electrical conductivity, electromagnetic interference
TRANSCRIPT
University of Calgary
PRISM: University of Calgary's Digital Repository
Graduate Studies The Vault: Electronic Theses and Dissertations
2014-02-14
Electrical Conductivity, Electromagnetic Interference
Shielding and Dielectric Properties of Multi-walled
Carbon Nanotube/Polymer Composites
Arjmand, Mohammad
Arjmand, M. (2014). Electrical Conductivity, Electromagnetic Interference Shielding and Dielectric
Properties of Multi-walled Carbon Nanotube/Polymer Composites (Unpublished doctoral thesis).
University of Calgary, Calgary, AB. doi:10.11575/PRISM/25855
http://hdl.handle.net/11023/1379
doctoral thesis
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UNIVERSITY OF CALGARY
Electrical Conductivity, Electromagnetic Interference Shielding and Dielectric Properties of
Multi-walled Carbon Nanotube/Polymer Composites
by
Mohammad Arjmand
A THESIS
SUBMITTED TO THE FACULTY OF GRADUATE STUDIES
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
DEPARTMENT OF CHEMICAL AND PETROLEUM ENGINEERING
CALGARY, ALBERTA
FEBRUARY 2014
© Mohammad Arjmand 2014
ii
To:
My Parents, Spouse and Siblings
for their heartfelt supports
iii
They did not know it was impossible, so they did it!
Mark Twain
iv
Acknowledgment
Back in September 2009, my great supervisor, Dr. Uttandaraman Sundararaj, and I were new
to the University of Calgary. At that time, Dr. Sundararaj had just moved to the University of
Calgary as the Head of the Department of Chemical and Petroleum Engineering and his
postdoctoral fellows were still at University of Alberta, who moved to Calgary a few months
later. Being my supervisor’s first graduate student at University of Calgary along with the
difficulties of occupying and organizing new laboratories depicted a challenging PhD career
towards me. Nonetheless, my supervisor was a tremendous source of management, unconditional
support and encouragement. I am truly indebted to his support during the last four years, not only
as a prominent supervisor, but also as an elder friend who guided me with academic and real
lives.
I would like to convey my wholehearted gratitude to the members of Polymer Processing
Group, particularly, Dr. Genaro Gelves and Mr. Ali Sarvi, who assisted me with my graduate life
in Calgary. I would like to thank the supervisory committee members for their insight and
comments, namely: Dr. Nader Mahinpei and Dr. Maen Husein. I express my warmest
appreciation to Dr. Simon Park and Dr. Mehdi Mahmoodi for their collaboration in
manufacturing the mold and injection molding of the composites (chapters 4 and 6). Special
thanks go to Dr. Michal Okoniewski and Mr. Thomas Apperley for their contributions to the
analysis of electrical properties data (chapter 5). A sincere appreciation goes to Dr. Rosario
Bretas and Dr. Aline Silva for their cooperation with producing the copper nanowire composites
and their characterization (chapter 8).
v
The financial supports from the Natural Science and Engineering Research Council (NSERC)
of Canada and Alberta Innovates Technology Futures (AITF) are highly appreciated. I also owe
a great deal of appreciation to Dr. Tieqi Li and Ms. Jeri-Lynn Bellamy in Nova Chemicals®,
Calgary, AB, Canada for the polymer extrusion/blending. I would like to thank Dr. Samaneh
Abbasi of Ecole Polytechnique (Montreal, Canada) for assistance with Raman spectroscopy. My
appreciation and thanks to Dr. Michael Schoel and Dr. Tobias Furstenhaupt who contributed me
with microscopy imaging. I am also very grateful to Americas Styrenics LLC, who generously
provided me with the neat polystyrene.
The deepest gratitude goes to my parents, spouse and siblings who though have been
geographically far away from me during my PhD career, but have always been in my heart.
vi
Abstract
Driven by the ever-growing demand for versatile electronics with increased functionality,
high performance, light weight, low cost and improved design options, conductive filler/polymer
composites (CPCs) have emerged as a distinctive solution. Manipulating the conductive network
formation in CPCs allows them to be employed in a wide range of applications, such as charge
storage, electrostatic discharge dissipation and electromagnetic interference (EMI) shielding.
In this dissertation, controlling the conductive network formation was the key aspect in
designing the morphology of CPCs for electrical applications. Multi-walled carbon nanotube
(MWCNT) was chosen as conductive filler due to its surprising electronic structure and growing
industrial usage. We employed two distinct techniques to improve or deteriorate conductive
network formation to improve the electrical properties in MWCNT/polymer composites, i.e.
electrical conductivity, EMI shielding and dielectric properties. These techniques comprise (1)
aligning MWCNTs using an injection molding machine, and (2) replacing MWCNTs with
copper nanowires (CuNWs).
Prior to exploring the influence of the above-mentioned techniques on the electrical properties
of CPCs, a series of studies were implemented on MWCNT/polymer composites to obtain a
general understanding from the electrical behaviors of CPCs as a function of MWCNT content.
The results over the X-band (8.2 – 12.4 GHz) showed that the electrical conductivity, EMI
shielding and dielectric properties rose with MWCNT content. The increase in electrical
conductivity with MWCNT loading was attributed to the formation of conductive paths across
the composite. Increase in EMI shielding with MWCNT content was related to a greater number
of interacting nomadic charges and also higher real permittivity (polarization loss) and imaginary
vii
permittivity (Ohmic loss). Moreover, the broadband dielectric spectroscopy (10-1
– 10+6
Hz)
showed that both real permittivity and imaginary permittivity increased drastically as the
MWCNT concentration approached the percolation threshold. Increase in real permittivity was
related to the formation of a large number of nanocapacitor structures, MWCNTs as electrodes
and polymer matrix as dielectric material, and increase in imaginary permittivity was ascribed to
greater number of dissipating charges, enhanced conductive network formation and boosted
polarization loss arising from interfacial polarization.
MWCNT alignment, induced by an injection molding machine, was observed to deteriorate
the conductive network formation. As inferior conductive network formation reduces imaginary
permittivity, this technique was introduced as an innovative technique to improve the dielectric
properties of MWCNT/polymer composites. Nonetheless, MWCNT alignment indicated an
adverse influence on the percolation threshold, electrical conductivity and EMI shielding due to
its negative influence on conductive network formation. In brief, unavoidable flow-induced
alignment of MWCNTs in injection molding process was presented as an opportunity to improve
the dielectric properties for charge storage or as a challenge to be avoided for producing
conductive CPCs.
CuNWs were creatively displayed to be competent substitutions for MWCNTs for charge
storage applications. Unavoidable oxide layer formation on the surface of CuNWs, which has
always been a disadvantage for electronics applications, was employed as a benefit to decay the
conductive network formation and reduce the imaginary permittivity. Moreover, higher
conductivity of fresh core of CuNWs relative to MWCNTs provided the composites with more
free charges contributing to real permittivity. In conclusion, high conductivity of fresh core of
viii
CuNWs combined with the presence of the oxide layer on CuNW surfaces depict a promising
future for CuNW/polymer composites as charge storage materials.
ix
Table of Contents
Dedication…………………………………………………………………………………………ii
Citation…………………………………………………………………………………………...iii
Acknowledgement………………………………………………………………………………..iv
Abstract…………………………………………………………………………………………...vi
Table of Contents………………………………………………………………..……..…………ix
List of Tables……………………………………………………………...…………………….xiv
List of Figures…………………………………………………………………………………...xv
List of Symbols and Abbreviations…………………………………………………………...….xx
Chapter 1 – Introduction………………………………………………………………………..1
1.1. General Background ................................................................................................................ 1
1.2. State-of-the-Art ........................................................................................................................ 2
1.3. References ................................................................................................................................ 5
Chapter 2 – Literature Review………………………………………………………………….6
2.1. Conductive Filler/Polymer Composites (CPCs): Structure, Applications and Market............ 6
2.2. Electrical Conductivity .......................................................................................................... 10
2.3. Electrostatic Discharge (ESD) ............................................................................................... 12
2.4. Electromagnetic Interference (EMI) Shielding ...................................................................... 16
2.4.1. General Background ....................................................................................................... 16
2.4.2. Magic of Shielding .......................................................................................................... 17
2.4.3. Shielding Effectiveness ................................................................................................... 20
2.4.4. Reflection, Absorption and Multiple-reflection for Conductive Monolithic Materials .. 22
2.4.4.1. Shielding by Reflection ............................................................................................ 22
2.4.4.2. Shielding by Absorption ........................................................................................... 24
2.4.5. Effect of Real Permittivity on Shielding of Conductive Monolithic Materials .............. 27
2.5. Dielectric Theory ................................................................................................................... 28
2.5.1. Dielectric Material .......................................................................................................... 28
2.5.2. Permittivity ..................................................................................................................... 29
2.5.3. Dielectric Mechanisms.................................................................................................... 31
2.5.4. The Electrical Current of Dielectrics under a Step DC Voltage ..................................... 35
2.6. Electrical Properties of Conductive Filler/Polymer Composites (CPCs) .............................. 38
x
2.6.1. Electrical Conductivity of CPCs ..................................................................................... 38
2.6.2. EMI Shielding of CPCs .................................................................................................. 43
2.6.3. The Mechanisms Behind the Broadband Dielectric Spectroscopy of CPCs .................. 49
2.7. Effects of Conductive Filler Type (MWCNT versus CuNW) on Electrical Properties of
CPCs ............................................................................................................................................. 51
2.7.1. Carbon Nanotubes ........................................................................................................... 53
2.7.1.1. Structure and Electrical Properties ........................................................................... 53
2.7.1.2. Carbon Nanotube Synthesis...................................................................................... 56
2.7.1.3. Carbon Nanotube Market ......................................................................................... 57
2.7.2. Copper Nanowire (CuNW) ............................................................................................. 58
2.8. MWCNT Alignment, Induced by Injection Molding, and Electrical Properties of CPCs .... 59
2.8.1. Flow Conditions in Injection molding and its Effect on Filler Alignment ..................... 60
2.8.2. A Brief Review on Electrical Conductivity of Injection Molded CPCs ......................... 62
2.9. Project Motivation and Objectives......................................................................................... 64
2.10. References ............................................................................................................................ 67
Chapter 3 – Materials, Processing and Characterization………………………...………….78
3.1. Methodology .......................................................................................................................... 78
3.2. Materials ................................................................................................................................ 79
3.3. Sample Preparation, Processing and Molding ....................................................................... 82
3.3.1. Phase I ............................................................................................................................. 82
3.3.2. Phase II............................................................................................................................ 83
3.3.2.1. Materials Preparation ................................................................................................ 83
3.3.2.2. Experimental Design and Composite Molding ........................................................ 84
3.3.3. Phase III .......................................................................................................................... 89
3.3.4. Phase IV .......................................................................................................................... 90
3.4. Electrical Properties Measurement Setups............................................................................. 91
3.4.1. Surface/Volume Resistivity Measurement ..................................................................... 91
3.4.2. EMI Shielding Setup ....................................................................................................... 95
3.4.3. Dielectric Spectroscopy Setup ........................................................................................ 98
3.5. References .............................................................................................................................. 99
Chapter 4 – Electrical and Electromagnetic Interference Shielding Properties of Flow-
induced Oriented Carbon Nanotubes in Polycarbonate…………………………...……….101
4.1. Presentation of the Article ................................................................................................... 101
xi
4.2. Abstract ................................................................................................................................ 102
4.3. Introduction .......................................................................................................................... 103
4.4. Experimental ........................................................................................................................ 106
4.4.1. Composite Preparation and Molding ............................................................................ 106
4.4.2. Electrical and EMI Shielding Measurements ............................................................... 108
4.4.3. Morphological Characterization ................................................................................... 109
4.4.4. Raman Spectroscopy ..................................................................................................... 110
4.5. Results and Discussion ........................................................................................................ 110
4.5.1 Electrical Conductivity of MWCNT/PC Composites .................................................... 110
4.5.2. Morphological Analysis ................................................................................................ 119
4.5.3. Raman Spectroscopy ..................................................................................................... 122
4.5.4. Electromagnetic Interference Shielding Measurements and Mechanism ..................... 124
4.6. Conclusions .......................................................................................................................... 129
4.7. References ............................................................................................................................ 130
Chapter 5 – Comparative Study of Electromagnetic Interference Shielding Properties of
Injection Molded versus Compression Molded Multi-walled Carbon Nanotube/Polystyrene
Composites………………………………………………………………………………...…...134
5.1. Presentation of the Article ................................................................................................... 134
5.2. Abstract ................................................................................................................................ 136
5.3. Introduction .......................................................................................................................... 137
5.4. Experimental ........................................................................................................................ 139
5.4.1. Composite Preparation .................................................................................................. 139
5.4.2. Experimental Design and Composite Molding ............................................................. 140
5.4.3. EMI Shielding Properties Measurements ..................................................................... 142
5.4.4. Morphological Characterization and Raman Spectroscopy .......................................... 144
5.5. Results and Discussion ........................................................................................................ 144
5.5.1. Morphological Analysis and Raman Spectroscopy ...................................................... 144
5.5.2. Comparison of Electrical Conductivity and EMI SE of Injection Molded versus
Compression Molded MWCNT/PS Composites .................................................................... 146
5.5.3. Effects of MWCNT Alignment on Shielding Mechanisms in MWCNT/PS Composites
................................................................................................................................................. 152
5.6. Conclusions .......................................................................................................................... 157
5.7. References ............................................................................................................................ 158
xii
Chapter 6 – An Innovative Method to reduce the Energy loss of Conductive Filler/Polymer
Composites for Charge Storage Applications……………………………...………………. 163
6.1. Presentation of the Article ................................................................................................... 163
6.2. Abstract ................................................................................................................................ 164
6.3. Introduction .......................................................................................................................... 165
6.4. Material and Methods .......................................................................................................... 166
6.4.1. Materials ....................................................................................................................... 166
6.4.2. Composite Molding ...................................................................................................... 167
6.4.3. Morphological Analysis ................................................................................................ 168
6.4.4. Determination of Carbon Nanotube Length Distribution ............................................. 169
6.4.5. Raman Spectroscopy ..................................................................................................... 170
6.4.6. Electrical and Dielectric Properties Measurements ...................................................... 170
6.5. Results and Discussion ........................................................................................................ 171
6.5.1. Morphological Analysis and Raman Spectroscopy ...................................................... 171
6.5.2. The Effects of Processing and Molding on MWCNT Length Distribution .................. 173
6.5.3. The Effects of MWCNT Alignment and Length on the Dielectric Properties ............. 174
6.6. Conclusions .......................................................................................................................... 182
6.7. References ............................................................................................................................ 183
Chapter 7 – Broadband Dielectric Properties of Multi-walled Carbon
Nanotube/Polystyrene Composites…………………………………………………………...186
7.1. Presentation of the Article ................................................................................................... 186
7.2. Abstract ................................................................................................................................ 187
7.3. Introduction .......................................................................................................................... 188
7.4. Experimental ........................................................................................................................ 189
7.4.1. Materials and Composite Preparation ........................................................................... 189
7.4.2. Electrical and Dielectric Properties Measurements ...................................................... 191
7.4.3. Morphological Characterization ................................................................................... 191
7.5. Results and Discussion ........................................................................................................ 192
7.5.1. Morphological Analysis ................................................................................................ 192
7.5.2. DC Conductivity ........................................................................................................... 195
7.5.3. AC Conductivity ........................................................................................................... 196
7.5.4. Charge Polarization Mechanisms in MWCNT/Polymer Composites .......................... 199
7.5.5. The Broadband Behavior of Real Permittivity ............................................................. 200
7.5.6. The Broadband Behavior of Imaginary Permittivity .................................................... 203
xiii
7.6. Conclusions .......................................................................................................................... 205
7.7. References ............................................................................................................................ 206
Chapter 8 – Novel Composites of Copper Nanowire/PVDF with Superior Dielectric
Properties………………………………...…………………………………………………….210
8.1. Presentation of the Article ................................................................................................... 210
8.2. Abstract ................................................................................................................................ 211
8.3. Introduction .......................................................................................................................... 212
8.4. Experimental ........................................................................................................................ 214
8.4.1. Materials ....................................................................................................................... 214
8.4.2. Mixture Preparation ...................................................................................................... 215
8.4.3. Characterization ............................................................................................................ 216
8.5. Results and Discussion ........................................................................................................ 217
8.5.1. Oxidation of CuNWs .................................................................................................... 217
8.5.2. Morphological Characterization of the Nanocomposites ............................................. 218
8.5.3. DC and AC Conductivity .............................................................................................. 220
8.5.4. Dielectric Permittivity and Dielectric Loss ................................................................... 224
8.6. Conclusions .......................................................................................................................... 231
8.7. References ............................................................................................................................ 232
Chapter 9 – Summary, Conclusions and Future Work…………………………….………236
9.1. General Background and Project Objectives ....................................................................... 236
9.2. Electrical Behaviors of CPCs and the Mechanisms Behind ................................................ 238
9.2.1. Volume Resistivity........................................................................................................ 238
9.2.2. EMI Shielding ............................................................................................................... 239
9.2.3. Broadband Dielectric Spectroscopy of CPC ................................................................. 242
9.3. Effects of MWCNT Alignment, Induced by Injection Molding, on Volume Resistivity and
EMI Shielding ............................................................................................................................. 244
9.4. Effects of MWCNT Alignment, Induced by Injection Molding, on Dielectric Properties .. 248
9.5. Novel CuNW/PVDF Nanocomposites for Charge Storage: Comparison of its Dielectric
Properties with MWCNT/PVDF Nanocomposite ...................................................................... 250
9.6. Recommendations ................................................................................................................ 251
9.7. References ............................................................................................................................ 255
xiv
List of Tables
Table 2-1: CPC applications with their required range of electrical conductivity [8]. ................... 7
Table 2-2: Classifications of materials in terms of surface resistivity [31]. ................................. 14
Table 2-3: Electrical conductivity and magnetic permeability of common materials used in
shielding barriers [33, 34]. ............................................................................................................ 27
Table 3-1: Physical properties of MWCNT (NC7000) [1]. .......................................................... 81
Table 3-2: The concentrations of the prepared MWCNT/PS nanocomposites in terms of weight
percent and volume percent. ......................................................................................................... 83
Table 3-3: Experimental design showing the two-level, four factor factorial design. The factors
are mold temperature (C1), melt temperature (C2), injection/holding pressure (C3) and injection
velocity (C4). ................................................................................................................................. 85
Table 3-4: Levels (set points) of the processing parameters used in the injection molding
experiments. The processing parameters are mold temperature (C1), melt temperature (C2),
injection/holding pressure (C3) and injection velocity (C4). ......................................................... 85
Table 3-5: Dimensions of the designed mold. .............................................................................. 86
Table 4-1: Percolation thresholds, critical exponents and correlation factors for compression-
molded samples and injection-molded samples at different areas, corresponding to different
alignments. .................................................................................................................................. 119
Table 4-2: Raman intensity ratios parallel/perpendicular to the flow direction of compression-
molded and injection-molded samples of PC/MWCNT. ............................................................ 124
Table 5-1: The concentrations of the prepared nanocomposites in terms of weight percent and
volume percent. ........................................................................................................................... 140
Table 5-2: Levels (set points) of the processing parameters used in the injection molding
experiments (EXPs). The processing parameters are mold temperature (C1), melt temperature
(C2), injection/holding pressure (C3) and injection velocity (C4). .............................................. 141
Table 5-3: Dimensions of the designed mold. ............................................................................ 142
Table 5-4: Raman intensity ratios parallel/perpendicular to the flow direction of the compression
molded and injection molded samples of 5.00 wt% MWCNT/PS composites. ......................... 146
Table 6-1: The concentrations of the prepared nanocomposites in terms of weight percent and
volume percent. ........................................................................................................................... 167
xv
List of Figures
Figure 2-1: Schematic of conductive network formation in a CPC [5]. ......................................... 6
Figure 2-2: The approximate range of electrical conductivity covered by CPCs [7]. .................... 7
Figure 2-3: Some important applications of CPCs. From left to right: Capacitors (charge
storage); airplane tire (antistatic dissipation); circuit board carrier (ESD protection); cell phone
enclosure (EMI shielding) [6, 12]. .................................................................................................. 8
Figure 2-4: Global market for CPCs in 2010-2016 [22]. ................................................................ 9
Figure 2-5: Simplified diagram of the electronic band structure in the Band Theory. ................. 11
Figure 2-6: Costs due to ESD damage at various incremental levels [30]. .................................. 13
Figure 2-7: The diagram of a typical static-safe workbench [32]. ................................................ 15
Figure 2-8: Illustration of the use of shielded enclosure (a) to contain radiated emission, (b) to
exclude radiated emission [34]. .................................................................................................... 16
Figure 2-9: Illustration of interaction between incident plane wave and conductive barrier [34].19
Figure 2-10: Schematic of the effects of multiple-reflection in a conductive shield: (a) combining
multiple transmissions, (b) calculations in terms of intrinsic impedance and reflection and
transmission coefficients [34]. ...................................................................................................... 26
Figure 2-11: Charges on a parallel-plate capacitor with (a) air between the plates, and (b) a
dielectric between the plates [25]. ................................................................................................ 28
Figure 2-12: (a) Circuit diagram of a dielectric under an AC field, (b) Argand diagram of
complex current-voltage relationship [25]. ................................................................................... 31
Figure 2-13: Frequency response of dielectric mechanisms [49, 54]. .......................................... 32
Figure 2-14: Typical DC response of a dielectric to a step voltage application [46]. .................. 36
Figure 2-15: Percolation curve of compression molded MWCNT/PS composite (A typical
percolation curve of CPCs) [41]. .................................................................................................. 41
Figure 2-16: Diagram of electron-transfer mechanisms between adjacent sites separated by a
potential energy barrier [77]. ........................................................................................................ 42
Figure 2-17: EMI SE of compression molded MWCNT/PS composite as a function of MWCNT
concentration and shielding plate thickness. ................................................................................. 44
Figure 2-18: Schematic of resistor and capacitor structures in a CPC. ........................................ 45
xvi
Figure 2-19: Contributions of (a) reflection and (b) absorption to the overall EMI SE for the
compression molded MWCNT/PS composites as a function of MWCNT concentration. The
thickness of all the samples is 2.0 mm [41]. ................................................................................. 47
Figure 2-20: Real permittivity and imaginary permittivity of MWCNT/PS composites over the
broadband frequency range [41] ................................................................................................... 48
Figure 2-21: The equivalent-circuit model of MWCNT/polymer composites. ............................ 50
Figure 2-22: TEM images of different CNTs : (a) SWCNT, (b) MWCNT with different layers of
5, 2 and 7 [112, 114]. .................................................................................................................... 53
Figure 2-23: Schematic diagram showing how a hexagonal sheet of graphene is rolled to form a
CNT with different chiralities; (a) Armchair; (B) Zigzag; (C) Chiral [68, 115]. ......................... 54
Figure 2-24: Basic hexagonal bonding structure for a graphite sheet; carbon nuclei shown as
filled circles, out-of-plane bonds represented as delocalized (dotted line), and bonds connect
the nuclei in-plane [119]. .............................................................................................................. 56
Figure 2-25: Global market for CNT grades based on committed production, (2011-2016),
($ Million) [125]. .......................................................................................................................... 58
Figure 2-26: Comparison between isothermal and non-isothermal velocity and shear rate
distributions for a non-Newtonian melt in thickness direction [126]. .......................................... 61
Figure 2-27: Influence of (a) convergent channel and (b) divergent channel on filler alignment in
a small element of polymer melt. (c) Schematic of fountain flow at the melt front [126]. .......... 62
Figure 2-28: Schematics showing (a) randomly distributed MWCNT/polymer composites, (b)
aligned MWCNT/polymer composites, and (c) CuNW/polymer composites. ............................. 65
Figure 3-1: Experimental Strategy. ............................................................................................... 79
Figure 3-2: Consecutive steps of nanowires synthesis [2, 3]. ....................................................... 82
Figure 3-3: An image of Coperion ZSK co-rotating intermeshing twin-screw extruder employed
for diluting the MWCNT/PS masterbatch. ................................................................................... 84
Figure 3-4: A schematic view of the designed mold. ................................................................... 86
Figure 3-5: Volume resistivities of the injection molded MWCNT/PS composites with 5.00 wt%
MWCNT loading at different molding conditions in the thickness direction [4]. ........................ 87
Figure 3-6: Minitab main effect plot of the volume resistivity mean of the injection molded
samples [4]. ................................................................................................................................... 88
Figure 3-7: The equivalent circuit for 8009 Test Fixture used to measure volume resistivity [6].
....................................................................................................................................................... 92
xvii
Figure 3-8: The equivalent circuit for 8009 Test Fixture used to measure surface resistivity [6].93
Figure 3-9: (a) Electrode construction, (b) equivalent circuit for 4-point probe technique [7]. ... 94
Figure 3-10: (a) Schematic of network analyzer diagram, (b) S-parameters diagram in a network
analyzer [8, 9]. .............................................................................................................................. 97
Figure 3-11: Electrode arrangement of 12962A sample holder [10] ............................................ 98
Figure 4-1: (a) Schematic of the dog-bone sample. The three different areas studied in the
specimens are indicated, (b) Experimental setup. ....................................................................... 108
Figure 4-2: Percolation curve for rectangular (compression-molded) samples of MWCNT/PC
composite. ................................................................................................................................... 111
Figure 4-3: Percolation curve for rectangular (compression-molded) samples and injection-
molded samples (parallel and perpendicular to the flow direction) at (a) area 1, (b) area 2 and (c)
area 3. .......................................................................................................................................... 115
Figure 4-4: Current-voltage characteristics of a) compression-molded sample, b) injection-
molded sample (area 3) in thickness direction. 1The measured current of composites holding 0.5
wt% of MWCNT in Fig. 3(a) and 1.5 wt% of MWCNT in Fig. 3(b) have been multiplied by 50
to enable its visualization in the plot........................................................................................... 117
Figure 4-5: SEM images of PC+1.5 wt% MWCNT. (a) compression-molded sample; (b) aligned
injection-molded sample (area 3), parallel to the flow direction; (c) aligned injection-molded
sample (area 3), perpendicular to the flow direction. ................................................................. 120
Figure 4-6: TEM micrograph of aligned injection-molded sample (area 3): a) Parallel to the flow
direction, b) Perpendicular to the flow direction. ....................................................................... 122
Figure 4-7: Raman spectra of PC/5 wt% MWCNT nanocomposites. ........................................ 123
Figure 4-8: EMI SE of MWCNT/PC compression-molded samples as a function of MWCNT
concentration and shielding plate thickness. ............................................................................... 127
Figure 4-9: (a) Contribution of absorption, (b) Contribution of reflection to the overall EMI SE
for compression-molded samples as a function of shielding material thickness and MWCNT
concentration. .............................................................................................................................. 128
Figure 5-1: A schematic view of the designed mold. ................................................................. 142
Figure 5-2: TEM micrographs of (a) an injection molded sample (EXP #1), and (b) a
compression molded sample. Both are 5.00 wt% MWCNT/PS composite. The white arrow in (a)
indicates the flow direction. ........................................................................................................ 145
Figure 5-3: (a) Electrical conductivity and (b) EMI SE for the compression molded and injection
molded samples of the MWCNT/PS composites as a function of MWCNT concentration. The
xviii
data related to the electrical conductivity of the injection molded samples were achieved in
parallel to the flow direction. The thickness of all the samples was 2.0 mm. ............................ 148
Figure 5-4: EMI SE, as a function of electromagnetic wave frequency, of (a) the compression
molded samples and (b) injection molded (EXP #1) samples. The thickness of all the samples
was 2.0 mm. ................................................................................................................................ 151
Figure 5-5: Contributions of (a) reflection and (b) absorption to the overall EMI SE for the
compression molded and injection molded samples of the MWCNT/PS composites as a function
of MWCNT concentration. The thickness of all the samples was 2.0 mm. ............................... 154
Figure 5-6: (a) Real permittivity and (b) imaginary permittivity for the compression molded and
injection molded samples of the MWCNT/PS composites as a function of MWCNT
concentration. .............................................................................................................................. 156
Figure 6-1: TEM micrographs of (a) an injection molded sample, and (b) a compression molded
sample. Both are 5.00 wt% MWCNT/PS composite. The white arrow in (a) indicates the flow
direction. ..................................................................................................................................... 172
Figure 6-2: Effects of molding on length distribution of MWCNTs in 2.00 wt% MWCNT/PS
composites................................................................................................................................... 174
Figure 6-3: Volume resistivity for the compression molded and injection molded samples of the
MWCNT/PS composites as a function of MWCNT concentration. ........................................... 176
Figure 6-4: (a) Imaginary permittivity and (b) real permittivity, as a function of MWCNT
concentration, for the compression molded and injection molded samples of the MWCNT/PS
composites in the X-band............................................................................................................ 179
Figure 6-5: Dissipation factors for the compression molded and injection molded samples of the
MWCNT/PS composites as a function of MWCNT concentration in the X-band. .................... 182
Figure 7-1: LM micrograph of MWCNT/PS composites with 1.00 wt% loading...................... 193
Figure 7-2: TEM micrographs of the solution-mixed samples at (a) low magnification, (b) high
magnification (polymer-rich area) and (c) high magnification (agglomerated area). ................ 194
Figure 7-3: The percolation curve (DC conductivity) of the solution-mixed samples of the
MWCNT/PS composites. ............................................................................................................ 196
Figure 7-4: AC conductivity of the solution-mixed MWCNT/PS composites. .......................... 198
Figure 7-5: Real permittivity, as a function of frequency, of the solution-mixed samples at
different MWCNT concentrations. ............................................................................................. 201
Figure 7-6: Imaginary permittivity, as a function of frequency, of the solution-mixed samples at
different MWCNT concentrations. ............................................................................................. 205
xix
Figure 8-1: TEM micrographs of (a) as-received MWCNT (NC7000), (b) synthesized CuNW.
