for the degree of doctor of philosophyshodhganga.inflibnet.ac.in/bitstream/10603/44269/2... · dr....
TRANSCRIPT
2014
By
Thesis
UNDER THE SUPERVISION OF
SUBMITTED TO THE
UNIVERSITY OF LUCKNOW
FOR THE DEGREE OF
Doctor of PhilosophyIn
PHYSICS
DIELECTRIC AND ULTRASONIC STUDIES OF
SOME POLYMERS AND CERAMIC MATERIALS
Sudir Kumar
Prof. Manisha Gupta
DEPARTMENT OF PHYSICSUNIVERSITY OF LUCKNOW
LUCKNOW 226 007INDIA
CONDENSED MATTER PHYSICS LAB
Dedicated to my adorable parents to give me so
much courage, strength and faith to complete my
Doctor of Philosophy Degree.
i
CONTENTS
Acknowledgement vi
Certificate I viii
Certificate II ix
List of Published and Communicated Papers x
List of Conference Papers xii
List of Workshops Participation xiv
Abstract xv
1 General Discussion
1.1 Introduction……..………………………………………………………………1
1.2 Ultrasonics………...…………………………………………………………….5
1.2.1 Methods for Production of Ultrasonics..…………...………..……..........6
1.2.2 Importance of Ultrasonics..……………...……………………………....7
1.3 Viscometry………………...…..………………………………………………..9
1.3.1 Classification of Fluids….……………………………………………...10
1.3.2 Importance of Viscometry….…………….…………………………….11
1.4 Refractometry…………………………….…………………………………....12
1.5 Volumetric…………………………………………………………………......14
1.6 Dielectric……………………………………………………………………….15
1.7 NMR Spectroscopy…………………………………………………………….15
1.7.1 Applications of NMR……………….………………………………….16
1.8 Thermodynamic Excess Parameters…………………………………………...18
1.9 Objective and Scope of Present Study…………………………………………18
References……………...………………….…………………………………………...20
ii
2 Techniques of Measurement: Apparatus used and Mathematical
Evaluations
2.1 Ultrasonic Velocity Measurement………..……………..……………………..24
2.1.1 Principle of Interferometric Technique…………..………………….....24
2.1.2 Experimental Set-Up ……………………………………………..……27
(a) High Frequency Generator ………………………………………...…….27
(b) Measuring cell…………………………...……………………………….28
2.2 Refractive Index Measurement ………………....……………………………..32
2.2.1 Principle of Abbe’s Refractometer……..……………………………....32
2.2.2 Calibration and Mode of Operation.........................................................36
2.3 Viscosity Measurement ……………………..………………………………..37
2.3.1 Principle of Operation……………………………..…………………...37
2.3.2 Experimental Set Up……………………..…………………………….37
2.3.3 Electronic Gap Setting…..……………………………………………..38
2.3.4 Software……..………………………………………………………....38
2.3.5 Specifications…..……………………………………………………....40
2.4 Temperature Controller...……….…………………………………………….41
2.5 Density Measurement........................................................................................41
2.6 1H NMR Spectroscopy Measurement…….…...……………………………...43
2.6.1 Principle of N.M.R…………………….………………………….........43
2.7 Preparation of Mixtures …………..…………….………………………….....46
2.8 Evaluation of Acoustical, Thermodynamic and Excess
Parameters….....................................................................................................46
2.8.1 Isentropic Compressibility (ks)...............................................................46
2.8.2 Surface Tension( σ)………………………………………….……...…48
2.8.3 Acoustic Impedance (Z)……………………………………………….49
2.8.4 Optical Dielectric Constant (ε), Polarisability (α) and Molar Refraction
(Rm)……………………………………………………………………………..49
2.8.5 Intermolecular Free Length (Lf)……………………………………….50
2.8.6 Gibb’s Free Energy of Activation for Viscous Flow ( *G )…..………52
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2.8.7 Free Volume (Vf) and Internal Pressure (πi)…………………………...52
2.8.8 Excess Parameters………………………………………………….….54
2.9 Analysis of Data………………..…………………………………………......57
2.9.1 Redlich- Kister Polynomial Equation…………………………………57
2.9.2 Data Correlation..…………….……………………………………......58
2.10 Mixing Rules………..…………………………………………..…………….58
2.10.1 Mixing Rules for Refractive Index…………………...…..………….58
2.10.2 Mixing Rules for Ultrasonic Velocity……………………………….60
2.10.3 Mixing Rules for Dielectric Constant……………………………….61
2.10.4 Mixing Rules for Viscosity………………………………………….64
2.10.5 Flory’s Statistical Theory……………………………………………65
2.10.6 Excess Thermodynamic Functions………………………………….68
2.11 Samples Under Investigation ……..….……………………………....………69
References……………………….…………………………………………………….71
3 Acoustical, Optical and Dielectric Studies on Solutions of Poly (Propylene
Glycol)Monobutyl Ether 1000 with 1-Butanol/MAE
3.1 Introduction……………………………………………………………………74
3.2 Results and Discussion…….………………………………………………….75
3.2.1 Experimental Data……………………………………………………..75
3.2.2 Thermoacoustical Parameters…………………………………………76
3.2.3 Excess Parameters……………………………………………....……..82
3.2.4 Redlich-Kister Polynomial Equation Data………….…………………88
3.3 Conclusion……………………………………………….……………………89
References………….……………………………………………………….………...90
4 Study of Molecular Interaction in Binary Mixtures of Poly (Propylene
Glycol) Monobutyl Ether(PPGMBE) 1000 with 2-(Methylamino) Ethanol
(MAE) and 1-Butanol using Thermodynamic and 1H NMR Spectroscopy
iv
4.1 Introduction……………………………………………………………………91
4.2 Results and Discussion….………………………………………………….....92
4.2.1 Thermodynamic Study…………………………………………………92
4.2.1.1 Experimental Data………………………………………………….92
4.2.1.2 Thermophysical Parameters…………………………………..........93
4.2.1.3 Excess Parameters………………………………………………….96
4.2.1.4 Redlich-Kister Polynomial Equation Data………………………....98
4.2.2 1H NMR Spectroscopy Study………………………………………….99
4.3 Conclusion…………………………………………………………………...103
References…………………………………………………………………..............104
5 Thermoacoustical and Optical Study of Poly (Ethylene Glycol) Butyl Ether
(PEGBE) 206 with 1-Butanol and 2-(Methylamino) Ethanol(MAE)
5.1 Introduction…………………………………………………………………..106
5.2 Results and Discussion……………..………………………………………...107
5.2.1 Experimental Data……………………………………………………107
5.2.2 Derived Parameters…………………………………………………..108
5.2.3 Excess Parameters……………………………………………………111
5.2.4 Redlich-Kister Polynomial Equation Data…………………………...116
5.3 Conclusion……………………………………………………………………116
References…………………………………………………………………………….117
6 Molecular Association of Binary Mixtures of Polyethylene Glycol Butyl
Ether (PEGBE) 206 with 1- Butanol and 2-(Methylamino)ethanol(MAE) –
A Thermodynamic and 1H NMR Spectroscopy Study
6.1 Introduction…………………………………………………………………..118
6.2 Results and Discussion………..……………………………………………...119
6.2.1 Thermodynamic Study…………………………..……………………..119
6.2.1.1 Experimental Data……………………………………………………119
6.2.1.2 Excess Parameters……………………………………………………120
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6.2.1.3 Redlich-Kister Polynomial Equation Data…………………………..124
6.2.2 1H NMR Spectroscopy Study………………………………………….125
6.3 Conclusion……………………………………………………………………130
References……………..……………………………………………………………...131
7 Dielectric, Ultrasonic and Refractive Index Studies of Binary Mixtures of
Some Polymers and Ceramic materials: A Conformational Analysis
7.1 Introduction…………………………………………………………………..132
7.2 Results and Discussion………..……………………………………………...134
7.2.1 Dielectric Study………..…………………………………………………134
7.2.2 Ultrasonic Study………..………………………………………………...138
7.2.3 Refractive Index study………...………………………………………….141
7.3 Conclusion………………...………………………………………………….144
References…………………….………………………………………………………146
vi
Acknowledgement
I humbly prostrate myself before the Almighty for his grace and abundant blessings
which enabled me to complete my work successfully.
It gives me immense pleasure to express my deep sense of gratitude to my supervisor
Prof. Manisha Gupta, Department of Physics, University of Lucknow, Lucknow for her
invaluable guidance, motivation, constant inspiration and above all her ever co-operating
attitude enabled me in bringing up this thesis in present elegant form.
I would like to express my sincere thanks to Prof. J. P. Shukla, Former Head,
Department of Physics, University of Lucknow, Lucknow for his kind support and
valuable suggestions in making my dream come true. I am grateful to Dr. (Mrs.) Shukla
for her hospitality and encouragements.
I express my sincere thanks to Prof. Kriti Shinha, Head, Department of Physics,
University of Lucknow, Lucknow for providing me the necessary facilities in the
department.
I would like to sincerely acknowledge the continuous support of my seniors, special
thanks are due to Dr. Rahul Singh, Dr. Maimoona Yasmin, Mr. Harshit Agarwal, and
Dr. Vivek Kumar Shukla for their support and encouragement.
vii
I am also thankful to Ms. Sangeeta Sagar, for her help, words and suggestions
that boosted my courage and determination to finish my research work and write this
thesis.
I am indebted to my family, especially my Parents for their encouragement and
support throughout my entire education. Without their support and encouragement, it is
hard to imagine how much I can complete.
Date:
Place: (Sudir Kumar)
viii
CERTIFICATE I
This is to certify that all the regulations necessary for the
submission of Ph.D thesis of Mr. Sudir Kumar have been fully
observed.
Date: (Prof. Kirti Sinha)
Head of the Department
ix
CERTIFICATE II
Certified that this work on “Dielectric and Ultrasonic Studies of
Some Polymers and Ceramic Materials” has been carried out by
Mr. Sudir Kumar under my supervision and the work has not been
submitted elsewhere for the award of degree.
Date: (Prof. Manisha Gupta)
Supervisor
x
List of Published and Communicated Papers
1. Study of Molecular Investigation in Binary Mixtures of Poly (Propylene Glycol)
Monobutyl Ether (PPGMBE) 100 with 2- (Methylamino) Ethanol (MAE) and 1- Butanol
using Thermodynamic and 1H NMR Spectroscopy;
Manisha Gupta and Sudir Kumar.
Proceeding of International Conference on Machine Learning, Electrical and Mechanical
Engineering (ICMLEME 2014) Jan 8- 9, 2014 Dubai (UAE).
2. Determination of Ultrasonic Velocities and Excess Parameters of Polymer Solutions by
Means of Piezoelectric Sensor-Transducer
Maimoona Yasmin, Harshit Agarwal, Vivek K. Shukla, Sudir Kumar, Manisha Gupta and
Jagdish P. Shukla
Lucknow Journal of Science, 8(1) (2011) 293.
3. Molecular Interactions in Binary Mixtures of Formamide with Alkoxyalcohols at Varying
Temperatures.
Maimoona Yasmin, Rahul Singh, H. Agarwal, V.K. Shukla, Sudir Kumar, M. Gupta and
J.P. Shukla
Lucknow Journal of Science, 8(2), (2011), 324.
4. Study of Binary Mixtures of Acetonitrile with Alkoxyalcohols,
Sudir Kumar, R. Singh, M. Yasmin, M. Gupta and J.P. Shukla.
Proceeding of National Conference on Advancements and Futuristic Trends in Material
Science, Bareilly, Mar. 26-27, 2011.
5. Thermodynamic Properties of Solutions of Pentanol with Poly (Ethylene Glycol)
Diacrylate and Poly (Ethylene Glycol) Dimethacrylate at 298.15 K,
Maimoona Yasmin, Sudir Kumar, Manisha Gupta and J.P. Shukla.
Proceeding of National Conference on Advancements and Futuristic Trends in Material
Science, Bareilly, Mar. 26-27, 2011.
xi
6. Molecular Association of Binary Mixtures of Plyethylene Glycol Butyl Ether (PEGBE)
206 with 1- Butanol and 2- (Methylamino) Ethanol (MAE) – A Thermodynamic and 1H
NMR Spectroscopy Study.
Sudir Kumar, Sangeeta Sagar and Manisha Gupta
Journal of Chemical Thermodynamics, Communicated 2014.
7. Study of Density, Viscosity, Refractive index and their Excess Parameters of Binary Liquid
Mixtures, N, N-dimethylacetamide with 1- Propanol, Methanol and Water at 293.15,
303.15 and 313.15 K.
Harshit Agarwal, V. K. Shukla, Sudir Kumar, Maimoona Yasmin Sangeeta Sagar and
Manisha Gupta.
Journal of Chemical Engineering Data, Communicated 2014.
8. Acoustical, Optical and Ultrasonic Studies on Solutions of Poly (Propylene Glycol)
Monobutyl Ether 1000 with 1-Butanol/MAE
Sudir Kumar, Sangeeta Sagar and Manisha Gupta.
Journal of Molecular Liquids, Communicated 2014.
9. Thermodynamic and 1H NMR Spectroscopy Study of Binary Mixtures of Polymer
Solutions with 2-(Methylamino) Ethanol (MAE) and 1-Butanol.
Sudir Kumar, Sangeeta Sagar and Manisha Gupta.
Europian Polymer Journal, Communicated 2014.
xii
List of Conference Papers
1. Interaction Study of 2-(Methylamino) Ethanol(MAE) with Poly(propylene Glycol) Mono
Butyl Ether (PPGMBE) 1000 and Poly(Ethylene Glycol) Butyl Ether 206 by NMR
Spectroscopy and Thermodynamical Analysis.
Sudir Kumar, Sangeeta Sagar and Manisha Gupta
International Symposium on Advances in Biological & Material Science, July 15, 2014,
University of Lucknow, Lucknow.
2. Study of Molecular Interaction of Binary Mixtures of the Poly (ethylene Glycol) Butyl
Ether (PEGBE) 206 with 1-Butanol and 2-(Methylamino) Ethanol (MAE).
Sudir Kumar, Rahul Singh, Sangeeta Sagar and Manisha Gupta
National Conference on Challenges & Opportunities for Technological Innovation In
India (COTTI) Feb. 22, 2014, Ambalica Institute of Technology, Lucknow.
3. Molecular Intraction in Binary Mixtures of Polypropylene Glycol Monobutyl Ether
(PPGMBE) with 1-Butanol and 2-(Methylamino) Ethanol.
Sudir Kumar, Sangeeta Sagar, Harshit Agarwal, V. K. Shukla, Maimoona Yasmin,
Manisha Gupta and J. P. Shukla.
101st Indian Science Congress, Feb. 3-7 2014, Jammu.
4. Interaction of Poly (Propylene Glycol) Monobutyl Ether with 2- (Methylamino) Ethanol
and 1- Butanol: A Thermodynamic and NMR Spectroscopy Study
Sudir Kumar, Sangeeta Sagar, Maimoona Yasmin, V. K. Shukla, Manisha Gupta and J.
P. Shukla.
International Seminar on Advances in Bio & Nano Material Science, Nov. 17, 2013,
University of Lucknow, Lucknow.
5. Investigation of Rheological Properties of Binary Mixture PEG 200 with MEA and
Theoretical Evaluation of Refractive Indices of PEG Solutions.
Maimoona Yasmin, Sudir Kumar, Sangeeta Sagar and Manisha Gupta,
International Seminar on Advances in Bio & Nano Materials, University of Lucknow,
Lucknow, Nov. 17, 2013
xiii
6. Ultrasonic, Refractrometric and Dielectric Study of Binary Mixtures of the Polypropylene
Glycol Monobutyl Ethers (PPGMBE) 1000 with 1- Butanol and (Methylamino) Ethanol
(MAE),
Sudir Kumar, S. Sagar, V.K. Shukla. M. Yasmin, M. Gupta & J.P.Shukla.
8th
National Conference on Thermodynamics of Chemical, Biological and Environmental
Systems (TCBES), BBAU, Lucknow, Nov. 25- 26, 2013.
7. Thermoacoustical Properties of Binary Liquid Mixtures of Methylcynide with 2 – Ethoxyethanol
and 2 – Butoxyethanol at Temperatures 293 K, 303K, 313K.
Maimoona Yasmin, Rahul Singh , Sudir kumar, Manisha Gupta and J. P. Shukla,
100th Session of Indian Science Congress, Kolkata, January 3-7, 2013.
8. Molecular interactions in Binary Mixtures of Formamide with Alkoxyalcohols at varying
Temperatures.
M. Yasmin, , R. Singh, H. Agarwal, V.K. Shukla, Sudir Kumar, Manisha Gupta and J.P.
Shukla.
National Conference on Nanomaterials and Nanotechnology, University of Lucknow,
Lucknow Dec. 21-23, 2011.
9. Determination of Ultrasonic Velocities and Excess Parameters of Polymer Solutions by
Means of Piezoelectric Sensor-Transducer,
M. Yasmin, H. Agarwal, V.K. Shukla, S. Kumar, M. Gupta and J.P. Shukla.
16th
National Seminar on Physics and Technology of Sensors, Lucknow Feb. 11 – 13,
2011
10. Molecular Intraction in Binary Mixtures of Poly (Ethylene Glycol) 200 with
Ethanolamine, m-Cresol and Aniline at 298.15K
Maimoona Yasmin, Sudir Kumar, Manisha Gupta and J. P. shukla
98th
Indian Science Congress, Chennai, January 3-7, 2011.
11. Thermodynamical Study of Solutions of PEG200 in Ethanolamine, m-Cresol and Aniline
at 298.15 K.
M. Yasmin, Sudir Kumar, Manisha Gupta and J.P. Shukla.
National Conference on Experimental Tools for Material Science Research: State of Art,
BHU, Varanasi, Dec. 3-4, 2010.
xiv
List of Workshops Participation
1. National Workshop on “Recent Advances in Materials Science (NWRAMS-2013)”.
March 15-16, 2013, Department of Physics, University of Lucknow, Lucknow.
2. Workshop on” Writing Research papers”,
June 10-11, 2011, Banaras Hindu University, Varanasi.
3. Workshop on “ E-Learning and Preparation of E-Learning Materials”
Aug. 17, 2013, University of Lucknow, Lucknow.
xv
Abstract
The present thesis reports investigation on the solution of polymers,
polymer/ceramic composition and complex forming systems using acoustical,
optical, volumetric, viscometric, NMR spectroscopy techniques. From the
experimentally measured values of density, ultrasonic velocity, viscosity and
refractive index, various thermodynamic parameters have been evaluated which
help to predict the nature of the mixture at different concentrations and
temperatures. Further thermodynamical results have been verified by 1H NMR
spectroscopy analysis by studying the NMR chemical shifts for various protons.
Excess thermodynamical parameters have also been calculated and correlated by
Redlich - Kister type polynomial at varying concentration and temperatures. The
obtained results have been interpreted in terms of molecular interactions and
structural changes occurring in the process of mixing.
The thesis is divided into seven chapters. Chapter 1 of the thesis deals with
general discussion on fundamental forces acting between like and unlike molecules
of the mixture, their effects on thermodynamic parameters and their use as a tools of
gathering information about the behavior of mixture. A brief discovery of ultrasonic
wave is discussed in conjugation with viscometry, refractometery, dielectric, NMR
and excess parameters. This chapter also explains the objective and scope of the
present study.
xvi
Chapter 2 provides a brief description of experimental techniques and
evaluation of various thermoacoustic parameters i.e. ultrasonic velocity, density,
viscosity and refractive index. Evaluation of excess parameters using Redlich –
Kister polynomial equation has also been discussed in this chapter. Various
methods, mixing rules and theories to evaluate dielectric, ultrasonic velocity,
density, refractive index and surface tension are also given in this chapter.
Chapter 3 reports the acoustical, optical and dielectric study of binary
mixtures of Poly (Propylene Glycol) Monobutyl Ether 1000 with 1-Butanol/MAE at
various concentrations at 293.15. 303.15 and 313.15 K. The calculated values of
acoustic impedance (Z), pseudo-Grüneisen parameter ( ), specific heat ratio ( ),
heat capacity (Cp), molar volume ( mV ) and optical dielectric constant (ɛr), excess
properties viz. deviation in isentropic compressibility (Δks), excess intermolecular
free length (𝐿𝑓𝐸), deviation in ultrasonic velocity (∆u) and molar refraction deviation
(∆Rm) have been used to investigate intermolecular interaction present in the
systems. Excess parameters have been correlated with Redlich-Kister polynomial
equation.
To understand the molecular interaction and possibility of complex formation
in binary mixtures of Poly (Propylene Glycol) Monobutyl Ether (PPGMBE) 1000
with 2-(Methylamino) Ethanol (MAE) and 1-Butanol, a thermodynamic and 1H
NMR technique have been used in chapter 4. Surface tension (σ), relaxation time
(τ), deviation in viscosity (∆η) and excess Gibb’s free energy of activation of
xvii
viscous flow (∆G*E
) have been calculated from the experimental values. The values
of excess parameters were fitted to Redlich – Kister polynomial equation.
Chapter 5 reports the measurements of ultrasonic velocities (um) and
refractive index (nm) for the two binary mixtures viz. poly (ethylene glycol) butyl
ether (PEGBE) 206 with 1- butanol and 2(Methylamino) ethanol (MAE) over the
entire composition range at three temperatures T=293.15, 303.15, and 313.15 K and
at atmospheric pressure. Polarisability(α), molar refraction (Rm), free volume (Vf),
deviation in isentropic compressibility (Δks), excess intermolecular free length (𝐿𝑓𝐸),
deviation in ultrasonic velocity (∆u), excess internal pressure ( Ei ) and molar
refraction deviation (∆Rm) have been computed from experimental data at all the
three temperatures. These excess parameters have been correlated with Redlich -
Kister polynomial equation. The results have been interpreted on the basis of
strength of intermolecular interaction occurring in these mixtures.
With the aim to study the behavior of polymer solutions, density, viscosity
and NMR spectroscopy of binary mixtures of poly (ethylene glycol) butyl ether
(PEGBE) 206 with 1- butanol and MAE respectively at different concentration and
atmospheric pressure have been reported in chapter 6. From the experimental data
of density and viscosity, thermodynamic parameters viz. deviation in viscosity (∆η),
and Gibbs free energy of activation of viscous flow (∆G*E
) have been calculated
over whole composition range at 293.15, 303.15, and 313.15 K. The data have been
fitted to the Redlich–Kister equation, to obtain the binary coefficients and standard
deviations.
xviii
The chapter 7 intends to estimate the dielectric, ultrasonic and refractive
index of binary mixtures of some polymers and ceramic materials. Dielectric
constant (ε) of BaTiO3/ Poly (ethylene glycol) diacrylate (PEGDA), BaTiO3/
trimethylolpopane triacrylates (TMPTA) and BaTiO3/ epoxy have been investigated
by using different theoretical models and mixing rules like Jayasundere and Smith,
Lichtenecker logarithmic, Maxwell Garnett, Sillar and Yamada. The experimental
data have been taken from the work reported by R. Popielarz et.al and N. Hadik
et.al. The computation of ultrasonic velocity and refractive index using various
models and mixing rules like Nomoto’s, Van dael and Van Geel’s, Junjui’s,
Schaaff’s and Flory statistical theory for ultrasonic velocity and five mixing rules
for prediction of refractive index like Lorentz–Lorenz (L–L), Eykmen (Eyk),
Oster's, Gladstone–Dale (G–D) and Newton (N) have also been applied to various
systems to analyze and verify with the experimental data. The results have been
expressed in terms of average percentage deviation.
CHAPTER 1 General Discussion
1.1 Introduction
1.2 Ultrasonics
1.2.1 Methods for Production of Ultrasonics
1.2.2 Importance of Ultrasonics
1.3 Viscometry
1.3.1 Classification of Fluids
1.3.2 Importance of Viscometry
1.4 Refractometry
1.5 Volumetric
1.6 Dielectric
1.7 NMR Spectroscopy
1.7.1 Applications of NMR
1.8 Thermodynamic Excess Parameters
1.9 Objective and Scope of Present Study
References
1
1.1 Introduction
Polymers have been with us from the beginning of time; they form the basis
(building blocks) of life. Animals, plants - all classes of living organisms - are
composed of polymers. Developments of plastics are true manmade materials that
are ultimate to tribute to man‟s creativity and ingenuity. The use of polymeric
materials has permeated every facet of our lives. It is hard to visualize today‟s world
with all its luxury and comfort without man made polymeric materials.
Polymers may either be naturally occurring or purely synthetic. All the
conversion processes occurring in our body (e.g., generation of energy from our
food intake) are due to the presence of enzymes. Life itself may cease if there is a
deficiency of these enzymes. Enzymes, nucleic acid and proteins are polymers of
biological origin. Their structures are normally very complex. Starch - a staple food
in most cultures- cellulose, a natural rubber ,on the other hand, are polymers of
plant origin and have relatively simple structure as compared to those of enzymes or
proteins. There are large numbers of manmade (synthetic) polymers consisting of
various families: fibers, elastomers, plastics, adhesives, etc. Each family itself has
subgroups [1].
The physical properties of polymers are related to the strength of the covalent
bond, the stiffness of the segments in the polymer backbone, and the strength of the
intermolecular forces between the polymer molecules. The chemical properties of
polymers (e.g. tensile strength and melting point) are determined by the types of
atoms in the polymer, and by the strength of the bonds between adjacent polymer
chains. The stronger the bonds, the greater the strength of the polymer, and the
higher its melting point. Properties of polymers are related not only to the chemical
2
nature of the polymer but also to other factors such as extent and distribution of
crystallinity, distribution of polymer chain lengths, and nature and amount of
additives, such as fillers, reinforcing agents, and plasticizers. These factors
influence essentially all the polymeric properties to some extent, such as hardness,
flammability, weatherability, chemical resistance, biologic responses, comfort,
appearance, dyeability, softening point, electrical properties, stiffness, flex life,
moisture retention etc.[2].
