang et al. [66] who

studied the effect of moisture uptake on the tensile properties of Polyurethane-Polysulfide

blends. They found that the incorporation of the polysulfide did result in a net reduction in water

uptake from 6.2 % over 96 h with for the plain polyurethane to 3.4 % over 96 h for the


22

polyurethane blended with 20% by weight polysulfide. This was attributed to the introduction

of S-S bonds in the polyurethane backbone. As far as mechanical properties are concerned, the

tensile strength of the polyurethane decreased from 26.5 MPa to 19.7 MPa after immersion in

water for 96 h, with a retention of 74.3% as compared to the dry material. Meanwhile, the blends

only showed a slight decrease. In particular, when the content of polysulfide was 20% by

weight, the tensile strength retention reached 91.7% (Table 2.2), showing excellent water

resistance not only in terms of permeability but also in terms of mechanical strength. The

enhanced retention in tensile strength can attributed to the limited hydrolysis of the urethane

bond. The added polysulfide hindered the penetration of moisture and delayed the process of

the decomposition reaction demonstrating that blends can be designed to not only have

controlled permeability but also retain their mechanical performance after being completely wet

by the liquid permeant. It has to be noted that the reported properties were over a time of 96 h

which is much lower than the time scales of storage and contact in rotomolded tanks of the

optimized composition developed in this thesis may entail.

Table 2.2: Tensile strength (MPa) of polyurethane polysulfide blends with varying polysulfide

content and different soaking times. From Zhang et al. [66].

Sample Tensile strength (MPa) after soaking in water Retention

after 96 h 0 h 24 h 48 h 72 h 96 h

Neat Polyurethane 26.5 25.1 24.6 22.2 19.7 74.3

10% Polysulfide 24.7 23.5 22.9 22.7 22.3 90.1

20% Polysulfide 23.7 23.2 22.8 22.6 21.8 91.7

30% Polysulfide 22.9 22.3 21.5 20.9 20.5 89.5

The effect of non-aqueous permeant uptake on the mechanical properties of polymer

blends was carried out by analysed by Sujith et al. [67]. They studied the effects of aromatic

solvent, specifically, benzene, toluene and xylene uptake, on the behavior of nitrile rubber-

natural rubber blends compatibilised using EVA. Sujith et al. [67] waited for equilibrium to be

attained while studying the solvent uptake and then dried those samples at 60°C to desorb off

the water. The tensile properties of the desorbed samples were then compared to those of the

dry blends with whom no solvent contact had occurred. They found no significant difference in

tensile properties between the dry and desorbed specimens indicating that the blend they had

prepared was pretty resistant to solvent induced weakening. However, we have to note that the


23

entire solvent uptake testing was carried over a time period of 96 h which, while significant, is

not long enough in order to act as an indicator of viability for the materials that will be tested

in this thesis. Longer term testing is necessary to prove the viability for storage application and

the details of those types of tests are given in Section 3.1 of this thesis. Specifically, the creep

compliance and equilibrium moduli of the fabricated compositions will be studied as a function

of the solvent uptake. Secondly, while the effects of solvent uptake on the tensile properties on

the blend are reported in [67] we will be providing a much bigger picture view of our system

wherein the effects of solvent uptake are not only studied on the static properties but also on

the dynamic properties such as storage moduli in different deformation modes (once again,

more details are provided in Section 3.1)

24

2.2 POLYMER COMPOSITES AND NANOCOMPOSITES

Polymer composites are multi-phase systems consisting of fillers dispersed in a polymer

matrix. If the dispersed filler has a dimension in the nano scale, then this system is referred to

a polymer nanocomposite [43, 68, 69]. Typically, for achieving control on the permeability and

the mechanical properties, nano fillers such as layered silicates (clays such as bentonite,

montmorillonite-MMT and sapiolite, talc, etc.), natural fibres (sisal, agave, cellulose, banana,

etc.), particulates like SiO2, CaCO3, ZnO, etc., specialty materials like carbon nanotubes (CNT;

or multi wall nano tubes- MWNT), graphene, fullerenes, etc. are used. The incorporation of

these fillers in the polymer matrix leads to a change in the tortuosity within the polymer matrix

as mentioned in Section 2.1 and thus, control on the permeability characteristics of the polymer

can be exerted [69]. Addition of fillers also affects mechanical properties like the elastic moduli

and impact strength which are very important parameters when considering usage in packaging

and storage sectors [69].

2.2.1 POLYMER NANOCOMPOSITES

A major facet of using nano-fillers is their large specific surface area values (m2/g). This

means that a very small incorporation (<5% by weight) is enough to bring about reinforcement

behaviour. This is also accompanied by significant changes in the mechanical and permeability

properties [43, 68, 69]. Industrially important polymer nanocomposites include the very first

Nylon-6 clay nanocomposite utilised as timing belt covers and engine covers in cars.

Polyolefin/clay nanocomposites shortly followed also being used in car doors, structural seat

backs and in fuel lines and fuel system components. Later, Nylon-6/Clay and PET/clay

nanocomposites were used to control permeability in commercial applications [70]. More

recently, there have been a remarkable number of publications on the control on permeability

properties of a wide range of polymers via the incorporation of nano-fillers of various types

using melt blending [71], batch mixing, solution casting, rotomolding, etc.

Mohammadi et al. [71] produced HDPE-fluoromica nanocomposites containing 6% by

weight of fluoromica using HDPE-grafted-Maleic Anhydride (HDPE-g-MA) as a

compatibilizer by melt blending and compression moulding. They discovered that the O2

Literature Survey: Polymer Nanocomposites

25

permeability reduced by 33% combined with a 30% improvement in the elastic modulus. They

also stated that the compatibilizer with the same chemical backbone as the matrix and lower

molecular weight was more desirable to improve nano-filler dispersion. Tayebi et al. [72]

synthesized LDPE-Reduced Graphene Oxide (RGO) and Graphene Oxide (GO)

nanocomposites via solution casting using EVA as a compatibilizer. For a 7 weight%

incorporation of RGO and GO there was a remarkable reduction of 91% and 97% respectively

in the oxygen permeability (Figure 2.6a) and 95% and 98% in the CO2 permeability respectively

(Figure 2.6b). This dramatic reduction in gas permeability was also accompanied by a 65%

(GO) and 92% (RGO) improvement in elastic modulus.

Figure 2.6: (a): O2 permeability and (b): CO2 permeability of LDPE-EVA-GO (■) and LDPE-

EVA-RGO (▲) nanocomposites. From Tayebi et al. [72].

Atayev et al. [73] incorporated unmodified and surface modified ZnO in PP using

extrusion and compression moulding. At a loading of 1 weight% of surface modified ZnO in

PP, a reduction of 17% in the oxygen permeability accompanied by a 2% improvement in the

elastic modulus was observed. Further incorporation of 5 weight% of MMT led to a total of

22.5% reduction in the oxygen permeability and a more significant 6.5% improvement in the

elastic modulus as compared to base PP. Al-Jabareen et al. [74] dispersed graphite nanoplatelets

(GNP) in PET using a microcompounder. The graphite was caged in a PET matrix by

sandwiching the nanoplatelets between two sheets of PET by compression moulding followed

by granulation. The oxygen barrier property of the PET-graphite nanocomposite was reduced

by 99% at only a 1.5% by weight amount of GNP. The elastic modulus of the matrix polymer


26

was also improved by 21%. The reason for the reduced permeability was two-fold, first being

the increased tortuosity and the second being the higher degree of crystallinity brought about

by the nucleation of the PET by the dispersed GNPs. They also found an increased dimensional

stability but accompanied by an increase in the brittleness. They suggested that for a

combination of minimum oxygen transmission and higher dimensional stability an optimised

composition and processing conditions has to be selected. They also studied the effect of

quenching on the crystallinity and the barrier properties and found that the quenched specimen

(ice water as the quenching medium) had ~1/4th the crystallinity and ~2 times the O2

permeability of a PET specimen annealed at 180°C. This indicates that changing the overall

crystallinity of a polymeric system done post processing had significant effects on its O2

permeability (Table 2.3).

Table 2.3: XC and O2 permeabilities of PET and PET/GNP nanocomposites. From Al-Jabareen

et al. [74]

Sample % Crystallinity (XC) O2 Permeability

[cm3/m2/day/atm]

PET (Quenched) 5.5 16.1

PET (Annealed at 180°C) 23.6 8.3

PET (Annealed at 240°C) 13.2 11.1

PET/1.5% GNP (240°C) 17.3 0.1

Li et al. [75] dispersed surfactant modified Mg/Al layered double hydroxides (LDH) in

a Polypropylene carbonate (PPC) matrix using a twin rotor batch mixer creating a

biodegradable nanocomposite with potential as a packaging film. The O2 and water vapour

permeabilities were reduced by a factor of 54% and 18% respectively for a 2% by weight

loading of the LDH attributed to the increased tortuoisity in the nanocomposite (Figure 2.7). In

terms of mechanical properties, the tensile strength was increased by 83% for a 2% loading.

They also found that the PPC nanocomposite film had far lower permeability than both

commercial PE and PA flexible package films.


27

Figure 2.7: Model for Tortuous pathway of gas through PPC/OLDH composites. From Li et

al. [75]

Pavani et al. [76] fabricated HDPE and HDPE-clay (5 weight% clay) nanocomposite

units with carbon filament winding via rotomolding and compared the permeability and

mechanical properties of the products. Pre-moulding dispersion of the clay in the polymer

matrix was carried out in a single screw extruder. It was found that due to the low shear

experienced in processing, the clay platelets are dispersed less uniformly in the polymer. As a

consequence, the permeability of the nanocomposite sample was higher than that of the virgin

polymer sample (Table 2.4). However, there was no major reduction in the tensile strength of

the rotomolded specimens suggesting that control on the permeability can be achieved by low

shear dispersion prior to moulding without substantial detriment to the mechanical properties.

Table 2.4: Tensile Strength and O2 permeabilities of rotomolded PE blend nano-clay

composites. From Pavani et al. [76].

Sample Tensile Strength (N) O2 Permeability [mL

(STP)/m2/day]

PE Blend [LLDPE-5% HDPE] 143.84 ± 32.03 13660

PE Blend-5 % Nano-clay 1 137.80 ± 11.38 32829

PE Blend-5 % Nano-clay 2 140.74 ± 6.25 150000

The effects of liquid permeant uptake on polymer clay nanocomposites has also been

analyzed quite extensively in literature. Some examples include Alateyah et al. [77] , Burcham

et al. [78], Zhou et al. [79], etc. Alateyah et al. [77] studied the effect of water uptake on the


28

properties of vinyl ester layered silicate nanocomposites with varying concentrations of cloisite

clay. Overall, all samples showed a reduction in hardness after exposure to water because of a

combination of permeant induced plasticization and an overall decrease in the interfacial

interaction between the layered silicate and the polymer. Alateyah et al. [77] also found that as

the clay content increased the relative loss of hardness also reduced. This was attributed to the

relatively lower equilibrium uptake of water in the nanocomposite specimens as opposed to the

plain vinyl ester material.

Figure 2.8: Effect of moisture uptake on the hardness (GPa) of vinyl ester clay nanocomposites.

From Alateyah et al. [77]

Therefore, with the use of a nanocomposite it is possible both to control the permeability

and ensure retention of mechanical properties. Thus, polymeric nanocomposites are one of the

classes of materials that could be explored as a solution for this particular thesis. However,

nanocomposites do require the use of compatibilizing aids and other materials to ensure the

nanoscale dispersion of the dispersed phase and the relative toxicity does end up limiting the

application of nanocomposites in food contact and storage applications that is the main

requirement of this thesis.

29

2.2.2 POLYMER COMPOSITES

Polymer composites are multi-phase systems consisting of fillers dispersed in a polymer

matrix. Typically, for achieving control on the permeability and the mechanical properties,

fillers such as layered silicates (clays such as bentonite, montmorillonite-MMT and sapiolite,

talc, etc.), natural fibres (sisal, agave, cellulose, banana, etc.), particulates like SiO2, CaCO3,

ZnO, etc., speciality materials like carbon nanotubes (CNT; or multi wall nano tubes- MWNT),

graphene, fullerenes, etc. are used. The incorporation of these fillers in the polymer matrix leads

to a change in the tortuosity within the polymer matrix and thus can help exert control on the

permeability characteristics of the polymer can be exerted [69]. Addition of fillers also affects

mechanical properties like the elastic moduli and impact strength which are very important

parameters when considering usage in packaging and storage sectors [80].

Polymer-Natural fibre reinforced polymer composites are of great interest because they

are recyclable, environmental friendly, biodegradable, and cheap materials as compared to, say,

glass fibre based polymer composites [81, 82]. Natural fibres like flax, hemp, jute, and sisal

have been well recognized for their potential as reinforcements for engineering polymers. The

main features of these fibres (called lignocellulosic fibres) are their lightweight nature, high

specific modulus, non-toxicity and ease of processing [81]. Similar to the action of nano-fillers

discussed previously, the presence of the natural fibres within the polymer matrix aids in the

development of a tortuous pathway leading to control on permeant diffusion but there are more

details that have to be taken into account specifically in the case of natural fibre reinforced

polymer composites. Natural fibre reinforcements have found industrial usage in a number of

applications in automotive parts [81]. Flax, sisal, and hemp are used while producing door

cladding, seatback linings, and floor panels. Coconut fibre is used to make seat bottoms, back

cushions, and head restraints. Cotton is used to provide sound proofing while wood fibre is used

in seatback cushions. Major automotive companies such as BMW, Audi Group, Ford, Opel,

Volkswagen, Daimler Chrysler, Proton, General Motors and Cambridge have incorporated the

use of natural fibre reinforced polymer composites. Daimler Chrysler use flax–sisal fibre mat

embedded in an epoxy matrix for the door panels of Mercedes Benz E-class model. In fact, up

to fifty different components of the Mercedes E Class have been from natural fibre based

polymer composites [81, 83]. A two fibre (kenaf and flax) mixture has been used for

manufacturing package trays and door panel inserts for the Saturn L300 and the Opel Vectra.

Literature Survey: Polymer Composites

30

Wood fibre has been used in seatbacks for the Cadillac DeVille and in the cargo area floor of

the GMC Envoy and Chevrolet Trail-Blazer. Coconut fibres bonded with natural rubber latex

are being used in seats of the Mercedes Benz A-class model. The Cambridge Industry has

utilised flax fibre-reinforced polypropylene for Freightliner century COE C-2 heavy trucks and

also rear shelf trim panels of the 2000 model Chevrolet Impala. Besides automotive industry,

natural fibre composites have also found their application in building and construction

industries such as for panels, ceilings, window frame, decking and partition boards, aerospace,

automotive parts, sports and recreation equipment, boats, office products, machinery, etc. [81,

83, 84]

An important aspect of dispersing natural fibres in a polymer matrix (thermoplastic or

thermoset) is the extent of wetting of the natural fibre surface by the polymer. The presence of

natural fibres in the polymer matrix can result in the creation of a preferential pathway for the

diffusion of gas/permeant at the fibre/matrix interface and the presence of little microscopic

holes in the matrix both of which can result in increased permeability. To ensure wetting and

adhesion between the dispersed and continuous, fibre surface treatments and use of

compatibilizing agents are the two most regularly used pathways. Cisneros-Lopez et al. [85]

dispersed treated agave fibres by rotomolding in a medium density PE (MDPE) matrix. The

different treatment methods are as follows, UF: untreated fibre, M24H: 5% NaOH treatment

for 24 h, 2CB: 2% NaOH treatment for 15 min (alkali pre-treatment) followed by 10 weight%

2-chlorobenzaldheyde in ethanol for 15 min at room temperature (RT) and washing in 50:50

water: ethanol, MAPE: Alkali pre-treatment followed by mixing in 1weight% MA-g-PE in

1,2,4-Tricholorobenzene (TCB) for 30 min and drying, AA: Alkali pre-treatment followed by

immersion in 0.3M Acrylic Acid, 0.01 M benzoyl peroxide in 9:1 water: benzene solution for

1h at 50°C and then soaking in 6M NaCl and 1M NaOH for 15 min at RT, MMA: AA treated

fibres placed in 10 weight% methyl methacrylate and 0.01 M benzoyl peroxide in 9: 1 ethanol:

water mixture for 1 h at 90°C followed by cooling and washing by distilled water and 7:3

water: ethanol for 24h, TVS: AA treated fibres immersed in 5 weight% Triethoxy vinyl silane

in 95:5 ethanol: water mixture at pH 3.5-4 for 90 min at RT. They later studied the effect of

these surface treatment techniques on the mechanical and water uptake properties. Now, there

has been precedent for using low shear processing methods to disperse a nano-filler into a

polymer matrix [76] and in that work, the use of a single screw extruder had resulted in an

increase in the permeability of the polymer nanocomposite and a slight reduction in the

mechanical properties [76]. Now, in [85], the rotomolding of the polymer-fibre mix resulted in


31

an increase in the water uptake, across the board for all the treated fibre-polymer composite

(Figure 2.9). They stated that the surface treatment of the fibres had extracted some of the waxes

on the fibre surface which led to a slight increase in the hydrophilic character. However, after

28 days, the PE-g-MA treatment lead to lower water absorption compared to untreated fibres,

thus showing the long-term efficacy of this treatment technique. In addition, the tensile strength

of the treated fibre-polymer composites was found to have reduced by ~25% except for the PE-

g-MA treated agave fibres (15% loading of fibre). This was attributed to low adhesion between

the treated fibres and the polymer matrix. In terms of elastic modulus, the PE-g-MA treated

agave fibre MDPE composite had a modulus about 30% higher than that of the virgin MDPE.

An increase in modulus was observed for all of the composites, attributed to the relative rigidity

of the fibre phase as compared to the polymer phase.

Figure 2.9: Liquid water uptake for rotomolded LMDPE-15% fibre composites. From

Cisneros-López et al. [85]

Siaotong et al. [86] used twin screw extrusion, pelletization and rotomolding to disperse

silane treated flax fibres in LLDPE and HDPE. It was found that the use of high screw speeds

and lower barrel temperature profile led to a more porous microstructure. In general, at lower

processing temperatures, higher fibre content resulted in a slower melt flow (especially in the

rotomolding process), high porosity, low density, high water absorption, and, lower tensile


32

strength [86]. The higher porosity at high screw speeds is also apparent from the SEM

micrographs of the LLDPE-flax fibre composites. Figure 2.10a which is a 12.5% flax fibre-

LLDPE composite fabricated using 140°C maximum barrel temperature and 150 rpm screw

speed. Figure 2.10b is a similar composition fabricated at 150°C maximum barrel temperature

using a lower 110 rpm screw speed. Thus, changing the extrusion profile could control the

porosity of the polymer microstructure which in turn, could control overall permeability.

Figure 2.10: SEM micrographs of LLDPE- flax fibre composites (a): (LLDPE: 12.5% fibre

content, 75, 110, 120, 130, and 140°C barrel temperature profile, and 150 rpm screw speed; (b):

LLDPE: 12.5% fibre content, 75, 120, 130, 140, and 150°C barrel temperature profile, and 110

rpm screw speed). From Siaotong et al. [86].

Krishnan et al. [87] isolated cellulosic nanofibrils from raw sisal fibres and dispersed

them in a PP/PS blend matrix in a high shear batch mixing environment. They discovered that

at very low weight loadings, there was a significant reinforcing action. At 0.5 weight% loading,

the presence of the nanofibrils increased the elastic modulus by ~46% the tensile strength by

~39% and doubled the impact strength. This is also accompanied by a 21% reduction in the

water vapour permeability (Table 2.5). This is attributed to the high interfacial adhesion

between the nanofibrils and the polymer matrix leading to an increased tortuosity and thus,

reduced permeability. At higher loadings, it was observed that the water vapour permeability

increased due to increase in the porosity of the polymer microstructure brought about by the

agglomeration of the fibrils. The dispersion of treated and untreated pineapple fibres in LDPE

was performed by George et al. [88]. They found that the treatment of the pineapple fibre with


33

an isocyanate, specifically poly (methyl) poly (phenyl isocyanate), reduced the water vapour

permeability by 67% and also, more than doubled the elastic modulus at a 20% by weight

loading. And similar to Krishnan et al. [87], the water vapour permeability increased at

increased fibre loading (Table 2.5) [88]. Thus, by choosing the right fibre concentration and

treatment method, the permeability performance of a natural fibre composite can be controlled.

While Siaotong et al. [86], Krishnan et al. [87] and George et al. [88] studied how these

porosities can be affected by the type of treatment used, no study was made of the mechanical

properties before and after permeant uptake. In fact, most of the tests were performed only

before the permeant uptake and were used for optimizing composition and treatment procedure

as shown in Tables 2.5 and 2.6.

Table 2.5: Tensile strength, Impact strength and water vapour permeability of PP/PS-Sisal

nanofibrils composite. From Krishnan et al. [87].

Sisal content

(weight%)

Elastic

Modulus

(MPa)

Tensile

Strength

(MPa)

Impact

Strength

(J/m)

Water vapour

Permeability [cm2 min-1]

at 1 atm and 28°C × 10-10

0 590 23.0 75 0.958

0.5 1520 31.5 160 0.758

1.5 1430 30.0 150 1.080

5 1320 28.4 130 1.774

Table 2.6: Water vapour permeabilities and elastic modulus of LDPE-Pineapple fibre (of

different surface treatments) composites. From George et al. [88]

Type of Pineapple

fibre

Tensile Strength

(MPa)

Water vapour Permeability [cm2

min-1] and 28°C × 10-9

20% Untreated 800 1.13

20% NaOH treated 1100 1.11

20% PMPI 1800 0.38

There are, however, examples where the extent of permeant uptake and its effect on the

mechanical properties of the polymer matrix has been studied. Singer et al. [89] did a


34

comprehensive study on water desorption on the mechanical properties of cured epoxies.

However, it was only for static properties such as Young’s Moduli shown in Figure 2.11. While

these properties are important for characterizing the effect of the dispersed phase and of matrix

consolidation, they provide very little information as to the time dependent properties which

are the most important factors for packaging applications.

Figure 2.11: Effect of water desorption on the Young’s modulus in the vinyl ester-based

material up to an equilibrium state at around 3% of weight loss. From Singer et al. [89].

In terms of thermoplastic natural fibre composites, the material that will be covered in

this thesis, the work by Camara Bezerra et.al [90] was done to show the effect of permeant

uptake on static mechanical properties, specifically, the tensile, impact and flexural strengths.

An equilibrium was established after about 21 days of solvent contact and corresponded to

weight uptake of 3% for a 10 mm thick sample and about 9% for a thinner 3 mm sample. For

the thinner specimen, the tensile, flexural and impact strengths reduced by 76%, 38% and 78%

respectively after 21 days of solvent contact. For the thicker specimen, the tensile, flexural and

impact strengths reduced by 50%, 60% and 17% respectively. However, the tests were only

done for the static properties and no dynamic properties like the storage moduli or equilibrium

moduli from creep were studied.

It is also possible to make polymer composites based on treated and untreated natural

fibre flour as reported by Tzerki et al. [91]. The polymer matrix was a copolymer of succinic

and adipic dimethylesters. The flours were isolated from olive, spruce and paper and were


35

treated via acetylation or a compatibilizing agent (MA-grafted polyester). In all cases, the

mechanical performance when the compatibilizer was used (with untreated fibres) was much

better than that with the surface treated fibres (and no compatibilizer). The water vapour

permeability for the compatibilized system was also higher than that seen when the surface

treated fibres (and no compatibilizer) were used. This indicates that the hydrophilic nature of

the composite was reduced when the fibres were surface treated. This also reduced the adhesion

between the polyester copolymer and the dispersed fibres thus leading to lowered water vapour

permeability and reduced mechanical properties. Therefore, it is important to choose the right

surface treatment technique depending upon the nature of the polymer matrix, mechanical and

permeability properties required. The degree of interfacial adhesion between the polymer

matrix and the fibres influences the overall porosity. Using this, control can be exerted on the

gas/vapour permeability but the accompanied changes in mechanical properties should be

accounted for.

Sreekumar et al. [92] compared different polymer-natural fibre composite fabrication

techniques. They fabricated a polyester-sisal fibre composite using compression molding and

resin transfer moulding (RTM). They found that the water uptake of the compression moulded

specimen was higher than that of the resin transfer moulded specimen at same fibre loading (43

vol%). Also, the mechanical properties of the RTM specimen were better than that of the

compression moulded specimen. This further proves that the interfacial adhesion and overall

porosity are essential factors in controlling the mechanical and permeability properties of the

composite. In RTM as the resin flow front advances through the fibres, the size of entrapped

air decreases due to the hydrostatic pressure. This low void content is one of the main reasons

for the increase in mechanical properties and reduction in permeability of composites fabricated

by RTM. Fendler et al. [7] attempted to study the effect of cooling rate (a post-processing

parameter) on the barrier properties of HDPE cellulose fibre melt blended composite using PE-

g-MA as a compatibilizer. They found that using a quenching process to cool the composite

resulted in higher permeability to oxygen than using a slow cooling approach. This was

attributed to the reduced crystallinity of the quenched specimens as compared to the slow cooled

ones. This is very similar to results seen by Al-Jabareen et al. [74] in their study on PET-GNP

nanocomposites. Thus, similar influences of post fabrication cooling rates are seen on both

lamellar and fibrillar nanocomposites. Fendler et al. [7] stated that a reduction of about 10%

(~66% crystallinity for the slow cooled, ~55% crystallinity for the quenched specimen) in

crystallinity resulted in more than doubling of the oxygen permeability- 4.02 × 10-18 kg.


36

m/m2/s/Pa for the slow cooled specimen as compared to 8.64 × 10-18 kg. m/m2/s/Pa for the

quenched specimen (Figure 2.12). Such a dramatic increase in the permeability was

accompanied by only a slight reduction in the mechanical properties. The elastic modulus of

the quenched specimen was ~500 MPa as compared to ~650 MPa for the slow cooled specimen

at 2% loading of cellulose fibre. The fact that the oxygen permeability could change so

significantly based on the methodology of cooling utilised after the fabrication of the composite

is an interesting result and it speaks to how intimately, the crystallinity (and hence the

microstructure) of the polymer composite is linked with its barrier properties.

Figure 2.12: O2 permeability for quenched and slow cooled HDPE-cellulose fibre composites.

From Fendler et al. [7].

Thus, with the use of natural fibres or natural fibre flour as a reinforcement, it is possible

to control the mechanical and permeability properties by changing the extent of adhesion

between the fibre phase and the polymer phase. Using surface treatments of the fibre (leading

to a roughened and cleaned fibre surface), using a compatibilizer (like PE-g-MA, vinyltrimethyl

silane, etc.) or utilising a polymer-fibre mixture of similar hydrophilicity are way in which

rigorous control on the permeant transport through the polymer can be obtained. This could

result in an increase in the number of production steps and production cost. Also, as mentioned

before, the inherent toxicity of the compatibilizer, surface treated natural fibres will affect the

application of the nanocomposite for applications where the permeability and mechanical

properties and the trend in values thereof are of importance as required in this thesis.


37

It is also important to note the following advantages and disadvantages. As observed,

with the incorporation of lamellar nano-fillers like layered silicates, a significant change in

mechanical and permeability properties as compared to the base material is seen at relatively

low weight fractions (typically <5 weight%). However, to ensure control on the properties, it is

required, in a lot of cases, to modify the surface of the nano-filler and ensure that there is no

agglomeration within the polymer matrix. This often results in an increase in the viscoelastic

parameters (specifically, the zero-shear viscosity and the storage and loss moduli) of the

material and thus ends up requiring potential modification of the processing technique used

[93]. These increases in viscosity have previously been attributed to the confinement of the

polymer chains between the layered silicate layers. However, Galgali et al. [93] proved that the

reason for this increased zero-shear viscosity is not due to confinement (i.e., a large activation

energy barrier) but rather due to the frictional interactions between the silicate layers. This

definitely limits the use of nanocomposite materials as rotomoldable compounds as a low zero

shear viscosity is an absolute requirement if the composition is to be rotomolded.

38

2.3 FOAMED POLYMERS

Foamed or porous materials are two-phase systems consisting of a continuous solid or

liquid phase and either a continuous or discontinuous gaseous phase [94]. Polymeric foams are

materials that belong to this category of porous materials and can be classified on the basis of

their topology or their average pore size [95]. In terms of topology, there are two types of porous

polymeric materials; open pore foams, where the gas is dispersed continuously in the solid

phase and closed pore foams wherein the gas is enclosed in the pores and thus, have a

continuous solid phase and a dispersed/discontinuous gas phase [95]. In terms of average pore

size, porous polymers are classified into conventional, microporous and nano-porous polymers.

Conventional porous polymers have average pore sizes larger than 100 μm whereas

microporous polymers have an average pore size in the order of 10 μm and nanoporous

polymers have an average pore size less than 1 μm [94]. Production of polymeric foams (i.e.,

porous polymeric materials, also known as cellular materials) is one approach to improve

several properties of the base polymer or to increase the range of potential applications. It is

seen that these porous (particularly microporous) polymeric materials or polymeric foams show

significant improvements of compressive, flexural, impact and tensile strength; increase in

fatigue life, toughness, thermal stability, light reflectivity, and lower thermal conductivity as

compared to the neat polymer [95].

Foaming is a particularly difficult process in the case of polymers because they are soft,

viscoelastic materials and have poor thermal stability (compared with other materials; i.e.,

metals, ceramics, etc.) [95]. Foams can be produced by extrusion, injection molding,

rotomolding or compression molding in the melt state or in the solid state by forcing gas into a

solid polymer followed by depressurization [96]. All methods can use either physical or

chemical foaming agents. Chemical foaming agents are substances which decompose via

chemical reaction at processing temperatures thus liberating gases like CO2 and/or N2. Physical

foaming agents are substances that gasify but do not react chemically under foaming conditions

[95, 96]. Chemical foaming agents may be of endothermic or exothermic in nature or a

combination of the two may be used as well. Exothermic foaming agents release heat while

decomposing and examples of those are azodicarbonamide (ADC; Figure 2.13), sulfonyl

hydrazides, etc. Endothermic foaming agents absorb heat during processing to decompose and

a main example of such an agent is CO2. Endothermic foaming agents are physiologically

Literature Survey: Foamed Polymers

39

harmless and have massive potential for use in fabricating foamed plastics for food contact and

storage applications [96].

Figure 2.13: Structure of azodicarbonamide (ADC).

Polymer foams were first made in the 1930s and 40s. Foamed polystyrene (PS) was the

first polymer foam produced in 1931 starting the era of cellular plastics. This was followed by

the invention of polyurethane and the following development of flexible polyurethane foam a

few years after the end of the Second World War [96]. With improvements in knowledge and

of technology, the porous polymer sector has evolved into a highly sophisticated field and

polymeric foams made today are used for a wide range of applications. Foamed plastics can

often be stronger than their non-foamed ones and because of the reduced weight can achieve

outstanding cost-to-performance and favourable strength-to-weight ratios [94]. Due to these

unique characteristics, foamed plastics can be used in producing light parts with high strength,

and industrial applications including automotive and aircraft, packaging, sporting goods and

electrical and thermal insulation. Their use as light-weight materials is a prominent example,

e.g., allowing the reduction of consumption of fossil fuels in transportation. Other applications

include, utilising their low thermal conductivity for heat insulation, low acoustic conductivity

for acoustical insulation, and flexibility for damage-absorbing behaviour. Moreover, foams are

also used for even more specialized applications, e.g., open-porous membranes or sensors. The

success of cellular polymers is also reflected in their market volume, which already exceeds

bulk polymers when the volume-based consumption is considered [94-96].

In polymeric blends and composites, the interface between the two phases is an

important source of voids and pores that act as pathways for the permeant molecule and large

interfacial adhesion or uniform filler dispersion leads to formation of tortuous pathways that

controls the permeability [96]. In polymer foams, the pores themselves act as channels for

permeant transport. In terms of application, it is seen that generally, closed-cell foams have

lower permeability, leading to better insulation properties while open-cell foams, on the other

hand, provide better absorptive capability. The formation of an either a closed cell or an open

cell porous microstructure will have significant effects on the permeant transport [95]. Changes


40

in the pore structure of a polymer can be brought about by directly processing the polymer in a

foaming process and varying parameters like the proportion of blowing agent, the temperature

profile used during processing, or indirectly, by incorporating a microporous filler [96] or a

combination of microporous and nano fillers [97, 98]. Most thermoplastic nanocomposite

foams including polyolefin types, to date are synthesized via a two-step process; the

nanocomposite is synthesized first and followed by foaming. The synthesized thermoplastic

nanocomposites can be used to produce nanocomposite foams. For large-scale production, the

direct utilization of foaming (blowing) agents is the most commonly used method [94].

Babaei et al. [97] studied the physical and mechanical properties of closed cell foamed

HDPE/wheat straw composites with and without the presence of nano-clay. In a batch mixer,

they mixed varying proportions of nano-clay to the HDPE- wood Flour (60% HDPE and 40%

wood flour) mixture followed by a chemical foaming agent (ADC). The foamed mix was then

pelletised and moulded. They found that the average cell size observed from SEMs increased

with increasing amounts of the chemical foaming agent. When the nano-clay was added to the

foamed composites, the cell size reduced but the cell density increased. The extremely fine

dimensions and high aspect ratio of the nano-clay helped create more foaming nucleation

centres in the polymer. This increased the polymer mixture viscosity and improved the

resistance against cell growth, producing cells with smaller dimensions. The overall material

density also decreased significantly (21.7%) with a 4 weight% incorporation of the chemical

foaming agent. At a combination of 5 weight% nano-clay and 4 weight% chemical foaming

agent an increase in the composite density is seen and that density is higher than that of the base

HDPE (1.19 g/cm3 for the composite, 0.965 g/cm3 for the base HDPE). Thus, a foam with both

low and high densities and consequently, differing permeability characteristics can be

fabricated. It is seen that the water absorption or uptake of the foam at 4% addition of foaming

agent (0% nano-clay) is 26.5% higher than that of the base HDPE but when 5% of nano-clay is

added the absorption of the foamed composite is nearly the same as that of the base HDPE

(Figure 2.14).


41

Figure 2.14: Liquid water absorption characteristics of HDPE-wood straw flour composites at

various proportions of foaming agent and nano-clay. From Babaei et al. [97].

The mechanism of water absorption is the saturation of the cell walls followed by

penetration into the void spaces. As the void spaces are occupied by the nano-clay, the

permeability is reduced. However, the control of the properties of this foam composite are

constrained by the overall reduction the mechanical properties observed (17% and 30%

reduction in impact strength and 33% and 50% reduction in tensile modulus for 2% and 4% of

chemical foaming agent respectively) [97]. Improper adhesion between the wood flour and the

HDPE matrix is attempted to be improved by using a PE-g-MA but no effective improvement

is seen. Therefore, there is room for improvement in this system, but the controllable density

and permeability properties and the use of a bio based dispersed phase (wood flour) make it an

attractive proposition as a packaging material, provided the mechanical properties are optimised

by better adhesion between the HDPE and the wood flour.

Park et al. [99] went with an alternate approach to increasing polymer permeability

without compromising on the mechanical properties by synthesizing a mesostructured filler and

then dispersing it into the polymer matrix. They synthesized a nano sized silica specimen with

large pores and a wormhole-like framework structure using a long chain amine and sodium

silicate. Two types of samples were made- calcinated and uncalcinated and it was found that

for a 5% loading of the as-synthesized, uncalcinated silica into a cured epoxy matrix, the oxygen

permeabilities increased by as much as 5 to 6 times as compared to the calcinated silica

dispersion. They stated that the major difference between the uncalcinated and calcinated silica

specimens is that the long chain amine is partitioned between the silica and the uncured polymer


42

in the former while in the latter, the long chain amine exists exclusively in the polymer phase.

This partitioning of the long chain amine (which is a curing agent for the epoxy) between the

silica phase and the polymer phase affects the diffusion rates of the polymer and the curing

agent in and out of the pores of the silica. This leads to non-uniform crosslinking in the silica-

polymer interface resulting in the formation of a more permeable polymer corona around the

silica particles. This corona provides a percolation pathway and enhanced oxygen permeation

is observed. Analysing 0.9-1.5 mm thick films, they were able to observe an increase of ~500%

in the O2 permeability for a 12% by weight incorporation of mesostructured uncalcinated silica

(Table 2.7). This was also accompanied by 4-to 5.5-times increase in the tensile modulus.

Moreover, the benefit in mechanical properties occurs with little or no change in the overall

transparency.

Table 2.7: Mechanical and permeability properties of pristine epoxy and mesostructured silica-

epoxy nanocomposite. From Park et al. [99].

Sample Tensile Modulus

(MPa)

O2 Permeability [cm3

mil/m2/day] × 10-4

Pristine Epoxy 2.96 2.3

Epoxy + 12 weight%

uncalcinated mesostructured

Silica

11.90 14.0

Like other polymer systems, post processing and fabrication treatment can be used to

tune the properties of a polymer foam. Mrlik and Madeed [100] studied the effects of gamma-

irradiation on biaxially oriented PP. The polymer used was produced using blow moulding and

already had a closed cellular structure. Just plain gamma-irradiation did not seem to have any

significant effect on the pore structure of the original foam, but the gamma-irradiation brings

about significant (depending on the extent of dose) chain scission and cross linking in the

polymer matrix. At lower dosages (1 kGy and 5 kGy), cross linking was the dominant

phenomenon resulting in slightly reduced swelling properties as the cross linking prevented the

absorption of water into the matrix. In fact, the examination of the mechanical properties in the

static mode as well as dynamic mode showed that, the samples irradiated at lower doses, below

5 kGy provide the enhancement due to the cross-linking of the polymer structure, while those


43

irradiated at higher doses also exhibit the cross-linking behaviour but they were considerably

affected by scission and provide samples with poor mechanical properties.

Willett and Shogren [101] fabricated open cell foams of biopolymeric materials ranging

from corn starch to poly (hydroxybutyrate-co-valerate)- PHBV via extrusion. Talc was used as

a nucleating agent and deionised water was injected into the barrel section of the extruder. They

found that the addition of PLA and PHBV significantly reduced the density of the foams. The

application of these foams may be in packaging application wherein mechanical properties and

water absorption and weight loss are significant parameters to be considered. The mechanical

property studied was the compressive strength and a strong correlation was found to exist

between foam density and compressive strength, regardless of the type of resin blended with

the corn starch. High density corn and potato starch foams showed high compressive strength

(0.3-0.35 MPa). There was no other mechanical property investigated in this report. Poly

(hydroxyester ether) - PHEE also significantly reduced water absorption (155% at 20%

incorporation as compared to 415% for the starch alone), with the effect increasing as the

proportion of PHEE increased. PLA also reduced water absorption, although the reduction was

not as great as with PHEE. With 20% of PLA being incorporated, this water absorption almost

halved as compared to the starch alone and the weight loss was reduced by almost 80%. The

resins which gave the densest foams had water absorption values equal to or greater than the

control starch. On the other hand, resins which gave the lowest density foams tended to absorb

less water than the starch control. As all the polymers used in this study had a lower surface

energy than starch, the overall energy of the system was minimized by a migration of the

polymer to the foam surface. In general, it was found that the water absorption decreased as the

polymer surface concentration gradually increased.