..................................................................................................................................................... 215
Figure 8-2: WAXD diffractogram of the CuNW. ....................................................................... 218
Figure 8-3: SEM images: a) MWCNT/PVDF nanocomposites; b) CuNW/PVDF nanocomposites,
both with 1.5v% of filler. ............................................................................................................ 219
Figure 8-4: TEM images of: a) MWCNT/PVDF nanocomposites; b) CuNW/PVDF
nanocomposites, both with 1.5v% of filler. ................................................................................ 220
Figure 8-5: a) DC conductivity as a function of volume concentration, and linear fitting of the
data to the power law equation for electrical conductivity; b) AC conductivity of the
MWCNT/PVDF nanocomposites as a function of frequency. ................................................... 223
Figure 8-6: a) DC conductivity as a function of volume concentration, and linear fitting of the
data to the power law equation for electrical conductivity; b) AC conductivity of the
CuNW/PVDF nanocomposites as a function of frequency. ....................................................... 224
Figure 8-7: Dielectric permittivity (ɛ´): (a) MWCNT/PVDF nanocomposite; (b) CuNW/PVDF
nanocomposites. .......................................................................................................................... 226
Figure 8-8: Dielectric loss (ɛ) :(a) MWCNT/PVDF; (b) CuNW/PVDF nanocomposites. ....... 227
Figure 8-9: Dissipation factor (tanδ) as function of the frequency: (a) MWCNT/PVDF
nanocomposites; (b) CuNW/PVDF nanocomposites. ................................................................. 230
Figure 8-10: Scheme of core-shell structured CuNW, composed of a non-conductive shell (oxide
layer) and a conductive core (fresh copper), showing the blocking of the charge carriers at
internal interfaces of the individual CuNW…………………………………………………….230
xx
List of Symbols and Abbreviations
Abbreviations
AC Alternating current
ASTM American society for testing and material
CISPR Comité International Spécial des Perturbations Radioélectriques
CNT Carbon nanotube
CPC Conductive filler/polymer composites
CuNW Copper nanowire
CVD Chemical vapor deposition
DC Direct current
DMF N,N-Dimethylformamide
EMI Electromagnetic interference
ESD Electrostatic discharge
hr Hour
LED Light-emitting diode
LFD Low-frequency dispersion
LM Light microscopy
MeOH Methanol
min Minute
MUT Material under test
MWCNT Multi-walled carbon nanotube
MWS Maxwell-Wagner-Sillars
NIR Near-infrared
PAO Porous aluminum oxide
PC Polycarbonate
PCB Printed circuit board
PNA Programmable network analyzer
PPG Polymer Processing Group
PVDF Poly(vinylidene fluoride)
xxi
PS Polystyrene
RC Resistance/capacitance
SiP System-in-package
SE Shielding effectiveness
SEM Scanning electron microscopy
SWCNT Single-walled carbon nanotube
TEM Transmission electron microscopy
VGCNF Vapor grown carbon nanofiber
VNA Vector network analyzer
WAXD Wide angle x-ray diffraction
3-D Three dimensional
Symbols
A
Area of sample
Electric or magnetic field strength unit vector
C0 Capacitance of free space
C1 Mold temperature
C2 Melt temperature
C3 Injection/holding pressure
C4 Injection velocity
d Thickness of sample
dB Decibel (unit of shielding effectiveness)
e Charge of an electron
E Electric field
EI Incident electric field
ET Transmitted electric field
f Electromagnetic wave frequency
H Magnetic field
HI Incident magnetic field
HT Transmitted magnetic field
I Electric current
IR Resistive current
xxii
IC Capacitive current
J Current density
M Ratio of conducting aggregate to average gap width
Ne Number of electrons
P Power density
PI Incident power
PT Transmitted power
Q Stored charge
q Charge of particle
R Resistance
r1 Contact resistance
r2 Resistance of cable
Rx Resistance of sample
S Siemens (unit of electrical conductivity)
SEOA Overall shielding effectiveness
SER Shielding by reflection
SEA Shielding by absorption
SEMR Shielding by multiple-reflection
S11 Ratio of reflected power to incident power in port 1
S12 Ratio of transmitted power from port 1 to port 2 to incident
power in port 1
S21 Ratio of transmitted power from port 2 to port 1 to incident
power in port 1
S22 Ratio of reflected power to incident power in port 2
t Critical exponent of percolation threshold
T Torque
tanδ Dissipation factor
V Voltage
W Watt (Unit of power)
VC Percolation threshold
Z Real impedance
Z" Imaginary impedance
xxiii
Greek Letters
α Attenuation constant
β Phase constant
γ Propagation constant
δ Skin depth
ε' Dielectric (real) permittivity
ε" Dielectric loss (Imaginary permittivity)
ε0 Dielectric permittivity of free space
εr Relative dielectric permittivity
η Intrinsic Impedance of shielding materials
η0 Intrinsic impedance EM wave in free space
μ Magnetic permeability
μ0 Magnetic permeability of free space
μr Relative magnetic permeability
ρ0 Volume resistivity of conductive filler
ρs Surface resistivity
ρv Volume resistivity
σ Electrical conductivity
σ0 Electrical conductivity of copper
σr Relative electrical conductivity
τ Time constant
Ω Ohm (unit of resistance)
ω Angular frequency
1
Chapter 1
Introduction
1.1. General Background
In today’s marketplace, consumers are demanding lighter weight and smaller electronic devices
with improved functionality and design options. Accordingly, conductive filler/polymer composites
(CPCs) have recently drawn great interest to be employed in electronics, due their superior
properties such as tunable electrical conductivity, light weight, low cost, corrosion resistance,
processability, etc. Tunable electrical conductivity of CPCs allows them to be used in a broad range
of applications, such as charge storage, antistatic dissipation, electrostatic discharge (ESD)
protection and electromagnetic interference (EMI) shielding [1-3].
The significance of CPCs can be illustrated by the applications of these materials in a cell phone.
In a typical printed circuit board (PCB) of a cell phone, the discrete passives dominate the active
integrated circuits in terms of number and occupied surface area [4]. Therefore, the passive
components are the major challenge in the development and miniaturization of PCBs. Embedded
passive components have, thus, been introduced as a breakthrough in the size reduction and
performance enhancement of PCBs. CPCs, due to their unique features, have shown as promising
materials for producing embedded passive components, which are meritorious substitutions for the
surface-mounted passive components [5]. In terms of EMI shielding, by using CPCs, manufacturers
are able to produce lighter and smaller cell phone enclosures with improved design options and
2
dramatically reduced electromagnetic emissions having direct impact on peoples’ health.
Employing CPCs as packaging materials of cell phones is useful to dissipate the electrostatic
discharge, which can horribly damage the cell phones during shipping. Annually, the electronics
industry incurs great losses due to lack of proper packaging for electronics, which are sensitive to
electrostatic discharge.
1.2. State-of-the-Art
The main objective of this dissertation is to determine how unique morphologies of
nanocomposites can be created by manipulating mixing methods and processing conditions using
various nanofillers, and how that morphology relates to the final electrical properties, i.e., electrical
conductivity, EMI shielding and dielectric properties. In order to carry out the objectives, multi-
walled carbon nanotube (MWCNT) was selected as the conductive filler, due to its great electrical
properties and growing industrial usage; and polycarbonate (PC), polystyrene (PS) and
poly(vinylidene fluoride) (PVDF) were used as the polymer matrices.
In this dissertation, controlling the conductive network formation is the key aspect in designing
the morphology of CPCs for electrical applications. Improving the conductive network formation
enhances electrical conductivity and EMI shielding; whereas, deteriorating the conductive network
formation reduces the leakage current, thus developing dielectric properties [6-8]. Having a
comprehensive understanding how to manipulate the conductive network formation enables the
manufacturers to employ cost-effective materials and appropriate processing conditions to obtain
3
the desired electrical properties. In this dissertation, two different techniques were employed to
control the conductive network formation including:
Aligning the conductive filler (MWCNT) using an injection molding machine
Changing the type of conductive filler (substituting MWCNTs with copper nanowires
(CuNWs))
Employing the above-mentioned techniques to regulate the conductive network formation is quite
novel and introduced for the first time in the area tailoring the electrical properties. Accordingly,
this thesis is composed of the following sections:
1. Literature review, which mainly details the mechanisms behind the electrical properties of
conductive monolithic materials and CPCs.
2. Materials, processing and characterization section, which provides further information about
the used matrices and conductive fillers, experimental design, composite preparation
methodologies and electrical setups.
3. The main achievements of the thesis given in the format of five scientific papers as follows:
First paper: “Electrical and electromagnetic interference shielding properties of
flow-induced oriented carbon nanotubes in polycarbonate”; investigating the effects of
alignment on electrical conductivity of MWCNT/PC composites and also providing
useful information about the shielding mechanisms of CPCs.
Second paper: “Comparative study of electromagnetic interference shielding properties
of injection molded versus compression molded multi-walled carbon
4
nanotube/polystyrene composites”; exploring the impacts of MWCNT alignment on
EMI shielding properties of MWCNT/PS composites over the X-band frequency range
(8.2 – 12.4 GHz) and inspecting the mechanisms behind.
Third paper: “An innovative method to reduce the energy loss of conductive
filler/polymer composites for charge storage applications”; creatively introducing
MWCNT alignment as a novel technique to improve the dielectric properties of
MWCNT/PS composites.
Fourth paper: “Broadband dielectric properties of multi-walled carbon
nanotube/polystyrene composites”; detailing the broadband dielectric behaviors of
MWCNT/polymer composites, i.e., 10-1
– 10+6
Hz. This paper is a decent introductory
section for comparing the broadband dielectric properties of CPCs holding MWCNTs
and CuNWs.
Fifth paper: “Novel composites of copper nanowire/PVDF with superior dielectric
properties”; innovatively presenting CuNW, as a competent substitution for MWCNT,
with enhanced broadband dielectric properties.
4. Finally, a general discussion, including the obtained achievements and brief summary of
results, is given followed by conclusions, recommendations and proposed future work.
5
1.3. References
[1] Al-Saleh MH, Sundararaj U. Electromagnetic interference (EMI) shielding effectiveness of
PP/PS polymer blends containing high structure carbon black. Macromolecular Materials
and Engineering. 2008;293(7):621-30.
[2] Yang SY, Lozano K, Lomeli A, Foltz HD, Jones R. Electromagnetic interference shielding
effectiveness of carbon nanofiber/LCP composites. Composites Part a-Applied Science and
Manufacturing. 2005;36(5):691-7.
[3] Strumpler R, Glatz-Reichenbach J. Conducting polymer composites. Journal of
Electroceramics. 1999;3(4):329-46.
[4] Kakimoto MA, Takahashi A, Tsurumi TA, Hao J, Li L, Kikuchi R, et al. Polymer-ceramic
nanocomposites based on new concepts for embedded capacitor. Materials Science and
Engineering B-Solid State Materials for Advanced Technology. 2006;132(1-2):74-8.
[5] Lu JX, Moon KS, Xu JW, Wong CP. Synthesis and dielectric properties of novel high-K
polymer composites containing in-situ formed silver nanoparticles for embedded capacitor
applications. Journal of Materials Chemistry. 2006;16(16):1543-8.
[6] Arjmand M, Apperley T, Okoniewski M, Sundararaj U. Comparative study of
electromagnetic interference shielding properties of injection molded versus compression
molded multi-walled carbon nanotube/polystyrene composites. Carbon. 2012;50(14):5126-
34.
[7] Chung DDL. Electromagnetic interference shielding effectiveness of carbon materials.
Carbon. 2001;39(2):279-85.
[8] Al-Saleh MH, Sundararaj U. Electromagnetic interference shielding mechanisms of
CNT/polymer composites. Carbon. 2009;47(7):1738-46.
6
Chapter 2
Literature Review
2.1. Conductive Filler/Polymer Composites (CPCs): Structure, Applications and Market
The rapid growth in portable electronics market has accelerated the demand for electronics with
(1) reduced PCB size, (2) light-weight conductive enclosures to decrease EMI pollution, and (3)
appropriate packaging presenting ESD protection [1-4]. CPCs have drawn great interest to meet
these requirements, due to their tunable electrical conductivity, light weight, low cost, corrosion
resistance and easy processability [5, 6]. CPCs are produced by incorporating conductive filler into
a polymer matrix. Conventional polymers such as PC, PS and PVDF are insulative; however,
adding conductive fillers to these polymer matrices can give them broad range of conductivities
through the formation of two- or three-dimensional conductive network. Figure 2-1 shows a
schematic of conductive network formation in a CPC.
Figure 2-1: Schematic of conductive network formation in a CPC [5].
7
The ability to manipulate the conductive network formation in CPCs entitles them to present
wide spectrum of conductivity, and to perform as insulative, semi-conductive or conductive
materials (Figure 2-2). The level of electrical conductivity determines the applications in which
CPCs can be employed. Charge storage, ESD protection and EMI shielding are the major
applications of CPCs, requiring low, medium and high electrical conductivity, respectively. Table
2-1 lists the required range of electrical conductivity for each application.
Figure 2-2: The approximate range of electrical conductivity covered by CPCs [7].
Table 2-1: CPC applications with their required range of electrical conductivity [8].
Application Electrical Conductivity (Sm-1
)
Charge Storage < 10-11
Antistatic Dissipation 10-7 – 10
-10
ESD Protection 10-3 – 10
-6
EMI Shielding > 10+1
8
Figure 2-3 depicts some applications of CPCs requiring different ranges of electrical
conductivity. CPCs with low electrical conductivity present desirable dielectric properties for
charge storage applications. This is due to their unique structure holding a large number of
nanocapacitor structures, i.e., conductive filler as nanoelectrode and polymer matrix as
nanodielectric [9-14]. CPCs with medium electrical conductivity can be used for antistatic
dissipation and ESD protection. Antistatic dissipation is required where relative motion between
dissimilar materials takes place, such as conveyor belts and airplane tires. ESD protection is used to
bleed off charge on the surface to avert harmful arcing discharges. ESD protection applications
comprise chip or circuit board carriers for shipping of electronic equipments [6].
Figure 2-3: Some important applications of CPCs. From left to right: Capacitors (charge storage);
airplane tire (antistatic dissipation); circuit board carrier (ESD protection); cell phone enclosure
(EMI shielding) [6, 12].
EMI shielding is the most demanding application of CPCs in terms of required electrical
conductivity [15-19]. Electronic devices innately emit electromagnetic (EM) waves. Since these
waves can interfere with the operation of other electronic devices, related agencies have applied
regulations for electromagnetic compatibility (EMC) of electronics housings [20]. EMC means that
a device does not affect itself or other devices by emitted emissions. In order to comply with EMC
regulations, electronics should be enclosed with appropriate conductive shields. Conventional
polymers, due to their insulative nature, are inherently transparent to incident EM waves. However,
9
CPCs due to presence of interacting mobile charge carriers in conductive filler can attenuate the EM
wave efficiently. The CPCs used in EMI shielding applications typically have electrical
conductivity more than 10+1
S·m-1
[21]. Highly electrical conductive CPCs, i.e. CPCs holding large
number of interacting mobile charge carriers, can shield the EMI effectively.
The ever-increasing demands of high-performance electronic devices has led to flourishing
market for CPCs. Figure 2-4 demonstrates the global market for CPCs in 2010-2016 [22]. The
global market for CPCs was $1.7 billion and $1.8 billion in 2010 and 2011, respectively, and is
expected to reach $2.4 billion by 2016 at a compound annual growth rate of 5.9%. The market for
CPCs includes those for EMI shielding, ESD/antistatic packaging, electrostatic painting, printed
circuit board components, etc. EMI shielding comprises stationary and mobile enclosures. ESD
technologies include those used for packaging, furniture, apparel, flooring and electronics; whereas,
PCB components comprise batteries, transistors, capacitors, corrosion-resistant coating products,
etc [23]. This huge competitive market has stimulated companies to perform intense research to
develop novel high-performance CPCs.
Figure 2-4: Global market for CPCs in 2010-2016 [22].
10
2.2. Electrical Conductivity
Electrical conductivity originates from the ordered movement of charges (electric current). In the
absence of electric field, the conduction electrons are scattered freely in a solid due to their thermal
energy. If an electric field, E, is applied, the force on an electron, e, is –eE and the electron is
accelerated in the opposite direction to the electric field due to its negative charge. Then, there is a
net velocity and the current density is given by
J=Ne e E (2-1)
where J the current density, Ne the number of electrons, e charge of electron, the electron
mobility, and E the applied electric field [24]. The applied electric field equals to applied voltage
over the thickness of a sample. Then, the electrical conductivity can be defined as
(2-2)
where is the electrical conductivity and its SI unit is Siemens per meter (S·m-1
). Electrical
conductivity of materials is a property, which spans a very wide range. The conductivity of
insulators is typically less than 10-12
Sm-1
, that of semi-conductive materials covers the range 10-12
to around 10+2
Sm-1
, and for semi-metals and metals is more than 10+2
Sm-1
.
The conductivity of materials can be explained using the Band Theory [25]. In the Band Theory,
the energy level of each electron is considered as a horizontal line. As any solid has a large number
of electrons with different energy levels, the sets of energy levels form two continuous energy
bands, called the valence band and the conduction band. The energy gap between two bands
represents the forbidden zone for electrons. Electrons restricted to individual atoms or interatomic
bonds are, in the Band Theory, said to be in the valence band. Those electrons that have sufficient
11
energy to be delocalized by an applied electric field lie in the conduction band. Figure 2-5 shows a
schematic of the bands in a solid identifying three main types of materials: insulators,
semiconductors and metals.
Figure 2-5: Simplified diagram of the electronic band structure in the Band Theory [24].
The energy gap between valence and conduction bands in metals is negligible and they mostly
overlap each other; therefore, metals show very high conductivity. In intrinsic semiconductors, the
valence-conduction gap is larger than metals, but small enough so that the electrons in valence band
can be excited to conduction band by thermal energy. Among the three types of materials shown in
Figure 2-5, insulators show the largest valence-conduction band gap and; therefore, fewer electrons
can be found in or excited to their conduction band by an applied electric field. This leads to very
low conductivity in insulators.
12
2.3. Electrostatic Discharge (ESD)
All people know static electricity as the static cling of clothing or arcing when touching a
doorknob or metallic object. Static electricity is a surface phenomenon and static charges just exist
on the surface and not in the bulk of materials [26, 27]. Static electricity can be produced in various
ways, but the most common method is triboelectric charging, which is the charge production by
contact and separation of materials [28]. Upon contact of materials, some materials tend to absorb
free charges, while some others are prone to give up free charges. Thus, the material with higher
affinity to absorb electrons will be charged negatively and the other material will acquire positive
charges. The magnitude of charge transfer depends on the difference in the affinity of two materials
to absorb electrons, surface tidiness, the pressure of contact, surface smoothness, speed of
separation, amount of rubbing, etc.
Triboelectric charging occurs only when two insulators or one insulator and one conductor
contact each other and then get separated. In these cases, some charges will be transferred from one
material to another. As the charges in an insulator are not nomadic, the transferred charges will not
return to their original position after separation and two materials will remain charged. If two
conductors contact each other, upon their separation the charges will return to their original
position, since the mobility of charges is high in conductors, and the conductors become neutral.
The science of static electricity has been employed to design many useful devices, such as
electrostatic copier, air purifier and dust precipitators. Nevertheless, uncontrolled ESD has appeared
as a threat to the industry of electronics. ESD costs the electronics industry millions of dollars
annually in damaged and degraded parts at different incremental levels (Figure 2-6). Accordingly,
13
related agencies have adjusted standards, under the overall subject of EMC, to protect the
electronics from ESD. Usually, the same techniques as EMI shielding regulations have been utilized
to satisfy the ESD protection standards [29].
Figure 2-6: Costs due to ESD damage at various incremental levels [30].
A charged insulator by itself is not an ESD threat, since the charges are not nomadic in an
insulator, and is not able to generate ESD. The danger will emerge when this charge is transferred
to a conductor, by contact or induction, which is capable of discharging. Charges stored on an
insulator leave it in two ways, leakage or arcing. Arcing is an electrical breakdown of a
nonconductive media such as air, leading to intense current through the media. Arcing is avoided
due to damage from intense current; therefore, leakage is the preferred way of discharging
materials.
14
As rapid discharge may result in large peak current that can damage electronic components, it is
of great significance to leak off the charges over a period of time. The leak off time for an object is
proportional to its surface resistivity. Hence, it is very important to select a material with an
appropriate surface resistivity to avert large peak current. If a charge exists on a surface, it should
be discharged slowly to limit the current and avoid harm [28].
DOD-HDBK-263 categorizes the material into four classifications in terms of surface resistivity,
which are listed in Table 2-2 [31]. Conductive materials, due to their high electrical conductivity,
are the rapidest to discharge the free charges. Grounded conductive materials may damage
electronics if they come in contact with electronic devices, since they will leak free charges off over
a short time with a large peak current.
Table 2-2: Classifications of materials in terms of surface resistivity [31].
Grounded static dissipative and antistatic materials, with the range of surface resistivity shown
in Table 2-2, are the desirable candidates to dissipate accumulated charges on sensitive electronics.
Static dissipative materials dissipate free charges at a slower rate relative to conductive materials
due to higher surface resistivity. Grounded static dissipative materials can be employed to prevent
charge buildup and dissipate safely the charges already stored. Antistatic materials are the slowest
Material Surface Resistivity (ohmsq-1
)
Conductive < 105
Static Dissipative 105 – 10
9
Antistatic 109 – 10
14
Insulative > 1014
15
to dissipate charge. Nonetheless, they are useful since they are able to dissipate charges faster than
it is generated and thus they can preclude materials from accumulating charges. Insulators, due to
their high surface resistivity, hold whatever charge they have and they should not be employed in
ESD-sensitive environment alone. Figure 2-7 shows a schematic of static-safe workbench, which
should be used for handling electronic setups. The tabletop, floor mat and wrist strap are made or
covered by ESD protective or static dissipative materials which are grounded through 1 M
resistor. This configuration can reduce the damages arising from ESD tremendously.
Figure 2-7: The diagram of a typical static-safe workbench [32].
16
2.4. Electromagnetic Interference (EMI) Shielding
2.4.1. General Background
Many electronic devices inherently irradiate electromagnetic signals. EMI occurs when emitted
signals from a device interfere with its operation or operation of other electronic devices. EMI
effects can range from interruption of operation to degradation of electronics or electrical
equipments [21]. Therefore, developing appropriate EMI shields has emerged as an important
technical challenge considering the upward market of electronic devices, such as laptops, cell
phones, weather radars, TV picture transmitters, etc [1-3, 16, 33]. Figure 2-8 depicts the usage of
shielded enclosures to contain or exclude radiated emissions.
Figure 2-8: Illustration of the use of shielded enclosure (a) to contain radiated emission, (b) to
exclude radiated emission [34].
To reduce EMI issues, appropriate agencies such as CISPR (Comité International Spécial des
Perturbations Radioélectriques) have adjusted regulations for electromagnetic compatibility (EMC)
of electronic enclosures. EMC means that a device does not affect itself or other devices by its
radiations and these regulations must be satisfied or exceeded for commercial electronics.
Considering EMC regulations, an EMI shielding effectiveness (EMI SE) of at least 30 dB, which
corresponds to shielding of 99.9% of incident radiation, i.e., 0.1% is transmitted, is considered
17
commercially as a sufficient level of shielding for many applications [33, 35]. In order to meet these
extremely large values for EMI SE, the electronics must be entirely enclosed by the shield. Any
penetration into the shield, unless appropriately treated, can significantly reduce the EMI SE [8].
Metals are definitely the most commonly employed materials for the EMI shielding of
electronics. Nevertheless, when metal sheets are used as shields, poor quality seams can form slots,
which lead to leakage of radiation reducing the EMI shielding. In addition, there are some other
serious deficiencies in metal-coated polymers, such as recyclability and delamination that
necessitate the development of versatile substitutions for the future [4]. CPCs have, thus, recently
drawn great attention, due to their light weight and processability which aids to reduce or omit the
seams and penetrations in electronics’ enclosures.
2.4.2. Magic of Shielding
To design a shield (CPC or metal-coated polymer) appropriately, an understanding of the
shielding mechanisms is critical, so that both overshielding, which results in higher product cost,
and undershielding, which may cause failure in the final material application, can be avoided [17,
36-39].
Based on the distance between EMI source and the shielding enclosure, the radiation can be
classified as near field or far field [33, 35]. The transition point is the wavelength divided by 2.
The EMI setup employed in this dissertation for EMI shielding measurements operated in the far
field; accordingly, all the equations and shielding mechanisms will be presented for the far field. In
the far field, the EM wave is considered a plane wave. In a plane wave, the electric and magnetic
18
fields are perpendicular to each other and these fields are transverse to the direction of wave
propagation. In the near field, however, the fields are often much more complex.
When an EM wave strikes a shield, the electrons in the shield respond to the electric and
magnetic fields according to Lorentz’s force law [33, 34]:
(2-3)
where q is the charge of each particle of velocity, ; is the magnetic permeability of free space
equal to 4π×10-7
H·m-1
; and, and are the electric and magnetic fields, respectively. The charged
particles actually diminish the incident EM wave in two ways: (1) the charges absorb energy from
the incident wave and move in response to the EM wave; and, (2) these moving charges also
generate an electromagnetic field, called an induced field, which decreases the power of the
transmitted EM wave.
As schematically illustrated in Figure 2-9, three mechanisms are generally involved in EMI
shielding, namely: reflection, absorption and multiple-reflection [16, 33, 40-42]. When an EM wave
strikes a conductive material, a fraction of the wave is reflected from the shield due to interaction
with surface charges and a fraction is transmitted through the shield with its energy dissipated via
absorption. The amplitude of the wave that penetrates through the conductive material is attenuated
by a factor of
, where z is the distance that EM wave penetrates into the shield and δ is the skin
depth of the conductive material. The skin depth is the distance inside the conductive material at
which the wave power decreases to of its incident value and is defined as √ ,
where f is the wave frequency, μ is shield’s magnetic permeability and σ is the shield’s electrical
conductivity [43]. The greater the amount of mobile charge carriers in the shield, the greater is the
19
ability of the shield to attenuate the EM wave through reflection and absorption mechanisms [3,
18]. When the EM wave strikes the backside of the shield (shield-to-air interface), a fraction of the
wave is transmitted through the interface; and, a fraction is reflected off the interface. This reflected
wave from the second interface is also a part of the reflection mechanism. The final mechanism of
shielding is multiple-reflection, which usually occurs in materials with large interfacial areas, such
as filler-added polymers. Multiple-reflection is actually re-reflection of waves already reflected
inside the shield. Multiple-reflection has a negative effect on the overall EMI shielding and it can be
ignored if the shield’s thickness is larger than the shield’s skin depth [16].
Figure 2-9: Illustration of interaction between incident plane wave and conductive barrier [34].
20
2.4.3. Shielding Effectiveness
An EM wave is composed of two fields: electric field and magnetic field. The ratio of electric
field to magnetic field of a propagating wave in any media is called intrinsic impedance [33]. This
ratio is extremely important in the degree of shielding and prevailing shielding mechanisms in
conductive shields. The unit of intrinsic impedance is E/H = (V/m)/(A/m) = ; where E is electric
field and H is magnetic field. The intrinsic impedance of a material can be defined as following:
√
(2-4)
where is intrinsic impedance, is electrical conductivity, is angular frequency and and are
permeability and permittivity, respectively. The permittivity and permeability of free space are
equal to 8.85×10-12
F·m-1
and 4×10-7
H·m-1
, respectively. Considering low conductivity of free
space, the intrinsic impedance of free space is equal to 377 . As an incident EM wave penetrates
into a conductive shield, the intrinsic impedance decreases tremendously and, therefore, electric
field transforms partially to magnetic field. The degree of transformation depends on the degree of
impedance mismatch between two media.