For engineering purposes, the most useful classification of polymer is based
on their thermal (thermo- mechanical) response. Under this scheme, polymers are
classified as thermoplastics or thermosets. Thermoplastics polymers soften and flow
under the action of heat and pressure. Upon cooling, the polymer hardens and
assumes the shape of mould (container). A thermoset is a polymer that, when
heated, undergoes a chemical change to produce a cross- linked solid polymers.
Thermodynamic properties of pure polymers or their mixtures are
determined by intermolecular forces which operate between molecules of that
substance or between the molecules of the mixture. To interpret and correlate
thermodynamic properties of solutions it is therefore necessary to have some
understanding of the nature of intermolecular forces. When a molecule is in the
proximity of another, forces of attraction and repulsion strongly influence its
behaviour [3]. The attractive forces between polymer chains play an important role
in determining a polymer's properties. Because polymer chains are so long, these
inter-chain forces are very important. It is usually the side groups on the polymer
that determine what types of intermolecular forces will exist. The greater the
3
strength of the intermolecular forces, the greater will be the tensile strength and
melting point of the polymer.
The definition generally given for a ceramic material is “a product obtained
through the action of fire upon an earthy material”. The definition is sufficiently
broad to include not only structural products, such as refractories and building
materials, but also glass, enamelled ware, abrasives, cements, electrical and thermal
insulation [4, 5]. Ceramic material are molded from earthy inorganic materials and
permanently hardened by a firing or sintering process. It will not include ceramic
products molded in viscous liquid state, while hot, or glass, glass - bounded
products are excluded. However these products play an increasingly important role
as electric materials.
Ceramic dielectric may be conveniently classified in four groups [6]:
1) Materials with a dielectric constant below 12.
2) Materials with a dielectric constant above 12.
3) With piezoelectric and ferroelectric properties.
4) With ferromagnetic properties.
The forces present in nature are often divided into primary and secondary
forces. Primary forces can be further subdivided into ionic (characterized by lack of
directional bonding; between atoms of largely differing electronegativity; not
typically present within the polymer backbone), metallic (the number of outer,
valence electrons is too small to provide complete outer shells; often considered as
charged atoms surrounded by a potentially fluid sea of electrons; lack of bonding
directions; not typically found in polymers ) and covalent (including coordinate and
4
dative) bonding (which are major means of bonding within polymers; directional).
Secondary forces, frequently called Vander Waal‟s forces, since they are
responsible for Vander Waal‟s corrections to the ideal gas relationships, are of
longer interactions. Thus, many physical properties of polymers are indeed quite
dependent on both the conformation (arrangement related to rotation about single
bonds) and configuration (arrangement related to the actual chemical bonding about
a given atom). Secondary, intermolecular forces include London dispersion forces,
induced permanent forces, and dipolar forces, including hydrogen bonding.
Intermolecular forces of non- spherical molecules depend not only on the
centre- to- centre distance but also on the relative orientation of molecules. The
effect of molecular shape is most significant at low temperatures, when the
intermolecular distances are small i.e. in condensed state. When macromolecules
are under consideration the size and shape of molecules also play an important role
in the thermodynamic properties of solution. Studies of thermodynamic properties
have been quite applicable in understanding physical and chemical behaviour and
nature of intermolecular interactions in the polymers and their solutions [7].
Molecular interaction provides a better understanding of fundamental
problems related to the mechanism of chemical and biochemical catalysis and the
path of chemical reactions because this is the key to understand the structure and
properties of liquids, solids and gases. Therefore, the study of molecular interaction
is one of the most fascinating areas of research in condensed matter physics [8-15].
Investigation into the properties of liquid mixtures is the direct way to study the
various parameters arising from the properties of the liquid in terms of
intermolecular forces. It also influences the arrangement, orientation and
5
conformation of the molecules in solutions. Study of liquid mixtures has been an
active area of research and various detailed theories have been given by Moelwyn-
Hughes [16], Hilderbrand [17], Marcus [18], Kihara [19], and Murrel [20]. Both
experimental observations and theoretical approaches are important for the
knowledge of intermolecular forces.
A lot of experimental and theoretical work has been made on the properties of
the liquid mixtures because firstly, they provide way of studying the physical forces
acting between the molecules of different species. Secondly, the appearance of new
phenomenon in mixtures which are absent in pure substance. The most interesting
of these are new types of phase equilibrium which arise from the exact degree of
freedom introduced by the possibility of varying the proportions of the components
[21]. To study the molecular interaction and its relationship with ambience
parameters, a number of techniques have been utilized, viz, NMR, FTIR, X-ray,
vapour pressure, dielectric, ultrasonic, viscometric, volumetric etc. [22, 26], Among
these, the dielectric, ultrasonic, viscometric, volumetric and refractometric
techniques are widely used because of less demanding experimental technology.
1.2 Ultrasonics
Ultrasonics is defined as that band above 20 kHz. It continues up into the
megahertz range and finally, at around 1GHz, goes over into what is conventially
called the „hypersonic‟ regime. Optics and acoustics have followed parallel paths of
development from the beginning. Indeed most phenomena that are observed in
optics also occur in acoustics. But acoustics has something more the longitudinal
mode in bulk media, which leads to density changes during propagation [27].
6
1.2.1 Methods for Production of Ultrasonics
There are several methods for the production of ultrasonics. Mechanical
method is one of the earliest methods for producing ultrasonic waves of frequencies
up to 100 KHz with the help of Galton‟s whistle. The method is rarely used due to
its limited frequency range.
In 1917, Langevin used piezoelectric effect for the generation of ultrasonic
waves describing the piezoelectric generator. Piezoelectric effect was discovered by
J. Curie and P. Curie in the year 1980. They discovered that when mechanical
pressure are applied to the opposite faces of certain crystal slices cut suitably, then
equal and opposite electric charges are developed on the other faces resulting a
difference of potential. The magnitude of the potential difference so developed is
proportional to the applied pressure. However, when pressure is replaced by tension,
the sign of charges is reversed. This phenomenon is called piezoelectric effect. The
converse effect is also possible i.e., if a potential difference is applied to the
opposite faces of the crystal, then a change in dimension in the other faces would
take place according to the direction of potential difference. Most generally used
crystals for ultrasonic wave generation are quartz, Rouchelle salt,
ammoniumdihydrogen phosphate (ADP), lithium sulphate (LH), dipotassiumtertrate
(DKT), potassium dihydrogen phosphate (KPD). Quartz crystal has a property of
expanding and sending out an ultrasonic wave when it is mechanically vibrated.
Besides quartz, Rochelle salt is one of the principal materials used in the generation
of ultrasonics, especially in the low frequency ranges and signaling [28].
Tourmaline lends itself to the production of higher frequency ultrasonic waves than
quartz. Barium titanate is a generic term covering a number of components which
7
may be moulded into crystals with electrostictive properties. Lithium sulphate is
beginning to be used for ultrasonic apparatuses.
Another way of producing high frequency ultrasonic waves is
magnetostrictive method. It is a phenomenon only found in ferromagnetic
materials. When alternating current is passed through a coil in which a
ferromagnetic rod is kept along the axis of the coil then the length of the rod will
change twice in each cycle of the magnetic field of the coil due to magnetostriction,
because the change in the length is independent of the direction of the magnetic
field. The periodic change in the length of the rod produces ultrasonic waves when
applied current is of suitable frequency.
The modern technique for producing ultrasonic wave is Laser Beam
Ultrasonic (LBU). Laser-ultrasonic uses lasers to generate and detect ultrasonic
waves. It is a non-contact technique used to measure materials thickness, detect
flaws and materials characterization. The basic components of a laser ultrasonic
system are a generation laser, a detection laser and a detector. LBU systems operate
by first generating ultrasound in a sample using a pulsed laser. When the laser pulse
strikes the sample, ultrasonic waves are generated through a thermo elastic process
or by ablation. Its accuracy and flexibility have made it an attractive new option in
the non-destructive testing market. Well established applications of laser- ultrasonic
are composite inspections for the aerospace industry and on-line hot tube thickness
measurements for the metallurgical industry.
1.2.2 Importance of Ultrasonics
The velocity of sound wave is the most important parameter that can be
measured experimentally. The speed of ultrasound in a homogenous medium and is
8
directly related to both elastic modulus and density; thus changes in either elasticity
or density will affect pulse transit time through a sample of a given thickness.
Ultrasonic waves are fruitful to investigate about the molecular structures,
interactions and molecular energies, due to the fact that the natural frequencies of
ultrasonic waves are comparable to the natural frequencies of vibration and rotation
of the molecules of the matter [29]. Therefore, the ultrasonic velocity measurements
in liquids and gases and its variation with temperature, pressure and frequency etc.
provide detailed information regarding the properties of the medium, such as
absorption compressibility, intermolecular forces and molecular interactions,
chemical structure and the energies of the molecules in motion. Over the years,
ultrasonic technique [30-33] has been found to be one of the most powerful tools for
studying the structural and other physico-chemical properties of liquids and liquid
mixtures. Boyle initiated the study of propagation of ultrasonic wave in liquids.
Lagemann and Dunbar [34] were the first to point out the sound velocity approach
for qualitative determination of the degree of association in liquids. In recent years,
the measurement of ultrasonic velocity has been successfully employed in
understanding the nature of molecule interaction in pure liquids and liquids
mixtures. Ultrasonic velocity measurements are highly sensitive to molecular
interactions and can be used to provide qualitative information about the physical
nature and strength of molecule interaction in liquid mixture [35-37].
Ultrasonic velocity in conjunction with density measurements permits the
direct estimation of adiabatic compressibility, intermolecular free length and other
co-related parameters, which cannot be conveniently deduced by any other method.
9
Many workers have examined the validity of various theories [38-47] by ultrasonic
velocity, density, refractive index and viscosity measurements.
Ultrasonic spectroscopy [48-51] has become a valuable tool in the field of
applied chemistry, physical chemistry and chemical physics, as well as
biochemistry, biophysics and material science. Because of its sensitivity and far
reaching universality the ultrasonic approach has the potential to afford valuable
insights into the molecular order and microdynamics of the liquid phase. It can
substantially contribute to our knowledge of molecular interactions and of the
kinematics of elementary processes in liquids.
1.3 Viscometry
Viscosity is a key fundamental property which plays an important role in
fluid transport, mixing, heat transfer, mass transfer operation. Polymer solutions
viscosities at high pressure are also of importance in reactive system such as
polymerizations.
The viscosity of a fluid is a measure of its resistance to gradual deformation
by shear stress or tensile stress. Viscosity is due to friction between neighboring
parcels of the fluid that are moving at different velocities.
According to Newton Viscosity of the liquid is defined as is the ratio of the
applied shear stress to the resulting strain rate (or equivalently, the ratio of the shear
stress required to move the solution at a fixed strain rate to that strain rate).
nshearstrai
sshearstres
10
One of the most obvious factors that can have an effect on the rheological
behaviour of a material is temperature. Some materials are quite sensitive to
temperature, and a relatively small variation in temperature will result in a
significant change in viscosity as temperature increases, the average speed of the
molecules in a liquid increases and the amount of time they spend "in contact" with
their nearest neighbors decreases. Thus, as temperature increases, the average
intermolecular forces decrease. The exact manner in which the two quantities vary
is nonlinear and changes abruptly when the liquid changes phase.
Viscosity of a polymer solution depends on concentration and size (i.e.,
molecular weight) of the dissolved polymer. By measuring the solution viscosity we
should be able to get an idea about molecular weight. Viscosity techniques are very
popular because they are experimentally simple [52].
1.3.1 Classification of fluids
Fluids can be classified as: Newtonian and Non – Newtonian.
Newtonian
According to Newtonian laws, the viscosity of a fluid is constant. As shear
stress changes in proportion such that viscosity is constant (Figure 1.1). Common
fluids that exhibit such behaviour are: water, glycerin, mineral oil, solvents.
Newtonian flow is most easily understood by thinking of a liquid that has a constant
viscosity over a wide range of shear rate at a giving temperature. The viscosity is
independent of shear rate at which it is measured. If viscosity of a fluid is measured
at different shear rates and the resulting viscosity are equivalent, the material is
Newtonian over the shear rate range that it is measured.
11
Figure 1.1 Schematic plots of shear stress vs. shear rate for Newtonian and non-Newtonian fluids.
Non-Newtonian
For a non-newtonian fluid, viscosity is dependent upon the shear action
(shear rate or shear stress) at which it is measured (Figure 1.1). Non -newtonian
flow may be classified into two categories: non Newtonian time independent flow
and non-newtonian time dependent flow. The time dependency is the time the fluid
is subjected to shear action. Non - newtonian time independent flow can be
pseudoplastic, dilatants or plastic. Pseudoplastic fluids display a decreasing
viscosity with an increasing shear rate. Increasing viscosity with increasing shear
rate characterizes the dilatants fluids. Plastic fluids will behave as solid under static
conditions.
Non- newtonian time dependent flow be thixotropic or rheotropic depending
or decreasing or increasing in viscosity respectively with time at constant shear rate.
1.3.2 Importance of Viscometry
The knowledge of viscosity is needed for proper design of equipments for
storage, pumping or injection of fluids at required temperature. There are number of
different techniques by which fluid‟s resistance to flow is measured. Viscosity data
12
is of great importance in many chemical engineering disciplines such as simulation
of processes or the design of chemical equipments. Literature survey shows that
several workers [53-57] have measured viscosity in liquids and utilized viscosity
data to study the molecular interactions. Viscosity is also important in many
commercial applications, such as consumer products like shampoo, and viscometers
are used extensively in quality control.
1.4 Refractometry
Refractive index is one of the most important optical properties of a medium.
It plays vital role in many areas of material science with special reference to thin
film technology and fiber optics. Refraction occurs with all types of waves but is
most familiar with light waves. By measuring the refractive indices at different
temperatures, the temperature coefficient of refractive index (dn/dT) can be
determined. Refractive index (n) of any medium is a quantitative measure of the
response of constituent molecules of the medium to the electromagnetic waves and
is defined as the ratio of the velocity of electromagnetic wave in vacuum to the
velocity of that in the medium. H.A. Lorentz, on the basis of electromagnetic theory
of light and L.V. Lorenz, on the basis of wave theory of light, independently
deduced following relationship between the refractive index ( n) and density (ρ )
viz.
1
2n
1n2
2
Constant
This constant is called specific refraction. The molar refraction (Rm) is a
derived quantity and is defined as [58]
13
m2
2
m V2n
1nR
where n is the refractive index of the medium and Vm is the molar volume of
the medium.
Measurements of refractive indices provide significant insight into the
molecular arrangement in liquids and help one to understand the thermodynamic
properties of liquid mixtures. The study of the variations of refractive index of a
liquid with temperature and with mixing of different solutes in varying
concentration gives valuable information about the structure of liquids or liquid
mixtures. Literature survey reveals that enormous amount of the work has been
done to measure or evaluate the refractive index of liquids, liquid mixtures and
polymers [59-60].
The refractive index plays a vital role in many branches of physics, biology
and chemistry. Knowledge of the refractive index of aqueous solutions of salts and
biological agents is of crucial importance in applications of evanescent wave
techniques in biochemistry [61]. Chemical modifications may be detected by
measurements of refractive index. Among the many possible applications is the
control of adulteration of liquids. Different methods have been developed to
measure the refractive index of liquids. The most common type of refractometer
measures the refractive index of the samples by detecting the critical angle of total
14
reflection [62]. Many kinds of interferometric methods for determining the
refractive index of materials have also been developed [63-65].
1.5 Volumetry
Density describes the degree of compactness of a substance or in other words,
how the atoms of an element or molecules of a compound are closely packed
together.
Density measurements provide interesting information regarding the ion-ion,
ion-solvent and solvent-solvent interactions and also on structural effect of solute
and solvent in solution. Liquid densities are important for the design of new
processes, simulations equipment, pipe design and liquid metering calculations.
Many workers [66-69] have measured the density of liquid systems and utilized it to
compute the parameters like excess molar volume. Molar volume can be easily
measured from the experimental data of density and mole fraction and provides an
efficient and convenient tool to study the molecular level interactions.
Non - zero values of excess molar volume, which measures the deviation of
molar volume from ideality has been interpreted by many workers [70-72] as a
commutative manifestation of three effects such as physical, chemical and
structural.
15
1.6 Dielectric
Dielectrics and insulators can be defined as materials with high electrical
resistivities. A good dielectric is, of course, necessarily a good insulator, but the
converse is by no means true [73].
Dielectrics are a class of materials that are poor conductors of electricity, in
contrast to materials such as metals that are generally good electrical conductors.
Many materials, including living organisms and most agricultural products, conduct
electric currents to some degree, but are still classified as dielectrics. The electrical
nature of these materials can be described by their dielectric properties, which
influence the distribution of electromagnetic fields and currents in the region
occupied by the materials, and which determine the behaviour of the materials in
electric fields. Thus, the dielectric properties determine how rapidly a material will
heat in radio-frequency or microwave dielectric heating applications. Their
influence on electric fields also provides a means for sensing certain other
properties of materials, which may be correlated with the dielectric properties, by
non destructive electrical measurements [74].
The measurement of dielectric properties has gained importance because it
can be used for non-destructive monitoring of specific properties of materials
undergoing physical or chemical changes.
1.7 NMR Spectroscopy
Nuclear magnetic resonance spectroscopy, most commonly known as NMR
spectroscopy, is a non-destructive research technique that exploits the magnetic
properties of certain atomic nuclei. It determines the physical and chemical
16
properties of atoms or the molecules in which they are contained. It relies on the
phenomenon of nuclear magnetic resonance and can provide detailed information
about the structure, dynamics, reaction state, and chemical environment of
molecules. This technique is widely applied in chemistry, physics, biochemistry and
materials science, and also in many areas of biology and medicine. A simple NMR
experiment produces information in the form of a spectrum, which is able to provide
details about:
The types of atoms present in the sample.
The relative amount of atoms present in a sample.
The specific environment of atoms within a molecule.
The purity and composition of a sample.
Nuclear magnetic resonance (NMR) spectroscopy can be used for
quantitative measurements, but it is most useful for determining the structure of
molecules (along with IR spectroscopy and mass spectrometry). The utility of NMR
spectroscopy for structural characterization arises because different atoms in a
molecule experience
slightly different magnetic fields and therefore transitions at
slightly different resonance frequencies in NMR spectrum. Furthermore, splitting of
the spectra lines arise due to interactions between different nuclei, which provide
information about the proximity of different atoms in a molecule.
1.7.1 Applications of NMR
Today, NMR has become a sophisticated and powerful analytical technology
that has found a variety of applications in many disciplines of scientific research,
medicine, and various industries. The most important role NMR plays in
17
pharmaceutical analysis is its use in elucidating and/or confirming the structures of
drug-related substances. However, NMR is also used to study drug impurities and
contaminants including solvents, synthetic precursors, synthetic intermediates, and
decomposition products. In the case of natural products, NMR may be used to
determine the identity of co-extractives. It also has a role to play in the study of
drug metabolism where it has been used for identification and quantification of
many metabolites [75].
Some of the important applications of NMR spectroscopy are listed below
Material science A powerful tool in the research of polymer chemistry and
physics.
Hydrogen bonding A unique technique for the direct detection of hydrogen
bonding interactions.
Weak intermolecular interactions Allowing weak functional interactions
between macrobiomolecules (e.g., those with dissociation constants in the
micromolar to millimolar range) to be studied, which is not possible with other
techniques.
Solution structure The only method for atomic-resolution structure
determination of bio-macromolecules in aqueous solutions under near
physiological conditions or membrane mimeric environments.
Chemical analysis A matured technique for chemical identification and
conformational analysis of chemicals whether synthetic or natural.
Native membrane protein Solid state NMR has the potential for determining
atomic-resolution structures of domains of membrane proteins in their native
membrane environments, including those with bound ligands.
18
Metabolite analysis A very powerful technology for metabolite analysis.
Drug screening and design Particularly useful for identifying drug leads and
determining the conformations of the compounds bound to enzymes, receptors,
and other proteins.
Protein folding The most powerful tool for determining the residual structures
of unfolded proteins and the structures of folding intermediates.
1.8 Thermodynamic Excess Parameters
Excess thermodynamic functions have been used as qualitative and
quantitative guide to predict the extent of complex formation in binary and ternary
systems. In recent years [76-79] there has been considerable advancement in the
theoretical and experimental investigations of the excess thermodynamic properties
of binary liquid systems.
For the design of separation equipment and to test theories of solutions there
is a constant need for thermodynamic excess properties data. Knowledge of mixing
properties, such as excess enthalpies, excess Gibb‟s free energy of activation for
viscous flow, deviation in viscosity, excess molar volume, excess internal pressure,
excess free volume, molar refraction deviation etc, which are derived from
experimentally determined values of ultrasonic velocity, density, refractive index
and viscosity give the better understanding of molecular interactions and variation
of nature of molecular unit.
1.9 Objective and Scope of Present study
The main aim of the present work is to study the molecular interaction in
various binary systems at varying temperatures covering the entire composition
19
(0<x>1) so that the precise knowledge about the behaviour of the molecules in
mixing can be ascertained. Results of one experimental technique often contradict
the results obtained from some other technique; therefore attempt has been made by
using more than one technique to establish the nature of interaction, so that precise
correlation between microscopic structure and macroscopic properties can be made.
The aim of this thesis is to create a source of information regarding the
interaction present in polymer solutions i.e. how the individual functional groups in
long chain molecules interact when they are mixed with hydrogen bonding
molecules. In order to examine degree of association in industrially important
polymers using thermodynamic and spectroscopy techniques, several polymer-
solvent systems viz. PPGMBE + 1-butanol, PPGMBE + 2-(Methylamino) ethanol
(MAE), PEGBE + 1-butanol, and PEGMBE + 2-(Methylamino) ethanol (MAE),
were under taken.
The data given in the thesis and theories tested would provide some important
information, which will be useful for industrial applications. It may also be utilized
further for exploring new theories which may lead in preparing experimental ground
to develop, modify and test them.
20
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CHAPTER 2 Techniques of Measurement: Apparatus used and Mathematical
Evaluations
2.1 Ultrasonic Velocity Measurement
2.1.1 Principle of Interferometric Technique
2.1.2 Experimental Set-Up
(a) High Frequency Generator
(b) Measuring cell
2.2 Refractive Index Measurement
2.2.1 Principle of Abbe’s Refractometer
2.2.2 Calibration and Mode of Operation
2.3 Viscosity Measurement
2.3.1 Principle of Operation
2.3.2 Experimental Set Up
2.3.3 Electronic Gap Setting
2.3.4 Software
2.3.5 Specifications
2.4 Temperature Controller
2.5 Density Measurement
2.6 1H NMR Spectroscopy Measurement
2.6.1 Principle of N.M.R
2.7 Preparation of Mixtures
2.8 Evaluation of Acoustical, Thermodynamic and Excess
Parameters
2.8.1 Isentropic Compressibility (ks)
2.8.2 Surface Tension(σ)
2.8.3 Acoustic Impedance (Z)
2.8.4 Optical Dielectric Constant (ε), Polarisability (α) and
Molar Refraction (Rm)
2.8.5 Intermolecular Free Length (Lf)
2.8.6 Gibb’s Free Energy of Activation for Viscous Flow ( *G )
2.8.7 Free Volume and Internal Pressure
2.8.8 Excess Parameters
2.9 Analysis of Data
2.9.1 Redlich- Kister Polynomial Equation
2.9.2 Data Correlation
2.10 Mixing Rules
2.10.1 Mixing Rules for Refractive Index
2.10.2 Mixing Rules for Ultrasonic Velocity
2.10.3 Mixing Rules of Dielectric Constant
2.10.4 Mixing Rules for Viscosity
2.10.5 Flory’s Statistical Theory
2.10.6 Excess Thermodynamic Functions
2.11 Samples Under Investigation
References
fV i
24
Measurements of physico - chemical properties such as density, refractive
index and ultrasonic velocity of pure components and their binary mixtures are
being increasingly used as tools for investigations of the properties of pure
components and the nature of intermolecular interactions between the components
of liquid mixtures. The dynamical behaviour of liquid can be studied by the accurate
measurement of the ultrasonic velocity, density, viscosity and refractive index of
liquids. A brief description of apparatus and their principle of working for the
accurate measurement of ultrasonic velocity, absolute viscosity and refractive index
have been discussed in this chapter. Various theories, empirical and semi- empirical
relations and mixing rules have also been mentioned.
2.1 Ultrasonic Velocity Measurement
Measurements of ultrasonic velocities are made in liquids in order to get an
idea of their chemical and physical characteristics. A large number of such
measurements have been made and given in the literature [1, 2]. Generally, three
techniques namely echo- pulse, optical diffraction and interferometric technique are
employed for the measurements of ultrasonic velocity in liquids. In the present
work, the ultrasonic velocity measurements were made by an interferometric
method [3].
2.1.1 Principle of Interferometric Technique
For exact measurement of wavelength of any wave motion interferometer is
used. One of the most accurate ways of measuring ultrasonic constants in fluids or
gases is, to set up stationary wave resonances. This is, usually done in a column at
one end of which the source is located and at the other end reflector is placed. This
25
is known as single interferometer and was originally proposed by Perrin [4]. The
working of such a device can be illustrated with the help of a schematic diagram
given in Figure 2.1(a). T represents an X- cut quartz crystal transducer which is gold
or silvered polished to provide metallic contacts to an oscillator O. When the
frequency of driving oscillator O coincides with the natural frequency of
piezoelectric transducer T, it vibrates with appreciable amplitude. The moving
surface of the crystal generates a plane sound wave which travels through the
medium towards a plane reflecting plate R, maintained parallel to the crystal
surface. A crystal source transmits ultrasonic wave into the medium; they impinge
upon a parallel reflector and are reflected back to the source. The parallel reflector
is ordinarily mounted on a very fine screw, which can move the reflector in small
fractions of centimeter at a time. Standing waves are set up in the medium, when the
distance between the reflector and the crystal is an integral number of half
wavelengths. The reflected wave arriving back at the crystal is then 1800out of
phase with the vibration of the crystal.