Along with the use of foaming agents, there is another technique for making polymer

foams. Guo et al. [102] placed PLA sheets obtained commercially in a CO2 pressure vessel

under different saturation pressures. The samples were then removed from the vessel and

allowed to undergo desorption. Finally, they heated the desorbed PLA sheets in a water bath

and post drying the sheet was in the form of a closed cell foam. They took these closed cell

foams and converted them to open cell structures by using ultrasonic input. Thus, it is possible

to generate both types of cellular structures without the need for actual melt processing. The

open cell PLA foams synthesized post ultrasound input were tested for acoustic shielding and

the overall sound permeability properties of the foam were studied. It is plausible that the

improved acoustic permeability may translate to improved gas transfer as well. They also


44

suggested that to improve the uniformity of the properties, it may be needed to have ultrasonic

input on both sides of the PLA foam.

Bledzki and Faruk [103] used injection moulding to fabricate closed cell PP-wood fibre

foam composites with and without the use of PP-g-MA as a compatibilizer and a 4% proportion

of the chemical foaming agent. Using wood fibre content of 30% and 50% by weight, they were

able to demonstrate that the foamed PP-wood fibre composites showed substantial reductions

in density (1.01 g/cm3 for unfoamed 30% wood fibre composites to 0.76 g/cm3 for 4% foamed

30% wood fibre composite and 0.74 g/cm3 for 4% foamed 30% wood fibre composite with 5%

PP-g-MA). This was also accompanied by slight improvements in both the specific tensile and

flexural strengths. The permeability of the fabricated composites to liquid water was tested next

and they found that the microcellular structure of the foamed PP-wood fibre composites resulted

in an increase in the water uptake, but the extent of water uptake could be controlled by the use

of the PP-g-MA compatibilizing agent. Thus, they were able to fabricate a foamed product with

controllable mechanical and permeability characteristics using a dispersed phase primarily

consisting of bio-sourced materials.

A situation wherein a foam is the dispersed phase in a matrix can also be accomplished.

Ramkumar et al. [13] studied the mechanical and flow properties of foamed LLDPE for

rotomolding application. A powder mixture of LLDPE and LLDPE foam containing up to 10

weight% of LLDPE foam was moulded in a rotomolding unit and it was seen that a proportion

of 6 weight% of foam produced the foam blend with the best mechanical properties. However,

no characterization with respect to the permeability properties was conducted. Low density

closed cell foams were successfully fabricated using rotomolding on both a lab and an industrial

scale by Bush and Ademosu [104]. The two component polymer foams were fabricated in such

a way that the skin of the outer polymer was not pierced by the expanding foam within. The

outer skin was comprised of LLDPE while the foam was primarily of PS. A solid low-density

PS foam was formed within the air space of a hollow shape with the walls formed from LLDPE.

This specialised process, known as ROTOFOAM ©, was able to fabricate a foam with intimate

contact between the LLDPE skin and the PS inner foam. The raw materials were PS beads

containing 6% w/w of n-pentane and LLDPE powder. The expansion of the foam was

controlled using pressurised water vapour generated from hydrated powders at about 60-80°C.

The n-pentane from the PS beads is evaporated without distinctly softening the PS. The PS

beads coalesce and expand while the LLDPE powder fuses and forms the skin while some

migration of the LLDPE from the skin to the core of the product helped improve the degree of


45

adhesion between the skin and the core. The overall process depended on the temperatures

applied at the inside mould surfaces and within the moulding cavity itself so that the skin could

substantially form before the foam expanded significantly. On both the experimental and

industrial scales the use of a hydrated powder foaming agent coupled with a relatively low

maximum foam temperature below 90°C, enabled a regular box-like foam to be made with cells

of 150–200 μm within a sintered structure. Again, no test on permeability characteristics of the

fabricated foams were carried out but the adjustable skin and foam thickness of the LLDPE-PS

foam could lead to interesting gas transport properties [104].

Thus, polymeric foams combine good mechanical properties, tuneable cellular

structures and the ability to be produced by a wide variety of processing techniques ranging

from low to high shear processes. This makes them very interesting materials for application in

controlled gas permeability systems. By varying parameters such as processing temperature and

its profile, using a chemical or physical blowing agent, nano-fillers, polymer blends,

compatibilizers, post processing techniques and indeed, solid state fabrication, it is possible to

produce polymeric foams with controlled cell size, distribution and morphology. The porous

microstructure also makes it possible to fabricate thicker cross sections and not massively

influence the overall permeability. The thicker cross sections can also ensure that the overall

stiffness of the structure is maintained. Another advantage of the use of polymeric foams is that

for an ultimate application involving food storage and possibly, increased permeability, the use

of a polymer foam seems to have the largest advantage provided the blowing agent used is a

benign gas (such as endothermic foaming agent) or a food contact approved chemical. The very

microstructure of a polymeric foam suggests that gas and vapour transport are greatly increased

as compared to the bulk polymer, in most cases. Also, by incorporating fillers and ensuring

good adhesion with the polymer matrix, it is possible to improve the mechanical properties of

the polymer system while keeping the cellular structure intact.

46

2.4 POLYMER LAMINATES

In the fabrication of polymeric laminates for packaging or storage application, a plastic

barrier is combined with other materials i.e. other plastics or foil, often via co-extrusion [105].

Multi-layer polymer matrices can either be in the form of a laminate or have a single thin coat

of a non-polymeric material on the surface [106]. Several transparent metals or their oxides as

well as high aspect ratio material fillers such as cellulose fibres, mica, etc. have been used for

this purpose [105, 106]. The natural result of the formation of a laminate or any sort of multi-

layer matrix is the creation of additional interfaces between the layers. In some cases, these

additional interfaces take the form of a trans-crystalline layer between two immiscible polymer

layers. This happens as a result of high polydispersity and the diffusion of shorter chains at the

interface [107]. Control on the overall permeability to both liquids and gases can be achieved

as the permeability of this interface can be massively different than that of the bulk polymers.

The reasoning behind using multi-layer polymeric laminates is bringing about changes in the

tortuosity, which as mentioned before is a significant parameter in controlling the permeability

properties of the overall product. If more individual layers (polymeric or otherwise) are present

between one side of the polymer matrix and the other, it only follows that the permeability of

this multi-layer system should be lower than that of individual layers and more rigorous control

on the flow of permeant (gas/vapour/liquid) can be exerted if there are multiple layers forming

the barrier. Using this principle, a number of multi-layer films and laminates have been used

for applications ranging from food storage to filtration/separation, protecting semiconductors

and flexible electronics from dust and oxidation [105]. In addition, polymer laminates are also

used in combination with textiles wherein the laminate can act as a barrier to liquid water but

is sufficiently permeable to water vapour and allows for sweat to evaporate through the clothing

[108-110].

The use of specialised vapour deposition systems is required for inorganic or metallic-

polymer laminates fabrication. Multiple dedicated extrusion units, dies and adhesives are

required for polymer-polymer or some inorganic-polymer laminates to keep the heterogenous

system uniform and stable [111]. Hence, new efforts are more directed towards the directed

deposition of a single layer of a multi-phase film. The ability to accurately control the

permeability characteristics is an important requirement for today’s applications and polymeric

laminates have been used commercially for such purposes. Examples include Gore-Tex® [an

Literature Survey: Polymer Laminates

47

expanded Polytetrafluouroethylene (PTFE) membrane coated one side- with infiltration- by a

blend of polyaklylene oxide (PAO) poly(urethane-urea) or a PTFE/PAO/PU membrane

adhesively laminated to an outer and inner layer of Nylon], Sympatex ® (a single layer of a

polyester-polyether blend or a polyester-polyether membrane adhesively laminated to an outer

and inner layer of Nylon) and Nafion ® (a perfluorosulfonate ionomer membrane). Sandwiched

layers of glass between those of polycarbonate using EVA as an adhesive- a technology

developed by (amongst others) SABIC and their Insulgard ™ line are bullet resistant laminates.

Packaging applications that required excellent barrier properties were once, predisposed to use

metal foils but a lower cost method was developed and that resulted in the commercial

application of metallised films. For instance, the metallized line of polyester by Mitsubishi

Polyester Film LLC. Other commercial laminates include the Norplex-Micarta line of

thermosetting laminates (compression molding of prepregs of phenolic, epoxy, silicone or

melamine resin laminate with fibreglass, cork, cotton, paper, carbon fibre, etc.) and Ashland

Inc.’s flexible laminates based on urethane acrylates, etc. Thus, there is a wide range of

commercialised application for polymer laminates [108-112]. The fabrication of polymer

laminates, as seen, is an interdisciplinary exercise as it involves first, the fabrication of a

polymer blend or composite and then the controlled deposition of this heterogenous material on

to a base polymer forming a multi-phase laminate [113]. As mentioned before, the different

kinds of polymer laminates are stand-alone polymeric systems which may or may not be multi

layered and/or multi-phased, polymeric layers coated with an inorganic material or

nanocomposite systems wherein nanoscale fillers are a part of this multi-phase polymeric layer.

The deposition of metallic layers on a polymer substrate is done by using techniques

such as PECVD (Plasma Enhanced Chemical Vapour Deposition) and RF (Radio-Frequency)-

PECVD [113]. In these techniques, the substrate is placed in an evacuated chamber where a

plasma is generated and a vapour stream containing the metal precursor is slowly introduced.

The vapour stream encounters the plasma, gets ionised and eventually gets deposited onto the

substrate. A characteristic of PECVD and RF-PECVD is that lower operation temperatures are

used and the chances of cracking the deposited layer are lower. In addition, the bombardment

of the plasma onto the substrate also helps reduce the amount of surface impurities and thus,

rigorously control the permeability of the fabricated laminate.

Howells et al [113] fabricated a silicon oxide layer onto different grades of PET and

PEN and found that the deposition of a very uniform thin film on the substrate led to the

development of a highly tortuous pathway. In certain cases, they found that the permeability of


48

the composite to water vapour was as much as 750 times lower than that of the uncoated

substrate when a 1000 nm thick layer of silicon oxide was deposited. At that thickness, the

nature of the polymer did not matter as the permeability reduction in PEN was the same as that

reported for PET. Another encouraging result was that even a thick deposition layer did not

result in any cracking showing the uniformity and stability of deposition achieved. Shim et al.

[114] deposited silicon oxynitride on polyether sulfone using PECVD and RF-PECVD and

found that when a silicon based undercoat layer was used as a compatibilizer between the PES

and the oxynitride layer, an oxygen permeability of as low as 0.2 cm3/m2/day was achieved at

only a 25 nm deposition thickness as compared to ~20 cm3/m2/day for the laminate without the

undercoat layer. In further dynamic bending tests, the composite film was subject to high stress

and tested for crack formation and no significant change in gas permeability was seen (Table

2.8).

Table 2.8: O2 Transmission rates of the composite films before and after bending tests. (U:

Undercoat, NC= No change). From Shim et al. [114].

Mode

O2 Permeability [cm3 m2/day] × 10-4

25 nm SiOxNy 150 nm SiOxNy

PES/SiOxNy PES/U/SiOxNy PES/SiOxNy PES/U/SiOxNy

No bend 1.5 0.2 0.4 0.3

Bend in curling

direction NC NC NC NC

Bend in reverse of

curling direction NC NC ~29 NC

Inorganic polymer laminates can also be made by Physical Vapour Deposition

techniques such as Magnetron Sputtering. In this technique thin films are deposited onto a

polymer substrate using very high-power densities (kW cm-2) for very short pulses (tens of

microseconds). Without using toxic and flammable gases in depositing process (as are often

required in the PECVD process), magnetron sputtering technique takes advantage of using

target sputtering deposition to fabricate laminates with high microstructure density. Liu and

Chang [115] deposited thin silicon oxynitride films onto a PES substrate using this technique.

They changed the atmosphere under which the deposition was taking place by changing the N2

content and also the RF power applied. They discovered that the water vapour transmission rate


49

of the optimised composite (deposition carried out under pure N2 and high radio frequency

power) was 2 orders lower than that for the uncoated PES demonstrating the ability of this

technique to create highly defined microstructures.

Iwamori et al. [116] deposited thin layers of silicon oxide and silicon oxynitride onto

PET substrate using RF magnetron sputtering. They discovered that as the coating thickness

increases, the oxygen transmission rate of both films decreased but the OTR of the oxynitride

films were always lower than those of the oxide films. The reduction in permeability was

attributed to the lack of pinholes or cracks on the deposited thin film and the reason for the

uniformity of the film is characteristic of the magnetron sputtering technique. This, in

combination, with the non-use of toxic precursor gases, makes the RF magnetron sputtering

technique a desirable one for fabricating metallic polymer laminates. Also, the use of nitrogen

plasma, in place of oxygen plasma results in lower defects overall and this is attributed to the

lower amount of peroxide produced when there is no oxygen present in the fabrication

atmosphere [116]. However, using these solid state deposition techniques is not as suitable for

large-area applications because of the expensive and complicated processing environments (e.g.

a vacuum and/or an inert environment) and the most benign technique in that regard is sol-gel

based deposition [116]. The sol–gel process involves the formation of an oxide network through

hydrolysis and polycondensation reactions of molecular precursors in water and co-solvent

media. Different precursors provide different properties. Organically modified precursors with

organic functional groups can react with organic resins and in the meantime condense with

inorganic precursors to produce organic–inorganic hybrid coatings. In this way, two

incompatible phases are connected together with strong covalent bonds and create novel

properties. This facet of sol-gel deposition makes it an attractive prospect for creating inorganic

material- polymer frameworks, laminates and composites [117].

Rezaei et al. [117] deposited silica onto a corona treated BOPP matrix using the sol-gel

route. The synthesized sol was a mixture of tetraethylorthosilicate and 3-

methacryloxypropyltrimethoxysilane and was further mixed with different acrylate oligomers

and applied onto the BOPP substrate. The curing and final deposition was done using UV curing

under a high-pressure Hg lamp resulting in a 10 μm thick coating on the BOPP substrate. The

barrier properties of this inorganic-organic hybrid BOPP laminate were compared against that

of plain BOPP. The optimised coatings had water vapour and oxygen permeabilities of 0.96

g/m2/day and 159 cm3/m2/day compared to 11 g/m2/day and 566 cm3/m2/day for the plain BOPP

substrate showing a permeability reduction by factors of 12.5 and 3.54 for water and oxygen


50

respectively. This indicated that oxygen had more ability to permeate through hybrid films

compared to water vapour suggesting that oxygen penetrated through the coating defects and

despite the smaller kinetic radius, water vapour permeated less than oxygen through the film

because of the polarity and density of coating.

Park et al. [118] also attempted to deposit titanium oxide films on flexible PEN

substrates and systematically studied the water vapour permeabilities of the synthesized

laminates. They found that by utilising a two-stage thermal treatment to evaporate the solvent

and allow for polycondensation a close packed, physically stable film was deposited that was

highly crack resistant. The schematic for that method is shown in Figure 2.15. The barrier

properties of the laminate were checked, and it was found that for an 86 nm thick deposit on

the PEN substrate reduced the water vapour transmission rate from 1.55 g/m2/day to 0.133

g/m2/day at 60ºC and 0.0387 g/m2/day at room temperature. The high barrier properties and the

crack resistance showed that this laminate had potential for application as passivation layers in

organic flexible electronic devices.

Figure 2.15: Schematic for sol-gel deposition of TiOx films on PEN substrate. Pre-heating step

makes the film denser by inducing solvent evaporation. Post heating promotes

polycondensation. From Park et al. [118].

There are also several studies and patents available on the use of low shear processing

techniques like rotomolding for producing polymeric laminates wherein a layer of one polymer

is deposited onto another by using successive charging steps while carrying out the rotomolding

process. A technique for making a multi-layer article via rotomolding was developed by Carrow

and Rees [119]. They carried out a two stage moulding procedure wherein the first polymer is

introduced into the mould, heated and subsequently melted. After this, particles of the second

polymer are introduced just before the first polymer layer becomes smooth and glassy. The

mould is then heated and rotated and the second polymer is melted leading to the formation of


51

a multi-layer article post cooling. A peroxide based crosslinking agent is also used in

combination with the first polymer (typically LLDPE or LDPE) in order to have a continuous

top layer with no pinholes or punctures. The suggested peroxide was 2,5-dimethyl-2,5-di(t-

butylperoxy) hexyne-3 and the suggested second polymer was Nylon 11. Gardebjer et al. [120]

fabricated multi-layer LDPE- Ethylene acrylic acid (EAA) films via hot-melt extrusion and

studied their permeability to carboxylic acids for potential use in packaging. They modelled the

overall permeability of the system and took into consideration the interfacial contribution so

essential to laminate type materials. The model they developed consequently shows how the

overall permeability can be controlled based on the properties of the interface and the number

of interfaces present in the system.

Choi and Sankar [121] studied the effects of massive temperature changes (via

cryogenic cycling) on the H2 permeability of plain epoxy/graphite composite and

epoxy/graphite/nano-alumina composite laminates. Conditions resembling space vehicle

refuelling cycles were recreated by subjecting the laminates to cryogenic cooling for several

cycles. The results showed that the permeability increased as the number of cryogenic cycles

increased and then reached a constant value. They also discovered that the laminate which had

a dispersion of nano alumina showed a higher permeability than that seen for the laminates

without the nano alumina. They conjectured that the cryogenic cycling, in general, had

increased the number of microcracks in the specimens and hence it became easier for the gas to

permeate which was proven by optical microscopy. Importantly, one of the samples they tested

was a textile specimen which showed microcrack formation, but these cracks did not connect

and hence no significant change in permeability was observed for this specimen. In general, the

permeability of laminated composites was found to increase anywhere between 3% and 12%

after cryogenic cycling.

There are many advantages involved in using polymer laminates for controlling the

permeability properties. For instance, it only takes a very small amount of the barrier material

thickness on the polymer substrate and that there has been recent significant mathematical

development in more accurately understanding their permeability behaviour. However, it is

apparent that the cost involved (in designing the fabrication set up in case of PECVD and

magnetron sputtering) and the scale at which the deposition is performed is not enough to justify

a manufacturing application especially for storage units. Such a deposition of a barrier layer

would necessitate either a post fabrication step or inherent modifications of the moulding

process making it an expensive investment. There are processes like lay-up, vacuum assisted


52

resin transfer molding (VARTM) or even low shear process like rotomolding where fabrication

of a large and complex laminate polymers or even nanocomposite structures can be done at a

larger scale [121, 122]. However, there are some associated disadvantages like the increased

cycle times for the moulding operations (multiple mold charging required or manual fabrication

required in the lay-up operations) and possible non-reusability of consumables vacuum bag,

peel ply, sealing tube and resin tubing, low/limited injection pressures on account of air

leakages and related factors, low compressive pressure on the preform leading to low air void

compressibility in the VARTM process [119, 121, 122].

In terms of the effects of liquid uptake on the mechanical properties, the work of Pillay

et al. [49] is of special relevance. The main advantage of the use of multi-layer polymer

laminates is the improvement in flexural properties and this was investigated for Nylon based

laminates in [49]. Visually speaking the effect of liquid permeant contact (in this case, water)

with the laminate system is showed in Figure 2.16. In terms of mechanical properties, the

average flexural modulus was lowered by 15% after exposure to moisture at 100°C. However,

the modulus of the material was fully recovered after drying. The flexural strength was lowered

by 45% after exposure to moisture and recovered to within 10% after drying. Both of these

indicate the high resistance of the laminate to mechanical detonation post permeant contact.

However, as seen from Figure 2.16, some amount of mechanical damage is unavoidable.

Figure 2.16: SEM images of Nylon/carbon fibre laminates after contact with water. From

Pillay et al. [49]

Literature Survey

53

Based on the comprehensive study of advantages and disadvantages in the different

multi-phase polymeric systems the polymer natural fibre composites are most suited for this

purpose. Now, when considering the use of a polymer natural fibre composite in an industrial

application (such as storage unit manufacture), it may be required to have a pre-dispersion step

before the processing and product fabrication. This is done in order to ensure compatibility and

effective dispersion and to avoid use of a compatibilizing agent. This results in an increase in

production time and adds to product cost. Also, the incorporation of even small amount of nano

fillers leads to significant changes in the viscoelasticity [123] which can imply that changes in

the processing equipment design or type may be required to help compound the polymer system

effectively. In conclusion, it is essential to juxtapose the stringent control on mechanical and

permeability properties often obtained with nano-filler incorporation with the corresponding

increase in processing and production complexity, time and cost and also, the toxicity of the

potential compatibilizing agent. In order to have an economically viable large-scale

manufacturing process of a polymeric system that allows for control of gas permeability without

major changes to the overall mechanical properties, modifications of several operational,

processing and design parameters will be required. The following statements may be used as

guides:

1. The processing technology used, and the associated parameters can greatly affect

permeability. An example of this is the cooling rate utilised post fabrication which can

be either slow and controlled or rapid (quenching). When quenching is carried out, the

polymer chains have a reduced capacity to form a crystalline structure which results in

lowered crystallinity, increasing void volume/porosity and has been shown to increase

gas/vapour permeability.

2. Geometric parameters like product wall thickness and the presence/absence of sharp

corner are very important factors when it comes to controlling the overall permeability.

However, lower wall thickness and the presence of sharp corners may have a detrimental

effect on the mechanical properties and hence, the geometry has to be given careful

consideration before large scale manufacture can be done.

3. The overall porosity of the system can also be controlled by varying the shear utilised

while processing. The use of an overall low shear fabrication technique or using a

combination of low barrel temperature profile and high screw speeds (in extrusion) can

have a significant effect on the porosity. However, this could be at a cost of poorer filler

dispersion or the possibility of effectively dispersing only low dispersed phase

Literature Survey

54

concentrations. This often results in increased void space, larger segmental mobility and

increased permeability. Irrespective of the chemical compatibilizing treatment done on

the dispersed phase (say, natural fibres), the combination of the low shear and

temperature profiles with high screw speeds (low residence time) contributes to

increased permeability. In applications wherein, an increased permeability is necessary

this may be the route to head down but it is essential that the mechanical properties of

the fabricated polymer are not reduced significantly as reduced interfacial adhesion

between the dispersed and continuous phases can have a detrimental effect on the

mechanical properties. The reduction in mechanical properties can be resolved by using

an external scaffold to hold the structure together but the scaffold has to be designed in

such a way that it does not reduce the cross-sectional area available for permeability

4. Using certain naturally occurring and naturally permeable dispersed phase

materials, it is possible to have a control on the water vapour and possibly the oxygen

permeability of the fabricated polymer. This control means both an increase and a

reduction in overall permeability can be seen with changes in concentration of the

nanofibrils. Dispersing crystalline natural fibres at a high concentration could result in

agglomeration that may create voids for allowing gas/vapour transport and the

orientation/rigidity of the fibrils will ensure there is little reduction in the mechanical

properties Using hydrophilic natural fibres as the dispersed phase in a hydrophobic

polymer matrix with little/no compatibilization will increase the hydrophilicity and

consequently water vapour permeability of the composite. It is also possible to have a

controlled increase in the permeability by surface treatment of natural fibres but it is

essential to account for the toxicity of the treated fibres for food storage applications.

However, the reduction in the mechanical properties like impact strength which can

arise from such agglomeration has to be addressed before the units fabricated from such

a composite may be used commercially.

With an effective combination of some or all of these methods, it may be possible to

design a manufacturing technique and a potential product of controlled gas permeability at an

industrial scale with attention also given to the overall economics of the process. By ensuring

that the additives and other materials utilised in the manufacturing process are at levels

compatible with the standards and practises of the food industry, the fabricated polymeric unit

can be used for storing food-based products.

55

2.5 MOLECULAR DYNAMICS (MD) BASED SIMULATIONS

Molecular dynamics (MD) simulations, first developed in the late 70s for protein folding

and conformational analyses have advanced from simulating several hundreds of atoms to

systems with several thousand or even millions of atoms [17, 18, 124]. The methodology of

MD involves simulating the motions of particles (atoms, molecules, granules, etc.) via a

classical approach and solving Newton’s second law [17, 18, 124]. It is by far the most efficient

and widely used numerical approach for studying thermodynamic properties in atomic and

molecular systems. In MD, atoms with initial positions and velocities are exposed to collisions

governed by the empirical interatomic potentials (EIP). As a consequence of these collisions,

the atoms making up the simulated system occupy several different coordinate positions based

on time. Such a system can, in effect, be defined by a mathematical expression that correlates

total energy to particle coordinates. This expression is known as a forcefield (FF). Generically,

a force field can be expressed in analytical form as U(r1, r2, r3,......rn) where r represents the

positional coordinates. Before carrying out a MD simulation, information is required about the

initial positions (r), velocity (v), charge (q) and bond information (type of atoms, bond angles,

lengths, etc). To run a simulation, in addition to above, information is also needed about the

force acting on each particle and the acceleration. The parameters are typically obtained either

from ab initio or semi-empirical quantum mechanical calculations or by fitting to experimental

data such as neutron, X-ray and electron diffraction, NMR, infrared, Raman and neutron

spectroscopy, etc. Molecules are simply defined as a set of atoms that is held together by simple

elastic (harmonic) forces and the FF replaces the true potential with a simplified model valid in

the region being simulated. Ideally it must be simple enough to be evaluated quickly, but

sufficiently detailed to reproduce the properties of interest of the system studied.

In a MD simulation, all of the atoms are treated as point masses and all the electrons are

assumed to be in the ground state. To determine the positions of the various atoms at different

simulation times, methods such as the Verlet algorithm [125] are used to solve the equations of

motion. If the initial position of the atom is given by r(t) then:

r(t + Δt) = r(t) + v(t)Δt +1

2a(t)Δt2 +

1

3!

r (t)Δt3 + O(Δt4) (2.8)

r(t − Δt) = r(t) − v(t)Δt +1

2a(t)Δt2 −

1

3!

r (t)Δt3 + O(Δt4) (2.9)

Molecular Dynamics based simulations

56

r(t + Δt) + r(t − Δt) = 2r(t) + a(t)Δt2 + O(Δt4) (2.10)

r(t + Δt) = 2r(t) − r(t − Δt) + a(t)Δt2 + O(Δt4) (2.11)

Thus, the position in the next time step can be described in terms of the previous position

and the current acceleration. Next, the individual atoms making up the simulated molecule are

described using a potential energy function (U) given by:

d2Ri

dt2 = −1

mi∇iU(R) (2.12)

Eq (2.12) is then solved, subject to the following initial conditions, R = R(0) and v =

v(0) and applying relevant boundary conditions (Ri, vi, and mi are position and velocity and

mass of atom i). Defining the inter and intra-atomic and molecular interactions happening

within the simulation box involves solving the electronic Schrödinger equation for each atom

in the system. This becomes extremely complicated, especially in a polymeric system with

several hundreds or thousands of atoms. Therefore, analytical representations of the potential

surface inside the box are utilised. For instance, it is possible to express the overall potential

energy of the system (Upot) as:

Upot = Ubond + Unon bond (2.13)

Ubond potentials and arise because of near neighbour connections in the molecular

structure. Unon-bond potentials depend upon the distance between the interacting species. These

non-bonded potentials are calculated between atoms belonging either to the same chain (but

separated by more than two or three bonds depending on the definition of the torsional potential)

or to different molecules. Depending on the different ways of defining Ubond and Unon-bond there

are several different force fields. A generic example is shown in Eq (2.14) wherein the first four

terms constitute the intramolecular terms Ubond and the last two represent the repulsive and Van

der Waals interactions (by means of a 12,6 Lennard-Jones type potential) and the Coulombic

interactions and constitute Unon- bond. In Eq (2.14), r, θ, q and g are the actual values for bond

length, bond angle, improper and proper dihedral angles while r0, θ0, q0 and g0 are the

equilibrium values, kd, kθ, kϕ and kg are the associated force constants with n being the

periodicity of the torsional potential. rij is the distance between the two non-bonded atoms i and


57

j, εij and σij are the well depth and contact radius of the Lennard-Jones potential between these

atoms, ci and cj are the charges on i and j, 7ε0 is the vacuum permittivity (8.854 × 10-12 C2 J-1m-

1) and ε is the effective dielectric constant of the medium.

Upot = ∑kd

2(r − r0)2

bonds

+ ∑kθ

2(θ − θ0)2

bond angles

∑k∅

2(q − q0)2

improper dihedrals

+ ∑kτ

2[1 − cos(ng − g0)]

torsion

+ ∑ 4εij [(σij

rij)

12

− (σij

rij)

6

]

non−bonded

+ 1

4πεε0

cicj

rij

(2.14)

One of the major limitations of MD can be seen from the expressions used to define the

intramolecular bonds. The first expression in Eq (2.14), represents the dynamics of bond

stretching and squeezing and is of a simple harmonic form. The values for r0 can be obtained

using Raman spectroscopy or from X-ray diffraction experiments. However, in general, a

harmonic potential loses a lot of accuracy for any displacement of more than 10% from the

equilibrium value. But more importantly, the use of the harmonic function implies that the bond

cannot be broken, so no chemical processes can be studied. This is one of the main limitations

of forcefield based MD simulations compared to ab initio MD. The second expression in Eq

(2.14) is for angular bending of the bonds and is also represented using a harmonic potential as

in Eq (2.15) but in some cases a trigonometric potential can also be used as shown in Eq (2.16).

Ubend = ∑kb

2(θ − θ0)2

angles (2.15)

Ubend = ∑kb

2(cos θ − cos θ0)2

angles (2.16)

As angle bending is also associated with vibrational movements additional harmonic

terms are sometimes added to the Ubend term as shown in Eq (2.17) where s represents the

distance between the two external atoms forming the bond and is referred to as the Urey-Bradley

or U-B potential.


58

Uvib = ∑kb

2(s − s0)2

angles (2.17)

The third expression in Eq (2.14) represents the torsion observed in any molecule

containing more than 4 atoms in a row. Torsional motions are much less stiff than bond

stretching motions and are necessary for ensuring the correct degree of rigidity of the molecule

and to reproduce the major conformational changes due to bond rotation. For polymers and

other macromolecules, this is an extremely important term as it helps determine the local

structure and relative stability thereof. However, an additional term is needed with the torsional

terms to ensure planarity for some types of bonding systems such as sp2 hybridized carbon

atoms in carbonyls or aromatic rings. This extra component describes the positive contribution

to the energy of those out-of-plane motions and is shown in Eq (2.18) where 𝜆 is the improper

angle corresponding to the deviation from planarity. An alternative to Eq (2.18) is shown in Eq

(2.19)

Uimp = ∑kimp

2[1 + cos(2λ − π)]

impropers (2.18)

Uvib = ∑kimp

2(λ − λ0)2

impropers (2.19)

The first of the two intermolecular/ non-bonding terms used in Eq (2.14) represent the

repulsive and attractive Van der Waals forces between the atoms. The repulsion is a

consequence of the overlap of the electronic orbitals of both atoms while the interaction

between the induced dipoles leads to an attractive force. These two forces vary as different

power functions of the interatomic distance. Non-bonded interactions are usually excluded

between atoms which are already interacting by a bond or bond angle term (first and second

neighbours) and they are often modified for the end atoms of a dihedral angle (third

neighbours). Van der Waals forces act between any pair of atoms belonging to different

molecules, but they also intervene between atoms belonging to the same molecule that are

sufficiently separated, as described later. It is possible to define a set of parameters (e.g. σij and

ε𝑖𝑗) for each different pair of atoms, but for convenience most force fields give individual

atomic parameters (i.e. σ𝑖 and ε𝑖), together with some rules to combine them. The Lennard-


59

Jones parameters for pairs of unlike atoms are often derived by mixing rules, e.g. the Lorentz-

Berthelot combining rules shown in Eq (2.20) and Eq (2.21) [126]:

εij = √εiiεjj (2.20)

σij = σii+ σjj

2 (2.21)

Depending on the type of forcefields used, the forms of the individual terms may vary.

For instance, a different expression may be used for non-bonded van der Waal’s interaction like

the Lennard-Jones 9, 6 potential [127] instead of the 12, 6 expression shown in Eq (2.14). The

final term in Eq (2.14) serves to describe the electrostatic interactions. Some forcefields can

also include cross terms between different degrees of freedom/ interactions. These are good for

describing the coupling between stretching, bending, and torsion. They bring corrections to the

intramolecular energy and allow to reproduce better the observed spectra of intramolecular

vibrations. Some examples of cross terms are Ubond-bond, Ubond-bend and UH-Bonding and are shown

in Eq (2.22), (2.23) and (2.24) where rAD is the distance between the donor and the acceptor

atoms, and θAHD is the angle between the donor, the hydrogen, and the acceptor atoms.

Ubond−bond = kbb

2(r − r0)(r′ − r0

′ ) (2.22)

Ubond−bend = k

bb′

2[(r − r0)(r′ − r0

′ )] (2.23)

UH−bonding = [(A

rAD12

) − (B

rAD10

)] cos2θAHD (2.24)

The final aspect of MD forcefields is the mechanism by which polarizability can be

introduced into the system. In a condensed matter system, the emergence of local electric fields

induces the appearance of dipoles in the system and describing only the average polarization

through the entire system is not enough as local effects are not described well enough by the

average value. Essentially, in the absence of polarizability, the simulated molecule would

behave the same way irrespective of the state it is in or the medium it has been dispersed in.

Interactions such as solvation, H- bond directionality and cation-aromatic interactions cannot


60

be effectively modelled. Hence, most modern forcefields explicitly include the polarization. In

this case, for each atom or molecule the surrounding particles will induce a charge redistribution

that needs to be modelled which is done in either one of three ways. The charges can be allowed

to fluctuate according to the environment so that the charge flows between the atoms till the

instantaneous electronegativities are equal. Using shell model or defining Drude type particles

wherein the polarizability is incorporated by representing the atom itself as a combination of a

charged core and a charged shell. The interactions between the core and shell are modelled by

a harmonic oscillator as in Eq (2.14) where the force constant in this case is inversely

proportional to the polarizability and the total displacement depends on the simulated medium

and the electrostatic environment created thereof. The final method is to define induced point

dipoles associated with each polarizable atom.

The origin of the use of forcefields in contemporary MD simulations were with the goal

of predicting molecular structures and relative conformational enthalpies. These include the

Molecular Mechanics or MM category forcefields. Now, originally these forcefields were used

for hydrocarbon molecules but soon expanded into the simulation of carbonyl compounds and

organic sulphides and amides. However, they were still used for isolated molecules. New

developments needed to be done for using MD for more complex systems. The Dreiding and

Universal Force Fields (UFF) systems were the next set of developed force fields that contained

parameters for all atoms in the periodic table. In terms of the mathematics, Dreiding [128] and

UFF (Universal Force Fields) [129] are known as Class I forcefields and the equations that

define these forcefields are like Eq (2.14). There is a distinct lack of cross terms in their

expressions and the incorporation of cross terms such as Eq (2.22), (2.23) and (2.24) were done

in the Class II forcefields. Some examples of these are the CHARMM (Chemistry at HARvard

Molecular Mechanics) [130], AMBER (Assisted Model Building and Energy Refinement)

[131], GROMOS (GROningen MOlecular Simulation) [132], OPLS (Optimized Potentials for

Liquid Simulations) [133, 134], TRAPPE (Transferable Potentials for Phase Equilibria Force

Field) [135] and the entire category of Consistent Force Fields (CFF) [136].

The ultimate goal of a force field is to describe in classical terms all the quantum

mechanical facts, partitioning the total electronic energy into well separated atom-atom

contributions, such as Coulombic, polarization, dispersion, and repulsive energies.

Unfortunately, even disposing of very accurate Quantum Mechanical (QM) calculations, it is

impossible to fully separate the intricate electronic effects. This implies that the simulation

operators are obliged to employ significant physical approximations to describe in a tractable


61

manner the intermolecular interactions, which limits their accuracy. Therefore, they are called

empirical potentials or empirical force fields, and depending on the procedure followed to

develop them and the set of input data used to optimize their parameters, different force fields

applicable to different systems or problems are obtained. Thus, each force field has its own

strengths and weaknesses related to the data and procedure employed in its parametrization, so

the final choice depends on the particular problem being considered. However, as of today all

leading force fields provide quite reasonable results for a wide range of properties of isolated

molecules, pure liquids, and aqueous solutions [134]. The specific force fields that were used

in this thesis, the modifications done to the different ensembles used and the methodology for

modelling and predicting the relevant physical phenomena for this thesis are covered in more

detail in Section 3.2.

Some examples of forcefields and details about them are shown in Table 2.9.

Table 2.9: Functional forms of several Class I and Class II forcefields.

Name Functional form of energies associated with different bonding and non-

bonding terms

AMBER

[131]

Bonding terms:

Bond length: E = ∑𝑘b

2(r − r0)2

bonds

Bond angles: E = ∑𝑘a

2(θ − θ0)2

angles

Bond torsion: E = ∑𝑘t

2[1 + cos(nφ + δ𝑛)]torsion ;

n can be as high as 12 for some dihedral angles.

Bond dihedrals: E = ∑ kd(ψ − ψ0)2dihedrals

Non-bond terms:

Van der Waals defined by Lennard Jones 12,6 potential:


62

E = ∑ 4εij [(σij

rij)

12

− (σij

rij)

6

]

non−bonded

For the case when or are fluorine atoms the Lennard-Jones form above is

replaced by a Hill potential

E = ∑ εij [6

α − 6𝑒

α(1−rij

6√2𝜎𝑖𝑗)

−2α

α − 6(

σij

rij)

6

]

non−bonded

where the free parameter α = 12 is chosen to reproduce the long range

behaviour of the Lennard-Jones potential. As with the electrostatic interaction,

the van der Waals interaction is neglected for 1-2 and 1-3 bonded atoms, and

it is scaled by 0.5 for 1-4 bonded atoms.

Electrostatic interactions defined by Coulombic expression.

E = ∑1

4πεε0

qiqj

rijnon−bonded

CHARMM

[130]

Bonding terms:

Bond length: E = ∑ 𝑘b(r − r0)2bonds

Bond angles: E = ∑ 𝑘a(θ − θ0)2angles

Bond torsion: E = ∑ kt[1 + cos(nφ + φ0)]torsion


63

Bond dihedrals: E = ∑ 𝑘d(ψ − ψ0)2dihedrals

Non-bond terms:



rij)

12

− (σij

rij)

6

]

non−bonded

Electrostatic interactions by Coulombic expression.