The EM wave expressions can be written with the same analogy of the power expressions with
the circuit variables [33, 34]. For an electrical circuit, the instantaneous power dissipated by resistor
is given by
( ) ( ) ( ) (2-5)
where v(t) and i(t) are instantaneous voltage and current, respectively. Analogously, the
instantaneous power density P(t) for a plane wave, with the electric and magnetic field
perpendicular to each other, is given by
21
( ) ( ) ( ) (2-6)
Due to time-changing nature of EM wave, the average power Pave is typically used:
( )
( )
(2-7)
where Ex and Hy are the root means square of electric and magnetic fields in x and y directions,
respectively, and is the intrinsic impedance of conductive material. Equation 2-7 shows that
power is proportional to square of amplitude of electric field or magnetic field.
The ability of conductive materials to attenuate EM wave is stated as EMI shielding
effectiveness (EMI SE). EMI SE is expressed in dB and defined as logarithm of incident electric
(magnetic) field to transmitted electric (magnetic) field
( ⁄ ) (2-8)
or considering that the power is proportional to square of amplitude of electric field or magnetic
field leads to
( ⁄ ) ( ⁄ ) (2-9)
where PI is the incident power, PT is the transmitted power and EI and ET are the root mean square
of incident and transmitted electric fields, respectively, and HI and HT are the root mean square of
incident and transmitted magnetic fields, respectively. It should be mentioned that second and third
parts in Equation 2-9 are equivalent when the media on both sides of the shield are the same.
Equation 2-8 says that the lower the transmitted EM power to free space, the higher the EMI SE of
the shielding material. Equations 2-8 and 2-9 can also be used to calculate the contributions of
reflection and absorption to overall EMI SE considering relevant incident and transmitted fields.
22
2.4.4. Reflection, Absorption and Multiple-reflection for Conductive Monolithic Materials
The shielding mechanisms presented in the following sections are developed for conductive
monolithic materials, such as bulk of metals. The presented equations need to be modified for
heterogeneous structures, such as CPCs.
2.4.4.1. Shielding by Reflection
As shown in Figure 2-9, an incident EM wave interacts with the conductive shield through
reflection, absorption and multiple-reflection mechanisms. For an incident EM wave, the reflection
and transmission coefficients from the first and second interfaces, in the absence of absorption, can
be defined as follows:
(2-10)
(2-11)
where η0 is the impedance of free space and η1 is the intrinsic impedance of shielding material.
Considering impedance as the ratio of electric field to magnetic field gives
(2-12)
(2-13)
In view of the above equations and lower intrinsic impedance of conductive shield relative to
free space, it can be claimed that the primary transmission of magnetic field takes place at the first
interface; whereas, the primary transmission of electric field occurs at the second interface. As a
23
matter of fact, at the first interface the transmitted magnetic field may have greater strength than
incident magnetic field due to electric field-magnetic field transformation. The same scenario is true
for the electric field at the second interface. However, it is notable that the transmitted power is
always smaller than incident power.
Therefore, effective shields for the attenuation of electric field can be constructed from thin
shield with very high conductivity to short out the electric field at the first interface; whereas, the
shields for the attenuation of magnetic field can be constructed from thick shields with high
electrical conductivity and magnetic permeability [33].
In the absence of absorption and using Equations 2-9 to 2-11, shielding by reflection can be
defined as:
(
) (
)
( ) (2-14)
In a conductive material, the conduction current is much greater than the displacement current, i.e.,
. Thus, substituting the approximate formula for intrinsic impedance of a conductive shield
into Equation 2-14 gives
(2-15)
where is magnetic permeability of conductive shield relative to that of free space and is the
conductivity of shield relative to the conductivity of copper. For the permittivity and permeability
of metals, it is customary to refer to that of free space, while for the conductivity of metals, it is
usually referred to that of copper:
= Permeability = r0 = r (4 10-7
H·m-1
)
24
= Permittivity = r0 = r (8.85 10-12
F·m-1
)
= Conductivity = r0 = r (5.8 10+7
Sm-1
)
Equation 2-15 gives a good idea to select appropriate materials to present a high reflection loss.
According to Equation 2-15, the reflection loss is proportional to
, i.e., the materials with higher
conductivity present higher reflection loss, while the magnetic materials degrade the reflection loss.
2.4.4.2. Shielding by Absorption
Absorption attenuates EM wave through interaction with mobile charge carriers and
electric/magnetic dipoles [16]. The amplitude of EM wave that penetrates through a conductive
material is attenuated by factor , where = √ ( ) and z is the distance
inside the shield. γ, α and β are called propagation constant, attenuation constant and phase constant,
respectively. For the conductive materials, the amplitude of the wave is attenuated by factor
and =1/, where is the skin depth of conductive shield. Therefore, for the conductive shield
shown in Figure 2-9 with a thickness of t, shielding by absorption can be defined as following:
(
)
√
(2
(2-16)
Equation 2-16 elucidates that a material with high conductivity and magnetic permeability can
absorb the EM wave efficiently. In addition, there is a linear relationship between shielding by
absorption and thickness of shielding material. As a matter of fact, the higher the thickness of a
conductive material, the greater is the amount of interacting mobile charge carriers and/or
electric/magnetic dipoles.
25
2.4.4.3. Shielding by Multiple-Reflection
Multiple-reflection represents internal reflections inside a conductive barrier. As the resultant of
multiple-reflection is an increment in transmitted wave, it has a negative influence on overall EMI
shielding. Figure 2-10 illustrates the effect of multiple-reflection inside a conductive shield with the
calculations in terms of intrinsic impedance and reflection and transmission coefficients.
Considering multiple-reflection effect, the overall transmitted electric field can be defined as
( ) and ( )
( ) (2-17)
If | | as is the case for conductive shield, the shielding by multiple-reflection can be defined as
| | | (
)
| (2-18)
As in conductive monolithic materials, the propagation constant is almost equal to attenuation
constant or inverse of skin depth; therefore, multiple-reflection is negligible when the thickness of a
material is much greater than its skin depth ( √ ).
Given the equations for shieldings by reflection, absorption and multiple-reflection, the overall
EMI SE, SEOA, can be defined as
]+ [ √ ] | (
)
| (2-19)
26
Figure 2-10: Schematic of the effects of multiple-reflection in a conductive shield: (a) combining
multiple transmissions, (b) calculations in terms of intrinsic impedance and reflection and
transmission coefficients [34].
Table 2-3 presents a list of common materials employed in shielding barriers with their electrical
conductivity and magnetic permeability. This table can give a good idea for choosing proper
materials to shield an EM wave with specific features. As mentioned before, the reflection loss is a
function of
, whereas the absorption loss is a function of rr; and reflection is more important
for the electric field while absorption is of more consequence for the magnetic field. Thus, having
27
the knowledge of the nature of field and limitations for conductive shield in terms of weight and
cost, an efficient and cost-effective shielding material can be selected to shield an EM wave.
Table 2-3: Electrical conductivity and magnetic permeability of common materials used in shielding
barriers [33, 34].
Material r r A rr R r /r
Silver 1.05 1 1.05 1.05
Copper 1 1 1 1
Gold 0.7 1 0.7 0.7
Aluminum 0.61 1 0.61 0.61
Nickel 0.2 600 120 3.3×10-4
Stainless Steel 0.02 500 10 4×10-5
2.4.5. Effect of Real Permittivity on Shielding of Conductive Monolithic Materials
Effect of real permittivity on EMI shielding in conductive monolithic materials is negligible
since the ratio of conduction current to displacement current is small. If a known alternating voltage
is applied to a conductive monolithic material, the resultant current is almost in phase with the
applied voltage. The real permittivity of conductive monolithic materials is small and is presumed
to be equal to that of free space. Therefore, shielding arising from polarization loss in conductive
monolithic materials is negligible and permittivity does not play any role in the equations developed
in the preceding sections. However, CPCs due to their unique structure holding a large number of
nanocapacitors present a high real permittivity. Hence, there is a phase difference between the
applied alternating voltage and measured current in CPCs. Due to high real permittivity of CPCs,
there is a considerable shielding originating from polarization loss. Accordingly, the formulas
28
developed for conductive monolithic materials must be modified for CPCs in order to consider the
effect of polarization loss and real permittivity.
2.5. Dielectric Theory
2.5.1. Dielectric Material
A material is classified as “dielectric” if it has the ability to store energy when an external
electric field is applied. The degree to which a dielectric responds to an applied electric field can be
acknowledged by parallel-plate capacitor configuration. If a DC voltage of V is applied to such a
capacitor, where the plates are separated by the distance d, the electric field between the plates is
uniform and equal to E=V/d. This electric field leads to charge polarization within the dielectric
material, i.e., separation of positive and negative charges. In other words, dielectric material
increases the storage capacity of capacitor by neutralizing charges at the electrodes (Figure 2-11).
Figure 2-11: Charges on a parallel-plate capacitor with (a) air between the plates, and (b) a
dielectric between the plates [25]. (Reprinted with the Permission of Cambridge University Press)
29
When the dielectric material is free space, the charges per area stored on the surface of plates is
equal to , where 0 is real permittivity of free space. However, if free space is replaced with
a dielectric material, an extra charge (denoted as P) is stored on the surface of capacitor originating
from higher polarisability of dielectric material relative to free space. This extra charge is defined as
following:
( ) (2-20)
where r is real permittivity of dielectric material relative to free space. The higher the real
permittivity of a dielectric material and the greater the applied electric field, the higher is the stored
energy on surface of a capacitor.
2.5.2. Permittivity
Permittivity has two components; namely real permittivity (ε´) and imaginary permittivity (ε˝).
Real permittivity shows how much energy from an external field is stored in a material, however,
imaginary permittivity shows how dissipative a material is to an external electric field. Therefore,
permittivity can be defined as a complex quantity as below
(2-21)
where ɛ´ and ɛ˝ are real permittivity and imaginary permittivity, respectively. It is worth noting
that in literature real permittivity is also called dielectric permittivity or dielectric constant; whereas,
imaginary permittivity has other names such as dielectric loss or loss factor.
As no perfect dielectric material exists, all dielectric materials can be modeled in terms of an
equivalent circuit of a resistor in parallel with an ideal capacitor [25, 44-46]. When an AC voltage
30
source “V” is applied to a dielectric material, two different electrical currents are induced within the
dielectric, i.e., conduction current and displacement current (Figure 2-12). The former arises from
free electrons and will give rise to electric loss (imaginary permittivity) while the latter is due to
charge polarization (real permittivity).
The current I that flows through such a circuit after applying an alternating voltage
can be calculated as follows
( )
(
) (2-22)
where Q, t, ω and C0 are stored charge, time, angular frequency and the capacitance of free space,
respectively. Equation 2-22 shows that the induced current has two components; i.e. IC (capacitive
component) which leads the voltage by 90° and IR (resistive component) which is in phase with
voltage. The resistive current passes through the capacitor (leakage current), whereas the capacitive
current does not pass through the capacitor; but flows in the circuit to compensate for the charges
stored on the surface of capacitor.
(2
(2-23)
(2-24)
The real and imaginary permittivities or capacitive and resistive currents are linked together with
the term dissipation factor, which is of great importance in industry.
(2-25)
Notice that when , the material is considered as a good conductor, and when ,
the material is regarded as a good insulator.
31
Figure 2-12: (a) Circuit diagram of a dielectric under an AC field, (b) Argand diagram of complex
current-voltage relationship [25]. (Reprinted with the Permission of Cambridge University Press)
2.5.3. Dielectric Mechanisms
A dielectric material has an arrangement of electric charge carriers that can be reorganized by
applying an electric field, i.e., the charges get polarized to compensate for the applied electric field.
As illustrated in Figure 2-13, there are several dielectric mechanisms that contribute to overall real
permittivity, namely: interfacial, dipolar, atomic and electronic. All or some of these polarization
mechanisms may occur in a material depending on morphology and frequency range [46-48].
Interfacial polarization is broadly observed in heterogeneous systems with phases with different
conductivities or real permittivities, such as suspension of colloids, blends and CPCs [45, 49, 50].
This polarization is referred to as Maxwell-Wagner-Sillars (MWS) after the study of Maxwell who
first recognized the mechanism for DC field [51] and Wagner and Sillars who extended the theory
for AC field [52-54]. Interfacial polarization occurs due to the accumulation of mobile charges, on a
mesoscopic scale, at the interface of dissimilar phases with different electrical conductivities or
32
permittivities. As interfacial polarization takes place at large scale (mesoscopic scale), it has usually
been observed at low frequencies, due to its large relaxation time with respect to electric field
frequency at high frequencies [9, 11].
Figure 2-13: Frequency response of dielectric mechanisms [49, 54].
Dipolar (Orientational) polarization happens in polar materials, which contain permanent dipoles
in their structure, such as molecule of water [46, 49, 55]. The dipole moments are oriented in a
random manner in the absence of electric field. By applying an electric field, electric dipoles
experience a torque T and rotate in response to applied field. The friction due to orientation of
dipoles in an AC field is used in many applications, such as warming foods up in microwave ovens.
The frequency range over which dipolar polarization occurs depends on the size of molecule, from
105 Hz for large molecules such as a protein in solution to around 10
9 Hz for smaller molecules
33
such as amino acids [49]. Above these frequencies, the dipolar polarization diminishes due to
relaxation phenomenon.
Atomic polarization process originates from displacement of charged ions with respect to each
other in a crystal lattice. An applied field leads to separation of positive and negative ions, inducing
a dipole moment. This type of polarization is the predominant form of polarization in inorganic
crystals, glasses and ceramics, while in organic compounds, where ions are absent; this type of
polarization does not contribute to total polarization. The high real permittivity in conventional
ferroelectric ceramics originates from atomic polarization, where polarization happens collectively
in domains [46]. Atomic polarization extends from DC up through infrared frequencies.
Electronic polarization takes place inside atoms when an electric field displaces the nucleus with
respect to the electrons that surround it. For many dry solids, this is the dominant polarization
mechanism. Electronic polarization continues over the whole frequency range from DC up through
optical frequency. The reason that electronic polarization has the largest frequency coverage among
all polarization mechanisms is its smallest scale of charge polarization, i.e., intra-atomic scale.
The electric dipole has a magnitude equals to strength of each charge times the separation
between charges. Considering the scale at which charges are polarized at different polarization
mechanisms, the degree of contribution of polarization mechanisms to real permittivity has the
following order: interfacial, dipolar, atomic and electronic. Therefore, at low frequencies, all the
mechanisms may contribute to real permittivity; however, the role of the ones with larger
polarization scale is more significant than the others. With frequency increase, the sluggish
34
mechanisms drop out in turn, leaving the faster ones to contribute to real permittivity. This leads to
a descending trend for real permittivity as a function of frequency.
The imaginary permittivity (dielectric loss) is the part of energy of an AC field in a dielectric
material which is dissipated into heat. The dielectric loss is composed of two components; namely
Ohmic loss and polarization loss. Ohmic loss arises from DC conduction and represents the
dissipation of electrical energy by mobile charge carriers moving through the dielectric material. In
fact, the nomadic charges dissipate the electrical energy via collision with other particles. The
dissipation by Ohmic loss weakens with frequency due to the reduced available times for free
electrons to sweep the network in each half cycle of alternating field. It is notable to declare that DC
conduction is independent of frequency.
The polarization loss in a dielectric material includes: interfacial, dipolar, atomic and electronic.
As the magnitude and direction of electric field vary in an AC field, the polarized charges also
change in magnitude and direction. It was explained that the polarized charges contribute to real
permittivity by generating a momentum arising from separation of positive and negative charges.
Simultaneously, the friction accompanying the orientation of electric dipoles in each half cycle of
an AC field raises the dielectric loss. Therefore, it can be said that the polarization loss, as a portion
of imaginary permittivity, has a direct relationship with real permittivity. In other words, the higher
the real permittivity of a dielectric, the greater is the momentum generated by the charge
polarization, and thus the higher is the dissipation of energy to come over the momentum to reorient
the dipoles in each half cycle of alternating field. Thus, the order of magnitude of polarization loss
mechanisms is: interfacial, dipolar, atomic and electronic.
35
If a dipole is oriented due to an applied electric field, the orientation of dipole requires a certain
amount of time (relaxation time). Relaxation time is a measure of mobility of dipoles within a
dielectric [47]. At frequencies below relaxation time, the electric field is slow enough that the
dipoles keep pace with alternating field. Thus, the imaginary permittivity demonstrates a direct
relationship with frequency at frequencies below relaxation. In fact, at frequencies below relaxation
time, increasing frequency facilitates more frequent occurrence of fully reorientation of dipoles in a
time frame. Thus, imaginary permittivity ascends with frequency till reaching to a maximum where
dielectric relaxation or resonant occurs (Figure 2-13). The relaxation or resonant frequency is the
maximum frequency in which the dipoles can adapt themselves to an alternating electric field.
Above the relaxation or resonant frequency, both real and imaginary permittivities diminish since
the electric field is too fast to affect the dipole rotation, and charge polarization disappears.
A resonant effect is usually engaged with electronic and atomic polarizations and relaxation
effect is linked to interfacial and atomic polarizations [47]. The resonant frequency and relaxation
frequency are defined by a peak of maximum absorption in and a response in (Figure 2-13).
Above the resonance and relaxation, the contributions of charge polarization mechanisms to real
and imaginary permittivities vanish [47].
2.5.4. The Electrical Current of Dielectrics under a Step DC Voltage
It is easier to understand the frequency dependence of AC conductivity by exploring the current
response of a dielectric under a step DC voltage. The spectra of currents, depicted in Figure 2-14,
36
are generated to compensate for the charges stored on the surface of dielectric due to step DC
voltage. The stored charges arise from polarization mechanisms within the dielectric material.
Figure 2-14: Typical DC response of a dielectric to a step voltage application [46].
By applying a DC voltage, a pulse of initial current with very short duration is generated. This
current is associated with electronic (IElectronic) or atomic (IAtomic) polarization, which develops in
times of the order of a half cycle of optical or infrared frequencies, respectively. Although the
amount of stored charges due to atomic and electronic polarization is very small, but due to their
very short time of occurrence, the generated current is quite large. Next, if dielectric is inherently
polar, another high level of current (IDipolar) is generated, which is related to dipolar polarization.
IDipolar is smaller than IElectronic or Iatomic due to longer time frame of occurrence. Then, there is a
current related to interfacial polarization (IInterfacial), which diminishes more slowly than IDipolar, due
to its larger time constant. Finally, the insulation current levels off to long time DC conductivity.
The electrical currents from electronic, atomic, dipolar and interfacial polarizations are capacitive or
37
out-of-phase, which do not pass through the insulator but are generated to compensate for the
charges stored on the surface of capacitor. The DC current is in-phase or resistive and is real flow of
charges through the dielectric under an applied electric field.
2.5.5. DC and AC Conductivity
The electrical conductivity of a material is proportional to induced electrical current over the
applied voltage (
), where electrical conductivity, I electrical current and V applied voltage.
The electrical current is defined as the amount of charges passes a cross section in a time frame.
This definition is the basis to illuminate the difference between DC and AC conductivities.
The frequency responses of electrical current in DC and AC fields are different. In an AC field,
at low frequencies, the electrical current is just due to DC conductivity. With increase in frequency,
the role of capacitive current highlights, since high-frequency voltage facilitates frequent
development of capacitive currents in a time frame. For instance, for an AC voltage with optical
frequency, the role of Ielectronic is significant since it can be generated at each half cycle of optical
frequency. Although the amount of capacitive charges are smaller than resistive charges; however,
due to very short occurrence time of polarization mechanisms, the magnitude of capacitive current
is much higher than DC current. Hence, AC conductivity, which is proportional to sum of resistive
and capacitive currents, shows a strong ascending trend with frequency. Of interest to note, DC
conductivity, which originates from resistive current, is usually independent of frequency and is
industrially measured under a low-frequency AC voltage, where the influence of capacitive currents
is negligible [56].
38
AC conductivity can be obtained using the real permittivity and imaginary permittivity
(capacitive currents and resistive current, respectively) data. Real permittivity corresponds to
currents arising from charge polarization and is out-of-phase with voltage; whereas imaginary
permittivity corresponds to leakage current through a capacitor, which is in-phase with voltage.
Thus, combining Equations 2-2 and 2-22 gives
( ) ( )
(2
(2-26)
where AC is AC conductivity, 0 is permittivity of free space, is angular frequency and ´and
ʺare real and imaginary permittivities, respectively. This equation shows that the real part of AC
conductivity is proportional to imaginary permittivity and occurs due to flow of charges through the
dielectric material (leakage current) or dissipation of energy by polarization loss. It is worth noting
that the leakage current for an ideal capacitor is zero. The imaginary part of AC conductivity occurs
to compensate for the charges which are polarized inside the dielectric material. In fact, the current
due to imaginary conductivity does not pass through the dielectric but moves in the circuit to
compensate for the charges which are stored on the surface of capacitor.
2.6. Electrical Properties of Conductive Filler/Polymer Composites (CPCs)
2.6.1. Electrical Conductivity of CPCs
High electrical conductivity, i.e., conductive network formation, at very low filler content has
made CPCs distinctive materials for industrial applications [6, 40, 57-64]. Conductive network
formation in CPCs is better comprehended with the concept of percolation threshold [15, 65, 66].
Percolation means that at least one conductive pathway forms to allow electrical current to pass
39
across the composite, and to transform the composite from insulative to conductive. Percolation
occurs at a narrow filler concentration range, where the volume resistivity of composite abruptly
decreases by several orders of magnitude. Electrical percolation at very low filler concentrations in
CPCs leads to the production of cost-effective composites.
Many statistical, geometric, thermodynamic and structure-based models have been introduced to
anticipate the percolation threshold and electrical conductivity of CPCs [65, 67]. Even though the
percolation theory is just valid at conductive filler concentration above the percolation threshold;
however, it is the most acceptable one. Statistical percolation theory [65] estimates the percolation
threshold of CPCs as:
( )
(2
(2-27)
where ρ is the volume resistivity of CPC, ρ0 is the volume resistivity of conductive filler, V is
volume content of conductive filler, and Vc and t are percolation threshold and critical exponent,
respectively. The equation is valid for the concentrations above the percolation threshold, i.e., V >
Vc. Higher t value and lower percolation threshold correspond to well-dispersed high aspect ratio
fillers [68, 69].
As the focus of this dissertation is on MWCNT as conductive filler, the general electrical
behaviors, i.e., electrical conductivity, EMI shielding and dielectric properties, of CPCs are
investigated by presenting the electrical properties of compression molded MWCNT/PS composite,
as a typical CPC. The MWCNT/PS composites with different loading levels were prepared by
diluting the masterbatch of 20.0 wt% MWCNT in PS (MB2020-00) using a Coperion ZSK co-
40
rotating intermeshing twin-screw extruder operated at barrel temperature of 200 °C and extruder
speed of 150 rpm. Further information on material preparation can be found in our studies [41, 70].
Figure 2-15 presents a typical percolation curve of CPCs (percolation curve of MWCNT/PS
composite). In general, percolation curve of CPCs can be divided into three zones: 1) the zone far
below the percolation threshold (insulative zone), (2) the zone where percolation occurs
(percolation zone) and (3) the zone far above the percolation threshold (conductive zone).
In the insulative zone, the conductive filler loading is very low with the fillers far from each
other; thus, polymer matrix controls the charge transfer. In this zone, CPCs demonstrate resistivity
above around 10+11
Ω·m, which is close to the resistivity of pristine polymer. Conductive fillers and
insulating gaps, i.e. polymer matrix, between them can be modeled as a capacitor [63,71, 72]. At
low filler concentration, the insulating gaps are very large and the chance that nomadic charges are
transferred between conductive fillers is very low. Therefore, conductivity is the result of transport
processes within the host matrix; and as the bound charges of polymer matrix belong to valence
band, the whole composite shows insulative behavior.
41
Figure 2-15: Percolation curve of compression molded MWCNT/PS composite (A typical
percolation curve of CPCs) [41].
By increasing filler concentration, the gaps between conductive fillers decrease. When the mean
particle–particle distance reaches to below 1.8 nm, the dominant electron transfer mechanisms
become tunneling and hopping mechanisms [50, 73-75]. In narrow insulating gaps between
conductive fillers, very high field strength may develop which is higher than the macroscopic
voltage by a factor M, which is the ratio of average size of conducting aggregate to the average gap
width [75, 76]. This high field strength provides free electrons in conductive filler with sufficient
energy to tunnel through or hop over the insulative gaps (Figure 2-16). Quantum tunneling refers to
the quantum mechanical phenomenon where a particle tunnels through a barrier, that
it classically unbeatable, and emerges with the same energy in a new lattice site. For quantum
tunneling, the site separation must be small enough for the tail of electron wavefunction to extend
through the barrier. However, hopping occurs when an electron receives sufficient energy to pass an
energy barrier to change its lattice site [73-77].
42
Figure 2-16: Diagram of electron-transfer mechanisms between adjacent sites separated by a
potential energy barrier [77]. (Reprinted with the Permission of Cambridge University Press)
By further adding filler loading, the fillers get closer and ultimately at a narrow concentration
range called the percolation zone, the first conductive path forms letting the current pass through the
composite. In the percolation zone, due to direct contact between conductive fillers, the nomadic
charges in conductive filler play the dominant role in conduction mechanism. Since these free
charges belong to the conduction band, the resistivity of nanocomposite reduces by several orders
of magnitude in the percolation zone.
Next, by adding more filler content, a well-developed 3-D conductive network starts to form;
however, the volume resistivity reduces only marginally. This is due to considerable current
dissipation at the contact spots between conductive fillers, i.e., the constriction resistance, which
leads to a plateau in the percolation curve [78].
43
The electrical conductivity and percolation threshold of MWCNT/polymer composites depend
on many factors, such as intrinsic conductivity, size and aspect ratio of MWCNT, intrinsic
properties of polymer matrix (molecular structure, viscosity and crystallinity), the quality of
interaction between MWCNT and polymer matrix, mixing technique, etc [5]. Accordingly, it is
expected to observe a variety of percolation threshold and electrical conductivity for various types
of MWCNT/polymer composites. In literature, there are some good review papers discussing the
impacts of conductive filler and polymer matrix features and their interaction on electrical
conductivity and percolation threshold [68, 69, 79].
2.6.2. EMI Shielding of CPCs
CPCs present a sophisticated EMI shielding behavior due to their heterogeneous structure
holding phases with different electrical conductivities. Shielding by CPCs depends on many factors,
such as conductivity of filler and polymer matrix, dispersion of conductive filler, interaction
between conductive filler and polymer matrix, range of shielding frequency, content of filler,
thickness of shielding material, etc [20, 41, 80-85]. Achieving the knowledge of the effects of these
parameters on EMI shielding requires comprehensive theoretical and experimental study of
shielding behaviors of different types of CPCs.
Figure 2-17 demonstrates the EMI shielding behavior of MWCNT/PS composites as functions
of MWCNT concentration and composite thickness over the X-band frequency range (8.2 – 12.4
GHz). As shown in Figure 2-17, EMI SE increases with both MWCNT concentration and composite
thickness. It can be observed that for the composites with 3.0 mm thickness, the EMI SE increases
44
from 1.1 dB to 63 dB by incorporating 20.0 wt% MWCNT to the pristine PS. For the composites
with 20.0 wt% MWCNT, the EMI SE rises from 29 dB for 0.4 mm thickness to 63 dB for 3.0 mm
thickness. Polymer matrix, due to lack of nomadic charges, is transparent to EM wave, however
conductive fillers are able to attenuate EM wave. Higher EMI SE at greater MWCNT concentration
and composite thickness is due to greater amount of interacting conductive filler and
electric/magnetic dipoles.
Figure 2-17: EMI SE of the compression molded MWCNT/PS composite as functions of MWCNT
concentration and shielding plate thickness.
The direct relationship of EMI shielding and MWCNT concentration is related to two
mechanisms: Ohmic loss and polarization loss. As shown in Figure 2-18, individual conductive
fillers can be considered as a resistor holding nomadic charges; and the combination of two
individual conductive fillers and polymer matrix between them can be regarded as a nanocapacitor.
Hence, it can be claimed that a CPC is comprised of a great deal of resistor and capacitor structures,
which are in series or parallel to each other. Increase in MWCNT concentration and composite
45
thickness leads to a greater number of both resistor and capacitor structures resulting in higher
Ohmic loss and polarization loss, respectively. As a matter of fact, with increasing the content of
conductive filler, the amount interacting nomadic charges and electric/magnetic dipoles increase.
This attenuates EM wave much more efficiently.
Figure 2-18: Schematic of resistor and capacitor structures in a CPC.