As the reflector is moved through a given distance, the plate current of the
oscillator that provides the driving force for the sending crystal is observed and
points during which the current is a minimum are noted. The distance between two
successive minima (or maxima) is λ/2, where λ is the wavelength of the sound wave
in the medium between crystal and reflector as shown in Figure 2.1 (b). Once the
wavelength is known, the ultrasonic velocity (u) in the liquid can be obtained using
the following relation:
u = frequency ( f ) × wavelength ( λ ) (2.1)
26
(a)
(b)
Figure 2.1 Principle of the Ultrasonic Interferometer: T, Transducer silvered on
opposite faces; R, Movable Reflector; O, Oscillator
27
2.1.2 Experimental Set-Up
In the present work the interferometer (Figure 2.2) used is a variable path
fixed frequency interferometer provided by Mittal Enterprises, New Delhi (Model
F-81). It consists of a high frequency generator, a measuring cell and a digital
display micrometer.
(a) High Frequency Generator
This is a high frequency crystal controlled oscillator based on modified Piere
circuit operating in the megahertz region. The circuit diagram of ultrasonic
interferometer is shown in Figure 2.3. It is used to excite the piezoelectric
transducer which is a quartz crystal fixed at the bottom of the measuring cell to
produce ultrasonic waves at its resonant frequency in the experimental liquid filling
the cell. The oscillator is provided with a micro-ammeter to observe the changes in
current and two trimmer condensers marked A and B on the backside of the
generator assembly. These are used to adjust or tune the instrument so that sufficient
deflection in anode current can be observed. Two controls, one for the adjustment of
micro-ammeter and other for controlling gain, are provided. The detailed technical
specifications are as given below:
(a) Mains voltage - 220V, 50Hz
(b) Measuring frequency - 2 MHz
(c) Glow lamp - 6.3 V, 0.3 A
(d) Fuse - 150 mA
28
(b) Measuring Cell
The coupling of the generator to the crystal is such that it prevents high-
voltage breakdown and also provides a maximum transfer of power. Measuring cell
is a double walled cylindrical metallic container (Figure 2.4) attached vertically into
a slot on a heavy metal base which works as the coupler between piezoelectric
crystal and the high frequency generator. Piezoelectric crystal is fixed at the base of
this measuring cell. For maintaining the temperature of the experimental liquid,
filled in this cell, there is a provision for circulation of water or any other liquid of
known temperature in the space between the two walls of the cell. A quartz crystal
of a particular natural frequency of vibration, which acts as piezoelectric transducer,
is fixed at the bottom of the cell. A movable metallic reflector plate, attached to a
micrometer screw arrangement and kept parallel to the crystal, is housed inside the
cell. The measuring cell can be easily dismantled into three pieces viz. metal base,
container, and reflector such that the experimental liquid can be easily poured into
the cell. The transducer is coupled to the high frequency oscillator by a coaxial
cable. The detailed technical specifications are as under:
(a) Maximum displacement of the reflector: 25 mm
(b) Capacity of a cell: 12 ml
(c) Least count of micrometer: 0.001 mm.
The calibration of ultrasonic interferometer was done by measuring the
velocity (u) in AR grade benzene (C6H6) and carbon tetra chloride (CCl4). These
values of u agree closely with the corresponding standard values. The maximum
estimated error has been found to be + 0.08 %.
29
Figure 2.2 Experimental Setup of Ultrasonic Interferometer
30
Fig
ure
2.3
Cir
cuit
dia
gra
m o
f U
ltra
son
ic I
nte
rfe
rom
ete
r
31
Figure 2.4 Measuring Cell of Ultrasonic Interferometer
32
2.2 Refractive Index Measurement
Refractive index of a liquid is an important physical property. In the present
work refractive indices of pure liquid and liquid mixtures were measured by the
Abbe‟s refractometer supplied by the Optics Technologies, New Delhi, which
works with the wavelength corresponding to the D-line of sodium. Refractometer
measures refractive indices in the range of 1.300 to 1.700 with an accuracy of
±0.001 unit.
2.2.1 Principle of Abbe’s Refractometer
The working of the Abbe‟s refractometer is based on the accurate
measurement of critical angle. The critical angle for a boundary separating two
optical media is defined as the smallest angle of incidence in the medium of greater
refractive index, for which the light is totally internally reflected [5]. Figure 2.5
shows the schematic diagram of the Abbe‟s refractometer.
A light-beam from a monochromatic source, a sodium lamp in the present
work is illuminated on the face AB. P and Q is right-angled prisms, each of
refractive index higher than that of the experimental liquid. A thin layer of the
experimental liquid is introduced between them using a hypodermic glass syringe.
The prism Q and mirror M simply provide a convenient method of passing
light from the liquid into prism P. The light ray incident on face AB of the prism P
at an angle i is refracted at an angle r and strikes at the face AC at an angle i .
i is the angle of emergence from the face AC. If c is the critical angle for the
interface between the prism and liquid, then
33
Figure. 2.5 Abbe’s Refractometer
34
pc nn θ sin , (2.2)
where, n and pn are refractive index of the liquid and prism material
respectively. For grazing incidence on the face AB (i.e. i ≈ 90o), the light will be
refracted at an angle ci due to principle of reversibility [6] and thus emerges
from the face AC at an angle c (say).
For any other incidence, i.e. i < 90o, the light will be refracted at an angle less than
c and therefore will emerge from the face AC at an angle greater than c . Thus, no
light ray will emerge at an angle of emergence less than c . Hence along the line in
the plane of Figure 2.6, across the field of view of telescope T, the intensity will
show a sudden rise at the point corresponding to the angle of emergence c ; a line of
demarcation will appear the right hand side of which will appear brighter.
If is the angle of the prism, then
cpl sinnn
p
lc
n
nsin
cp sinn (2.3)
[from cc,AMN ]
cpcp sincosncossinn
cc22
pl sincossinnsinn (2.4)
35
Fig
ure
2.6
Wo
rkin
g o
f A
bb
e’s
re
fra
cto
me
ter
36
pc
c
n
1
sin
sin,laws'Snellfrom
Thus by knowing the value of c , we can measure the value of refractive
index of the liquid with respect to air [6]. To measure c , telescope T is adjusted to
bring the demarcation line on the cross-wire. T is then swung round until, using the
Gauss eye-piece; it is set with its axis perpendicular to face AC. The angle turned
through by T is obviously c . Usually T is carried on an arm attached to a scale that
is calibrated to directly read the refractive index of the liquid.
2.2.2 Calibration and Mode of Operation
The prism chamber and the scale of the Abbe‟s refractometer rotate together
about the same axis when the milled head is operated. There is a provision for
circulating water from the water bath around the prism chamber in order to maintain
the desired temperature of the prism chamber and hence the experimental liquid.
A small quantity of the experimental liquid is introduced between the two
prisms. The reflector fitted on the base of the instrument is adjusted in such a way
that a beam of light passes through the opening at the bottom of the lower prism.
The eyepiece of telescope is focused on the cross-wire in its focal plane. The prism
chamber is rotated by operating the milled head until the cross-wire coincides with
the line of demarcation between bright and dark halves of the field of view. At this
position, the reading on the scale directly gives the value of refractive index of the
liquid. The calibration of the refractometer was made by measuring the refractive
indices of standard liquids viz. benzene (C6H6) and carbon tetra chloride (CCl4) at
293 K.
37
2.3 Viscosity Measurement
Viscosity of liquid mixtures was measured by using LVDV II+ Pro
viscometer supplied by Brookfield Engineering Laboratories Inc, USA. with
complete control by PC using Brookfield Rheocalc32 Software (Figure 2.7).
2.3.1 Principle of Operation
The principle of operation of LVDV- II+ Pro viscometer to drive a spindle
(which is immersed in test fluid) through a calibrated spring. The viscous drag of
fluid against the spindle is measured by the spring deflection and spring deflection
is measured with a rotatory transducer. Cone/ plate geometry offers absolute
viscosity determinations with precise shear rate and shear stress information readily
available. Cone/ plate geometry is particularly suitable for advanced rheological
analysis of non- Newtonian fluids.
2.3.2 Experimental Set Up
The viscometer is compared of several mechanical subassemblies. The
stepper drive motor is located at the top of the instrument inside housing. The
viscometer case contains a calibrated beryllium-copper spring, one end of which is
attached to the pivot shaft; the other end is connected directly to the dial. The dial is
driven by the motor drive shaft and in turn drives the pivot shaft through the
calibrated spring. The relative angular position of the pivot shaft is detected by a
rotary variable displacement transducer (RVDT) and is read put on a digital display.
Below the main case is the pivot cup through which the lower end of the pivot shaft
protrudes. A jewel bearing inside the pivot cup rotates the transducer. The pivot
shaft is supported on this bearing by the pivot point. The lower end of the pivot
38
shaft comprises the spindle coupling to which the viscometer‟s spindles are
attached.
2.3.3 Electronic Gap Setting
The gap between the cone and the plate is adjusted by moving the plate (build
into the sample cup) up towards the cone until the pin in the centre of the cone
touches the surface of the plate, and then by lowering the plate 0.0005 inch. This
gap setting is required because most of the fluids are dependent on shear rate and
the spindle geometry conditions. The specifications of the viscometer spindle and
chamber geometry will affect the viscosity readings. The faster the spindle is shear
rate. The shear rate of a given measurement is given by the rotational speed of the
spindle, the size and shape of the container used and therefore the distance between
the container wall and the spindle surface.
2.3.4 Software
Rheocalc32 is a control program which operates the LV DV- ІІ + Pro in
external control via a PC, as well as a data gathering program which collects the
data output from DV- ІІ+ Pro and provides the capability to perform graphical
analysis and data file management. Important features and benefits in Rheocalc32
enhance operator versatility in performing viscosity tests. It is compatible with
Windows 95, 98, ME, 2000 and NT operating systems. Its 32 bit operation makes
the performance rapid.
39
Figure 2.7 Brookfield Viscometer for Viscosity Measurement
40
2.3.5 Specifications
Each spindle has a two digit entry code which is entered via the keypad on
the LV DV- ІІ+ Pro. The entry code allows the LV DV- ІІ+ Pro to calculate
viscosity, shear rate and shear stress value. Each spindle has two constants which
are used in these calculations. The Spindle Multiplier Constant (SMC) used for
viscosity and shear stress calculations and the Shear Rate Constant (SRC), used for
shear rate and shear stress calculations. For spindle CPE-40(entry code 40) SMC
value is 0.327 and SRC is 7.5, while for spindle CPE- 52 (entry code 52) SMC is
9.922 and SRC is 2. The spring torque constant (TK) IS 0.09373. Using these
constants, the full scale viscosity range is calculated using following equations
1) Full Scale Viscosity Range [cP] = TK×SMC×100/RPM×Torque
2) Shear Rate (1/sec) = SRC×RPM
3) Shear Stress (Dynes/ cm2) = TK×SMC×SRC×Torque
The experiment assembly allows measurement of viscosities in the range of
0.15 cP to 3,065 cP (with CPE-40) and 4.6 cP to 92,130 cP (with CPE-52) with an
accuracy of +1.0% of full scale range and repeatability of 2.0%.
The apparatus measure fluid absolute viscosity directly in cP. The apparatus
was calibrated by two viscosity standards (Polydimethylsiloxane with viscosity 4.6
and 485 cP) provided by the Brookfield Engineering Laboratories. The viscosity
standards are Newtonian and therefore have the same viscosity regardless to the
spindle speed.
41
2.4 Temperature Controller
Temperature control during the various experimental measurements helps to
ensure accurate test results. We are using the digital temperature controller model
TC-502 supplied by Brookfield Engineering Laboratories Inc, USA. (Figure 2.8) It
has temperature range from -20oC to 200
oC with an accuracy of ±0.01
oC. This
temperature controller consists of two speed pump with unique rotatory control.
2.5 Density Measurement
There are several methods for evaluating density of liquid mixtures. In the
present work, single-limbed calibrated pyknometer with a bulb capacity of
approximately 8.0 ml volume was used for determining the densities of the
mixtures. The pyknometer stem, with uniform fine bore, had uniform graduations of
0.01 ml over it. To minimize the loss of liquid due to evaporation, teflon cap was
used for closing the open end of the capillary stem, with a small orifice to ensure
that the pressure inside the capillary was equal to the atmospheric pressure. The
weight of empty, well cleaned and dried pyknometer was taken accurately by
electronic balance OHAUS(AR 2140) and then the liquid was introduced into the
bulb of the pyknometer with the help of hypodermic syringe having a needle long
enough to reach the bottom of the bulb so as to avoid the undesired sticking of the
solution to the inner wall of the pyknometer stem. Filled pyknometer was again
weighed accurately. For maintaining the temperature, filled pyknometer was kept
inside a double wall glass jacket having provisions for water circulation. For
maintaining temperature, filled pyknometer was kept inside a double wall glass
jacket having provisions for circulation of water from thermostated water bath.
42
Figure 2.8 Temperature Controller Setup (Model TC-502)
43
Sufficient time was given before taking reading at a given temperature so as
to ensure thermal equilibrium between the contents of the pyknometer and the water
circulating around it. The density of the experimental liquid, at the given
temperature, is calculated using the values of its mass and volume. The pyknometer
was calibrated using AR grade C6H6 and CCl4 at 293 K. The maximum possible
percentage error in density is +0.08%.
2.6 1H NMR Spectroscopy Measurement
Nuclear Magnetic Resonance (NMR) Spectroscopy is a non-destructive
analytical technique that is used to probe the nature and characteristics of molecular
structure of pure and binary liquid mixtures. 1H-NMR spectra were obtained at
room temperature using Bruker DRX- 400 spectrometer operating at 400 MHz
(Figure 2.9), no other NMR solvent was added. For analyzing NMR spectra a
TOPSPIN software used.
2.6.1 Principle of N.M.R
Principle of N.M.R is based upon the spin of nuclei in an external magnetic
field. In absence of magnetic field, the nuclear spins are oriented randomly. Once a
strong magnetic field is applied they re-orient their spins i.e. aligned with the field
or against the field. Orientation parallel to alignment of applied force is lower in
energy. When nuclei are irradiated with RF radiation the lower energy nuclei flip to
high state and nuclei said to be in resonance, hence the term nuclear magnetic
resonance.
44
In quantum mechanical terms, the nuclear magnetic moment of a nucleus can
align with an externally applied magnetic field of strength B0 in only 2I+1 ways,
either re-inforcing or opposing B0.
The energetically preferred orientation has the magnetic moment aligned
parallel with the applied field (spin = +1/2) and is often given the notation is
aligned, whereas the higher energy anti-parallel orientation (spin = -1/2) is referred
to as is anti - parallel. The rotational axis of the spinning nucleus cannot be
orientated exactly parallel (or anti-parallel) with the direction of the applied field B0
(defined in our coordinate system as about the z axis) but must precess about this
field at an angle with an angular velocity given by the expression;
= B0 (2.5)
The constant is called the magnetogyric ratio and relates the magnetic
moment and the spin number I for any specific nucleus;
= 2/hI (2.6)
If angular velocity is related to frequency by ωo = 2πυ, then
= Bo/ 2π (2.7)
It follows that proton NMR transitions (∆I=1) have the following energy;
hυ = ∆E = hγBo/2π (2.8)
For a proton γ = 26.75 x 107 rad T
-1 s
-1 and Bo ~ 2T, ∆E = 6 x 10
-26 J.
45
Figure 2.9 Bruker DRX- 400 spectrometer
46
The NMR method for the study of molecular structures depends on the
sensitive variation of the resonance frequency of a nuclear spin in an external
magnetic field with the chemical structure, the conformation of the molecule, and
the solvent environment. The dispersion of these chemical shifts ensures the
necessary spectral resolution, although it usually does not provide direct structural
information. Different chemical shifts arise because nuclei are shielded from the
externally applied magnetic field to differing extent depending on their local
environment.
2.7 Preparation of Mixtures
Liquid mixtures were prepared in thoroughly washed and dried narrow-
mouthed weighing glass-bottles, with ground-glass stoppers, by mixing the
component liquids by mass on an electronic balance (Model: OHAUS AR 2140)
(Figure 2.10) with a stated precision of 0.1 mg. The masses of the component
liquids, required for preparing the mixture of known composition, were calculated
before hand and then a pseudo-binary mixture of two particular components, in a
fixed weight fraction ratio, was prepared each time. Extreme care was taken to
minimize the preferential evaporation during the process. The maximum possible
error in the estimation of mole fraction is 0.0001.
2.8 Evaluation of Acoustical, Thermodynamics and Excess Parameters
2.8.1 Isentropic Compressibility (ks)
The study of sound propagation both in the hydrodynamic treatment and
relaxation process yields that in the limit of low frequencies; sound velocity u in a
fluid medium is expressed as:
47
Figure 2.10 Electronic Balance (Model: OHAUS AR- 2140)
48
s
2 Pu
(2.9)
which gives rise to the well-known Laplace‟s equation,
sku
12
(2.10)
2
1
uks
(2.11)
where P, and sk respectively are pressure, density, and isentropic
compressibility of the medium.
The importance of the isentropic compressibility in determining the physico-
chemical behaviour of liquid mixtures has been reported by earlier workers [7, 8].
2.8.2 Surface Tension (ς)
Surface tension is a diagnostic parameter for describing various properties of
liquids and liquid mixtures. Surface tension of liquid mixtures is useful in the
design of separation processes as it has significant effect on engineering and
biotechnology considerations. However experimental values of surface tension are
not always available especially for multi- component mixtures. Surface tension (ζ)
and relaxation time (η) can be calculated using density and velocity data with the
help of Auerbach relation [9]
ζ= 6.3 ×10 -4
ρu3/2
(2.12)
Relaxation time [10] is calculated as
η = (4η) / (3u2 ρ) (2.13)
49
2.8.3 Acoustic Impedance (Z)
Sound travels through materials under the influence of sound pressure.
Because molecules or atoms of a solid are bound elastically to one another, the
excess pressure results in a wave propagating through the solid.
The acoustic impedance (Z) of a material is defined as the product of its
density ( ) and ultrasonic velocity (u ).
uZ (2.14)
Acoustic impedance is important in determination of acoustic transmission
and reflection at the boundary of two materials having different acoustic
impedances, the design of ultrasonic transducers and assessing absorption of sound
in a medium.
2.8.4 Optical Dielectric Constant, Polarisability and Molar Refraction
Optical properties of liquids and liquid mixtures have been widely studied to
obtain information on their physical, chemical and molecular behaviour. Maxwell‟s
theory for electromagnetic materials [10-13] gives the following relation between
optical dielectric constant and refractive index, assuming that for non- magnetic
materials permeability approximately approaches unity.
ε = n2
D (2.15)
The permittivity ε, of nonpolar solvents can be determined by both the
properties by the isolated molecules and the effects of molecular interactions. At
different densities, the variations of permittivity with temperature are calculated
50
from theories that take account only of pair interactions. The classical calculations
of the average field at a molecule due to identically polarized neighbours in a
structure of cubic symmetry lead to the Clausius – Mossotti equation [14-15], which
gives polarizability as
α = 3/4πρ × [ε-1/ε+2] (2.16)
where ρ is the density and ε is the total polarisability of the isolated
molecule, assumed to be independent of interactions with neighbours. From the
values of determined optical dielectric constant, molar refraction Rm can be
calculated using the relation proposed by Lorentz – Lorentz.
Rm= [ε-1/ε+2]Vm (2.17)
This property has great importance as it gives an account of the dispersion
forces present in the mixture.
2.8.5 Intermolecular Free Length (Lf)
In the analysis of propagation of sound wave through a loosely packed
medium, a simple model that envisages the molecules as rigid billiard-balls was
developed by many workers [16-19]. Let L be the average distance between the
centers of the molecules and the distance between the surfaces of two neighboring
molecules, which is called the intermolecular free length, be Lf. The mechanical
momentum of a sound wave is transferred from one molecule to the next with gas
kinetic mechanism with velocity m , such that
51
om
P3 (2.18)
where, Po is pressure in the space unoccupied by matter called available or
free volume.
Since the molecules are assumed to be rigid, they must travel only the
fraction Lf /L of any distance over which momentum is transmitted. A part of the
path of the sound wave is thus short- circuited by the molecule i.e. in the time
interval Δt between two collisions the molecules have travelled a distance Lf = νm
Δt , but the momentum is transferred over a greater distance L = u Δt [20]. The
distance Lf is directly related to available volume per mole Va and is given as:
Y
V2L a
f (2.19)
where, Va = VT – Vo ,
V (36 Y (2.20)
and
3.0
cTo
T
T1V V
(2.21)
where Vo, VT, Tc and NA are molar volume at absolute zero temperature, molar
volume at absolute temperature T, critical temperature of the liquid, and Avogadro‟s
number respectively.
Jacobson [21] has shown that if Tc for a liquid is not available, then the
intermolecular free length can be estimated from the experimental density and
ultrasonic velocity‟ data using the relation:
52
2/1f
u
KL
(2.22)
or sf kK L
(2.23)
where, K is temperature dependent dimensionless empirical constant,
proposed by Jacobson [21], having values 195x10-8
, 200 x10-8
and 203 x10-8
at 293,
303 and 313 K respectively.
A number of workers [22, 24] have reported the importance of intermolecular
free length in the study of molecular interactions.
2.8.6 Gibb’s Free Energy of Activation for Viscous Flow ( *G )
On the basis of the theory absolute reaction rates [25], the Eyring‟s kinematic
viscosity model is expressed as
RT
G exp hN V
*
A
(2.24)
where , V, NA, h, R,T and *G are kinematic viscosity, molar volume,
Avogadro‟s constant, Planck‟s constant, Universal gas constant, absolute
temperature, and activation free energy of flow required to move the fluid particles
from a stable state to an activated state respectively. Many workers [26, 27] have
discussed the importance of excess value of *G in the study of molecular
interactions.
2.8.7 Free Volume (Vf) and Internal Pressure (πi)
The relationship among applied pressure (P), molar volume (Vm), temperature
(T), and molar internal energy (U) is given by the thermodynamic relation:
53
PT
P T
V
U
VT
(2.25)
The isothermal internal energy volume co-efficient (∂U/∂V)T is often called
internal pressure i . So, the above equation can be written as:
PT
P T
Ti
(2.26)
Since externally applied pressure is negligible as compared to the internal
pressure i , it can be rewritten as
V
iT
P T
(2.27)
or T
i
T
(2.28)
where, PT
V
V
1
and T
TP
V
V
1
where is the thermal expansion coefficient and T is the isothermal
compressibility.
From the work of Eyring and Hirschfelder [27] the free volume in liquids is
given as:
2
3
T
fV
1
V
uP
bRTV
(2.29)
54
where b is packing factor in liquid and is equal to 1.78 for closely packed
hexagonal structure. For, negligible values of P, equ. (2.29) reduces to:
2
3
T
fV
1
V
u
bRTV
(2.30)
or 2
3
if
V
1bRTV
(2.31)
Suryanarayan and Kuppusami [28, 30] proposed the following relation for
free volume in liquids:
2/3
fk
MuV
(2.32)
Solving these equations, we get
6/7
3/22/1
iMu
kbRT
. (2.33)
Here, M is the effective molecular mass; k is a dimensionless temperature-
independent constant having a value of 4.28 Χ 109, is the viscosity, is the
density, u is the sound velocity and T is the absolute temperature.
2.8.8 Excess Parameters
The excess properties are fundamentally important in understanding the
intermolecular interactions and nature of molecular agitation in dissimilar
molecules. The excess properties provide valuable information about molecular
interactions and macroscopic behaviour of liquid mixtures and can be used to test
55
and improve thermodynamic models for calculating and predicting the fluid phase
equilibria. These functions give an idea about the extent to which the given liquid
mixtures deviate from ideality. Non – ideal liquid mixtures show considerable
deviation from linearity in their physical behaviour with respect to concentration
and these have been interpreted as arising from the presence of weak or strong
interactions. These are found to be sensitive towards difference in size and shape of
the molecules [31].
Excess parameters, associated with a liquid mixture, are a quantitative
measure of deviation in the behaviour of the liquid mixtures from ideality. The most
common way to evaluate the excess value of a given thermodynamic parameter is to
use the equation
AE
=Aexp - ∑xi Ai (2.34)
where Aexp, Ai and xi are experimentally measured value of the parameter A,
value of parameter a for ith
component (i= 1, 2 for binary mixture) respectively. AE
is
deviation/ excess value of the respective parameter.
The excess / deviations parameters of molar volume EmV , ultrasonic velocity
u , viscosity , molar refraction mR , isentropic compressibility sk , acoustic
impedance EZ , intermolecular free length EfL , internal pressure E
i , free energy of
activation for viscous flow E*G , free volume EfV and molar enthalpy E
mH have
been calculated from following relations:
2
22
1
11
m
2211Em
MxMxMxMxV
(2.35)
56
)uxux(uu 2211m (2.36)
)xx( 2211m (2.37)
idm
texpmm RRR (2.38)
where
m
22112m
2mtexp
m
MxMx
2n
1nR
(2.39)
and
2
2
222
22
11
121
21id
m
M
2n
1nM
2n
1nR
(2.40)
2
2
2
2
1
2
1
1
m
2
m
su
x
u
x
u
1k
(2.41)
)uxux()u(Z 222111mmE (2.42)
2
1
222
2
2
1
121
1
2
1
m2
m
Ef
)u(
Kx
)u(
Kx
)u(
KL
(2.43)
6
7
2
1
2
3
2
22
1
22
1
2
6
7
2
1
1
3
2
12
1
12
1
1
6
7
2
1
m
3
2
m2
1
m2
1
Eim
Mu
bRTkx
Mu
bRTkx
Mu
bRTk
(2.44)
2m2
1m11
2m2
mmE*
V
Vlnx
V
VlnRTG
(2.45)
2/3
2
22
1
112
3
k
uMx
k
uMx
k
uMV
effeff
m
meffE
f
(2.46)
mim22i211i1Em VVxVxH (2.47)
57
where M1, M2; 1 , 2 1u , 2u ; 1 , 2 ; 1 , 2 ; 1i , 2i and V1, V2 denote
molecular weight, density, ultrasonic velocity, viscosity, volume fraction, internal
pressure and molar volume respectively of the pure components. m , mu , m , im
and Vm represent density, ultrasonic velocity, viscosity, internal pressure and molar
volume of the mixtures respectively. K, R, T and k denote Jacobson constant, gas
constant, absolute temperature and dimensionless temperature independent constant
having a value of 4.28×109.