E = ∑1

4πεε0

qiqj

rijnon−bonded

DREIDING

[128]

Bonding terms:

Bond length: E = ∑ kb(r − r0)2bonds

Bond angles: E = ∑ ka(θ − θ0)2angles

Bond torsion: E = ∑ kt[1 + cos(nφ + φ0)]torsion


Non-bond terms:



rij)

12

− (σij

rij)

6

]

non−bonded


64


E = ∑1

4πεε0

qiqj

rijnon−bonded

TRAPPE

[135]

Bonding terms:

Bond length: E = ∑ kb(r − r0)2bonds

Bond angles: E = ∑ ka(θ − θ0)2angles

Bond torsion: E = ∑ 𝑘0 + k1(1 + cos φ) + k2(1 − cos 2φ) +torsion

K3(1 + cos 3φ)


Non-bond terms:



rij)

12

− (σij

rij)

6

]

non−bonded


E = ∑1

4πεε0

qiqj

rijnon−bonded


65

GROMOS

[132]

Bonding terms:

Bond length: E = ∑Kb

4(r2 − r0

2)2

bonds

Bond angles: E = ∑Ka

2(cos θ − cos θ0)2

angles

Bond torsion: E = ∑ K1(1 + cos 𝛿𝑛 cos m𝑛φ𝑛)torsion ; cos 𝛿𝑛 = ±1

Bond dihedrals: E = ∑ Kd(ψ − ψ0)2dihedrals

Non-bond terms:



rij)

12

− (σij

rij)

6

]

non−bonded

Electrostatic interactions by Coulombic expression with three contributions.

E1 = ∑1

4πεε0

qiqj

rijnon−bonded

E2 = ∑qiqj

4πεε0

−12 𝐶𝑟𝑓rij

2

𝑅𝑟𝑓3

non−bonded

E3 = ∑qiqj

4πεε0

−(1 −−12 Crf)

Rrfnon−bonded

Crf is related to the cut off radius Rrf, the relative permittivity and the inverse

Debye screening length of the medium outside the cutoff sphere.


66

OPLS

[133, 134]

Bonding terms:

Bond length: E = ∑ Kb(r − r0)2bonds

Bond angles: E = ∑ Ka(θ − θ0)2angles

Bond torsion: E = ∑𝑉1

2[1 + cos(φ + f1)] torsion +

𝑉1

2[1 + cos(2φ + f2)] +

𝑉1

2[1 + cos(3φ + f3)]

V1, V2, and V3 are the coefficients in the Fourier series, and f1, f2, and f3

are phase angles

Non-bond terms:



rij)

12

− (σij

rij)

6

]

non−bonded


E = ∑1

4πεε0

qiqj

rijnon−bonded

UFF

[129]

Bonding terms:

Bond length: E = ∑Kb

2(r − r0)2

bonds or E = ∑ 𝐷𝑖𝑗(𝑒−𝑥(𝑟−𝑟𝑖𝑗) − 1)

2

bonds


67

Where x = √kij

2D𝑖𝑗

The Morse function is a more accurate description since it implicitly includes

inharmonic terms near equilibrium (rij) and leads to a finite energy (Dij) for

breaking bonds

Bond angles: E = ∑Ka

𝑛2(1 − cos 𝑛𝜃)

angles

Bond torsion: E = ∑Kt

2[1 − cos(𝑛φ0) cos(nφ)]torsion

Non-bond terms:



rij)

12

− (σij

rij)

6

]

non−bonded


E = ∑1

4πεε0

qiqj

rijnon−bonded

PCFF/

SciPCFF

[136]

Bonding terms:

Bond length: E = ∑ K2(r − r0)2bonds

Bond length quartic: E = ∑ K2(r − r0)2bonds

+ K3(r − r0)3 + K4(r − r0)4


68

Bond angles: E = ∑ Ka(θ − θ0)2angles

Bond angle quartic: E = ∑ K2(r − r0)2bonds

+ K3(r − r0)3 + K4(r − r0)4

Bond torsion: E = ∑ 𝐾1(1 + cos(nφ + φ0)torsion

Bond dihedrals: E = ∑ Kd(ψ − ψ0)2dihedrals

Cross Terms:

Bond-bond: E = K𝑏𝑏′(r − r0)(r′ − r0′ )

Bond-angle: E = K𝑏𝜃(r − r0)(𝜃 − θ0)

End bond torsion: E = (r − r0) ∑ V(n)cos (nφ)

V(n) ranges from -2.4 to 1.6

Middle bond torsion: E = (r − r0)[F(1) cos φ + F(2) cos 2φ +

F(3) cos 3φ]

F(1) ranges from -13.80 to 54.88, F(2) ranges from -7.93 to 6.05, F(3) ranges

from 0 to 2.34.

Angle-angle: E = Kbθ(θ − θ0)(θ′ − θ0′ )

Angle-torsion: E = (θ − θ0)[F(1) cos φ + F(2) cos 2φ + F(3) cos 3φ]

F(1) ranges from -8.04 to 69.73, F(2) ranges from -2.77 to 3.29 , F(3) ranges

from -7.03 to 7.44

Angle-angle-torsion: Kθθ′φ(θ − θ0)(θ′ − θ0′ )(φ − φ0)

Non-bond terms:


69


E = ∑ εij [2 (σij

rij)

9

− 3 (σij

rij)

6

]

non−bonded


E = ∑1

4πεε0

qiqj

rijnon−bonded

Now, the several ensembles in which the MD simulations, particularly for estimating

physical properties of polymers, are carried out in will be discussed. Essentially, an MD

simulation can be characterized by 5 parameters viz,

1. Total number of atoms (N),

2. Volume (V)

3. Temperature (T)

4. Pressure (P)

5. Total energy (E).

Based on which parameters are kept constant, there are three set ups that can be used in

any MD simulation:

1. The first one is the Microcanonical ensemble or the NVE set up. Here, the particle

number (N), volume (V) and total energy (E) (sum of Kinetic and Potential Energies)

are constant and Temperature (T) and Pressure (P) are unregulated.

2. The second set up is the Canonical ensemble or the NVT set up. Here, N, V are constant,

T is regulated by a thermostat and P is unregulated.

3. The third set up is known as the Isothermal-Isobaric ensemble or the NPT set up. This

is similar to NVT except that P is regulated while V and E are the observables to be

calculated.


70

A period of equilibration is usually necessary at the beginning of a simulation to allow

for the system to relax toward equilibrium. Following this period, the runs are carried out for

1–100 ns, with the configurations and thermodynamic data stored for analysis [137].

The exact sort of post run analysis and interpretation will be explained in Section 3.2

but in general, the NVE, NVT and NPT ensembles can be visually represented as seen in Figure

2.17. From Figure 2.17, it is also apparent why the NPT ensemble is used mostly for estimating

physical properties owing to it being closest to representing pressure equilibration.

Figure 2.17: (a): NVE ensemble (closed system), (b): NVT ensemble (closed system but not

heat isolated), (c): NPT ensemble (isobaric-isothermal)

Some examples of MD used in literature for simulating and predicting some transport

properties of polymers are listed below. Typically, the force fields used in all of these systems

were of the Class II category and included AMBER, DREIDING and some proprietary

forcefields such as COMPASS. However, the principle aim was understanding the

methodology used for predicting transport phenomena of small molecular weight permeants of

different phases. The hope was that these major observations that could help while building up

simulated versions of Polyethylene, the dispersed phase and the different permeants that would

be studied in this thesis.

The first example is not for Polyethylene but for an amorphous polymer that is used in

several applications- Polystyrene (PS). Asahi and Tamai [138] simulated the transport of CO2

and N2 in PS for which they used the AMBER forcefield while carrying out the simulation. The

cut off distance used was 9 Å and used the Verlet algorithm shown in Eq (2.9)- Eq (2.11) with

a time step of 1 fs. The initial structure was equilibrated for 50 ps and sampled for 100 ps at

300 K. Twenty gas molecules were then inserted into separate cavities in the PS simulation to

simulate the diffusion behaviour. The PS simulation itself was built using the crystal unit cell


71

dimensions obtained from X- ray diffraction studies and the unit cell itself was repeated 3, 4

and 6 times in the x, y and z direction respectively creating a supercell with 9216 atoms. In

order to properly estimate D, they had to use a relatively higher temperature of 500 K for

simulation. The diffusion coefficients D of the gases were calculated from the mean-square

displacement sampled for 10 ns for each model gas and averaged over three independent runs.

They found that the interaction parameter and axial length of penetrant molecules were found

to be the two most important facets affecting D.

Simulation of commercial PS (an atactic polymer and thus, possessing low crystallinity)

was also done by Mozaffari et al. [139]. Unlike Asahi and Tamai [138], they used a higher time-

step of 1.5 fs and a cut off distance of 10 Å. In addition, they constrained all bond length. They

found that the center-of-mass mean-square-displacement of the permeant (whether argon,

nitrogen, carbon dioxide, methane or propane is shown to pass through three distinct regimes

irrespective of temperature. The first is the short-time ballistic regime. Then a regime of

anomalous diffusion occurs, in which the mean-square-displacement is proportional to tx with

x< 1. Finally, for sufficiently long times, the Fickian regime occurs, for which the mean-square-

displacement is proportional to t. This is the minimum time that the simulation needs to be run

for to get an accurate value for D. The reason for anomalous diffusion is a structure of the

environment which alters the possible diffusion pathway by introducing extra tortuosity on a

certain length scale, or which delays the diffusion by forcing the permeant molecules to adopt

certain shapes in order to be able to slip through openings.

According to Asahi and Tamai [138], the axial length of the permeant contributed to the

diffusive transport. In this work, the diffusion coefficient was found to be correlated also to the

permeant shape (Figure 2.18) as follows where deff is the effective molecular diameter [Eq

(2.25)]:

ln(D) = K1 − K2deff2 (2.25)

It was also found that the penetrant molecule shape consideration lead to changes in

calculated values. For instance, approximating non-spherical molecular molecules to be

spherical molecules lead to massive deviations while estimating D. Also, D could be correlated

to the average jump distance between neighbouring cavities or free volume pores (o) and also,

the amount of residence time (tc) the permeant molecule had in the cavity [Eq (2.26)].


72

D =o2

6tC (2.26)

Figure 2.18: Logarithm of the diffusion coefficients as a function of square effective diameters.

From Mozaffari et al. [139]

Another interesting result from Mozaffari et al. [139] was that all calculated transport

coefficients (diffusion, solubility and permeability) were found to be higher than the

experimental data but the ratios of calculated permeabilities are in a very good agreement with

experiment. This is an attribute of MD that seems to be universal. The overestimation of specific

values but experimental agreement with the ratios and the overall trends are often seen for a

range of material properties and polymers simulated using MD. It is a result that is addressed

in this thesis in Section 4.2 but for the time being, exploration of similar works of molecular

simulation in literature will be continued.

Using MD to simulate diffusion in PE was done by Börjesson et al. [140]. They

developed a periodic cell as shown in Figure 2.19 and used several forcefields to simulate PE.

Using equilibrated density as an indicator, they found that the AMBER force field worked best

as compared to other forcefields like OPLS and Dreiding for the same cut off distance (10 Å).


73

Figure 2.19: PE matrix containing six polymer chains, each having 200 C atoms. The ball-and-

stick model represents the PE chains with their centre of mass in the unit cell and the thin-line

model represents their periodic replicas. From Börjesson et al. [140]

The larger observation, however, from their work indicated the need for High

Performance Computing in MD simulations, especially when dealing with transport

phenomena. In Figure 2.20, there are several trajectories that a permeant molecule (in this case,

oxygen) can take when diffusing in the PE simulation box. However, when several of these

trajectories were combined, it is seen that there is a proportional relationship to MSD with time.

Figure 2.20: Three typical MSDs of an oxygen molecule in PE at 308 K. The average MSD,

shown in black, reveals a linear increase in MSD with time. From Börjesson et al. [140]


74

The number of runs they carried out were 128. While for other operations, this is a very

large number of runs, for simulating transport in polymeric systems via MD, such a high

number is essential. Therefore, it was decided that in this thesis, the High-Performance

Computing (HPC) system at the Department of Astrophysics, Swinburne University of

Technology would be utilized for the MD runs. The details of the HPC used and the number of

runs is all detailed in Section 3.2 but at this juncture, it is important to note the effective

confluence of parallel computing and molecular simulations. On a regular computing system,

carrying out such data intensive simulations would be quite difficult but the presence of an HPC

greatly facilitates such work.

Polyethylene (PE) composite systems were then studied by Erdtman et al. [141] who, in

particular, analyzed the transport of the permeants in the direction exactly perpendicular and

parallel to the dispersed phase (graphene or carbon nanotubes-CNTs) orientation in a simulated

PE. The built simulations of PE with graphene and PE with CNT are shown in Figure 2.21. The

structures were first equilibrated by studying the variation in structure density with time. Once

the density fluctuations with time had stopped, the structures were further optimized using

dispersion corrected density functional theory (DFT-D) with the B3LYP hybrid functional and

the 6-311G(d, p) and 6-311G(2d,2p) basis sets. All DFT-D geometry optimizations were

performed using the General Atomic and Molecular Electronic Structure System (GAMESS-

US). The dimensions of the periodic cell were 34.08 Å, 31.97 Å, 30 Å in the x-, y-, and z-

dimensions, respectively. This is sufficiently large to prevent interaction between an atom and

its periodic image. 6 PE chains (220 atoms). However, the chirality of polymer and additives

not considered. For estimating diffusion coefficients, the slope of the mean squared

displacement curve was only calculated form first 30% of trajectory (without the first 20 ps)

because initial movement of penetrant molecules is too ballistic while the final 70% had

statistical uncertainty.


75

Figure 2.21: Equilibrated structures of (a): PE–graphene and (b): PE–CNT nanocomposites.

From Erdtman et al. [141]

Interestingly, they observed that there was a slightly elevated density for the PE regions

in the presence of the fillers as compared to the density value obtained for pure amorphous PE

showing that the PE chains pack more tightly in the presence of CNT/Graphene. It was almost

like an induced crystallinity was observed and made evident from the structures observed post

equilibration in the presence of the dispersed phases (Figure 2.22a and b). The addition of a

graphene sheet or CNT induced a layered PE structure near the additive surface and that the

ordered structure decreases with increasing distance to the additive. At long distances (beyond

~15 Å), the layering diminished, and the PE structure remained amorphous.

Figure 2.22: Layering in (a): PE–graphene and (b): PE–CNT (right) systems. From Erdtman et

al. [141].

a b

a b


76

Another example of a composite system was studied by Bai et al. [142]. They simulated

Polyvinylidene fluoride (PVDF) - SiO2 composites and investigated the effects of the

concentration and size of silica particles on the diffusion behavior of water through the

composite. They used the COMPASS forcefield for this purpose. The simulated SiO2 and

PVDF structures are shown in Figure 2.23 and a cutoff distance of 9.5 Å was employed to

evaluate the non-bond interaction with a time step of 1 fs.

Figure 2.23: Simulated (a): SiO2 and (b): PVDF-SiO2 composites. From Bai et al. [142]

The PVDF polymer chain consisted of 100 repeat units while the silica particle had an

approximate radius of 7.94 Å and had α-quartz silica crystal structure. The properties they

simulated included the X ray diffraction pattern, PVDF chain mobility, free volume, diffusion

of water and the effect of SiO2 particle size on all these properties. Bai et al. [142] used a

simulated probe in order to calculate the free volume and porosity in the simulation box. This

method is known as a Connolly probe and was developed by Connolly [143]. Essentially, a

probe “molecule” with the radius RP rolls over the van der Waals surface that defines the

simulated molecule, and the free volume is defined as the volume on the side of the Connolly

surface without atoms. The fractional free volume (FFV) is determined by the ratio of the free

volume to the total volume of the model. The results showed that the diffusion coefficients of

water were positively correlated with the mobility of the PVDF chain, and the free volume of

the membranes. The diffusion coefficient of water was also negatively correlated with the

a b


77

crystalline domains of the polymer chain. They also found from the simulated XRD that the

crystalline region of the PVDF polymer were disrupted owing to the interaction between the

SiO2 and the polymer chains similar to results of Edrtman et al. [141].

MD simulations of transport have also been done for polymer blends such as those of

Polypropylene (PP) with Polylactic acid (PLA) and Polyethylene terephthalate (PET) and

Polyethylene naphthanate (PEN). Deghani et al. [144] conducted the manufacture and

molecular simulation of PP/PLA blends (Figure 2.24). The approach they used was to simulate

diffusion separately in the two phases and then combine the results using semi-empirical

modelling.

Now, the semi-empirical approach is something that will also be used in this thesis and

further explanation of this is given in Section 3.2. Essentially, the modelling a physical

phenomenon can be done using either Empirical, Deterministic or Semi-Empirical techniques.

Semi-empirical modelling helps combine the advantages of the empirical and deterministic

techniques while minimizing the inherent drawbacks and has been used successfully in several

engineering fields. The results of MD for the work of Deghani et al. [144] helped confirm that

the PP-rich blends have greater oxygen barrier properties compared to those for the PLA-rich

blends due to lower MSD value and thus, D of the oxygen in the simulated PP as opposed to

the simulated PLA (Figure 2.24).

Figure 2.24: The graphs of MSD vs. time after MD, representing the fitting line relation. From

Deghani et al. [144].


78

PET/PEN blends were simulated by Fermeglia et al. [145] using the COMPASS

forcefield. They built systems of PET and PEN with industrially utilized molecular weights

(Mw of 18000 g/mol). The built polymer molecules were subjected to successive annealing

cycles under an NVT protocol. After each annealing the structures were minimised with respect

to energy and only those structures corresponding to the minimum energy were used for further

modeling. From the fully relaxed models, NPT MD experiments were run at 583 K for all

systems, and at 298 K for the PET and PEN pure homopolymers. They identified the Hildebrand

solubility parameter for each polymer and used the output of the MD results as inputs for a

mesoscale simulation. This work demonstrated the potential of using MD for simulating the

distribution of the individual PET and PEN phases in the microstructure of the blend in the

presence of absence of transesterification between the two polymers. Another important result

showed that there was a bimodal distribution in oxygen permeability values in the absence of

transesterification while with transesterification, the permeability trend pointed to a single

averaged value through the structure of the blend. This showed an MD and mesoscale

simulation proof for introducing blend miscibility by bringing about esterification between the

two components of the blend (Figure 2.25).

Figure 2.25: Oxygen permeability along the z axis for simulated PET/PEN blends (a): without

transesterification and (b): with transesterification. From Fermeglia et al. [145]

While the predictions of transport properties are important for this thesis, predictions of

other material properties such as the mechanical properties are also extremely important for

storage applications. With that in mind, the use of MD for predicting mechanical properties of

both macromolecules, such as the polyolefin raw material used in this thesis and (inorganic and


79

organic based) dispersed phase materials was carried out. There are several examples of the use

of MD for such a purpose in literature and some of them are reported below.

Figure 2.26: Simulating effect of branch length effect on PE strength for different branch

moieties (black: methyl, red: ethyl, brown: butyl) and comparing with available experimental

data (blue). 2n is the number of C atoms in the PE backbone chain (50). From Liao et al. [146]

The use of MD for simulating the mechanical behavior of PE as a function of branching

was demonstrated by Liao et al. [146] who also took into account the effect of chain branching

on the system. They suggested that the role of the branched chains in a mostly linear polymer

is similar to that of rubber particles in a rubber toughened blend. They used the OPLS field for

the simulation and a cut off distance of 10 Å. They simulated a tensile yield stress in the y-

direction for the built PE with branches of either methyl, ethyl or butyl moieties and studied the

evolution of the normalized stress σy/σy_avg_max as a function of branch length ‘l’. The simulated

trend was then compared with experimental data obtained after normalizing the fracture tensile

stress observed experimentally. Their results are shown in Figure 2.26 and it seen that there is

decent agreement, but the accuracy is a bit short.

An example of MD used for simulating the mechanical deformation of a thermoplastic

composite is the work of Jia and Qingsheng [147]. The system they explored was that of PE

and CNTs similar to the work done by Edrtman et al. who estimated the transport properties

and layering in PE/CNT nanocomposites. Jia and Qingsheng [147] used the NVT ensemble to


80

carry out this simulation and found that the CNT at first is covered completely by the PE chains

and as the simulation proceeds and the displacement is higher, the CNT gets slowly gets

delaminated off the PE chains (Figure 2.27).

Figure 2.27: CNT (brown) delaminates from PE chains (Green). From Jia and Qingsheng

[147].

Amongst amorphous polymers, the simulation and analysis of Polymethylmethacrylate

(PMMA) was done by Sahputra et al. [148]. They used a range of forcefields viz., OPLS,

Dreiding, AMBER etc and compared their individual effectiveness in simulating the structure

and predicting the properties of PMMA for both smaller and larger systems. They used 3

different versions of PMMA for each forcefield and these versions had molecular weights of

7510, 15010 and 30010 respectively. Interestingly, while Sahputra et al. [148] did predict the

mechanical properties (specifically, Young’s modulus) of the PMMA using MD, they did so

over a range of temperatures (150 K to 750 K) and plotted the trends in Young’s modulus as a

function of temperatures. Using this plot, they were able to predict a Tg for the simulated

PMMA by concentrating on the inflection point on the graph where there is a marked drop in

modulus value as shown in Figure 2.28. Also, at room temperature, the Young’s modulus for

the simulated PMMA is about 3.74, 3.69 and 4.68 GPa for the simulations using the

DREIDING, AMBER, and OPLS force fields respectively while the experimental modulus

value is about 3-5 GPa [148, 149]. At temperatures between 200 and 300 K, all force fields also

predicted that the Young’s modulus is in close agreement with experimental data (between 3-

4.8 GPa).


81

Figure 2.28: Trends in mechanical properties of PMMA as a function of temperature using

different MD forcefields. From Sahputra et al. [148]

In addition to simulating material properties, over the past few decades, there has been

enough progress in computation and parameterized forcefields that MD has been used

successfully to recreate simulated models of biological relevance. Examples like entire proteins

in solution with explicit solvent representations, membrane embedded proteins, or large

macromolecular complexes like nucleosomes or ribosomes have been simulated and modelled

using MD. Irrespective of how complicated the built system gets, the typical MD algorithm

used for simulating tends to follow a predictable path and is as follows:

1. An initial model of the system is obtained from either experimental structures or

comparative modeling data. The simulated system could be represented at different

levels of detail. Atomistic representation is the one that leads to the best reproduction

of the actual systems. However, coarse-grained representations are becoming very

popular when large systems or long simulations are required.

2. Once the system is built, forces acting on every atom are obtained by deriving

equations, the force-fields, where potential energy is deduced from the molecular

structure.

3. Once the forces acting on individual atoms are obtained, classical Newton’s law of

motion is used to calculate accelerations and velocities and to update the atom

positions. As integration of movement is done numerically, to avoid instability, a

time step shorter than the fastest movements in the molecule should be used. This


82

ranks normally between 1 and 2 fs for atomistic simulations and is the major

bottleneck of the simulation procedure.

There are several ways that the simulations can be sped while using the algorithm

described earlier. The first deals with the use of periodic boundary conditions. This has to do

with the fact that the use of MD is to predict bulk properties of materials and not really simulate

molecules in vacuum. For a system of N atoms or molecules or particles, the number of particles

close to the wall of the simulation cell or box of side length ‘L’ would be proportional to N-1/3

which means that with an increase in the number of atoms simulated and the complexity of the

simulation, it is no longer viable to consider the walls of the simulation box as a rigid surface.

In fact, what is done in MD is that the simulation box is surrounded by an infinite number of

replicas of itself. Only the N atoms inside the main cell are considered explicitly, but as soon

as one of the atoms leaves the cell, an image particle enters from the opposite side to replace it.

The second deals with the analysis of long-range interactions and electronic density.

While the molecular electronic density can be obtained with a high accuracy by means of high-

level quantum-mechanical calculations, the problem of reducing such density to a manageable

description to be used in a MD simulation is not trivial. The usual choice is to assign a partial

atomic charge to each nucleus and use Coulomb’s law to compute their contribution to the total

energy. The partial charges can be derived from a fit to experimental thermodynamic data, but

this approach is only practical for small molecules. Also, electrostatic interactions are long-

ranged, so they require particular treatment when truncating them while carrying out the

simulation. Typically, a cut off distance (Rrf) is included as part of the simulation algorithm.

Typical values given for this cut off distance are about 8-10 Å i.e. the non-bond interactions

smoothly decay to 0 at 8-10 Å from each atom. This also helps greatly reduce the degree of

computation required by essentially all atoms that are beyond that distance as part of a dielectric

continuum.

The third method is to use neighbor and cell lists. Based on the previous two steps, a

specific number of ‘N’ atoms or particles in a box of side L are assigned and all long-range

interactions beyond a distance RC from an atom are cut off. The MD run for this system will

then involve evaluating the total force on an atom ‘i’ arising from all other atoms that are within

a sphere of radius Rrf with ‘i' as centre. Thus, the number of operations involved would be 1

2 N

(N-1). Now, by ensuring that Rrf is much smaller than L a list of all atoms that are at a distance

smaller than Rrf + l where l is user chosen value (like 1 Å) is kept. So, at each time step, the


83

search for the atoms situated at a distance < Rrf of a given atom is done only over the atoms

included in its neighbour list. The list has to be updated regularly to take into account the atoms

that enter or leave the sphere, or even better one can keep a record of the atomic displacements

and update it whenever one of them has moved more than l. Another way would be to define a

distance l’ ≥ Rrf and dividing the entire simulation cell into sub-cells of side l’. Each particle in

the system is assigned to one of these sub-cells. For each atom ‘i’, only the atoms located in the

same sub-cell or adjacent sub-cells can be at a distance < Rrf and so the search can be limited

to only those sub-cells.

The fourth method deals with the use of simulation time steps. MD runs are done at user

defined timesteps and the effective use of these timesteps can also markedly increase the

simulation speed. A smaller time step will improve the accuracy solution, but at the cost of

requiring a much larger number of time steps to obtain a trajectory of the required length. On

the other hand, a too large value for timestep will cause large fluctuations or drifts in the energy

and can even make the simulation unstable. In any case the timestep should not be larger than

the mean time between each interatomic collision.

The fifth method is the use of United Atom Models. This method involves the

combination of several atoms in the simulation by defining them as a single interaction site.

The most typical case consists in replacing -CH3 or =CH2 groups by a single site. In this way,

not only the fastest degrees of freedom are removed, but additionally the number of atoms

composing the system is largely reduced. However, some atomic details are inevitably lost, so

this method can be considered already as a kind of coarse grained simulation.

The sixth and final method involves the use of High Performance Computing systems

(HPC). The parallel processing capabilities of HPC ensure that vastly larger numbers of

simulations can be carried out simultaneously.

Finally, the results obtained from MD simulation were then combined with semi-

empirical models found in literature to analyse the effectiveness of the MD method to build

accurate versions of the materials studied in this thesis. In order to model transport properties,

the models used are shown in Table 2.10 and in order to model mechanical properties such as

the elastic modulus as done in this thesis, the models used are shown in Table 2.11. In terms of

the models in Table 2.11 it important to note that the relatively small aspect ratios of the wood

flour particles used (~4.5), effective load transfer across the fibre matrix interface is more

difficult and therefore, a limitation on the efficacy of modelling the elastic properties is exerted.


84

Table 2.10: Semi-empirical models for estimating D

Model Expression

Maxwell

[150]

𝐃 = 𝐃𝐂 𝐃𝐃 + 𝟐𝐃𝐂 + 𝟐𝛟(𝐃𝐃 − 𝐃𝐂)

𝐃𝐃 + 𝟐𝐃𝐂 − 𝛟(𝐃𝐃 − 𝐃𝐂)

This model was developed for permeability but the relevance of this

model for diffusion is studied in this work.

This model assumes the system to be a random dispersion of non-

interacting impermeable spheres that comprises the dispersed phase in a

continuous matrix where D, Dc and DD refers to the overall, continuous

phase and dispersed phase diffusion coefficient respectively, ϕ is the

dispersed phase volume fraction.

This model works in low dispersed phase concentration environments

(volume fraction ϕ ~ 0.2 and below) and for blends and composites systems

where the properties of the dispersed phase can be accurately measured

[151, 152].

Kalnin

[152]

𝐃 =𝐃𝐂

𝟏 − 𝛟 +𝐂𝟏

𝐂𝟐𝛟

[𝟏 +ⅆ (𝐃𝐃

𝐂𝟏

𝐂𝟐− 𝐃𝐂) 𝛟

(ⅆ − 𝟏)𝐃𝐂 −𝐂𝟏

𝐂𝟐𝐃𝐃 − (

𝐂𝟏

𝐂𝟐𝐃𝐃 − 𝐃𝐂) 𝛟

]

Where the ratio C1/C2 is the partition coefficient and d is the number of

dimensions (in this case, 3). For this work, C1/C2 is estimated to be f2/f1

where f1 and f2 are the fractional free volumes of the simulated amorphous

and crystalline PE systems. The calculation and other details are given in

Section 4.2). However, more accurate values can be obtained by carrying

out dedicated MD simulations.


85

Maxwell-

Wagner-Sillar

(M-W-S)

[151]

𝐃 = 𝐃𝐂 𝐧 𝐃𝐃 + (𝟏 − 𝐧)𝐃𝐂 + (𝟏 − 𝐧)𝛟(𝐃𝐃 − 𝐃𝐂)

𝐧 𝐃𝐃 + (𝟏 − 𝐧)𝐃𝐂 − 𝐧𝛟(𝐃𝐃 − 𝐃𝐂)

Equation derived for a dilute dispersion of ellipsoids and n is a factor that

denotes the shape of the dispersed phase.

For n = 0, this model reduces to the Rule of Mixtures:

𝐃 = 𝛟𝐃𝐃 + (𝟏 − 𝛟)𝐃𝐂

For spherical shape of the dispersed phase, n = 1/3 and the model reduces

to Maxwell Model [150].

For n = 1, this model reduces to the Laminate Model

𝟏

𝐃=

𝛟

𝐃𝐃+

(𝟏 − 𝛟)

𝐃𝐂

For prolate ellipsoids, in which the longest axis of the ellipsoid is directed

along the applied pressure gradient: 0 ≤ n ≤ 1/3. n was chosen to be the

average i.e. 1/6 in this work.

For oblate ellipsoids in which the shortest axis of the ellipsoid is directed

along the applied pressure gradient: 1/3≤n≤1. n was chosen to be the

average i.e. 2/3 in this work.

Fredrickson

and Bicerano

(F and B)

[153]

This model describes D through a disperse phase that is defined as a

random array of disk shaped nanoplatelets. These nanoplatelets have

radius Rn, thickness Wn and are separated by an average distance that

exceeds Rn.

For a dilute regime where α= dispersed phase aspect ratio and ϕ =volume

fraction, αϕ << 1. This model is referred to as “F and B dilute” in this paper.


86

𝐃

𝐃𝐂=

𝟏

𝟏 + 𝐊𝛂𝛟

Where,

𝛂 =𝐑𝐧

𝐖𝐧

𝐊 = 𝛑

𝐥𝐧 𝛂

In a semi dilute regime, the interparticle distance is less than R and the

dispersed phase particles are almost overlapping. This creates a more

tortuous pathway. This model is referred to as “F and B semi dilute” in this

paper.

𝐃

𝐃𝐂=

𝟏

𝟏 + 𝛍𝛂𝟐𝛟𝟐

𝛍 = 𝛑𝟐

𝟏𝟔 𝐥𝐧𝟐 𝛂

Equations for deriving α are covered in Section 4.3.

Weissberg[154]

𝐃

𝐃𝐂=

𝟏 − 𝛟

𝟏 − 𝟎. 𝟓𝐥𝐧(𝟏 − 𝛟)

This model can be considered an amalgamation of the Maxwell model

[151, 152] and an additive logarithmic relationship between the

diffusivities of the continuous amorphous and volume fraction of the

dispersed crystalline phase. This model is applicable to systems wherein

the dispersed phase is comprised of randomly overlapping

(interpenetrating) spheres of either uniform or non-uniform sizes.


87

The expression for the conventional Logarithmic Model is:

𝐃 =𝛟

𝐥𝐧(𝐃𝐃)+

(𝟏 − 𝛟)

𝐥𝐧(𝐃𝐂)

Table 2.11: Semi-empirical models for estimating elastic moduli for composites with randomly

oriented dispersed phase.

Model Expression Reference

Rule of

Mixtures

𝐄 = (𝟏 − 𝛟)𝐄𝐂 + 𝛟𝐄𝐃

ϕ is the volume fraction of the dispersed phase while E, EC and

ED are the moduli of the composite, continuous and dispersed

phases respectively.

[155]

Laminate

𝐄 =𝟏

(𝟏 − 𝛟)𝐄𝐂

+𝛟𝐄𝑫

[155]

Hirsch

𝐄 = 𝐚𝐇𝐄𝐌 + (𝟏 − 𝐚𝐇)𝐄𝐏

𝐚𝐇 is a semi-empirical parameter which represents the stress

transfer between the fibre and matrix while EM and EP represent

the modulus values obtained from using the rule of mixtures and

the laminate model.

[155]

Short Fibre

𝐄 = 𝐄𝐂 +√𝟏𝟔𝛑𝛟𝟐𝟑

𝟒(𝐄𝐃 − 𝐄𝐜)

[156]


88

Carman-

Reifsnider

𝐄 = 𝐄𝛈𝛟 + 𝐄𝐂(𝟏 − 𝛟)

𝐄𝛈 = 𝛈𝐄𝐃

𝛈 = 𝟏 −𝐭𝐚𝐧𝐡 (𝛂𝐊)

𝐚𝐊

𝐊 = √

−𝟐𝟏 + 𝛔𝐏𝐑

𝐄𝐃

𝐄𝐂⋅ 𝐥𝐧 𝛟

α and σPR are the aspect ratio of the dispersed phase and

Poisson’s ratio of the continuous phase respectively.

[157]

Halpin-

Tsai

𝐄 = 𝐄𝐂 (𝟏 + 𝛃𝛈𝛟

𝟏 − 𝛈𝛟𝐃)

𝛈 =

𝐄𝐃

𝐄𝐂− 𝟏

𝐄𝐃

𝐄𝐂+ 𝛃

𝛃 = 𝟐𝛂

Or

𝛃 =𝟐(𝟏 − 𝟐𝛔𝐏𝐑)

𝟏 + 𝛔𝐏𝐑

When β is expressed in terms of α, the model is referred to as

Halpin-Tsai 1 and in the other case as Halpin-Tsai 2.

[155],

[158]


89

Cox

Krenchel

𝐄 = 𝐧𝟏𝐧𝟎𝐄𝐃𝛟𝐃 + 𝐄𝐂(𝟏 − 𝛟)

𝐧𝟎 = 𝐜𝐨𝐬𝟒(𝛂)

𝐧𝟏 = 𝟏 −𝐭𝐚𝐧𝐡 (

𝐛𝐜𝐤𝐥𝟐

)

(𝐛𝐜𝐤𝐥

𝟐)

𝐛𝐜𝐤 =𝟐

ⅆ𝐃√

𝐄𝐂

𝐄𝐥𝐟𝐦(𝟏 − 𝛔𝐏𝐑) 𝐥𝐧 (𝛑

𝐱𝐜𝐤𝛟)

[159]

Tsai

Pagano

𝐄 =𝟑

𝟖𝐄𝟏𝟏 +

𝟓

𝟖𝐄𝟐𝟐

𝐄𝟏𝟏 = 𝐄𝐜 [𝟏 + 𝟐𝛂𝐧𝐇𝐓𝐋𝛟

𝟏 − 𝐧𝐇𝐓𝐋𝛟]

𝐧𝐇𝐓𝐋 =(

𝐄𝐥𝐟𝐦

𝐄𝐂) − 𝟏

(𝐄𝐥𝐟𝐦

𝐄𝐂) + 𝟐𝛂

𝐄𝟐𝟐 = 𝐄𝐜 [𝟏 + 𝟐𝐧𝐇𝐓𝐓𝛟

𝟏 − 𝐧𝐇𝐓𝐓𝛟]

𝐧𝐇𝐓𝐓 =(

𝐄𝐭𝐟𝐦

𝐄𝐂) − 𝟏

(𝐄𝐭𝐟𝐦

𝐄𝐂) + 𝟐

E11 is higher than E22 for all composites we have studied.

E11 is about 9% greater than E22 at 5% wood and ~30% greater

at 20% wood content

[159]

90

CHAPTER 3

MATERIALS AND

METHODS

3.1 MATERIALS AND PROCESSING

Rotomolding grade LLDPE with brand name: Alkatuff LL710UV and melt flow index

(MFI) of 10 g/min and average particle size of 300 µm was provided by Price Plastics Pty. Ltd.,

Dandenong, Victoria. Untreated fine pine flour was purchased from Pollard’s Sawdust Supplies

Pty. Ltd., Plenty, Victoria. Oak flour was obtained from contacts at Flexcube Pty. Ltd.

Denatured ethanol (drum grade) was procured from Sigma Aldrich. The oak and pine flour

particles both had a particle size of about 350 µm and based on thermogravimetric analysis had

a water content of 8 ± 1%. Using a nanoindenter (described in more detail in Figure 3.13) the

moduli of single pine and oak particles were found to be 3650±1400 MPa and 4900±800 MPa

respectively. AR Grade citric acid and sodium citrate dihydrate were also obtained from Sigma

Aldrich and were dissolved in distilled water to form a buffer solution of pH 4.5 ± 0.5.

Compression molding was carried out on a LabTech Scientific compression molding

machine at the Materials Processing Laboratory, ATC, Swinburne University of Technology

(Figure 3.1). Rotomolding was carried out at Roto Industries Pty. Ltd., Pakenham, Victoria

(Figure 3.2). The processing cycle details are in Tables 3.1 and 3.2 and the compositions of the

different samples molded via compression and rotomolding are enlisted in Table 3.3. Pictures

of the molded specimens are shown in Figure 3.3.

All samples were analysed for their mechanical, thermal, morphological, porosity and

transport properties.

Materials and Methods: Materials and Processing

91

Table 3.1: Process cycle time and other parameters of the compression molding technique

Cycle Pressure (kPa) Temperature (°C) Time (min)

Pre-heating 101.325 190 7

Venting 7600 190 5

Heating 10000 190 5

Cooling 7600 13 5

Table 3.2: Process cycle time and other parameters of the rotomolding technique

Cycle RPM Temperature (°C) Time (min)

Heating Major axis: 7.5, Minor axis: 5 240 12

Ambient cooling - Room temperature 4

Fan cooling - Room temperature 6

Cooling chamber - 13 12

Figure 3.1: (a): Compression Molding machine, (b): Chilling unit of compression molding

machine.

a b


92

Figure 3.2: (a): Rotomolding machine, (b): Control unit of Rotomolding machine

Table 3.3: Samples made from each molding method with wood flour content.