Overall EMI shielding in CPCs is composed of three components: reflection, absorption and
multiple-reflection. As multiple-reflection cannot be measured independently, its influence is
inherent in shieldings by reflection and absorption. It was stated that in conductive monolithic
materials both reflection and absorption have a direct relationship with electrical conductivity, i.e.,
quantity of nomadic charges. Therefore, it is expected to observe an ascending trend for shieldings
by reflection and absorption as a function of filler content in CPCs. As depicted in Figure 2-19, both
reflection and absorption increase with MWCNT concentration. Shielding by reflection is attributed
to surface nomadic charges. Higher MWCNT concentration is associated with greater number of
surface nomadic charges, leading to larger impedance mismatch between two media. This means
46
that at a larger MWCNT concentration, there are a greater number of interacting surface nomadic
charges to reflect the incident wave.
Absorption mechanism in CPCs, due to their heterogeneous structure, is much more
sophisticated than that in conductive monolithic materials. Absorption in CPCs arises from Ohmic
loss and polarization loss. Therefore, understanding the influence of filler content on Ohmic loss
and polarization loss can direct us to obtain a better comprehension from absorption mechanism in
CPCs.
Imaginary permittivity represents the energy dissipated within CPCs by Ohmic loss and
polarization loss, and polarization loss (as a part of imaginary permittivity) is linked to real
permittivity. Figure 2-20 shows that both real permittivity and imaginary permittivity increase with
MWCNT concentration, confirming the positive influence of filler content on polarization loss and
Ohmic loss. Real permittivity in CPCs is due to the formation of a large number of nanocapacitors,
i.e., conductive fillers acting as electrodes and insulative polymeric layer acting as dielectric
material [9, 12, 86-89]. Increasing MWCNT concentration results in an increase in the number of
nanocapacitors leading to higher real permittivity (charge polarization). In addition, increasing
MWCNT concentration accompanies with a reduction in the thickness of insulative polymeric gaps
between MWCNTs causing higher applied field and greater electronic polarization of polymeric
layer. Hence, there is a direct relationship between MWCNT concentration and polarization loss,
which gives rise to shielding by absorption. In fact, the higher the real permittivity of a CPC, the
greater is the momentum generated by charge polarization, and thus the higher is the dissipation of
energy to come over the momentum to reorient the dipoles in each half cycle of alternating field.
47
Of interest to note, real permittivity in conductive monolithic materials is equivalent to that of
free space since the conduction current is much greater than the displacement current [33, 34].
Accordingly, contrary to CPCs, polarization loss does not play an important role in EMI shielding
of conductive monolithic materials.
Figure 2-19: Contributions of (a) reflection and (b) absorption to the overall EMI SE for the
compression molded MWCNT/PS composites as a function of MWCNT concentration. The
thickness of all the samples is 2.0 mm [41].
48
Imaginary permittivity of MWCNT/PS composites also contributes significantly to shielding by
absorption, where energy is dissipated by Ohmic loss and polarization loss. For Ohmic loss,
increasing MWCNT concentration leads to an increase in the number of dissipating mobile charge
carriers resulting in higher imaginary permittivity and, consequently, higher shielding by
absorption. In addition, increasing conductive filler content leads to the formation of conductive
networks in the composite. At greater network formation, the electrons have greater mean free paths
in which to move according to the direction of electric field in each half cycle and, consequently,
can dissipate more electrical energy [41, 90, 91].
Figure 2-20: Real permittivity and imaginary permittivity of MWCNT/PS composites over the
X-band frequency range [41].
Multiple-reflection occurs in shields where there are numerous interfacial areas like CPCs or
foamed samples [33, 80]. Multiple-reflection decreases the EMI shielding by blocking and
reflecting back the reflected waves from shielding material interior surface area. It was shown in
Equation 2-18 that for conductive monolithic materials, multiple-reflection can be ignored if
49
material’s thickness is greater than material’s skin depth. Skin depth is the distance inside a
conductive shied at which the wave power diminishes to of its incident value and has an
inverse relationship with conductivity, magnetic permeability and wave frequency. However, skin
depth in CPCs needs to be defined with a more complicated equation. For instance, two CPCs with
the same conductive filler content, or even the same electrical conductivity, may present very
different electrical properties or skin depth due to their dissimilar morphologies [41, 92].
Accordingly, it can be claimed that skin depth and multiple-reflection in CPCs are functions of
many parameters, such as conductivity and magnetic permeability of filler and polymer matrix,
dispersion of conductive filler within polymer matrix, aspect ratio of conductive filler, interaction of
conductive filler and polymer matrix, molecular structure of polymer matrix, alignment of
conductive filler, etc.
2.6.3. The Mechanisms behind the Broadband Dielectric Spectroscopy of CPCs
The dielectric spectroscopy in the heterogeneous structure of MWCNT/polymer (nonpolar)
composites can be explored by its equivalent-circuit model, as shown in Figure 2-21 [13, 93-96].
The parallel capacitor, CPE, represents the electronic polarization in polymer matrix that happens in
a time constant less than a half cycle of optical frequency (≈1015
Hz). Electronic polarization
extends from DC up to optical frequency; however, its effect is minor at low frequencies due to
strong interfacial polarization. The electronic polarization can contribute significantly to the charge
polarization at high frequencies, especially when the DC conductivity is low.
50
The RC circuit of RS-CNT-CS-CNT represents the polarization within MWCNTs, which plays an
important role at high frequencies. The polarization in MWCNTs occurs due to presence of lattice
defects (e.g., vacancies, dislocations and CO and CH attachments) in molecular structure of
MWCNTs [97-103]. For example, a defect in the armchair-type MWCNT, which can conduct
electricity, can cause the surrounding region to be semiconducting. Therefore, in molecular
structure of MWCNTs, there may be two regions with unlike conductivities that induce charge
polarization on molecular scale.
Figure 2-21: The equivalent-circuit model of MWCNT/polymer composites.
The resistance/capacitance (RC) circuit of CSI-RSI signifies the interfacial polarization that is
broadly observed at low frequencies in heterogeneous structures, such as CPCs [104]. The time
constant of an RC circuit is . At frequencies below 1/τ, the charges have enough time to
build up at the interface of the MWCNT and polymer; thus, the interfacial polarization contributes
significantly to the charge polarization. In other words, at low frequencies the accumulated charges
51
at the interface find sufficient time to adapt themselves to alternating voltage, contributing to real
permittivity. By increasing the frequency, the contribution of interfacial polarization to real
permittivity diminishes, due to insufficient time for electrons to accumulate at the interface in each
half cycle of alternating field (relaxation phenomenon).
The parallel resistor, RP-CNT, represents the resistance against the movement of free charges
across MWCNT network and corresponds to DC conductivity. The DC conductivity is in phase
with alternating voltage and originates from movement of free charges into interconnected network
of MWCNTs. The DC conductivity is usually measured under a low-frequency AC voltage, where
the effects of frequency-dependent dielectric dispersion are insignificant [56].
2.7. Effects of Conductive Filler Type (MWCNT versus CuNW) on Electrical Properties of
CPCs
Fillers are usually added to polymer matrix for many purposes, such as reducing final material
cost and/or improving electrical, thermal and mechanical properties. Many parameters play role in
filler selection, such as desired properties of composite, physical properties of filler, filler price,
compatibility between filler and polymer matrix, availability, recyclability, and so on [105].
The most desirable characteristic in CPCs is high electrical conductivity at very low filler
content. The CPCs with highly conductive fillers can surpass the conventional materials for
advanced applications like new generation of microelectronics. Therefore, intrinsic conductivity of
conductive filler is one of the most important factors to be considered in filler selection for
electrical applications.
52
As described previously, conductive network formation in CPCs is better understood based on
the concept of percolation threshold. Percolation occurs at a concentration where conductive filler
particles contact each other and begin to form a continuous network throughout the matrix. As
conductive filler is usually much more expensive than polymer matrix, the conductive network
formation at lower filler content is highly desirable for the manufacturers. The fillers with higher
aspect ratio (length over diameter) have more probability to contact each other; therefore,
presenting lower percolation threshold [62, 69, 106]. Moreover, in some CPC applications, high
thermal conductivity is required [107-109]. Examples include PCBs, which require dissipating the
generated heat during operation. Accordingly, the fillers incorporated in CPCs for advanced
applications are needed to present high electrical and thermal properties along with large aspect
ratio.
To meet the demanding requirements for advanced electrical applications, many nanofillers can
be nominated as conductive filler. However, the focus of the dissertation is on MWCNT and
CuNW. MWCNT was selected due to its high aspect ratio, unique electronic structure,
extraordinary electrical, thermal and mechanical properties and growing industrial usage. However,
the limited conductivity of MWCNT prompted us to study CuNW, too, which have higher intrinsic
conductivity but lower aspect ratio than MWCNTs.
53
2.7.1. Carbon Nanotubes
2.7.1.1. Structure and Electrical Properties
The discovery of carbon nanotubes (CNTs) can be traced back to the origin of fullerene chemistry.
Fullerenes (C60) are geometric cage-like structures of carbon atoms made of pentagonal and hexagonal
items [68, 110, 111]. This discovery led to synthesis of CNT by Iijima in 1991 [112, 113]. Nanotubes
are slender elongated fullerene where the walls are hexagonal carbon and often capped at each end.
There are two general types of carbon nanotubes: multi-walled carbon nanotube (MWCNT) and
single-walled carbon nanotubes (SWCNT). MWCNT consists of multiple rolled layers of graphite
coaxially arranged around a central hollow core with van dar Waals forces between adjacent layers,
while SWCNT is made of a single graphene cylinder [68]. Figure 2-22 depicts TEM images of
different kinds of CNTs.
Figure 2-22: TEM images of different CNTs : (a) SWCNT, (b) MWCNT with different layers of 5,
2 and 7 [112, 114].
The atomic structure of CNTs is determined in terms of chirality, which is defined by chiral vector
and chiral angle. In general, three different chiralities can be defined for CNTs: armchair, zigzag and
54
chiral (Figure 2-23). The tube chirality is defined by the chiral vector, which is explained by the
following equation:
(2-28)
where the integers (n, m) are the number of steps along the unit vector and of the hexagonal
lattice. The chiral angle determines the amount of twist in CNT [68, 115]. Using this (n, m) naming
systems, three types of orientation of carbon atoms around the nanotube circumference are itemized. If
, the nanotubes are called “armchair”. If , the CNTs are called “zigzag”. Otherwise, they
are called “chiral”. The chirality of CNTs has considerable implications on the transport properties,
specifically the electronic properties. It has been revealed that nanotubes can be either metallic or
semi-conducting, depending on tube chirality [116]. Each MWCNT contains a multi-layer of
graphene, and each layer can have different chiralities, thus the prediction of MWCNT electrical
properties is more sophisticated than that of SWCNTs.
Figure 2-23: Schematic diagram showing how a hexagonal sheet of graphene is rolled to form a
CNT with different chiralities; (a) Armchair; (B) Zigzag; (C) Chiral [68, 115].
The theoretical and experimental results have demonstrated that CNTs have extremely high
elastic modulus, greater than 1 TPa (near elastic modulus of diamond) and strength of 10-100 times
55
greater than steel but with a lower density [68]. CNTs are also fascinating materials in terms of
electrical and thermal properties. CNTs are stable up to 700°C in air, and 2800°C in vacuum; their
thermal conductivity is about two times greater than diamond while their electrical conductivity is
as high as metallic materials [117].
The electrical properties of CNTs, which is the focus of this dissertation, are closely linked to the
nature of the bonds between the carbon atoms. As a CNT can be considered as a rolled-up graphene
sheet, the bonding mechanism in a CNT is similar to that of graphite. When carbon atoms combine
to form graphite, sp2 hybridization takes place. In this process, one s-orbital and two p-orbitals
combine to form three hybrid sp2-orbitals at 120° to each other within a plane depicted in Figure 2-
24. The in-plane bond is denoted as bond. This strong covalent bond ends in the high stiffness and
strength of CNTs. The remaining p-orbital is perpendicular to the plane of the bonds and interacts
with p-orbital in the adjacent layer to form a bond. The delocalized bonds are much weaker than
bonds and are distributed over the CNT circumference. These delocalized bonds account for
high electrical conductivity of CNTs [118].
However, the presence of crystallographic defects affects the electrical properties of CNTs.
These defects include vacancies, dislocations and CO and CH attachments, etc. For convention, a
nanotube is called defect free if it is of only hexagonal [118]. The presence of structural defects in
CNTs can be viewed as a challenge as well as an opportunity for electrical applications. CNTs with
perfect molecular structure show eminent electrical conductivity and EMI shielding; whereas
manipulating the structural defects of CNTs can be useful for charge storage applications.
56
Figure 2-24: Basic hexagonal bonding structure for a graphite sheet; carbon nuclei shown as filled
circles, out-of-plane bonds represented as delocalized (dotted line), and bonds connect the
nuclei in-plane [119].
2.7.1.2. Carbon Nanotube Synthesis
Primary synthesis methods for carbon nanotubes include arc-discharge [113, 120], laser ablation
[121], gas-phase catalytic growth from carbon monoxide [122] and chemical vapor deposition
(CVD) from hydrocarbons [123]. For applications of carbon nanotubes in polymer composites,
large quantities of carbon nanotube are required. Thus only the two latter techniques, due to their
continuous mechanism, have the potential to find industrial applications.
MWCNTs employed in this dissertation, both pristine and masterbatch, are commercial products
made by CVD technique, according to the suppliers. Thus, only the mechanism behind CVD
57
technique is briefly detailed here. In this technique, a substrate is prepared with a layer of metal
catalyst particle. The substrate is heated to approximately 700 C. Then, the mixture of two gases,
i.e., a process gas (such as nitrogen) and a carbon-containing gas (such as ethylene) is flown into the
reactor. Afterwards, thermal catalytic decomposition of hydrocarbon occurs at the surface of
catalyst, where it forms CNTs. As the carbon source is provided with flowing gas, this process
draws a promising future for mass production [123, 124].
2.7.1.3. Carbon Nanotube Market
Among the abundant types of newly synthesized nanomaterials, CNTs are perhaps among the
most dynamic ones. Academia, small businesses as well as large companies, have pursued to
exploit numerous commercial applications of CNTs. Therefore, mass production of CNTs have
realized industrial feasibility and new CNT producers are now enable to produce CNTs in large
scales, depending on the specific grade, at more cost-effective prices. Figure 2-25 shows the global
market for CNT grades based on commitment production (2011-2016). The global market for
different types of CNTs was $192 and $239 million in 2011 and 2012, respectively, and is projected
to grow within the next five years at a compound annual growth rate (CAGR) of 22.4%, reaching
$527 million by 2016 [125]. This large increase can be explained in terms of technical momentum
and enormous business potential.
58
Figure 2-25: Global market for CNT grades based on committed production, (2011-2016),
($ Million) [125].
2.7.2. Copper Nanowire (CuNW)
CuNWs, due to their higher electrical conductivity relative to carbon-based materials, are
receiving great attention to be used in CPCs [19, 39]. However, there are challenges as well as
opportunities in employing CuNWs in CPCs as substitutions for carbon-based materials:
(1) Beyond the percolation threshold, the filler conductivity plays the dominant role in
defining the electrical conductivity of CPCs [42, 66]. Therefore, above the percolation
threshold, CuNW/polymer composites can present higher electrical conductivity than
CNT/polymer composites. However, oxide layer formation on the surface of CuNWs
restricts electrical conductivity and should be avoided.
(2) CuNWs are still made in batch process with low yield. This issue can overshadow the
superiority of CuNWs to CNTs in terms of industrial applications.
(3) CuNWs possess larger amount of nomadic charges than CNTs, thus demonstrate higher
EMI shielding than CNTs. However, the oxide layer formation on the surface of CuNWs
should be evaded since it prohibits the conductive network formation and reduces EMI
shielding.
59
(4) Low imaginary permittivity in CPCs is plausible by avoiding conductive network
formation. On the other hand, larger amount of nomadic charge carriers in highly
conductive fillers lead to higher real permittivity in CPCs. Having known these two
concepts, CuNWs can be innovatively introduced as novel conductive fillers for charge
storage applications. As a matter of fact, unavoidable oxide layer on the surface of
CuNWs combined with high conductivity of fresh core of CuNWs can lead to low
imaginary permittivity and high real permittivity, respectively.
The above-mentioned concepts and issues provide huge stimulation to investigate the dielectric
properties of CuNW/polymer composites for charge storage applications.
2.8. MWCNT Alignment, Induced by Injection Molding, and Electrical Properties of CPCs
The key aspect of conductive filler alignment and its influence on electrical properties is very
often disregarded during the design process of CPCs. Treating CPCs as isotropic, results in
conservative design and underutilization of CPCs at best, or can lead to insecure design at worst.
Furthermore, most of investigations on the electrical properties of CPCs have been devoted to
compression molded composites, which have randomly dispersed conductive filler; this has led to
the results that are not applicable to injection molded composites where the conductive filler is
aligned. Hence, a portion of this PhD thesis has been dedicated to investigating the influence of
MWCNT alignment on the electrical properties of MWCNT/polymer composites.
60
2.8.1. Flow Conditions in Injection molding and its Effect on Filler Alignment
In order to anticipate the pattern of conductive filler alignment in an injection molded composite,
it is a must to obtain a general understanding from the melt flow behavior in injection molding
process. During injection molding process, polymer melt undergoes a complex flow condition in the
part cavity. In fact, the combination of three major types of flow influences filler alignment,
namely: (a) in-plane shear flow, (b) in-plane tensile or compressive flow and (c) out-of-plane
fountain flow [126].
In-plane shear flow, which is the most common type of flow, occurs due to pressure gradient
along the length of a uniform cross-section. For the simplified Newtonian polymer melts, there is a
parabolic distribution for velocity, leading to maximum shear rate at the wall and no shear rate at
the center (Figure 2-26). Nevertheless, in real life polymer melts are non-Newtonian and non-
isothermal. Non-Newtonian feature of polymer melts alters the parabolic velocity distribution to a
flatter distribution. In addition, freezing occurring on the mold walls leads to temperature gradient
through thickness direction. In the cooler region near the wall, the melt viscosity rises and melt
velocity decreases. This causes a shift in maximum shear rate to a location further away from the
wall. The high shear rate at the location of peak leads to maximum filler alignment close to the wall,
but not at the wall. The low shear rate close to the center does not impact the filler alignment.
Additionally, in the center of cavity the filler reorientation could process easier due to longer
relaxation time for polymer melt.
61
Figure 2-26: Comparison between isothermal and non-isothermal velocity and shear rate
distributions for a non-Newtonian melt in thickness direction [126].
The in-plane compressive and tensile flows occur when there is a change in the shape of flow
channel (Figures 2-27 (a) and (b)). For the convergent channel, the melt undergoes a stretching
action (tensile flow) and fillers within the melt are aligned in the direction of flow. For the divergent
channel, the melt experiences compression (compressive flow) and fillers are aligned perpendicular
to the flow direction. The third type of flow is fountain flow that takes place at the melt front and
arises from thickness velocity gradient and conservation of mass (Figure 2-27(c)). The velocity
gradient conducts the melt at the front to splay outward and deposit on the wall as a thin frozen
layer. As the melt moves toward the wall in the fountain flow, the fillers undergo stretching and
rotation.
In addition to the mentioned mechanisms, the pattern of conductive filler alignment also depends
on rheological properties of melt, characteristics of filler, geometry of cavity and processing
conditions of injection molding process.
62
Figure 2-27: Influence of (a) convergent channel and (b) divergent channel on filler alignment in a
small element of polymer melt. (c) Schematic of fountain flow at the melt front [126].
2.8.2. A Brief Review on Electrical Conductivity of Injection Molded CPCs
In recent years, several studies have been performed on the electrical conductivity of injection
molded CPCs [66, 127-130]. They all reported a loss in conductivity of injection molded CPCs
relative to compression molded CPCs around the percolation threshold. Hong et al. [130]
investigated the electrical conductivity of injection molded carbon black/polystyrene composites
and claimed that conductive filler experienced a shear-induced migration from the walls to the
center. They revealed that injection molded carbon black/polystyrene composites showed a loss in
conductivity by several orders of magnitude when mean particle concentration was at or slightly
above the percolation threshold. They related this observation to conductive filler depletion on the
surface. They also claimed that removing the surface layer in micrometer scale by excimer laser led
to restoration of conductivity, confirming migration of conductive fillers.
63
In another study, Villmow et al. [127] employed a two-level, four-factor factorial design to
investigate the influence of melt temperature, injection velocity, injection pressure and mold
temperature on the electrical conductivity of MWCNT/PC composites. Their results revealed that
the melt temperature followed by the injection velocity had the greatest impact on MWCNT
alignment and electrical conductivity, while the influences of mold temperature and injection
pressure were insignificant. In other words, the composites produced at lower melt temperature and
higher injection velocity experienced higher shear rate, and thus presented greater MWCNT
alignment. They asserted that greater MWCNT alignment was associated with inferior conductive
network formation and lower electrical conductivity.
They believed that the loss in the electrical conductivity of injection molded composites relative
to compression molded composites was mostly due to highly aligned skin layer, which acted as
insulating layer due to absence of contacts between MWCNTs. They also did not observe any fiber
depletion on the composite surface. However, microscopy images showed that at composite depth
of micrometer scale, the conductive network was entirely formed. Higher conductivity at locations
close to the center was ascribed to lower shear rate and also longer relaxation time for polymer
chains to reorient.
Although the electrical conductivity of injection molded CPCs has been investigated by some
researchers; however, there is still a large vacant area to investigate the influence of conductive
filler alignment, induced by injection molding process, on other electrical properties, i.e., EMI
shielding and real and imaginary permittivities. This poses the alignment of conductive filler as an
opportunity to employ or a challenge to be avoided for electrical applications.
64
2.9. Project Motivation and Objectives
The ability to manipulate the conductive network formation within CPCs allows them to be used
in wide range of applications, such as charge storage, antistatic dissipation, ESD protection and
EMI shielding. Accordingly, the main objective of this dissertation is to create unique morphologies
of CPCs to control the conductive network formation to achieve desired electrical properties. This
was performed through manipulating mixing methods and processing conditions using various
nanofillers, and then relating the developed morphologies to the final electrical properties. Having a
comprehensive understanding of conductive network formation enables the manufacturers to
employ cost-effective raw materials and appropriate processing conditions to achieve desired
electrical properties.
It is believed that enhanced conductive network formation improves electrical conductivity and
EMI shielding; whereas, decayed conductive network formation reduces leakage current (imaginary
permittivity), which is desirable for charge storage applications [17, 104]. Accordingly, this PhD
thesis is dedicated to introducing innovative techniques to improve or deteriorate conductive
network formation to obtain desired electrical properties. In other words, conductive network
formation is considered as the key point to design innovative morphologies to achieve desired
electrical properties. Hence, the following techniques were employed to manipulate the conductive
network formation:
Aligning the conductive filler (MWCNT) using an injection molding machine
Changing the type of conductive filler (Copper Nanowire (CuNW) versus MWCNT)
65
Figure 2-28 shows the schematics of expected morphologies created by the above-mentioned
techniques. As depicted in Figure 2-28, playing with the employed techniques can influence the
electrical properties by improving or deteriorating conductive network formation. Figure 2-28(a)
demonstrates random distribution of MWCNTs in polymer matrix. This schematic shows a partial
conductive network formation of MWCNTs, but not a well-established one. This morphology
represents the compression molded MWCNT/polymer composites, and is used as the reference to
compare with the newly developed morphologies.
Figure 2-28: Schematics showing (a) randomly distributed MWCNT/polymer composites, (b)
aligned MWCNT/polymer composites, and (c) CuNW/polymer composites.
Figure 2-28(b) shows a schematic of aligned composites. It is believed that alignment reduces
the chance of conductive fillers contacting each other leading to decayed conductive network
formation. It has been observed that the MWCNT alignment reduces electrical conductivity [127,
128]; however, to the best of our knowledge, no study has been performed to investigate the effects
of MWCNT alignment on EMI shielding and dielectric properties. Furthermore, among the various
techniques employed for mass production of CPCs, injection molding is of great industrial
significance. The unavoidable flow-induced alignment of MWCNTs in injection molding process
66
was the stimulation to investigate effects of MWCNT alignment on the electrical properties of
MWCNT/polymer composites.
The key aspect of conductive filler alignment and its influence on electrical properties is very
often disregarded during the design process of CPCs. Treating CPCs as isotropic results in
conservative design and underutilization of CPCs at best, or can lead to insecure design at worst.
Having known these concepts, the main objective of a portion of this dissertation is to verify the
effect of MWCNT alignment on electrical properties of MWCNT/polymer composites to discover
the challenges to avoid or opportunities to employ.
In order to employ CPCs for charge storage applications, highly conductive fillers are greatly
acknowledged. Accordingly, the limited electrical conductivity of MWCNTs prompted us to
investigate the dielectric properties of CuNW/polymer composites, due to superior electrical
conductivity of CuNWs relative to MWCNTs. Highly conductive CuNWs are potentially able to
provide enhanced charge polarization. However, unavoidable oxide layer formation on the surface
of CuNWs sounds as a barrier to spoil the electrical conductivity of CuNWs.
Nonetheless, oxide layer formation can be innovatively considered as a benefit to decay
conductive network formation to reduce imaginary permittivity. As shown in Figure 2-28(c), the
oxide layer around CuNWs have the potential to avoid the direct contacts between CuNWs leading
to inferior conductive network formation (lower energy loss). On the other hand, the fresh core of
CuNWs can provide the composite with considerable free charges for interfacial polarization. This
hypothesis prompted us to compare the dielectric properties of CPCs holding MWCNTs and
CuNWs.
67
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Chapter 3
Materials, Processing and Characterization
3.1. Methodology
The main objective of this dissertation is to determine how unique morphologies of CPCs can be
created to control conductive network formation. This has been performed through manipulating
processing parameters and molding conditions using various nanofillers, and then relating the
obtained morphologies to the final electrical properties, i.e., electrical conductivity, EMI shielding
and dielectric properties. Figure 3-1 presents a flowchart showing the experimental strategy
employed in this dissertation to explore novel techniques to regulate conductive network formation.
In the phase I, the effects of MWCNT loading on the electrical properties of MWCNT/polymer
composites and the mechanisms behind are investigated. This phase gives a comprehensive
understanding about the relationships between conductive network formation and electrical
properties. Phase II covers the effects of MWCNT alignment induced by injection molding process
on electrical properties in the X-band (8.2 – 12.4 GHz), and introduces MWCNT alignment as a
challenge to be avoided for electrical conductivity and EMI shielding or as an opportunity to be
employed to improve dielectric properties. Phase III investigates the effects of MWCNT content on
the broadband dielectric properties of MWCNT/polymer composites, i.e., 10-1
– 10+6
Hz. Phase IV
presents CuNW as a promising filler, to be incorporated into CPCs, with superior dielectric
properties to MWCNT.
79
Figure 3-1: Experimental Strategy.
3.2. Materials
Masterbatch: Two kinds of masterbatch were used in this project: a masterbatch of 15.0 wt%
MWCNT in PC (MB6015-00) and a masterbatch of 20.0 wt% MWCNT in PS (MB2020-00). Both
masterbatches were obtained in the form of cylindrical pellets from Hyperion Catalysis
International, Cambridge, MA, USA. The length and diameter of pellets were 2.50 ± 0.25 mm and
3.50 ± 0.25 mm, respectively. According to the supplier, the MWCNTs were vapor grown and
80
typically had an outer diameter of 10-15 nm wrapped around a hollow core with a diameter of 5 nm.
The length distribution ranged between 1 and 10 µm, while the density was approximately 1.75
g/cm3.
Polycarbonate (PC): Being a good electrical insulator and having heat-resistant and flame-
retardant properties, PC is employed in various applications engaged with electrical hardwares. The
pristine PC used was LexanTM
141, kindly provided by Sabic Innovative Plastics, with melt flow
rate of 10.5g/10 min (at 300 C/1.2 kgf). According to the supplier, the density and melt
temperature are 1.19 g/cm3 and 295-315 C, respectively. The volume resistivity is 10
17 cm
according to ASTM D257 and the real permittivities at 50 Hz and 1 MHz are 3.17 and 2.96,
respectively, according to ASTM D150.
Polystyrene (PS): The neat PS employed in this dissertation was Styron® 610, which is a heat-
resistant insulating thermoplastic. Styron® 610 was kindly supplied by Americas Styrenics LLC. Its
melt flow rate and density are 10.0g/10 min (at 200 C/5.0 kgf) and 1.06 g/cm3, respectively. The
volume resistivity is 1016
cm.
Poly(vinylidene Fluoride) (PVDF): PVDF is a specialty plastic material in the fluoropolymer
family, which has many applications in electronics industry, due to its low electrical conductivity,
resistance to heat, and piezoelectric properties. The PVDF Kynar® 1000HD was purchased from
Arkema Inc. The density and melt flow rate are 1.78 g/cm3 and 1.1g/10 min (at 230 C/5.0 kgf),
respectively. The volume resistivity is 2014
cm according to ASTM D257. The real
permittivities are 10.5 and 7.0 at 100 Hz and 1 MHz according to IEC 60250, respectively.