2.9 Analysis of Data
2.9.1 Redlich- Kister Polynomial Equation
The composition dependence of the excess properties are correlated by the
Redlich- Kister polynomial equation. The values of excess parameters for each
mixture were fitted to the Redlich- Kister polynomial equation [32] of the type,
1i5
1i1i11
E )1x2(ax1xY
(2.48)
where ia is the polynomial co-efficients.
The values of the co-efficients ia were obtained by the least squares method
with all points weighted equally. In each case, the optimum number of co-efficients
was ascertained from an examination of the variation of the standard deviation
EY with no. of co-efficients (p).
2/1
2caltexpE
pn
YYY
(2.49)
where n is the number of measurements.
58
2.9.2 Data Correlation
The physical properties ( m , mu and mn ) were correlated to a first and
second order polynomial equation with respect to mole fraction using the
following equations
1xZ (2.50)
211 xxZ (2.51)
where Z refers to physical property 1x , is the mole fraction of component 1,
, and represent the coefficients. The values of coefficients, and were
determined by least-squares method.
2.10 Mixing Rules
2.10.1 Mixing Rules for Refractive Index
The Lorentz-Lorentz (L-L) relation [33] given below for refractive index is
based on the change in the molecular polarizability with volume fraction
2
2
22
22
1
1
21
21
m2m
2m w
2n
1nw
2n
1n1
2n
1n
(2.52)
Gladstone-Dale (G-D) equation [34] for predicting the refractive index of a
binary mixture is as follows
1n1n1n 2211m (2.53)
Wiener’s (W) relation [35] is applied to isotropic bodies of spherically
symmetrical form and proposes volume additively and represented as
59
22
1
2
2
2
1
2
2
2
1
2
1
2
22
nn
nn
nn
nn
m
m (2.54)
Heller’s (H) relation [36] assumed equivalence of light- scattering equations
of Debye and Rayleigh and is given by
22
2
1
1m
2m
1m
2
3
n
nn
(2.55)
where 1
2
n
nm
Arago-Biot (A-B) [37], assuming volume additivity, proposed the following
relation for refractive index of binary mixtures
2211 nnnm (2.56)
Newton (N) [38] gave the following equation
111 2
22
2
11
2 nnnm (2.57)
Eykman’s (Eyk) relation [39] may be represented as
22
2
22
11
1
21
m
m
2m xV
4.0n
1nxV
4.0n
1nV
4.0n
1n
(2.58)
Oster’s relation [40] for binary mixtures can be given as
m2
m
2m
2m V
n
12n 1n 222
2
22
22
1121
21
21 xV
n
12n 1nxV
n
12n 1n
(2.59)
where nm is the refractive index of the mixture of x1 and x2, n1 and n2 are the
refractive indices of the pure components respectively.
60
2.10.2 Mixing Rules for Ultrasonic Velocity
Nomoto [41], assuming the linearity of the molar sound velocity and the
additivityof the molar volumes in liquid solutions, gave the following relation
3
2211
2211
3
m
mm
VxVx
RxRx
V
Ru
(2.60)
Van Dael and Vangeel [42] proposed the following ideal mixing relation for
predicting speed of sound of a binary liquid mixture
222
2
211
1
2m2211 uM
x
uM
x
u
1
MxMx
1 (2.61)
Zhang Junjie [43] gave following relation for the ultrasonic velocity in a
binary mixture
222
22
211
112211
2211m
uρ
Vx
uρ
VxMxMx
VxVxu (2.62)
Schaaffs’ relation [44], which is based on the Collision Factor Theory
(CFT), for predicting ultrasonic velocity in pure liquids, has been extended to the
binary liquid mixtures by Nutsch-Kuhnkies [45] and is given as
m
22112211m
V
BxBxSxSxuu
(2.63)
where M, ρ, n, , w, u, R and x represent molecular weight, density,
refractive index, volume fraction, weight fraction, ultrasonic velocity, molar sound
61
velocity and mole fraction of mixtures respectively. Symbols 1, 2 and m, in suffix
represent pure components and mixtures respectively.
2.10.3 Mixing Rules for Dielectric Constant
The dielectric constant is a magnitude that provides important information
about intermolecular interactions, the structure and energy interactions in liquid
state. In this work, experimental optical dielectric constant for the polymer solutions
have been compared to those estimated by the existent expression in literature.
Using the mixing rules for refractive index [45-46] along with the relation between
refractive index and optical dielectric constant according to Maxwell‟s theory
(ε = n2
D), optical dielectric constant of the mixtures were calculated using relations
(equation no. 2.52 – 2.59).
Apart from these relations following relations were also used for calculating
optical dielectric constant of the polymer solutions under study.
Looyenga relation
𝜀 = 𝜀1
1
3 + 𝜙2 𝜀2
1
3 − 𝜀1
1
3
1/3
(2.64)
Lichtenecker- Rotherand Zakri relation
𝜀 = 𝜀1𝜙1𝜀2
𝜙2 (2.65)
Kraszewski relation
ε1/2 = ϕ1ε11/2
+ ϕ2ε21/2
(2.66)
Bruggeman asymmetric relation
62
𝜀2−𝜀
𝜀/𝜀1 3 = 1 − 𝜙2 𝜀2 − 𝜀1 (2.67)
where ɸi and εi are the volume fractions and permittivities of the components
of the mixtures.
The dielectric behaviour of polymer/ceramic composition systems has been
analyzed by many scientists and many equations have been derived based on
experimental results and theoretical derivation. An attempt has been made to
compute dielectric constant theoretically for the polymer – ceramic composition.
The most commonly used equation is the Lichtenecker logarithmic law of
mixing and is written for a two-component system as
𝑙𝑜𝑔 𝜀 = 𝜐𝑝 𝑙𝑜𝑔𝜀𝑝 + 𝜐𝑐 𝑙𝑜𝑔𝜀𝑐 (2.68)
𝑙𝑜𝑔 𝜀 = 𝑙𝑜𝑔𝜀𝑝 + 𝜐𝑐 1 − 𝑘 𝑙𝑜𝑔𝜀𝑐/𝜀𝑝 (2.69)
Jayasundere and Smith [47] have worked together in deriving an
equation which was modified from the well-known Kerner equation by
including interactions betweenneighboring spheres for the measurement of
dielectric constant of binary composites and the equation is shown in equation
𝜀𝑒𝑓𝑓 = 𝑣𝑝 𝜀𝑝 +𝑣𝑐𝜀𝑐
3𝜀𝑝
𝜀𝑐+2𝜀𝑝 1+
3𝑣𝑐 𝜀𝑐−𝜀𝑝
𝜀𝑐+2𝜀𝑝
𝑣𝑝 +𝑣𝑐 3𝜀𝑝
𝜀𝑐+2𝜀𝑝 1+
3𝑣𝑐 𝜀𝑐−𝜀𝑝
𝜀𝑐+2𝜀𝑝
(2.70)
The Maxwell-Garnett mixing rule was initially used in a system where metal
particles are encapsulated in an insulating matrix [48]. But in recent times the
same mixing rule is applied for ceramic particle inclusions. This mixing rule is
then modified and the effective dielectric constant for a polymer/ceramic
63
composite incorporating homogeneous distribution of spherical ceramic material
can be determined by the equation developed by Maxwell and Wagnar [49] which is
known as Maxwell- Wagnar mixing rule
𝜀𝑒𝑓𝑓 = 𝜀𝑝 2𝜀𝑝 +𝜀𝑝 +2𝑣𝑐(𝜀𝑐−𝜀𝑝 )
2𝜀𝑝 +𝜀𝑐−𝑣𝑐(𝜀𝑐−𝜀𝑝 ) (2.71)
Yamada have studied the polymer/ceramic binary system and proposed a
model using the properties of its constituent materials [50]. Considering the system
to comprise ellipsoidal particles dispersed continuously, the dielectric constant
is given by the equation
𝜀𝑒𝑓𝑓 = 𝜀𝑝 1 +𝜂 𝑣𝑐(𝜀𝑐−𝜀𝑝 )
𝜂𝜀𝑝 + 𝜀𝑐−𝜀𝑝 (1−𝑣𝑐) (2.72)
𝜀𝑒𝑓𝑓 = 𝜀𝑝 1 +𝑣𝑐(𝜀𝑐−𝜀𝑝 )
𝜀𝑝 +𝑛 𝜀𝑐−𝜀𝑝 (1−𝑣𝑐) (2.73)
where n is 0.2
Parallel mixing rule
𝜀𝑚 = 𝑣𝑝𝜀𝑝 + 𝑣𝑐𝜀𝑐 (2.74)
Serial mixing rule
1
𝜀𝑚 =
𝑣𝑝
𝜀𝑝+
𝑣𝑐
𝜀𝑐 (2.75)
where vp and vc are volume fraction of Polymer and Ceramic respectively
and εp and εc are dielectric constant of Polymer and Ceramic materials respectively
64
2.10.4 Mixing Rules for Viscosity
Bingham proposed [51] the following relation for ideal viscosity of a binary
mixture
2211m xx (2.76)
This relation assumes that no changes in the volume of the mixture on mixing
the components have taken place.
The Additive relation, based on Arrhenius model [52] and Eyring‟s model
for the viscosity of pure liquids can be modified for binary mixtures as
222111mm V ln xV ln xV ln (2.77)
According to Kendall-Munroe [53] the viscosity of a binary mixture is given
by,
ln x ln x ln 2211m (2.78)
and it assumes logarithmic additivity of viscosity.
Hind et.al [54] gave the following relation for predicting viscosity of a binary
mixture, taking into consideration of the molecular interactions
12212221
21m xx2xx (2.79)
Frenkel [55], using the Eyring’s model, developed the following logarithmic
relation for non-ideal binary liquid mixtures
12212221
21m lnxx2 lnx lnx ln (2.80)
65
which takes into account the molecular interaction.
The Sutherland-Wassiljewa [56] equation for viscosity of liquid mixtures is
i
jjij
iim
xA
x (2.81)
In equation (2.62), Aij is the Wassiljewa coefficient which is independent of
composition.
2.10.5 Flory’s Statistical Theory
Flory statistical theory (FST) has been used to evaluate the ultrasonic velocity
in binary liquid mixtures. Patterson and Rastogi [57] have used this theory to
calculate surface tension which in turn is used to evaluate ultrasonic velocity in
liquid mixtures. The following relation to calculate characteristic surface tension
was used
3/1*3/2*3/1* TPk (2.82)
where k , *P and *T are the Boltzmann constant, characteristic pressure and
temperature respectively. Here,
T
2* V
~ T
P
(2.83)
where is the thermal expansion coefficient and T is the isothermal
compressibility, given by the following equation
66
3/12/19/1
3
uT
10X6.75
(2.84)
23/49/4
3
uT
10X71.1
(2.85)
The reduced volume V~
for a pure substance in terms of thermal expansion
coefficient is given as,
3
T13
T1V
~
(2.86)
The characteristic temperature *T is given as
1V~V~
T*T3/1
3/4
(2.87)
The characteristic and reduced parameters have been used to evaluate the
surface tension of binary liquid mixtures, and aregiven by the following relations.
*22
*11
*m VxVxV (2.88)
}VxVx{
VV~
*22
*11
mm
(2.89)
1221*22
*11 XPP*P (2.90)
*2
*22
*1
*11
*
T
P
T
P
P*T
(2.91)
67
where , 2 and 12X are the segment fraction, the site fraction and the
interaction parameter respectively and these are expressed as :
*22
*11
*11
1VxVx
Vx
(2.92)
12 1
3/1
*1
*2
12
22
V
V
(2.93)
and
22/1
*1
*2
6/1
*1
*2*
112P
P
V
V1PX
(2.94)
Starting from the work of Priogogine and Saraga [58] the equation for
reduced surface tension is given by:
1V~
5.0V~
nV~
1V~
V~
MV~~
3/1
3/1
2
3/13/5 (2.95)
where, M is the fraction of nearest neighbours that a molecule loses on
moving from the bulk of the liquid to the surface.
Thus the surface tension of a liquid mixture is given by the relation,
V~~*
m (2.96)
The values of surface tension obtained by Flory theory have been used to
evaluate ultrasonic velocity, making use of the well-known Auerbach relation [59]
68
3/2
m4
mm
103.6u
(2.97)
2.10.6 Excess Thermodynamic Functions
The whole approach assumes that the molecules are rigid spheres and the
potential of interaction between two molecules is a function of intermolecular
separation.
The shape of the average potential function of mutual interaction is nearly
like a square well. Making use of the partition function and the equation of state,
Arakawa and Kiyohara [60] derived the following excess functions for binary liquid
mixtures:
Excess energy
)rxrx(V
V
rV
Vx
rV
VxRT3E
3*B2
3*A1m
m
*B2
*2
o22
*A1
o1
o11E
(2.98)
Excess entropy
2
*
2
*
3*
2
3*
1
3*
222
2
*
1
*
3*
2
3*
1
3*
111
)(ln
)(ln3
A
A
BAm
A
o
A
A
BAm
A
oE
r
r
rxrxV
rVx
r
r
rxrxV
rVxRS
(2.99)
where 01V ,
02V ; the volume per molecules of the pure components, β; the
common packing parameter, *Ar , *
Br ; the collision diameter of the molecule within
each cell and *A1r , *
B2r ; the diameter of each species in pure state.
69
Schaaff‟s [61] equation for ultrasonic velocity has been employed for the
calculation of the molecular diameter of pure liquids, for the computation of the
above mentioned excess functions.
The molecular diameters are related to the collision diameter of the molecules
within each cell by formulae:
*AB2
*A11
*A rxrxr (2.100)
and *B22
*AB1
*B rxrxr (2.101)
where *B2
*A1
*AB rr
2
1r
The packing parameter is given by the relation:
3
1
101
3*A1
T3
41
T1Vr
(2.102)
where 1 , is the thermal expansion co-efficient of component 1.
2.11 Samples Under Investigation
Polypropylene glycol monobutyl ethers (PPGMBE) average molecular
weight Mn-1000, Poly (ethylene glycol) butyl ether (PEGBE) Mn-206, 2-
(Methylamino) ethanol (MAE) (98.5℅) Mn-75.11 g.mol-1
and 1-butanol (99.8%)
Mn-74.12 g.mol-1
obtained from Sigma-Aldrich Chemicals Pvt. Ltd. were purified
by standard procedure discussed by Perrin and Armarego and the purity of each
chemical was verified by literature comparison of their physical parameters. The
binary systems investigated are PPGMBE 1000 + 2-(Methylamino) ethanol (MAE),
70
PPGMBE 100 + 1-butanol, Poly (ethylene glycol) butyl ether (PEGBE) 206 + 2-
(Methylamino) ethanol (MAE), and Poly (ethylene glycol) butyl ether (PEGBE)
206 + 1-butanol.
Dielectric constant of BaTiO3/PEGDA at 1 GHz, BaTiO3/PEGDA at 1 MHz,
BaTiO3/PEGDA at 1 KHz, BaTiO3 / Epoxy thick film (0.4), BaTiO3 / Epoxy thick
film (0.2) and BaTiO3/TMPTA was calculated from various existing mixing rules.
The experimental data for these systems were taken from the literature [62, 63].
71
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73
[59] R. Auerbach, Experimentia, 4 (1948) 473.
[60] K. Arakawa, O. Kiyohara, Bull. of the Chem. Soc. of Japan, 43 (1970) 975.
[61] W. Schaafs, Z. Phys., 69 (1939) 115.
[62] R. Popielarz, C. K. Chinag, R. Nozaki and J. Obrzut, Macromolecules 34, (2001) 5910.
[63] N. Hadik, A. Outazourhit, A. Elmansouri, A. Abouelaoualim, A. Oueriagli and E. I.
Ameziane, Active and Passive Electronic components (Research Article ID 437130) volume
(2009).
CHAPTER 3 Acoustical, Optical and Dielectric Studies on Solutions of Poly
(Propylene Glycol) Monobutyl Ether 1000 with 1-Butanol/MAE
3.1 Introduction
3.2 Results and Discussion
3.2.1 Experimental Data
3.2.2 Thermoacoustical Parameters
3.2.3 Excess Parameters
3.2.4 Redlich-Kister Polynomial Equation Data
3.3 Conclusion
References
74
3.1 Introduction
Properties of liquid mixtures are thermodynamically very important as a part
of studies of thermodynamic, acoustic and transport aspects. The compositional
dependence of thermodynamic properties is proved to be very useful tool in
understanding the nature and extent of pattern of molecular aggregation resulting
from intermolecular interaction between components [1].
The method of studying
the molecular interaction from the knowledge of variation of thermodynamic
parameters and their excess values with composition gives an insight into the
molecular process [2-4]. The ultrasonic velocity measurements find wide
applications in characterising the physico- chemical behaviour of liquid mixtures
[5-
7] and in the study of molecular interactions. Ultrasonic velocity of a liquid is
related to the binding forces between the atoms or the molecules. Ultrasonic
velocity has been adequately employed in understanding the nature of molecular
interaction in pure liquids [8]
and binary mixtures.
Polypropylene glycol monobutyl ethers were tested extensively as lubricants
for automobile engines. The synthetic lubricants, based on polypropylene glycol
monobutyl ethers, were evaluated in engine test stands and in extensive vehicle
trials. The fluids showed the expected low carbon and low sludge, as well as clean
engine parts and satisfactory cranking at low temperature. Over 2 million miles of
operation using these oil were experienced [9].
2-(Methylamino) ethanol (MAE) is a secondary amine often used in
industrial operations. In the MAE molecule, a methyl group substitutes a hydrogen
atom of the amino group of a monoethanolamine (MEA, a primary amine).
75
However, the methyl group is supposed to enhance the reaction kinetics as it
increases the basicity of the amine without appreciably increasing the hindrance
around the nitrogen atom [10].
Alcohols are widely used solvents with their characteristic protic and self
associative nature. Moreover, the refrigerant properties of alcohols and their
mixtures with other compounds are related to the hydrogen bonding capability of
the alcohols. Ultrasonic velocity ( mu ) and refractive index (nm) for binary mixtures
of PPGMBE + 1-butanol and PPGMBE + MAE solutions at the temperature range
293.15, 303,15, and 303.15K have been measured and reported in this chapter.
The experimental data are used to calculate the acoustic impedance (Z),
pseudo-Grüneisen parameter ( ) specific heat ratio ( ), heat capacity (Cp), molar
volume ( mV ),and optical dielectric constant (ɛr), excess properties viz. deviation in
isentropic compressibility (Δks), excess intermolecular free length (𝐿𝑓𝐸), deviation in
ultrasonic velocity (∆u) and molar refraction deviation (∆Rm) have also been
computed over the whole range of composition at three temperatures. These excess
parameters have been correlated with Redlich-Kister polynomial equation. The
results have been interpreted on the basis of strength of intermolecular interaction
occurring in these mixtures.
3.2 Results and Discussion
3.2.1 Experimental Data
The ultrasonic velocity and refractive index of the pure liquids at 293.15,
303.15, and 313.15K along with literature data are given in table 3.1 and found to
be in good agreement.
76
Table 3.1 Comparison of ultrasonic velocity (u) and refractive index (n) with
literature data at different Temperatures
Ultrasonic velocity(u) Refractive index (n)
Component T (K) Observed
Literature
Observed Literature
293.15 1368.0 -- 1.4480 --
PPGME 303.15 1341.6 -- 1.4440 --
313.15 1308.8 -- 1.4400 --
293.15 1440.0 -- 1.4401 1.4393
MAE 303.15 1416.8 -- 1.4350 1.4356d
313.15 1399.2 -- 1.4312 1.4318d
293.15 1258.0 1256
c 1.3970 1.399
a
1-Butanol 303.15 1224.0 1223
d 1.3930 1.392
a
313.15 1195.0 1193b 1.3891 1.389
a
aRef. [18],
bRef. [19],
cRef. [20],
dRef. [21],
The experimental values of ultrasonic velocity ( mu ) and refractive index (nm)
for PPGMBE + 1-butanol and PPGMBE + MAE mixtures at temperatures
293.15K, 303.15K and 313.15K are given in table 3.2.
3.2.2 Thermoacoustical parameters
Pseudo-Grüneisen parameter (Γ), acoustic impedance (Z), specific heat ratio
( ), heat capacity ( PC ), molar volume ( mV ) and optical dielectric constant (ɛr) were
calculated using experimental data.
Tables 3.3 and 3.4 show the values of estimated parameters viz.; acoustic
impedance (Z), pseudo-Grüneisen parameter (Γ), specific heat ratio ( ), heat
capacity ( PC ) and molar volume ( mV ) in varying temperature range for the binary
systems PPGMBE 1000 + MAE and PPPGMBE 1000 + 1- butanol respectively.
77
Table 3.2 Experimental values of ultrasonic velocity (um), and refractive index (nm)
for the systems PPGMBE + MAE and PPGMBE + 1-butanol with respect to the mole
fraction x1 of PPGMBE.
PPGMBE1000+MAE(a) PPGMBE1000+1-butanol(b)
x1 um nm
(m/sec)
x1 um nm
(m/sec)
293.15K 293.15K
0.0000 1440.0 1.4401 0.0000 1258.0 1.3970 0.1000 1400.2 1.4440 0.0997 1280.8 1.4282 0.1977 0.3006
1384.5 1.4452 0.2000 1302.4 1.4367 1376.8 1.4463 0.3166 1320.0 1.4418
0.3985 1372.0 1.4466 0.3901 1331.2 1.4431 0.4982 1368.7 1.4472 0.4988 1344.0 1.4457 0.5996 1368.4 1.4474 0.5995 1353.6 1.4454 0.7000 0.8000
1364.8 1.4476 0.6997 1358.4 1.4469 1364.2 1.4477 0.7992 1363.2 1.4467
0.9000 1368.0 1.4478 0.9000 1364.8 1.4473 1.0000 1368.0 1.4480 1.0000 1368.0 1.4480
303.15K 303.15K
0.0000 0.1000 0.1977 0.3006 0.3985 0.4982 0.5996 0.7000
1416.8 1.4350 0.0000 1224.0 1.3930 1364.0 1.4370 0.0997 1261.6 1.4243 1344.0 1.4391 0.2000 1286.4 1.4325 1338.8 1.4400 0.3166 1304.0 1.4377 1330.8 1.4402 0.3901 1316.8 1.4391
1.4408 1.4415 1.4426
1327.2 1.4411 0.4988 1324.7 1328.0 1.4414 0.5995 1327.2 1330.4 1.4418 0.6997 1333.6
0.8000 1333.4 1.4425 0.7992 1336.8 1.4433 0.9000 1333.6 1.4438 0.9000 1336.8 1.4432 1.0000 1341.6 1.4440 1.0000 1341.6 1.4440
313.15K 313.15K
0.0000 0.1000
1399.2 1.4312 0.0000 1195.0 1.3891 1347.2 1.4352 0.0997 1240.0 1.4193
1.4272 0.1977 1330.4 1.4364 0.2000 1256.0 0.3006 1320.8 1.4374 0.3166 1263.2 1.4325 0.3985 1318.4 1.4378 0.3901 1276.0 1.4351 0.4982 0.5996
1314.8 1.4382 0.4988 1280.0 1.4362 1316.4 1.4386 0.5995 1288.0 1.4378
0.7000 1315.6 1.4389 0.6997 1293.6 1.4383 0.8000 1312.8 1.4393 0.7992 1297.6 1.4385 0.9000 1310.0 1.4397 0.9000 1301.6 1.4398 1.0000 1308.8 1.4400 1.0000 1308.8 1.4400
78
Table 3.3 Acoustic impedance (Z), pseudo-Grüneisen parameter (Γ), specific heat ratio ( ), heat capacity (Cp) and molar volume (Vm) for PPGMBE 1000 + MAE mixture with
mole fraction of PPGMBE 1000 ( 1x ) at T= 293.15, 303.15 and 313.15K.