Molding

technique Sample name Type of Wood

Wood flour content

(weight %)

Compression

Molding

CM0 None 0

CM5 Pine 5

CM10 Pine 10

CM20 Pine 20

CM5_O Oak 5

CM10_O Oak 10

Rotomolding

RM0 None 0

RM5 Pine 5

RM10 Pine 10

RM20 Pine 20

RM5_O Oak 5

RM10_O Oak 10

a b


93

Figure 3.3: (a): Compression molded with pine flour L-R: 0%, 5%, 10% and 20% by weight

pine flour, (b) Rotomolded specimens with pine flour L-R: 0%, 5%, 10% and 20% by weight

pine flour (c): Rotomolded specimens 5% and 10% by weight of oak flour.

c

94

3.2 TESTING MATERIAL PROPERTIES

The molded specimens were cut into samples for carrying out the Tensile, Flexural and

Izod Impact tests. Examples of the samples are shown in Figure 3.4. The tensile and flexural

strengths were tested on a Zwick Z010 Universal testing machine with a 10 kN load cell (Figure

3.4a and 3.4b). The strain rates were 50 mm/min for the tensile strength (ASTM D638) and 3

mm/min for the flexural strength (ASTM D790) analysis.

Figure 3.4: Zwick Z010 Universal Testing Machine with (a): tensile grips, (b): flexural grips,

(c): Samples for tensile and flexural testing.

a b

c

Materials and Methods: Testing Material Properties

95

Izod impact tests (ASTM D256) were done on a CEAST Impact testing machine (Figure

3.5) with the notch on the sample being made on an Instron notch cutter. For each test, a

minimum of 3 samples were analysed per composition.

Figure 3.5: (a): CEAST Impact Testing machine, (b): Samples for impact testing.

Morphological properties of the samples were analysed using a and an Olympus BX61

Optical Microscope (OM) shown in Figure 3.6 and a Zeiss Supra 40 Vp Scanning Electron

Microscope (SEM) shown in Figure 3.7. The samples analysed via SEM were first coated with

gold on an Emitech K975X sputtering unit (Figure 3.8).

Figure 3.6: Olympus BX61 Optical Microscope (OM)

a

b


96

Figure 3.7: Zeiss Supra 40 Vp Scanning Electron Microscope (SEM)

Figure 3.8: Emitech K975X sputtering unit


97

Some molded specimens cut for mechanical testing were dipped in solutions of 100%

by volume of ethanol (adjusted to pH of 4.5± 0.5 using citric acid buffer) in water at 6 ºC and

30ºC to study the influence of material processing technique on solvent uptake characteristics

of the samples. ASTM D570 normally used for measuring water uptake of plastic materials was

used for this purpose. The mass, length, width and thicknesses of the sample were monitored

over time and followed by mechanical testing at the end of the sorption test, in order to

determine the effect of the solution uptake on the composite’s mechanical properties. Samples

were wiped off with a soft cloth and left in a fume cupboard for 5-10 min after removal from

sorption set up before testing the mechanical properties. The diffusion coefficient (D) was

obtained from the sorption data using Eq (3.2.1)

D = −h

π2

d

dtln (1 −

C

C∞) (3.2.1)

Where C∞ is the mass uptake at equilibrium and d

dtln (1 −

C

C∞) represents the slopes of

the plot of ln (1 −C

C∞) vs time and h is the thickness of the sample in cm, C and C∞ are the

ethanol uptakes at any time t and at equilibrium respectively.

Figure 3.9: Oven where solvent uptake experiments are conducted. Maintained at an average

temperature of 30 ±1ºC


98

Figure 3.10: Refrigerator where solvent uptake experiments are conducted. Maintained at an

average temperature of 6±2 ºC

Figure 3.11: (a): Differential Scanning Calorimeter, (b): Chiller Unit attached to DSC machine.

The crystallinity of all the molded specimens was tested using a TA DSC 2010

Differential Scanning Calorimeter (Figure 3.11a). Heating runs were conducted from room

temperature to 300°C at a heating rates of 5, 10 and 15°C/min to check the trends in and the

effect of heating rate on the % crystallinity of the composite specimens. The weights of the

specimens for DSC were 7-10 mg, taken from the powdered raw material and from the molded

specimens. The % crystallinity of the specimen was determined by dividing the heat of fusion

a b


99

for the analysed specimen obtained by integrating the area under the fusion/melting peak in the

DSC graph by 293.1 J/g which is the heat of fusion for 100% crystalline LLDPE.

Storage moduli of the samples before and after ethanol contact were measured on a TA

Dynamic Mechanical Analyzer DMA 2980 (Figure 3.12a) in the tensile and single cantilever

modes. Sample dimensions were 25.4 mm × 12.5 mm with the thickness being 1.5-2.5 mm.

Testing span of 17.5 mm was used in single cantilever and about 20 mm in tensile modes. The

frequency used was 1 Hz and the analysis was carried out from 30°C to 100°C at a heating rate

of 3°C/min. Creep analysis of the specimens was also done under similar circumstances (tensile

mode, before and after ethanol contact) and over a period of 24 h under a stress of 1 MPa.

Equilibrium compliance values (Jeq) from using the DMA set up in tensile mode was then

converted to the corresponding equilibrium modulus values using Eq 3.2.2.

Eeq =1

Jeq (3.2.2)

Figure 3.12: (a): TA DMA 2980 Dynamic Mechanical Analyzer, (b): Specimens for creep

and storage modulus measurement

Elastic modulus of the pine and oak flour themselves were estimated using the

indentation technique on a Hysitron TI Premier Nanoindenter at Swinburne University of

Technology. Samples were encapsulated in an epoxy matrix followed by polishing of the top

surface in order to expose the powders to the indenter and further analysis.

a b


100

Figure 3.13: Hysitron TI Premier Nanoindenter

Oxygen permeability of the samples was tested on a MOCON OxTran 2/21 Oxygen

Permeability Tester at Gunn Labs, Black Rock, Victoria (Figure 3.14). The analysis was carried

out at 23°C, 0% Relative Humidity (RH) under ASTM F1927. The samples were cut into disks

of ~90 mm diameter (Figure 3.15).

Figure 3.14: MOCON OxTran 2/21 Oxygen Permeability Tester


101

Figure 3.15: Disc samples for Oxygen Permeability testing

The densities, and thus, the macroporosities of the samples were estimated using the

pycnometer method. Initially the clear glass pycnometer is weighed to find out its empty weight

(W0). Then some quantity of the sample is added to the pycnometer and weighed (W1). The

displacement fluid (in this case, water) is poured into the pycnometer till it is full and weighed

again (W2). Then the fluid and the sample are removed from the pycnometer and only the

displacement fluid is poured into the pycnometer till full and weighed again (W3). The density

(or specific gravity as the value obtained is the ratio of the density of the sample to the density

of the displacement fluid which is 1 g/cm3 for water) is given by:

ρ =𝑊1−𝑊0

[(𝑊1−W0)−(W2−W3)] (3.2.3)

If the densities of the constituent materials i.e. LLDPE (ρ1) and wood flour (ρ2) and the

composition (ϕ is the volume fraction of the LLDPE) are known, then the rule of mixtures can

be used to estimate the theoretical densities of the samples.

ρ𝑇𝐻 = ϕρ1 + (1 − ϕ)ρ2 (3.2.4)

Knowing the values of ρTH and ρ, the overall porosity (Vp) in the system can be estimated

by the following formula:

V𝑃 = 100 (1 −ρ

ρΓH) (3.2.5)


102

Figure 3.16: Pycnometer with water filled up to mark.

Microporosity of the composites were analysed using Positron Annihilation Lifetime

Spectroscopy (PALS). This technique employs a positronium, Ps (a bound state between a

positron and an electron) to probe the void sites associated with free volume in condensed

matter systems and can measure the average diameters of pores from 0.1 – 20 nm [160]. The

average lifetime of the positronium is measured with ORTEC spectrometers using 22Na as the

positron source. The exponential decay data obtained from the PALS measurement was fitted

to three components with the characteristic lifetimes of τ1, τ2 and τ3. The first component, τ1

was fixed to 0.125 ns and is attributed to para-Positronium (p-Ps) annihilation (a bound state

of the positron with an electron of opposite spin) [161]. The second component, τ2, is attributed

to the free annihilation of the generated positrons with free electrons within the sample. The

final component, τ3, is attributed to the annihilation of the ortho-Ps or o-Ps which is the bound

state of the positrons with electrons of the same spin. The τ3 lifetime is used to correlate the

micropore diameters within the sample using the Tao-Eldrup [160, 161] equation given by Eq

(3.2.6). Here, τ3 is in ns, d is the average pore diameter in nm and Δ is an empirical parameter

equal to 0.166 nm. The tested specimens were prepared to 2 mm thick and placed each side of

the Mylar sealed source to ensure that all the positrons annihilate within the sample [160]. A

source correction of 1.613 ns and 3.32% was used.

𝜏3 =1

2[1 −

𝑑

d+Δ+

1

2πsin (

2πd

d+Δ)]

−1

(3.2.6)


103

Figure 3.17: (a): Positron source of PALS machine, (b): Sample chamber for PALS analysis

a b

104

3.3 MOLECULAR DYNAMICS AND SEMI-

EMPIRICAL MODELLING

MD simulations were carried out using the Materials and Process Simulation (MAPS)

software developed by Scienomics Inc. The building, equilibration and simulation of

polyethylene and wood flour systems were carried out using MD. All simulations were run on

the gStar and OzStar High Performance Computing Systems at the Department of Astrophysics,

Swinburne University of Technology.

First, the simulation of Polyethylene and the methods used to build amorphous,

crystalline and semi crystalline simulation cells will be discussed. The Crystalline Builder

Module of the MAPS program was used to construct both the crystalline unit cell (and a

crystalline Supercell. The dimensions of the crystalline unit cell were a = 7.121 Å, b = 4.851 Å

and c = 2.548 Å and all unit cell angles are 90°. These dimensions were obtained from the data

provided by Bruno et. al. [162]. The Crystalline Builder module has provisions for constructing

cells of various space groups as required. From the data of Bruno et. al. [162], the geometry of

the crystalline unit is orthorhombic in nature. The specific positions (knowns as the partial

coordinates) of the H and C atoms in the unit cell provided in [162] helped us create a

crystallographic information file or a .cif file which could be used to construct both the unit

cells (Figure 3.18) and the supercell (comprised of 4116 atoms; Figure 3.19) in the MAPS

program.

Figure 3.18: Crystalline Unit cell of PE constructed using the partial coordinates suggested

by Bruno et. al. [162] with carbon atoms shown in blue and hydrogen atoms in green.

MD and semi-empirical modelling

105

Figure 3.19: Crystalline supercell of PE with carbon atoms shown in blue and hydrogen atoms

in green made up of several individual units of Figure 3.18.

The amorphous cell of PE was constructed using 8 PE chains of DP (degree of

polymerization) of 75 corresponding to a total of 3600 atoms using the Amorphous Builder

Module of the MAPS program (Figure 3.20). The use of several thousand atoms in the

simulation has been shown to achieve more exact predictions of bulk properties as indicated in

[140].

Figure 3.20: Amorphous simulation box of PE with carbon atoms shown in blue and hydrogen

atoms in green.


106

Following this, the validities of the constructed models were tested. The first step

involves assigning a force field for the simulated systems. The SciPCFF field, developed by

Scienomics Inc, parameterised for polymeric systems was chosen. It is an extension of the

Polymer Consistent Force Field (PCFF). SciPCFF is intended for applications to polymers,

organic materials and porous materials and can be used for calculations of cohesive energy,

compressibility, heat capacity, elastic constants and mechanical properties. More details on

SciPCFF are seen in Table 2.9 in Section 2.5. After the assignment of the force field, the systems

were subjecting to the following MD operations outlined in Algorithm A described in steps a1-

a4.

ALGORITHM A

a.1. The geometry of the system was optimised and the overall energy minimized using the

steepest descent method for a total of 2000 steps (2000 is the recommended number of

steps for the Optimizer module of the MAPS program)

a.2. After the geometry optimization, the simulation boxes were subjected to a NVT step.

Non-bond interactions were controlled by using a cutoff distance of 10 Å and the Ewald

summation method was used to quantify electrostatic (Coulomb) interactions. The

duration of the run was 0.2 ns and the temperature (set at 298K) was controlled using a

Nose-Hoover thermostat with a damping coefficient of 10 fs.

a.3. The NVT run was followed by a NPT dynamics step for 2 ns. This was also carried out

at 298 K under 101.325 kPa pressure and the Ewald summation method was used to

quantify electrostatic (Coulomb) interactions with the same cut off distance as in Step

2. Temperature was controlled again using the Nose-Hoover thermostat with a damping

coefficient of 10 fs.

a.4. After the NPT dynamics run, the density of the simulated system is compared against

density values mentioned in literature for amorphous and crystalline PE.

After the optimization of the simulation boxes with respect to density, the atomistic pore

size distribution in the simulation boxes were estimated. This was done in order to quantify the

accessible volume in the systems and also to get a perspective on the nature of diffusive

transport through the amorphous and crystalline sections of a semi crystalline polymer and

through wood flour. The Trajectory Analysis menu on the MAPS program was used to estimate


107

the free volumes of the system and the pore size distribution within each simulation box was

estimated.

Estimating the capability of the MD technique to predict more relevant transport

properties was then carried out. First, a single O2 molecule was introduced into the amorphous

and crystalline PE simulation boxes (in accordance to the method developed by Börjesson et

al. [140]) and the D value for the O2 in the amorphous and crystalline PE systems were

estimated as a function of temperature. The most common way to evaluate D in MD simulations

involves the calculation of the mean-square displacements, MSDs that is given by:

MSD = ⟨r(t + t0) − r0(t0)⟩2 (3.3.1)

Here, r0 is the initial position and ri indicates the position at time ti = t + t0. The ‘⟨⟩’

indicates that the MSD values are averaged over all penetrant molecules and all possible time

origins of the simulation runs. The MSDs and the simulation run time (t) can then be used to

evaluate the D of the gas using Einstein’s relation shown in Eq (3.3.2) with the caveat that the

gas molecules follow a random walk. This leads to certain deviations with high density

polymers. In addition, this equation can be applied only for sufficiently long times. Over those

time scales, the simulated gas molecules have experienced enough jumps in their trajectories

so that a random walk scheme could be considered and in effect, the overall MSD becomes

proportional to ‘t’ [140]. Hence, long simulation times are often needed to obtain an accurate

value of D from Eq (3.3.1). Therefore, simulation times of 5 ns were chosen for the O2 diffusion

studies in amorphous PE and 10 ns for crystalline PE.

D =1

6t⟨𝑟𝑖(𝑡 + 𝑡0) − 𝑟0(𝑡0)⟩2 (3.3.2)

The pathway used to estimate the diffusion coefficients via MD simulations in the

MAPS program is as outlined in Algorithm B described in steps b1-b10.

ALGORITHM B

b.1. Use the Matrix Builder command that is part of the Amorphous Builder module to

incorporate the O2 molecule in the matrix corresponding to either the Crystalline or

Amorphous PE simulation box.


108

b.2. Subject the combined system to an energy minimization step by utilizing the Optimizer

module. Use the Steepest descent method with a total 2000 steps as described in

Algorithm A.

b.3. Longer NVT (2 ns) and NPT (5 ns) steps were used when estimating D and studying

the diffusive transport of O2 as compared to when building only the amorphous and

crystalline simulation boxes as explained in Algorithm A.

b.4. D was estimated from the overall MSD in the NPT run using Eq (3.3.1).

b.5. 30 NPT runs were carried out at each temperature (293, 298, 303 and 308 K) to obtain

some statistical rigour for the calculation of D.

b.6. These were done for both the Crystalline and Amorphous PE systems to compare the

diffusive transport seen in the crystalline region of PE as compared to the amorphous

region.

b.7. The obtained D values were plotted as a function of temperature.

b.8. The data obtained from the simulation of O2 diffusion in purely crystalline and the

purely amorphous polyethylene was attempted to be fit to the averaged diffusivity

experimental data obtained from 5 representative papers on the analysis of O2 transport

in LLDPE [52-56] using several semi-empirical diffusion models shown in Section 2.5,

Table 2.10. The crystallinities of the samples analysed in the papers [38, 163-166] were

found to be all around 30 ± 5% (estimated from the enthalpy of 100% crystalline PE in

J/g). This would correspond to a volume crystallinity of 26.8% taking into account the

densities of 100% amorphous (0.85 g/cm3) [167] and 100% crystalline PE (1 g/cm3)

[168]).

b.9. The deviation of the predicted D values from the experimental values can be quantified

using Eq (3.3.3) where Di, E represents the experimental value and Di,M is the predicted

value by the model at temperature “i”, ‘n’ is the number of data points and DA, E is the

average experimental value over the considered temperature range. Based on the values

of average absolute relative error (δ) for the different models they can be ranked in terms

of their accuracy in predicting the diffusion of O2 through a semi crystalline LLDPE

δ =100

N∑ |

Di−DEexp

Dexp|

N

i=1 (3.3.3)


109

b.10. The most ideal model is then recommended and possible ways of improving the

simulation so as to be more reflective of the reality of transport of O2 through LLDPE

are suggested.

Once, it had been established that the physical and transport properties of the simulated

PE molecules were similar to experimental values available in literature, simulation boxes of

materials that resemble and represent the raw materials viz., semi-crystalline LLDPE and pine

flour were constructed. First, a semi-crystalline LLDPE cell was constructed as outlined in

Algorithm C described in steps c1-c5.

ALGORITHM C

c.1. The AMBER [169] force field was used to carry these MD simulations. Details about

AMBER are in Table 2.9, Section 2.5.

c.2. The constructed and equilibrated crystalline simulation cell was extended in the z

direction by 40 Å.

c.3. Using the Matrix builder module again, the simulated amorphous PE chains are then

introduced into the extended box.

c.4. A geometry optimization/energy minimization step was then performed and then the

procedure is the same as the method employed to construct the individual amorphous

and crystalline simulation boxes. An NVT run of 2 ns and NPT run of 5 ns was done

and the system was equilibrated.

c.5. The final system had the empirical formula of C3864H7758 (Figure 3.21) and the box had

the dimensions of 55 Å x 37 Å x 56 Å. The proportions of the amorphous and

crystalline PE molecules were so that the overall product had ~ 46% crystallinity to

reflect the properties of the Alkatuff LL710UV (Section 3.1) used as the main raw

material.

Schematically, the whole process can be shown as in Figure 3.21.


110

Figure 3.21: Constructing the semi crystalline simulation cell.

The construction of the pine flour simulation cell involved incorporating the 4 major

phases in the pine flour viz., cellulose, hemicellulose, lignin and water into the same box in

specific proportions. Cellulose (Figure 3.22a) and hemicellulose monomers (Figure 3.22b) with

ab initio charges assigned to the terminal chain atoms were constructed using the Sketching

tool of the MAPS program and the systems were optimised using PCFF [170] as the forcefield.

The monomer unit for the lignin molecule (Figure 3.22c) was adapted from Dabral et. al [171].

The cellulose molecule had a degree of polymerization of 25 and two molecules were generated

with an overall empirical formula of C600H1004O500 (Figure 3.22e), the hemicellulose molecule

has a DP of 13 and an overall empirical formula of C507H703O327 (Figure 3.22f) and the lignin

molecule had a DP of 5 and an empirical formula of C430H462O145 (Figure 3.22g). The cellulose,

hemicellulose and lignin molecules were combined to form a single simulation box of a wood

molecule (Figure 3.22h) with all sides of the simulation box being 31.5 Å. The ratios of the

cellulose to lignin was then 40:30:30 by weight to approximate the proportions of the cellulose,

hemicellulose and lignin molecules in softwood [172]. The overall empirical formula of this

system was C600H1004O500 and to this system molecules of water were introduced which

constituted 8% by weight of the overall system which was the equilibrium amount of moisture

in the pine flour measured on a TA Thermogravimetric Analyzer. This system was used to

approximate the wood flour dispersed in the LLDPE matrix.


111

Figure 3.22: Simulated molecules of (a): Cellulose, (b): Lignin, (c): Hemicellulose, (d): Water,

(e): Cellulose polymers, (f): Hemicellulose polymer, (g): Lignin polymer, (h): Simulated wood

flour with cellulose in brown, water in yellow, hemi cellulose in green and lignin in blue.

Using these equilibrated systems of semi-crystalline PE and pine flour, physical and

transport properties of interest could be predicted and modelled. The two properties that have

g f e

a

b

d

h


112

been predicted using Molecular Dynamics were the diffusion coefficient of ethanol and the

elastic modulus in tensile mode. The ethanol diffusion in semi-crystalline PE and pine flour

were simulated at 6 ± 2 °C and 30°C as done experimentally. The simulated D values were then

estimated using the same methodology as used for the diffusion of oxygen through simulated

PE and were compared with the experimental values obtained using Eq (3.2.1). The major

difference being that the time of simulation used for the ethanol diffusion was 10 ns for all the

systems analysed. In order to predict the ethanol diffusion in semi crystalline PE, the simulated

D value was input into various expressions of material tortuosity. The tortuosity parameter was

discussed in brief in Chapter 2 but now more detail about the influence of microstructure

tortuosity on small molecule transport in polymers is provided.

According to Compan et al. [37], the overall diffusion (D) coefficient of a semi-

crystalline polymer can be defined in terms of the diffusion through the completely amorphous

phase of a semi-crystalline polymer (DC) as shown in Eq (3.2.4) where τ represents the

geometrical impedance of the impermeable crystalline phase and is known as ‘tortuosity’ and

β is a measure of the immobilization effect generated by the crystalline phase on the amorphous

phase and is known as the ‘chain immobilization factor’.

𝐃 = 𝐃𝐂

𝛃𝛕 (3.3.4)

τ can be defined in Eq (3.3.5) where d’ and L, are the distances that the permeant

molecule must travel to diffuse through the semi-crystalline matrix and the pure amorphous

polymer respectively. τ depends upon the aspect ratio, the shape, orientation and the extent of

dispersion of the dispersed phase in the matrix [27].

𝛕 = ⅆ′

𝐋 (3.3.5)

Geometrically speaking, tortuosity can be visualized within the microstructure of a

polymer and the corresponding path taken by a permeant molecule by means of Figure 2.7. The

mathematical representation of β at any temperature T is shown in Eq (3.3.6) where m2 is the

molecular diameter squared in angstrom2 and R is the universal gas constant. γ is a

proportionality constant defined by Eq (3.3.7) where NA is Avogadro’s number, ΔEC is the


113

difference in cohesive energy density between the completely amorphous PE and semi-

crystalline PE, and j is the characteristic jump distance for a single permeant molecule [37].

𝛃 = 𝐞𝐱𝐩 (𝐣𝐦𝟐

𝐑𝐓) (3.3.6)

𝛄 =−𝛑

𝟒𝛌𝐍𝐀𝚫𝐄𝐂 (3.3.7)

Compan et al. [37] then plotted variations in β as a function of molecular diameter at

various LLDPE crystalline volume fractions ( ϕCr) and is shown in Figure 3.23. The

crystallinity of the LLDPE specimens used to make all samples is 49 ± 1 % as mentioned earlier

which corresponds to a ϕCr of 0.44. For a polymer of that crystallinity, a molecule of ethanol

with diameter of 4.4 Å (similar to propane- 4.3 Å – as studied by Compan et al. [37]) will have

a γ value of about 250 [37]. Based on this, using Eq (3.3.6) and Eq (3.3.7), β comes out to be

~6.8.

Figure 3.23: γ vs crystalline volume fraction ϕCr for different sized permeants through

LLDPE. From [37]

The interpretation of τ is a bit more complicated as it depends on dispersed phase aspect

ratio (α) and dispersed phase volume fraction (ϕ). There are several expressions for τ and

include the ones by Cussler [173, 174] shown in Eq (3.3.8) and Eq (3.39) respectively, Lape et

al. [175] shown in Eq (3.3.10), Gusev and Lusti [176] shown in Eq (3.3.11), Frederickson and

Bicerano’s two separate versions depending on dilute [Eq (3.3.12) and Eq (3.3.13)] or semi


114

dilute [Eq (3.3.14) and Eq (3.3.15)] volume fractions of the dispersed phase [153], Nielsen

[177] shown Eq (3.3.16) and by Hendeknvist and Gedde [154] shown in Eq (3.3.17).

𝛕 = 𝟏 +(𝛂𝝓)𝟐

𝟒(𝟏−𝛟𝐂) (3.3.8)

𝛕 = 𝟏 +𝟏

𝟖(𝛂𝝓)𝟐

(𝟏−𝛟𝐂)

(3.3.9)

𝛕 = 𝟏 +(𝛂𝝓)𝟐

𝟗 (3.3.10)

𝛕 = 𝐞𝐱𝐩 [(𝛂𝛟

𝟑.𝟒𝟕)

𝟎.𝟕𝟏

] (3.3.11)

𝛕 = 𝟒 [(𝟏+𝐱+𝟎.𝟏𝟐𝟒𝟓𝐱𝟐)

(𝐱+𝟐)]

𝟐

(3.3.12)

𝐱 =𝛑𝛂𝛟

𝟐 𝐥𝐧(𝛂

𝟐) (3.3.13)

𝛕 = 𝟏

𝟏+𝛍𝛂𝟐𝛟𝐂𝟐 (3.3.14)

𝝁 = 𝝅𝟐

𝟏𝟔 𝐥𝐧𝟐 𝜶 (3.3.15)

𝛕 = 𝟏 + 𝟎. 𝟓𝛂𝛟 (3.3.16)

𝛕 =

𝟑+𝛟[(𝛂

𝟏.𝟓𝟕−𝟏𝛂

)−𝟏]

𝟑 (3.3.17)

Modifications to the Cussler model [173, 174] shown in Eq (3.3.8) were done by Aris

[178] shown in Eq (3.3.18) and by Falla et al. [179] and Wakeham and Mason [180] shown in


115

Eq (3.3.19). In these modifications, the term k is used which was defined by Cussler [173, 174]

as the ratio of the average pore radius (s) to the average crystalline lamellar thickness (lC).

𝛕 =𝟏

[𝟏+𝛂𝟐𝛟𝟐

𝟒(𝟏−𝛟)+

𝛂𝛟

𝟐𝐤+

𝟐𝛂𝛟

𝛑(𝟏−𝛟)𝐥𝐧(

𝛑𝛂𝟐𝛟

𝟒𝐤(𝟏−𝛟))]

(3.3.18)

𝛕 =𝟏

[𝟏+𝛂𝟐𝛟𝟐

𝟒(𝟏−𝛟)+

𝛂𝛟

𝟐𝐤+𝟐(𝟏−𝛟) 𝐥𝐧(

𝟏−𝛟

𝟐𝐤𝛟)]

(3.3.19)

Eq (3.3.8) through Eq (3.3.19) were input into Eq (3.3.4) and the DC value was obtained

from the MD algorithm (b.1-b.10) but by incorporating an ethanol molecule instead of oxygen

molecule. In addition, the analysis was done in the simulated pine flour (Figure 3.22h)

following also the algorithm b.1-b.10 with a single ethanol molecule and only in the amorphous

PE (Figure 3.20) and not the semi-crystalline (Figure 3.21) or crystalline PE (Figure 3.19)- the

reasons for which will be explained in Section 4.2.2. The simulated D values for the PE and the

simulated pine flour were then combined to estimate the D of ethanol through the PE-pine flour

composite. The semi-empirical models used for this purpose were the Maxwell, M-W-S, Kalnin

and Weissberg models shown in Table 2.10. In order to estimate the efficacy of the models, the

average absolute relative error (δ) was used. The expression for δ values is previously shown

in Eq (3.3.3).

The simulated elastic moduli were also compared and fit with experimental values of

storage modulus in tensile mode obtained from Dynamic Mechanical Analysis (for the semi-

crystalline PE and the composite specimens) at 30°C and with modulus data obtained from the

Hysitron Nanoindenter (for the pine flour). The methodology for measuring the elastic modulus

of a simulated molecule is as outlined in Algorithm D described in steps d1-d3:

ALGORITHM D

d.1. The equilibrated system obtained after NPT dynamics is enlarged/strained

continuously in one direction and the instantaneous pressure in that direction is

recorded while the other two directions are kept at the same initial (in this case,

atmospheric) pressure.


116

d.2. This enlargement is done stepwise till the required maximum strain is reached. The

simulation is carried out till about 10% of strain but for both the simulated PE and

wood, the reported modulus values are those obtained at ~0.1% of strain.

d.3. Total run time of simulation is 1 ns. 15 MD runs each were carried out at 30 °C (303

K) for the semi-crystalline PE and the simulated pine flour.

The models listed out in Table 2.11 were then used to determine the efficacy of the

simulation similar to the O2 and ethanol diffusion methodology which used the models listed in

Table 2.10.

117

CHAPTER 4

RESULTS AND

DISCUSSION

4.1 INFLUENCE OF MATERIAL COMPOSITION AND

PROCESSING TECHNIQUE ON THE

MICROSTRUCTURAL, MECHANICAL AND GAS

TRANSPORT PROPERTIES OF LLDPE WOOD

FLOUR COMPOSITES

This chapter has the following aims:

1. The analysis and characterization of the microstructural and morphological features

developed in the composite materials produced during the course of this thesis. These

parameters are highly dependent on the nature of the processing method used to

manufacture the composite. Thus, the compression and rotomolding techniques can be

compared and contrasted in terms of the type of morphology developed.

2. The mechanical properties of the fabricated composites and their correlation to the type

of processing method and type of microstructure is analyzed.

3. The composite microstructure can have profound effects on the composite gas transport

characteristics. Therefore, the oxygen transport characteristics of the composites are

measured, and an attempt is made to model the transport coefficient as a function of the

wood flour.

Influence of Material Composition and Processing Technique.

118

One of the main techniques used to characterize microstructural and morphological

features of polymer composites is the SEM. However, first, it is important to have a visual

understanding of the raw materials used to build up the composite. This method of isolating and

studying each component of a composite separately and then using the combined results to

characterize the composite is something that will be studied in detail in Section 4.2. In this

section, analysis of the raw materials LL710 UV, pine and oak flour- representative images of

which are shown in Figure 4.1, will be carried out. While the LLDPE powder is mostly spherical

in shape (Figure 4.1a), the pine and oak flour consist of fibrous particles (Figure 4.1b and c).

The aspect ratios of both the pine and oak flour were measured by averaging out the length to

diameter ratios of ~100 particles. Both the pine and oak flour were found to have an aspect ratio

of 4.5±0.5.

Figure 4.1: SEM images of the raw materials (a): LLDPE, (b): Pine flour, (c): Oak flour.

In order to develop the understanding and optimize cycle times and temperature of the

rotomolding process, a simple sintering study was carried out and is shown in Figure 4.2.

Analysis of the plain rotomolded specimen and the reasoning behind the relatively high (240

°C) processing temperature needed can be done through Figures 4.2 a-d. From those figures,

microstructure transition from a particulate nature (Figure 4.2a) to a mixed particulate-

coalesced domain (Figure 4.2b) to a more consolidated and condensed structure (Figures 4.2c

and 4.2d) is demonstrated. However, the Figures 4.2 a-d are at a temperature of 200 °C and at

a cycle time of 5 min (Figure 4.2a) to 30 min (Figure 4.2d). Thus, at a cycle time of 30 min and

a temperature of 200 °C the microstructure is completely devoid of any particulates and is a

single coalesced domain. To reduce cycle time, the same test was carried out at 240 °C for 12

min (Figure 4.2e). It is seen that the nature of the cross section in Figure 4.2d and 4.2e are very

similar and thus, a cycle time of 12 min at 240 °C was utilised for all rotomolded compositions.


119

Figure 4.2: Evolution of microstructure in the LLDPE raw material as a function of time at 200

°C: (a): 5 min, (b): 10 min, (c): 15 min, (d): 30 min. (e): 240 °C at 12 min.

As far as the sintering behavior of the composites are concerned, trends similar to Figure

4.2 can be seen. Micrographs of the RM5, RM10 and RM20 specimens are shown in Figures

4.3, 4.4 and 4.5 respectively. Micrographs of the composites with oak flour are shown in Figure

4.6 (RM5_O) and Figure 4.7 (RM10_O). It has to be noted that the design of the composite

materials studied in this thesis were intentionally considered without surface modification of

the wood. This was specifically done for ensuring the viability of the composite materials for

a b

c d

E

e


120

food contact applications. Secondly, the interfacial pores thus generated could be potentially

used as a pathway for modifying permeability.

Figure 4.3: Evolution of microstructure in LLDPE raw material with 5% pine flour as a

function of time (a): 200°C, 5 min, (b): 200°C, 10 min, (c): 240 °C at 12 min.


function of time: (a): 200°C, 5 min, (b): 200°C, 10 min, (c): 240 °C at 12 min.

a b c

a b c


121


function of time at (A): 200°C, 5 min, (B): 200°C, 10 min, (C): 240 °C at 12 min.

Figure 4.6: Evolution of microstructure in LLDPE raw material with 5% oak flour as a function

of time at (a): 200°C, 5 min, (b): 200°C, 10 min, (c): 240 °C at 12 min.

a b c

a b c


122

Figure 4.7: Evolution of microstructure in LLDPE raw material with 10% oak flour as a

function of time at (a): 200°C, 5 min, (b): 200°C, 10 min, (c): 240 °C at 12 min.

In all cases a highly consolidated structure was seen after the optimized cycle time. It is

seen, once again, that the microstructure transitions from a loose grouping of particulates to a

particulate domain and finally to a consolidated structure. However, differences between the

samples could be quantified in terms of the densities of the composites. These trends in density

and their correlation to overall porosity are the first set of results presented in this thesis.

The trends in density with wood flour incorporation for all the composites produced and

is shown in Table 4.1. It can be clearly seen that the densities of the rotomolded composites

consistently reduce with increasing wood flour concentration. That is also independent of the

type of wood flour used (pine or oak). The trends in density can also be visualized using the VP

parameter explained in Eq (3.2.5) and is shown in Figure 4.8. Only the pine flour composites

are plotted but as seen in Table 4.1, the differences in densities between the oak and pine flour

composites are insignificant. This is attributed to two factors, firstly that the average particle

sizes for the pine and oak flour are both around 350 µm and secondly, because there is no

chemical compatibilization carried out between the PE and the wood flour.

a b c


123

Table 4.1: Densities of all the specimens obtained from pycnometry

Sample Density (g/cm3) CM0 0.94 ± 0.01 CM5 0.95 ± 0.01

CM5_O 0.96 ± 0.01 CM10 0.95 ± 0.03

CM10_O 0.94 ± 0.03 CM20 0.97 ± 0.01 RM0 0.93 ± 0.02 RM5 0.88 ± 0.02

RM5_O 0.87 ± 0.04 RM10 0.85 ± 0.04

RM10_O 0.83 ± 0.01 RM20 0.82 ± 0.04

Raw PE 0.96 ± 0.02 Pine flour 1.18 ± 0.05 Oak Flour 1.12 ± 0.07

In terms of VP, it is seen that the VP values for the compression molded composites

remains fairly independent of the wood flour concentration (Figure 4.8). The VP for the

rotomolded composites increases consistently with increased wood flour concentration and this

corresponds to the generation of porous microstructures and surfaces. The RM20 has a density

of 0.82 g/cm3 and a porosity of 18.33% as compared to 0.97 g/cm3 and 3.4% porosity for CM20.

Essentially, for the rotomolded specimens, an increased presence of pores reduces the extent of

packing and dispersion of the continuous (LLDPE) and dispersed (wood flour) phases leading

to a net reduction in density. This shall be discussed in more detail by comparing the SEM

images of the surfaces and the microstructures of the compression and rotomolded composites.

Once again, the SEM images shown are those of the pine flour composites as the oak flour

composites visually are quite similar to the pine flour composites due to the lack of any

chemical compatibilization carried out before processing.


124

Figure 4.8: VP of all the pine flour composite samples as determined by Eq (3.2.5).

The SEM images of the plain samples (i.e. samples without any wood flour

incorporation) are shown in Figure 4.9. The first observation that can be made from the samples

is that the Compression Molded specimens seem to have no differences in terms of their surface

(Figure 4.9a) while the rotomolded specimens have two distinct surfaces: a smooth surface that

is molded in contact with the mold surface (Figure 4.9b) and a rough surface away from the

mold (Figure 4.9c).

0

5

10

15

20

25

0 5 10 15 20 25

Vp

(%)

Wood Flour Content (Weight%)

ROTOMOLDED

COMPRESSIONMOLDED

a b


125

Figure 4.9: SEM images of samples with no pine flour incorporation. (a): CM0, (b): Smooth

surface of RM0; (c): Rough surface of RM0.

The next set of samples studied are the ones with wood flour incorporation. Amongst

those, it can be seen that there is a migration of wood particles to the surface in the rotomolded

specimens while no such migration is observed amongst the compression molded specimens

(Figure 4.10 a, b, c and d). Also, this tendency of surface migration is more pronounced on the

rough surface of the rotomolded specimens. For instance, the RM20 specimen has several wood

flour particles clearly visible on both the rough (Figure 4.10h) and smooth (Figure 4.10g)

surfaces while such wood particles are only observed on the rough surfaces of the RM5 and

RM10 samples as seen from Figure 4.10h and 4.10i respectively. This is attributed to a

combination of the presence of the wood flour without compatibilization and lower dispersive

effects (as seen in the rotomolding process). It is also noticeable that the smooth surface of the

rotomolded samples show larger pores (Figure 4.10 e, f and g) than what is observed for the

rotomolded sample with no wood flour incorporation (Figure 4.9b).

c


126

a b

c d

e f


127

Figure 4.10: SEM images of samples with wood flour incorporation. (a): CM5, (b): CM5_O,

(c): CM 10, (d): CM 20, (e): RM5 smooth surface, (f): RM10 smooth surface, (g): RM20

smooth surface, (h): RM5 rough surface, (i): RM10 rough surface, (j): RM20 rough surface

In terms of the microstructure, it is a different story as the porosity is seen only in the

samples with wood incorporation (Figures 4.11 b, c and d and Figures 4.12 b, c and d) and both

CM0 and RM0 show no visible pores (Figure 4.11a and 4.12a). It is important to note that while

the control of porosity is the overall objective, that attaining this objective is not at the cost of

significant reduction in mechanical properties. A manifestation of this is seen in the RM20

specimen. While there is significant porosity that could be used for controllably increasing gas

permeation, the visible holes on the molded specimen (Figure 4.13) indicates that this

composition is not viable and that the dispersive effects in rotomolding can only be effective

for lower concentrations of dispersed phase incorporation.

g h

i j


128

Figure 4.11: SEM images of microstructure of compression molded samples. (a): CM0, (b):

CM5, (c): CM10, (d): CM20.

a b

c d

a b


129

Figure 4.12: SEM images of microstructure of rotomolded samples (a): RM0, (b): RM5, (c):

RM10, (d): RM20.