81
MWCNT: The MWCNTs (NanocylTM
NC7000) were obtained from Nanocyl S.A. (Sambreville,
Belgium). According to the manufacturer, the MWCNTs were produced by catalytic carbon vapor
deposition (CCVD) process. Table 3-1 details the physical properties of NC7000.
Table 3-1: Physical properties of MWCNT (NC7000) [1].
Property Unit Value
Average Diameter Nanometer 9.5
Average Length Micron 1.5
Electrical Conductivity S/cm 104-10
5
Specific Gravity g/cm3 1.3-2.0
Carbon Purity % 90
Surface Area m2/g 250-300
Copper Nanowire (CuNW): CuNWs synthesized and employed in this dissertation had an average
diameter of 30 nm and average length of 1.5 µm (L/D ~50). The synthesis of nanowires is an
advanced technique whose science is understood by a limited number of research groups in the
world, including Polymer Processing Group (PPG) at University of Calgary. Figure 3-2 shows
schematic of synthesis of metal nanowires by template-directed synthesis [2, 3]. In order to
synthesize the CuNW; firstly, the aluminum plates are annealed in air at 500 °C for 24 hr. The
porous aluminum oxide (PAO) templates were prepared by anodization of Al templates in dilute
solution of sulfuric acid. Afterwards, the electrodeposition is carried out by dipping the PAO
templates in an electrolyte solution between two metal plates and applying an alternating voltage for
a period of time, i.e. 10 min. Finally, nanowires are liberated by dissolving alumina in 1 M NAOH
82
solution. The metal nanowires can be functionalized to disperse better in CPCs. More information
on the nanowires synthesis is detailed elsewhere [2, 3].
Figure 3-2: Consecutive steps of nanowires synthesis [2, 3].
3.3. Sample Preparation, Processing and Molding
3.3.1. Phase I
In this phase, 15.0 wt% MWCNT/PC masterbatch and pristine PC were dried under vacuum at
120 oC for 4 hr. A Haake rheomix series 600 batch mixer was utilized to dilute the masterbatch to
make composites with different loading levels. Pristine PC was first mixed for 5 min at 300 ˚C and
50 rpm, and then the masterbatch was inserted to the melt and mixed for additional 10 min. A
Carver (Carver Inc. Wabash, IN) compression molder was used to make rectangular samples 42×25
mm with four different thicknesses of 0.25, 0.60, 1.50 and 1.85 mm to obtain electrical conductivity
and EMI shielding data. The compression molding process was carried out at 280 oC for 5 min
AC
Electrodeposition
Synthesis of
Template
Liberation
of
nanowires
Polymer
Blending
Polymer
Nanocomposite
Al Plate
annealed in
air 550 C
Surface
functionalization
Cu, Fe, Ni or Ag
Remove
bulk
depositionReuse Al
83
under pressure of 34.4 MPa. The data obtained from phase I provide significant information
regarding the mechanisms behind electrical conductivity and EMI shielding of CPCs as functions of
composite thickness and filler loading.
3.3.2. Phase II
3.3.2.1. Materials Preparation
MWCNT/PS masterbatch and pristine PS were dried at 50 °C for at least 4 hr under vacuum. The
composites with different concentrations of MWCNT were prepared using a 25 mm Coperion ZSK
co-rotating intermeshing twin-screw extruder operated at extruder speed of 150 rpm and residence
time of 2 min (Figure 3-3). The twin-screw extruder included 10 thermal zones starting from the
hopper and ending at the die. The temperature profile of the extruder was set as follows considering
the processing conditions recommended by the PS supplier:
Zone 1 (Hopper): 190 C; Zone 2: 194 C; Zone 3: 204 C; Zone 4: 189 C; Zone 5: 179 C; Zone
6: 182 C; Zone 7: 181 C; Zone 8: 180 C; Zone 9: 180 C; Zone 10 (Die): 200 C
Considering the density of neat PS and MWCNT are 1.06 and 1.75 g/cm3, respectively; the
concentrations of prepared nanocomposites in terms of weight percent and volume percent are
presented in Table 3-2.
Table 3-2: The concentrations of the prepared MWCNT/PS nanocomposites in terms of weight
percent and volume percent.
MWCNT Concentration (wt%) 0.1 0.30 0.50 1.0 2.00 3.50 5.00 10.0 20.0
MWCNT Concentration (vol%) 0.06 0.18 0.30 0.60 1.22 2.15 3.09 6.30 13.2
84
Figure 3-3: An image of Coperion ZSK co-rotating intermeshing twin-screw extruder employed for
diluting the MWCNT/PS masterbatch.
3.3.2.2. Experimental Design and Composite Molding
In order to explore the effects of molding conditions on the electrical properties of the injection
molded MWCNT/PS composites, a series of injection molding experiments, denoted as EXP, were
carried out on a 5.00 wt% MWCNT/PS composites using a two-level, four-factor factorial design to
study the impact of four processing parameters, i.e., mold temperature (C1), melt temperature (C2),
injection/holding pressure (C3) and injection velocity (C4) on the volume resistivity of the molded
composites. The set points were selected with the maximum possible interval, considering the
limitations of the employed injection molding machine and also the recommended processing
conditions of pure PS. Constant holding and cooling times of 8 and 10 seconds were applied for all
the experiments, respectively. Further details on the employed experimental design can be found
85
elsewhere [4]. Tables 3-3 and 3-4 show the experimental design and the set points of the processing
parameters, respectively.
Table 3-3: Experimental design showing the two-level, four factor factorial design. The factors are
mold temperature (C1), melt temperature (C2), injection/holding pressure (C3) and injection velocity
(C4).
EXP # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Fac
tors
C1 - - - - - - - - + + + + + + + +
C2 - - - - + + + + + + + + - - - -
C3 - - + + - - + + - - + + + + - -
C4 - + + - - + + - - + + - - + + -
Table 3-4: Levels (set points) of the processing parameters used in the injection molding
experiments. The processing parameters are mold temperature (C1), melt temperature (C2),
injection/holding pressure (C3) and injection velocity (C4).
Figure 3-4 shows a schematic of the mold employed in the injection molding process with the
dimensions provided in Table 3-5. The cavity was fed by an edge gate and its thickness was 2.0
mm. A detailed description of the designed mold and injection molding machine can be found
elsewhere [5].
Processing Parameters
C1 (°C) C2 (°C) C3 (bar) C4 (mm.sec-1
)
+ 60 240 100 240
- 25 215 60 24
86
Figure 3-4: A schematic view of the designed mold.
Table 3-5: Dimensions of the designed mold.
Figure 3-5 shows the resistivity of the injection molded MWCNT/PS composites in thickness
direction at different processing conditions. The results showed a decrease of up to ten orders of
magnitude in volume resistivity by adding 5.00 wt% MWCNT, compared with pure PS.
Interestingly, depending on the processing conditions, differences in the volume resistivity up to six
orders of magnitude was observed in the thickness direction of the injection molded
nanocomposites. As depicted in Figure 3-5, the highest resistivity of the composites was obtained
for the first three and last three experiments, where C2 (melt temperature) was minimal. In addition,
the lowest amount of volume resistivity can be seen in EXPs 5, 8, 9 and 12, where C2 (melt
temperature) had the highest values, and C4 (injection velocity) had the lowest values. A lower melt
temperature and higher injection velocity impose greater shear stress on the polymer matrix melt
leading to greater MWCNT alignment. As there is a reverse relationship between MWCNT
alignment and conductive network formation, the composites showed higher volume resistivity at
lower melt temperature and higher injection velocity and vice versa [4].
Parameter a b c, d e f
Value 22.86 10.16 1 2 10
87
Figure 3-5: Volume resistivities of the injection molded MWCNT/PS composites with 5.00 wt%
MWCNT loading at different molding conditions in the thickness direction [4].
To analyze the data of the resistivity, statistical software (MinitabTM
, ver. 14) was used to find
the importance of each factor. The effects of the main factors on the volume resistivity of the
molded nanocomposites are plotted in Figure 3-6. As can be seen in Figure 3-6, C2 (melt
temperature) and C4 (injection velocity) showed the greatest impact on the volume resistivity of the
samples, while the impacts of C1 (mold temperature) and C3 (injection/holding) pressure were
insignificant. Therefore, it can be concluded that the melt temperature had the greatest impact on
volume resistivity of the molded samples followed by the injection velocity, while the impacts of
mold temperature and injection/holding pressure were insignificant. Further information on the
main factor effects and interaction effects can be obtained elsewhere [4].
88
Figure 3-6: Minitab main effect plot of the volume resistivity mean of the injection molded samples
[4].
To investigate the influence of MWCNT alignment on electrical properties at different MWCNT
concentrations, we used the results obtained from experimental design of 5.00 wt% MWCNT to
select three processing conditions with the maximum possible variation in MWCNT alignment, i.e.,
volume resistivity. In other words, knowing the tremendous influence of melt temperature and
injection velocity on MWCNT alignment and volume resistivity of MWCNT/PS nanocomposites,
three different injection molding experiments, i.e., EXP #11, 12 and 14 were employed to make
samples with various MWCNT alignments at different MWCNT concentrations. The samples
fabricated using EXPs #11, 12 and 14 were used to investigate the effects of MWCNT alignment on
the electrical properties of MWCNT/PS composites at different MWCNT concentrations (chapters
5 and 6). EXPs #11, 12 and 14 correspond to EXPs # 2, 3 and 1 in chapters 5 and 6, respectively.
To have a better understanding of the effects of MWCNT alignment on the electrical properties,
the electrical properties of the injection molded samples were compared with those of the
compression molded samples. A Carver compression molder (Carver Inc., Wabash, IN) was used to
89
make the samples of randomly distributed MWCNTs, with the same dimensions as the injection
molded samples. The compression molding process was performed at 210 °C for 10 min under 38
MPa pressure.
3.3.3. Phase III
In this phase, pristine polystyrene (Styron® 610) and MWCNTs (Nanocyl
TM NC7000) were dried
at 50 °C for 4 hr under vacuum. Nanocomposites with different concentrations of MWCNTs were
manufactured through solution mixing technique. In the solution mixing method, nanocomposites
with various MWCNT contents were made by mixing different volumes of 100 mg/ml PS/N,N-
dimethylformamide (DMF) solution and 0.66 mg/ml MWCNT/DMF suspension. Each mixture was
stirred for 15 min and then ultrasonicated for 30 min in a sonication bath. The two mixtures were
then combined and stirred for an extra 10 min. Afterwards, the suspension was dripped into a large
amount of methanol, where the volume ratio of methanol to DMF was approximately three to one.
Upon contact of the suspension with the methanol, the PS chains coagulated instantly, because of
their insolubility in methanol. The coagulated chains captured the MWCNTs and prohibited them
from reagglomeration. The final mixture was filtered and dried in a fume hood for 16 hr and then
transferred to a vacuum oven for 12 hr at 50 °C to remove the remaining solvents.
The composites obtained from the solution mixing technique were then molded using a Carver
compression molder (Carver Inc., Wabash, IN) at 210 °C for 10 min under a pressure of 38 MPa.
The compression molded samples had a thickness of 1.0 mm, width of 25.0 mm and length of 42.0
mm. Then, the broadband dielectric properties of molded samples were measured.
90
3.3.4. Phase IV
The PVDF Kynar® 1000HD and MWCNTs (Nanocyl
TM NC7000) were dried at 50 °C for 4 hr
under vacuum. The MWCNT/PVDF and CuNW/PVDF nanocomposites were produced by solution
mixing technique. PVDF was dissolved into DMF at 80 ºC under continuous stirring to obtain a
solution with concentration of 0.1 g/ml. Meanwhile, MWCNTs and CuNWs were also dispersed
into DMF under sonication at room temperature for 30 min. The concentrations of MWCNT and
CuNW suspensions were 0.00033 and 0.00500 g/ml, respectively. Cooling down the PVDF/DMF
solution to room temperature, the MWCNT/DMF and CuNW/DMF suspensions were mixed with
PVDF/DMF solution separately using magnetic stirring for 5 min. Subsequently, the suspensions
were dripped into methanol (non-solvent to PVDF), where the volume ratio of DMF to methanol
was 1:3. Upon contact of the suspension with the methanol, the PVDF chains retracted and
precipitated instantly, due to their insolubility in methanol. The retracted chains entrapped the fillers
and prevented them from reagglomeration.
The mixtures were then filtered and placed in an evaporation dish for 24 hr in a fume hood.
Next, the MWCNT/PVDF nanocomposites were dried at 80ºC for 24 h in a vacuum oven; whereas,
the CuNW/PVDF nanocomposites were dried for 96 hr at room temperature under vacuum. Finally,
the MWCNT/PVDF and CuNW/PVDF nanocomposites with the concentrations between 0.4 and
1.5 vol% were produced by the compression molding of the prepared materials at 200 ºC for 10 min
under pressure of 35 MPa.
91
3.4. Electrical Properties Measurement Setups
3.4.1. Surface/Volume Resistivity Measurement
Usually, the setups utilized to measure the conductivity of materials displays the conductance in
terms of surface/volume resistivity. Volume resistivity is reciprocal of electrical conductivity and
defined as the electrical resistance through a cube of a material. When expressed in ohmcm, it
would be the electrical resistance through a one-centimeter cube of a material. Volume resistivity is
considered as an important factor while dealing with the bulk of materials, such as EMI shielding
and charge storage.
Surface resistivity is reciprocal of surface conductivity and defined as the electrical resistance of
the surface of a material. When expressed in ohm per square, it is equivalent to resistance across a
square section of a material. Since the surface length is fixed, the measurement is independent of
the physical dimensions (i.e., thickness and diameter) of the sample. Surface resistivity is an
important term when coping with the static electricity of materials, such as ESD protection and
antistatic dissipation.
In this PhD thesis, the resistivity measurements were performed using two different setups. For a
volume resistivity of more than 10+4
ohm·cm, a Keithley 6517A electrometer connected to a
Keithley 8009 test fixture was used. For the samples with a volume resistivity of less than 10+4
ohm·cm, the measurements were conducted according to the ASTM 257-75 standards, using a
Loresta GP resistivity meter (MCP-T610 model, Mitsubishi Chemical Co., Japan) connected with a
four-pin probe. The applied voltage for all the resistivity measurements was 10 V.
92
In the 8009 Test Fixture, as shown in Figure 3-7, volume resistivity is measured by applying a
voltage potential across opposite sides of an insulator sample and measuring the resultant current
through the sample.
Figure 3-7: The equivalent circuit for 8009 Test Fixture used to measure volume resistivity [6].
For the configuration shown in Figure 3-7, the volume resistivity can be calculated as following:
(3-1)
v: volume resistivity
R: measured resistance in ohms (
)
A: area of the sample
t: average thickness of the sample
Surface resistivity of insulative samples is measured by applying a voltage potential across the
surface of the sample and measuring the resultant current (Figure 3-8). The same model of test
fixture as volume resistivity but unlike configuration was used to measure the surface resistivity
93
(Figure 3-8). For the configuration shown in Figure 3-8, the surface resistivity can be calculated as
following:
(3-2)
: surface resistivity (per square)
R: measured resistance in ohms (
)
P: the effective perimeter of the guarded electrode
g: distance between the guarded electrode and the ring electrode
Figure 3-8: The equivalent circuit for 8009 Test Fixture used to measure surface resistivity [6].
For the samples with a low surface/volume resistivity, it is very significant to reduce or eliminate
the contact resistance to avoid any confounding effect: a voltage drop forms due to an interfacial
phenomenon at a point (between the current electrode and the sample surface), where the specific
current flows in. Accordingly, a four-point probe configuration was used to eliminate the effect of
contact resistance. Figure 3-9 shows a schematic of electrode construction and 4-terminal
configuration for the four-point probe. In the four-terminal method, a known current is passed
94
through the two outer probes and output voltage (V) is measured across the inner probes using a
voltmeter. In Figure 3-9, r1, r2 and Rx represent the contact resistance, resistance of cable and
resistance of sample, respectively. It is necessary to keep the impedance of voltmeter high not to let
electrical current flow into the terminal measuring the voltage.
Figure 3-9: (a) Electrode construction, (b) equivalent circuit for 4-point probe technique [7].
95
3.4.2. EMI Shielding Setup
EMI shielding properties measurements in the X-band (8.2 – 12.4 GHz) frequency range were
carried out in a WR-90 rectangular waveguide using an Agilent programmable network analyzer
(PNA) (Model E8364B). Figure 3-10 depicts a schematic diagram of network analyzer used to
measure the EMI shielding properties. A network analyzer consists of a signal source, a receiver
and a display. The source dispatches a signal at a single frequency to the material under test (MUT).
The receiver is adjusted to that frequency to detect the reflected and transmitted waves from MUT.
The magnitude and phase data will be measured for each signal. The source then switches to the
next frequency and the measurement is repeated. Finally, the reflection and transmission
measurement responses as a function of frequency will be displayed.
Scatter parameters, also called S-parameters, are used to calculate shielding parameters in a
two-port EMI shielding setup. The S-parameters describe the performance of a two-port EMI
shielding setup completely [8, 9]. The S-parameters are defined as:
| S11 |: Reflected voltage magnitude divided by the incident voltage magnitude in port 1
| S12 |: Transmitted voltage magnitude from port 2 to port 1 divided by incident voltage magnitude
in port 2
| S21 |: Transmitted voltage magnitude from port 1 to port 2 divided by incident voltage magnitude
in port 1
| S22 |: Reflected voltage magnitude divided by the incident voltage magnitude in port 2
If MUT is homogeneous, S11 should be equal to S22, and S21 also should be equivalent to S12.
Since power of each signal is proportional to square of field strength, | S11 |2
is equivalent to
96
reflected power divided by incident power in port 1 or | S12 |2
is equivalent to transmitted power
from port 1 to port 2 divided by incident power in port 1. The parameters a1 (a2) are the incident
field strengths and b1 (b2) are the transmitted plus reflected field strengths. As the reflector detector
for port 1 detects the sum of reflected wave from port 1 and transmitted wave from port 2 to port 1;
hence, the S-parameters can be obtained solving following matrices:
(3-3)
(3-4)
The reflectance and transmittance are defined as follow:
|
| | |
| | (3-5)
|
| | |
| | (3-6)
where R and T are reflectance and transmittance, respectively, and PI, PR and PT are incident,
reflected and transmitted powers, respectively.
Thus,
(
) ( ( | |
)) (3-7)
(
) (
| |
| |
) (3-8)
(3-9)
where SER and SEA are shieldings by reflection and absorption, respectively, and SEOA is overall
shielding effectiveness. It is worth mentioning that no device has been developed to measure
shielding by multiple-reflection separately; thus, shielding by multiple-reflection is inherent in
shieldings by reflection and absorption.
97
Figure 3-10: (a) Schematic of network analyzer diagram, (b) S-parameters diagram in a network
analyzer [8, 9].
98
3.4.3. Dielectric Spectroscopy Setup
In this dissertation, the broadband dielectric spectroscopy of CPCs was carried out with an
impedance / gain-phase analyzer (Solartron SI 1260) in the frequency range of 10-1
– 10+6
Hz. The
sample holder used for dielectric spectroscopy was a 12962A sample holder with electrode diameter
of 10 mm. Prior to the measurements, the electrodes were painted on the samples with a silver paste
to reduce the effect contact resistance with sample holder electrodes. The impedance analyzer
generated a voltage over a wide frequency band and applied it to the sample through the sample
holder, and then measured in-phase and out-of phase currents. The obtained voltage and current
data were used to calculate impedance and dielectric properties.
Figure 3-11 shows a schematic of the sample holder employed for dielectric spectroscopy. The
sample holder make use of a guard ring on the fixed electrode in order to decrease the influence of
stray field lines at the edge of the sample which would otherwise result in measurement errors. The
guard ring ensures that the electric field lines are parallel throughout the part of the sample, which
improves the impedance measurement [10].
Figure 3-11: Electrode arrangement of 12962A sample holder [10]
99
The impedance of nanocomposites was calculated using the following equations:
(3-10)
(3-11)
(3-12)
where Z is impedance, is AC voltage and IR and IC are resistive and capacitive
currents, respectively. Substituting IR and IC from Equations 2-23 and 2-24 and reorganizing the
final equations give:
( ) (3-13)
( ) (3-14)
(3-15)
where, : real permittivity, : Imaginary permittivity, ε0: the real permittivity of free space and S
and d: the area and thickness of the sample, respectively.
3.5. References
[1] NanocylTM
NC7000 series – Product Datasheet – Thin Multi-walled Carbon Nanotubes.
Available from: http://www.nanocyl.com: Nanocyl S.A.; 2009.
[2] Gelves GA, Al-Saleh MH, Sundararaj U. Highly electrically conductive and high
performanceEMI shielding nanowire/polymer nanocomposites by miscible mixing and
precipitation. Journal of Materials Chemistry. 2011;21(3):829-36.
100
[3] Gelves GA. Synthesis of copper and silver nanowires in porous aluminum oxide templates
and preparation of polymer nanocomposites. Edmonton, AB, Canada, University of Alberta,
PhD Thesis, 2007.
[4] Mahmoodi M, Arjmand M, Sundararaj U, Park S. The electrical conductivity and
electromagnetic interference shielding of injection molded multi-walled carbon
nanotube/polystyrene composites. Carbon. 2012;50(4):1455-64.
[5] Mahmoodi M, Arjmand M, Sundararaj U, Park S. Effect of gate and runner design on
electrical properties of multi-walled carbon nanotube/polystyrene nanocomposites. Extended
abstracts, SPE-ANTEC Tech. Boston, 2011; p. 525-30.
[6] Instruction manual for model 8009 resistivity test fixture. Keithley Instruments, Inc.; 2003.
[7] Instruction manual for low resistivity meter (Lorest-GP). Mitsubishi Chemical Co.; 2004.
[8] Basics of measuring the dielectric properties of materials. Application note; Agilent
Technolgies, 2006, p. 1-31.
[9] Agilent network analyzer basics. Agilent Technologies, 2004, p. 1-94.
[10] Instruction guide for Solartron sample holder. Available from:
http://www.solartronanalytical.com: AMETEK, Inc. [cited August 2013].
*Carbon. 2011;49(11):3430-3440.
101
Chapter 4
Electrical and Electromagnetic Interference Shielding Properties of Flow-
Induced Oriented Carbon Nanotubes in Polycarbonate*
4.1. Presentation of the Article
This article can be divided into two general sections as followings:
Investigating the electrical properties of MWCNT/PC composites as functions of MWCNT
loading and composite thickness, i.e., electrical conductivity and EMI shielding
Effect of MWCNT alignment on electrical conductivity of MWCNT/PC composites
In the first section, it was observed that there was an ascending trend for electrical conductivity
and EMI shielding as a function of MWCNT content. This was related to increased amount of
interacting mobile charges and also enhanced conductive network formation. Furthermore, the
mechanisms behind the electrical behaviors of CPCs are comprehensively discussed. In the second
section, the influence of MWCNT alignment, induced by an injection molding machine, on
electrical conductivity of MWCNT/PC composites is detailed. The results revealed that MWCNT
alignment had an adverse influence on electrical conductivity, which was related to inferior
conductive network formation at greater MWCNT alignments. The information presented in this
article is an appropriate starting point exploring the realm of electrical properties of CPCs.
102
Electrical and Electromagnetic Interference Shielding Properties of Flow-
Induced Oriented Carbon Nanotubes in Polycarbonate
Mohammad Arjmand1, Mehdi Mahmoodi
2, Genaro A. Gelves
1, Simon Park
2, Uttandaraman
Sundararaj1
1Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Canada 2Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary,
Canada
4.2. Abstract
The electrical and electromagnetic interference shielding effectiveness (EMI SE) properties of
multi-walled carbon nanotubes/polycarbonate (MWCNT/PC) composites are investigated. The
composites were prepared by diluting masterbatch (15 wt% MWCNT) using a Haake mixer and
then injection molding into a dog-bone mold. Various MWCNT alignments were created by
changing operating conditions. Electrical resistivity measurements were carried out at three
different areas at both parallel and perpendicular to the flow direction. The results showed higher
resistivity and percolation threshold at higher alignments in both parallel and perpendicular to the
flow directions. By applying Ohm’s law it was seen that after percolation, the field emission
mechanisms are more important at higher orientations. Higher MWCNT alignments were observed
in areas with higher resistivities, and this was verified using SEM, TEM and Raman spectroscopy
techniques. Additionally, EMI SE measurements were done on compression-molded samples at
different concentrations and thicknesses. The results showed that both EMI SE by reflection and
absorption increased with increase in MWCNT loading and shielding material thickness.
103
4.3. Introduction
Owing to their unique properties such as excellent electrical and mechanical properties, low
density and high aspect ratio, carbon nanotubes (CNTs) have outstanding potential to be used as
nanofiller for polymer composites [1-3]. In the last decade, applications of CNT have been mostly
dedicated to polymer/CNT composites due to their versatility, easy processability, potential to
reduce production cost and flexibility in final material design.
Outstanding electrical properties of CNTs have led to fast growth in research and development
of conductive polymer composites (CPCs). Conductivity at very low concentrations has made CPCs
ideal materials for industrial applications. Conductive network formation in CPCs is better
understood based on the concept of percolation threshold [4]. Percolation means that at least one
pathway forms to allow the electrical current to pass through the sample which alters the material
from insulative to conductive. Percolation occurs at a particular filler concentration where the
electrical conductivity of the composite abruptly increases by several orders of magnitude.
Electrical percolation at very low filler concentration in CNT-polymer composites leads to
production of cost-effective composites.
Electrostatic discharge (ESD) dissipation and electromagnetic interference (EMI) shielding are
the major applications for CPCs [5]. The surface resistivity or volume resistivity of filled polymer
defines its application. For ESD dissipation, typically a surface resistivity of 106-10
9 Ω/□ is required
while for EMI shielding applications, a surface resistivity of lower than 10 Ω/□ and EMI SE of
around 30 dB is needed [6]. If a part has conductivity in the ESD dissipation range, it can be
utilized to bleed off charge to avert harmful arcing discharges. ESD applications comprise chip and
104
circuit board carries for shipping of electronic equipments [7]. Many electronic devices innately
emit electromagnetic signals. Since these signals can interfere with the operation of other electronic
devices, related agencies have applied regulations for electromagnetic compatibility of electronic
housings. Electromagnetic compatibility (EMC) means that a device does not affect itself or other
devices by emitted emissions. Therefore, EMC standards must be met or exceeded for saleable
electronics products [8]. An EMI SE of 30 dB, corresponding to 99.9% of incident radiation, is
regarded as an adequate level of shielding for many applications [6,9].
Among the materials used as EMI shielding barriers, metal-coated polymers own the largest
share of shielding material for electronic enclosures in the market; however, there are serious
drawbacks such as recyclability, delamination and hidden cost in coating that can make CPCs more
promising materials than metal-coated polymers for the future. The EMI shielding mechanisms in
CPCs are more sophisticated than in metal-coated polymers. Understanding these mechanisms is
critical to design these materials appropriately to avoid overshielding which results in higher
product cost and to avoid undershielding which may cause failure in the final material application
[10]. Reflection, absorption and multiple-reflection are three dominant mechanisms of EMI
shielding in CPCs [11]. To reflect electromagnetic waves, shielding materials should have mobile
charge carriers on the surface to interact with the incoming electromagnetic waves [12-14]. Metals
are by far the most used materials for shielding due to the presence of free electrons that can reflect
and absorb incident waves. The absorption loss is a function of σ·μ whereas reflection loss is a
function of σ/μ where σ and μ are conductivity and magnetic permeability, respectively [7]. The
third mechanism of shielding is multiple-reflection, which usually occurs when there are numerous
surface areas or interfacial areas in conductive material like filler-added or foamed material.
105
Generally speaking, parameters such as aspect ratio, conductivity, orientation, dispersion and
concentration of conductive filler influence percolation threshold, conductivity and EMI SE of
CPCs [15]. Processing method is another significant factor that can influence the above-mentioned
parameters. Accordingly, having a good comprehension of processing methods gives direction to
researchers to control the final properties appropriately. Usually, homogeneous dispersion cannot be
attained because of high van der Waals interactions between CNTs, which leads to tangled
intertwined agglomerates. To exploit CNT properties, including electrical properties, efficiently,
these fillers should be dispersed in polymer well. Among the known methods to disperse CNT, melt
mixing is the most popular due to its compatibility with current industrial methods and because it is
environmentally benign. It has been reported that composites filled with higher aspect ratio fibers
have higher EMI SE and conductivity [16,17] and lower percolation threshold than those with lower
aspect ratio fibers; therefore, the blending conditions should be optimized to have the best
dispersion and lowest aspect ratio loss to get the best electrical properties.