x1 Γ Z Cp
(cal.mol-1
) Vm
T = 293.15K
0.0000 1.2560 1353.8031 1.3981 134.1469 79.8922 172.4895 0.1000 1.2040 1360.3590 1.3828 296.0711
0.1977 1.1883 1356.1902 1.3789 452.6484 263.3166 358.9289 449.8035 541.7130
0.3006 1.1805 1354.0460 1.3770 617.4592 0.3985 1.1761 1353.5490 1.3758 774.5928
0.4982 1.1715 1356.7670 1.3745 936.5080 0.5996 1.1708 1357.1781 1.3742 1100.4811 636.1329 0.7000 1.1690 1356.3642 1.3742 1261.851o 729.7967
821.8067 0.8000 0.9000 1.0000
1.1672 1358.3160 1.3734 1424.3599 1.1691 1357.3873 1.3735 1585.0561 915.2753 1.1647 1362.1261 1.3716 1749.4570 1004.3131
T = 303.15K
0.0000 1.2125 1321.6581 1.4017 135.9596 80.5169
173.8226 265.3868
0.1000 1.1569 1325.2420 1.3863 299.3456 0.1977 1.1401 1312.5543 1.3825 454.6632 0.3006 1.1332 1314.5022 1.3805 622.0230 361.6656
0.3985 0.4982 0.5996
1.1278 1316.4225 1.3794 781.7967 453.3205 1.1231 1319.0301 1.3779 944.6388 545.7135
641.3287 1.1236 1318.6894 1.3780 1109.7961 0.7000 1.1234 1319.7312 1.3774 1273.6630 734.9440
828.2674 922.0555
1012.7850
0.8000 0.9000
1.1237 1320.7586 1.3770 1437.2445 1.1236 1320.8311 1.3769 1600.2572
1.0000 1.1238 1324.6640 1.3754 1765.9387
T = 313.15K
0.0000 0.1000
1.1732 1296.1891 1.4050 138.2271 81.0791
1.1212 1287.9530 1.3903 301.7475 175.3150 0.1977 1.1055 1283.4864 1.3861 460.9335 267.4568
0.3006 1.0973 1279.9083 1.3840 627.8886 364.4867 456.8369 0.3985
0.4982 1.0940 1280.6452 1.3829 788.4410 1.0895 1281.2561 1.3815 951.1930 549.9241
0.5996 0.7000 0.8000
1.0888 1284.6419 1.3808 1119.9531 645.2876 1.0881 1284.3874 1.3806 1284.5265 740.0917 1.0860 1282.8223 1.3802 1446.6102 834.0821
927.7650 0.9000 1.0839 1281.4017 1.3797 1608.2076 1.0000 1.0810 1283.4941 1.3785 1772.9492 1019.7163
79
Table- 3.4 Acoustic impedance (Z), specific heat ratio ( ), heat capacity (Cp) and
molar volume (Vm) for PPGMBE 1000 + 1- butanol mixture with mole fraction of
PPGMBE 1000 ( 1x ) at T= 293, 303 and 313K.
x1 Γ Z Cp
(cal.mol-1
) Vm
T = 293.15K 0.0000 1.3170 1018.7280 1.4694 108.3399 91.5287
181.9855 274.0692 381.8877
0.1000 1.2114 1171.8051 1.4108 260.9826 0.2000 1.1881 1232.2454 1.3951 420.2201 0.3171 1.1795 1269.5716 1.3875 608.4274 0.4274 1.1795 1286.6302 1.3852 729.1051 450.3957
548.6919 640.8717
0.5001 1.1743 1312.8148 1.3804 911.4695
0.5999 1.1731 1329.1084 1.3780 1080.8821 0.7000 1.1727 1336.9601 1.3769 1246.1503 733.5733 0.8000 1.1717 1345.7177 1.3755 1412.4865 824.7111
0.9000 1.0000
1.1706 1349.5428 1.3747 1577.7289 917.7324 1.1679 1357.9609 1.3730 1746.4485 1007.3935
T = 303.15K
0.0000 1.2645 982.0152 1.4740 108.6315 92.3843 0.1000 1.1707 1144.3056 1.4149 265.0987 183.8022 0.2000 1.1492 1207.7295 1.3987 427.5289 276.1865 0.3171 1.1399 1246.0628 1.3905 620.2232 384.8520 0.4274 1.1383 1267.6397 1.3871 803.3456 488.0999
553.9761 0.5001 1.1345 1284.6675 1.3837 927.6297
0.5999 0.7000
1.1309 1293.0844 1.3815 1091.9328 646.2288 739.7043 1.1315 1302.1223 1.3806 1260.0821
0.8000 1.1321 1306.2963 1.3802 1425.6525 833.8611 925.0726 0.9000 1.1283 1311.3102 1.3784 1590.9885
1.0000 1.1268 1320.6471 1.3768 1762.9763 1015.8661
T = 313.15K
0.0000 0.1000 0.2000
1.2164 948.3157 1.4785 109.0037 93.24443 1.1306 1115.9801 1.4186 268.1824 185.2406 1.1063 1170.1742 1.4023 429.5545 278.3140
0.3171 0.4274 0.5001 0.5999 0.7000 0.8000 0.9000 1.0000
1.0947 1195.8824 1.3948 591.0918 371.7372
1.0906 1220.6603 1.3900 801.4978 491.1797 1.0869 1231.5629 1.3873 922.0284 558.3531 1.0858 1245.2385 1.3851 1090.1311 651.2386 1.0851 1254.6611 1.3836 1258.0918 744.6593 1.0850 1260.9973 1.3827 1425.2537 838.4853 1.0838 1268.7038 1.3813 1594.7055 930.9624 1.0839 1279.6284 1.3799 1770.0332 1022.7971
80
A perusal of tables 3.3 and 3.4 reveal that the values of specific heat ratio ( ),
heat capacity ( PC ) and molar volume ( mV ) for both the mixtures increase as the
temperature increases. However, acoustic impedance (Z) decreases with increase in
temperature. The non-linear variation of , Γ, Cp, mV and Z with composition shows
the existence of complex formation between unlike molecules. Similar variation in
these parameters with temperature has been reported earlier by Shukla et al. [11] in
molten binary mixtures and Yashmin et.al. [12] in THF and o-cresol / methanol
binary mixtures.
(a)
(b)
Fig 3.1 Pseudo-Grüneisen parameter (Γ) for the system (a) PPGMBE + MAE, (b) PPGMBE + 1- butanol at ■, 293.15; ▲,303.15; and ♦,313.15K with
respect to the mole fraction of PPGMBE.
1.05
1.1
1.15
1.2
1.25
1.3
0 0.2 0.4 0.6 0.8 1
Γ
x1
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
0 0.2 0.4 0.6 0.8 1
Γ
x1
81
Pseudo-Grüneisen parameter (Γ) is one of the important parameter which is
used to study internal structure, clustering phenomenon and thermodynamic
properties of solid crystalline lattice. It is well established that liquids support a
quasi-crystalline model for their structure, the lattice nature being increased at high
pressure and low temperature hence the pseudo-Grüneisen parameter can also be
used to study liquids.
(a)
(b)
Figure 3.2 Optical dielectric constant (ɛr) for the system (a) PPGMBE + MAE, (b) PPGMBE + 1- butanol at ■, 293.15; ▲,303.15; and ♦,313.15K with
respect to the mole fraction of PPGMBE.
Figure 3.1 reveals that the pseudo- Grüneisen parameter of mixture decreases
with increase in mole fraction of PPGMBE as well as with rise in temperature. The
non-linear behaviour of this parameter suggests the presence of specific interaction
2.04
2.06
2.08
2.1
0 0.2 0.4 0.6 0.8 1
ε r
x1
1.9
1.95
2
2.05
2.1
2.15
0 0.2 0.4 0.6 0.8 1
ε r
x1
82
in the mixtures. Similar variations in pseudo-Grüneisen parameter for the system
THF + o-cresol have been also found by Yasmin et al. [12].
Figure 3.2 reveals that the optical dielectric constant of the systems PPGMBE
+ MAE and PPGMBE + 1- butanol vary non-linearly with the mole fraction of
PPGMBE. The values slightly decrease with increase the temperatures. This small
effect of temperature might be due to small permanent electric dipole moments of
the components and their mixtures, as orientation of molecular dipoles is slightly
disturbed by temperature.
3.2.3 Excess Parameters
Excess properties provide information about the molecular interactions and
macroscopic behaviour of fluid mixtures and can be used to test and improve
thermodynamic models for calculating and predicting the fluid phase equilibria.
The excess isentropic compressibility (∆ks), excess intermolecular free length
(LfE), deviation in ultrasonic velocity (∆u) and molar refraction deviation (∆Rm) of
the two binary mixtures viz. (PPGMBE+ MAE) and (PPGMBE+ 1- butanol) have
been computed.
Values of the deviation in ultrasonic velocity (∆u) for PPGMBE 1000 + 1-
butanol system were found to be positive and negative for PPGMBE 1000 + MAE
system over the entire composition range at all three investigated temperatures
(Figure 3.3). The positive values of ∆u for all considered temperatures indicate that
the molecular order originating from the mixing process is larger than the one from
ideal behavior. It has been suggested by Krishnaiah et al. [13] that the negative
deviation in sound velocity may be due to the presence of dispersion forces and a
83
positive deviation in sound velocity may be due to charge-transfer, dipole-dipole
and dipole - induced dipole interactions.
(a)
(b)
Figure 3.3 deviation in ultrasonic velocity (∆u) versus the mole fraction of PPGMBE1000 (x1) for binary mixtures: (a) PPGMBE1000 + MAE and
(b) PPGMBE + 1-butanol at 293.15, 303.15 and 313.15K.
-60
-50
-40
-30
-20
-10
0
0 0.2 0.4 0.6 0.8 1
Δu
(m
.s-1
)
x1
∎293.15K
▲303.15K
♦ 313.15K
0
10
20
30
40
50
0 0.2 0.4 0.6 0.8 1
Δu
(m
.s-1
)
x1
∎293.15K
▲303.15K
♦ 313.15K
84
It is noteworthy that the variation of ∆u with temperature for both systems is
not the same. A similar temperature dependence of ∆u has also been reported in the
case of PEGDME 250 + methanol by Periera et al. [14].
(a)
(b)
Figure 3.4 Excess isentropic compressibility (∆ks), versus the mole fraction of PPGMBE1000 (x1) for binary mixtures: (a) PPGMBE1000 + MAE and
(b) PPGMBE + 1-butanol at 293.15, 303.15 and 313.15K.
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.2 0.4 0.6 0.8 1
Δk
s X
10
10(N
-1m
-2)
x1
∎293.15K
▲303.15K
♦ 313.15K
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0 0.2 0.4 0.6 0.8 1
Δk
s X
10
10
(N-1
m-2
)
x1
∎293.15K
▲303.15K
♦ 313.15K
85
Figure 3.4 shows that the excess values of isentropic compressibility (∆ks) are
found positive in the system PPGMBE+ MAE however it is found to be negative in
the system PPGMBE+1- butanol. Fort and moore [15] have
found that the negative
value of excess compressibilites indicates greater interaction between the
components of the mixtures. Positive values in excess properties correspond mainly
to the existence of dispersive forces. Dispersive forces which are generally present
in systems PPGMBE+ MAE would make positive contribution.
The negative value of ∆ks
is associated with a structure forming tendency
while a positive value is taken to indicate a structure breaking tendency due to
hetero-molecular interaction between the component molecules of the mixtures. The
negative ∆ks
values for binary mixtures indicate, the formation of H-bonds between
the -OH group of PPGMBE and the –OH group 1-butanol. The positive excess
compressibility indicates that molecules are packed loosely in the mixtures. In the
present investigation the positive deviations of ∆ks
in systems PPGMBE + MAE
have been attributed to dispersive forces that show weak molecular interaction
between the unlike molecules.
The Figure 3.5 shows that the non-linear variation of excess intermolecular
free length is positive in systems PPGMBE + MAE whereas negative in system
PPGMBE + 1-butanol. According to Ramamoorthy et. al.[16]
negative values of
excess intermolecular free length (LfE)
indicate that sound waves cover longer
distances due to decrease in intermolecular free length ascribing the dominant
nature of hydrogen bond interaction between unlike molecules.
86
(a)
(b)
Figure 3.5 Excess free length (LfE), versus the mole fraction of PPGMBE1000 (x1) for binary mixtures: (a) PPGMBE1000 + MAE, and (b) PPGMBE + 1-butanol at 293.15,
303.15 and 313.15K.
Fort and moore [15] indicated that the positive values of excess free length
should be attributed to the dispersive forces, and negative excess values should be
due to charge transfer and hydrogen bond formation. In the present study the
positive contribution in the systems PPGMBE + MAE shows a weak interaction
while, negative contribution in system PPGMBE + 1-butanol prevails the existence
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0 0.2 0.4 0.6 0.8 1
293.15K
303.15K
313.15K
x1
LfE
(A
º)
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
0 0.2 0.4 0.6 0.8 1
293.15K
303.15K
313.15K
LfE
(A
º)
x1
87
of strong interactions. Spencer et. al.[17]
have also reported a similar observation on
the basis of excess values of free length.
(a)
(b)
Figure 3.6 Molar refraction deviation (∆Rm) versus the mole fraction of PPGMBE1000 (x1) for binary mixtures: (a) PPGMBE1000 + MAE, and (b) PPGMBE + 1-butanol at
293.15K, 303.15K and 313.15K.
From Figure 3.6 it can be seen that ∆Rm values are negative for both the
mixtures at all the temperatures. ∆Rm gives the strength of interaction in a mixture
and is a sensitive function of wavelength, temperature and mixture composition.
-160
-140
-120
-100
-80
-60
-40
-20
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
ΔR
m
x1
∎293.15K
▲303.15K
♦ 313.15K
-160
-140
-120
-100
-80
-60
-40
-20
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
ΔR
m
x1
∎293.15K
▲303.15K
♦ 313.15K
88
∆Rm represents the electronic perturbation due to orbital mixing of two components.
In the present investigation the order of negative magnitude of ∆Rm values is
PPGMBE + 1-butanol > PPGMBE + MAE. The slightly higher negative values of
∆Rm for PPGMBE + 1-butanol mixture suggest that interaction between PPGMBE
and 1-butanol is stronger as compared to that of between PPGMBE and MAE. The
effect of temperature on ∆Rm values is not very significant for both binary mixtures.
3.2.4 Redlich-Kister Polynomial Equation Data
The values of co-efficient ai of Redlich – Kister polynomial equation
evaluated using the method of least squares for the mixtures are given in table 3.5
and 3.6 along with the standard deviation ζ(YE).
Table 3.5 Adjustable parameters ai with the standard deviations EY for deviation
in ultrasonic velocity (∆u), deviation in isentropic compressibility (∆kS), excess intermolecular free length (LEf) and molar refraction deviation (∆Rm) for binary mixture of PPGMBE 1000 + 1- butanol at temperature 293.15, 303.15 and 313.15K.
Parameters Temp(K) a1 a2 a3 a4 a5
∆u(m.s-1)
293.15 114.523 26.1741 70.0391 2.8648 -122.877 0.4012
303.15 161.179 63.0599 72.9529 108.330 -61.2044 1.2832
313.15 119.190 71.6761 63.7197 175.007 149.808 0.4656
293.15 -0.1345 -0.0646 -0.0805 -0.1688 -0.7780 0.0003
LE
f (A°) 303.15 -0.1586 -0.0943 -0.0985 -0.2070 -0.1070 0.0008
313.15 -0.1524 -0.1006 -0.1169 -0.2743 -0.1796 0.0001
∆Ks x 1010
293.15 -3.6238 -1.8377 -2.3104 -4.7480 -2.3537 0.0078 (N
-1.m
2) 303.15 -4.3438 -2.4986 -2.3516 -6.0451 -3.7390 0.0208
313.15 -4.2233 -3.0200 -2.1282 -6.8112 -7.8692 0.0080
293.15 -413.505 -348.21 -240.75 -55.7239 41.6874 0.1903
∆Rm 303.15 -403.197 -320.64 -298.32 -409.1 -270.102 1.7692
313.15 -405.243 -299.75 -283.84 -460.474 -331.405 2.1535
EY
89
Table 3.6 Adjustable parameters ai with the standard deviations EY for deviation
in ultrasonic velocity (∆u), deviation in isentropic compressibility (∆kS), excess intermolecular free length (LEf) and molar refraction deviation (∆Rm) for binary mixture of PPGMBE 1000 + MAE at temperature 293.15, 303.15 and 313.15K.
Parameters Temp(K) a1 a2 a3 a4 a5
∆u(m.s-1)
293.15 -130.2926 -130.0748 -121.9684 -86.2638 -21.2049 0.3328
303.15 -145.0741 73.0193 -684.9443 -415.2566 856.6399 0.7159
313.15 -125.6986 -129.0778 -188.8272 -178.5554 -85.5840 0.8437
293.15 -0.1345 -0.0646 -0.0805 -0.1688 -0.7780 0.0003
LE
f (A°) 303.15 -0.1586 -0.0943 -0.0985 -0.2070 -0.1070 0.0008
313.15 -0.1524 -0.1006 -0.1169 -0.2743 -0.1796 0.0001
∆Ks x 1010
293.15 -3.6238 -1.8377 -2.3104 -4.7480 -2.3537 0.0078 (N
-1.m
2) 303.15 -4.3438 -2.4986 -2.3516 -6.0451 -3.7390 0.0208
313.15 -4.2233 -3.0200 -2.1282 -6.8112 -7.8692 0.008
293.15 -422.4018 -329.3091 -321.4609 -447.6781 -257.3066 0.3247
∆Rm 303.15 -425.2030 -329.2957 -321.9254 -443.2822 -262.9791 0.3801
313.15 -417.5818 -343.2357 -424.7094 -654.6919 -412.2322 0.6418
3.3 Conclusion
It may be concluded that in the present study the observed positive and
negative values of excess parameters exhibit the presence of strong molecular
association in the system PPGMBE + 1-butanol where as the system PPGMBE
1000 + MAE shows the predominance of dispersive forces.
EY
90
References
[1] T. Karunakar, C. H. Srinivasu and K. Narendra, J. Pure and Appl. Phys. 1 (2013) 1.
[2] M. Ciler and D. Kesanovil, Hydrogen Bonding editted by Ha, dn, Zi, D Peragamon Press,
London, 7 (1957).
[3] R. J. Fort and W. R. Moore, Trans. Faraday Society, 62 (1966) 1112.
[4] R. J. Large Man and W. S. Dundbar, J. Phys. Chem., 49 (1945) 428.
[5] Kinocid, J. Am. Chem. Soc., S1 (1929) 2950.
[6] M. K. Sajnami, Indian J. Pure & Appl. Phys., 38 (2000) 760.
[7] R. J. Fort and W. R. Moore, Trans. Faraday Society, 61 (1965) 2102.
[8] S. B. Kasare and B.A. Patdai, Indian J. Pure & Appl. Phys., 25 (1987) 180.
[9] J. M. Russ, Lubri. Eng., (1946) 151.
[10] K. Juelin Li, M Mundhwa, P. Tontiwachwuthikul and A. Henni J. Chem. Eng. Data, 52 (2)
(2007) 565.
[11] R. K. Shukla, S. K. Shukla, V. K. Pandey and P. Awasthi, J. Phys. Chem Liq., 45 (2007)
169.
[12] M. Yasmin, K. P. Singh, S. Parveen, M. Gupta and J. P. Shukla, Acta Physica Polonica
A, 115 (5) (2009) 890.
[13] A. Krishnaiah, D. N. Rao and P. R. Naidu, Indian J. Chem., 21A (1982) 290.
[14] S. M Pereira, M. A. Rivas, J. L. Legido and T. P. Iglesias, J. Chem. Therm. 35, (2003)
383.
[15] R. J. Fort, and W. R. Moore, Trans. Faraday Society, 61, (1965) 2102.
[16] K. Ramamoorthy, and S. Alwan, Current Sci., 47 (1978) 334.
[17] J. N. Spencer, E. Jeffery and C. Robert, J. of Phys. Chem., 83 (1979) 1249.
[18] S. Singh, S. Parveen, D. Shukla, M. Gupta and J. P. Shukla, Acta Phys. Pol. A 111 (2007)
847.
[19] T. M. Aminbhavi, M. I. Aralguppi, S. B. Horogappad, and R. H. Balundgi, J. Chem. Eng.
Data 38 (1993) 31.
[20] K. Bebek, A. Strugala-Wilczek, Int. J. Thermophys. (2009).
[21] L. Juelin M. Mundhwa, P. Tontiwachwuthikul, and A. Henni J. Chem. Eng. Data, 52
(2007) 560.
CHAPTER 4
Study of Molecular Interaction in Binary Mixtures of Poly
(Propylene Glycol) Monobutyl Ether(PPGMBE) 1000 with 2-
(Methylamino) Ethanol (MAE) and 1-Butanol using
Thermodynamic and 1H NMR Spectroscopy
4.1 Introduction
4.2 Results and Discussion
4.2.1 Thermodynamic Study
4.2.1.1 Experimental Data
4.2.1.2 Thermophysical Parameters
4.2.1.3 Excess Parameters
4.2.1.4 Redlich-Kister Polynomial Equation Data
4.2.2 1H NMR Spectroscopy Study
4.3 Conclusion
References
91
4.1 Introduction
Knowledge of thermodynamic properties of polymer solutions has been
proven to be a very useful tool in evaluating the structural interactions occurring in
polymer solutions. Physico-chemical properties of liquid mixtures formed by two or
more components associated through hydrogen bonds is important from theoretical
and process design aspects [1- 3]. The formation of hydrogen bond in solutions and
its effect on the physical properties of the mixtures have received much attention.
Hydrogen bonding and complex formation in liquid mixtures have been extensively
studied using thermodynamic technique by many workers [4- 6]. Earlier studies of
our group suggest that various types of interaction prevail in the binary mixtures of
polymers and organic solvents [7 - 11].
NMR spectrum is very important to study the interactions and the chemical
changes appearing in the mixture. The NMR spectrum of a molecule serves not
only “fingerprint” but it usually allows to drive quite detailed conclusion regarding
its isomeric structure, the influence of a solvent, formation of inter and
intramolecular hydrogen bonds etc.[12]. The viscosity and density data of poly
(propylene glycol) monobutyl ether 1000 (PPGMBE) are important for
development of the lubricants [13]. The very high viscosity indices and inherent
good lubricity of these products resulted in wear of engine parts comparable to that
of the best petroleum oils of the time. The viscosity index is a measure of how much
the viscosity changes as temperature change. The viscosity of motor oil must be
high enough to maintain a lubricanting film, but low enough that the oil can flow
around the engine parts under all conditions. Thus, mixing MAE/1-butanol with
PPGMBE, decreases the viscosity index. This means that the PPGMBE molecule
92
become shorter. Shorter molecules cannot unfold as for at increased temperature,
giving a lower degree of chain entanglement and viscosity. The viscosity and
density data of 2-(Methylamino) ethanol (MAE) are important for development of
the proper design of the absorption and stripping operations [14].
In this chapter, the molecular interactions between the poly (propylene
glycol) monobutyl ether 1000 (PPGMBE) with 2-(Methylamino) ethanol (MAE)
and 1- butanol have been investigated at varying concentrations and temperatures
using thermodynamic and spectroscopy (1H NMR) techniques. Surface tension (ζ),
relaxation time (η), deviation in viscosity (∆η) and excess Gibb‟s free energy of
activation of viscous flow (∆G*E
) have been calculated from the experimental
values. The values of excess parameters were fitted to Redlich – Kister polynomial
equation.
4.2 Results and Discussion
4.2.1 Thermodynamic Studies
4.2.1.1 Experimental Data
Experimental values of density and viscosity of the pure liquids at 293.15 K,
303.15K and 313.15K are compared with literature and listed in table 4.1. The
experimental values of density ( m ) and viscosity (ηm) of poly (propylene glycol)
monobutyl ether 1000(PPGMBE) with 2-(Methylamino) ethanol (MAE) and 1-
butanol mixtures at temperatures 293.15K, 303.15K and 313.15K are given in table
4.2.
93
PPGMBE 1000 MAE 1-Butanol
Figure 4.1 Structure of Polypropylene glycol monobutyl ethers (PPGMBE) 1000, 2-(Methylamino) ethanol (MAE) and 1-butanol used.
Table 4.1 Comparison of density (ρ) and viscosity (η) data with literature data at
different Temperatures.
Density (ρ) viscosity(η)
Component T (K)
Observed
Literature
Observed Literature
293.15
0.9926
0.989(25)
134.4185
--
PPGMBE 303.15
0.9843
--
83.0000
--
313.15
0.9777
--
54.2605
--
293.15
0.9401
--
12.8347
--
MAE 303.15
0.9328
0.933789a
8.4538
8.5221d
313.15
0.9263
0.925948a
5.9198
5.8331d
293.15
0.8097
0.8098c
2.8100
2.8200b
1-Butanol 303.15
0.8020
0.8017c
2.2400
2.2700b
313.15
0.7945
0.7934c
1.7500
1.7600b
aRef. [34],
bRef. [10],
cRef. [15],
dRef. [14],
4.2.1.2 Thermo-physical Parameters
The variation of relaxation time and surface tension with temperature and
concentration is shown in table 4.3. It is observed from table 4.3, that relaxation
time decreases with increase in temperature and increases with increasing
concentration of PPGMBE for both the systems. Similar changes are also observed
in viscosity (table 4.2) which indicates that viscous forces play a dominant role in
the relaxation process. The measurements of relaxation time seem to indicate that
viscosity contributes in a significant way to the absorption.