Figure 4.13: Rotomolded RM20 specimen with physical holes indicated by the red circle.

A rough estimate is also made of the pore size distribution in the microstructure of the

composites both compression and rotomolded. In addition to the VP values, this also provides a

visual proof of the increased porosity in the rotomolded specimens as compared to the

compression molded specimens. An example of the way such a pore size distribution was

estimated is shown in Figure 4.14a and 4.14b. For each composite, pore size values were

obtained by averaging the results for 5 such images. The overall pore size distribution obtained

using this method is then shown in Figure 4.15. It can be clearly seen that all the rotomolded

composites show a higher pore size average than the corresponding compression molded

equivalents. The RM20 specimen has a much higher proportion of pores than all the other

composites, once again, indicating that this composition is not viable for use.

c d


130

Figure 4.14: Estimating pore sizes through microstructural SEM of a RM5 sample.

Figure 4.15: Rough pore size distribution estimates of all composites.

The mechanical properties of the composites were then tested in order to understand the

influence of the type of processing, and by extension, the microstructure on the fabricated

material. The tensile strengths of the rotomolded and compression molded samples are shown

in Figure 4.16. It can be seen that the tensile properties reduce consistently with wood flour

incorporation irrespective of type in the rotomolded system while a consistent increase is seen

for the compression molded composites. This is clearly down to the fact that the dispersive

0

10

20

30

40

0 500 1000 1500 2000

%

Pore size (micron)

a b


131

ability of the compression molding process is better than that of rotomolding. That being said,

at 5% of the wood flour concentration, the tensile strengths of both the compression and

rotomolded composites are quite similar at around 12 MPa. This indicates that up to 5% by

weight the rotomolded composite is comparable to a compression molded composite and is

more porous (as seen in the VP trends in Figure 4.8) which helps with a controlled increase in

permeability.

0

5

10

15

0 5 10 15 20 25

Tens

ile S

tren

gth

(MPa

)

Wood Flour weight fraction (%)

Pine FlourRotomolded

Oak FlourRotomolded

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

Rel

ativ

e Te

nsile

Str

engt

h



Oak FlourRotomolded

b

a


132

Figure 4.16: Absolute and Relative Tensile strengths of (a), (b): Rotomolded and (c), (d):

Compression Molded composites

The flexural strengths of the rotomolded and compression molded samples are shown

in Figure 4.17 and show a similar trend to what is seen for the tensile strengths in Figure 4.16.

For liquid storage applications such as the one explored in this thesis the flexural strengths of

the composites are of higher relevance. Based on these trends it may be necessary to have

external strengthening of the final molded product. However, before that the strength of the

0

5

10

15

20

0 5 10 15 20 25

Tens

ile S

tren

gth

(MPa

)


Pine FlourCompressionMolded

Oak FlourCompressionMolded

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 5 10 15 20 25

Rel

ativ

e Te

nsile

Str

engt

h




d

c


133

composites has to be tested after they have been exposed to liquid uptake in order to recreate

application conditions. That will be detailed in Section 4.3.

0

5

10

15

20

0 5 10 15 20 25

Flex

ural

Str

engt

h (M

Pa)



Oak FlourRotomolded

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 5 10 15 20 25

Rel

ativ

e Fl

exur

al S

tren

gth



Oak FlourRotomolded

b

a


134

Figure 4.17: Absolute and Relative Flexural strengths of (a), (b): Rotomolded and (c), (d):


The impact strengths of the rotomolded and compression molded samples are shown in

Figure 4.18. Once again there is a clear reducing trend but this time it is seen for both the

compression molded and rotomolded composites. This is because both sets of composites are

uncompatibilised in nature. Here, like Figure 4.16, it can be seen that as long as the dispersed

0

2

4

6

8

10

12

14

16

0 5 10 15 20 25

Flex

ural

Str

engt

h (M

Pa)




c

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

Rel

ativ

e Fl

exur

al S

tren

gth Pine Flour

CompressionMolded


d


135

phase concentration is around 5% by weight, the drop is not as significant as it is at higher

concentrations.

0

10

20

30

40

50

0 5 10 15 20 25

Impa

ct S

tren

gth

(kJ/

m2 )



Oak FlourRotomolded

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

Rel

ativ

e Im

pact

Str

engt

h



Oak FlourRotomolded

a

b


136

Figure 4.18: Absolute and Relative Impact strengths of (a), (b): Rotomolded and (c), (d):


The storage moduli in single cantilever mode of the rotomolded and compression

molded samples are shown in Figure 4.19 while the storage moduli in tensile mode are shown

in Figure 4.20. The trends in these properties are similar, in the sense that, the moduli increase

with increasing dispersed phase concentration for the compression molded composites while a

0

10

20

30

40

50

0 5 10 15 20 25

Impa

ct S

tren

gth

(kJ/

m2 )

Wood flour weight fraction (%)



c

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

Rel

ativ

e Im

pact

Str

engt

h




d


137

slight reduction is seen for the rotomolded composites. This speaks to the lower dispersive

power of the rotomolding system.

0

200

400

600

800

1000

0 5 10 15 20 25

Stor

age

Mod

ulus

(MPa

)



Oak FlourRotomolded

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

Rel

ativ

e St

orag

e M

odul

us



Oak FlourRotomolded

b

a


138

Figure 4.19: Absolute and Relative Storage Modulus in Single Cantilever mode of (a), (b):

Rotomolded and (c), (d): Compression Molded composites

0

500

1000

1500

0 5 10 15 20 25

Stor

age

Mod

ulus

(MPa

)




c

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 5 10 15 20 25

Stor

age

Mod

ulus

(MPa

)

Wood Flour weight content (%)



d


139

0

100

200

300

400

500

600

0 5 10 15 20 25

Stor

age

Mod

ulus

(MPa

)



Oak FlourRotomolded

a

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

Rel

ativ

e St

orag

e M

odul

us



Oak FlourRotomolded

b


140

Figure 4.20: Absolute and Relative Storage Modulus in Tensile mode of (a), (b): Rotomolded

and (c), (d): Compression Molded composites

Now that the trends in mechanical properties for the compression and rotomolded

composites have been established, we move our attention to modelling the trends in composite

permeability. It is well known that intensive properties such as crystallinity and density of a

polymer significantly influence the overall permeation characteristics [181]. However, models

developed on this basis are not completely deterministic in nature because they often include

0

200

400

600

800

0 5 10 15 20 25

Stor

age

Mod

ulus

(MPa

)




c

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 5 10 15 20 25

Rel

ativ

e St

orag

e M

odul

us




d


141

parameters that are customised to individual systems. One such model that correlates

crystallinity to polymer permeability is the one by Duan et. al. [181] shown in Eq (4.1.1).

P = PC (1− Xc

1+0.5Xc) (4.1.1)

Here, Xc refers to the fractional degree of crystallinity. The logic behind the

development of this model is that while a linear model would show zero permeability at <100%

crystallinity, this particular model shows zero permeability at exactly 100% crystallinity. In

order to estimate the differences in crystallinity between the different composites, Differential

Scanning Calorimetry (DSC) was carried out. The area under the melting curve was estimated

from the DSC graph and divided by the heat of fusion for purely crystalline PE which is 293.1

J/g. based on this, the % crystallinities of all the composite specimens and the raw material

LL710UV are shown in Table 4.2.

Table 4.2: Heat of fusion (ΔHM; J/g) and % Crystallinities of all samples at 3 different heating

rates

Sample 5°C/min 10°C/min 15°C/min

ΔHM XC ΔHM XC ΔHM XC

LL710UV 143 48.8 135 46.1 138 47

CM0 135 46.1 131 44.6 137 46.7

CM5 144 49.1 131 44.6 139 47.4

CM5_O 151 51.5 137 46.7 142 48.5

CM10 139 47.4 143 48.7 130 44.4

CM10_O 133 45.4 133 45.4 144 49.1

CM20 129 44.2 130 44.4 132 45.1

RM0 130 44.4 140 47.8 133 45.4

RM5 140 47.8 137 46.7 134 45.7

RM5_O 141 48.1 144 49.1 137 46.7

RM10 133 45.4 130 44.4 135 46.1

RM10_O 148 50.5 137 46.7 130 44.4

RM20 146 49.8 130 44.4 146 49.8


142

From Table 4.2, it can be seen that there are no major differences or trends in %

crystallinity values. Therefore, other intensive properties are needed to effectively model

polymer permeability. The trends in VP (Figure 4.8) and the pore size distribution (Figure 4.15)

both indicate an increased porous microstructure for the rotomolded composites with wood

flour incorporation. Hence, to confirm whether these trends also correlated with increased O2

permeabilities, gas permeability testing of the RM0, RM5, RM5_O, RM10 and RM10_O

samples was carried out. No testing was done on the compression molded samples because they

were used to benchmark the trends in properties and had no potential for manufacturing storage

tanks. The values are shown in Table 4.3 and the trends were fit using the Alter model [182].

The Alter model is another expression that correlates an intensive property (in this case, density

or ‘ρ’) to polymer permeability [182]. The model expression is shown in Eq (4.1.2), and is

based on the observation that density is a parameter that can help correlate subtle differences

between different areas of the polymer sample to its overall permeability [182].

P = K (1 − ρ)n (4.1.2)

Figure 4.21: Oxygen Permeability of all rotomolded composites


143

Based on the trends it is clearly seen that with an increase in pine or oak flour content

(Figure 4.21) there was a definite increase in O2 permeability. Thus, one of the primary aims of

the project with respect to controlled permeability increase has been achieved.

Table 4.3: Experimental (Pexp) vs predicted (Ppred) oxygen permeability values of rotomolded

composites

Wood Flour weight %

(type)

ρ (g/cm3)

Pexp (cm3.mm/m2/year)

Ppred (cm3.mm/m2/year)

0 0.93 28616 ± 716 31065

5 (Pine) 0.90 34492 ± 1534 35829

10 (Pine) 0.86 38544 ± 658 40991

5 (Oak) 0.89 38835 ± 3407 35829

10 (Oak) 0.84 39712 ± 2500 41336

Based on Figure 4.21, it is possible to state the model equations for oxygen permeability

(Ppred) of the rotomolded composites. The model equation for the pine composites is shown in

Eq (4.1.3) and that for the oak composites is shown in Eq (4.1.4).

PPRED = 9.1 × 104 × (1 − ρ)0.4 (4.1.3)

PPRED = 8.3 × 104 × (1 − ρ)0.4 (4.1.4)

Thus, the two aims laid out in the start of this chapter have been achieved in the

following ways:

1. The compression molded and rotomolded composites have the following morphological

and microstructural characteristics:

a. The surfaces of the rotomolded composites differ based on whether they are in

contact with the inner surface of the mold and thus, possess a smoother outer

surface in contact with the mold and a rough inner surface. The compression


144

molded composites show no such morphological difference between the

surfaces.

b. Pores are found on the rough surface, smooth surface and the microstructure of

the rotomolded LLDPE wood flour composites while the pores are only found

in the microstructure of the compression molded composites.

2. The composites do not differ noticeably in terms of crystallinity but do in terms of

density. In terms of gas transport, the porosity created can be directly correlated to

changes in density. As density is an intensive parameter it is an effective tool for

modelling this transport phenomenon. The model of Alter [182] performs quite

acceptably for all rotomolded composites made in this thesis independent of the type of

dispersed phase used.

However, to design a viable storage unit it has to be ensured that the introduction of

porosity to controllably increase permeability does not result in a major detriment to the

mechanical properties. A second aspect to be considered is that with increased microstructural

porosity, the diffusion tendency of the stored liquid material also increases. Therefore, it is

essential that these results of controlled permeability increase are also juxtaposed with the

corresponding trends in the mechanical and liquid uptake properties. This will be carried out in

Section 4.2.

145

4.2 CORRELATING PROCESSING TECHNIQUE TO

PERMEANT TRANSPORT PHENOMENA

4.2.1 COMBINING MOLECULAR DYNAMICS AND SEMI-

EMPIRICAL MODELLING FOR PREDICTING GAS

DIFFUSION.

The aims of this chapter are to follow on the results shown in Section 4.1. Those results

indicated that controlled increase in gas permeability can be achieved by introducing a wood

flour dispersed phase in the rotomolded composites. The gas permeability can be modelled

based on changes in composite density obtained using the pycnometry method. Independent of

the nature of the dispersed phase i.e, whether it is oak or pine flour, the composite permeability

can be described in the form of the Alter model shown in Eq (4.1.2). The individual model

expressions for the pine and oak flour composites are shown in Eq (4.1.3) and Eq (4.1.4).

In this chapter, a methodology for predicting physical properties of composite materials

is developed. The methodology is as follows:

1. Defining a composite as a multi-phase material and thus, the overall properties are a

function of the properties of each individual phase with a weighing parameter that

describes the interaction between the phases and its effect on the overall property-

essentially semi-empirical modelling.

2. The use of Molecular Dynamics (MD), as explained in Section 3.3 for building

representative models of the continuous and dispersed phases for carrying out the

simulation. Using and optimizing the forcefield used to define the interactions and the

algorithm used to equilibrate the system.

3. Establishing proof of concept and then modelling analogous properties. In this chapter,

the proof of concept is established by predicting the temperature variation of oxygen

diffusion in semi-crystalline Polyethylene similar to the raw material (LLDPE) used.

The analogous property that will be modelled here is the diffusion of ethanol and it is

analyzed whether the developed methodology is versatile enough to predict both gas

and liquid diffusion.

Combining MD and Semi-empirical Modelling for Predicting Gas Diffusion.

146

Using the steps a1-a4 for algorithm A stated in Section 3.3, equilibrated simulation cells

of amorphous and crystalline PE were built. From these cells, the first set of simulated results

obtained are the densities and are shown in Table 4.4. Reference data of densities were obtained

from [167, 168]. This helped to validate the simulation with respect to one intensive property

viz., density.

Table 4.4: Experimental and simulated densities

Molecule Simulated molecule

density (g/cm3)

Experimental density

(g/cm3)

Amorphous PE 0.83 ± 0.03 0.85 [167]

Crystalline PE 1.04 ± 0.04 1.00 [168]

Figure 4.22: Pore size distribution of the simulated amorphous and crystalline polyethylene

molecules.

The averaged pore size distribution from the Trajectory Analysis module at T = 298 K

is shown in Figure 4.22. The pore sizes observed in the crystalline and amorphous PE boxes

ranged from 1.9 Å to 3.5 Å (average of ~2.6 Å) and 2 Å to 6.0 Å (average of ~4 Å) respectively.

As stated before, the proof of concept of this methodology is established by predicting the


147

phenomenon and extent of oxygen diffusion in a simulated Polyethylene. From the pore size

distribution obtained the following claims can be made:

1. The wider distribution of pore sizes for the amorphous PE indicate that diffusion

through the amorphous section is more favourable than the crystalline PE, which is

characterised by its narrower pore size distribution.

2. The average hydrodynamic radius of an oxygen molecule is kinetic diameter of O2

molecule is 3.46 Å and falls within the size distribution ranges of both the amorphous

and crystalline PE systems. This indicates the possibility of diffusion in both the

crystalline and amorphous section of a PE specimen [183].

Based on this, a single oxygen molecule of oxygen was introduced into the equilibrated

simulation cells of both amorphous and crystalline PE obtained using Algorithm A (as detailed

in Section 3.3) shown in Figure 4.23. The reason for choosing a single molecule of oxygen is

based on the inherently low solubility of oxygen in LLDPE as measured and used for MD

simulations by Börjesson et al. [140].

Figure 4.23: (a): Amorphous PE and (b): Crystalline PE simulation boxes with a single oxygen

molecule in red.

Another interesting result was seen when the CM0 and RM0 samples were analysed for

the pore size results using the PALS technique. The PALS spectrum for one example of the

a b


148

CM0 sample is shown in Figure 4.24 with the results for RM0 and CM0 shown in Table 4.5. It

can be clearly seen that the R values are very similar to the CM0 sample irrespective of the

different mechanism of product formation in rotomolding as opposed to compression molding.

This indicated that in terms of microporosity (the extent and distribution of pores < 5 nm in

size), the compression molded and rotomolded materials are very similar. In fact, when all of

the samples containing wood flour were analysed it was found that they too had very similar

pore sizes to CM0 and RM0. Thus, showing that all composites differed very little in

microporosity and that perhaps the driving force behind the physical differences between the

composites, such as density was, in fact, the macroscopic porosities. In effect, by using MD a

system identical to the real-life material in terms of microporosity can be built. Then, by

comparing and contrasting the differences in simulated and experimental physical properties

such as diffusion coefficients and mechanical properties, the extent of macroporosity can be

isolated and later correlated to a parameter such as VP that will be studied in detail in this

Chapter.

Table 4.5: PALS data indicating average pore size (R; in Å) compression molded and

rotomolded composites and the raw material

Sample R (Å)

CM0 6.46 ± 0.01

CM5 6.45 ± 0.03

CM10 6.43 ± 0.02

CM20 6.35 ± 0.04

RM0 6.45 ± 0.02

RM5 6.44 ± 0.03

RM10 6.40 ± 0.04

RM20 6.38 ± 0.03


149

Figure 4.24: PALS spectrum of Compression Molded LLDPE specimen where the yellow,

blue, grey and black lines correspond to τ1, τ2, τ3 and the source component.

Once, the oxygen molecule was introduced by using the Matrix Builder module in the

MAPS program, Algorithm B comprising of steps b1-b10 stated in Section 3.3 was used to

simulate oxygen diffusion in both crystalline and amorphous Polyethylene over a temperature

range of 293 K to 308 K in steps of 5 K. 30 runs were carried out for each temperature point

for both the amorphous and crystalline PE systems. The MSD of the oxygen molecule was

tracked and the averaged MSD over 30 runs were plotted as a function of time (Figure 4.25)


150

Figure 4.25: Comparison of MSD of O2 molecule averaged over 30 runs observed in

Amorphous (A) and Crystalline (C) PE with the linear fit over a temperature range of 293-308

K with a 5 K temperature step.

The plot itself starts from 1 ns onwards and the reason for that is clear from Figure 4.26

which shows the evolution of the total energy as a function of simulation time. Diffusion in

polymers is speculated to go through an initial (short time) ballistic regime for several

picoseconds before reaching the region where MSD(t) is directly proportional to time [184].

This leads to the clearly observed offset of the MSD values in the initial stages of the simulation.

To account for this, the D values were estimated only from the MSD data in the time range 1–

5 ns for the amorphous system and 1–10 ns for the crystalline system. It is clearly observed that

the cumulative displacement seen in the amorphous PE is higher than what is seen for a

corresponding crystalline PE if the MSDs are compared at the same temperature, indicating that

the diffusion of O2 in amorphous PE would be higher than what would be seen in crystalline

PE.


151

Figure 4.26: Evolution of the total energies of the simulated Amorphous and the Crystalline

PE systems with inserted oxygen molecule.

It is also observed that the MSD in the crystalline region is still a non-zero quantity

(Figure 4.25). To our knowledge, this is the first time that this has been demonstrated. It is

important to consider the transport through the crystalline regime because it leads to much better

prediction using semi-empirical modelling. This is because, the simulated D values of O2

through both the amorphous and crystalline PE simulation boxes when juxtaposed with

experimental data of oxygen diffusion through semi-crystalline LLDPE (Figure 4.27) form an

upper and lower bound for D values. It has to be noted that the experimental values of D were

chosen from [38, 163-166] because the % crystallinities of all the LLDPE specimens considered

amongst the papers in [38, 163-166] were similar at 30±5%.


152

Figure 4.27: Comparison of D (cm2/s) between reported values obtained from [38, 163-166]

and simulated PE molecules (crystalline and amorphous).

By assuming that LLDPE or any such semi-crystalline polymers can be visualised as a

composite with dispersed PE crystallites in a matrix of completely amorphous PE, different

models that correlate D to parameters such as volume fraction, shape, size and orientation of

the dispersed phase (Table 2.10) could be used to confirm or deny the validity of the simulation.

The predictions obtained from the different models using the simulated data is shown in Figure

4.28. The corresponding deviation of the predicted values (using the models in Table 2.10) from

the experimental values can be done using the % average absolute relative error (δ) shown

previously in Eq (3.3.3). This equation can be customised for diffusion modelling as shown in

Eq (4.2.1.1) where Dexp is the experimental D value obtained from averaged values from [38,

163-166], N is the number of values (in this case, N= 4), Di is the D value predicted by the

model.

δ =100

N∑ |

Di−Dexp

Dexp|

N

i=1 (4.2.1.1)

0.E+00

1.E-07

2.E-07

3.E-07

4.E-07

5.E-07

6.E-07

7.E-07

8.E-07

290 295 300 305 310

Diff

usio

n C

oeff

icie

nt (c

m2 /s

)

Temperature (K)

Amorphous PE simulated

Reported

Crystalline PE Simulated


153

Figure 4.28: Predicted D values compared to the reported data.

As mentioned in Chapter 1, mathematical models for predicting physical phenomena

can be divided into three categories viz., Empirical, Deterministic or Semi-Empirical

techniques. Now, the models listed in Table 2.10 fall into either the empirical or semi-empirical

category. The rule of mixture, laminate and logarithmic models are purely empirical models

and have no direct relevance to gas diffusion in semi-crystalline systems. The five Maxwell

model variants viz., Maxwell, Weissberg, Kalnin and the two M-W-S models and the two

Frederickson and Bicerano (F and B dilute and F and B semi dilute) models are semi-empirical

expressions that have been developed for transport property modelling.

0.E+00

1.E-07

2.E-07

3.E-07

4.E-07

5.E-07

6.E-07

7.E-07

8.E-07

290 295 300 305 310

Diff

usio

n C

oeff

icie

nt (c

m2 /s

)

Temperature (K)

Reported

Amorphus PE Simulated

Crystalline PE Simulated

Rule of Mixtures

Laminate

Logarithmic

Weissberg

Maxwell

Kalnin

MWS; n = 1/6

MWS; n = 2/3

F and B Dilute α = 10.2

F and B Semi dilute α = 10.2F and B Dilute α = 2.795

F and B Semi dilute α = 2.795


154

Table 4.6: δ values for the various models listed in Table 2.10

Model δ

Rule of Mixtures 13.0

Laminate 56.4

Logarithmic 20.0

Maxwell 12.0

Weissberg 5.90

Kalnin 54.0

Maxwell-Wagner-Silar (M-W-S); n = 1/6 8.40

Maxwell-Wagner-Silar (M-W-S); n = 2/3 15.1

F and B dilute (α =2.795) 54.7

F and B semi dilute (α =2.795) 12.1

F and B dilute (α =10.2) 68.0

F and B semi dilute (α =10.2) 19.6

From Table 4.6, it can be seen that amongst the empirical models, the rule of mixtures

has the lowest δ value. Now, the rule of mixtures assumes that there is no interaction between

the different phases that make up the composite and that interparticle distances are very large.

Both are not true in case of semi crystalline systems. Thus, the efficacy of this model for this

phenomenon is out of chance. However, this model could be improved by introducing a

parameter that considers the effect of the crystalline phase on the amorphous. This can be seen

especially when it comes to modelling mechanical properties (specifically the elastic modulus

which will be done in Section 4.3) as is known from the Halpin-Tsai method [185]. In this

approach a mixing parameter ξ is introduced which at values of zero indicates a lower bound in

the elastic modulus while at values of infinity indicates an upper bound in the elastic modulus

values. A complementary approach to the rule of mixtures for estimating the effective D value

could involve the use of a mixing parameter. The logarithmic model also seems to be a good fit

and while it also is an empirical model, it is known that the Solubility coefficient (S) of the

permeant in a polymer is inherently linked to the Cohesive Energy Density (EC) of the polymer

[186]. A linear relationship is also found between log D (Diffusion coefficient) and the EC

[187]. Hence, the logarithmic model works out to be relevant to diffusion.

Amongst the semi-empirical models, the Maxwell models provide an effective way of

modelling the diffusion behaviour in semi-crystalline PE. At low crystallinities, PE could be


155

considered to be a dispersion of equi-axed and particle like crystallites reinforcing an

amorphous matrix [188]. Thus, the Maxwell model, which assumes spherical particles to be the

dispersed phase, seems to be able to accurately predict the D values. The highest accuracy

amongst the Maxwell model variants is obtained by using the Weissberg model where

interactions and overlapping between the dispersed phase particles is considered [154]. Despite

the accurate predictions of the Weissberg model, the underlying assumption is that the dispersed

phase is of spherical morphology. Thus, this model could be made more rigorous by considering

the shape and orientation and aspect ratio of the dispersed phase.

The two M-W-S models consider the crystallites to be ellipsoidal. Depending on the

orientation of the ellipsoids, there are two versions of the M-W-S model as shown in Table 2.10

and they are both very effective in modelling D as a function of temperature. The reason that

the δ values for these models are slightly higher has clearly got to do with the choice of n. While

average values of 1/6 or 2/3 have been chosen by us in this work, the real picture is that the

value of n lies between 0 and 1/3 for prolate elliposids and between 1/3 and 1 for oblate

ellipsoids. Thus, the use of a single value of n is not the best approach but for the sake of

demonstrating a model’s viability to predict D is enough. It is for this purpose that the M-W-S

model is also effective for modelling liquid diffusion- a facet that will be covered later in this

Chapter when discussing the MD based simulation of ethanol diffusion in the composites.

However, as demonstrating proof of concept for the combined MD and semi-empirical

modelling technique is the aim at this point in this thesis, remaining models listed in Table 3.4

are now analyzed.

For application of the Kalnin model, the ratio C1/C2 has to be estimated and is shown

in Eq (4.2.1.2)

C1

C2=

Volume O2Occupied Volume crystal

Volume O2Occupied Volume amorphous

= Vol O2

Volume crystal ×(100−fc)/100Vol O2

Volume amorphous ×(100−fa)/100

(4.2.1.2)

In Eq (4.2.1.2), fa and fc represent the percentage free volumes of the simulated

amorphous and crystalline molecules respectively. The equilibrated simulation boxes after

Algorithm B steps b1-b10 (mentioned in Section 3.3) had been run were analysed and the

average volumes of the amorphous and crystalline boxes in the simulations were 34000±330

Å3 and 31000±200 Å3 respectively while fa and fc are 36 ± 2% and 21 ± 1% as shown earlier in

Table 3.4. Therefore, as a single O2 molecule has been used in each system, C1/C2 becomes


156

0.89. However, this is an approximation and much more dedicated MD work must be done to

find an exact value for C1/C2. It is seen from Figure 4.29 that the Kalnin model is not able to

predict D with as much accuracy as the Maxwell model. However, this is because the actual

partition coefficient of the permeant has not been estimated in this thesis. It can be suggested

that by accurately measuring the amorphous and crystalline oxygen volume fractions and by

extension, the partition coefficient, better predictions can be achieved using the Kalnin model.

The two F and B models are the only set of semi-empirical models that take into account

physical properties of the dispersed phase such as its aspect ratio (α). A probable definition for

α is the ratio of the largest to smallest dimension of the PE crystalline unit cell as stated by

Bruno et. al. [162]. This would be given by 7.121/2.548 i.e. 2.795.

An alternative as suggested by Hedenkvist and Gedde [154] correlates α to the tortuosity

(τ) where w is the width and l is the thickness of the crystal and ϕ is the dispersed phase volume

fraction.

α =w

l=

1

0.785−√0.616−x

x+3

(4.2.1.3)

x =ϕ

τ−1 (4.2.1.4)

On the basis of work done by Michaels and Parker [189] and Compan et. al. [37], an

equation for τ was obtained, shown in Eq (4.2.1.5), where n is 1.88 for branched and linear PE.

ln τ = −n ln(1 − ϕ) (4.2.1.5)

Based on Eqs (4.2.1.3), (4.2.1.4) and (4.2.1.5), a value of 10.2 was obtained for α. These

two values of α viz., 2.795 and 10.2 were then input into the model equation. The F and B

models themselves were developed for two separate regimes and are shown in Table 2.10:

1. F and B dilute for dispersed phase concentrations wherein no overlap is observed

between two dispersed phase ellipsoids.

2. F and B semi-dilute for dispersed phase concentrations where overlap is possible.

Visually speaking, the F and B type dispersion in a semi-crystalline polymer could be

as seen in Figure 4.29.


157

Amongst the results from the F and B models, it is seen that α of 2.795 leads to more

accurate prediction of D values when combined with the F and B semi-dilute model. Based on

the δ values the following was concluded for the simulation via MD and modelling via semi-

empirical approaches of the diffusion of O2 in semi-crystalline LLDPE:

1. The Rule of Mixtures is an empirical model but is able to predict D values quite

accurately, but this accuracy is incidental. The development of the rule of mixtures

does not provide any mechanistic information regarding the diffusion process. In

keeping with theme of semi-empirical modelling that is a major part of this thesis,

the introduction of a parameter akin to ξ as in the Halpin-Tsai model [190] in the

rule of mixtures expression can be considered. However, once again, no

improvement of the interpretation of diffusion may be achieved by this. In fact, a

more relevant model for this purpose may very well be the logarithmic model based

on the close relationship between D, S and log (CED) [186, 187]. This is also

demonstrated by the viability of the Weissberg model which is a logarithmic

interpretation of the semi-empirical Maxwell class of models. However, there is no

parameter in the Weissberg model expression for quantifying the nature of the

dispersed phase (aspect ratio, orientation, amongst others). This model can be

improved by treatment similar to what has been done in the M-W-S and the F and

B models.

2. The M-W-S model (at n values of 1/6 and 2/3) was developed for an ellipsoidal

shape of a dispersed phase while the Maxwell model assumes a spherical shape of

the dispersed phase. From Table 4.6, it is seen that the M-W-S model assuming a

prolate ellipsoidal dispersion (n = 1/6) shows a lower value of δ compared to n =

2/3. This indicates that the shape of the PE crystallites in the amorphous PE matrix

is closer to being ellipsoidal than spherical with the diffusion taking place

preferentially along the longer axis of the crystallite. Also, the values of n chosen

while fitting the model are arbitrarily chosen as the average of the ranges in which

they are applicable i.e n = 1/6 when in reality it is some value between 0 and 1/3,

and n = 2/3 when in reality it is some value between 1/3 and 1. Therefore, the δ for

the M-W-S models are lower than the classical Maxwell model. This does not

indicate that the Maxwell model is better but rather that a more accurate value for n

needs to be found. In essence, the M-W-S model is more relevant because ellipsoidal


158

crystallite morphology has been found to be more realistic than spherical crystallites

in Polyethylene.

3. More accurate estimation of the permeant partition coefficients in the amorphous

and crystalline phases will lead to better predictions when using the Kalnin model.

4. The semi dilute version of the F and B models show lower values for δ as opposed

to the dilute ones. Previous works on semi-crystalline polymers have suggested that

the crystalline phase of the PE itself transitions from a discontinuous domain at

lower % crystallinities to a continuous crystal domain at higher % crystallinities

[191]. It may be possible that at the crystallinity values studied (26.8% by volume)

corresponds to a crystalline phase domain that is closer to being discontinuous than

continuous. This also explains why a smaller value of α show a better prediction

than the value offered by Eqs (4.2.1.3), (4.2.1.4) and (4.2.1.5). However, as

crystallinity increases, the crystallites will stack up leading to an increased

crystalline phase aspect ratio as seen in Figure 4.29. It can be contended that an

increased % crystallinity results in the crystallites proceeding to stack together.

Thus, a more rigorous expression for α based on improvements in Eq (4.2.1.5) and

combined with TEM images that focus on the crystalline domains in the PE samples

can help make better predictions of α and consequently, D.

Figure 4.29: Visualising the crystallite and amorphous segments of Polyethylene with

increasing crystallinity.

Based on points 1-4 mentioned above, it can be claimed that this methodology based on

isolating and simulating the continuous and dispersed phases separately and combining the


159

individual results using semi-empirical modelling can be used effectively for predicting

transport coefficients such as D in semi crystalline polymers. After establishing the proof of

concept, this technique can be further used to predict diffusion of ethanol in the rotomolded and

compression molded LLDPE wood flour composites studied in Section 4.2.2.

160

4.2.2 COMBINING MOLECULAR DYNAMICS AND SEMI-

EMPIRICAL MODELLING FOR PREDICTING LIQUID

DIFFUSION.

From the previous chapter, it is clear that the technique of isolating individual phases of

the composite and simulating the transport phenomena through them separately leads acuuarte

predictions of transport phenomena in the composite itself. In Section 4.2.1 it was established

for gas (oxygen) diffusion and in this chapter, this methodology is expanded to include liquid

diffusion. As the potential application for all of the products manufactured and studied in this

thesis is for food storage application with the food item itself being a wine or a spirit (materials

consisting of high alcohol content), the liquid diffusant of choice is ethanol. Therefore, in this

Chapter, the method and the models applied for gas diffusion are analysed with respect to their

efficacy in predicting liquid ethanol diffusion. In Section 4.2.1, Figure 4.22 represented the pore

size distributions of crystalline PE (Figure 3.19) and amorphous PE (Figure 3.20) and was used

to check the possibility of diffusion through the conventionally impermeable crystalline phase

of a semi crystalline polymer. The same procedure was also carried out for the simulated wood

system (shown in Figure 3.22h) and the results are shown in Figure 4.30. The averaged size

was 4.50 Å which is close to the 4.83±0.06 Å estimated using PALS. The simulated value of

density for the wood system (1.27 ± 0.03 g/cm3) was also quite close to the experimental value

of 1.18 ± 0.05 g/cm3 indicating the high accuracy of the simulated systems as relates to intensive

properties such as density and pore size (Table 4.7).

Table 4.7: Experimental and simulated densities

Molecule Simulated molecule

density (g/cm3)

Experimental density

(g/cm3)

Semi-crystalline PE 0.80 ± 0.05 0.96 ± 0.02

Wood 1.27 ± 0.03 1.18 ± 0.03

Combining MD and Semi-empirical Modelling for Predicting Liquid Diffusion.

161

Figure 4.30: Pore size distribution of the simulated wood molecule shown in Section 3.3,

Figure 3.22h.

Now, when it comes to simulating ethanol diffusion, akin to oxygen diffusion, of the

extent of diffusion that may happen in all the three simulated phases need to be estimated viz.,

the amorphous PE, the crystalline PE and the wood system. In the previous chapter, it is

postulated that, as the average size of the oxygen molecule is less than the largest pore size

observed in both the amorphous and crystalline PE systems, there must be a finite, non-zero

amount of diffusion happening through both phases. In the case of ethanol, the same kinetic

molecular diameter is 4.40 Å [192] and based on this value, it can be categorically stated that,

while there will be diffusion through both the amorphous PE and wood phases, the diffusion

through the crystalline phase is impossible. In case of oxygen and its diameter of 3.46 Å there

are at least some pores in the crystalline PE pore size distributiuon shown in Figure 4.22 that

will be accessible to the O2 molecules but it is clear that at a size of 4.40 Å, no pores in the

crystalline PE are accessible to the ethanol molecules and hence, only the amorphous PE and

the wood syatem are simulated with ethanol molecules. The methdology followed by Algorithm

B using steps b1-b5 (mentioned in Section 3.3) and the MSD was then measured for each of

the 30 NPT runs carried out at 303 K (corresponding to the samples kept in the vacuum oven

as in Figure 3.9) and 279 K (corresponding to the samples kept in the fridge as in Figure 3.10).

First, the simulated results of ethanol diffusion will be presented. In Figure 4.31 and

Figure 4.32 examples of amorphous PE and the wood system with a single molecule of ethanol


162

are shown. This system was then simulated using Algorithm B as mentioned before and the

averaged (over 30 runs) MSD results of the ethanol molecule are shown in Figure 4.33.

Figure 4.31: Amorphous PE molecules in red. Ethanol in green.

Figure 4.32: Cellulose in brown, water in yellow, hemi cellulose in green and lignin in blue.

Ratio is 40:30:30 by weight cellulose: lignin: hemicellulose. 8% by weight of water. 1 molecule

of Ethanol in black.


163

Figure 4.33: Mean square displacement (MSD) of the ethanol molecules in the Polyethylene

simulation box with trajectory segment showing MSD α t. Averaged over 30 simulations and a

period of 10 ns.

The major difference between the MSD plots in this Chapter and the ones in Section

4.2.1, is that the MSD in Figure 4.33 in this section reaches proportionality with t much quicker

in the systems explored in Section 4.2.1. Also, in Section 4.2.1, the D value had to be obtained

from MSD plots after 1 ns to take into account the initial ballistic type movement of the oxygen

molecule, no such behavior was seen for the ethanol systems. The reasons for this, at this point

of time, are not exactly clear. In Figure 4.33, there are 4 MSD plots and the D of ethanol

obtained from Eq (3.2.1) are shown in Table 4.8.

Table 4.8: Slopes of MSD plot and simulated D from Eq (3.2.1)

System Slope of MSD plot (cm2/s) Simulated D (cm2/s)

Amorphous PE 30°C 5 × 10-6 8.3 × 10-7

Amorphous PE 6°C 6 × 10-7 1.0 × 10-7

Simulated wood flour 30°C 4 × 10-7 6.7 × 10-8

Simulated wood flour 6°C 9 × 10-9 1.5 × 10-9


164

Now, in terms of experimental results, the ethanol uptake technique was explained in

Section 3.2 and the D value can be estimated quantitatively from the sorption plots shown in

Figure 4.34 and 4.35 using Eq (3.2.1).

Figure 4.34: Uptake of Ethanol of all samples at 6°C

Figure 4.35: Uptake of Ethanol of all samples at 30°C


165

There are two major conclusions that can be drawn from the sorption plots of the

composites at 6°C and 30°C

1. The extent of ethanol uptake is higher for the rotomolded specimens than the

corresponding compression molded specimens at both temperatures and irrespective of

the use of pine or oak flour to manufacture the composite.

2. An increase in the wood flour content results in an increase in the ethanol uptake

regardless of the use of processing method but the increase in ethanol uptake is much

more significant for the rotomolded composites.

These observations correlate perfectly with the observed density trends shown in

Section 4.1 (Table 4.1 and Figure 4.8) and also show that by changing the shear involved in

processing, it is possible to produce a composite specimen with controllable transport

characteristics. While visually speaking the trends do tend to match, it important to note that

verification of correlation can only be done by referring to values of correlation coefficients.

The Pearson coefficient (p)- the definitions for which are shown in [193, 194] was used for

estimating the type of relationship between VP (shown in Figure 4.8) and ethanol uptake

(Figures 4.34 and 4.35) for both the compression molded and rotomolded samples. The p values

are shown in Table 4.9 while the D of ethanol as a function of wood flour concentration obtained

using Eq (3.2.1) on the sorption plots are shown in Figure 4.36 and 4.37.