CNT alignment can affect the electrical properties of CPCs greatly. Alignment of one-
dimensional CNTs leads to strong anisotropy in mechanical, electrical and even optical properties
of composites [18-25]. Behnam et al [26] simulated the dispersion of high aspect ratio conductive
filler and alleged that minimum resistivity occurs for partially aligned nanotubes. Abbasi et al [19]
studied the influence of nanotube alignment on electrical properties of CNT-based polycarbonate
nanocomposites using micro-injection molding and compared the results with compression-molded
samples. They reported that the high degree of alignment achieved by micro-injection molding led
to higher percolation threshold than that seen in compression-molded samples. However, Jou et al
[18,20] reported that they achieved higher EMI SE and conductivity in LCP composites with
106
longitudinal fiber orientation than the ones with random fiber orientation. In addition, Du et al [23]
also found that in SWNT/PMMA composite the highest conductivity occurs for slightly aligned
rather than isotropic systems.
The focus of this paper is the effect of multi-walled carbon nanotube (MWCNT) alignment on
electrical properties of MWCNT/polycarbonate (PC) system using dog-bone samples made via
injection molding. Flow-induced alignment of MWCNTs was achieved by applying intensive
drag/shear force during the molding process. The degrees of alignment were investigated using
SEM, TEM and Raman spectroscopy. The data were compared with the alignment data for
compression-molded rectangular samples, which give random distribution of MWCNT. Besides,
EMI SE of rectangular compression-molded samples was measured and corresponding shielding
mechanisms were analyzed.
4.4. Experimental
4.4.1. Composite Preparation and Molding
In this study, 15 wt% MWCNT/PC masterbatch was purchased from Hyperion Catalysis
International, Cambridge, MA, USA. The pristine polycarbonate used was Lexan 141, kindly
provided by Sabic Innovative Plastics, with melt flow index of 10.5 g/min and density of 1.19
g/cm3. Prior to mixing, all the materials were dried under vacuum at 120
oC for 4 hours.
A Haake rheomix series 600 batch mixer was used to dilute the PC/MWCNT masterbatch to
make samples with 0.1, 0.3, 0.5, 1.0, 1.5, 2.0, 3.5, 5.0, 7.5 and 10 wt% MWCNT. Granular
107
polycarbonate was first mixed for 5 minutes at 300 ˚C and 50 rpm, and then masterbatch was added
to the melt and mixed for additional 10 minutes. In all cases, the amount of material added filled
78% of the mixer volume at the mixer temperature. To prepare the material for use in the injection
molding system, the mixed compound was ground using a Retsch Brinkmann grinder with a 3 mm
sieve while liquid nitrogen was poured into the grinding system to avoid overheating and
morphology alteration.
An injection molding machine (Boy 12A) was used to inject the material into a two-cavity mold
according to the ASTM D638 test method. As demonstrated in Figure 4-1(a), the dog-bone
specimens were 63.5 mm in total length with a gage section of 9.53 mm, 3.18 mm and 4 mm in
length, width and thickness, respectively. The screw diameter was 18 mm with a length/diameter
(L/D) ratio of 20. The mold base was made out of steel, and the mold insert was fabricated from
Aluminum 7075. An electrical heating system was used to control the mold temperature. Injection
molding was performed with a holding pressure of 60 bar, mold temperature of 80 oC and barrel
temperature of 300 oC. Figure 4-1(b) depicts the experimental setup of the injection molding
system. A Carver (Carver Inc. Wabash, IN) compression molder was used to make rectangular
samples 42×25 mm with four different thicknesses of 0.25, 0.60, 1.50 and 1.85 mm to get EMI SE
data. The compression molding process was carried out for 5 min at 5000 psi.
108
(a) (b)
Figure 4-1: (a) Schematic of the dog-bone sample. The three different areas studied in the
specimens are indicated, (b) Experimental setup.
4.4.2. Electrical and EMI Shielding Measurements
The electrical resistivity measurements were done on both rectangular and dog-bone samples. All
the sample surfaces were cleaned with ethanol prior to measurements. For dog-bone samples, the
measurements were done at three different areas, as demonstrated in Figure 4-1(a), in directions
both parallel and perpendicular to the flow. To measure the volume resistivity of the molded
samples, two different resistivity measurement machines were used. For the samples with volume
resistivity less than 104 Ω·cm, volume resistivity measurements were performed according to
ASTM 257-75 standards employing a Loresta GP resistivity meter (MCP-T610 model, Mitsubishi
Chemical Co., Japan). We used a four-pin probe so that the effect of contact resistance does not
confound the measurement. In this method, a constant current is passed through the two outer
probes and output voltage (V) is measured across the inner probes using a voltmeter. For volume
109
resistivity larger than 104 Ω·cm, a Keithley 6517A electrometer connected to Keithley 8009 test
fixture (Keithley instruments, USA) was used and resistivity was measured at an applied voltage of
10 V.
The EMI shielding measurements were carried out over the X-band (8.2 – 12.4 GHz). The
sample under test was sandwiched between two X-band waveguide sections, which were connected
to separate ports of an Agilent Vector Network Analyzer (model 8719 ES). The Vector Network
Analyzer (VNA) sends a signal down the waveguide incident to the sandwiched sample and then
the reflected and transmitted signals are measured by the VNA. EMI SE is expressed in dB and
defined by the following equation [9,11]:
(
) (
) ( ) (4-1)
where Pin is the incident energy field, Pout is the transmitted energy field and E and H are the root
mean square (rms) of electric and magnetic field strength of the electromagnetic wave, respectively.
Equation 4-1 can also be used to calculate the contributions of reflection and absorption to total
EMI SE considering relevant incident and transmitted energy fields.
4.4.3. Morphological Characterization
Scanning and transmission electron microscopy (SEM and TEM) were used to investigate the
morphology of molded nanocomposites. A high resolution Philips XL30 was used to obtain SEM
images. All the samples were cryo-fractured prior to SEM tests. TEM tests were processed using a
Hitachi H-7650. The samples were ultra-microtomed using diamond knife at room temperature
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before TEM observation. For dog-bone samples, morphological characterizations were done for the
samples in directions both parallel and perpendicular to the flow.
4.4.4. Raman Spectroscopy
Raman spectroscopy method was used to further investigate the degree of alignment in different
areas, namely area 1, 2 and 3 and to compare it with compression-molded samples. In order to do
this, a Renishaw spectrometer equipped with an in Via Raman microscope was employed.
Excitation was provided by NIR laser (785 nm) in regular mode. Measurements were performed in
directions both parallel and perpendicular to the flow. The MWCNT alignment was determined
comparing the Raman spectra obtained from parallel and perpendicular directions.
4.5. Results and Discussion
4.5.1 Electrical Conductivity of MWCNT/PC Composites
Statistical percolation theory [2,4] predicts the dependence of volume resistivity on filler
concentration using a scaling law of the form
( ) (4-2)
where ρ is the composite volume resistivity, ρ0 is the volume resistivity of conductive filler and Vc
and t are percolation threshold and critical exponent, respectively. Higher t values and lower
percolation thresholds correspond to well-dispersed high aspect ratio fillers [4].
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Figure 4-2 presents the percolation curve for compression-molded samples. Using percolation
theory, the percolation threshold and critical exponent of the compression-molded samples were
found to be 2.63 and 0.28 vol%, respectively. Compared to other studies on MWCNT/PC [19, 27-
30], our results show lower percolation threshold, which indicates better dispersion of MWCNT in
polymer matrix and less reduction in MWCNT aspect ratio during mixing.
Figure 4-2: Percolation curve for rectangular (compression-molded) samples of MWCNT/PC
composite.
Understanding the conduction mechanisms will allow us to determine applications for CPCs at
various concentrations. Figure 4-2 can be divided into three regions: 1) the region before
percolation at low concentrations, (2) the region where percolation occurs and (3) the region after
percolation. In the region before percolation, the MWCNTs are far from each other and the
conductance is limited by the polymer matrix which has resistivity on the order of 1015
-1017 Ω·cm.
The MWCNTs and the insulating gap, i.e. polymers, between them can be modeled as a capacitor
[31]. When the concentration of MWCNTs is very low, the insulating gaps between the capacitor
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plates, i.e. MWCNTs, are very large and the chance that electrons are transferred from one plate to
another is very low. When the mean gap width between MWCNTs is larger than 10 nm,
conductivity is the result of transport processes within the polymer host matrix [6]. By applying an
electric field, the insulative material starts to redistribute its charges (protons and electrons)
partially; this is called polarization. The higher the polarization, the higher are the permittivity and
the electrical conductivity [31]. In this case, polarized charges are bounded and cannot be easily
dislocated. According to Band Theory [32,33], only some electrons can get adequate energy to go
from the valence band to the conduction band. The gap between the valence band and the
conduction band is the forbidden zone. The higher the concentration of MWCNTs in polymers, the
lower is the gap width and the higher is the chance that electrons will pass the barrier.
By increasing MWCNT concentration, the gaps between the conductor materials (MWCNTs)
decrease. When the mean particle-particle distance goes below 10 nm, the dominant electron
transfer mechanism is internal field emission [34]. Internal field emission is a general term for
describing a number of processes in which the electrons have low probability of passing forbidden
zones [31-37]. In narrow insulating gaps between conductive fillers, very high field strength may
develop which is higher than the macroscopic voltage by a factor M that is the ratio of average size
of conducting aggregate to the average gap width [38,39]. This high field strength provides free
electrons sufficient energy to cross the insulative gap.
By increasing filler loading further, the filler particles get closer and eventually at percolation
threshold, the first network forms which lets the current pass through. In the second region, where
percolation occurs, the free electrons in conductive filler will play the role of charge carriers more
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dominantly due to direct contact between MWCNTs. Since these free electrons belong to the
conductive band [32], the resistivity of nanocomposite reduces by several orders of magnitude at
percolation threshold. After percolation, increasing the conductive filler content alters the volume
resistivity only marginally. In the third region, the region after percolation, two effects control the
conductivity: (1) the constriction resistance of contact spots and (2) tunneling resistance between
separated particles [40]. A Considerable amount of current dissipates at the contact spots between
the conductive fillers. After percolation, as the filler concentration increases, the clusters initiate
connections with each other to form a 3-D network which leads to increase in conductivity.
However, the constriction resistance restricts conductivity increase due to large number of contact
spots. Consequently, as demonstrated in Figure 4-2, constant resistivity at high concentrations was
achieved.
Figures 4-3(a-c) depict the percolation curve of compression-molded and injection-molded
samples. The percolation curve for compression-molded samples is presented in these figures to
better show the effect of alignment. For injection-molded samples, the percolation curve is
demonstrated for three different areas. As demonstrated in Figure 4-1(a), area 1 is the area near the
gate while areas 2 and 3 are the neck and runner parts, respectively. All the measurements for
injection-molded samples were carried out in directions both parallel and perpendicular to the flow.
In this article, parallel and perpendicular to the flow resistivities are denoted as and ,
respectively. As the size of four-pin probe used for characterization of conductive materials is larger
than the length of sample in the perpendicular to the flow direction, we were not able to measure
volume resistivity at high MWCNT concentrations. However, measuring volume resistivity at lower
concentrations, i.e. high resistivity, in the direction perpendicular to the flow was done employing
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the Keithley instrument. As confirmed in the following section by characterization methods, the
order of the degree of alignment is as following:
Area 3 > Area 2 > Area 1> Compression-molded samples
Greater alignment occurs due to higher levels of applied shear rate on the nanocomposite melt.
As can be seen in Figure 4-3, alignment of MWCNTs led to higher resistivity than compression-
molded samples (random distribution). Alignment of MWCNTs decreased the likelihood of
MWCNTs being adjacent or connected with each other. is higher than random distribution even
at high concentrations. Since alignment diminishes the likelihood of MWCNTs connection,
tunneling mechanism becomes significant after percolation in aligned samples. This means that in
aligned samples there may be lots of conductive pathways, which are near each other but not
connected.
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Figure 4-3: Percolation curve for rectangular (compression-molded) samples and injection-molded
samples (parallel and perpendicular to the flow direction) at (a) area 1, (b) area 2 and (c) area 3.
116
To investigate the above hypothesis, we applied the method introduced by Chakanov et al [38].
We applied very high voltage, 500 V, for very short time on aligned samples with different
concentrations and then measured resistivity at 10 V. Interestingly, it was observed that percolation
curve for aligned samples tended to the percolation curve for random distribution of nanofillers.
This thought to be a result of the dielectric breakdown of aligned injection-molded samples at high
electric field. Dielectric breakdown is irreversible damage that occurs due to high electric field and
is in the form of carbonization of polymer leading to formation of conductive pathways [31,38].
Compression-molded samples were also investigated for this effect and the changes were much
lower. We believe that changes in percolation curve when applying high voltage is due to high
electric field applied in small gaps between clusters that leads to dielectric breakdown making the
insulating gaps conductive. As explained before, the real voltage applied in the gaps is much larger
than the macroscopic voltage.
Figures 4-3(a-c) show that the electrical resistivity perpendicular to the flow is even higher than
electrical resistivity parallel to the flow. This anisotropy can be clarified using the concept that the
inherent resistance of a MWCNT is much lower than MWCNT-MWCNT contact resistance. Since
the current will need to cross less MWCNT-MWCNT contacts in the parallel direction compared to
the perpendicular direction, the resistivity and percolation threshold in the direction perpendicular
to the flow are higher.
In these injection-molded aligned samples, at high concentrations, resistivity decreases
marginally with increase in MWCNT volume fraction due to tunneling-conduction mechanism
transformation. For further investigation of the effect of alignment on the conduction mechanism,
the current-voltage characteristics were investigated for the composites at different concentrations
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of MWCNT in thickness direction (see Figure 4-4). Ohmic behavior is expected if the graphitic type
of conductivity exists in the composite [38,41,42]. According to Figure 4-4, the composite with
random distribution of MWCNT shows Ohmic behavior at around 1.5 wt% (R2 ≈ 1 for linear
regression), while in the injection-molded sample (area 3), Ohmic behavior is dominant at around
3.5 wt% (R2 ≈ 1 for linear regression).
Figure 4-4: Current-voltage characteristics of a) compression-molded sample, b) injection-molded
sample (area 3) in thickness direction. 1The measured current of composites holding 0.5 wt% of
MWCNT in Fig. 3(a) and 1.5 wt% of MWCNT in Fig. 3(b) have been multiplied by 50 to enable its
visualization in the plot.
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As previously explained, after percolation, tunneling mechanism is more significant in injection-
molded samples than compression-molded ones. Non-Ohmic behavior is due to increase in
probability of electron transfer through the insulative barrier with increase in electric field.
According to Figure 4-4, non-Ohmic behavior can be observed in aligned injection-molded sample
(area 3) at higher concentrations than compression-molded samples, which verifies that at high
concentrations, field emission mechanism is more dominant in aligned injection-molded samples
than compression-molded ones.
Table 4-1 shows percolation thresholds, critical exponents and correlation factors calculated
using percolation theory (see Equation 4-2) for the compression-molded samples and different areas
of dog-bone samples, corresponding to various alignments. According to Table 4-1, compression-
molded samples present higher critical exponent and lower percolation threshold than injection-
molded aligned samples owing to the higher probability of the connection between MWCNTs. By
increasing the alignment in injection-molded samples, the percolation threshold increases due to
reduced likelihood of connection. Critical exponent (t) is representative of conductivity increase
after percolation with increasing the filler content. The higher is the aspect ratio of filler, the larger
is the value of critical exponent [4]. Generally, high aspect ratio filler promotes the probability that
clusters will connect with each other to develop a 3-D network, which results in larger critical
exponents. Analogously, as evidenced in Table 4-1, by increasing the alignment, the critical
exponent decreases relating to a reduction in probability of connection of clusters after percolation.
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Table 4-1: Percolation thresholds, critical exponents and correlation factors for compression-
molded samples and injection-molded samples at different areas, corresponding to different
alignments.
Log (ρ0 (Ω·cm)) Vc t R2
Compression-
molded -1.81 0.0028 2.64 0.984
Injection-molded samples
Area 1 -0.6842 0.0064 2.52 0.9913
Area 2 -0.434 0.0083 2.38 0.9845
Area 3 +0.3035 0.0095 2.10 0.9945
4.5.2. Morphological Analysis
Figure 4-5(a) shows the SEM micrograph of the compression-molded sample of PC with 1.5
wt% MWCNT whereas Figures 4-5(b-c) show SEM images of aligned injection-molded sample
(area 3) in directions parallel and perpendicular to the flow, respectively. It is seen in Figure 4-5(a)
that MWCNTs are entangled to each other; however individual MWCNTs can be easily
distinguished. Analogous intertwined structures of MWCNTs have been reported in literature
[27,43,44]. The diameter seen in Figure 4-5(a) is larger than the diameter reported by Hyperion, 15-
50 nm, indicating that a polymer layer has been adsorbed on the MWCNT surface confirming good
adhesion between polymer and conductive filler. The bright dots observed throughout the PC matrix
are ascribed to the ends of the broken MWCNTs owing to their high conductivity.
Due to orientation of MWCNTs as a result of shear force, the microtomed sections in the flow
direction should exhibit more tube segments than sections cut perpendicular to the flow, which
120
should show more MWCNTs cross sections (bright spots). Possible appearances of cut surfaces in
flow-induced aligned samples were illustrated by Pötschke et al [27]. As can be seen in Figures 4-
5(b-c), for the sections parallel to flow, a lower number of bright spots, corresponding to MWCNTs
cross sections, can be observed than for sections perpendicular to the flow direction. These two
images confirm the partial alignment of MWCNTs in injection-molded samples.
Figure 4-5: SEM images of PC+1.5 wt% MWCNT. (a) compression-molded sample; (b) aligned
injection-molded sample (area 3), parallel to the flow direction; (c) aligned injection-molded sample
(area 3), perpendicular to the flow direction.
121
Figures 4-6(a-b) demonstrate the TEM micrographs of aligned injection-molded sample (area 3)
in directions parallel and perpendicular to the flow. As evidenced in Figure 4-6, the cut parallel to
the flow direction mostly shows MWCNT segments whereas the cut perpendicular to the flow
direction displays dark spots, corresponding to MWCNT cross sections. The MWCNTs are
uniformly dispersed as individual tubes in the whole polymer matrix without significant
agglomeration, which confirms our theory about low percolation threshold. It is worthwhile to
mention that applying high shear force also aids in MWCNTs deagglomeration. Due to the curved
structure of MWCNTs, some sections may be cut by the diamond knife or embedded in the polymer
matrix; therefore, the lengths visible in the TEM sections do not represent the whole length of
MWCNTs.
122
Figure 4-6: TEM micrograph of aligned injection-molded sample (area 3): a) Parallel to the flow
direction, b) Perpendicular to the flow direction.
4.5.3. Raman Spectroscopy
Raman spectroscopy was employed to verify MWCNT alignment at different sample areas. This
method counts on inelastic scattering of infrared light by molecules upon coming back to their
primary energy level after excitation [19]. Figure 4-7 shows Raman spectra of compression-molded
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sample and area 3 in the dog-bone sample corresponding to the lowest and highest degree of
alignment, respectively. Three bands can be observed in Raman spectra of PC/MWCNT, namely D,
G and G' bands. The D band is the most sensitive band to MWCNT alignment and corresponds to
sp2 hybridized graphitic structure. The G band relates to in-plane vibration of graphitic wall and is
less sensitive to MWCNT orientation than D band, and G' band is not sensitive to MWCNT
alignment [45]. The and parallel/perpendicular to the flow direction were utilized to
determine the degree of alignment. Table 4-2 summarizes the results obtained from Raman
spectroscopy of the compression-molded sample and various areas of the injection-molded sample.
As evidenced in Table 4-2, the intensity ratios for the compression-molded sample is near 1, which
shows no preferential alignment in the compression-molded sample. The intensity ratios and then
the alignment have the following order:
Area 3 > Area 2 > Area 1> compression-molded samples.
Figure 4-7: Raman spectra of PC/5 wt% MWCNT nanocomposites.
124
Table 4-2: Raman intensity ratios parallel/perpendicular to the flow direction of compression-
molded and injection-molded samples of PC/MWCNT.
Raman spectroscopy ratio parallel/perpendicular
Compression molding 1.042 1.026
Area 1 1.391 1.267
Area 2 1.559 1.378
Area 3 1.649 1.445
This result is in complete agreement with electrical conductivity data. According to Tables 4-
1and 4-2, the electrical resistivity increases with increase in alignment. Increasing alignment
decreases the chance of MWCNTs to contact with each other; therefore, volume resistivity and
percolation threshold increase while critical exponent decreases. For instance, area 3 with D band
intensity ratio of 1.649 has the highest alignment and percolation threshold of 0.95 vol%, while
compression-molded sample with D band intensity ratio of 1.042 shows a percolation threshold
around 0.28 vol%.
4.5.4. Electromagnetic Interference Shielding Measurements and Mechanism
Electromagnetic interference shielding effectiveness (EMI SE) is the ability of a material to
attenuate an incident electromagnetic wave and can be calculated using Equation 4-1. EMI SE
consists of three different mechanisms; namely reflection, absorption and multiple-reflection. When
an electromagnetic wave crosses a medium with different intrinsic impedance from the space in
which electromagnetic wave is propagating, a portion of electromagnetic wave is reflected from the
shielding material exterior surface. To reflect an electromagnetic wave, the shielding material
125
should have mobile charge carriers on the surface to interact with the incoming wave. It should be
considered that the first reflection from shielding material interior surface is a part of reflection
mechanism, too. The portion of electromagnetic wave that penetrates through the material can be
attenuated through absorption mechanism. The absorption loss is more important for magnetic
fields than electric fields since the electric field is mostly reflected at the first interface [12].
Generally, the penetrating wave leads to formation of electric/magnetic dipoles in the material.
Electric/magnetic dipoles can attenuate the electromagnetic field but their effect is less than the
effect of mobile charge carriers in the shielding material. Multiple-reflection is the third mechanism
which has negative effect on EMI SE [7,10,12]. This mechanism requires large surface or interfacial
area in the shield. Multiple-reflection represents internal reflections within the shielding material.
Several equations have been developed to quantify the contributions of reflection and absorption
to EMI SE of monolithic materials [8-10]. The shieldings by reflection and absorption are given by
the following equations:
( ) (4-3)
( ) (4-4)
where R and A are shielding by reflection and absorption, respectively; C1 and C2 are constants; f is
frequency; µ is magnetic permeability; σ is electrical conductivity; and t is thickness of shielding
material. Strictly speaking, these equations are not complete for filler-added materials since they do
not account for filler inherent specifications and volume fractions. In addition, the effect of
multiple-reflection is disregarded in these equations. Additionally, after the percolation threshold,
adding more filler increases EMI SE while the percolation curve reaches a plateau. According to
126
Equations 4-3 and 4-4, both absorption and reflection increase with increase in conductivity;
absorption has a direct relation with (fµ) while reflection decreases with increase in (fµ).
Figure 4-8 depicts EMI SE of compression-molded samples as a function of MWCNT
concentration and shielding plate thickness. Figure 4-8 shows the average values over the X-band
frequency range. As shown in this figure, EMI SE increases with both MWCNT concentration and
plate thickness. The increase in EMI SE by increase in MWCNT content is due to formation of
more networks of conductive filler and larger source of free electrons in the material that can
interact with incoming electromagnetic wave. Increase in MWCNT concentration leads to growth in
both conductivity and EMI SE; accordingly, it has been concluded that increase in EMI SE is due to
increase in conductivity. However, it is worthwhile to note that conductivity needs connectivity
while EMI SE does not [5,7]. According to Figure 4-8, EMI SE increases with increase in sample
thickness, which is due to higher amount of conductive filler that interact with the incoming
electromagnetic wave.
127
Figure 4-8: EMI SE of MWCNT/PC compression-molded samples as a function of MWCNT
concentration and shielding plate thickness.
To investigate the effect of thickness on EMI SE more precisely, the contributions of absorption
and reflection to EMI SE as a function of MWCNT concentration and material thickness were
inspected (Figure 4-9). Both reflection and absorption increase with increase in MWCNT
concentration and shielding material thickness. According to Equation 4-4, there is a direct relation
between absorption and material conductivity and shielding material thickness. Figure 4-9(a) shows
that absorption increases with both MWCNT concentration and shielding material thickness.
Actually, increasing conductive filler concentration and shielding material thickness is equivalent to
having more mobile charge carriers and more conductive filler networks that can attenuate the
penetrating wave.
As shown in Figure 4-9(b), the reflection also increases with both MWCNT content and
shielding material thickness. There is a direct relation between reflection and MWCNT
concentration because there are more mobile charge carriers on the surface at higher concentrations.
128
Figure 4-9: (a) Contribution of absorption, (b) Contribution of reflection to the overall EMI SE for
compression-molded samples as a function of shielding material thickness and MWCNT
concentration.
However, the relation between reflection and shielding material thickness is more sophisticated
and depends on factors such as conductive filler concentration and shape, shielding material skin
depth and the distance between fillers in polymer medium [10]. The measured shielding by
129
reflection is the sum of reflected wave from shielding material exterior and interior surfaces,
reflected wave from filler surface area and multiple-reflection effect. Increasing the shielding
material thickness increases the amount of filler reflecting surface area. The increase in filler
surface area in the shield can have two effects on the contribution of reflection to shielding: (1) it
can increase the reflection coefficient by increasing the reflecting surface area provided by
nanofiller and (2) it can decrease the reflection coefficient by blocking and reflecting back the
reflected waves from shielding material interior surface area and other filler surface area (multiple-
reflection effect).
Multiple-reflection effect decreases the chance of reflected waves from shielding material
interior surface and other filler surface area to reach exterior surface of the shielding material and to
join to total reflected wave. It is worthwhile to mention that the effect of multiple-reflection is
negligible if the contribution of absorption to EMI SE is more than 10 dB or the shielding material
thickness is larger than its skin depth. According to Figure 4-9(b), it can be seen that the positive
effect of thickness increase (more filler reflecting surface area) on reflection dominates its negative
effect (multiple-reflection effect); therefore, reflection increases with increase in thickness for the
range of concentrations studied.
4.6. Conclusions
Electrical resistivity measurements showed that increasing the alignment of nanotubes in
MWCNT/PC composites significantly reduces the likelihood of contact between MWCNTs.
Accordingly, higher percolation thresholds and lower critical exponents were achieved at greater
MWCNT alignments. At the same filler loading, higher electrical resistivity was observed in the
130
direction perpendicular to the flow relative to the direction parallel to the flow at all areas of the
dog-bone samples. Verifying Ohm’s law after percolation showed that the field emission
mechanism is much more dominant in injection-molded aligned samples than those with random
distribution of MWCNT. Characterization methods like SEM, TEM and Raman spectroscopy
confirmed higher orientation in areas with larger electrical resistivities.
For the samples with random distribution of MWCNT, shielding by reflection and absorption
increased with increase in MWCNT concentration and shielding material thickness. Increase in
shielding by absorption through increasing MWCNT concentration and shielding material thickness
is expected due to greater conductive filler content and higher conductivity. However, increase in
shielding effectiveness by reflection with increasing thickness indicates that the positive effect of
thickness increase (more filler reflecting surface area) on reflection is dominant over its negative
influence (multiple-reflection) for the range of concentrations studied.
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Chapter 5
Comparative Study of Electromagnetic Interference Shielding Properties of
Injection Molded versus Compression Molded Multi-walled Carbon
Nanotube/Polystyrene Composites*
5.1. Presentation of the Article
This article is concerned with comparing the electrical properties of injection molded versus
compression molded MWCNT/PS composites over the X-band frequency range in terms of
MWCNT alignment, i.e., electrical conductivity, EMI shielding and dielectric properties.
Unavoidable flow-induced alignment of MWCNTs in injection molding process was the stimulation
to investigate effects of MWCNT alignment on the electrical properties of MWCNT/polymer
composites. To the best of our knowledge, this study is the first one in the area investigating the
effects of MWCNT alignment on EMI shielding and dielectric properties and detailing the
mechanisms behind.
The information obtained from the experimental design of 5.00 wt% MWCNT/PS composites in
chapter 3 were used to select three processing conditions, with maximum possible variation in
MWCNT alignment, to make MWCNT-aligned composites at different MWCNT concentrations.
Accordingly, EXPs #11, 12 and 14 in the experimental design correspond to EXPs # 2, 3 and 1 in
this article, respectively. The electrical properties of injection molded composites were compared
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with those of compression molded composites, where MWCNTs were randomly distributed. The
results revealed that the injection molded composites showed poorer electrical properties than the
compression molded composites. This observation was related to inferior conductive network
formation arising from MWCNT alignment. As the electrical properties of the compression molded
samples were superior to those of the injection molded samples, it can be concluded that in injection
molding process molding conditions and mold design should be performed so as to obtain random
distribution of MWCNTs.