94
Table 4.2 Experimental values of density ( m ) and viscosity (ηm) of PPGMBE 1000 +
1- butanol and MAE mixture with mole fraction of PPGMBE 1000 ( 1x ) at T= 293.15,
303.15 and 313.15K. PPGMBE 1000 + 1- Butanol(a)
PPGMBE 1000 + MAE(b)
x1
ρm
(gm cm–3) ηm
(mPa s) x1
ρm
(gm cm–3) ηm
(mPa s)
293.15K
293.15K
0.0000 0.8097 2.810 0.0000 0.9401 12.834 0.0997 0.9149 18.851 0.1000 0.9716 52.870 0.2000 0.9461 38.472 0.1977 0.9799 76.106 0.3166 0.9617 57.646 0.3006 0.9840 91.871 0.3901 0.9665 73.028 0.3985 0.9865 107.206 0.4988 0.9767 89.895 0.4982 0.9892 118.285 0.5995 0.9819 106.387 0.5996 0.9899 126.384 0.6997 0.9842 117.276 0.7000 0.9900 132.391 0.7992 0.9871 127.312 0.8000 0.9917 132.909 0.9000 0.9888 132.321 0.9000 0.9915 133.687 1.0000 0.9926 134.418 1.0000 0.9926 134.418
303.15K
303.15K
0.0000 0.8020 2.240 0.0000 0.9328 8.453 0.0997 0.9070 13.865 0.1000 0.9642 33.436 0.2000 0.9388 26.370 0.1977 0.9722 49.963 0.3166 0.9555 38.364 0.3006 0.9765 59.793 0.3901 0.9626 48.749 0.3985 0.9788 66.876 0.4988 0.9697 56.501 0.4982 0.9820 72.218 0.5995 0.9742 64.662 0.5996 0.9818 73.867 0.6997 0.9763 73.782 0.7000 0.9831 75.717 0.7992 0.9771 78.975 0.8000 0.9840 76.553 0.9000 0.9809 82.069 0.9000 0.9842 79.509 1.0000 0.9843 83.000 1.0000 0.9843 83.000
313.15K
313.15K
0.0000 0.7945 1.7500 0.0000 0.9263 5.919 0.0997 0.8999 10.323 0.1000 0.9560 22.379 0.2000 0.9316 18.710 0.1977 0.9647 32.354 0.3166 0.9467 26.548 0.3006 0.9690 39.372 0.3901 0.9566 37.379 0.3985 0.9713 44.897 0.4988 0.9621 41.922 0.4982 0.9744 49.411 0.5995 0.9668 47.125 0.5996 0.9758 51.551 0.6997 0.9698 49.847 0.7000 0.9762 52.274 0.7992 0.9717 52.463 0.8000 0.9771 52.902 0.9000 0.9747 54.229 0.9000 0.9781 53.602 1.0000 0.9777 54.260 1.0000 0.9777 54.260
95
Table 4.3 Surface tension (ς) and relaxation time (τ) for the systems PPGMBE
1000 + 1-Butanol and MAE mixture against the mole fraction of PPGMBE 1000 ( 1x )
at T= 293.15, 303.15 and 313.15K.
PPGMBE + 1- Butanol(a)
PPGMBE + MAE(b)
x1 ςm τ x1011 x1 ςm τ x1011
293.15K
293.15K
0.0000 23.1435 2.9339 0.0000 31.4589 8.7782 0.0997 25.0096 16.7476 0.1000 31.2865 37.0145 0.2000 25.7810 31.9631 0.1977 31.1189 54.0635 0.3166 26.2747 45.8648 0.3006 31.0153 65.7456 0.3901 26.5189 56.8502 0.3985 30.9497 76.9716 0.4988 26.8798 67.9316 0.4982 30.9396 84.7559 0.5995 27.1397 78.8459 0.5996 30.8839 90.5645 0.6997 27.3344 86.1001 0.7000 30.7967 94.9950 0.7992 27.6613 92.5330 0.8000 30.7298 95.2576 0.9000 28.3107 95.7888 0.9000 30.6353 95.9231 1.0000 30.9278 96.4772 1.0000 30.9278 96.4772
303.15K
303.15K
0.0000 22.9041 2.5180 0.0000 31.6329 6.01957 0.0997 25.0019 12.8062 0.1000 31.4066 24.4767 0.2000 25.8419 22.6315 0.1977 31.0803 37.5962 0.3166 26.3587 31.4809 0.3006 31.0483 45.0596 0.3901 26.6710 38.9397 0.3985 31.0277 50.3685 0.4988 26.9123 44.2675 0.4982 31.0037 54.3491 0.5995 27.0573 50.2377 0.5996 30.9394 55.6126 0.6997 27.2814 56.6518 0.7000 30.8744 56.9859 0.7992 27.5650 60.3009 0.8000 30.7938 57.5785 0.9000 28.2399 62.4237 0.9000 30.7030 59.8079 1.0000 30.9506 63.0198 1.0000 30.9506 63.0198
313.15K
313.15K
0.0000 22.6952 2.0742 0.0000 31.9523 4.3521 0.0997 24.9591 9.9467 0.1000 31.5125 17.1974 0.2000 25.6668 16.9736 0.1977 31.3269 25.2640 0.3166 25.9979 23.4327 0.3006 31.1893 31.0535 0.3901 26.3555 31.9979 0.3985 31.1450 35.4557 0.4988 26.5135 35.4581 0.4982 31.0816 39.1084 0.5995 26.7504 39.1768 0.5996 31.0705 40.6454 0.6997 26.9787 40.9501 0.7000 30.9809 41.2486 0.7992 27.2935 42.7507 0.8000 30.8384 41.8839 0.9000 28.0239 43.7863 0.9000 30.6798 42.5759 1.0000 30.7696 43.1983 1.0000 30.7696 43.1983
96
A close perusal of table 4.3 indicates that the surface tension values increase
with increase in mole fraction of PPGMBE and decreases with increase in
temperature for the system PPGMBE + 1-butanol while for the system PPGMBE +
MAE decrease with increase in mole fraction of PPGMBE and decrease with
increase in temperature. Variation of surface tension is non-linear for both the
systems. Substance which involve in hydrogen bonding exist as associate molecules
and have high surface tension, in contrast to those substance which involve
intermolecular H-bond exist as discrete and hence low surface tension.
4.2.1.3 Excess Parameters
The experimental data are used to calculate the values of deviation in
viscosity (∆η) and excess Gibb‟s free energy of activation of flow (∆GE). The
calculated data were fitted to the Redlich – Kister polynomial equation.
Figure 4.2 shows that ∆G*E
values are positive for PPGMBE1000 + MAE and
PPGMBE + 1-butanol mixtures. The positive values of ∆G*E
indicate the presence
of strong interaction. No significant change has been observed in ΔG*E
values with
temperature. Singh et al. [15] have also reported similar variations in the ∆G*E
values for binary mixtures of butylamine + 1-butanol mixture and by Yasmin et al.
[16] for binary system of PEG + Ethanolamine, PEG +m-Cresol and PEG +Aniline.
The results of variation in viscosity deviations (Δη) of binary systems
consisting of PPGMBE1000 with MAE and 1-butanol at temperatures of 293.15K,
303.15K, and 313.15K are represented in figure 4.3 and show positive deviations
over the entire range of mole fraction. Δη values are found to decrease with
increasing temperature for both the systems. The viscosity of the mixture strongly
97
depends on the entropy of mixture, which is related with liquid‟s structure and
enthalpy.
(a)
(b)
Figure 4.2 Excess Gibb’s free energy of activation of flow (∆G*E) versus the mole fraction of PPGMBE1000 (x1) for binary mixtures: (a) PPGMBE1000 + MAE
and (b) PPGMBE + 1-butanol at 293.15K, 303.15K and 313.15K temperatures.
Consequently with the molecular interactions between the components of the
mixtures. Therefore the viscosity deviation depends on molecular interactions as
0
1
2
3
4
5
6
0 0.2 0.4 0.6 0.8 1
ΔG
*E(k
J m
ol-1
)
x1
∎ 293.15K
▲ 303.15K
♦ 313.15K
0
1
2
3
4
5
6
7
0 0.2 0.4 0.6 0.8 1
ΔG
*E(k
J m
ol-1
)
x1
∎ 293.15K
▲ 303.15K
♦ 313.15K
98
well as on the size and shape of the molecules. The positive of Δη values indicate
specific interaction [17].
(a)
(b)
Figure 4.3 Deviation in viscosity (Δη) versus the mole fraction of PPGMBE1000 (x1) for
binary mixtures (a) PPGMBE1000 + MAE and (b) PPGMBE + 1-butanol at 293.15K, 303.15K and 313.15K temperatures.
4.2.1.4 Redlich-Kister Polynomial Equation Data
Tables 4.3 and 4.4 report the standard deviations along with coefficients of
the respective functions at all three temperatures.
0
5
10
15
20
25
30
35
40
45
50
0 0.2 0.4 0.6 0.8 1
Δη
x 1
03 (m
Pa
s)
x1
∎ 293.15K
▲ 303.15K
♦ 313.15K
0
5
10
15
20
25
30
0 0.2 0.4 0.6 0.8 1
Δη
x 1
03 (m
Pa
s)
x1
∎ 293.15K
▲ 303.15K
♦ 313.15K
99
Table 4.3 Adjustable parameters ai with the standard deviations EY for deviation
in viscosity(∆η) and Excess Gibb’s free energy of activation of flow (∆G*E) for binary mixture of PPGMBE 1000 + 1- butanol at temperature 293.15, 303.15 and 313.15K.
Parameters
Temp. (K) 1a 2a 3a 4a 5a EY
∆η (mPa.s)
293.15 79.3325 -45.2640 68.9286 -18.0657 -112.7048 0.3885
303.15 53.0774 -22.1574 47.1962 -2.6730 -59.3609 0.4439
313.15 55.4940 -15.4940 -31.2051 3.7633 27.9934 0.6984
293.15 21.6161 19.4456 20.3052 -0.1688 -2.3986 0.0430
∆G*E (kJ mol-1) 303.15 19.3525 10.5260 13.7794 21.9458 12.9954 0.0677
313.15 21.9697 18.5753 16.5562 10.1274 3.8374 0.03643
Table 4.4 Adjustable parameters ai with the standard deviations EY for deviation
in viscosity(∆η) and Excess Gibb’s free energy of activation of flow (∆G*E) for binary mixture of PPGMBE 1000 + MAE at temperature 293.15, 303.15 and 313.15 K. Parameters
Temp. (K) 1a 2a 3a 4a 5a EY
∆η(mPa .s)
293.15 118.4596 42.4915 11.2453 114.9665 77.5232 0.8556
303.15 112.2222 -5.6152 136.7271 164.9991 -209.9957 0.4734
313.15 79.4516 24.3559 -18.3493 34.3043 76.7605 0.1537
293.15 16.5736 7.3478 5.2532 23.1680 20.1478 0.0279
∆G*E(kJ mol-1) 303.15 16.5695 16.8001 -4.3431 10.3431 34.4671 0.0251
313.15 17.2974 11.9866 10.3032 16.4588 12.7944 0.0274
4.2.2 1H NMR Spectroscopy study
Interaction can be easily identified by observation of spectral parameters like
selective line broadening or chemical shift displacements of 1H-NMR signals,
which is a direct molecular probe, This has been used to elucidate the change in
electronic environment of various protons of PPGMBE + MAE and PPGMBE+1-
butanol binary mixtures. Such an investigation will be of great importance, because
100
of the ability of this technique to identify the protons involved in interaction, if any,
with more precision and accuracy [18].
The 1H-NMR spectra of both the binary mixtures have been presented in
figure 4.4 and 4.5. Figure 4.4 shows the variation in observed chemical shift for
different protons of butanol in the binary mixtures as a function of mole fraction of
PPGMBE 1000. Values of chemical shift and deviation in chemical shift (∆δ) of
butanol measured over the different concentration of PPGMBE 1000 are listed in
table 4.5.
An up field shift in δOH, δCH2, and δCH3 has been observed for the system
PPGMBE+1-butanol with the increase in PPGMBE concentration. An up field shift
is indicative of an increase in electron density around the H nuclei of butanol which
is due to (i) breaking of the intermolecular hydrogen bonding in butanol (ii) less
hydrogen bonding type interactions between the hydroxyl proton of butanol and
PPGMBE 1000. Deviations of chemical shift (∆δ) provide important information on
relative strengths of chemical interactions between various protons of PPGMBE
1000 and 1-butanol [19]. The ∆δ for O-H and CH2 of butanol was found to be
negative for all the binary systems investigated over the whole composition range.
The position of minima in ∆δ, indicates the composition of maximum interaction
between components of the binary systems for different concentration of PPGMBE
1000. Such an upfield shift was also observed by Poppe et al. [20] who pointed out
that hydroxy protons involved in hydrogen bonds should be deshielded. Besides
temperature coefficients, coupling constants and chemical exchange, it has been
shown previously that the chemical shift difference ∆δ can also be used as a
conformational probe to study hydrogen bond interaction [21–23]. In agreement
101
with Kumar et al. [24] the negative ∆δ values indicate that strong interaction is
present in binary mixture of PPGMBE+1-butanol.
Figure 4.4 1D 1H NMR spectra of pure and binary mixture of PPGMBE + 1- butanol at different concentration of PPGMBE1000.
Figure 4.5 shows the variation in observed spectral parameters for different
protons of MAE in the binary mixtures as a function of mole fraction of PPGMBE
1000. No change in chemical shifts but line broadening was observed for the CH3
and CH2 protons in the binary mixture of PPGMBE 1000 + MAE. As the
concentration of PPGMBE 1000 increases the line broadening increases and then
vanishes. This is because the nucleus is rapidly transferred from one magnetization
condition to another or disorganizing effect, leading to the line broadening. The
disorganizing effects are also reflected on signals multiplicity. This disorganizing
effect is due to the interaction between the PPGMBE 1000 and MAE. Therefore, on
102
the basis of actual experimental evidence and literature information about the
internal structure of binary mixtures [25-34], it can be suggested that the addition of
PPGMBE 1000 to MAE would disrupt their self-associate structure and stabilizes
internal structure of mixed solvent and exhibit the existence of strong molecular
interactions. This also confirms the conclusion drawn from thermodynamic study.
Figure 4.5 1D 1H NMR spectrum of pure and binary mixture of PPGMBE 1000 + MAE at
different concentration of PPGMBE1000.
Table 4.5 Values of chemical shift and deviation in chemical shift (∆δ) of butanol
measured over the different concentration of PPGMBE 1000(x1).
x1
CH3
CH2 CH2
OH ∆δ CH3 ∆δ CH2 ∆δ OH
0
1.3
1.75 3.9
3.92 0 0 0 0.1
1.2
1.65 3.68
3.78 -0.083 -0.085 -0.122
0.3
1.16
1.62 3.65
3.74 -0.089 -0.085 -0.126 0.5
1.14
1.6 3.62
3.71 -0.075 -0.075 -0.12
0.7
1.13
1.6 3.63
3.74 -0.051 -0.045 -0.054 1
0 0 0
103
4.3 Conclusion
It may be concluded that in the present study the observed positive values of
excess parameters exhibit the presence of strong molecular association in binary
mixtures of PPGMBE with MAE and butanol. 1H NMR spectroscopic techniques
provide information about the molecular scale interactions prevailing in these
systems. A comparative analysis of thermodynamic and spectroscopic results shows
the presence of strong interaction in binary mixture of PPGMBE+1-butanol and
PPGMBE + MAE.
104
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39 (2009) 1749.
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(2006) 955.
CHAPTER 5
Thermoacoustical and Optical Study of Poly (Ethylene Glycol)
Butyl Ether (PEGBE) 206 with 1-Butanol and
2-(Methylamino) Ethanol(MAE)
5.1. Introduction
5.2. Results and Discussion
5.2.1. Experimental Data
5.2.2. Derived Parameters
5.2.3. Excess Parameters
5.2.4. Redlich-Kister Polynomial Equation Data
5.3. Conclusion
References
106
5.1 Introduction
Ultrasonic spectroscopy is an excellent non-destructive technique for probing
the structure of materials. The ultrasound waves when applied to liquids give
information about molecular motion. This study is a powerful tool in characterizing
the various aspects of physico - chemical behaviour of liquid mixture and studying
the interaction between the liquid mixtures [1, 2].
The variation of ultrasonic velocity and related acoustical parameters throw
much light upon the structural changes associated with the liquid mixtures having
weakly interacting components as well as strongly interacting components [3]. The
study and understanding of physico - chemical properties of liquid mixtures are
important for applications in industries. Such studies in multicomponents (binary,
ternary, quarternary etc) mixtures have been carried out by infra-red, [3, 4] Raman
[5], nuclear magnetic resonance [6], acoustical [2] and dielectric [7] techniques.
A measurement of ultrasonic velocity in the liquid mixtures and solutions has
been found to be an important tool to study the physico-chemical properties of
mixtures. When two or more liquids are mixed, the resulting mixture is not ideal.
The deviation of the ideality owes its gensis to the molecular interaction between
the components of the liquid mixtures.
In addition, excess properties provide information about the molecular
interactions and macroscopic behaviour of fluid mixtures and can be used to test
and to improve thermodynamical models for calculating and predicting the fluid
phase equilibria. In recent years, there has been considerable upsurge in the
theoretical and experimental investigation of the excess thermodynamic properties
107
of binary liquid mixtures [8, 9]. Thus an attempt has been made to investigate the
thermo physical properties of such mixtures.
Ultrasonic velocities (ρm) and refractive index (nm) for the two binary
mixtures viz. poly (ethylene glycol) butyl ether (PEGBE) 206 with 1- butanol and
2(Methylamino) ethanol (MAE) have been measured over the entire composition
range at three temperatures T=293.15, 303.15, and 313.15 K and at atmospheric
pressure, polarisability (α), molar Refraction (Rm), free volume (Vf), deviation in
isentropic compressibility (Δks), excess intermolecular free length (𝐿𝑓𝐸), deviation in
ultrasonic velocity (∆u), excess internal pressure ( Ei ) and molar refraction
deviation (∆Rm) have been computed from experimental data at all the three
temperatures. These excess parameters have been correlated with Redlich - Kister
polynomial equation. The results have been interpreted on the basis of strength of
intermolecular interaction occurring in these mixtures.
5.2 Result and Discussion
5.2.1 Experimental Data
The measured values of ultrasonic velocities and densities of pure
components compared with literature values are listed in Table 5.1 and found to be
in good agreement. The experimentally measured values of ultrasonic velocities
and densities for the systems PEGBE + 1-butanol and PEGBE + MAE at 293.15,
303.15 and 313.15K in whole composition rang are reported in table 5.2.
108
Table 5.1 Comparison of ultrasonic velocity (u) and Refractive index (n) with
literature data at different Temperatures
Ultrasonic velocity (u) Refractive index (n)
Component T (K) Observed
Literature
Observed Literature
293.15 1548.4 -- 1.4440 --
PEGBE 303.15 1516.0 -- 1.4400 --
313.15 1500.2 -- 1.4360 --
293.15 1440.0 -- 1.4400 1.4393
MAE 303.15 1416.8 -- 1.4350 1.4356d
313.15 1399.2 -- 1.4310 1.4318d
293.15 1258.0 1256c 1.3970 1.399a
1-butanol 303.15 1224.0 1223d 1.3930 1.392a
313.15 1195.0 1193b 1.3890 1.389a
aRef. [10],
bRef. [11],
cRef. [12],
dRef. [13],
5.2.2 Derived Parameters
The variation of free volume (Vf) with mole fraction of PEGBE for the
systems PEGBE + 1-butanol and PEGBE + MAE is shown in Figure 5.1. The
graphical representation of free volume shows that for the system PEGBE + 1-
butanol values of Vf are lesser than the pure components giving the minimum
around x= 0.1 to 0.3. The non-linear behaviour of Vf reflects the complex formation
near this concentration through hydrogen bonding.
The values of molar refraction (Rm) and polarizibility (α) are listed in Table
5.3. A close perusal of table reveals that the molar refraction values increases
considerably on mixing PEGBE for both the systems at all temperatures.
Polarizability of studied mixture decreases with increasing mole fraction of PEGBE.
The values slightly increase with temperature. This small effect of temperature
109
Table 5.2 Experimental values of ultrasonic velocity (um), and refractive index (nm) for the systems PEGBE + MAE and PEGBE + 1-butanol with respect to the mole fraction x1 of PPGMBE.
PEGBE+MAE PEGBE+1-butanol
x1 um (m/sec) nm x1 um (m/sec) nm
293.15K 293.15K
0.0000 1452.0 1.4400 0.0000 1258.0 1.3970
0.0997 1470.2 1.4422 0.0997 1308.5 1.4216
0.1986 1486.5 1.4424 0.1989 1345.3 1.4353
0.2988 1502.3 1.4426 0.2988 1386.8 1.4407
0.4000 1514.8 1.4429 0.4000 1418.6 1.4410
0.5000 1522.2 1.4433 0.5000 1446.2 1.4413
0.5994 1530.0 1.4435 0.6007 1474.4 1.4416
0.7021 1535.5 1.4437 0.7021 1506.7 1.4429
0.7990 1538.4 1.4438 0.8018 1526.5 1.4434
0.9019 1542.2 1.4439 0.9019 1540.6 1.4437 1.0000 1548.4 1.4440 1.0000 1548.4 1.4440
303.15K 303.15K
0.0000 1416.8 1.4350 0.0000 1224.0 1.3930
0.0997 1442.5 1.4372 0.0997 1284.5 1.4201
0.1986 1458.8 1.4381 0.1989 1330.5 1.4256
0.2988 1474.3 1.4384 0.2988 1368.8 1.4302
0.4000 1484.8 1.4387 0.4000 1400.6 1.4354
0.5000 1494.5 1.4390 0.5000 1434.2 1.4376
0.5994 1500.6 1.4392 0.6007 1456.0 1.4381
0.7021 1506.2 1.4395 0.7021 1484.6 1.4394
0.7990 1510.4 1.4397 0.8018 1498.3 1.4414
0.9019 1512.5 1.4399 0.9019 1512.4 1.4418 1.0000 1516.0 1.4400 1.0000 1516.0 1.4400
313.15K 313.15K
0.0000 1399.2 1.4310 0.0000 1195.2 1.3890
0.0997 1428.2 1.4340 0.0997 1262.5 1.4195
0.1986 1446.6 1.4343 0.1989 1308.8 1.4253
0.2988 1460.9 1.4347 0.2988 1352.3 1.4279
0.4.000 1472.5 1.4349 0.4000 1390.5 1.4291
0.5000 1481.3 1.4352 0.5000 1418.4 1.4326
0.5994 1486.2 1.4354 0.6007 1448.8 1.4343
0.7021 1493.4 1.4356 0.7021 1470.5 1.4357
0.7990 1495.7 1.4358 0.8018 1484.2 1.4361
0.9019 1498.5 1.4359 0.9019 1492.4 1.4359 1.0000 1500.2 1.4360 1.0000 1500.2 1.4360
110
Table 5.3 Molar Refraction (Rm) and Polarizibility (α) for the systems PEGBE + MAE and PPGMBE + 1-butanol with respect to the mole fraction x1 of PEGBE.
PEGBE+MAE(a) PEGBE+1-Butanol(b)
x1 Rm α
(cm3 mol
-1)
x1 Rm α
(cm3 mol
-1)
293.15K 293.15K
0.0000 21.0556 0.001070 0.0000 22.0442 0.001217
0.0997 24.4049 0.001060 0.0997 25.8593 0.001172
0.1986 27.6768 0.001055 0.1989 29.2359 0.001136 0.2988 30.9277 0.001045 0.2988 32.2300 0.001107
0.4000 34.2672 0.001038 0.4000 34.9855 0.001085
0.5000 37.6316 0.001034 0.5000 38.0985 0.001068
0.5994 40.9228 0.001030 0.6007 41.2017 0.001053
0.7021 44.4342 0.001027 0.7021 44.4286 0.001041
0.7990 47.6953 0.001025 0.8018 47.6892 0.001030 0.9019 51.2326 0.001024 0.9019 51.0748 0.001024
1.0000 54.4608 0.001020 1.0000 54.4608 0.001021 303.15K 303.15K
0.0000 21.0103 0.001092 0.0000 22.0572 0.001237
0.0997 24.3576 0.001078 0.0997 26.1880 0.001193
0.1986 27.6968 0.001068 0.1989 29.2735 0.001157
0.2988 31.0506 0.001059 0.2988 32.3696 0.001128
0.4000 34.4476 0.001053 0.4000 35.5607 0.001101
0.5000 37.7940 0.001048 0.5000 38.8704 0.001081
0.5994 41.2196 0.001045 0.6007 41.9327 0.001066
0.7021 44.7357 0.001042 0.7021 45.0620 0.001053
0.7990 48.0980 0.001041 0.8018 48.4136 0.001046
0.9019 51.6605 0.001039 0.9019 51.7982 0.001039
1.0000 55.0611 0.001038 1.0000 55.0611 0.001038 313.15K 313.15K
0.0000 20.9872 0.001101 0.0000 22.0642 0.001256 0.0997 24.3974 0.001086 0.0997 26.1954 0.001199
0.1986 27.6866 0.001075 0.1989 29.3573 0.001164
0.2988 31.0466 0.001067 0.2988 32.3361 0.001136
0.4.000 34.4409 0.001061 0.4000 35.3864 0.001111
0.5000 37.8311 0.001056 0.5000 38.7001 0.001094
0.5994 41.2045 0.001053 0.6007 41.9912 0.001079 0.7021 44.7290 0.001050 0.7021 45.1856 0.001064
0.7990 48.0616 0.001048 0.8018 48.3498 0.001054
0.9019 51.6478 0.001047 0.9019 51.5816 0.001048
1.0000 55.0420 0.001046 1.0000 55.0420 0.001046
111
might be due to small permanent electric dipole moments of the components and
their mixtures, as orientation of molecular dipole is slightly disturbed by
temperature.
Figure 5.1 Free volume for the systems (a) PEGBE + 1-butanol and (b) PEGBE + MAE at
■ , 293.15; ▲ , 303.15; and , 313.15K with respect of the mole fraction of PEGBE.
5.2.3. Excess Parameters
Deviation in isentropic compressibility (Δks), excess intermolecular free
length (𝐿𝑓𝐸), deviation in ultrasonic velocity (∆u), excess internal pressure ( E
i ) and
molar refraction deviation (∆Rm) for the binary mixtures under study have been
reported in Figures 5.2 to 5.6.
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
0 0.2 0.4 0.6 0.8 1
Vf(c
m3
mo
l-1)
x1
(a)
0
0.01
0.02
0.03
0.04
0.05
0 0.2 0.4 0.6 0.8 1
Vf(c
m3
mo
l-1)
x1
(b)
112
Figure 5.2 Deviation in isentropic compressibility (ΔKs) for the system (■ , ▲ ,) PEGBE + MAE and (□, Δ, ◊ ) PEGBE + 1-butanol at 293.15, 303.15 and 313.15 K with respect to
the mole fraction of PEGBE.
Deviation in isentropic compressibility ΔKs (Figure 5.2) are found to be
negative and decrease with the rise in temperature over whole composition range.
Thus it can be concluded that mixing of PEGBE with MAE and 1-butanol
respectively result in enhanced rigidity.