Figure 4.36: Ethanol diffusion coefficients for the compression and rotomolded composites at

6°C

0

1E-10

2E-10

3E-10

4E-10

5E-10

6E-10

7E-10

0 5 10 15 20

D (c

m2 /s

)


COMPRESSIONMOLDED PINE

ROTOMOLDEDPINE

COMPRESSIONMOLDED OAK

ROTOMOLDEDOAK


166

Figure 4.37: Ethanol diffusion coefficients for the compression and rotomolded composites at

30°C

Table 4.9: Pearson coefficient (p) between the D (cm2/s; shown in Figure 4.36 and 4.37) and

VP (Figure 4.8) for both compression and rotomolding techniques at two temperatures.

Molding technique Temperature (°C) p

Compression Molding 6 0.56

30 0.76

Rotomolding 8 0.96

30 0.99

The first observation made is that all p values are > 0 for all conditions indicating a

positive correlation between VP and D exists at all tested temperatures i.e. D increases with

increase in VP. The second observation is that the VP for the compression molded specimens

are consistently lower than what is seen for the rotomolded specimens. This indicates that the

effect of VP is more pronounced for rotomolding than it is for compression molding. Therefore,

not only are the porosities consistently higher for rotomolded composites, these porosities are

correlated to transport phenomena to a higher degree as well. To isolate the effects of sorption

and swelling, an analysis of the swelling coefficients was carried out and is shown in Figures

4.38 and 4.39.

0

2E-09

4E-09

6E-09

8E-09

1E-08

1.2E-08

1.4E-08

1.6E-08

1.8E-08

2E-08

0 5 10 15 20

D (c

m2 /s

)


COMPRESSIONMOLDED PINE

ROTOMOLDEDPINE

COMPRESSIONMOLDED OAK

ROTOMOLDEDOAK


167

Figure 4.38: Swelling of all composites at 6°C

Figure 4.39: Swelling of all composites at 30°C


168

The overall swelling coefficient values are tabulated in Table 4.10. It was found that

there is no observable difference in the swelling behaviour with pine flour incorporation. Also,

all of the samples showed a value of the swelling coefficient close to 0.005 ± 0.0007 at 6°C and

0.02 ± 0.002 at 30°C. As a consequence, the differences in sorption behaviour can be attributed

completely to the composite macroporosity.

Table 4.10: Thickness and Swelling coefficient for all samples.

Sample h (cm) of samples

dipped at 30°C

Swelling coefficient

at 30°C

h (cm) of

samples dipped

at 6°C

Swelling

coefficient at 6°C

CM0 0.185 ± 0.005 0.022 0.180 ± 0.005 0.005

CM5 0.193 ± 0.003 0.019 0.180 ± 0.003 0.005

CM5_O 0.185 ± 0.005 0.019 0.185 ± 0.005 0.005

CM10 0.178 ± 0.100 0.016 0.180 ± 0.100 0.005

CM10_O 0.185 ± 0.005 0.015 0.185 ± 0.005 0.004

CM20 0.195 ± 0.005 0.016 0.190 ± 0.005 0.004

RM0 0.188 ± 0.008 0.019 0.180 ± 0.010 0.005

RM5 0.202 ± 0.010 0.022 0.205 ± 0.010 0.005

RM5_O 0.230 ± 0.010 0.023 0.205 ± 0.015 0.006

RM10 0.209 ± 0.004 0.017 0.210 ± 0.010 0.006

RM10_O 0.225 ± 0.015 0.019 0.200 ± 0.010 0.006

RM20 0.238 ± 0.010 0.022 0.240 ± 0.010 0.006

In order to correlate the MD results to the experimental D values it is important to

understand that the D value obtained for PE is only for the amorphous phase of the PE.

According to Gibson [195], the impermeable cellulose phase exists in plant cell walls in the

forms of microfibrils. These microfibrils have an average diameter of 3.5 nm and possess both

crystalline and non-crystalline regions. The crystalline regions constitute the overwhelming

majority of the cellulose phase and are found to have an average length of about 20 nm [195]

while in the cell wall, thus leading to an α of 5.7. The ϕC is 0.4 in softwoods like Pinus Radiata


169

[172]. Thus, the overall τ is found to be ~3.15 using Eq (3.3.8), and consequently, the D for

ethanol in the simulated wood system is found to be 2.1 × 10-8 cm2/s at 30°C and 4.7 × 10-10

cm2/s at 6°C.

The estimation of D for semi-crystalline polymers such as PE from the simulated MSD

data is a bit more nuanced. In Section 3.3, the work of Compan et al. [37] has been noted, who

helped correlate the overall diffusion (D) coefficient in semi crystalline polymers (specifically

LLDPE) to the diffusion through the completely amorphous phase of the polymer (DC). This

has been explained in Eq (3.3.4) and Eq (3.3.5) and the terms τ (geometrical impedance of the

impermeable crystalline phase) and β (immobilization effect generated by the crystalline phase

on the amorphous phase) were defined. β has been defined using Eq (3.3.6) and Eq (3.3.7) while

τ is much more nuanced. A wide range of expressions have been developed over the years for

defining τ and they have been shown in Section 3.2, Eq (3.3.8) through Eq (3.3.19). All of those

equations were used and the predicted D values are shown in Table 4.11.

Table 4.11: Diffusion Coefficients obtained using several tortuosity models and comparing to

experimental values.

Model 𝛕 β𝛕

𝐃 = 𝐃𝐂

𝛃𝛕

at 30°C

(×10-9

cm2/s)

%

difference

from Dexp

at 30°C

𝐃 = 𝐃𝐂

𝛃𝛕

at 6°C

(×10-10

cm2/s)

%

difference

from Dexp

at 6°C

Cussler

(Eq 3.3.8) 1.7 11.8 70.6 1935 84.8 2951

Cussler

(Eq 3.3.9) 1.0 7.1 169.3 3270 140.4 4952

Lape et. al.

(Eq 3.3.10) 1.2 8.1 103.3 2876 124.0 4362

Gusev and Lusti

(Eq 3.3.11) 1.6 11.2 74.6 2050 89.6 3123

Frederickson and

Bicerano

Dilute

(Eqs 3.3.12, 3.3.13)

4.8 32.5 25.6 638 30.7 1006


170

Frederickson and

Bicerano Semi

Dilute (Eqs 3.3.14,

3.3.15)

1.9 12.9 64.7 1764 77.6 2694

Nielsen

(Eq 3.3.16) 1.6 11.2 74.5 2046 89.4 3117

Hedenkvist and

Gedde

(Eq 3.3.17)

1.2 8.2 101.6 2828 122.0 4289

Cussler-Aris

(Eq 3.3.18) 43.3 296.1 2.8 19 3.4 21

Cussler-Wakeham

and Mason and

Falla et al.

(Eq 3.3.19)

39.2 267.4 3.1 10 3.7 34

From Table 4.11, it can be clearly seen that Eq (3.3.18) and Eq (3.3.19) are the most

suitable in terms of predicting the experimental diffusion coefficient. Part of this is relies on the

derivation of those equations. The work of Aris [173, 174] shown in Eq (3.3.18), Falla et al.

[179] and Wakeham and Mason [180] shown in Eq (3.3.19) helped modify the Cussler approach

by defining the composite system as a 2-dimensional regular array of parallel strips and

expanded by integration for a 3-dimensional system for pure diffusive transport (Figure 4.40).

In both Eq (3.3.18) and Eq (3.3.19) - the term involving α2 reflects the contribution of the

tortuous path of the permeant through the dispersed phase. The second term represents the

resistance to permeation of the slits and depends on σ- the pore aspect ratio. The last term

represents the constriction from the wide space between the plates into the narrow slits and it

should depend on the constriction ratio, α/σ. Now, σ for the PE system was defined by Cussler

as the ratio of the average pore radius (s) to the average crystalline lamellar thickness (lC). Thus,

the calculation of σ requires the results of PALS which can provide information such as the

average pore radius (s). Values for lC were obtained by a survey of several papers that analysed

the crystallite structure of several polyethylene samples. Based on the results of 6 independent

studies, it was concluded that lC is ~17.1 ± 3 nm (171 ± 30 Å) [196-201]. This helped involve

not only intensive properties such as lC and s to the model equation but also, helped incorporate


171

experimental data from PALS to increase the relevance of Eq (3.3.18) and Eq (3.3.19) to the

composite specimens produced in this thesis.

Figure 4.40: Visualising tortuosity where s: average pore radius, lC: average crystalline lamellar

thickness and aspect ratio α = 2d/lC

The predicted values from these two techniques average to 3.06 ×10-9 cm2/s compared

to an average of 3.45 ×10-9 cm2/s experimentally at 30°C and 3.54 × 10-10 cm2/s compared to

an average of 2.80 × 10-10 cm2/s at 6 °C. Based on the simulated values of D of ethanol for PE

and wood, several semi-empirical models were used to predict the D of the composite samples.

These models were also used in Section 4.2.1 to estimate the diffusion coefficient of oxygen

through semi-crystalline PE and are listed out in Table 2.10. The predictive abilities of the

models can be seen in Figure 4.41 (30°C) and Figure 4.42 (6°C).


172

Figure 4.41: Predictive abilities of the models listed in Table 2.10 for ethanol diffusion at 30°C.

Figure 4.42: Predictive abilities of the models listed in Table 2.10 for ethanol diffusion at 6°C.

0

5E-09

1E-08

1.5E-08

2E-08

2.5E-08

0 5 10 15 20

D (c

m2 /s

)


COMPRESSION MOLDED

ROTOMOLDED

RULE OF MIXTURES

LAMINATE MODEL

LOGARITHMIC

MAXWELL

KALNIN

MWS n = 1/6

MWS n = 2/3

WEISSBERG

Vp ROTOMOLDING

Vp COMPRESSION MOLDING

0

5E-10

1E-09

1.5E-09

2E-09

2.5E-09

0 5 10 15 20

D (c

m2 /s

)


COMPRESSION MOLDED

ROTOMOLDED

RULE OF MIXTURES

LAMINATE MODEL

LOGARITHMIC

MAXWELL

KALNIN

MWS n = 1/6

MWS n = 2/3

WEISSBERG

Vp ROTOMOLDING

Vp COMPRESSION MOLDING


173

Table 4.12: δ values for all the models used in this thesis for ethanol diffusion

Model δ (Compression Molded) δ (Rotomolded)

6°C 30°C 6°C 30°C

Rule of Mixtures 17.8 14.41 15.9 150.1

Laminate Model 10.5 17.5 30.0 252.9

Logarithmic 10.8 17.3 26.2 216.8

Maxwell 15 14 200 200

Weissberg 10.0 17.0 27.4 230.1

Kalnin 426 972 657 4121

M-W-S; n = 1/6 11.0 16.2 25.9 195.0

M-W-S; n = 2/3 10.7 17.3 26.4 240.9

VP based scaling 20 16 55 11

Two results are immediately apparent from Figures 4.41 and 4.42 and from the δ

values presented in Table 4.12:

1. All semi-empirical models are able to predict the trends in the compression molded

samples.

2. Of those models that predict the trends in compression molded samples well, similar to

Section 4.2.1, the M-W-S models are the most effective thus demonstrating that models

developed for transport phenomena work effectively independent of the phase state of

the diffusant.

3. The predictive ability for these models for the rotomolde composites is pretty poor.

4. Of those models that are halfway decent in predicting these trends, the VP based scaling

model developed seems to work effectively for only one set of rotomolded composites.

The reasons for these observations may be the reasons outlined in Section 4.1 Figures

4.2 to 4.7. This set of figures shows the evolution of surface and microstructure of rotomolded

composites and establishes it as a molding tehcnique that involves sintering of the raw material

particles followed by phase consolidation and formation of a microstructure. It is important to

note that this sintering phenomenon is the driving force even if the molding temperature

(240°C) itself is several degrees higher than the polymer melting point and indeed is also higher

than the corresponding temperature used in compression molding (190°C). Secondly, the


174

rotomolding operation is carried out at atmospheric pressure while the compression molding is

carried out in the presence of higher pressure. The compression molding technique uses the

combination of elevated temperature and pressure to achieve phase change followed by cooling

and cosolidation to not only disperse the wood flour in the polymer matrix but also to develop

the microstructure. Rotomolding, on the other hand, uses rottaion about two axes (granted the

rotation in itself is at quite a slow raet) to achieve dispersion. Based on these observations, it is

clear why the models that have been developed for transport phenomena in composite materials

are not capable of modelling rotomolded materials as accurately as the compression molded

counterparts. That being said, it is important to note that there does exist a mathematical

parameter than can used quantitavely to differentiate between composites made by the phase

change and consolidation technique such as compression molding and also injection molding

and extrusion and those made by the sintering followed by consolidation method such as the

rotomolded composites. That parameter is VP. However, based on the trends in ethanol

diffusion at 6 °C and the corresponding incapabilities of all of the models whether the VP based

one or the other listed in Table 2.10, it is clear that the mere use of VP is not enough and that

new parameters will need to be developed to quantititavely model trends in physical properties

of rotomolded composites (which will be covered in Chapter 5).

A note is also to be made as to why the Maxwell family of models, specifically the M-

W-S expressions [151] are found to be useful for modelling transport phenomena in composite

systems. This is because they take into account the transport through the dispersed phase as

well. A lot of other models, including all of the tortuosity expressions listed out in Eq 3.3.8 to

3.3.19 assume that no transport happens through the dispersed phase. In Section 4.1, it is

demonstrated how this is an incorrect assumption to make, especially in polymeric systems,

which possess a range of pore sizes. Thus, an average size on its own is often not indicative of

the whole system.

175

4.2.3 USING MOLECULAR DYNAMICS IN CONJUNCTION

WITH SEMI-EMPIRICAL MODELS FOR PREDICTING

TRENDS IN ELASTIC MODULI.

The purpose of this thesis is to investigate the potential of LLDPE wood flour

composites for storage applications. To that effect, the transport phenomena of gaseous and

liquid permeants through such a composite system has been studied from a practical perspective

using liquid uptake and gas permeability measurements. These have then been analysed from a

theoretical perspective using MD. For storage application, the mechanical properties of the

fabricated system are also of equal importance. Hence, in Section 4.1, the effect of wood flour

incorporation on the various mechanical properties of the system have been investigated. Now,

in this Section, we will use MD to provide a molecular prediction of the trends in mechanical

properties as a function of temperature. Using Algorithm D comprised of steps d1-d5, simulated

stress vs strain curves were obtained for both the semi-crystalline PE (Figure 4.43a) and the

simulated wood flour (Figure 4.43b). In order to obtain a more holistic molecular interpretation

of the continuous and dispersed phases, it is important that the simulation not only is able to

predict values at just one temperature point but rather over several temperatures. The objective

of this would be the prediction of properties over a whole temperature spectrum. At this

juncture, three separate temperature points

The simulated stress vs strain curves for the semi-crystalline PE (Figure 4.43a) showed

that there was a drop in the modulus value with increase in simulation temperature. This,

however, is an expected result, and in order to establish the effectiveness of Algorithm D shown

in Section 3.3, comprised of steps d1-d5, the stress vs strain curves were simulated for 3

different temperatures viz., 30°C, 60°C, 90°C and the corresponding simulated modulus values

were used to estimate the relative drop in modulus value with an increase in temperature. As

established throughout this thesis, all of the simulated values should always be presented in

juxtaposition with experimental data and the deviation of the simulated data from the

experimental results should be quantified. To this end, DMA of the CM0 and RM0 in tensile

mode of values were carried out from 30°C to 100°C in order to estimate the storage moduli of

these specimens over a range of temperatures. These values were then used to estimate the

relative drop of storage modulus from 30°C to 100°C. The 3 simulated modulus values are

Using MD in Conjunction with Semi-empirical Models for Predicting Trends in Elastic Moduli

176

plotted in juxtaposition with the DMA obtained values (averaged from the CM0 and RM0

values shown later on in Figure 4.52). It is seen that the simulated values are quite close to the

experimental values indicating that, in addition, to transport phenomena, the MD method was

also quite effective in predicting trends in mechanical properties of the semi-crystalline PE

(Figure 4.43c).

Algorithm D shown in Section 3.3 comprised of steps d1-d5 was also repeated for the

simulated wood molecule and the corresponding stress vs strain curves for the wood system

were obtained for 30°C, 60°C and 90°C similar to the semi-crystalline PE and is shown in

Figure 4.44b. While the availability of the TA DMA 2980 (Figure 3.12) helped measure the

mechanical properties as a function of temperature for the PE samples, a machine that could

help measure the mechanical properties of the wood flour used in this thesis (oak and pine flour)

was not available at the time of writing this thesis and so the viability of the MD method had to

be estimated by comparing the simulated and experimental modulus values at a single

temperature unlike the range of temperatures used for PE validation. The Hysitron nano

indenter shown in Figure 3.13 was used to estimate the elastic modulus of the pine flour at

30°C.

a


177

Figure 4.43: Simulated stress vs strain curves in tensile mode for (a): semi-crystalline PE at

30°C, 60°C and 90 °C and (b): simulated wood flour at 30°C, 60°C and 90 °C, (c): Relative

drop in modulus value (E) as compared to modulus value at the start (Ei) for the simulated PE

vs experimental values

b

c


178

Table 4.13: Storage modulus from tensile mode DMA of compression molded and rotomolded

plain Polyethylene

Sample Elastic Modulus

(MPa)

CM0 493 ± 17

RM0 540 ± 20

It is seen that the simulated value of elastic modulus for the simulated PE (702 MPa) is

larger than the experimental values of both the compression (CM0–493 MPa) and rotomolded

(RM0–540 MPa) samples. This is because the simulated semi-crystalline PE possesses only

microporosity and no macroscopic porosity that can be seen in the real molded specimens. The

main influencing factor for creating the macroporosity is the processing technique itself. Thus,

using MD simulations, it is possible to analyze a material completely separated from the

influence of manufacturing. It could be that the simulated modulus values represent a sort of

upper bound on the modulus of LLDPE. The larger the deviation from this value, the larger is

the influence of macroscopic porosity and it is thus possible to rank various processing methods

based on their abilities to produce macroscopic porosities in a LLDPE specimen. The simulated

elastic modulus value for the pine flour obtained at 30°C was 5730±1630 MPa, which is

comparable to the experimental values of 3650±1400 MPa obtained from nanoindentation

analysis of the pine flour specimen. However, as the MD model developed in this study is still

a simplified one, further analysis of other material properties will require an improvement,

which we hope to achieve in our future work.

The theoretical modulus values are predicted using the models as shown in Table 2.11.

shown in Section 2.5. Based on optical microscopy results, the aspect ratio (α) of the pine flour

particles was found to be 4.5±0.5, while Poisson’s ratio (σPR) of the matrix polymer LLDPE is

0.44. The absolute and relative change in elastic modulus of the PE-pine flour composite as a

function of pine flour weight fraction are presented in Figure 4.44a and b respectively, with the

percentage average absolute relative errors (δ estimated using Eq 3.3.3) as presented in Table

4.14.


179

Figure 4.44: Comparisons with experimental value; (a): Absolute and (b): Relative composite

elastic modulus

0

200

400

600

800

1000

1200

1400

1600

1800

0 5 10 15 20

Stor

age

Mod

ulus

(MPa

)


Compression Molded

Rotomolded

Rule of Mixtures

Laminate

Short Fibre

Hirsch

Carman-Reifsnider

Halpin Tsai

Halpin Tsai2

Tsai Pagano

Cox Krenchel

0

0.5

1

1.5

2

2.5

0 5 10 15 20

E/E

C


Rotomolded

Compression Molded

Rule of Mixtures

Laminate

Short Fibre

Hirsch Model

Carman-Reifsnider

Halpin Tsai

Halpin Tsai 2

Tsai Pagano

Cox Krenchel

b


180

Table 4.14: δ values for the models when compared to the experimental modulus values of the

compression and rotomolded sample.

Model Compression Molded

δ

Rotomolded

δ

Rule of Mixtures 13 122

Laminate 39 42

Short fibre 78 86

Hirsch 58 64

Carman-Reifsnider 54 60

Halpin-Tsai1 71 78

Halpin-Tsai2 38 42

Tsai Pagano 61 59

Cox Krenchel 36 33

From Figure 4.44a, it can be seen that the simulated modulus values predicted using the

models in Table 2.11 are all higher than what is observed experimentally. This overestimation

can be attributed to the simulated molecules being idealized and also the inability to recreate

processing created inconsistencies and voids in a MD environment. From Table 4.14, when the

respective δ values are considered, it can be seen that the Halpin-Tsai2 and the Cox and

Krenchel models, which include structural parameters such as a and σPR is the most accurate.

That being said, the δ value is still quite high at 38 and 36 respectively for compression-molded

samples, which shows that much more improvements to the simulated molecules are needed.

Indeed, when the corresponding δ values for the rotomolded specimens are considered, it is 33

and 42 respectively. This clearly indicates that there should be a parameter in the models in

Table 2.11 that reflects the VP of the composite. That being said, the laminate model is also

able to predict relative elastic moduli relatively well. However, as the laminate model is

analytical in nature, it does not provide an effective way to represent the physical characteristics

of our system.

The model developed by Hirsch and reported by Cao et al. [155] combines the results

of the rule of mixtures and the laminate models and when it comes to the relative changes in

modulus values as shown in Figure 4.44b, an α value of 0.25 provides an excellent agreement

between the experimental and predicted trends for the compression-molding samples. However,

it has to be noted again that this agreement is analytical in nature and that further rigor has to


181

be introduced by incorporating characteristic parameters of the matrix polymer and the

dispersed phase.

The Carman-Reifsnider [157], the two versions of the Halpin-Tsai models [155], [158]

and the Cox and Krenchel [159]models all attempt this by using the single fibre moduli, α and

σPR, which are characteristic properties of the dispersed and continuous phases. It can be seen

that the use of these characteristic parameters helps in achieving accurate predictions of the

trends in elastic moduli in the case of the Halpin-Tsai and Cox and Krenchel models. Further,

the Halpin-Tsai and the Cox and Krenchel approaches can be customized for any and all

composite systems. Also, more precise predictions can be obtained by improving the simulated

systems by incorporating factors such as branching and co-monomers in the simulated

molecules. However, for all of the models except the Cox and Krenchel models, it is quite clear

that the accuracy of these predictions is only for the compression-molded samples. The overall

reduction in elastic moduli with increase in dispersed phase concentration in rotomolding is

only recreated by the Cox and Krenchel model which takes into account (in addition to intensive

properties of the continuous and dispersed phases), the influence of dispersed phase orientation

and volume dispersion effects. Thus, the effect of interfacial porosity required to study the

trends in elastic moduli as a function of dispersed phase concentration for low shear processing

techniques like rotomolding, is only considered by the Cox and Krenchel model.

Now, to further enhance accuracy of the proposed methodology here, the following

considerations will be taken into account in a separate publication, while addressing the

potential contributing factors related to the interface:

1. Having an equilibrated density closer to experimental values by developing the

transitionary regions between the crystalline and amorphous phase in polyethylene.

2. Simulating the trends in elastic modulus values as a function of temperature and

increasing the accuracy of this prediction by comparing with temperature-ramped

DMA.

3. Developing a semi-empirical expression for elastic moduli of polymer composites by

considering the differences between the theoretical and experimental composite

densities.

Now, the conclusions that may be made from Section 4.2 as a whole are as follows:

1. Isolating the individual phases of a composite systems and then simulating the particular

phenomenon of interest on the isolated phase, can lead to accurate predictions of the

phenomenon in the composite system.


182

2. As far as transport properties such as diffusion are concerned, irrespective of the state

of the diffusant, the models that take into account interaction and overlaps between the

dispersed and continuous phases (for instance, the M-W-S and the F and B models) are

the best suited.

3. The models, however, only seem to work for compression molding based on the

observation that the average absolute relative error (δ) values seen for the rotomolding

process are all consistently higher (bar the Rule of Mixtures but this is because of the

purely empirical nature of that model) than that seen for compression molding. In some

case, the δ values seen are in excess of 100 indicating that the composite created by

rotomolding is completely unlike the ones created by phase change and consolidation

like compression molding. One of the ways to address this would be to incorporate

macroscopic porosity indicators like VP in the model expression but, at best, this is a

stop gap, which means there is big potential to develop semi-empirical models for

sintering based process like rotomolding.

4. This Chapter has comprehensively covered transport phenomena but for packaging

system both the transport and mechanical performance are important. Hence, the

mechanical behaviour of the fabricated composites, subsequent measurement, analysis,

simulation and predictive modelling will be shown in Section 4.3.

183

4.3 ETHANOL UPTAKE AND INFLUENCE ON LONG-

AND SHORT-TERM MECHANICAL

PROPERTIES.

The simulation work presented in Section 4.2.1 and 4.2.2 were aimed at providing a

novel outlook regarding transport phenomena in composite systems. Based on those results it

is claimed that the combination of MD and semi-empirical modelling is an effective method for

predicting trends in transport phenomena independent of the phase of the permeant. That was

demonstrated by modelling gas (oxygen) diffusion and also liquid (ethanol) diffusion in

LLDPE-wood composites. In this Chapter, those results will be used to predict the stiffness

(through storage moduli measurement) of the composites produced in this thesis. In addition to

that, a comprehensive overview of how the compression and rotomolded composites respond

mechanically to ethanol uptake will be provided. In Section 4.2.2, it was found that the diffusion

of the ethanol through the composites is well correlated to the VP, which in turn, is related to

the macroscopic porosity in the composites. This is because not only were the microporosities

of all the samples similar (Table 4.5) but also were the swelling coefficients at both tested

temperatures of 6°C and 30°C (Figures 4.38 and 4.39 and Table 4.10). Thus, the entire

phenomenon of diffusion and the reason for the trends in diffusion coeffcinet can be attributed

to the macroscopic porosoity indicated by VP.

In this Chapter, the effect of ethanol uptake on the long and short term mechanical

properties of the composites are studied. Similar to the diffusion coefficient modelling done in

Section 4.2.2, the modulus of the composite samples were measured experimentally as a

function of dispersed phase concentration. The modulus values of the LLDPE and the wood

flour were then predicted using MD simulations as described by Algorithm D based on steps

d1-d3. After which, semi-empirical models such as the ones mentioned in Table 2.11 were used

to model the trends. In addition, similar to Section 4.2.1 and 4.2.2, the models were then ranked

based on the respective δ values.

The first set of the results in this Chapter are the static mechanical properties viz., the

tensile and flexural strengths and the corresponding effect of ethanol contact on the properties

of the compresssion and rotomolded samples. This is followed by the effect of ethanol uptake

on the trends in the dynamic mechanical properties of the compression and rotomolded

Ethanol Uptake and Influence on Long-term and Short-term Mechanical Properties.

184

composites viz., the storage modulus in both tensile and cantlever modes and also, the creep

properties.

The tensile strength of the composites and the effect of ethanol contact is shown in

Figures 4.45 (compression molded composites) and 4.46 (rotomolded composites). First, the

trends in Figure 4.45 are examined. It can be seen that with an increase in wood flour content

(independent of the tyep of wood), there is a slight increase in the tensile strength value. For

instance, the CM10 and CM10_O specimens showing tensile strengths of 13.4 ± 1.0 MPa and

12.8 ± 1.0 MPa respectively. These represent a 12% and 7% improvement respectively over the

CM0 specimen which had a tensile strength of 12.0 ± 0.4 MPa. This increase with wood flour

incorporation is also maintained with ethanol uptake as, independent of the sorption being

carried out at 6 °C or 30°C, the tensile strength of the composite specimens are larger than of

the plain CM0. It is important to also note that there is no major decrease in the tensile strength

of the compression molded composites at all compositions.

Figure 4.45: Tensile strength vs ethanol uptake % for all compression molded samples

0

2

4

6

8

10

12

14

16

0.00 1.00 2.00 3.00

Tens

ile S

tren

gth

(MPa

)

Alcohol uptake (vol%)

CM0

CM5

CM5_O

CM10

CM10_O

CM20


185

When juxtaposed with Figure 4.45, the trends in Figure 4.46 has some differences. First

and foremost, is that with an increase in the wood flour concentration, the tensile strength starts

reducing with the RM10 and RM10_O samples showing tensile strengths of 9.7 ± 0.2 MPa and

9.8 ± 0.2 MPa as compared to the RM0 value of 13.1 ± 0.5 MPa. The reasons for this are clearly

the lower dispersive efficiency of the rotomolding process. That being said, it is very possible

that this lower dispersive efficiency can be exacerbated in the presence of sorbed ethanol.

Evidence of this, however, is not seen amongst the RM5, RM10, RM20, RM5_O, RM10_O

specimens. On average the overall tensile strength of the specimens is maintained after ethanol

sorption and in the RM0 specimen, there is a slight increase after ethanol sorption at 30°C. But

this supposed increase is only of the order of 3% so could be attributed to experimental variation

rather than a true increase in tensile strength via plasticization.

Figure 4.46: Tensile strength vs ethanol uptake % for all rotomolded samples

The flexural strength of the composites and the effect of ethanol contact is shown in

Figures 4.47 and 4.48. Once again, the disucssion will be started with the trends in the

0

2

4

6

8

10

12

14

16

0.00 2.00 4.00 6.00 8.00 10.00

Tesn

ile S

tren

gth

(MPa

)


RM0

RM5

RM5_O

RM10

RM10_O

RM20


186

compression molded samples shown in Figure 4.47. As compared to the trends in tensile

strength values after wood flour incorporation, no trend is found in the Flexural Strength values.

All of the samples seem to form a band on the graph between 12 MPa and 13 MPa both before

and after contact with ethanol indicating that neither wood flour incorporation nor ethanol

sorption have a pronounced effect on the flexural behaviour of the compression molded

composites.

Figure 4.47: Flexural strength vs ethanol uptake % for all compression molded samples

In Figure 4.48, the trends for the rotomolded composites are presented. Similar to the

rotomolded composite trends in tensile strength, the flexural strength also reduces with the

incorporation of wood flour (pine or oak). The results in Figure 4.46 and 4.48, when juxtaposed

with the results in Section 4.1 present an interesting quandary. At the outset, the purpose of this

work is to check whether controlled increase in permeability is possible with the use of low

shear processing of composites. The use of wood flour is precipitated from its low cost,

biocompatible and food contact approved nature, but it is also clear that any storage unit made

from this process will have reduced mechanical strength. Therefore, at this juncture, it is

0

2

4

6

8

10

12

14

16

0.00 1.00 2.00 3.00

Flex

ural

Str

engt

h (M

Pa)


CM0

CM5

CM5_O

CM10

CM10_O

CM20


187

essential to note that while the main objective of this research is achieved from the trends seen

in Section 4.1, Figure 4.21 and Table 4.3, it should not be at the cost of vastly reduced

mechanical strength. For instance, with the incorporation of 5% by weight of wood flour, the

flexural strength is found to reduce by 4-17%. The overall flexural strength comes into play

when considering the stacking of these storage containers and therefore, it is important that a

proper choice of dispersed phase concentration is done. What is encouraging, however, is that

the flexural strength is maintained before and after the ethanol sorption at different

temperatures. Thus, when considering alcohol-based food contact applications, the sorption of

the food product into the pores of the designed storage will not have any major detriment on

the mechanical performance of the unit.

Figure 4.48: Flexural strength vs ethanol uptake % for all rotomolded samples

The variation in impact strength of the compression and rotomolded specimens as a

function of ethanol uptake are shown in Figure 4.49 and 4.50. The incorporation of solid fillers

without any sort of compatibilization between the matrix and the dispersed phase can lead to

0

2

4

6

8

10

12

14

16

18

20

0.00 2.00 4.00 6.00 8.00 10.00

Flex

ural

Str

engt

h (M

Pa)


RM0

RM5

RM10

RM5_O

RM10_O

RM20


188

delamination and poor interfacial properties [74]. This can have an adverse effect on the ability

of the composite specimens to absorb impact and is demonstrated conclusively by the reducing

trend in impact strength with increase in wood flour content. However, the better dispersive

properties of the compression molding process owing to the generation of a high pressure

environment compared to rotomolding ensures that, although impact strength reduces for all

composite specimens, the extent of this reduction (65% reduction for CM20 compared to CM0

and 78% for RM20 compared to RM0) and the absolute values of impact strength are always

higher for the compression molded specimens. This trend is also maintained with ethanol

sorption. It must be noted that after a 5% incorporation in the rotomolded system there is a

much more significant drop in impact properties irrespective of oak or pine flour being used as

the dispersed phase.

Figure 4.49: Impact strength vs ethanol uptake % for all compression molded samples

0

5

10

15

20

25

30

35

40

45

0.00 0.50 1.00 1.50 2.00 2.50 3.00

Impa

ct S

tren

gth

(kJ/

m2 )


CM0

CM5

CM5_O

CM10

CM10_O

CM20


189

Figure 4.50: Impact strength vs ethanol uptake % for all rotomolded samples

The next set of results are obtained from the DMA set up described in Chapter 3, Section

2. These properties of the composites and their variation with wood flour concentration and

ethanol uptake are analysed. The first of these properties studied is the storage modulus. It is

known that the storage modulus of a material indicates its inherent stiffness under dynamic

loading. Similar to the tensile and flexural modes of static analysis, tensile and single cantilever

modes of dynamic loading were exerted onto the samples. Therefore, in the following results,

the trends in storage moduli in the tensile and single cantilever modes the effect of ethanol

contact thereof will be presented. The trends in tensile mode storage moduli for the compression

and rotomolded composites are shown in Figures 4.51 and 4.52.

Amongst the compression molded samples, it is found that, once again, an increase in

modulus value is seen with increased wood flour concentration. As an example, the CM10 and

CM10_O samples show a modulus value that is 12% and 22% rspectively larger than the CM0

sample. It can be observed that the increase is higher with the oak flour as compared to the pine

flour and this could be attributed to the hardwood nature of oak.

0

5

10

15

20

25

30

35

40

45

0.00 2.00 4.00 6.00 8.00 10.00

Stor

age

Mod

ulus

(MPa

)


RM0

RM5

RM5_O

RM10

RM10_O

RM20


190

Figure 4.51: Storage Modulus (Tensile mode) vs ethanol uptake % for all compression molded

samples

Amongst the rotomolded composites observed in Figure 4.52, it is seen that there is a

formation of a band of results like Figure 4.47 between ~500 and 550 MPa for all the samples

except for RM20. This indicates that below the 20% by weight incorporation of the wood flour,

no major effect is seen on the overall storage modulus. More importantly, the storage moduli

for all samples except RM20 are not affected by ethanol sorption. Therefore, except for RM20,

all the samples maintain their mechanical performances in the presence or absence of ethanol.

With RM20, there is a pronounced reduction in the modulus value. For an ethanol uptake of

about 8% by weight at equilibrium, there is a 23% drop in storage modulus (415±30 MPa) as

compared to RM0 (534±20 MPa). This is also reflected in the slopes of the linear fits of the

storage moduli. The RM20 specimen shows an ~ 13 times larger rate of drop of modulus value

with ethanol sorption as the RM0 and a 4-11 times larger rate of drop than the specimens with

5% wood flour incorporation. Thus, with an increase in wood flour content in the rotomolded

0

100

200

300

400

500

600

700

0.00 1.00 2.00 3.00

Stor

age

Mod

ulus

(MPa

)


CM0

CM5

CM5_O

CM10

CM10_O

CM20


191

system there is a more pronounced drop in mechanical performance. This, once again, indicates

that, the dispersed phase concentration needs to be ≤ 10% by weight (pine or oak).

Figure 4.52: Storage Modulus (Tensile mode) vs ethanol uptake % for all rotomolded samples

The storage modulus in cantilever mode of the composites and the effect of ethanol

contact is shown in Figures 4.53 and 4.54. For the compression molded specimens in Figure

4.53, there is a consistent increase in modulus value with wood flour incorporation (oak or

pine). Now, comparing the modulus in cantilever mode vs the one in tensile mode, it is found

that the cantilever moduli are consistently higher than the tensile mode moduli. This is because

when strained under cantilever mode, the lower layers of the composite material are constantly

reisting the top layer that is directly in contact with the straining apparatus. That is, in the

cantilever mode, the modulus value reflects modes of tension and compression simultaneously

and hence, the cantilever modulus values are consistently higher than those in the tensile mode.

This will be relevant later in this section when will be discussing the predictions of MD

simulations, modelling the trends in simulated modulus value and comparing those with the

0

100

200

300

400

500

600

0.00 2.00 4.00 6.00 8.00 10.00

Stor

age

Mod

ulus

(MPa

)


RM0

RM5

RM5_O

RM10

RM10_O

RM20


192

experimental values. The experimental values chosen will be the storage modulus in tensile

mode because pure tension strain can be simulated while a combination of tensile and

compressive strain cannot be simulated in an MD environment.

Figure 4.53: Storage Modulus (Cantilever mode) vs ethanol uptake % for all compression

molded samples

The trends in cantilever storage modulus for the rotomolded samples reflect the trends

in the tensile mode (Figure 4.54). However, owing to the fact that the cantilever strain represents

a combination of tensile and compressive strain, the extent of the drop in the modulus value

with wood flour incorporation and ethanol contact is much more pronounced. One fact that is

consistent, however, is that the rate of drop in modulus value with ethanol sorption is highest

for the RM20 specimen.

0

200

400

600

800

1000

1200

0.00 1.00 2.00 3.00

Stor

age

Mod

ulus

(MPa

)


CM0

CM5

CM5_O

CM10

CM10_O

CM20


193

Figure 4.54: Storage Modulus (Cantilever mode) vs ethanol uptake % for all rotomolded

samples

The second set of results of DMA testing are the long term properties specifically, the

creep compliance. As a consequence of the viscoelasticity of the polymer matrix, a major

concern in using polymer composites are the long-term dimensional stability and their long-

term strength. Information on long-term deformation and strength are normally obtained by

extrapolation of short-term test data, obtained under accelerated testing conditions such as

higher temperature, stress and humidity, to service conditions by using a prediction model

[202]. The mechanism of creep deformation involves the polymer chains uncoiling and slipping

past each other when a constant stress is applied [202]. This phenomena is temperature

dependant since increased temperatures will decreases secondary bonding and increases chain

mobility. The creep compliance of the composites and the effect of ethanol contact is shown in

Figures 4.56, 4.57 and 4.58 for the compression molded specimens and Figures 4.59, 4.60 and

4.61 for the rotomolded specimens. The equilibrium moduli which are obtained by taking the

reciprocal of the equilbrium compliance are shown in Table 4.15 (compression molded

0

100

200

300

400

500

600

700

800

900

1000

0.00 2.00 4.00 6.00 8.00 10.00

Stor

age

Mod

ulus

(MPa

)


RM0

RM5

RM5_O

RM10

RM10_O

RM20


194

specimens) and 4.16 (rotomolded specimens). The fit was provided by using the Burger model

[203] shown in Eq (4.3.1) where EM and EK represent the Maxwell and Kelvin-Voigt elastic

moduli in MPa and tr is the relaxation time in s. Visually speaking the model of the material

can be represented by Figure 4.55. Burger’s model is a parallel combination of an elastic

Maxwell element (with characteristic modulus EM and visocosity 𝜂𝑀) with a viscous Kelvin-

Voigt element with characteristic modulus EK and visocosity 𝜂𝐾). The model displays a lagging

elastic response to stress represented by a relaxation time (tr). Mathematically speaking, tr is the

time required for the strain of a suddenly strained substance to reduce to 1/e of its initial value.