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Comparative Study of Electromagnetic Interference Shielding Properties of
Injection Molded versus Compression Molded Multi-walled Carbon
Nanotube/Polystyrene Composites
Mohammad Arjmand1, Thomas Apperley
2, Michal Okoniewski
2, Uttandaraman Sundararaj
1
1Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Canada 2Department of Electrical and Computer Engineering, University of Calgary, Calgary, Canada
5.2. Abstract
This study compares electromagnetic interference (EMI) shielding properties of injection molded
versus compression molded multi-walled carbon nanotube / polystyrene (MWCNT/PS) composites,
i.e., properties such as EMI shielding effectiveness (EMI SE), electrical conductivity, real
permittivity and imaginary permittivity. The injection molded (MWCNT-aligned) samples showed
lower EMI shielding properties than compression molded (randomly distributed MWCNT) samples,
that was attributed to lower probability of MWCNTs contacting each other due to MWCNT
alignment. The compression molded samples showed higher electrical conductivity and lower
electrical percolation threshold than the injection molded samples. The compression molded
samples at MWCNT concentrations of 5.00 and 20.0 wt% showed real permittivity 2 times and
imaginary permittivity 5 times greater than the injection molded samples. The EMI SE for the
compression molded samples at MWCNT concentrations of 5.00 and 20.0 wt% was 15.0 and 30.0
dB, respectively, significantly greater than EMI SE for the injection molded samples. Lower EMI
SE for the injection molded samples was ascribed to lower electrical conductivity, real permittivity
(polarization loss) and imaginary permittivity (Ohmic loss). Comparison of the EMI shielding
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properties of the compression molded versus injection molded samples confirmed that EMI
shielding does not require filler connectivity; however it increases with filler connectivity.
5.3. Introduction
Electromagnetic interference (EMI) occurs when undesirable signals superimpose upon a signal
of interest. These signals may originate from a device used as a transmitter or from a device that is
not supposed to transmit but has parts that transmit in a certain frequency range. EMI effects can
range from interruption of operation to degradation of electronics or electrical equipments [1].
Accordingly, EMI has become a significant technical challenge given the rapid development of
electronic devices, such as laptops, cell phones, weather radars, TV picture transmitters, and the
like. [2-7].
To reduce EMI issues, appropriate agencies such as CISPR (Comité International Spécial des
Perturbations Radioélectriques) have applied regulations for electromagnetic compatibility (EMC)
of electronic enclosures. EMC means that a device does not influence itself or other devices by its
emissions and these standards must be met or exceeded for commercial electronics. Considering
EMC regulations, an EMI shielding effectiveness (EMI SE) of at least 30 dB, which corresponds to
shielding of 99.9% of incident radiation, i.e., 0.1% is transmitted, is regarded commercially as an
adequate level of shielding for many applications [1, 7].
Recently, conductive filler/polymer composites (CPCs) have attracted a great deal of interest to
be used for EMI shielding applications due to their light weight, low cost, resistance to corrosion
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and design flexibility [8,9]. Different conductive fillers have been embedded into polymer matrices
in order to get CPCs with desired EMI shielding properties, such as EMI SE, electrical conductivity,
real permittivity and imaginary permittivity [8-14]. Among different conductive fillers used in
CPCs, carbon nanotubes (CNTs) have fascinated researchers due to their unique electronic structure
and extraordinary properties. CNTs are capable of carrying a high current density (ca. 106-10
9
A/cm2) without observable oxidative damage, which makes them versatile fillers for composites
used for electrical and EMI shielding applications [15, 16].
Structural perfection, aspect ratio, dispersion, distribution and alignment of CNTs are among the
most important parameters that have great influence on the EMI shielding properties of
CNT/polymer composites. It has been shown that for greater metallic behavior, higher aspect ratio
and better dispersion of CNTs, there is an enhancement in the EMI SE of CNT/polymer composites
[4, 5, 17]. This enhanced EMI SE may be due to higher amount of available interacting mobile
charge carriers leading to more energy dissipation. Nevertheless, the effects of alignment of CNTs
on electrical conductivity, real permittivity and imaginary permittivity and their relationship with
EMI SE is a concept that has not been well comprehended and requires further investigation.
Hitherto, to the best of our knowledge, only a few papers have been dedicated to the study of effects
of alignment on electrical conductivity of CNT/polymer composites [18-21]; moreover,
investigations discussing effects of CNT alignment on the other EMI shielding properties are even
more rare [22, 23].
The inevitable flow-induced alignment of CNTs in injection molding process was the inspiration
to investigate effects of CNT alignment on the EMI shielding properties of CNT/polymer
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composites. Most of investigations on the EMI shielding properties of CPCs have been devoted to
compression molded samples which have randomly distributed conductive filler; this has led to
results that are not applicable to injection molded samples where the conductive filler is aligned
[3,5,9]. Therefore, this study compares the EMI shielding properties of injection molded versus
compression molded multi-walled carbon nanotube / polystyrene (MWCNT/PS) composites in
terms of MWCNT alignment.
5.4. Experimental
5.4.1. Composite Preparation
A masterbatch of 20.0 wt% MWCNT in PS was obtained in the form of cylindrical pellets from
Hyperion Catalysis International, Cambridge, MA, USA. The length and diameter of pellets were
2.50 ± 0.25 mm and 3.50 ± 0.25 mm, respectively. The masterbatch was diluted with a neat PS
(Styron® 610) kindly supplied by Americas Styrenics LLC, to prepare the nanocomposite samples
of various loadings.
Prior to mixing, all the materials were dried at 50 °C for at least 4 hr under vacuum. The
composites with different concentrations of MWCNT were prepared using a 25 mm Coperion ZSK
co-rotating intermeshing twin-screw extruder operated at barrel temperature of 200 °C and extruder
speed of 150 rpm. At these conditions, the residence time was 2 min. Considering the density of
neat PS and MWCNT are 1.06 and 1.75 g/cm3, respectively; the concentrations of prepared
nanocomposites in terms of weight percent and volume percent are presented in Table 5-1.
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Table 5-1: The concentrations of the prepared nanocomposites in terms of weight percent and
volume percent.
5.4.2. Experimental Design and Composite Molding
In our previous studies [23, 24], a series of injection molding experiments were carried out on a
5.00 wt% MWCNT/PS composites using a two-level, four-factor factorial design to study the
impact of four processing parameters, i.e., mold temperature (C1), melt temperature (C2),
injection/holding pressure (C3) and injection velocity (C4) on the volume resistivity of the molded
samples. The results showed that the melt temperature had the greatest impact on volume resistivity
of the molded samples followed by the injection velocity, while the impacts of mold temperature
and injection/holding pressure were insignificant. It was also shown that the volume resistivity had
a direct relationship with MWCNT alignment [21, 23]. A lower melt temperature and higher
injection velocity impose greater shear stress on the polymer matrix melt which leads to greater
MWCNT alignment [18, 19].
Accordingly, knowing the tremendous influence of melt temperature and injection velocity on
MWCNT alignment and volume resistivity of MWCNT/PS nanocomposites, three different
injection molding experiments, called EXP #1, 2 and 3, with various levels of melt temperature and
injection velocity were employed to make samples with various MWCNT alignments at different
MWCNT concentrations. Levels of processing parameters used in EXP #1, 2 and 3 are shown in
Table 5-2. The samples fabricated using EXP #1, 2 and 3 were used to investigate the effects of
MWCNT Concentration (wt%) 0.1 0.30 0.50 1.0 2.00 3.50 5.00 10.0 20.0
MWCNT Concentration (vol%) 0.06 0.18 0.30 0.60 1.22 2.15 3.09 6.30 13.2
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MWCNT alignment on the EMI shielding properties of MWCNT/PS composites at different
MWCNT concentrations.
Table 5-2: Levels (set points) of the processing parameters used in the injection molding
experiments (EXPs). The processing parameters are mold temperature (C1), melt temperature (C2),
injection/holding pressure (C3) and injection velocity (C4).
An injection molding machine (Boy 12A) was used to inject MWCNT/PS nanocomposite melt
into a 1-cavity mold. The melt temperature and injection velocity set points were selected to be as
large as possible within the limitations of the injection molding machine and the recommended
processing conditions of neat PS. Constant holding and cooling times of 8 and 10 seconds,
respectively, were applied for all runs. The holding pressure was set to be the same as the injection
pressure for all the experiments.
Figure 5-1 shows a schematic of the mold design employed in the injection molding process and
the mold dimensions are listed in Table 5-3. The thickness of cavity was 2.0 mm. To make sure that
all the cavities were filled simultaneously, the runner and gate dimensions were balanced using
CFD software (MoldflowTM
, Ver. 5) for neat PS. A detailed description of the designed mold and
injection molding machine can be found in our previous study [23]. To have a better understanding
of the effects of MWCNT alignment on the EMI shielding properties, the EMI shielding properties
of the injection molded samples were compared with those of the compression molded samples. A
Processing Parameters
C1 (°C) C2 (°C) C3 (bar) C4 (mm.sec-1
)
EXP #1 60 215 100 240
EXP #2 60 240 100 240
EXP #3 60 240 100 24
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Carver compression molder (Carver Inc., Wabash, IN) was used to make the samples of randomly
distributed MWCNTs, with the same dimensions as the injection molded samples. The compression
molding process was performed at 210 °C for 10 min under 38 MPa pressure.
Figure 5-1: A schematic view of the designed mold.
Table 5-3: Dimensions of the designed mold.
5.4.3. EMI Shielding Properties Measurements
In order to cover a large range of electrical conductivities (10-15
-10+1
S·cm-1
), three measurement
systems were used to determine the electrical conductivity of the molded samples. For samples with
an electrical conductivity of larger than 10-2 S·cm
-1, the electrical conductivity measurements were
conducted according to the ASTM 257-75 standards using a Loresta GP resistivity meter (MCP-
T610 model, Mitsubishi Chemical Co., Japan) connected with a four-pin probe, which was used so
Parameter Value (mm)
a 22.86
b 10.16
c, d 1
e 2
f 10
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that the effect of contact resistance did not impact the measurements. The inter-pin spacing was 5.0
mm and the pin diameter was 2.0 mm. For an electrical conductivity between 10-2
and 10-5 S·cm
-1, a
Keithley 617 (Keithley instruments, USA) connected to an 804B disk & ring test fixture (Electro-
Tech systems, Inc., USA) was employed. The samples were placed between the elastomeric disk
electrode with 10.0 mm diameter and base copper plate. A conductive rubber was also used to
decrease the contact resistance between the samples and base copper plate. For electrical
conductivities less than 10-5 S·cm
-1, the measurements were performed using a Keithley 6517A
electrometer connected to a Keithley 8009 test fixture (Keithley instruments, USA). The applied
voltage for all the conductivity measurements was 10 V. The samples were rectangular with the
dimensions of 22.86 mm × 10.16 × 2.0 mm. The conductivity measurements were carried out in
directions both parallel to the flow and thickness. For each datum, the conductivity of at least three
specimens was measured.
EMI SE, real electrical permittivity and imaginary electrical permittivity were also found for the
samples used in the conductivity experiments. EMI shielding properties measurements in the X-
band (8.2 – 12.4 GHz) frequency range were carried out in a WR-90 rectangular waveguide using
an Agilent programmable network analyzer (PNA) (Model E8364B). To measure the EMI shielding
properties, the MWCNT/PS samples were placed inside the cross section of the rectangular
waveguide. The S-parameters of each sample were recorded and used to calculate EMI SE and also
real permittivity and imaginary permittivity via the Nicolson-Ross-Weir method [25, 26]. EMI SE is
expressed in dB and is the logarithm of the ratio of the incident power to the transmitted power [7,
21]. Contributions of reflection and absorption to overall EMI SE were also calculated using
relevant incident and transmitted power for each mechanism.
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5.4.4. Morphological Characterization and Raman Spectroscopy
In order to investigate the morphology of the molded nanocomposites, TEM observations were
performed using a Hitachi H-7650. Prior to the TEM observations, the samples were
ultramicrotomed using a diamond knife at room temperature.
In order to obtain detailed information about the alignment of MWCNTs, Raman spectra were
collected from the compression molded and injection molded samples. A Renishaw spectrometer
equipped with an inVia Raman microscope was employed to obtain the Raman spectra. Excitation
was provided by a near-infrared (NIR) laser beam (785 nm) in regular mode. Measurements were
performed at two normal orientations of the laser beam with respect to the flow direction in the
samples. The MWCNT alignment was determined by comparing the Raman spectra obtained from
parallel and perpendicular directions.
5.5. Results and Discussion
5.5.1. Morphological Analysis and Raman Spectroscopy
TEM micrographs of an injection molded sample (EXP #1) and a compression molded sample
of 5.00 wt% MWCNT/PS composite are shown in Figures 5-2(a) and 5-2(b), respectively. As
shown in these images, the MWCNTs are uniformly dispersed as individual tubes in the polymer
matrix without any significant agglomeration, which shows that MWCNTs were well dispersed
during mixing via twin-screw extrusion. It should be mentioned that applying a high shear force in
the injection molding process also contributed to a better dispersion of MWCNTs.
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Figure 5-2: TEM micrographs of (a) an injection molded sample (EXP #1), and (b) a compression
molded sample. Both are 5.00 wt% MWCNT/PS composite. The white arrow in (a) indicates the
flow direction.
The aligned segments of MWCNTs can be easily seen in Figure 5-2(a), where the white arrow
shows the direction of MWCNT alignment. Due to the curved structure of MWCNTs, some
portions of MWCNTs may be embedded in the PS matrix; as a result, the observable length in
Figure 5-2(a) may not be the entire length of MWCNTs. Possible appearances of cut surfaces in
MWCNT-aligned samples have been illustrated by Pötschke et al. [27]. Figure 5-2(b) shows the
random distribution of MWCNTs in the PS matrix. No distinct direction can be observed for the
alignment of MWCNTs.
The Raman spectroscopy technique was applied to the 5.00 wt% MWCNT/PS composites.
Two significant characteristics in the Raman spectra of the MWCNT/polymer composites are the D
band (disorder band), and the G band (graphite band). The disorder-induced D band, related to sp2
hybridized graphitic structure, is a more responsive band to the MWCNT alignment than G band,
which corresponds to in-plane vibration of the graphitic wall. The DPA/DPE and GPA/GPE
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parallel/perpendicular to the flow direction were used to determine the degree of MWCNT
alignment [28]. Table 5-4 presents the results from the Raman spectra of the compression molded
samples and injection molded samples. The compression molded samples demonstrated intensity
ratios near one, which proves a random distribution of MWCNTs; whereas, the EXP #1 of the
injection molded samples showed the highest intensity ratios, correlated to the greatest MWCNT
alignment. Greater alignment occurs due to higher levels of applied shear rate on the nanocomposite
melt. According to Table 5-4, the order of the intensity ratios, and consequently MWCNT
alignment, from the highest to the lowest were EXP #1 > EXP #2 > EXP #3 > compression molded
samples. Considering the different morphologies of the injection molded and compression molded
samples and Raman spectroscopy results, partial alignment of MWCNTs in the injection molded
samples is confirmed.
Table 5-4: Raman intensity ratios parallel/perpendicular to the flow direction of the compression
molded and injection molded samples of 5.00 wt% MWCNT/PS composites.
5.5.2. Comparison of Electrical Conductivity and EMI SE of Injection Molded versus Compression
Molded MWCNT/PS Composites
The formation of a conductive network in CPCs can be clarified with the concept of the
electrical percolation threshold [28, 29]. Electrical percolation is the concentration at which the
Raman spectroscopy ratios parallel/perpendicular
DPA/DPE GPA/GPE
Compression Molding 1.01 1.01
EXP #1 1.66 1.51
EXP #2 1.53 1.44
EXP #3 1.35 1.27
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filler particles come into contact with each other and form a continuous conductive pathway in the
composite, which allows the electrical current to pass through the sample.
Figure 5-3(a) shows the percolation curves of the injection molded (parallel to the flow) samples
and compression molded samples. As can be seen in Figure 5-3(a), the injection molded (MWCNT-
aligned) samples showed a lower electrical conductivity and higher percolation threshold than
compression molded (randomly distributed MWCNTs) samples. Considering Figure 5-3(a) and
Raman spectroscopy results, it can be stated that the greater the alignment of MWCNTs, the lower
the electrical conductivity and the higher the percolation threshold of CPCs. As a matter of fact, the
alignment of MWCNTs decreased the likelihood of MWCNTs being connected with each other,
which resulted in a lower electrical conductivity and higher percolation threshold [21, 30].
At high concentrations of MWCNT, increasing MWCNT content resulted in relatively lower
enhancement in the electrical conductivity than the enhancement in electrical conductivity at
MWCNT concentrations around percolation threshold. The constriction resistance at the MWCNT’s
contact spots restricted the increase in electrical conductivity at high MWCNT concentrations [31].
As can be seen in Figure 5-3(a), all the percolation curves reach a plateau at high MWCNT
concentrations with approximately the same electrical conductivity for all the samples. However,
the plateau is reached at different MWCNT concentrations for each sample: compression molded
samples reach a plateau at 5.00 wt%, EXP #3 at 10.0 wt%, EXP #2 at 15.0 wt% and EXP# 1 at 20.0
wt%. These results suggest that the MWCNT networks were well formed in both the injection
molded and compression molded samples at high MWCNT concentrations. It should be mentioned
that the percolation curves of the parallel to the flow and thickness directions showed almost the
148
same trend, however the parallel to the flow electrical conductivities were around one order of
magnitude higher than those in the thickness direction for most of MWCNT concentrations.
Therefore, there must be a better conductive network formation in the direction parallel to the flow
[23, 32].
Figure 5-3: (a) Electrical conductivity and (b) EMI SE for the compression molded and injection
molded samples of the MWCNT/PS composites as a function of MWCNT concentration. The data
related to the electrical conductivity of the injection molded samples were achieved in parallel to
the flow direction. The thickness of all the samples was 2.0 mm.
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Figure 5-3(b) shows the EMI SE of the compression molded and injection molded samples as a
function of MWCNT concentration. The EMI SE results are the average values over the X-band
frequency range. The EMI SE increased with increase in MWCNT concentration for both the
compression molded and injection molded samples. The EMI SE for the compression molded
samples at 5.00 wt% was 25.4 dB while it increased to more than 63.6 dB at 20.0 wt%. This
increase was mostly due to greater amount of interacting mobile charge carriers at higher MWCNT
concentrations [2, 4]. However, it was interesting to observe that the EMI SE in the injection
molded samples was significantly lower than compression molded samples, particularly at high
MWCNT concentrations. For instance, the injection molded samples made by EXP #1 at 5.00 and
20.0 wt% MWCNT exhibited EMI SE around 15 and 30 dB, respectively, lower than compression
molded samples. Even more interesting was the fact that all the samples had the same volume
resistivity at 20.0 wt% but exhibited significantly different EMI SE. For example, although the
compression molded sample and EXP# 1 sample both had electrical conductivity around 1.0 S·cm-1
at 20.0 wt% MWCNT, the EMI SE was double for the compression molded sample versus the EXP
#1 sample. This discrepancy between the compression molded and injection molded samples
suggests that the compression molded samples had more extensive connected MWCNT network
than the injection molded samples.
Figures 5-4(a) and 5-4(b) show the EMI SE of the compression molded and injection molded
(EXP #1) samples, respectively, at different MWCNT concentrations as a function of
electromagnetic wave frequency. The MWCNT concentrations shown in Figure 5-4 cover low,
medium and high MWCNT loadings. EXPs #2 and #3 in the injection molding process
demonstrated the same trend as EXP #1.
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The EMI SE for the compression molded samples showed a slight ascending trend with increases
in frequency. For instance, the compression molded samples at 2.00 wt% of MWCNT showed an
EMI SE of around 4.5 dB at 8.2 GHz, which increased to 7.2 dB at 12.4 GHz. The differences
between the EMI SEs at low and high frequencies increased with increases in MWCNT
concentration. The compression molded samples at 20.0 wt% of MWCNT showed an EMI SE of
57.4 dB at 8.2 GHz, which increased to 66.4 dB at 12.4 GHz. For the injection molding process, the
composites showed EMI SE performances that were almost independent of the frequency.
Considering 30 dB as an adequate level of shielding for commercial applications, it can be claimed
that compression molded and injection molded samples at 10.0 and 20.0 wt% of MWCNT,
respectively, satisfy the requirement for commercial EMI shielding applications over the whole X-
band frequency range.
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Figure 5-4: EMI SE, as a function of electromagnetic wave frequency, of (a) the compression
molded samples and (b) injection molded (EXP #1) samples. The thickness of all the samples was
2.0 mm.
In view of Figure 5-3(b) and Raman spectroscopy results, it can be claimed that the CPCs with
greater MWCNT alignment showed lower EMI SE. Besides, it can be interpreted that greater
MWCNT connectivity in the compression molded samples caused higher EMI SE in the
compression molded samples than injection molded samples. These results are in agreement with
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researchers who believe that EMI shielding does not require filler connectivity; however, it
increases with filler connectivity [2, 4, 33, 34].
5.5.3. Effects of MWCNT Alignment on Shielding Mechanisms in MWCNT/PS Composites
To investigate effects of MWCMT alignment on EMI shielding more precisely, the contributions
of the reflection and absorption to the overall EMI SE were examined as a function of MWCNT
concentration and alignment (Figures 5-5(a) and 5-5(b)). The difference in the connectivity of the
MWCNTs in the compression molded and injection molded samples is the key to interpret the
reflection and absorption mechanisms.
To shield by reflection, the material must have mobile charge carriers (electrons or holes) to
interact with incoming electromagnetic wave [4]. As shown in Figure 5-5(a), the shielding by
reflection increased with increase in MWCNT concentration, which can be related to higher amount
mobile charge carriers at greater MWCNT concentrations. The shielding by reflection was 2.7 dB at
2.00 wt% of MWCNT, which increased to 7.8 dB at 20.0 wt% of MWCNT. As there is a direct
relationship between electrical conductivity and shielding by reflection in conductive monolithic
materials [6, 35], a higher shielding by reflection was expected in the compression molded CPCs
than injection molded ones. However, as shown in Figure 5-5(a), it is surprising to observe that the
shieldings by reflection of the compression molded and injection molded samples were almost the
same at different MWCNT concentrations. The similar shieldings by reflection in the compression
molded and injection molded samples may be explained by comparable area of the MWCNT
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surface projection normal to the incoming electromagnetic wave whether the MWCNTs were
aligned or not.
Figure 5-5(b) shows that the shielding by absorption increased with increase in MWCNT
concentration and decrease in MWCNT alignment. Increase in absorption by increasing MWCNT
concentration is a well-established concept, which has been ascribed to higher amount of mobile
charge carriers at higher MWCNT concentrations [2, 4, 5]. According to Figure 5-5(b), unlike the
shielding by reflection, the shielding by absorption was highly sensitive to MWCNT alignment. The
samples made by EXP #1, which had the greatest MWCNT alignment, showed the lowest
absorption; whereas, the compression molded samples demonstrated the highest absorption. These
results suggest that shielding by absorption is related to MWCNT connectivity. Accordingly,
electrical parameters influencing shielding by absorption and related to filler connectivity must be
investigated.
Higher absorption at greater MWCNT concentrations can also be related to higher imaginary
permittivity (Ohmic loss) and higher real permittivity (polarization loss) of the MWCNT/PS
composites [17]. Figures 5-6(a) and 5-6(b) show the real permittivity and imaginary permittivity,
respectively, of the compression molded and injection molded samples as a function of MWCNT
concentration. The absolute values of the permittivities of the compression molded samples shown
in Figure 5-6 are of the same order of magnitude as those reported in previous studies that were also
performed in the X-band [36-39].
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Figure 5-5: Contributions of (a) reflection and (b) absorption to the overall EMI SE for the
compression molded and injection molded samples of the MWCNT/PS composites as a function of
MWCNT concentration. The thickness of all the samples was 2.0 mm.
Real permittivity in MWCNT/polymer composites originates from a large number of
nanocapacitors, i.e., MWCNTs acting as electrodes and insulative polymeric layer acting as
dielectric material, and also presence of structural defects (polarization centers) in MWCNTs [40-
43]. Increasing MWCNT concentration led to an increase in both the number of nanocapacitors and
155
polarization centers, leading to higher real permittivity (charge polarization). Additionally,
increasing MWCNT concentration led to a decrease in the thickness of insulative polymeric gaps
between MWCNTs leading to greater electronic polarization of polymeric layer [44]. Therefore,
increasing MWCNT concentration led to greater polarization loss giving rise to shielding by
absorption. Imaginary permittivity of MWCNT/PS composites resulting from Ohmic loss also
contributed significantly to shielding by absorption, where energy is dissipated by movement of
mobile charge carriers along the MWCNTs. Increasing MWCNT concentration resulted in an
increase in number of dissipating mobile charge carriers leading to higher imaginary permittivity
and, consequently, higher shielding by absorption.
As can be observed in Figure 5-6(a), the real permittivity in the compression molded samples
was greater than injection molded samples. The large difference between the real permittivities of
the compression molded and injection molded samples suggests that the polarization of PS matrix
contributed significantly to the real permittivity in the X-band. In narrow insulative gaps between
conductive fillers, very high field strength may build up, which is higher than the macroscopic field
strength by a factor of M (i.e., M is the ratio of the average size of the conducting MWCNT
aggregates to the average gap width) [10, 45, 46]. This high field strength contributes significantly
to the electronic polarization of the polymer matrix. Since the chance of MWCNTs contacting each
other in the compression molded samples was greater, the insulative gaps of the polymer were
thinner, leading to a higher electric field and greater electronic polarization of the PS matrix.
Therefore, the compression molded samples showed greater real permittivity than injection molded
samples. Higher polarization of the PS matrix played an important role in greater polarization loss
and increased shielding by absorption in the compression molded samples.
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Figure 5-6: (a) Real permittivity and (b) imaginary permittivity for the compression molded and
injection molded samples of the MWCNT/PS composites as a function of MWCNT concentration.
Figure 5-6(b) shows that the imaginary permittivity of the injection molded samples was lower
than that of the compression molded samples and the amount of this difference increased
tremendously with increase in MWCNT concentration. For instance, at 5.00 wt%, the imaginary
permittivities of the compression molded and injection molded (EXP #1) samples were 36 and 5,
respectively, while they increased to 502 and 94, respectively, at 20.0 wt%. The higher imaginary
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permittivity of the compression molded samples may be related to the greater network formation,
i.e., there was greater MWCNT connectivity in these samples. Therefore, the electrons had a greater
mean free path in which to move according to the direction of electric field in each half cycle and,
consequently, could dissipate more electrical energy [47]. Greater electrons’ mean free path at
lower MWCNT alignments can be related to lower thickness of insulative gaps between MWCNTs,
i.e., greater MWCNT network formation, leading to larger conduction current via mechanisms of
conduction, hopping and tunneling. The greater electrical energy loss by free electrons in the
compression molded samples, due to greater electrons’ mean free path, contributed to higher
shielding by absorption in these samples.
5.6. Conclusions
Comparing the EMI shielding properties of the injection molded samples, where the conductive
filler is aligned, versus compression molded samples, which have randomly distributed conductive
filler, of MWCNT/PS composites showed that MWCNT alignment had an adverse effect on EMI
shielding properties. Inferior EMI shielding properties, i.e., properties such as EMI SE, electrical
conductivity and real and imaginary permittivities of the injection molded samples relative to the
compression molded samples were related to MWCNT alignment which led to poorer MWCNT
network formation.
The injection molded samples showed lower electrical conductivity and higher percolation
threshold than compression molded samples due to MWCNT alignment. The lower real permittivity
for the injection molded samples was ascribed to lower electric field in insulative gaps between
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MWCNTs, due to lower chance of MWCNT connectivity, resulting in lower electronic polarization
of polymeric layer. The lower imaginary permittivity of the injection molded samples was also
attributed to inferior MWCNT network formation, where the smaller mean free paths of the
conduction electrons led to decreased energy dissipation. Lower EMI SE for the injection molded
sample than the compression molded samples was related to lower electrical conductivity, real
permittivity (polarization loss) and imaginary permittivity (Ohmic loss) leading to lower
electromagnetic wave energy dissipation. Comparison of the EMI shielding properties of
composites with different states of conductive network formation verified that EMI shielding does
not require filler connectivity; however it significantly increases with filler connectivity.
Since the electrical conductivity, EMI SE, real permittivity and imaginary permittivity of the
compression molded samples were greater than those of the injection molded samples, it can be
concluded that designing a mold for injection molding that achieves a random MWCNT distribution
is crucial in order to attain high EMI shielding properties.