Figure 5.3 Excess intermolecular free length (𝑳𝒇𝑬) for the system (■ , ▲ ,) PEGBE + MAE
and (□, Δ, ◊ ) PEGBE + 1-butanol at 293.15, 303.15 and 313.15 K with respect to the mole fraction of PEGBE.
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0 0.2 0.4 0.6 0.8 1
ΔK
sX
10
10
(N-1
m
2)
x1
▢ 293.15K
∆ 303.15K
◊ 313.15K
∎ 293.15K▲303.15K
♦ 313.15K
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
0 0.2 0.4 0.6 0.8 1
L fE
(A⁰ )
x1
▢ 293.15K
∆ 303.15K
◊ 313.15K
∎ 293.15K▲303.15K
♦ 313.15K
113
Fort and Moore [14] has shown earlier that liquids of different molecular size
usually mix with decrease in volume resulting in negative ΔKs values, similar result
have been found by Singh et. al [15] for the binary mixtures of 2-butoxyethanol
with PEG 200 and PEG 400.
The values of excess intermolecular free length (LfE) are negative and
decrease with increase in temperature as shown Figure 5.3. The decrease in excess
intermolecular free length with increase in mole fraction PEGBE is indicating a
formation more tightly bound structure of the molecules. The close packing of the
molecules is caused by the hydrogen bonding between the solute and solvent
molecules. This reduces the free length of the system. For the system PEGBE +
MAE lesser negative values of excess intermolecular free length show H – bond
formation to the lesser extent.
Figure 5.4 Deviation in ultrasonic velocity (∆u) for the system (■ , ▲ ,) PEGBE + MAE and (□, Δ, ◊ ) PEGBE + 1-butanol at 293.15, 303.15 and 313.15 K with respect to the
mole fraction of PEGBE.
Figure 5.4 shows the deviation in ultrasonic velocity (Δu) is positive and
increases with a rise in temperature for both the system, also the deviation in
0
10
20
30
40
50
60
70
80
0 0.2 0.4 0.6 0.8 1
Δu
(m
s-1
)
x1
▢ 293.15K
∆ 303.15K
◊ 313.15K
∎ 293.15K▲303.15K
♦ 313.15K
114
ultrasonic velocity is more positive for the system PEGBE + 1-butanol as compared
to the system PEGBE + MAE. This kind of variation suggests that significant
interaction are present in these mixtures. Similar variation is also found by Ali and
Tariq et.al [16] for the binary system of benzyl alcohol with benzene.
Due to intermolecular interactions, structure of the molecules is changed,
which affect the compressibility and thus a change in ultrasonic velocity. The
ultrasonic velocity in a mixture is mainly influenced by the free length between the
surfaces of the molecules of the mixtures. The inverse dependence of intermolecular
free length and ultrasonic velocity have been evolved from the model of sound
propagation proposed by Eyring and Kincaid [17]. Our results for excess
intermolecular free length and deviation in ultrasonic velocity support each other.
Figure 5.5 Excess internal pressure (Ei ) for the system (■ , ▲ ,) PEGBE + MAE and
(□, Δ, ◊ ) PEGBE + 1-butanol at 293.15, 303.15 and 313.15 K with respect to the mole fraction of PEGBE.
The role of internal pressure ( Ei ) in solution thermodynamics was
recognized many years ago by Hilderband following earlier work of Van Laar [18].
The variation of internal pressure may give some suitable information regarding the
nature and strength of the forces existing between the molecules. In fact, the internal
0
10
20
30
40
50
60
0 0.2 0.4 0.6 0.8 1
πiE
X 1
0-5
(Nm
-2)
x1
▢ 293.15K
∆ 303.15K
◊ 313.15K
∎ 293.15K▲303.15K
♦ 313.15K
115
pressure is a broader concept and it is a measure of the totality of forces of the
dispersion, ionic and dipolar interaction that contribute to be overall cohesion of the
liquid systems [19]. For both the mixtures, values are found to be positive, and
increases with rise in temperature which indicates the presence of strong hydrogen
bonding due to the charge transfer complex (Figure 5.5). Similar results were
observed by Parveen et. al [20] in the mixtures of THF + o-cresol.
Figure 5.6 Molar refraction deviation (∆Rm) for the system (■ , ▲ ,) PEGBE + MAE and (□, Δ, ◊ ) PEGBE + 1-butanol at 293.15, 303.15 and 313.15 K with respect to the mole
fraction of PEGBE.
It can be seen from Figure 5.6 that the ΔRm values are negative for both the
systems under investigation. The observed large negative values for both the
systems indicate the presence of strong intermolecular bonding between PEGBE
and MAE/ 1-butanol molecules. The effect of temperature on ΔRm is not prominent
in both the mixtures. Similar results have also been found for system
PEG+ethanolamine, PEG+m-cresol and PEG+aniline [21].
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
ΔR
m
x1
▢ 293.15K
∆ 303.15K
◊ 313.15K
∎ 293.15K▲303.15K
♦ 313.15K
116
5.2.4. Redlich-Kister Polynomial Equation Data
The values of co-efficients ai evaluated using the method of least squares for
the mixtures as described in chapter 2, equation 2.41 are given in table 5.4 with the
standard deviations.
Table 5.4 Coefficents ai of Redlich – Kister equation using the method of least squares for the mixtures along with the standard deviations Parameters Temp(K) a1 a2 a3 a4 a5
PEGBE + 1- Butanol
∆u (m s-1)
293.15 114.523 26.1741 70.0391 2.8648 -122.877 0.4012 303.15 161.179 63.0599 72.9529 108.330 -61.2044 1.2832 313.15 119.190 71.6761 63.7197 175.007 149.808 0.4656
293.15 -0.1345 -0.0646 -0.0805 -0.1688 -0.7780 0.0003 L
Ef (A°) 303.15 -0.1586 -0.0943 -0.0985 -0.2070 -0.1070 0.0008
313.15 -0.1524 -0.1006 -0.1169 -0.2743 -0.1796 0.0001
∆Ks x 10
10 293.15 -3.6238 -1.8377 -2.3104 -4.7480 -2.3537 0.0078
(N-1
.m2) 303.15 -4.3438 -2.4986 -2.3516 -6.0451 -3.7390 0.0208
313.15 -4.2233 -3.0200 -2.1282 -6.8112 -7.8692 0.0080
293.15 -413.5050 -348.21 -240.75 -55.7239 41.6874 0.1903
∆Rm 303.15 -403.1970 -320.64 -298.32 -409.1 -270.102 1.7692 313.15 -405.2430 -299.75 -283.84 -460.474 -331.405 2.1535
PEGBE + MAE
∆u (m s-1)
293.15 -130.2926 -130.0748 -121.9684 -86.2638 -21.2049 0.3328 303.15 -145.0741 73.0193 -684.9443 -415.2566 856.6399 0.7159 313.15 -125.6986 -129.0778 -188.8272 -178.5554 -85.5840 0.8437
293.15 -0.1345 -0.0646 -0.0805 -0.1688 -0.7780 0.0003 L
Ef (A°) 303.15 -0.1586 -0.0943 -0.0985 -0.2070 -0.1070 0.0008
313.15 -0.1524 -0.1006 -0.1169 -0.2743 -0.1796 0.0001
∆Ks x 1010
293.15 -3.6238 -1.8377 -2.3104 -4.7480 -2.3537 0.0078 (N
-1.m
2) 303.15 -4.3438 -2.4986 -2.3516 -6.0451 -3.7390 0.0208
313.15 -4.2233 -3.0200 -2.1282 -6.8112 -7.8692 0.008
293.15 -422.4018 -329.3091 -321.4609 -447.6781 -257.3066 0.3247
∆Rm 303.15 -425.2030 -329.2957 -321.9254 -443.2822 -262.9791 0.3801
313.15 -417.5818 -343.2357 -424.7094 -654.6919 -412.2322 0.6418
5.3. Conclusion
The above study infers the presence of specific intermolecular interaction in
the systems studied, with the order of strength of interaction as PEGBE + 1- butanol
> PEGBE + MAE.
EY
117
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[16] A. Ali and M. Tariq, J. Mol. Liqs., 128 (2006) 50.
[17] J. F. Kincaid and H. Eyring, J. Phys. Chem., 41 (1937) 249.
[18] J. M. Prausnitz, Molecular Thermodynamics of Fluid Phase Equilibria. 2nd edn, Prentice
Hall Engle Wood Cliffs, (1969).
[19] S. Thirumarans and N Karthikeyan International Journal of Chemical Research Vol. 3
(2011) 83.
[20] S. Parveen, S. Singh, D. Shukla, K.P. Singh, M. Gupta and J.P. Shukla Acta physica
polonica A 116 (2009) 1011.
[21] M. Yasmin, M. Gupta and J. P. Shukla Journal of Molecular Liquids 160 (2011) 22.
CHAPTER 6 Molecular Association of Binary Mixtures of Poly(Ethylene
Glycol) Butyl Ether (PEGBE) 206 with 1- Butanol and
2-(Methylamino)ethanol(MAE) – A Thermodynamic and 1H
NMR Spectroscopy Study
6.1 Introduction
6.2 Results and Discussion
6.2.1 Thermodynamic Study
6.2.1.1 Experimental Data
6.2.1.2 Excess Parameters
6.2.1.3 Redlich-Kister Polynomial Equation Data
6.2.2 1H NMR Spectroscopy Study
6.3 Conclusion
References
118
6.1 Introduction
When an organic solvent mixed with the polymer, competition between
various moetities present in the mixtures such as cation, anion and solvent
molecules for hydrogen and ionic bonding is expected [1]. Addition of hydrogen
bond donors such as 1-butanol and 2-(Methylamino)ethanol(MAE) can bring about
significant changes in the strength of hydrogen bonding interaction through
formation of new hydrogen bonding or breaking / weakening hydrogen bonds for
pure liquids [2]. The review of the literature data suggests that a wide range of
spectral methods, thermo-chemical methods and studies of intensive macroscopic
properties of solutions (such as density, viscosity etc.) in varying temperatures were
used to analyze the internal structures of liquid solvent mixtures [3]. Obviously,
when attempting to assess the structure of a two-component solvent mixture, one
needs to know the properties and structure of its components. The literature review
shows that the physico-chemical properties of (PEGBE +1-butanol) and (PEGBE +
MAE) binary mixtures have not been studied up to now. Therefore, density and
viscosity measurements have been carried out for these systems to study molecular
association between unlike molecules.
From the experimental data, deviation in viscosity (∆η) and Gibbs free energy
of activation of viscous flow (∆G*E
) have been calculated over whole composition
range at 293.15, 303.15, and 313.15 K. These data have been fitted to the Redlich–
Kister equation [4], to obtain the binary coefficients and standard deviations. 1H
NMR spectroscopic technique has been widely used because of its capability to
identify the protons involved in interaction, with precision and accuracy. Interaction
can be easily identified by observation of selective line broadening or chemical shift
119
displacements of 1H-NMR signals. Further, thermodynamical results have been
supported by 1H NMR spectroscopy analysis by studying the NMR chemical shifts
for various protons of PEGBE 206, 1- butanol and MAE molecules.
6.2 Results and Discussion
6.2.1 Thermodynamic Study
The thermodynamic properties of a binary mixture such as viscosity and
density are important from practical and theoretical points of view to understand
liquid theory.
6.2.1.1 Experimental Data
Experimental values of density and viscosity of the pure liquids at 293.15 K,
303.15K and 313.15K are compared with the literature and given in table 6.1.
Table 6.1 Experimental values of viscosities (η) and density (ρ) of pure components and their comparison with literature values.
ρ (gm.cm-3
) η (mPa . s)
Component T (K)
Observed
Literature
Observed Literature
293.15
1.0047
--
27.459
--
PEGBE 303.15
0.9861
--
21.149
--
313.15
0.9785
--
12.998
--
293.15
0.9401
--
12.839
--
MAE 303.15
0.9328
0.9337a
8.452
8.5221d
313.15
0.9263
0.9259a
5.917
5.8331d
293.15
0.8097
0.8098c
2.818
2.8200b
1-Butanol 303.15
0.8020
0.8017c
2.249
2.2700b
313.15
0.7945
0.7934c
1.758
1.7600b
aRef. [22],
bRef. [23],
cRef. [7],
dRef. [24],
120
The experimental values of density ( m ) and viscosity (ηm) of binary
mixtures of poly(ethylene glycol) butyl ether (PEGBE) 206 with 2-(Methylamino)
ethanol (MAE) and 1- butanol at temperatures 293.15K, 303.15K and 313.15K are
given in table 6.2.
The molecular structure of polymers PEGBE average molecular weight Mn-
206 g.mol-1
, 1-butanol Mn-74.12 g.mol-1
and 2-(Methylamino) ethanol (MAE) Mn-
75.11 g.mol-1
are shown in Figure 6.1.
PEGBE 206 MAE 1-Butanol
Figure 6.1 Molecular Structure of Poly(ethylene glycol) butyl ethers (PEGBE) 206, 2-(Methylamino) ethanol (MAE) and 1-butanol used.
6.2.1.2 Excess Parameters
The experimental data are used to calculate the values of deviation in
viscosity (∆η) and excess Gibb‟s free energy of activation of viscous flow (∆G*E).
A specific interaction is operating in the mixing process which is responsible for the
sign of excess parameters [5].
The variation of deviation in viscosity (Δη) and excessGibb‟s free energy of
activation of viscous flow (∆G*E
) with mole fraction of PEGBE for both the systems
at mentioned temperatures is shown in figures 6.2 and 6.3. A perusal of figure 6.2
shows that the values of deviation in viscosity (Δη) of binary systems consisting of
PEGBE206 with 1-butanol and MAE are positive over entire range of composition
at T = (293.15, 303.15 and 313.15) K.
121
Table 6.2 Experimental values of density ( m ) and viscosity (ηm) of PEGBE 206 + 1-
butanol and MAE mixture with mole fraction of PEGBE 206 ( 1x ) at T= 293.15, 303.15
and 313.15K.
PEGBE 206 + 1- butanola PEGBE 206 + MAE
b
x1
ρm ηm
x1
ρm ηm
(gm cm–3) (mPa s) (gm cm–3) (mPa s)
293.15K
293.15K
0.0000 0.8097 2.810 0.0000 0.9401 12.849
0.0997 0.8558 7.970 0.0997 0.9558 18.970
0.1989 0.8953 11.976 0.1986 0.9671 22.976
0.2988 0.9283 15.797 0.2988 0.9783 23.997
0.4000 0.9576 18.806 0.4000 0.9857 25.306
0.5000 0.9719 20.956 0.5000 0.9901 25.806
0.6007 0.9843 22.904 0.5994 0.9952 26.160
0.7021 0.9938 24.502 0.7021 0.9972 26.950
0.8018 0.9998 25.917 0.7990 0.9999 26.917
0.9019 1.0031 26.933 0.9019 1.0011 27.033
1.0000 1.0047 27.459 1.0000 1.0047 27.459
303.15K
303.15K
0.0000 0.8020 2.240 0.0000 0.9328 8.453
0.0997 0.8433 6.436 0.0997 0.9482 12.436
0.1989 0.8762 8.939 0.1986 0.9582 14.963
0.2988 0.9059 11.137 0.2988 0.9665 16.593
0.4000 0.9309 13.476 0.4000 0.9728 17.597
0.5000 0.9440 15.122 0.5000 0.9782 18.122
0.6007 0.9608 16.996 0.5994 0.9808 18.962
0.7021 0.9731 18.494 0.7021 0.9831 19.494
0.8018 0.9810 19.455 0.7990 0.9840 20.055
0.9019 0.9852 20.497 0.9019 0.9852 20.497
1.0000 0.9861 21.149 1.0000 0.9861 21.149
313.15K
313.15K
0.0000 0.7945 1.750 0.0000 0.9263 5.919
0.0997 0.8413 4.079 0.0997 0.9410 8.798
0.1989 0.8737 6.954 0.1986 0.9513 10.147
0.2988 0.9014 7.820 0.2988 0.9590 11.020
0.4000 0.9243 9.532 0.4000 0.9653 11.323
0.5000 0.9387 10.531 0.5000 0.9694 11.979
0.6007 0.9509 11.411 0.5994 0.9728 12.311
0.7021 0.9627 12.118 0.7021 0.9752 12.618
0.8018 0.9726 12.429 0.7990 0.9771 12.693
0.9019 0.9766 12.796 0.9019 0.9776 12.796
1.0000 0.9785 12.998 1.0000 0.9785 12.998
122
It is seen from figure 6.2 that the positive values of Δη increase with
temperature, which indicates that the temperature coefficients of deviation in
viscosity are negative for both the systems. As the temperature is increased, thermal
energy facilitates the breaking of bonds between the associated molecules of
PEGBE + 1-Butanol/MAE, resulting in decrease in the positive Δη values.
(a)
(b)
Figure 6.2 Deviation in viscosity (Δη)versus the mole fraction of PEGBE 206 (x1) for binary mixtures (a) PEGME 206 + 1-butanol and (b) PEGBE 206 + MAE at 293.15K,
303.15K and 313.15K.
0
1
2
3
4
5
6
7
0 0.2 0.4 0.6 0.8 1
293.15K
303.15K
313.15K
Δη
(mP
a s
)
x1
0
1
2
3
4
5
6
7
8
0 0.2 0.4 0.6 0.8 1
293.15K
303.15K
313.15K
Δη
(mP
a s
)
x1
123
The large positive values for the systems PEGBE 206 + 1-butanol and
PEGBE 206 + MAE indicate the presence of strong interactions between the
components of both the mixtures. Similar results have been found by Yasmin and
Gupta [5] for the system PEG + ethanolamine and PEG + m-cresol and by Li et al
[6] for binary system of triethylene glycol monomethyl ether + water.
(a)
(b)
Figure 6.3 Excess Gibb’s free energy of activation of viscous flow (∆G*E) versus the mole fraction of PEGBE 206 (x1) for binary mixtures: (a) PEGBE + 1-butanol and
(b)PEGBE 206 + MAE and at 293.15K, 303.15K and 313.15K.
The excess Gibb‟s free energy of activation of viscous flow are found to be
positive (Figure 6.3) for both the systems under investigation suggesting the
0
0.5
1
1.5
2
2.5
3
0 0.2 0.4 0.6 0.8 1
293.15K
303.15K
313.15K
ΔG
*E
(kJ
mo
l-1)
x1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1
293.15K
303.15K
313.15K
x1
ΔG
*E
(k
J m
ol-1
)
124
presence of strong interactions between unlike molecules. No significant change has
been observed in ∆G*E
values with temperature. Yasmin et al [7] have also reported
similar variations in the ∆G*E
values for binary mixtures of PEG+ethanolamine, m-
cresol and aniline. Higher positive values in binary system PEGBE + 1- butanol in
comparison to PEGBE + MAE suggest that the interaction is more stronger in
PEGBE + 1-butanol system. This may be due to the fact that butanol is more acidic
than MAE when molecules of butanol or MAE are mixed with PEGBE, Butanol
interacts more readily then MAE due to more acidic nature, thereby giving more
positive values of ∆G*E
.
6.2.1.3 Redlich-Kister Polynomial Equation Data
The calculated data of deviation in viscosity (Δη) and excess Gibb‟s free
energy of activation of viscous flow (∆G*E
) were fitted to the Redlich – Kister
polynomial equation. Tables 6.3 and 6.4 report the standard deviations along with
coefficients of Redlich – Kister polynomial equation of the respective functions at
all the three temperatures.
Table 6.3 Adjustable parameters ai for Redlich – Kister polynomial equation with the
standard deviations EY for deviation in viscosity(∆η) and Excess Gibb’s free
energy of activation of flow (∆G*E) for binary mixture of PEGBE 206 + 1- butanol at temperature 293.15, 303.15 and 313.15K.
Parameters
Temp.
(K) 1a 2a 3a 4a 5a EY
∆η(mPa . s)
293.15 80.2893 -44.8872 66.9871 -18.0891 -110.9932 0.3972
303.15 57.0932 -23.1990 43.4842 -5.9712 -55.8912 0.4812
313.15 52.4782 -16.4972 -39.2937 3.9832 26.8762 0.9732
293.15 25.7893 15.8932
17.8362 -0.8731 -8.8931 0.0892
∆G*E
(kJ mol-1) 303.15 18.8892 17.8932 18.7783 28.8832 15.8784 0.0853
313.15 20.9894 19.8934 14.6783 9.8965 5.6785 0.0587
125
Table 6.4 Adjustable parameters ai for Redlich – Kister polynomial equation with the
standard deviations EY for deviation in viscosity(∆η) and Excess Gibb’s free
energy of activation of flow (∆G*E) for binary mixture of PEGBE 206 + MAE at temperature 293.15, 303.15 and 313.15K.
Parameters
Temp.
(K) 1a 2a 3a 4a 5a EY
∆η(mPa . s)
293.15 121.1730 43.3730 17.1243 116.9432 73.5452 0.8872
303.15 115.3142 -6.7642 133.7981 167.9867 -203.9621 0.8742
313.15 79.2398 20.9785 -18.9723 32.3906 76.8921 0.2875
293.15 16.8931 8.8723 8.9845 23.9821 22.8312 0.0893
∆G*E
(kJ mol-1) 303.15 17.8371 15.9823 -6.9323 10.8722 30.8621 0.0756
313.15 18.9831 13.9872 9.3122 18.7831 13.8925 0.0982
6.2.2 1H NMR Spectroscopy Study
NMR studies were used to shed light on the underlying mechanism of
solubilisation and to establish the preferential interactions simultaneously with
functional groups of binary mixtures. The detection and analysis of the chemical
shift perturbation (Δδ) in NMR spectra have been extensively applied to prove the
existence of solvent–solute interactions [8 - 12]. The downfield shift (to lower
magnetic fields) of the resonance relative to the first component is represented by a
negative sign (−∆δ) and an upfield shift (to higher magnetic fields) is shown by a
positive sign (+∆δ) [13].
Figure 6.4 shows the 1H NMR spectrum of the pure PEGBE 206, 2-
(Methylamino) ethanol (MAE) and 1-butanol. The 1H-NMR spectra of binary
mixtures PEGBE + 1- butanol and PEGBE + MAE with varying concentration of
PEGBE 206 have been presented in figure 6.5 and 6.6. All spectra show clearly
defined peaks, corresponding to the CH3, CH2 and OH groups. The CH3 and CH2
126
peak shifts as a function of concentration are much smaller than that of the OH
peak.
(a)
(b)
(c)
Figure 6.4 1H NMR spectra of pure molecules (a) Pure PEGBE 206 (b) pure 1-Butanol and (c) pure 2-(Methylamino)Ethanol (MAE).
127
The change in chemical shift of the CH2 and CH3 groups can be attributed to
non-hydrogen binding interactions due to changes in the bulk magnetic
susceptibility [14] and density effects [15]. These effects are the same for all three
proton types (CH3, CH2 and OH). Thus, the effect of hydrogen bonding can be
isolated for investigation by consideration of the shift of the OH peak, relative to
either the CH2 or CH3 peak. Protons directly bonded to oxygen or nitrogen atom are
more prone to undergo complexation because they are exchangeable, capable of
forming hydrogen bonding and subject to partial or complete decoupling by the
electrical quadrupole moment of the 14
N nucleus[16].
Figures 6.5 and 6.6 show the variation in observed chemical shift for different
protons of binary mixtures PEGBE + 1- Butanol and PEGBE + MAE as a function
of mole fraction of PEGBE 206. The chemical shift of O-H proton for the system
PEGBE + 1-butanol is 4.60ppm, 4.81ppm and 4.92ppm for x1 = 0.2988, 0.5000 and
0.7021 respectively (Figure 6.5), and for the system PEGBE + MAE for x1 =
0.3008, 0.5006 and 0.7005 is 4.55ppm, 4.57 and 4.60 respectively (Figure 6.6).
Downfield shift is observed for O-H protons for both the (PEGBE + 1- Butanol and
PEGBE + MAE) systems. In case of PEGBE + 1-Butanol, a downward shift of 0.32
ppm (from x1 = 0.2988 to 0.7021) and for the system PEGBE + MAE of 0.03 ppm
(from x1 = 0.3001 to x1 = 0.7005) was observed. This may be due to the solute–
solvent interactions that gradually leads to the hydrogen bonded environment in
binary mixtures. Similar results were also observed by Poppe and Vanhalbeek [17],
who pointed out that hydroxy protons involved in hydrogen bonds should be
deshielded. Besides temperature coefficients, coupling constants and chemical
128
exchange, the chemical shift difference ∆δ can also be used as a conformational
probe to study hydrogen bond interaction [18 – 20].
Figure 6.5 1D 1H NMR spectra of binary mixture of PEGBE + 1- butanol at different
concentration of PEGBE 206.
An up field shift in δCH2 and δCH3 protons has been also observed for the
system PEGBE+ MAE with the increase in PEGBE concentration (Figure 6.6). An
up field shift is indicative of an increase in electron density around the H nuclei of
MAE which is due to (i) breaking the intermolecular hydrogen bonding in MAE (ii)
less hydrogen bonding type interactions [21].
Figure 6.6 1D 1H NMR spectra of binary mixture of PEGBE + MAE at different concentration of PEGBE 206.
Therefore, on the basis of the actual experimental evidence and literature
information about the internal structure of PEGBE, 1-butanol and MAE, it can be
129
suggested that the addition of pure 1-butanol or MAE to PEGBE disrupts their self-
associated structure and stabilizes the internal structure of mixed solvent
increasingly by hydrogen bonding between the component molecules.
The binary mixture of PEGBE with 1-butanol (Figure 6.5) shows more
pronounced changes in chemical shift of different protons than the binary mixture
with MAE (Figure 6.6) which reflects that the interaction is stronger in PEGBE + 1-
Butanol than in PEGBE + MAE mixtures. The findings from the molecular scale
studies conducted using NMR technique are strongly supported by thermodynamic
studies.