J(t) =1

EM+

1

EK(1 − e

−t

t𝑟 ) +t

𝜂𝑀 (4.3.1)

Figure 4.55: Burger’s representation of a viscoelastic material.

First, the trends in creep compliance of the specimens without ethanol contact is studied.

The creep compliance curve exhibited by both the compression molded (Figure 4.56) and

rotomolded (Figure 4.57) specimens contains the three classical regimes found in dynamic

response of semi crystalline materials viz., the instantaneous elastic response, the lagging

viscoelastic response and the permanent flow response [204]. As the wood content increases

(irrespective of pine or oak), the corresponding compliance values are found to reduce for the

compression molded composites which indicates that the compression molded composite has

higher stiffness than the matrix LLDPE. This is demonstrated by the higher storage modulus

value of the CM specimens with wood flour than that of CM0 as seen from Figure 4.51 and

4.53.


195

Figure 4.56: Creep compliance of all compression molded composites before ethanol contact.

With the rotomolded composites, however, the trend is exactly the opposite. With the

increase in wood content (pine or oak), there is a net reduction in the stiffness. This is

demonstrated by the lower storage modulus values of the RM specimens than that of RM0 as

seen in Figures 4.52 and 4.54. Once again, the fundamental difference in composite formation

mechanism between the rotomolding and compression molding processes is manifested in these

exactly opposing trends. The sintering and consolidation pathway by which the rotomolded

composites once again shows that the trends in its material properties are harder to predict than

trends in the material properties of the composites made by phase change and consolidation-

based techniques such as compression molding.

0

2000

4000

6000

8000

10000

12000

14000

16000

0 50000 100000 150000

Com

plia

nce

(µm

2 /N)

Time (s)

CM0_FIT

CM5_FIT

CM5_O_FIT

CM10_FIT

CM10_O_FIT

CM20_FIT

CM0

CM5

CM5_O

CM10

CM10_O

CM20


196

Figure 4.57: Creep compliance of all rotomolded composites before ethanol contact

Now amongst the compression and rotomolded composites, a similar trend between the

oak and pine flour-based composites would be expected. This is because these composites were

made in the absence of compatibilising and using the same processing conditions. Based on the

results while there are some minor differences that can be seen between the pine and oak flour

composites in terms of modulus value, by and large, within the 10% concertation range of the

dispersed phase, not many differences were observable in the modulus values before ethanol

contact. However, it is possible that the inherent higher stiffness of the oak particles (owing to

outs hardwood nature) may make them harder to disperse than the correspondingly more elastic

softwood pine particles at higher concentrations. A more detailed analysis of the EM, EK and tr

will be able to shed more light on the subtle differences between the behaviors of the pine and

oak flour composites and will be done later in this Chapter.

Carrying on from the creep compliance trends of the dry compression molded and

rotomolded composites, the effect on ethanol sorption on the creep compliances is studied next

and the trends are shown in Figures 4.58 and 4.59. It can be seen that the global trends are the

0

2000

4000

6000

8000

10000

12000

14000

16000

0 50000 100000 150000

Com

plia

nce

(µm

2 /N)

Time (s)

RM0_FIT

RM5_FIT

RM5_O_FIT

RM10_FIT

RM10_O_FIT

RM20_FIT

RM0

RM5

RM5_O

RM10

RM10_O

RM20


197

same as in Figure 4.56 and 4.57. Essentially, there is an increase in compliance with wood flour

(whether pine or oak flour) incorporation for the rotomolded composites and a reduction in

compliance with wood flour (whether pine or oak flour) incorporation for the compression

molded composites. However, there is also a difference in the absolute creep compliance values

for the samples with ethanol sorption as compared to those without. Also, the differences

between the compression molded composites exposed to ethanol are much less pronounced than

the corresponding rotomolded composites. For instance, the equilibrium compliance of CM10

and CM10_O after exposure to ethanol at 30°C increase by 4% and 9% as compared to CM0

while the corresponding changes for the rotomolded composites RM10 and RM10_O are 15%

and 25%. This increased change in compliance is due to the increased porosity in the

rotomolded composites and speaks for the need to cap the dispersed phase concertation in the

rotomolding process at 5% by weight. The changes in creep compliance for the 5% systems are

a much more manageable 5% and 11% for the RM5 and RM5_O respectively after exposure to

ethanol at 30°C.

0

2000

4000

6000

8000

10000

12000

14000

16000

0 50000 100000 150000

Com

plia

nce

(µm

2 /N)

Time (s)

CM0_POST_6_FIT

CM5_POST_6_FIT

CM5_O_POST_6_FIT

CM10_POST_6_FIT

CM10_POST_6_FIT

CM20_POST_6_FIT

CM0_POST_6

CM5_POST_6

CM5_O_POST_6

CM10_POST_6

CM10_O_POST_6

CM20_POST_6

a


198

Figure 4.58: Creep compliance of all compression molded composites after sustained ethanol

contact at (a): 6°C, (b): 30°C.

Previous work by Widiastuti et al. [205] had shown that the liquid sorption has a

significant plasticization effect on their model semi-crystalline polymer –Polylactic Acid

(PLA). They observed that the creep strain and compliance values at equilibrium increased with

liquid content at all tested temperatures. It has to be noted that while the creep experimental

itself was run only for 60 min, the changes in the creep compliance and strain values were

significant enough for comparisons to be possible. Now, the polymer used in this thesis is of a

semi-crystalline nature as well and from Figures 4.58 and 4.59 it can be seen that there is a

change in compliance at equilibrium with the sorption of ethanol when compared to those

values in Figure 4.56 and 4.57. Therefore, the results of Widiastuti et al. [205] can help

analyzing this material system as well. Following their example, the trends in equilibrium

modulus values are analysed using Eq (3.2.2) shown in Section 3.1. The plot of these values vs

ethanol uptake for the compression molded and rotomolded composites are shown in Figure

4.60 and 4.61 respectively

0

2000

4000

6000

8000

10000

12000

14000

0 50000 100000 150000

Com

plia

nce

(µm

2 /N)

Time (s)

CM0_POST_30_FIT

CM5_POST_30_FIT

CM5_O_POST_30_FIT

CM10_POST_30_FIT

CM10_O_POST_30_FIT

CM20_POST_30_FIT

CM0_POST_30

CM5_POST_30

CM5_O_POST_30

CM10_POST_30

CM10_O_POST_30

CM20_POST_30

b


199

Figure 4.59: Creep compliance of all rotomolded composites after sustained ethanol contact at

(a): 6°C, (b): 30°C.

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0 50000 100000 150000

Com

plia

nce

(µm

2 /N)

Time (s)

RM0_POST_6_FIT

RM5_POST_6_FIT

RM5_O_POST_6_FIT

RM10_POST_6_FIT

RM10_O_POST_6_FIT

RM20_POST_6_FIT

RM0_POST_6

RM5_POST_6

RM5_O_POST_6

RM10_POST_6

RM10_O_POST_6

RM20_POST_6

a

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

24000

0 50000 100000

Com

plia

nce

(µm

2 /N)

Time (s)

RM0_POST_30_FIT

RM5_POST_30_FIT

RM5_O_POST_30_FIT

RM10_POST_30_FIT

RM10_O_POST_30_FIT

RM20_POST_30_FIT

RM0_POST_30

RM5_POST_30

RM5_O_POST_30

RM10_POST_30

RM10_O_POST_30

RM20_POST_30

b


200

Figure 4.60: Equilibrium Modulus vs ethanol uptake of the compression molded samples.

Amongst the compression molded specimens, it can be seen that there is a slight

negative slope for all specimens indicating that the properties tend to diminish with increased

ethanol content and this slope further reduces with increased wood content. However, at no

point does the equilibrium modulus value of any compression molded composite specimen

become lower than that of the plain LLDPE i.e. CM0. Numerically speaking without ethanol

contact, the equilibrium moduli of CM5, CM5_O, CM10, CM10_O and CM20 are 12%, 10%,

59%, 36% and 66% higher than that of CM0. With the exposure to ethanol at 6°C, these values

change to 12%, 12%, 42%, 27% and 62% higher than that of CM0. With exposure to ethanol

at 30°C these values change to 9%, 12%, 41%, 27% and 50% higher than that of CM0.

0

20

40

60

80

100

120

140

160

180

0.00 1.00 2.00 3.00

Equ

ilibr

ium

Mod

lus (

MPa

)


CM0

CM5

CM5_O

CM10

CM10_O

CM20


201

Figure 4.61: Equilibrium Modulus vs ethanol uptake of the rotomolded samples.

Amongst the rotomolded composites, similar negative slopes are seen for the modulus

values with increase ethanol content (Figure 4.61). However, the major difference between the

compression and rotomolded composites comes about due to the higher VP of the rotomolded

composites as shown in Section 4.1, Figure 4.8. This increased macroporosity ends up leading

to a higher equilibrium ethanol uptake in the rotomolded composites at both 6°C and 30°C as

compared to the compression molded composites. What this means is that while there is a

reduction in the equilibrium modulus of the compression molded composites with increased

ethanol uptake, the modulus value of compression molded composite material is always higher

than that of the plain CM0. This luxury is not afforded to the rotomolded composites owing to

the low dispersive effects and the sintering-based mechanism of molding itself. Thus, for the

rotomolded composites, it must be acknowledged that beyond a loading of 10% by weight of

the wood flour phase, the reduction in the modulus values are quite unsustainable. However,

based on the results in Section 4.1, Figure 4.16 and combining that with the trends in

equilibrium moduli, only the 5% by weight composition of the storage unit seems to be the

ideal way forward.

0

20

40

60

80

100

120

140

0.00 2.00 4.00 6.00 8.00 10.00

Equ

ilibr

ium

Mod

lus (

MPa

)


RM0

RM5

RM5_O

RM10

RM10_O

RM20


202

Widiastuti et al. [205] also demonstrated how to fit a viscoelastic material model to the

creep results. This could be used to isolate and analyse the viscous and elastic components of

the system. While Widiastuti et al. [205] studied these for a polymeric system, in this thesis,

similar analysis was done for a polymer composite specifically a LLDPE-wood flour

composite. As mentioned earlier, the fit to the creep data was provided using the Burger model.

Based on the viscoelastic view of the polymeric systems offered by this model, the compliance

curves for the various compositions were fit using Eq (4.3.1). Based on the fit, individual values

of EM, ηM, EK and tr were obtained for each composition and for each ethanol uptake value and

are analyzed below. The trends in EM and ηM are shown in Table 4.15 for the compression

molded composites and in Table 4.16 for the rotomolded composites. The trends in EK and tr

are shown in Table 4.17 for the compression molded composites and in Table 4.18 for the

rotomolded composites

As staed previously, EM is an indicator of the stiffness and pure elastic response of the

polymer [205]. The difference in trends between the rotomolded and compression molded

composites can be explained based on the formation mechanism of these two different

composites. In rotomolding, due to the sintering based formation mechanism, we observe two

kinds of macroscopic pores- those present naturally on the pine particles and those that

constitute the interface between the LLDPE phase and the pine phase. Also, it has to be noted

that the compression and rotomolded composites differ only in their macroporosity as their

micropores are found to be of a similar diameter as proven by PALS analysis shown in [206].

The amount of interfacial pores is much higher in the rotomolded samples than in the

compression molded and this is manifested by the VP trends as explained earlier. This also

explains the relatively larger uptake of the ethanol in the rotomolded samples as seen in Figures

4.34 and 4.35. Now, when the ethanol uptake does occur, the pores on the interface are more

readily accessible than the pores on the pine particles and definitely more accessible than the

free volume associated micropores in the LLDPE matrix. The ethanol molecules then fill up

those interfacial pores and this results in a net reduction in the EM due to the plasticizing effects

of these ethanol molecules. Amongst the compression molded specimens, there is a relatively

smaller amount of interfacial pores and those do not increase dramatically with increased pine

content. This means that the compression molded system is more compact than the

corresponding rotomolded system and the compactness of the compression molded composites

is independent of pine concentrations. Therefore, the overall stiffness goes up with more pine

incorporation for the compression molded composites and the CM10 specimen shows an EM


203

value 48% higher than that of CM0. Even with ethanol uptake this trend of increase in EM

compared to CM0 is maintained for all compression molded composites. The same CM10

sample exposed to ethanol sorption at 30°C shows an EM value that is once again 35% higher

than that of the CM0. Thus, a slight drop is seen for CM10 with ethanol uptake and this negative

drop is much more pronounced for the CM20 specimen. Amongst the CM10_O specimen this

trend is repeated showing that the differences between composites made via pine or oak are

minimal. In the absence of ethanol, the CM20 specimen shows an EM value that is about 50%

higher than that of CM0 but this deteriorates to 33% higher than that of CM0 after ethanol

sorption at 30°C. Therefore, even with the compression molded systems there is an upper bound

to effectively disperse the pine particles.

Now, as far as ηM is concerned, all the compression molded samples show a trend similar

to what was seen in the EM. The increase in ηM implies that the samples with higher pine content

(CM5, CM5_O, CM10 and CM10_O) are stiffer than the correspnding CM0. When ethanol

uptake is taken into account however, CM10, CM10_O and CM20 show a signifcant drop in

ηM. A drop in ηM represents permanent viscous flow and thus, the introduction of ethanol seems

to have a plasticizing effect on the compression molded composites. It has to be noted that the

drop seems to be similar for CM10 and CM20 and this indiciates that any reinforcing or

stiffening action shows diminishing returns after 10% by weight of pine flour filler is introduced

via compression molding.

Table 4.15: EM and ηM for the compression molded composites

Sample Conditions EM (MPa) ηM (mPa.s)

CM0

No ethanol 232 41

6°C 242 48

30°C 230 46

CM5

No ethanol 254 46

6°C 267 49

30°C 252 48

CM5_O No ethanol 284 56

6°C 268 64


204

30°C 267 54

CM10

No ethanol 343 60

6°C 344 54

30°C 309 52

CM10_O

No ethanol 307 70

6°C 311 86

30°C 294 68

CM20

No ethanol 349 61

6°C 332 60

30°C 306 53

With the use of pine flour or oak flour in the rotomolded material, the EM values do

reduce compared to RM0. RM5 has an EM that is 24% lower than that of RM0 and further

addition of pine flour for RM10 and RM20 ends up producing composites with EM values that

are 27% and 29% respectively lower than that of RM0. RM5_O has an EM value that is 27%

lower than RM0 while RM10_O is 33% lower than RM0 and so, these trends are similar

between pine and oak flour based rotomolded composites.

Overall a reducing trend is seen and in the absence of ethanol uptake all the drops in EM

are quite similar. Once ethanol uptake occurs, the differences in durabvility amongst the

different rotomolded composites becomes quite clear. The RM5 and RM10 specimens seem to

handle ethanol uptake with minimal further reduction to EM at 6°C and even after ethanol uptake

at 30°C, RM10 sees an EM drop of about 36% while RM5 sees a similar drop to about 31%.

Thus, both RM5 and RM10 react similarly to ethanol uptake and are fairly capable at retaining

stiffness inspite of having quite porous microstructure shown by their corresponding VP values

of 9% and 13% respectively. RM5_O shows this sort of retention in modulus value with ethanol

uptake but RM10_O however drops by almost 50% after ethanol uptake at 30°C. Therefore,

RM10_O is not an approprate composition unless external strengthening of the structue is

provided. RM5_O, RM5 and RM10 seem to be the most appropraite based on these results.

RM20, also, fails quite significantly to maintain any durability at all with the EM dropping by

55% after ethanol uptake at 30°C and thus is not a viable composition for any potential storage

application.


205

Amongst the rotomolded composites, there is also a consistent reduction in the ηM at all

ethanol concentrations. Thus, while permanent viscous flow is seen for all rotomolded

composites, the extent of reduction in this viscosity is 44% for RM5, 63% for RM10 and 68%

for RM20 after ethanol contact at 30°C compared to those values before ethanol sorption. For

comparision, the compression molded specimens after contact with ethanol at 30°C show a

slight increase at all for CM10 and CM20 of 8% and10% respectively and a slight 4% drop for

CM5 indicating that the plasticizing action of ethanol is much more pronounced amongst the

rotomolded composites.

Table 4.16: EM and ηM for the rotomolded composites

Sample Conditions EM (MPa) ηM (mPa.s)

RM0

No ethanol 296 69

6°C 297 61

30°C 295 74

RM5

No ethanol 226 45

6°C 209 49

30°C 202 41

RM5_O

No ethanol 215 56

6°C 226 53

30°C 198 66

RM10

No ethanol 217 49

6°C 223 59

30°C 188 27

RM10_O

No ethanol 198 56

6°C 196 59

30°C 166 32

RM20 No ethanol 209 54


206

6°C 189 37

30°C 132 24

The second set of results obtained from fitting Burger’s model are related to the Kelvin

Voigt modulus and the relaxation time. Both parameters are associated with the amorphous part

of a semi-crystalline polymer. Amongst the various EK values it is seen that the compression

molded composites irrespective of composition or the type of dispersed phase used show a

maximum drop of around 10-12% from the values pre-ethanol sorption. This drop is due to the

slight plasticizing effect of the sorbed ethanol and is more obvious amongst the wood flour

composites than with the plain polymer because of the hydrophilic nature of both dispersed

phases and the permeant.

Table 4.17: EK for the compression molded composites

Sample Conditions EK (MPa)

CM0

No ethanol 140

6°C 134

30°C 136

CM5

No ethanol 156

6°C 155

30°C 146

CM5_O

No ethanol 156

6°C 144

30°C 150

CM10

No ethanol 219

6°C 201

30°C 195

CM10_O

No ethanol 184

6°C 173

30°C 174

CM20

No ethanol 226

6°C 210

30°C 199


207

Table 4.18: EK for the rotomolded composites

Sample Conditions EK (MPa)

RM0

No ethanol 151

6°C 160

30°C 150

RM5

No ethanol 153

6°C 142

30°C 139

RM5_O

No ethanol 156

6°C 131

30°C 121

RM10

No ethanol 126

6°C 123

30°C 120

RM10_O

No ethanol 135

6°C 106

30°C 96

RM20

No ethanol 110

6°C 83

30°C 89

The tr values (Figure 4.62 and Figure 4.63), for the most part, show a reducing trend

with increasing ethanol contact. This again speaks to the plasticizing nature of the ethanol for

the system. The only samples this is not seen for are the samples without any wood flour

incorporation i.e. CM0 and RM0. Therefore, the plasticizing effect of ethanol uptake in our

system can only be observed in the presence of the filler material.


208

Figure 4.62: tr for all compression molded composites

Figure 4.63: tr for all rotomolded composites

0

500

1000

1500

2000

2500

3000

0.00 1.00 2.00 3.00

tr (s

)


CM0

CM5

CM5_O

CM10

CM10_O

CM20

0

500

1000

1500

2000

2500

3000

3500

0.00 2.00 4.00 6.00 8.00 10.00

tr (s

)


RM0

RM5

RM5_O

RM10

RM10_O

RM20


209

Based on the results in dynamic properties and the trends thereof as a function of wood

flour concentration and ethanol uptake, an understanding of the maximum loading of wood

flour before a general downtrend in mechanical performance begins has been established. For

the compression molding process, this happens to be at a wood flour concentration of 10% by

weight while for the rotomolding process, it can be stated that it happens to be between 5% and

10% by weight of wood flour, both independent of the type of wood flour used.

210

CHAPTER 5

CONCLUSIONS AND

FUTURE WORK The conclusions of the work conducted in this thesis can be divided in two categories

as shown below:

1. Experimental conclusions

2. MD Simulation conclusions.

5.1 Experimental Conclusions

The experimental conclusions of this thesis are concerned with the nature of LLDPE

natural fibre composites and their efficacy for storage unit manufacture, the potential for

permeation property control and the retention of mechanical performance under stresses arising

from storage application.

1. From a survey of the available literature in Chapter 2, it was determined how the method

of processing used and the associated parameters can greatly affect permeability in

various multi-phase polymeric systems. Examples of such parameters were the cooling

rates post fabrication, geometric parameters like product wall thickness and the

presence/absence of sharp, the system porosity (specifically the effect of process shear

on porosity) and the type of dispersed phase used. As the control we wanted to achieve

involved a controlled increase in polymer permeability and most of the cases in

literature dealt with controlled reduction manipulating process shear and the effective

use of dispersed phases were found to have most potential.

2. In terms of process shear, we found that an overall low shear fabrication technique or

using a combination of low barrel temperature profile and high screw speeds (in

extrusion) would have a significant effect on the porosity and often results in increased

void space, larger segmental mobility and increased permeability. Any consequent

reduction in mechanical properties can be resolved by using an external scaffold to hold

Conclusions and Future Work

211

the structure together, but the scaffold has to be designed in such a way that it does not

reduce the cross-sectional area available for permeability.

3. In terms of the dispersed phases to be used, we found that by using certain naturally

occurring and naturally permeable dispersed phase materials, it is possible to have a

control on the water vapour and possibly the oxygen permeability of the fabricated

polymer. This control means both an increase and a reduction in overall permeability

can be seen with changes in concentration of the fibrils. Using hydrophilic natural fibres

as the dispersed phase in a hydrophobic polymer matrix with little/no compatibilization

would increase the permeability of the composite. While it is also possible to have a

controlled increase in the permeability by surface treatment of natural fibres, as we were

dealing with potential food contact applications, it is essential to account for the toxicity

of the treated fibres. However, the reduction in the mechanical properties like impact

strength which can arise from such agglomeration had to be addressed before the units

fabricated from such a composite may be used commercially.

4. At the end of Chapter 2, we outlined the main research and engineering objectives of

this thesis and the results we were looking for. In brief, they involved a thorough

analysis of the effect of microstructures and structural porosity on the gas and liquid

transport in and on the mechanical attributes of our composite system. They also

involved an in depth first principles study of the process of permeation, diffusion and

sorption of relevant low molecular weight permeants through Polyethylene and through

the chosen dispersed phase using MD. We also wanted to use the MD algorithms we

would develop in the thesis to be used to predict trends in transport and mechanical

properties of the composites in conjunction with semi-empirical modelling. We will

cover those in Section 5.2.

5. Visually speaking, the compression molded and rotomolded composites differed quite

significantly. The surfaces of the rotomolded composites possess a smooth outer surface

which is in contact with the mold and a rough inner surface away from the mold. The

compression molded composites show no such morphological difference between their

two surfaces. Further, the rotomolded composites show porosity on the rough surface,

smooth surface and in the microstructure while such porosity is only found in the

microstructure of the compression molded composites.

6. Some observations were also made regarding the nature of product formation in the

rotomolded systems. Using a series of micrographs obtained using optical microscopy,


212

we found that the rotomolded composite went through a sintering phase followed by

phase consolidation unlike the compression molded composites which went through

complete phase change followed by phase consolidation. This also explained why there

was a difference between the two surfaces of the rotomolded composites.

7. The observed porosity in the rotomolded composites was then attempted to be correlated

to a suitable intensive property. The two choices we had were either the density or the

overall crystallinity of the composites. Density and consequently, the VP parameter we

developed was found to be extremely effective in modelling oxygen permeability for

both types of LLDPE natural fibre composites we studied during the course of this

thesis. Thus, the overall oxygen permeability of the system could be directly correlated

to an easily measured intensive parameter.

8. In terms of the potential design of a viable storage unit, it had to be ensured that the

introduction of porosity to controllably increase permeability did not result in a major

detriment to the mechanical properties. Also, with increased microstructural porosity,

the diffusion tendency of the stored liquid material also increases. Therefore, we had to

ensure that these results of controlled permeability increase were also juxtaposed with

the corresponding trends in the mechanical and liquid uptake properties. The mechanical

properties were divided into two types viz., static (tensile strength, flexural strength and

impact strength) and dynamic (storage modulus in cantilever mode, storage modulus in

tensile mode and creep). We studied the trends in these properties as a function of

dispersed phase (oak or pine flour) concertation and ethanol uptake (no uptake, uptake

after sorption equilibrium at 6°C and uptake after sorption equilibrium at 30°C). Based

on these results and the trends thereof, an understanding of the maximum loading of

dispersed phase before a general downtrend in mechanical performance begins was

established. For the compression molding process, this happens to be at a wood flour

concentration of 10% by weight while for the rotomolding process, it can be stated that

it happens to be between 5% and 10% by weight of wood flour, both independent of the

type of wood flour used.


213

5.2 MD simulation conclusions

From the work done on molecular simulations, in this thesis, we obained the followiung

conclusions:

1. The assumption that transport activity in a semi-crystalline polymer happens only

through the amorphous phase of that polymer is an unnecessary assumption. In fact, the

simulation and analysis of the extremely small (and yet, non-zero) transport through the

crystalline phase will help offer a more holistic view of the entire process.

2. As far as transport properties such as diffusion are concerned, irrespective of the state

of the diffusant, the models that take into account interaction and overlaps between the

dispersed and continuous phases (for instance, the M-W-S and the F and B models) are

the best suited. The models, however, only seem to work for compression molding based

on the observation that the δ values seen for the rotomolding process are all consistently

higher (bar the Rule of Mixtures but this is because of the purely empirical nature of

that model) than that seen for compression molding. In some case, the δ values seen are

in excess of 100 indicating that the composite created by rotomolding is completely

unlike the ones created by phase change and consolidation like compression molding.

One of the ways to address this would be to incorporate macroscopic porosity indicators

like VP in the model expression but, at best, this is a stop gap, whihc means there is big

potential to develop semi-empirical models for sintering based process like rotomolding

(we will explain this in more detail in the Future Work in Chapter 5).

3. An effective combination of MD and semi-empirical modelling is a highly versatile

technique. In order to model any general phenomena of interest, we could follow the

steps below

a. Isolate the individual phases of a composite system and simulate and validate

those models. The validation can be performed using any intensive property such

as free volume pore size or density.

b. Simulate the particular phenomenon of interest on each isolated phase, and then

combine the results of each individual phase using semi-empirical models

available in literature.

4. The final conclusion is that the choice of semi-empirical model makes a masisve

difference to the accyracy of the methodology. In our work, it is found that the models

that incorporate more characteristic parameters of the system, for instance, aspect ratios,

constriction ratios, and values that represent the type of interfacial morphology (stacked


214

and overlapping as opposed to isolated and non-overlapping) are more preferable to

models that do not have any of these values as part of the model expression.

5.3 Future Work

Presented in this section are recommendations which, in the view of author, present

valuable extensions to the present work.

1. A more comprehensive study of the wetting process and surface interaction between

wood flour and polymer matrix in the rotomolding process

2. Increasing rigour of the VP parameter so that it can be used as a differentiator between

samples produced by sintering and those produced by phase change followed by

consolidation.

3. The present work may provide a feasible composition for storing food products with

high ethanol content. However, additional researches in development of a promising

rotomolded LLDPE-natural fibre composite package system are essential for

industrialization. According to the results revealed in this work, the optimal application

conditions for potential storage include: working at a dispersed phase concentration

between 5% and 10% by weight, operating at temperatures lower than 30 °C and

possibly using external scaffolds to compensate for long term creep displacement. The

next step is to assess manufacturing feasibility and then conduct a series of pilot scale

analysis based on the methodology proposed in this work.

4. Improvement of all the simulated models via the incorporation of transitional regimes

between the amorphous and crystalline phases.

5. Validating the MD + semi-empirical modelling approach for thermosetting composites

as opposed to the thermoplastic composites studied in this thesis.

215

REFERENCES [1] R.J. Shields, D. Bhattacharyya, S. Fakirov, Oxygen permeability analysis of microfibril

reinforced composites from PE/PET blends, Composites Part A: Applied Science and

Manufacturing 39(6) (2008) 940-949.

[2] J.W. Han, L. Ruiz‐Garcia, J.P. Qian, X.T. Yang, Food Packaging: A Comprehensive Review

and Future Trends, Comprehensive Reviews in Food Science and Food Safety 17 (4) (2018)

860-877.

[3] A. Azzi, D. Battini, A. Persona, F. Sgarbossa, Packaging Design: General Framework and

Research Agenda, Packaging Technology and Science 25(8) (2012) 435-456.

[4] J.-W. Han, L. Ruiz-Garcia, J.-P. Qian, X.-T. Yang, Food Packaging: A Comprehensive

Review and Future Trends, Comprehensive Reviews in Food Science and Food Safety 17(4)

(2018) 860-877.

[5] R. Kay, M. Desmulliez, A review of stencil printing for microelectronic packaging,

Soldering & Surface Mount Technology 24(1) (2012) 38-50.

[6] R. Geyer, J.R. Jambeck, K.L. Law, Production, use, and fate of all plastics ever made,

Science Advances 3(7) (2017) e1700782.

[7] A. Fendler, M.P. Villanueva, E. Gimenez, J.M. Lagarón, Characterization of the barrier

properties of composites of HDPE and purified cellulose fibers, Cellulose 14(5) (2007) 427-

438.

[8] H. Boukehili, P. Nguyen-Tri, Helium gas barrier and water absorption behavior of bamboo

fiber reinforced recycled polypropylene, Journal of Reinforced Plastics and Composites 31(23)

(2012) 1638-1651.

[9] S.C. George, S. Thomas, Transport phenomena through polymeric systems, Progress in

Polymer Science 26(6) (2001) 985-1017.

[10] A. Hiltner, R.Y.F. Liu, Y.S. Hu, E. Baer, Oxygen transport as a solid-state structure probe

for polymeric materials: A review, Journal of Polymer Science Part B: Polymer Physics 43(9)

(2005) 1047-1063.

[11] G. Choudalakis, A.D. Gotsis, Permeability of polymer/clay nanocomposites: A review,

European Polymer Journal 45(4) (2009) 967-984.

[12] R.J. Crawford, Recent advances in the manufacture of plastic products by rotomoulding,

Journal of Materials Processing Technology 56(1) (1996) 263-271.

References

216

[13] P.L. Ramkumar, D.M. Kulkarni, V.V.R. Abhijit, A. Cherukumudi, Investigation of Melt

Flow Index and Impact Strength of Foamed LLDPE for Rotational Moulding Process, Procedia

Materials Science 6 (2014) 361-367.

[14] P.L. Ramkumar, A. Ramesh, P.P. Alvenkar, N. Patel, Prediction of heating cycle time in

Rotational Moulding, Materials Today: Proceedings 2(4) (2015) 3212-3219.

[15] M.A. Rao, J.L. Throne, Principles of rotational molding, Polymer Engineering & Science

12(4) (1972) 237-264.

[16] K. Prasad, M. Nikzad, I. Sbarski, Permeability control in polymeric systems: a review,

Journal of Polymer Research 25(11) (2018) 232.

[17] B.J. Alder, T.E. Wainwright, Phase Transition for a Hard Sphere System, The Journal of

Chemical Physics 27(5) (1957) 1208-1209.

[18] A. Rahman, F.H. Stillinger, Molecular Dynamics Study of Liquid Water, The Journal of

Chemical Physics 55(7) (1971) 3336-3359.

[19] J.A. McCammon, B.R. Gelin, M. Karplus, Dynamics of folded proteins, Nature 267(5612)

(1977) 585-590.

[20] O. Maltseva, N. Mozhaeva, Empirical Modeling of the Total Electron Content of the

Ionosphere, Empirical Modeling and Its Applications, InTechOpen 2016.

[21] A. Scharnhorst, K. Börner, P. van den Besselaar, Models of Science Dynamics: Encounters

Between Complexity Theory and Information Sciences, Springer Berlin Heidelberg2012.

[22] E. Kayabasi, H. Kurt, Simulation of heat exchangers and heat exchanger networks with an

economic aspect, Engineering Science and Technology, An International Journal 21(1) (2018)

70-76.

[23] S. Septien, F.J. Escudero Sanz, S. Salvador, S. Valin, Steam gasification of char from wood

chips fast pyrolysis: Development of a semi-empirical model for a fluidized bed reactor

application, Biomass and Bioenergy 77 (2015) 64-74.

[24] Y.S. Choi, S.J. Kim, D. Kim, A Semi-empirical Correlation for Pressure Drop in Packed

Beds of Spherical Particles, Transport in Porous Media 75(2) (2008) 133-149.

[25] D.A. Matoz-Fernandez, M.V. Dávila, P.M. Pasinetti, A.J. Ramirez-Pastor, A

semiempirical model for adsorption of binary mixtures, Physical Chemistry Chemical Physics

16(43) (2014) 24063-24068.

[26] A.V. Fedorov, A.V. Shulgin, Y.S. Korneeva, Semi-empirical model of the combustion

wave in a gas suspension of magnesium particles, Combustion, Explosion, and Shock Waves

51(5) (2015) 560-567.

References

217

[27] K. Prasad, M. Nikzad, C.M. Doherty, I. Sbarski, Diffusion of low-molecular-weight

permeants through semi-crystalline polymers: combining molecular dynamics with semi-

empirical models, Polymer International 67(6) (2018) 717-725.

[28] O.L. Gaskova, Semiempirical model for the description of sorption equilibria on clay

mineral surfaces, Geochemistry International 47(6) (2009) 611-622.

[29] M. Corcione, A Semi-Empirical Model for Predicting the Effective Dynamic Viscosity of

Nanoparticle Suspensions AU - Corcione, Massimo, Heat Transfer Engineering 33(7) (2012)

575-583.

[30] D.G. Clerc, Mechanical hardness and elastic stiffness of alloys: semiempirical

models1Contribution of NIST—an agency of the U.S. Government. Not Subject to Copyright

in the United States1, Journal of Physics and Chemistry of Solids 60(1) (1999) 83-102.

[31] G.J. van Amerongen, The Permeability of different rubbers to gases and its relation to

diffusivity and solubility, Journal of Applied Physics 17 (1946) 972.

[32] P. Meares, The Diffusion of Gases Through Polyvinyl Acetate 1, Journal of the American

Chemical Society 76(13) (1954) 3415-3422.

[33] A.R. Berens, H.B. Hopfenberg, Diffusion of organic vapors at low concentrations in glassy

PVC, polystyrene, and PMMA, Journal of Membrane Science 10(2) (1982) 283-303.

[34] M. Buntinx, G. Willems, G. Knockaert, D. Adons, J. Yperman, R. Carleer, R. Peeters,

Evaluation of the Thickness and Oxygen Transmission Rate before and after Thermoforming

Mono- and Multi-layer Sheets into Trays with Variable Depth, Polymers 6(12) (2014) 3019.

[35] B. Tan, N.L. Thomas, A review of the water barrier properties of polymer/clay and

polymer/graphene nanocomposites, Journal of Membrane Science 514 (2016) 595-612.

[36] Y. Cui, S. Kumar, B. Rao Kona, D. van Houcke, Gas barrier properties of polymer/clay

nanocomposites, RSC Advances 5(78) (2015) 63669-63690.

[37] V. Compañ, L.F. Del Castillo, S.I. Hernández, M.M. López-González, E. Riande,

Crystallinity effect on the gas transport in semicrystalline coextruded films based on linear low

density polyethylene, Journal of Polymer Science Part B: Polymer Physics 48(6) (2010) 634-

642.

[38] V. Compañ, A. Andrio, M.L. López, E. Riande, Effect of annealing on the permeation

characteristics of gases of coextruded LLDPE films, Polymer 37(26) (1996) 5831-5837.

References

218

[39] L.F. del Castillo, S.I. Hernández, V. Compañ, Obtaining the Tortuosity Factor as a

Function of Crystallinity in Polyethylene Membranes, in: A. Maciel-Cerda (Ed.), Membranes:

Materials, Simulations, and Applications, Springer International Publishing, Cham, 2017, pp.

77-86.

[40] S. Fakirov, R.J. Shields, C. Fuchs, K. Friedrich, D. Bhattacharyya, Polyolefin/PET

Microplates–Reinforced Composites with Improved Barrier Properties, International Journal of

Polymeric Materials and Polymeric Biomaterials 57(1) (2008) 33-53.

[41] H. Su, J. Xue, P. Cai, J. Li, S. Guo, Structure and oxygen-barrier properties of (linear low-

density polyethylene/ethylene–vinyl alcohol copolymer)/linear low-density polyethylene

composite films prepared by microlayer coextrusion, Journal of Applied Polymer Science

132(27) (2015).

[42] J.T. Yeh, H.Y. Chen, Blending and oxygen permeation properties of the blown films of

blends of modified polyamide and ethylene vinyl alcohol copolymer with varying vinyl alcohol

contents, Journal of Materials Science 42(14) (2007) 5742-5751.

[43] A. Okada, Y. Fukushima, M. Kawasumi, S. Inagaki, A. Usuki, S. Sugiyama, T. Kurauchi,

O. Kamigaito, Composite material and process for manufacturing same, US Patent 4739007A,

Toyota Central R&D Labs Inc, United States, 1988.

[44] L.A. Utracki, Introduction to Polymer Blends, in: L.A. Utracki (Ed.), Polymer Blends

Handbook, Springer Netherlands, Dordrecht, 2003, pp. 1-122.

[45] Y. Zhong, D. Janes, Y. Zheng, M. Hetzer, D. De Kee, Mechanical and oxygen barrier

properties of organoclay-polyethylene nanocomposite films, Polymer Engineering & Science

47(7) (2007) 1101-1107.

[46] F. Garbassi, E. Occhiello, Plasma deposition of silicon-containing layers on polymer

substrates, Macromolecular Symposia 139(1) (1999) 107-114.

[47] S. Ahmadzadeh, A. Nasirpour, J. Keramat, N. Hamdami, T. Behzad, S. Desobry,

Nanoporous cellulose nanocomposite foams as high insulated food packaging materials,

Colloids and Surfaces A: Physicochemical and Engineering Aspects 468 (2015) 201-210.

[48] H.L. Stein, Composition and process for making porous articles from ultra high molecular

weight polyethylene, US Patent 4 925 880, CNA Holdings LLC, United States, 1990.

[49] S. Pillay, U.K. Vaidya, G.M. Janowski, Effects of moisture and UV exposure on liquid

molded carbon fabric reinforced nylon 6 composite laminates, Composites Science and

Technology 69(6) (2009) 839-846.

References

219

[50] C.H. Shen, G.S. Springer, Moisture Absorption and Desorption of Composite Materials,

Journal of Composite Materials 10(1) (1976) 2-20.

[51] Z.A.M. Ishak, J.P. Berry, Hygrothermal aging studies of short carbon fiber reinforced

nylon 6.6, Journal of Applied Polymer Science 51(13) (1994) 2145-2155.