(a)
(b)
Figure 6.7 Schematic representation of H-bond between PEGBE (monomer) with (a) 1-butanol and (b) MAE.
130
6.3 Conclusion
It can be concluded from the above study that there is a presence of specific
intermolecular interaction in both the systems. The interaction is found to be
stronger in the system PEGBE + 1- butanol than in PEGBE + MAE. A comparative
analysis of thermodynamic and 1H NMR spectroscopic results shows that the
multiple hydrogen bonding interactions occurring in the systems investigated at the
microscopic level are reflected in the mixing macroscopic behaviour.
131
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[2] W. Well and R. A. Pethrick, Polymer 23 (1982) 369.
[3] B. Gonzalez, A. Dominguez, J. Tojo and R. Cores, J. Chem. Eng. Data 49 (2004) 1225.
[4] O. Redlich and A. T. Kister, Ind. Eng. Chem., 40 (1948) 345.
[5] M. Yasmin and M. Gupta, J Solution Chem. 40 (2011) 1458.
[6] X . Li, G. Fan, Y. Wang, M. Zhang and Y. Lu, J. Mol. Liq. 151 (2010) 62.
[7] M. Yasmin, M. Gupta and J. P. Shukla, J. Mol. Liq. 160 (2011) 22.
[8] A. G. Avent, P. A. Chaloner, M. P. Day, K. R. Seddon and T. Welton, J. Chem. Soc.-
Dalton Trans., 23 (1994) 3405.
[9] J. M. M. Araújo, R. Ferreira, I. M. Marrucho and L. P. N. Rebelo, J. Phys. Chem. B, 115
(2011) 1073.
[10] M. R. Chierotti and R. Gobetto, Chem. Commun, (2008) 1621.
[11] E. Yashima, C. Yamamoto and Y. Okamoto, J. Am. Chem. Soc., 118 (1996) 4036.
[12] C. L. McCormick, P. A. Callais and B. H. Hutchinson, Macromolecules, 18 (1985) 2394.
[13] M. S. Bakshi and I. Kaur, Prog. Colloid Polym. Sci. 122 (2003) 37.
[14] M. M. Hoffmann and M. S. Conradi, Journal of Physical Chemistry B, 102 (1998) 263.
[15] S. L. Wallen, B. J. Palmer, B. C. Garrett and C.R. Yonker, Journal of Physical Chemistry,
100 (1996) 3959.
[16] R. M. Silverstein and F. X. Webster, New York: John Wiley & Sons, Inc., 1998.
[17] L. Poppe and H. Vanhalbeek, Nature Struct. Biology. 1, (1994) 215.
[18] C. M. Kinart, M. M. Rudnicka, W. J. Kinart, A. Cwiklinska and Z. Kinart J. Mol. Liq. 186
(2013) 28.
[19] I. Ivarsson, C. Sandstrom, A. Sandstrom and L. Kenne, J. Chem. Soc. Perkin.Trans.
2 (2000) 2147.
[20] C. Sandstrom, H. Baumann and L. Kenne, J. Chem. Soc. Perkin. Trans. 2(1998) 2385.
[21] B. Kumar, T. Singh, K. S. Rao, A. Pal and A. Kumar, J. Chem. Therm. 44 (2012) 121.
[22] E. Alvarez, D. G. Diaz, M. D. L. Rubia, and J. M. Navaza J. Chem. Eng. Data 51 (3)
(2006) 955.
[23] K. P. Singh, H. Agarwal, V. K. Shukla, I. Vibhu, M. Gupta and J.P. Shuka, J Sol. Chem 39
(2009) 1749.
[24] J. Li, M. Mundhwa, P. Tontiwachwuthikul, and A. Henni J. Chem. Eng. Data 52 (2007)
560.
CHAPTER 7
Dielectric, Ultrasonic and Refractive Index Studies of Binary
Mixtures of Some Polymers and Ceramic Materials:
A Conformational Analysis
7.1 Introduction
7.2 Results and Discussion
7.2.1 Dielectric Study
7.2.2 Ultrasonic Study
7.2.3 Refractive Index Study
7.3 Conclusion
References
132
7.1 Introduction
The advances in natural science follow two inseparably interrelated paths:
experimental and theoretical. Accumulation of an appropriate amount of
experimental data allows drawing generalized conclusions, deriving appropriate
formulas and formulating laws that govern the studied phenomena. This leads to the
possibility to predict and program expected effects for practical use. Obviously,
such a research cycle requires, particularly obtaining information about molecular
interaction and stereochemical effects, the theoretical results to be verified by
experimental results.
Engineers consistently demand new material systems for specific
applications. This demand dictates that material scientists develop new material
systems. The modern applications require diverse and specific properties in
materials which cannot be met in single-phase materials. The composites contain
two or more chemically different materials or phases. In these materials, it is
possible to tailor electrical and mechanical properties catering to a variety of
applications.
Dielectric constant of a composite is determined for applications and for
understanding the nature of the interactions between the constituents of the
composite. There are many theoretical studies on dielectric constant of composites
in order to describe its dependence on the volume fraction of the filler particles, the
dielectric constant of polymer and filler and the possible interaction between both
constituents [1-6]. Accuracy of different theoretical models is necessary for
designing of ceramics polymer composites for various applications.
133
In the literature, different theoretical models and mixing rules like
Jayasundere and Smith, Lichtenecker logarithmic, Maxwell Garnett, Sillar and
Yamada are typically applied to different ceramic/ polymer composite systems, with
the models introducing different physical fundaments for describing the interactions
between the ceramic and the polymer [7-10].
The study of ultrasonic velocity and refractive index in liquids is well
established for examination of the nature of intermolecular and intramolecular
interactions in liquid system. Therefore, the ultrasonic and refractive index
measurements in liquids and its variation with temperature provide detailed
information regarding the properties of the medium such as absorption,
compressibility, intermolecular forces, molecular interactions, chemical structure
and the energies of the molecules in motion [11-12].
In this chapter, different models and mixing rules eg. Nomoto‟s, Van dael and
Van Geel‟s, Junjui‟s, Schaaff‟s and Flory statistical theory [13-17] for ultrasonic
velocity and five mixing rules for prediction of refractive index eg. Lorentz–Lorenz
(L–L), Eykmen (Eyk), Oster's, Gladstone–Dale (G–D) and Newton (N) [18-22]
have been applied to the systems under study to analyze and verify applicability of
these models. The results have been expressed in terms of average percentage
deviations. A systematic comparison and critical analysis of the models and
mixing rules is also performed in order to evaluate applicability of these models and
mixing rules.
134
7.2. Results and Discussion
7.2.1 Dielectric Study
Dielectric constants of BaTiO3/polymer and BaTiO3/epoxy were calculated
from various existing mixing rules (equation no 2.75 to 2.82 given in chapter 2).
Maxwell – Garnett and Rayleigh‟s models have the same solutions, so just Maxwell
– Garnett is shown. Dielectric constant of pure polymer and BaTiO3 ceramics have
been taken from literature [23, 24]. The correlation between theoretical models is
presented in Figures 7.1 to 7.3. In each figure, the dielectric constant of the
composites is plotted as a function of volume fraction of the inclusions. The
theoretical predictions are drawn and are represented along with the experimental
results for different particle size in order to investigate the agreement between them.
The experimental and predicated values of dielectric constant (ε) using five
mixing rules for BaTiO3/ Poly (ethylene glycol) diacrylate (PEGDA) composite at
different frequency are presented in Figure 7.1. It is clear from the Figure 7.1 (a)
and (b) that out of five mixing rules/models, Lichtenecker model predicts ε values
best in term of average percentage deviations, while Jayasundere and Yamada
model are near to the experimental values over the whole composite range and
Maxwell- Garnett and Sillar models show a very distinct behaviour as compared
with other models. It is observed from Figure 7.1 (c) that dielectric constant
evaluated using Jayasunderea and Lichtenecker models are close to experimental
results, however other models/mixing rules show more deviation from the
experimental values.
135
Figure 7.1. Comparison of the experimental and theoretical values of Dielectric constant of BaTiO3/PEGDA with volume fraction of BaTiO3 at (a)1KHz (b) 1 MHz and
(c)1GHz frequency
Figure 7.2 is the graphical depiction of the dielectric constant of BaTiO3/
trimethylolpopane triacrylates (TMPTA) computed by various mixing rules and
shows the relative deviation from the experimental data.
10
20
30
40
50
60
70
80
0 0.1 0.2 0.3 0.4 0.5
experimental values lichtencher jayasundare
yamada maxwell siller
Die
lect
ric
Co
nst
an
t (ε
)
Volume Fraction of BaTiO3
6
16
26
36
46
56
66
76
0 0.1 0.2 0.3 0.4 0.5
experimental values lichtencher maxwell
jayasundare yamada siller
Die
lect
ric
Co
nst
an
t (ε
)
volume Fraction of BaTiO3
0
10
20
30
40
50
0 0.1 0.2 0.3 0.4 0.5
experimental values yamada jayasundaremaxwell lichtencher siller
die
lect
ric
Co
nst
an
t (ε
)
volume Fraction of BaTiO3
a
b
c
136
Figure 7.2. Comparison of the experimental and theoretical values of Dielectric constant of BaTiO3/TMPTA with volume fraction of BaTiO3 at 1GHz frequency
Figure 7.3. Comparison of the experimental and theoretical values of Dielectric constant of BaTiO3/Epoxy thik film with volume fraction of BaTiO3 at (a) BST (0.2) (b)
BST (0.4)
0
5
10
15
20
25
30
35
40
0 0.1 0.2 0.3 0.4 0.5
experimental values yamada jayasundarelichtencher MAXWELL sillar
Die
lect
ric
Co
nst
an
t (ε
)
Volume Fraction of BaTiO3
5
7
9
11
13
15
17
19
0 0.05 0.1 0.15 0.2
MAXWELL sillar experimental
lichtencher jayasundare yamada
Die
lect
ric
Co
nst
an
t (ε
)
Volume Fraction of BaTiO3
579
111315171921
0 0.05 0.1 0.15 0.2
experimental lichtencher jayasundareyamada MAXWELL sillar
Die
lect
ric
Co
nst
an
t (ε
)
Volume Fraction of BaTiO3
a
b
137
The values of ε calculated from the lichtenecker logarithmic law are found to
be in good agreement with the experimental values of the BaTiO3/TMPTA
composite materials.
Figure 7.3 shows the effective dielectric constant of two composites
BaTiO3/ epoxy with the 20 volume % ceramic filler. The ceramic – epoxy
composites were fabricated using Ba1-x Srx TiO3(x=0.2 and x=0.4) powder mixed
with Bisphonol an epoxy. Different mixing rules such as Maxwell- Garnett, Sillar,
Jayasundere & Smith, Yamada and Lichtenecker models used to compute ε values
and compared with the with the experimental results.
The Lichtenecker model fits better with the experimental results for both
composites (Figure 7.3). In case of BST (0.2) epoxy composite it is noticed that a
small deviation from the Lichtenecker models gives small deviation.
Table 7.1 Average percentage deviations of the values of dielectric constant calculated
using different mixing rules.
Compositions
Lichtenecker Jayasundare Yamada Maxwell Sillar
BaTiO3/TMPTA
1.313 22.608 25.831 39.942 45.733
BaTiO3/PEGDA at 1 GHz -6.886 12.109 16.228 32.644 39.510
BaTiO3/PEGDA at 1 MHz -1.158 10.948 14.878 31.496 38.378
BaTiO3/PEGDA at 1 kHz -4.901 3.556 7.896 25.923 33.427
BaTiO3 / Epoxy thick film (0.4) -3.517 19.223 15.755 12.698 27.516
BaTiO3 / Epoxy thick film (0.2) -0.633 14.080 10.420 10.400 23.132
The average percentage deviations of dielectric values for different
composites of polymer/ceramic are given in table 7.1. A close perusal of table 7.1
reflects that Lichtenecker model is best suitable for all the compositions with the
138
minimum percentage deviation -0.633 and maximum percentage deviation -6.886
for the composition ceramic/epoxy thick film (0.2) and BaTiO3/PEGDA respctively,
while Jayasundare and Yamada models give slightly large deviation for all
composition except BaTiO3/PEGDA at 1 kHz.
7.2.2 Ultrasonic Study
Ultrasonic study of liquid and liquid mixtures has been gained much
importance during the last two decades in assessing the nature of molecular
interactions and investigating the physicochemical behaviour of such systems [25-
28].
Table 7.2 Average percentage deviation in the values of ultrasonic velocity evaluated from various methods of PEGBE + 1-butanol and PEGBE + MAE mixtures at T=293.15, 303.15 and 313.15K.
Ultrasonic velocity (m. s-1
)
T/K Nomoto VanDeal Junjie Schaff FST
PEGBE + 1-Butanol
293.15 -0.1501 12.5260 1.5275 -11.8718 5.6681
303.15 -0.4467 13.3147 1.1475 -10.7612 3.0890
313.15 -0.1865 13.9275 1.5409 -10.2250 0.9238
PEGBE + MAE
293.15 -0.0153 8.7981 0.1399 -13.0607 4.3177
303.15 -0.1532 8.9876 0.2932 -13.0833 1.6901
313.15 0.2919 9.2913 0.4310 -12.9389 -0.6291
PPGMBE + 1- Butanol
293.15 -1.0866 9.7032 -0.6938 -29.9072 6.0294
303.15 -0.7173 10.5400 -0.3022 -28.8649 4.4226
313.15 -0.9977 10.1372 -0.5687 -29.2388 4.5360
PPGMBE + MAE
293.15 -0.1791 32.3459 -0.1658 -33.8134 -1.9083
303.15 -0.8671 31.8189 -0.8520 -35.0081 -3.5253
313.15 0.0588 31.9166 0.0814 -34.2751 -4.2109
139
Table-7.3 Experimental and theoretical values of velocities (m.s-1) in PEGBE + 1-Butanol system at different temperatures
PEGBE + 1-Butanol x1 Uexp Nomoto VanDeal Junjie Schaff FST
293.15K
0.0000 1258.0 1258.0 1258.0 1258.0 1258.0 1271.9
0.0997 1308.5 1312.5 1206.0 1290.4 1446.9 1281.4
0.1989 1345.3 1357.1 1173.8 1322.7 1568.3 1288.2
0.2988 1386.8 1394.7 1156.7 1354.7 1652.5 1302.0
0.4000 1418.6 1426.9 1153.3 1386.1 1707.6 1314.5
0.5000 1446.2 1454.3 1163.3 1416.1 1727.7 1333.9
0.6007 1474.4 1478.2 1188.0 1445.0 1726.7 1357.4
0.7021 1506.7 1499.2 1230.4 1472.9 1706.1 1388.0
0.8018 1526.5 1517.5 1295.3 1499.2 1668.3 1418.9
0.9019 1540.6 1533.8 1394.6 1524.4 1614.2 1455.0
1.0000 1548.2 1548.2 1548.2 1548.2 1548.2 1496.6
303.15K
0.0000 1224.0 1224.0 1224.0 1224.0 1224.0 1271.0
0.0997 1284.5 1279.1 1173.6 1257.4 1410.1 1288.5 0.1989 1330.5 1324.1 1142.4 1290.4 1527.0 1303.2
0.2988 1368.8 1362.0 1126.1 1322.8 1607.8 1316.9
0.4000 1400.6 1394.5 1123.1 1354.5 1658.4 1331.4
0.5000 1434.2 1422.0 1133.3 1384.5 1676.4 1354.5
0.6007 1456.0 1445.9 1157.8 1413.4 1680.8 1373.0
0.7021 1484.6 1467.0 1199.9 1441.2 1665.3 1401.0 0.8018 1498.3 1485.3 1264.2 1467.4 1631.7 1428.4
0.9019 1512.4 1501.6 1362.9 1492.4 1581.0 1464.5
1.0000 1516.0 1516.0 1516.0 1516.0 1516.0 1505.1
313.15K
0.0000 1195.2 1195.2 1195.2 1195.2 1195.2 1273.2
0.0997 1262.5 1252.5 1146.4 1229.5 1379.7 1292.5 0.1989 1308.8 1299.3 1116.4 1263.5 1497.3 1308.4
0.2988 1352.3 1338.8 1100.9 1297.0 1578.2 1326.4
0.4000 1390.5 1372.7 1098.6 1329.9 1629.4 1345.9
0.5000 1418.4 1401.4 1109.4 1361.2 1650.8 1366.3
0.6007 1448.8 1426.5 1134.4 1391.5 1652.3 1392.2
0.7021 1470.5 1448.6 1177.2 1420.8 1638.2 1418.2 0.8018 1484.2 1467.8 1242.4 1448.4 1609.5 1446.0
0.9019 1492.4 1484.9 1342.8 1474.9 1561.0 1480.9
1.0000 1500.0 1500.0 1500.0 1500.0 1500.0 1524.8
140
Table-7.4 Experimental and theoretical values of velocities (m.s-1) in PEGBE + MAE system at different temperatures
PEGBE + MAE x1 Uexp Nomoto VanDeal Z Junjie Schaff FST
293.15K
0.0000 1452.0 1452.0 1452.0 1452.0 1452.0 1423.2
0.0989 1470.2 1472.8 1388.4 1470.0 1646.3 1426.0
0.1997 1486.5 1489.1 1345.1 1485.1 1758.9 1430.3
0.3008 1502.3 1502.0 1318.5 1497.8 1821.8 1434.8
0.4060 1514.8 1512.9 1305.7 1508.9 1841.9 1440.1
0.5006 1522.2 1520.9 1306.2 1517.4 1839.8 1445.0
0.5994 1530.0 1528.1 1318.9 1525.2 1812.8 1450.9
0.7006 1535.5 1534.3 1345.9 1532.1 1764.6 1458.8
0.7990 1538.4 1539.6 1388.3 1538.1 1704.0 1466.8
0.9030 1542.2 1544.4 1455.8 1543.7 1626.1 1479.7
1.0000 1548.4 1548.4 1548.4 1548.4 1548.4 1496.8
303.15K
0.0000 1420.0 1420.0 1420.0 1420.0 1420.0 1428.3
0.0989 1442.8 1440.9 1357.9 1438.4 1612.0 1433.3 0.1997 1458.3 1457.2 1315.6 1453.7 1725.2 1438.1
0.3008 1474.5 1470.1 1289.6 1466.3 1786.9 1444.0
0.4060 1484.8 1480.9 1277.2 1477.3 1807.0 1448.9
0.5006 1494.7 1488.9 1277.8 1485.8 1806.9 1454.1
0.5994 1500.6 1495.9 1290.3 1493.4 1778.9 1460.0
0.7006 1506.1 1502.1 1316.8 1500.2 1732.7 1467.7 0.799 1510.0 1507.3 1358.6 1506.0 1671.6 1476.8
0.9030 1512.9 1512.1 1424.9 1511.4 1595.9 1488.3
1.0000 1516.0 1516.0 1516.0 1516.0 1516.0 1505.1
313.15K
0.0000 1404.0 1404.0 1404.0 1404.0 1404.0 1446.1
0.0989 1428.3 1424.9 1342.6 1422.4 1595.8 1452.6 0.1997 1446.0 1441.2 1300.8 1437.7 1707.5 1458.4
0.3008 1460.6 1454.1 1275.2 1450.4 1767.9 1463.8
0.4060 1472.5 1464.9 1263.0 1461.4 1787.9 1469.3
0.5006 1481.1 1472.9 1263.6 1469.8 1786.4 1475.2
0.5994 1486.9 1480.0 1276.0 1477.4 1759.4 1480.3
0.7006 1493.2 1486.1 1302.4 1484.2 1713.9 1488.6 0.7990 1495.6 1491.3 1343.8 1490.0 1654.8 1496.3
0.9030 1498.4 1496.1 1409.6 1495.4 1579.0 1508.8
1.0000 1500.0 1500.0 1500.0 1500.0 1500.0 1524.8
141
Mixing rules for evaluation of ultrasonic velocity have been applied on the
systems under investigation and their relative validity has been discussed in terms of
average percentage deviation with the experimental values. Table 7.2 shows the
average percentage deviation values of ultrasonic velocity of four binary systems
and tables 7.3 and 7.4 show the experimental and theoretically calculated values of
ultrasonic velocities of systems PEGBE + 1- butanol and PEGBE + MAE at three
temperatures. Experimental data for these systems reported here have been obtained
from the measurements carried out in our research laboratory.
Table 7.2 reveals that for all the systems average percentage deviation for
Nomoto‟s and Junjie methods are in fairly good agreement with the experimental
values. The average percentage values for van Deal and Flory methods are also
within limits of error. While the average percentage deviation of Schaaff‟s give
large deviation for all the systems.
7.2.3 Refractive Index Study
Table 7.5 Average percentage deviation in the values of Refractive Index evaluated from various methods of PPGMBE + 1-butanol and PPGMBE + MAE mixtures at T=293.15, 303.15 and 313.15K.
T/K Lorentz-Lorenz Gladstone-Dale Newton Eykman’s Oster's
PPGMBE + 1-butanol
293.15 0.0688 0.0532 0.0481 0.0642 0.0585 303.15 0.0398 0.0511 0.0460 0.4105 0.3786 313.15 0.5057 0.0542 0.0491 0.0432 0.0400
PPGMBE + MAE
293.15 0.0559 -0.0259 -0.0260 0.04948 0.0406 303.15 -0.0639 -0.1250 -0.1252 -0.0687 -0.0752 313.15 0.0103 -0.0658 -0.0659 0.0044 -0.0035
PEGBE + 1-butanol
293.15 0.1305 0.6919 0.6831 0.1675 0.2192 303.15 0.3192 0.6868 0.6779 0.3410 0.3719 313.15 -0.0839 0.0359 0.0358 -0.0749 -0.0625
PEGBE + MAE
293.15 -0.0534 0.0169 0.0168 -0.0479 -0.0406 303.15 -0.1042 0.0309 0.0308 -0.0939 -0.0798 313.15 -0.0839 0.0359 0.0358 -0.0749 -0.0625
142
The experimental refractive index data of PPGMBE with 1- butanol and MAE
binary systems were compared with the corresponding calculated values using five
mixing/empirical relations [29, 30] viz. Lorentz-Lorenz (L-L), Eykman‟s (Eyk),
Gladstone-Dale (G-D), Oster‟s and Newton (N) at temperatures 293.15, 303.15 and
313.13 K and are graphically presented in figures 7.4 and 7.5.
Figure 7.4 Comparison of the experimental and theoretical calculated values of
Refractive Index for the system PPGMBE + 1-butanol at (a) 293.15 K, (b) 303.15 K
and (c) 313.15 K
1.39
1.4
1.41
1.42
1.43
1.44
1.45
1.46
0 0.2 0.4 0.6 0.8 1
Newton nexp Lorentz-Lorentz Gladstone-Dale Eykman’s Oster's
a
n
x1
1.39
1.4
1.41
1.42
1.43
1.44
1.45
0 0.2 0.4 0.6 0.8 1
Gladstone-Dale Lorentz-Lorentz Eykman’s Oster's nexp Newton
b
n
1.391.4
1.411.421.431.441.451.46
0 0.2 0.4 0.6 0.8 1
Gladstone-Dale Newton nexp Lorentz-Lorentz Eykman’s Oster's
c
x1
n
143
Figure 7.5 Comparison of the experimental and theoretical calculated values of
Refractive Index for the system PPGMBE + MAE at (a) 293.15 K, (b) 303.15 K and (c)
313.15 K
1.438
1.44
1.442
1.444
1.446
1.448
1.45
0 0.2 0.4 0.6 0.8 1
Gladstone-Dale Newton nexp Eykman’s Oster's Lorentz-Lorentz
a
n
x1
1.434
1.436
1.438
1.44
1.442
1.444
1.446
0 0.2 0.4 0.6 0.8 1
Newton nexp Lorentz-Lorentz Gladstone-Dale Eykman’s Oster's
b
n
x1
1.43
1.432
1.434
1.436
1.438
1.44
1.442
0 0.2 0.4 0.6 0.8 1
Gladstone-Dale Oster's Lorentz-Lorentz Newton Eykman’s nexp
c
n
x1
144
Table 7.5 represents the average percentage deviation in the values of
refractive index. It is evident from table 7.5 that all mixing/empirical relations
exhibit excellent results for all the four binary systems. All these mixing rules
provide excellent results in the case of PPGMBE + 1-butanol and PPGMBE+ MAE
systems. However, in the case of PEGBE +1-butanol and MAE they show
comparatively higher APD though with in experimental error.
7.3 Conclusion
The Lichtenecker logarithmic rule and Jayasundere rules used for estimation
the dielectric constant show good agreement with the experimental values of
dielectric constants of polymer / ceramic compositions, BaTiO3/PEGDA at1 GHz,
BaTiO3/PEGDA at 1 MHz, BaTiO3/PEGDA at 1 KHz, BaTiO3/TMPTA, BaTiO3 /
Epoxy thik film (0.4) and BaTiO3 / Epoxy thik film (0.2) while and Maxwell-
Garnett and Sillar has a very distinct behaviour when compare with other rules. Out
of five mixing rules Lichtenecker is best suited in term of average percentage
deviations, while Jayasundere and Yamada are near to the experimental values over
the whole composite range
The theories used for estimation the ultrasonic velocity show good agreement
with the respective measured values of ultrasonic velocities for the systems PEGBE
+ 1-butanol, PEGBE + MAE, PPGMBE + 1-butanol and PPGMBE + MAE, except
Vandeal and Schaff, which give large deviation for the system PPGMBE + 1-
butanol and MAE. Nomoto and Junjie relation exhibit an excellent agreement
between the experimental and theoretical estimated values of ultrasonic velocities
for all the binary systems.
145
The mixing rule proposed by Gladstone-Dale and Newton was found to be
more suitable for prediction of refractive index for the systems PEGBE + 1-butanol,
PEGBE + MAE, PPGMBE + 1-butanol and PPGMBE + MAE.
146
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