[52] L. Robeson, Historical Perspective of Advances in the Science and Technology of Polymer

Blends, Polymers 6(5) (2014) 1251.

[53] T. Johnson, S. Thomas, Nitrogen/oxygen permeability of natural rubber, epoxidised natural

rubber and natural rubber/epoxidised natural rubber blends, Polymer 40(11) (1999) 3223-3228.

[54] Y. Geerts, S. Gillard, G. Geuskens, Morphology and permeability of polymer blends—I.

Crosslinked EPDM-silicone blends, European Polymer Journal 32(2) (1996) 143-145.

[55] B. Marcandalli, G. Testa, A. Seves, E. Martuscelli, Oxygen permeation through films of

polypropylene/hydrogenated oligocyclopentadiene blends, Polymer 32(18) (1991) 3376-3380.

[56] F. Roberto Passador, A. Collà Ruvolo-Filho, L.A. Pessan, Structural, thermal, and gas

transport properties of HDPE/LLDPE blend-based nanocomposites using a mixture of HDPE-

g-MA and LLDPE-g-MA as compatibilizer, Polymer Engineering & Science 56(7) (2016) 765-

775.

[57] J. Urquijo, S. Dagréou, G. Guerrica-Echevarría, J.I. Eguiazábal, Structure and properties

of poly(lactic acid)/poly(ε-caprolactone) nanocomposites with kinetically induced nanoclay

location, Journal of Applied Polymer Science 133(33) (2016).

[58] J. Lange, Y. Wyser, Recent innovations in barrier technologies for plastic packaging—a

review, Packaging Technology and Science 16(4) (2003) 149-158.

[59] B. John, S.P. Thomas, K.T. Varughese, Z. Oommen, S. Thomas, The effects of blend ratio,

compatibilization and dynamic vulcanization on permeation of gases through HDPE/EVA

blends, Journal of Polymer Research 18(5) (2011) 1101-1109.

[60] P. Santamaría, I. González, J.I. Eguiazábal, Mechanical and barrier properties of ternary

nanocomposite films based on polycarbonate/amorphous polyamide blends modified with a

nanoclay, Polymers for Advanced Technologies 26(6) (2015) 665-673.

[61] M.C. Mistretta, P. Fontana, M. Ceraulo, M. Morreale, F.P. La Mantia, Effect of

compatibilization on the photo-oxidation behaviour of polyethylene/polyamide 6 blends and

their nanocomposites, Polymer Degradation and Stability 112 (2015) 192-197.

[62] S.C. Agwuncha, S.J. Owonubi, E.R. Sadiku, R.D.S. Zwane, B. Manjula, J. Jayaramudu,

V.O. Ojijo, B.A. Aderibigbe, G.M. Raghavendra, Chapter 11 - Immiscible Polymer Blends

References

220

Stabilized with Nanophase, in: S. Thomas, R. Shanks, S. Chandrasekharakurup (Eds.), Design

and Applications of Nanostructured Polymer Blends and Nanocomposite Systems, William

Andrew Publishing, Boston, 2016, pp. 215-237.

[63] I.K. Hong, S. Lee, Properties of ultrasound-assisted blends of poly(ethylene terephthalate)

with polycarbonate, Journal of Industrial and Engineering Chemistry 19(1) (2013) 87-93.

[64] I. Krasnou, S. Gårdebjer, E. Tarasova, A. Larsson, G. Westman, A. Krumme, Permeability

of water and oleic acid in composite films of phase separated polypropylene and cellulose

stearate blends, Carbohydrate Polymers 152 (2016) 450-458.

[65] R. Lin, D. Bhattacharyya, S. Fakirov, Morphology of Rotationally Moulded Microfibril

Reinforced Composites and its Effect on Product Performance, Key Engineering Materials 334-

335 (2007) 349-352.

[66] Y. Zhang, L. Shao, D. Dong, Y. Wang, Enhancement of water and organic solvent

resistances of a waterborne polyurethane film by incorporating liquid polysulfide, RSC

Advances 6(21) (2016) 17163-17171.

[67] A. Sujith, G. Unnikrishnan, C.K. Radhakrishnan, Sorption and Mechanical Properties of

Nitrile Rubber Compatibilized Natural Rubber—Poly (Ethylene-Co-Vinyl Acetate) Blends,

Journal of Elastomers & Plastics 40(1) (2008) 17-38.

[68] P. Frisk, J. Laurent, Nanocomposite Polymer Container, US Patent 5972448, Tetra Laval

Holdings & Finance, United States, 1999.

[69] S.N.S. Tan, A.A. Somashekar, D. Bhattacharyya, Development and analysis of gas barrier

properties of microfibrillar polymer–polymer composites, Journal of Materials Science 50(22)

(2015) 7384-7397.

[70] D.R. Paul, L.M. Robeson, Polymer nanotechnology: Nanocomposites, Polymer 49(15)

(2008) 3187-3204.

[71] M. Mohamadi, H. Garmabi, F. Keshavarzi, An investigation of the effects of

organomodified-fluoromica on mechanical and barrier properties of compatibilized high

density polyethylene nanocomposite films, Journal of Plastic Film & Sheeting 32(1) (2016) 10-

33.

[72] M. Tayebi, A. Ramazani S.A, M.T. Hamed Mosavian, A. Tayyebi, LDPE/EVA/graphene

nanocomposites with enhanced mechanical and gas permeability properties, Polymers for

Advanced Technologies 26(9) (2015) 1083-1090.

References

221

[73] P. Atayev, T. Bekat, M. ÖNer, The effects of zinc oxide and clay nanoparticles on thermal,

barrier and mechanical properties of polypropylene and high density polyethylene, Sigma:

Journal of Engineering & Natural Sciences 33(1) (2015) 16-21.

[74] A. Al-Jabareen, H. Al-Bustami, H. Harel, G. Marom, Improving the oxygen barrier

properties of polyethylene terephthalate by graphite nanoplatelets, Journal of Applied Polymer

Science 128(3) (2013) 1534-1539.

[75] G.F. Li, W.H. Luo, M. Xiao, S.J. Wang, Y.Z. Meng, Biodegradable poly(propylene

carbonate)/layered double hydroxide composite films with enhanced gas barrier and

mechanical properties, Chinese Journal of Polymer Science 34(1) (2016) 13-22.

[76] G.J. Pavani, S. Pavani, S. Adalberto, C.A. Ferreira, Application of Polymeric

Nanocomposites and Carbon Fiber Composites in the Production of Natural Gas Reservoirs,

Journal of Nanomaterials 2015 (2015) 7.

[77] A.I. Alateyah, H.N. Dhakal, Z.Y. Zhang, Water Absorption Behavior, Mechanical and

Thermal Properties of Vinyl Ester Matrix Nanocomposites Based on Layered Silicate, Polymer-

Plastics Technology and Engineering 53(4) (2014) 327-343.

[78] L.J. Burcham, M.R. Vanlandingham, R.F. Eduljee, J.W. Gillespie Jr., Moisture effects on

the behavior of graphite/polyimide composites, Polymer Composites 17(5) (1996) 682-690.

[79] A. Zhou, L.H. Tam, Z. Yu, D. Lau, Effect of moisture on the mechanical properties of

CFRP–wood composite: An experimental and atomistic investigation, Composites Part B:

Engineering 71 (2015) 63-73.

[80] J. George, M.S. Sreekala, S. Thomas, A review on interface modification and

characterization of natural fiber reinforced plastic composites, Polymer Engineering & Science

41(9) (2001) 1471-1485.

[81] J. Holbery, D. Houston, Natural-fiber-reinforced polymer composites in automotive

applications, JOM 58(11) (2006) 80-86.

[82] F. Luzi, E. Fortunati, A. Jiménez, D. Puglia, D. Pezzolla, G. Gigliotti, J.M. Kenny, A.

Chiralt, L. Torre, Production and characterization of PLA_PBS biodegradable blends

reinforced with cellulose nanocrystals extracted from hemp fibres, Industrial Crops and

Products 93 (2016) 276-289.

[83] L. Mohammed, M.N.M. Ansari, G. Pua, M. Jawaid, M.S. Islam, A Review on Natural

Fiber Reinforced Polymer Composite and Its Applications, International Journal of Polymer

Science 2015 (2015) 15.

References

222

[84] S. Shinoj, R. Visvanathan, S. Panigrahi, M. Kochubabu, Oil palm fiber (OPF) and its

composites: A review, Industrial Crops and Products 33(1) (2011) 7-22.

[85] E.O. Cisneros-López, A.A. Pérez-Fonseca, F.J. Fuentes-Talavera, J. Anzaldo, R.

González-Núñez, D. Rodrigue, J.R. Robledo-Ortíz, Rotomolded polyethylene-agave fiber

composites: Effect of fiber surface treatment on the mechanical properties, Polymer

Engineering & Science 56(8) (2016) 856-865.

[86] B.A.C. Siaotong, L.G. Tabil, S.A. Panigrahi, W.J. Crerar, Extrusion Compounding of Flax-

Fiber-Reinforced Polyethylene Composites: Effects of Fiber Content and Extrusion Parameters,

Journal of Natural Fibers 7(4) (2010) 289-306.

[87] K.A. Krishnan, K.R. Jose, K.E. George, Sisal nanofibril reinforced

polypropylene/polystyrene blends: Morphology, mechanical, dynamic mechanical and water

transmission studies, Industrial Crops and Products 71 (2015) 173-184.

[88] J. George, S.S. Bhagawan, S. Thomas, Effects of environment on the properties of low-

density polyethylene composites reinforced with pineapple-leaf fibre, Composites Science and

Technology 58(9) (1998) 1471-1485.

[89] G. Singer, G. Sinn, K. Schwendtner, H.C. Lichtenegger, R. Wan-Wendner, Time-

dependent changes of mechanical properties of polymer-based composite materials for

adhesive anchor systems, Composite Structures 196 (2018) 155-162.

[90] A.F. Camara Bezerra, L. Hecker de Carvalho, W.S. Cavalcanti, A.G. Barbosa, Mechanical

behavior of composites reinforced with fibers caroa, Fibers and Polymers 17(11) (2016) 1908-

1915.

[91] V. Tserki, P. Matzinos, C. Panayiotou, Novel biodegradable composites based on treated

lignocellulosic waste flour as filler. Part II. Development of biodegradable composites using

treated and compatibilized waste flour, Composites Part A: Applied Science and Manufacturing

37(9) (2006) 1231-1238.

[92] P.A. Sreekumar, K. Joseph, G. Unnikrishnan, S. Thomas, A comparative study on

mechanical properties of sisal-leaf fibre-reinforced polyester composites prepared by resin

transfer and compression moulding techniques, Composites Science and Technology 67(3)

(2007) 453-461.

[93] G. Galgali, C. Ramesh, A. Lele, A Rheological Study on the Kinetics of Hybrid Formation

in Polypropylene Nanocomposites, Macromolecules 34(4) (2001) 852-858.

[94] C.C. Ibeh, M. Bubacz, Current Trends in Nanocomposite Foams, Journal of Cellular

Plastics 44(6) (2008) 493-515.

References

223

[95] J. Pinto, M. Dumon, M.A. Rodriguez-Perez, 9 - Nanoporous polymer foams from

nanostructured polymer blends: Preparation, characterization, and properties, in: P.M. Visakh,

G. Markovic, D. Pasquini (Eds.), Recent Developments in Polymer Macro, Micro and Nano

Blends, Woodhead Publishing2017, pp. 237-288.

[96] S.T. Lee, D.P.K. Scholz, Polymeric Foams: Technology and Developments in Regulation,

Process, and Products, CRC Press2008.

[97] I. Babaei, M. Madanipour, M. Farsi, A. Farajpoor, Physical and mechanical properties of

foamed HDPE/wheat straw flour/nanoclay hybrid composite, Composites Part B: Engineering

56 (2014) 163-170.

[98] F. Wan, M.P. Tran, C. Leblanc, E. Béchet, E. Plougonven, A. Léonard, C. Detrembleur,

L. Noels, J.M. Thomassin, V.D. Nguyen, Experimental and computational micro-mechanical

investigations of compressive properties of polypropylene/multi-walled carbon nanotubes

nanocomposite foams, Mechanics of Materials 91 (2015) 95-118.

[99] I. Park, H.G. Peng, D.W. Gidley, S. Xue, T.J. Pinnavaia, Epoxy−Silica Mesocomposites

with Enhanced Tensile Properties and Oxygen Permeability, Chemistry of Materials 18(3)

(2006) 650-656.

[100] M. Mrlík, M. Maadeed, Tailoring of the thermal, mechanical and dielectric properties of

the polypropylene foams using gamma-irradiation, Polymer Degradation and Stability 133

(2016) 234-242.

[101] J.L. Willett, R.L. Shogren, Processing and properties of extruded starch/polymer foams,

Polymer 43(22) (2002) 5935-5947.

[102] G. Guo, Q. Ma, B. Zhao, D. Zhang, Ultrasound-assisted permeability improvement and

acoustic characterization for solid-state fabricated PLA foams, Ultrasonics Sonochemistry

20(1) (2013) 137-143.

[103] A.K. Bledzki, O. Faruk, Injection moulded microcellular wood fibre–polypropylene

composites, Composites Part A: Applied Science and Manufacturing 37(9) (2006) 1358-1367.

[104] S.F. Bush, O.K. Ademosu, Low-density rotomoulded polymer foams, Colloids and

Surfaces A: Physicochemical and Engineering Aspects 263(1) (2005) 370-378.

[105] C.M. Wu, M. Chen, J. Karger-Kocsis, Transcrystallization in syndiotactic polypropylene

induced by high-modulus carbon fibers, Polymer Bulletin 41(2) (1998) 239-245.

[106] R.W.H. Gore, S.B. Allen Jr., Waterproof laminate, Application number 4194041, W. L.

Gore & Associates, Inc. (Newark, DE), United States, 1980.

References

224

[107] A.A. Gokhale, I. Lee, Recent Advances in the Fabrication of Nanostructured Barrier

Films, Journal of Nanoscience and Nanotechnology 14(3) (2014) 2157-2177.

[108] W.G.C.F. Grot, J.T. Rivers, R.H.Silva, Protective clothing of fabric containing a layer of

highly fluorinated ion exchange polymer, Application number 4518650, E. I. Du Pont de

Nemours and Company (Wilmington, DE), United States, 1985.

[109] R.G. Posey, Coating composition for adhering metallized layers to polymeric films, US

Patent 7 427 435 B2, 2008.

[110] G.B.M. Wittmann, M. Van De Ven, A. Kiel, Waterproof, Water Vapour-Permeable

Multilayer Membrane, Application number 20090098352, United States, 2009.

[111] G.E.H. Booth, R.A. Johnson, G.M. Carlson, R.S. Harvey, T.M. Moy, Method of

producing flexible laminates, Application number 20080099141, Ashland Inc. (Columbus, OH,

US), United States, 2008.

[112] J. Yun, Y. Jeong, G.H. Lee, Direct synthesis of silicon oxide nanowires on organic

polymer substrates, Nanotechnology 20(36) (2009) 365606.

[113] D.G. Howells, B.M. Henry, J. Madocks, H.E. Assender, High quality plasma enhanced

chemical vapour deposited silicon oxide gas barrier coatings on polyester films, Thin Solid

Films 516(10) (2008) 3081-3088.

[114] J. Shim, H.G. Yoon, S.-H. Na, I. Kim, S. Kwak, Silicon oxynitride gas barrier coatings

on poly(ether sulfone) by plasma-enhanced chemical vapor deposition, Surface and Coatings

Technology 202(13) (2008) 2844-2849.

[115] C.C. Liu, L.S. Chang, Gas permeation properties of silicon oxynitride thin films deposited

on polyether sulfone by radio frequency magnetron reactive sputtering in various N2 contents

in atmosphere, Thin Solid Films 594 (2015) 35-39.

[116] S. Iwamori, Y. Gotoh, K. Moorthi, Characterization of silicon oxynitride gas barrier films,

Vacuum 68(2) (2002) 113-117.

[117] M. Rezaei, M. Mohseni, H. Yahyaei, A study on water and oxygen permeability of BOPP

coated with hybrid UV cured nanocoatings, Progress in Organic Coatings 99 (2016) 72-79.

[118] S. Park, L.H. Kim, Y.J. Jeong, K. Kim, M. Park, Y. Baek, T.K. An, S. Nam, J. Jang, C.E.

Park, Reduced water vapor transmission rates of low-temperature-processed and sol-gel-

derived titanium oxide thin films on flexible substrates, Organic Electronics 36 (2016) 133-139.

[119] G.E.B. Carrow, R.L. Rees, Rotationally molding a multilayered article, US Patent

3976821, Phillips Petroleum Company (Bartlesville, OK), United States, 1976.

References

225

[120] S. Gårdebjer, T. Gebäck, T. Andersson, E. Fratini, P. Baglioni, R. Bordes, A. Viridén, M.

Nicholas, N. Lorén, A. Larsson, The impact of interfaces in laminated packaging on transport

of carboxylic acids, Journal of Membrane Science 518 (2016) 305-312.

[121] S. Choi, B.V. Sankar, Gas permeability of various graphite/epoxy composite laminates

for cryogenic storage systems, Composites Part B: Engineering 39(5) (2008) 782-791.

[122] K.T. Hsiao, J.W. Gillespie, S.G. Advani, B.K. Fink, Role of vacuum pressure and port

locations on flow front control for liquid composite molding process, Polymer Composites

22(5) (2001) 660-667.

[123] H.M. Lee, B.J. Park, H.J. Choi, R.K. Gupta, S.N. Bhattachary, Preparation and

Rheological Characteristics of Ethylene‐Vinyl Acetate Copolymer/Organoclay

Nanocomposites, Journal of Macromolecular Science, Part B 46(2) (2007) 261-273.

[124] A. Rahman, Correlations in the Motion of Atoms in Liquid Argon, Physical Review

136(2A) (1964) A405-A411.

[125] L. Verlet, Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties

of Lennard-Jones Molecules, Physical Review 159(1) (1967) 98-103.

[126] C.L. Wennberg, T. Murtola, S. Páll, M.J. Abraham, B. Hess, E. Lindahl, Direct-Space

Corrections Enable Fast and Accurate Lorentz–Berthelot Combination Rule Lennard-Jones

Lattice Summation, Journal of Chemical Theory and Computation 11(12) (2015) 5737-5746.

[127] A. Warshel, S. Lifson, Consistent Force Field Calculations. II. Crystal Structures,

Sublimation Energies, Molecular and Lattice Vibrations, Molecular Conformations, and

Enthalpies of Alkanes, The Journal of Chemical Physics 53(2) (1970) 582-594.

[128] S.L. Mayo, B.D. Olafson, W.A. Goddard, DREIDING: a generic force field for molecular

simulations, The Journal of Physical Chemistry 94(26) (1990) 8897-8909.

[129] A.K. Rappe, C.J. Casewit, K.S. Colwell, W.A. Goddard, W.M. Skiff, UFF, a full periodic

table force field for molecular mechanics and molecular dynamics simulations, Journal of the

American Chemical Society 114(25) (1992) 10024-10035.

[130] B.R. Brooks, R.E. Bruccoleri, B.D. Olafson, D.J. States, S. Swaminathan, M. Karplus,

CHARMM: A program for macromolecular energy, minimization, and dynamics calculations,

Journal of Computational Chemistry 4(2) (1983) 187-217.

[131] W.D. Cornell, P. Cieplak, C.I. Bayly, I.R. Gould, K.M. Merz, D.M. Ferguson, D.C.

Spellmeyer, T. Fox, J.W. Caldwell, P.A. Kollman, A Second Generation Force Field for the

Simulation of Proteins, Nucleic Acids, and Organic Molecules, Journal of the American

Chemical Society 117(19) (1995) 5179-5197.

References

226

[132] D. Van Der Spoel, E. Lindahl, B. Hess, G. Groenhof, A.E. Mark, H.J.C. Berendsen,

GROMACS: Fast, flexible, and free, Journal of Computational Chemistry 26(16) (2005) 1701-

1718.

[133] W.L. Jorgensen, J. Tirado-Rives, The OPLS [optimized potentials for liquid simulations]

potential functions for proteins, energy minimizations for crystals of cyclic peptides and

crambin, Journal of the American Chemical Society 110(6) (1988) 1657-1666.

[134] W.L. Jorgensen, J. Tirado-Rives, Potential energy functions for atomic-level simulations

of water and organic and biomolecular systems, Proceedings of the National Academy of

Sciences of the United States of America 102(19) (2005) 6665-6670.

[135] B.L. Eggimann, A.J. Sunnarborg, H.D. Stern, A.P. Bliss, J.I. Siepmann, An online

parameter and property database for the TraPPE force field, Molecular Simulation 40(1-3)

(2014) 101-105.

[136] H. Sun, COMPASS: An ab Initio Force-Field Optimized for Condensed-Phase

ApplicationsOverview with Details on Alkane and Benzene Compounds, The Journal of

Physical Chemistry B 102(38) (1998) 7338-7364.

[137] H.K. Chilukoti, F. Müller-Plathe, H. Yang, Application of Reverse Nonequilibrium

Molecular Dynamics to the Calculation of the Mutual Diffusion Coefficient of Alkane

Mixtures, The Journal of Physical Chemistry B 122(39) (2018) 9210-9217.

[138] S. Asahi, Y. Tamai, Diffusion mechanism of CO2 in a crystalline polymer membrane

studied using model gases, Molecular Simulation 41(10-12) (2015) 974-979.

[139] F. Mozaffari, H. Eslami, J. Moghadasi, Molecular dynamics simulation of diffusion and

permeation of gases in polystyrene, Polymer 51(1) (2010) 300-307.

[140] A. Börjesson, E. Erdtman, P. Ahlström, M. Berlin, T. Andersson, K. Bolton, Molecular

modelling of oxygen and water permeation in polyethylene, Polymer 54(12) (2013) 2988-2998.

[141] E. Erdtman, M. Bohlén, P. Ahlström, T. Gkourmpis, M. Berlin, T. Andersson, K. Bolton,

A molecular-level computational study of the diffusion and solubility of water and oxygen in

carbonaceous polyethylene nanocomposites, Journal of Polymer Science Part B: Polymer

Physics 54(5) (2016) 589-602.

[142] R. Bai, H. Wang, P. Zhang, B. Xiao, B. Jiang, G. Zhou, Molecular dynamics simulation

of the diffusion behavior of water in poly(vinylidene fluoride)/silica hybrid membranes, RSC

Advances 5(70) (2015) 57147-57154.

[143] M.L. Connolly, Analytical molecular surface calculation, Journal of Applied

Crystallography 16(5) (1983) 548-558.

References

227

[144] H. Ebadi-Dehaghani, M. Barikani, H.A. Khonakdar, S.H. Jafari, U. Wagenknecht, G.

Heinrich, On O2 gas permeability of PP/PLA/clay nanocomposites: A molecular dynamic

simulation approach, Polymer Testing 45 (2015) 139-151.

[145] M. Fermeglia, P. Cosoli, M. Ferrone, S. Piccarolo, G. Mensitieri, S. Pricl, PET/PEN

blends of industrial interest as barrier materials. Part I. Many-scale molecular modeling of

PET/PEN blends, Polymer 47(16) (2006) 5979-5989.

[146] L. Liao, C. Huang, C. Meng, Study on mechanical properties of polyethylene with chain

branching in atomic scale by molecular dynamics simulation, Molecular Simulation 44(12)

(2018) 1016-1024.

[147] L. Jia, Y. Qingsheng, Molecular dynamics simulation for mechanical properties of

CNT/Polyethylene composites, Journal of Physics: Conference Series 188 (2009) 012052.

[148] I.H. Sahputra, A. Alexiadis, M.J. Adams, Temperature and configurational effects on the

Young’s modulus of poly (methyl methacrylate): a molecular dynamics study comparing the

DREIDING, AMBER and OPLS force fields, Molecular Simulation 44(9) (2018) 774-780.

[149] J. Richeton, G. Schlatter, K.S. Vecchio, Y. Rémond, S. Ahzi, A unified model for stiffness

modulus of amorphous polymers across transition temperatures and strain rates, Polymer

46(19) (2005) 8194-8201.

[150] H. Zhou, S. Zhang, M. Yang, The effect of heat-transfer passages on the effective thermal

conductivity of high filler loading composite materials, Composites Science and Technology

67(6) (2007) 1035-1040.

[151] R.H.B. Bouma, A. Checchetti, G. Chidichimo, E. Drioli, Permeation through a

heterogeneous membrane: the effect of the dispersed phase, Journal of Membrane Science

128(2) (1997) 141-149.

[152] J.R. Kalnin, E.A. Kotomin, J. Maier, Calculations of the effective diffusion coefficient

for inhomogeneous media, Journal of Physics and Chemistry of Solids 63(3) (2002) 449-456.

[153] G.H. Fredrickson, J. Bicerano, Barrier properties of oriented disk composites, The Journal

of Chemical Physics 110(4) (1999) 2181-2188.

[154] M. Hedenqvist, U.W. Gedde, Diffusion of small-molecule penetrants in semicrystalline

polymers, Progress in Polymer Science 21(2) (1996) 299-333.

[155] Y. Cao, W. Wang, Q. Wang, Application of mechanical model for natural fibre reinforced

polymer composites, Materials Research Innovations 18(sup2) (2014) S2-354-S2-357.

[156] J.Z. Liang, Predictions of Young's Modulus of Polymer Composites Reinforced with

Short Natural Fibers, Journal of Macromolecular Science, Part B 55(6) (2016) 566-574.

References

228

[157] A. Martone, G. Faiella, V. Antonucci, M. Giordano, M. Zarrelli, The effect of the aspect

ratio of carbon nanotubes on their effective reinforcement modulus in an epoxy matrix,

Composites Science and Technology 71(8) (2011) 1117-1123.

[158] J.C. Halpin, J.L. Kardos, The Halpin‐Tsai equations: A review, Polymer Engineering &

Science 16(5) (1976) 344-352.

[159] W.P. Raharjo, R. Soenoko, A. Purnowidodo, M.A. Choiron, Experimental and

micromechanical modelling of randomly oriented zalacca fibre/low-density polyethylene

composites fabricated by hot-pressing method, Cogent Engineering 5(1) (2018) 1518966.

[160] S.K. Sharma, K. Sudarshan, P.K. Pujari, Unravelling the surface chemical characteristics

and nanostructure of MgO/NiO catalyst using positronium probe: positron annihilation lifetime

and age momentum correlation study, RSC Advances 4(28) (2014) 14733-14739.

[161] Z. Yu, J.D. McGervey, A.M. Jamieson, R. Simha, Can Positron Annihilation Lifetime

Spectroscopy Measure the Free-Volume Hole Size Distribution in Amorphous Polymers?,

Macromolecules 28(18) (1995) 6268-6272.

[162] J.A.O. Bruno, N.L. Allan, T.H.K. Barron, A.D. Turner, Thermal expansion of polymers:

Mechanisms in orthorhombic polyethylene, Physical Review B 58(13) (1998) 8416-8427.

[163] V. Compañ, A. Ribes, R. Díaz-Calleja, E. Riande, Permeability of co-extruded linear low-

density polyethylene films to oxygen and carbon dioxide as determined by electrochemical

techniques, Polymer 37(11) (1996) 2243-2250.

[164] V. Compañ, A. Andrio, M.L. López, C. Alvarez, E. Riande, Effect of Time of Annealing

on Gas Permeation through Coextruded Linear Low-Density Polyethylene (LLDPE) Films,

Macromolecules 30(11) (1997) 3317-3322.

[165] V. Compañ, R. Diaz-Calleja, A. Ribes, A. Andrio, M.L. López, E. Riande, Mechanical

relaxations and diffusive changes in linear low density polyethylene (LLDPE) films subject to

induced stretching, Journal of Applied Polymer Science 60(5) (1996) 767-778.

[166] D. Klepac, M. Ščetar, M. Kurek, P.E. Mallon, A.S. Luyt, K. Galić, S. Valić, Oxygen

permeability, electron spin resonance, differential scanning calorimetry and positron

annihilation lifetime spectroscopy studies of uniaxially deformed linear low-density

polyethylene film, Polymer International 62(3) (2013) 474-481.

[167] G.A.G. Gee, G.J. Wilson, Intermolecular forces and chain flexibilities in polymers: I.

Internal pressures and cohesive energy densities of simple liquids, Polymer 1 (1960) 456-466.

[168] C. Vasile, M. Pascu, Practical Guide to Polyethylene, RAPRA Technology, Shrewsbury,

UK, 2005.

References

229

[169] D.A. Pearlman, D.A. Case, J.W. Caldwell, W.S. Ross, T.E. Cheatham, S. DeBolt, D.

Ferguson, G. Seibel, P. Kollman, AMBER, a package of computer programs for applying

molecular mechanics, normal mode analysis, molecular dynamics and free energy calculations

to simulate the structural and energetic properties of molecules, Computer Physics

Communications 91(1) (1995) 1-41.

[170] H. Sun, S.J. Mumby, J.R. Maple, A.T. Hagler, An ab Initio CFF93 All-Atom Force Field

for Polycarbonates, Journal of the American Chemical Society 116(7) (1994) 2978-2987.

[171] S. Dabral, M. Turberg, A. Wanninger, C. Bolm, J. Hernández, Mechanochemical Lignin-

Mediated Strecker Reaction, Molecules 22(1) (2017) 146.

[172] E. Sjostrom, Wood Chemistry: Fundamentals and Applications, Elsevier Science,

Oxford, UK, 2013.

[173] C. Yang, E.E. Nuxoll, E.L. Cussler, Reactive barrier films, AIChE Journal 47(2) (2001)

295-302.

[174] C. Yang, W.H. Smyrl, E.L. Cussler, Flake alignment in composite coatings, Journal of

Membrane Science 231(1) (2004) 1-12.

[175] N.K. Lape, E.E. Nuxoll, E.L. Cussler, Polydisperse flakes in barrier films, Journal of

Membrane Science 236(1) (2004) 29-37.

[176] A.A. Gusev, H.R. Lusti, Rational Design of Nanocomposites for Barrier Applications,

Advanced Materials 13(21) (2001) 1641-1643.

[177] L.E. Nielsen, The Thermal and Electrical Conductivity of Two-Phase Systems, Industrial

& Engineering Chemistry Fundamentals 13(1) (1974) 17-20.

[178] R. Aris, On a problem in hindered diffusion, Archive for Rational Mechanics and

Analysis 95(2) (1986) 83-91.

[179] W.R. Falla, M. Mulski, E.L. Cussler, Estimating diffusion through flake-filled

membranes, Journal of Membrane Science 119(1) (1996) 129-138.

[180] W.A. Wakeham, E.A. Mason, Diffusion through Multiperforate Laminae, Industrial &

Engineering Chemistry Fundamentals 18(4) (1979) 301-305.

[181] Z. Duan, N.L. Thomas, Water vapour permeability of poly(lactic acid): Crystallinity and

the tortuous path model, Journal of Applied Physics 115(6) (2014) 064903.

[182] H. Alter, A critical investigation of polyethylene gas permeability, Journal of Polymer

Science 57(165) (1962) 925-935.

[183] J. Durão, L. Gales, Permeation of Light Gases through Hexagonal Ice, Materials 5(9)

(2012) 1593.

References

230

[184] A.H.H. Alirezaie, A.H. Navarchian, H. Sabzyan, Molecular dynamics simulation of gas

diffusion in polyethylene-clay nanocomposites with different silicate layers configurations,

Polymer Science Series A 58(3) (2016) 487-498.

[185] Z. Luo, X. Li, J. Shang, H. Zhu, D. Fang, Modified rule of mixtures and Halpin–Tsai

model for prediction of tensile strength of micron-sized reinforced composites and Young’s

modulus of multiscale reinforced composites for direct extrusion fabrication, Advances in

Mechanical Engineering 10(7) (2018) 1687814018785286.

[186] D.M. Koenhen, C.A. Smolders, The determination of solubility parameters of solvents

and polymers by means of correlations with other physical quantities, Journal of Applied

Polymer Science 19(4) (1975) 1163-1179.

[187] P. Kubica, A. Wolinska-Grabczyk, Correlation between Cohesive Energy Density,

Fractional Free Volume, and Gas Transport Properties of Poly(ethylene-co-vinyl acetate)

Materials, International Journal of Polymer Science 2015 (2015) 8.

[188] M.J. Doyle, On the effect of crystallinity on the elastic properties of semicrystalline

polyethylene, Polymer Engineering & Science 40(2) (2000) 330-335.

[189] A.S. Michaels, R.B. Parker, Sorption and flow of gases in polyethylene, Journal of

Polymer Science 41(138) (1959) 53-71.

[190] J.C. Halpin, J.L. Kardos, The Halpin-Tsai equations: A review, Polymer Engineering &

Science 16(5) (1976) 344-352.

[191] S. Kanehashi, A. Kusakabe, S. Sato, K. Nagai, Analysis of permeability; solubility and

diffusivity of carbon dioxide; oxygen; and nitrogen in crystalline and liquid crystalline

polymers, Journal of Membrane Science 365(1) (2010) 40-51.

[192] H.J. Huang, S. Ramaswamy, U.W. Tschirner, B.V. Ramarao, 10 - Separation and

purification processes for lignocellulose-to-bioalcohol production, in: K. Waldron (Ed.),

Bioalcohol Production, Woodhead Publishing, 2010, pp. 246-277.

[193] K. Pearson, F. Galton, VII. Note on regression and inheritance in the case of two parents,

Proceedings of the Royal Society of London 58(347-352) (1895) 240-242.

[194] J.L. Rodgers, W.A. Nicewander, Thirteen Ways to Look at the Correlation Coefficient,

The American Statistician 42(1) (1988) 59-66.

[195] L.J. Gibson, The hierarchical structure and mechanics of plant materials, Journal of The

Royal Society Interface 9(76) (2012) 2749-2766.

[196] Y.A. Akpalu, E.J. Amis, Evolution of density fluctuations to lamellar crystals in linear

polyethylene, The Journal of Chemical Physics 111(18) (1999) 8686-8695.

References

231

[197] M. Eslamian, R. Bagheri, G. Pircheraghi, Co-crystallization in ternary polyethylene

blends: tie crystal formation and mechanical properties improvement, Polymer International

65(12) (2016) 1405-1416.

[198] S. Fatahi, A. Ajji, P.G. Lafleur, Correlation between Structural Parameters and Property

of PE Blown Films, Journal of Plastic Film & Sheeting 21(4) (2005) 281-305.

[199] S. Hosoda, Y. Nozue, Y. Kawashima, K. Suita, S. Seno, T. Nagamatsu, K.B. Wagener,

B. Inci, F. Zuluaga, G. Rojas, J.K. Leonard, Effect of the Sequence Length Distribution on the

Lamellar Crystal Thickness and Thickness Distribution of Polyethylene: Perfectly

Equisequential ADMET Polyethylene vs Ethylene/α-Olefin Copolymer, Macromolecules 44(2)

(2011) 313-319.

[200] H. Teng, Y. Shi, X. Jin, Novel characterization of the crystalline segment distribution and

its effect on the crystallization of branched polyethylene by differential scanning calorimetry,

Journal of Polymer Science Part B: Polymer Physics 40(18) (2002) 2107-2118.

[201] R.J. Xu, X.D. Chen, Q. Cai, C.B. Chen, Y.F. Lin, C.H. Lei, L.B. Li, In situ study of the

annealing process of a polyethylene cast film with a row-nucleated crystalline structure by

SAXS, RSC Advances 5(35) (2015) 27722-27734.

[202] J. Raghavan, M. Meshii, Creep of polymer composites, Composites Science and

Technology 57(12) (1998) 1673-1688.

[203] F. Mainardi, G. Spada, Creep, relaxation and viscosity properties for basic fractional

models in rheology, The European Physical Journal Special Topics 193(1) (2011) 133-160.

[204] H. Sun, R.S. Cooke, W.D. Bates, K.J. Wynne, Supercritical CO2 processing and annealing

of polytetrafluoroethylene (PTFE) and modified PTFE for enhancement of crystallinity and

creep resistance, Polymer 46(20) (2005) 8872-8882.

[205] I. Widiastuti, I. Sbarski, S.H. Masood, Creep behavior of PLA-based biodegradable

plastic exposed to a hydrocarbon liquid, Journal of Applied Polymer Science 127(4) (2013)

2654-2660.

[206] K. Prasad, M. Nikzad, C.M. Doherty, I. Sbarski, Predicting trends in structural and

physical properties of a model polymer with embedded natural fibers: Viability of molecular

dynamics studies for a bottom up design, Journal of Applied Polymer Science 136(45) (2019)

48189.

List of Publications and Presentations

232

LIST OF PUBLICATIONS

AND PRESENTATIONS

1. K Prasad, M Nikzad, I Sbarski, ‘Modelling permeability in multi-phase polymer

composites: A critical review of semi-empirical approaches’, Polymer Reviews,

https://doi.org/10.1080/15583724.2020.1743306.

2. K Prasad, M Nikzad, I Sbarski, ‘Using viscoelastic modelling and molecular dynamics

based simulations to characterize polymer natural fibre composites’, Journal of Applied

Polymer Science, https://doi.org/10.1002/app.49220

3. K Prasad, M Nikzad, CM Doherty, I Sbarski, ‘Predicting trends in structural and

physical properties of a model polymer with embedded natural fibres: Viability of

molecular dynamics studies for a bottom up design’, Journal of Applied Polymer

Science 136 (2019) 48189.

4. K Prasad, M Nikzad, I Sbarski, ‘Permeability control in polymeric systems: a review’,

Journal of Polymer Research 35 (2018) 232 (1-20).

5. K Prasad, M Nikzad, CM Doherty, I Sbarski, ‘Diffusion of low‐molecular‐weight

permeants through semi‐crystalline polymers: combining molecular dynamics with

semi‐empirical models’, Polymer International 67 (2018) 717-725

6. K Prasad, M Nikzad, I Sbarski, ‘Predicting Trends in Structural and Physical properties

of hybrid polymer composites using Molecular Dynamics’, 22nd International

Conference on Composite Materials (ICCM22), Melbourne, 2019.

7. K Prasad, ‘A Bottom-Up Design Approach for a Controlled Bulk Properties in Polymer

Structures using Molecular Dynamics’, Swinburne Research Conference, Swinburne

University of Technology, Hawthorn, 2018.

8. K Prasad, ‘A Bottom-Up Design Approach for a Controlled Bulk Properties in Polymer

Structures using Molecular Dynamics’, Borland Materials Forum, La Trobe University,

Bundoora, 2017.

https://doi.org/10.1080/15583724.2020.1743306

https://doi.org/10.1002/app.49220

development of polymer composite materials for ......abs acrylonitrile butadiene styrene terpolymer...

Documents