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Chapter 6
An Innovative Method to Reduce the Energy Loss of Conductive Filler/Polymer
Composites for Charge Storage Applications*
6.1. Presentation of the Article
This article introduces conductive filler alignment, induced by injection molding process, as an
innovative technique to improve the dielectric properties of MWCNT/PS composites for charge
storage applications. The information obtained from the experimental design of 5.00 wt%
MWCNT/PS composites in chapter 3 were used to select three processing conditions, with
maximum possible variation in MWCNT alignment, to make MWCNT-aligned composites at
different MWCNT concentrations. Accordingly, EXPs #11, 12 and 14 in the experimental design
correspond to EXPs # 2, 3 and 1 in this article, respectively. In order to prove the positive impact of
MWCNT alignment on dielectric properties, the dielectric properties of the injection molded
composites, where MWCNTs were aligned, were compared with those of the compression molded
composites, where MWCNTs were randomly distributed. The results demonstrated that MWCNT
alignment reduced the dissipation factor through deteriorating the conductive network formation. It
is notable to mention that the findings regarding the positive influence of MWCNT alignment,
induced by injection molding machine as a mass production setup, on the dielectric properties of
MWCNT/PS composites is of great industrial significance.
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An Innovative Method to Reduce the Energy Loss of Conductive Filler/Polymer
Composites for Charge Storage Applications
Mohammad Arjmanda, Mehdi Mahmoodi
b, Simon Park
b, Uttandaraman Sundararaj
a
a Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Canada
b Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, Canada
6.2. Abstract
In this study, we present conductive filler alignment as a novel approach to reduce the
dissipation factor of conductive filler/polymer composites and to widen the typically narrow
concentration window near the percolation threshold, which is used to tune the dielectric properties,
i.e., real permittivity and imaginary permittivity. The effects of multi-walled carbon nanotube
(MWCNT) alignment on the dielectric properties for MWCNT/polystyrene composites in the X-
band (8.2 to 12.4 GHz) were investigated by comparing the dielectric properties of injection molded
samples, where MWCNTs were aligned, versus compression molded samples, where MWCNTs
were randomly distributed. Raman spectroscopy technique was employed to verify partial
alignment of MWCNTs in the injection molded samples. The compression molded samples showed
an insulator-conductor transition window at 0.50 - 2.00 wt% of MWCNT, whereas the injection
molded samples showed a significantly wider transition window at 3.50 - 10.00 wt% of MWCNT.
Broader insulator-conductor transition window reduces challenges and risks in manipulating
conductive filler/polymer composites around the percolation threshold to regulate the dielectric
properties. Moreover, it was observed that MWCNT alignment improved the dielectric properties
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by reducing the dissipation factor. For instance, at MWCNT concentrations of 0.50 and 2.00 wt%,
the compression molded samples showed dissipation factors of 0.06 and 0.59, respectively, while
the injection molded samples presented the dissipation factors considerably lower and equal to 0.01
and 0.18, respectively. This study shows that injection molding process, as an industrial technique,
can be employed to improve significantly the dielectric properties of conductive filler/polymer
composites for charge storage applications.
6.3. Introduction
Consumers are demanding lighter weight and smaller electronic devices in today’s marketplace;
therefore, printed circuit board (PCB) space is becoming a scarce resource. Accordingly, industry is
now moving toward replacing large surface mounted capacitors with miniature capacitors
embedded into PCBs [1,2]. The material requirements for embedded capacitors include high real
permittivity, low leakage current (imaginary permittivity) and process compatibility with PCBs.
Recently, conductive filler/polymer composites (CPCs) have been proposed as candidates for
embedded capacitors, due to their high real permittivity, low cost, light weight and process
compatibility with PCBs [3-5]. According to the percolation theory, a high real permittivity with a
low leakage current in CPCs can only be achieved at filler loadings very close to the percolation
threshold [6]. This poses a challenge to use CPCs as charge storage materials, because of the
typically narrow insulator-conductor transition window around the percolation threshold. Two
strategies are usually used to avoid the direct contact between conductive fillers and thereby
obstruct the insulator-conductor transition: (1) covering the surface of conductive fillers with an
insulative layer [3,7]; and, (2) introducing secondary particles as insulating barriers between
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conductive fillers [8,9]. Both of these methods require additional processing steps to obtain the final
composite and may also adversely affect the real permittivity.
Herein we present conductive filler alignment as a novel approach to reduce imaginary
permittivity and to hinder the sharp insulator-conductor transition in CPCs. In this study, a multi-
walled carbon nanotube/polystyrene (MWCNT/PS) composite, as a typical CPC, was employed to
investigate the effects of conductive filler alignment on dielectric properties, i.e., real permittivity
and imaginary permittivity. MWCNTs were chosen as the conductive fillers, due to their unique
electronic structure and growing industrial usage. The alignment of MWCNTs was induced by
applying a high shear/drag force using an injection molding machine. The results showed that the
MWCNT alignment led to a tremendous decrease in the dissipation factor of the molded samples
arising from lower probability of the MWCNTs neighboring or contacting each other. The
alignment of the MWCNTs also impeded the sharp increase in the imaginary permittivity near the
percolation threshold. This feature of the MWCNT-aligned samples broadens the narrow filler
concentration window near the percolation threshold in CPCs, which is used to adjust the dielectric
properties.
6.4. Material and Methods
6.4.1. Materials
A masterbatch of 20.0 wt% MWCNT in PS was obtained from Hyperion Catalysis International,
Cambridge, MA, USA. According to the supplier, the MWCNTs were vapor grown and typically
had an outer diameter of 10-15 nm wrapped around a hollow core with a diameter of 5 nm. The
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lengths ranged between 1 and 10 µm, while their density was approximately 1.75 g/cm3. The
masterbatch was diluted with a pure PS (Styron® 610), with a density of 1.06 g/cm
3, kindly
provided by Americas Styrenics LLC, in order to prepare nanocomposite samples with different
MWCNT concentrations. Prior to mixing, all the materials were dried at 50 °C for at least 4 hr
under vacuum. The composites with different concentrations of MWCNT were prepared employing
a 25 mm Coperion ZSK co-rotating intermeshing twin-screw extruder operated at a barrel
temperature, extruder speed and residence time of 200 °C, 150 rpm and 2 min, respectively.
Considering the densities of neat PS and MWCNTs, the concentrations of prepared nanocomposites
in terms of weight percent and volume percent are presented in Table 6-1.
Table 6-1: The concentrations of the prepared nanocomposites in terms of weight percent and
volume percent.
6.4.2. Composite Molding
Our previous investigations showed that there is a direct relationship between MWCNT
alignment and volume resistivity [10,11]. This relationship and also the inverse relationship
between volume resistivity and imaginary permittivity were the inspirations for the investigation of
the effects of MWCNT alignment on the dielectric properties. Our previous studies showed that the
melt temperature followed by the injection velocity had the greatest impact on the MWCNT
alignment of the injection molded MWCNT/PS nanocomposites [12]. On the other hand, the mold
temperature and injection/holding pressure did not significantly affect the MWCNT alignment.
MWCNT Concentration (wt%) 0.1 0.30 0.50 1.0 2.00 3.50 5.00 10.0 20.0
MWCNT Concentration (vol%) 0.06 0.18 0.30 0.60 1.22 2.15 3.09 6.30 13.2
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Given the remarkable effects of the melt temperature and injection velocity on the MWCNT
alignment in the injection molded MWCNT/PS nanocomposites, the injection molding process was
carried out at the lowest possible melt temperature, i.e., 215 °C and the highest possible injection
velocity, i.e., 240 mm.sec-1
to obtain the MWCNT/PS nanocomposites with the greatest MWCNT
alignment. The mold temperature and injection/holding pressure employed were 60 °C and 100 bar,
respectively. The injection molded samples were used to investigate the effect of MWCNT
alignment on the dielectric properties.
An injection molding machine (Boy 12A) was used to inject the MWCNT/PS nanocomposite
melt into a rectangular cavity. The cavity was fed with an edge gate and had dimensions of 22.86 ×
10.16 × 2.0 mm. A detailed description of the designed mold and injection molding machine can be
found in our previous studies [11,12]. To achieve a more comprehensive picture of the effects of
MWCNT alignment on the dielectric properties, the dielectric properties of the aligned injection
molded samples were compared with those of the compression molded samples, where MWCNTs
were randomly distributed. A Carver compression molder (Carver Inc., Wabash, IN) was employed
to fabricate the compression molded samples with the same dimensions as the injection molded
samples. The compression molding process was carried out at 210 °C for 10 min under 38 MPa
pressure.
6.4.3. Morphological Analysis
In order to investigate the morphology of the compression and injection molded samples,
transmission electron microscopy (TEM) was employed. The TEM analysis of the nanocomposites
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was carried out on ultramicrotomed sample sections using a Tecnai TF20 G2 FEG-TEM (FEI,
Hillsboro, Oregon, USA) at a 200 kV acceleration voltage with the standard single-tilt holder. The
samples were ultramicrotomed to sections of ~ 70 nm at room temperature using a Leica EM UC6.
The images were captured by a Gatan UltraScan 4000 CCD (Gatan, Pleasanton, California, USA) at
2048x2048 pixels.
6.4.4. Determination of Carbon Nanotube Length Distribution
The investigations of carbon nanotube length distribution using a TEM procedure was developed
by Krause et al. [13].The evaluation of nanotube length distribution was conducted for the as-
extruded, compression molded and injection molded composites containing 2.00 and 10.0 wt% of
MWCNT to examine the effects of both the processing and the MWCNT concentration (viscosity)
on length distribution.
In order to assess the nanotube length distribution in the composites, chloroform was used to
dissolve the PS matrix at room temperature for 4 hr without any additional treatment, until only
MWCNTs remained. All dispersions were treated with a low energy ultrasonic equipment for 3
min, and then one drop of dispersion was placed on a copper grid and dried at air. A transmission
electron microscope was used to take images of the collected MWCNTs. Measurement of the length
of the MWCNTs was carried out for 500 individual MWCNTs using the ImageJ software. In order
to measure the length of very long nanotubes, several images were stiched together.
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6.4.5. Raman Spectroscopy
Raman spectroscopy was employed to verify the alignment of MWCNTs in the injection molded
samples. A Renishaw spectrometer equipped with an inVia Raman microscope was used to obtain
the Raman spectra from the molded samples. The samples were excited by a near-infrared (NIR)
laser beam in regular mode. The Raman intensity measurements were performed at two normal
orientations of the laser beam with respect to the flow direction, i.e., parallel and perpendicular, to
obtain information about the MWCNT alignment.
6.4.6. Electrical and Dielectric Properties Measurements
The in-flow volume resistivity measurements were performed using two different setups. For the
samples with a volume resistivity of less than 104 Ω·cm, the measurements were conducted
according to the ASTM 257-75 standards, using a Loresta GP resistivity meter (MCP-T610 model,
Mitsubishi Chemical Co., Japan) connected with a four-pin probe. For a volume resistivity of more
than 104 Ω·cm, the measurements were performed using a Hiresta-UP resistivity meter (MCP-
HT450 model, Mitsubishi Chemical Co., Japan) connected with a piece of URS probe.
The thickness volume resistivity measurements were conducted employing two different
systems. For the samples with a volume resistivity of less than 104 Ω·cm, the volume resistivity
measurements were conducted using a Keithley 2400 sourcemeter, while for a volume resistivity
more than 104 Ω·cm, a Keithley 6517A electrometer was used. Both types of Keithleys were
connected to a Keithley 8009 test fixture (Keithley Instruments, USA). The applied voltage for all
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the resistivity measurements was 10 V. For each datum, the resistivity of at least three specimens
was measured.
To evaluate the potential of CPCs as charge storage materials for high-frequency range
applications, it is essential to characterize the high-frequency dielectric properties of CPCs.
Accordingly, the dielectric properties in the X-band (8.2 to 12.4 GHz) frequency range were
investigated in this study. The dielectric properties in the X-band are important for many military
and commercial applications, e.g., Doppler, weather radars and TV picture transmitters [14]. The
complex permittivity measurements in the X-band were carried out in a WR-90 rectangular
waveguide using an Agilent programmable network analyzer (Model E8364B). The S-parameters of
each sample were recorded one at a time and used to calculate the complex permittivity with the
Nicolson-Ross-Weir method [15,16]. For each datum, the S-parameters of at least three specimens
were measured. It should be mentioned that in the dielectric spectroscopy, the electromagnetic wave
interacted with the samples in the thickness direction; therefore, all the dielectric properties reported
in this article belong to the thickness direction.
6.5. Results and Discussion
6.5.1. Morphological Analysis and Raman Spectroscopy
TEM micrographs of an injection molded sample and a compression molded sample of 5.00 wt%
MWCNT/PS composite are shown in Figures 6-1(a) and 6-1(b), respectively. In these images,
individual MWCNTs are clearly observable without any significant agglomeration, indicating that
the MWCNTs were disentangled and dispersed well during mixing via twin-screw extrusion.
172
The aligned segments of MWCNTs can be easily seen in Figure 6-1(a), where the white arrow
shows the direction of MWCNT alignment. Due to the curved structure of MWCNTs, the
MWCNTs were not ideally aligned in the flow direction; however, Figure 6-1(a) confirms partial
alignment of MWCNTs in the injection molded samples. Figure 6-1(b) shows that MWCNTs were
randomly distributed in the compression molded samples, and no distinct direction can be observed
for the alignment of MWCNTs.
Figure 6-1: TEM micrographs of (a) an injection molded sample, and (b) a compression molded
sample. Both are 5.00 wt% MWCNT/PS composite. The white arrow in (a) indicates the flow
direction.
In order to obtain more detailed information about the alignment of MWCNTs, a Raman
spectroscopy technique was employed. The Raman spectra of MWCNT/polymer composites
provide two important features: the D band (disorder band) and G band (graphite band). The D
band, correlating to disorder in the sp2 hybridized graphitic structure, is more responsive to the
alignment of MWCNTs than the G band, which corresponds to the in-plane vibration of the
graphitic wall [17] Higher intensity ratios of and (parallel/perpendicular to the flow
direction) correspond to higher MWCNT alignment. The injection molded samples showed
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and ratios equal to 1.66 and 1.51, respectively, whereas the compression molded samples
exhibited and of 1.01 and 1.01, respectively. From the Raman spectroscopy results, it
can be claimed that the MWCNTs were randomly distributed in the compression molded samples,
while they were partially aligned in the injection molded samples.
6.5.2. The Effects of Processing and Molding on MWCNT Length Distribution
Figure 6-2 presents the length distribution of MWCNTs for the as-extruded, injection molded
and compression molded MWCNT/PS composites with 2.00 wt% MWCNT loading. The MWCNT
length distribution for the as-extruded composites ranged from less than 100 nm to 2400 nm.
Considering the length distribution of MWCNTs in the masterbatch, i.e. 1-10 µm, it is obvious that
twin-screw extrusion significantly shortened the length of MWCNTs by applying a high shear rate.
Investigating the MWCNT length distribution of the composites showed that the as-extruded,
compression molded and injection molded composites presented average MWCNT lengths of 417,
411 and 363 nm, respectively. All the composites showed standard deviations equal to 230 nm.
These results show that the compression molding process did not affect the MWCNT length while
the injection molding process led to a 12% reduction in the MWCNT length. This reduction can be
attributed to the shear rate applied in the injection molding process.
To investigate the effect of MWCNT concentration, which correlates to melt viscosity, on the
MWCNT length distribution, MWCNT length distributions of 2.00 and 10.0 wt% MWCNT/PS
composites were compared with each other. It was observed that 10.0 wt% MWCNT/PS composites
174
showed a very similar length distribution to that of 2.00 wt% MWCNT/PS composites, indicating
that MWCNT concentration did not impact the MWCNT length distribution.
Figure 6-2: Effects of molding on length distribution of MWCNTs in 2.00 wt% MWCNT/PS
composites.
6.5.3. The Effects of MWCNT Alignment and Length on the Dielectric Properties
In addition to a high dielectric permittivity, CPCs used as capacitors must show a low leakage
current. In general, the leakage current of a CPC has an inverse relationship with its volume
resistivity; therefore, investigating the effect of the MWCNT alignment on the volume resistivity
will aid us in comprehending the effect of the MWCNT alignment on the leakage current. Figure 6-
3 depicts the volume resistivity of the compression molded and injection molded samples in the
flow and thickness directions as a function of MWCNT concentration. Despite the MWCNT
alignment, the volume resistivity of the injection molded samples showed very similar trends in
175
both the in-flow and thickness directions. This fact can be related to comparable MWCNT network
formation in both directions, arising from the curved structure of the MWCNTs. For both injection
molded and compression molded samples, the volume resistivity showed a steep decline at a
particular concentration (percolation threshold) and a decaying trend at higher MWCNT
concentrations which can be ascribed to the formation of additional conductive networks in the
composites.
As shown in Figure 6-3, the volume resistivity and percolation threshold in the injection molded
samples were higher than those in the compression molded samples. The percolation threshold in
the compression molded samples obtained from the percolation theory was 0.70 wt%; however, it
was interesting to observe that the percolation threshold in the injection molded samples was about
six times greater than the percolation threshold in the compression molded samples. The higher
volume resistivity and percolation threshold in the injection molded samples can be attributed to the
lower probability of MWCNTs neighboring or contacting each other due to MWCNT alignment
[10,18]. Lower aspect ratio of the MWCNTs in the injection molded samples can also be considered
as another reason for higher volume resistivity of the injection molded samples. Other studies
showed that decrease in MWCNT aspect ratio can lead to lower conductivity and higher percolation
threshold, due to significant decrease in chance of MWCNTs contacting each other [19,20].
Another important characteristic depicted in Figure 6-3 is that the steep decline in the volume
resistivity of the injection molded samples around the percolation threshold was muted in
comparison to that of the compression molded samples. The logarithm of the volume resistivity for
the compression molded samples at 0.50, 1.00 and 2.00 wt% of MWCNT are 13.3, 8.7 and 5.5,
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respectively, showing an insulator-conductor transition at the concentration window of 0.50 - 2.00
wt%. The logarithm of the volume resistivity for the injection molded samples at the MWCNT
concentrations of 3.50, 5.00 and 10.00 wt% are 13.0, 10.2 and 3.6, respectively, roughly indicating
an insulator-conductor transition at the concentration window of 3.50 - 10.0 wt%. The broader
concentration window of the insulator-conductor transition in the injection molded samples can be
attributed to MWCNT alignment and a lower MWCNT aspect ratio in the injection molded
samples. This provides a significant advantage for aligned samples for use as capacitors.
Figure 6-3: Volume resistivity for the compression molded and injection molded samples of the
MWCNT/PS composites as a function of MWCNT concentration.
As mentioned previously, a high real permittivity with a low leakage current in CPCs can only
be achieved at filler loadings very close to the percolation threshold. The increased real permittivity
observed in CPCs near the percolation threshold results from the formation of a large number of
nanocapacitors, i.e., conducting clusters isolated by thin layers of polymer [14]. These
nanocapacitors enable CPCs to store large amount of charges. The insulator-conductor transition
177
that occurs in CPCs at the percolation threshold leads to a drastic variation in the volume resistivity
and imaginary permittivity; thereby it prohibits using CPCs as charge storage materials above the
percolation threshold. Accordingly, there is a very narrow concentration window near the
percolation threshold for high aspect ratio fillers, such as MWCNTs, to adjust the dielectric
properties. In contrast, for samples with significant MWCNT alignment, there is a moderate
descending trend of the volume resistivity around the percolation threshold; thus it can be claimed
that the MWCNT alignment can provide a wider concentration window around the percolation
threshold to regulate the dielectric properties.
Figures 6-4(a) and 6-4(b) show the imaginary and real permittivities, respectively, of the
compression molded and injection molded samples as a function of MWCNT concentration in the
frequency range of the X-band. The absolute values of the complex permittivities of the
compression molded samples, shown in Figure 6-4, are of the same order of magnitude as those
reported previously in the X-band [21, 22]. As can be observed in Figure 6-4(a), the imaginary
permittivity increased with increase in the MWCNT concentration for both types of samples. In
general, the imaginary permittivity of CPCs can result from the polarization loss, e.g., distortional
and interfacial, and/or Ohmic loss. Increase in the MWCNT concentration is equivalent to an
increase in the amount of mobile charge carriers (Ohmic loss) and the number of nanocapacitors
(polarization loss), both of which can account for an enhancement in the imaginary permittivity.
Figure 6-4(a), however, shows that the imaginary permittivities of the injection molded samples
were significantly lower than those of the compression molded samples. The imaginary
permittivities for the compression molded samples at the MWCNT concentrations of 0.50, 1.00 and
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2.00 wt% (compression molding transition window) were 0.21, 1.16 and 6.14, respectively;
whereas, the imaginary permittivities for the injection molded samples at these concentrations were
significantly lower and equal to 0.02, 0.12 and 0.35, respectively. Lower imaginary permittivity of
the injection molded samples relative to the compression molded samples can be related to inferior
network formation arising from MWCNT alignment and lower MWCNT aspect ratio.
The differences between the imaginary permittivities of the compression molded and injection
molded samples were even greater at higher MWCNT concentrations. The compression molded
samples at MWCNT concentrations of 3.50, 5.00 and 10.00 wt% (the injection molding transition
window) showed the imaginary permittivities equal to 17.52, 36.24 and 189.85, respectively, while
the injection molded samples showed the imaginary permittivities equal to 1.48, 5.01 and 42.63,
respectively. By increasing the MWCNT concentration, the imaginary permittivities of the
compression molded samples grew more than those of the injection molded samples; therefore, it
can be claimed that the movement scales of the electrons in each half cycle of the alternating field
in the compression molded samples, because of the greater network formation, must have grown
considerably more than those of the injection molded samples. This is what led to a very large
difference between the imaginary permittivities for the two types of samples at high MWCNT
concentrations. Moreover, the higher applied field between the conductive fillers in the compression
molded samples provided more chances for the electrons to pass through the polymer layer in the
form of conduction current. This fact originated from higher probability of the conductive fillers
neighboring each other and thus lower thickness of the insulative gaps. This resulted in more energy
loss for the compression molded samples.
179
Figure 6-4: (a) Imaginary permittivity and (b) real permittivity, as a function of MWCNT
concentration, for the compression molded and injection molded samples of the MWCNT/PS
composites in the X-band.
Figure 6-4(b) shows that the real permittivity increased with increases in the MWCNT
concentration. The enhancement of the real permittivity with an increased MWCNT concentration
is well-established, and is attributed to an increase in number of nanocapacitors and a decrease in
180
the thickness of insulative polymer gaps (nanodielectrics), both of which contributed to greater
charge polarization. Moreover, it is believed that the real permittivity of MWCNT/polymer
composites is influenced by the polarization within the MWCNTs, and this also contributes to the
greater real permittivity at higher MWCNT concentrations [2,14].
As presented in Figure 6-4(b), it was surprising to observe that the MWCNT alignment had an
adverse influence on the real permittivity. At MWCNT concentrations of 0.50, 1.00 and 2.00 wt%
(the compression molding transition window), the compression molded samples showed the real
permittivities equal to 3.58 and 5.06 and 10.37, respectively, while the real permittivities of the
injection molded samples were 3.21, 3.70 and 5.24, respectively. At the MWCNT concentrations of
3.50, 5.00 and 10.00 wt% (the injection molding transition window), the compression molded
samples showed the real permittivities equal to 15.20, 21.25 and 41.30, respectively; whereas the
injection molded samples exhibited the real permittivities equal to 8.22, 12.29, and 15.52,
respectively. The difference between the real permittivities of the compression molded and injection
molded samples can be ascribed to the greater probability that MWCNTs are in close proximity to
each other in the compression molded samples. In the narrow insulative gaps between the
conductive fillers, there may be a buildup of very high field strength, which is higher than the
macroscopic field strength by a factor of M (i.e., the ratio of the average size of the conducting
MWCNT aggregates to the average gaps width) [23, 24]. This high field strength significantly
contributed to the electronic polarization of the PS matrix. In the compression molded samples, the
insulative gaps of the polymer were thinner leading to a higher applied field and greater electronic
polarization of the PS matrix. Therefore, the compression molded samples showed greater real
permittivity than the injection molded samples.
181
Chin et al. [25] measured the dielectric properties of MWCNTs in three distinct arrangements
with respect to incident electromagnetic wave, namely parallel, perpendicular and random
distributions. Their results showed that dielectric properties were very high when the
electromagnetic wave oscillated along the axis of the nanotubes and dropped significantly when it
oscillated normal to the axis of MWCNTs. Random distribution of MWCNTs showed an
intermediate value due to the combination of vertical and horizontal arrangements of MWCNTs
from the electromagnetic wave. Higher dielectric properties in the longitudinal direction were
related to field induced intra-band transition.
The data presented in this article are in a very good agreement with the data reported by Chin et
al. As verified by the TEM images, the MWCNTs in the injection molded samples showed mostly
perpendicular arrangements with respect to the incident electromagnetic wave. However, the
compression molded samples, due to the random distribution of MWCNTs, showed a combination
of vertical and horizontal arrangements of MWCNTs. Therefore, the inferior dielectric properties of
the injection molded samples, relative to the compression molded samples, can also be justified
considering different MWCNT arrangements.
MWCNT alignment reduced both the real permittivity and imaginary permittivity; therefore, it is
necessary to evaluate the overall impact of MWCNT alignment on the dielectric properties. Hence,
the dissipation factors (imaginary permittivity/real permittivity) of the compression molded and
injection molded samples at different MWCNT concentrations were compared with each other. As
can be observed in Figure 6-5, the MWCNT alignment decreased the dissipation factors at all the
MWCNT concentrations, demonstrating its positive effect on the dielectric properties. For instance,
182
at the MWCNT concentrations of 0.50, 1.00 and 2.00 wt%, the dissipation factors of the
compression molded samples were 0.06, 0.23 and 0.59, respectively, while the injection molded
samples presented the dissipation factors significantly lower and equal to 0.01, 0.03 and 0.07,
respectively. These results prove that the positive effect of the MWCNT alignment on reducing the
dissipative energy dominated its adverse effect on decreasing the capacitive energy.
Figure 6-5: Dissipation factors for the compression molded and injection molded samples of the
MWCNT/PS composites as a function of MWCNT concentration in the X-band.
6.6. Conclusions
In conclusion, it was shown MWCNT alignment, induced by an injection molding machine, in
the MWCNT/PS composites positively influenced the dielectric properties. MWCNT alignment
widened the typically narrow concentration window near the percolation threshold, which is used to
tune the dielectric properties, thereby reducing challenges and risks in manipulating CPCs as charge
storage materials. It was also shown that the MWCNT alignment reduced both the real permittivity
183
and imaginary permittivity; nonetheless, the positive effect of the MWCNT alignment on reducing
the imaginary permittivity overshadowed its negative effect of reducing the real permittivity. The
positive impact of MWCNT alignment on the dielectric properties presented in this article is
industrially significant because injection molding is one of the most common fabrication methods
for polymer nanocomposites and it can be used to control and tune dielectric properties.
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multiwalled carbon nanotubes from iron-phthalocyanine polymer and their novel dielectric
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Xu JW, Wong M, and Wong CP. Super high dielectric constant carbon black-filled polymer
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Dang ZM, Yao SH, Yuan JK, and Bai JB. Tailored Dielectric Properties based on
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[7]
Czerw R, Guo ZX, Ajayan PM, Sun YP, and Carroll DL. Organization of polymers onto
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Yao SH, Yuan JK, Dang ZM, and Bai JB. High dielectric performance of three-component
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Shen Y, Lin YH, Li M, and Nan CW. High dielectric performance of polymer composite
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Arjmand M, Mahmoodi M, Gelves GA, Park S, and Sundararaj U. Electrical and
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Mahmoodi M, Arjmand M, Sundararaj U, and Park S. The electrical conductivity and
electromagnetic interference shielding of injection molded multi-walled carbon
nanotube/polystyrene composites. Carbon 2012; 50: 1455-64.
[13] Krause B, Villmow T, Boldt R, Mende M, Petzold G, Potschke P. Influence of dry grinding
in a ball mill on the length of multiwalled carbon nanotubes and their dispersion and
percolation behavior in melt mixed polycarbonate composites. Compos Sci Tech 2011; 71:
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Jiang MJ, Dang ZM, Bozlar M, Miomandre F, and Bai JB. Broad-frequency dielectric
behaviors in multiwalled carbon nanotube/rubber nanocomposites. J Appl Phys 2009; 106:
084902-6.
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Nicolson AM and Ross GF. Measurement of intrinsic properties of materials by time-
domain techniques. IEEE Trans Instrum Meas 1970; IM19: 377-82.
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Weir WB. Automatic measurement of complex dielectric-constant and permeability at
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Abbasi S, Carreau PJ, and Derdouri A. Flow induced orientation of multiwalled carbon
nanotubes in polycarbonate nanocomposites: Rheology, conductivity and mechanical
properties. Polymer 2010; 51: 922-35.
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Behnam A, Guo J, and Ural A. Effects of nanotube alignment and measurement direction on
percolation resistivity in single-walled carbon nanotube films. J Appl Phys 2007; 102:
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threshold, dispersion state, and aspect ratio of carbon nanotubes. Adv Funct Mater 2007; 17:
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[20] Kim D, Yun Y, Bak H, Cho S, Jin H-J. Aspect ratio control of acid modified multiwalled
carbon nanotubes. Current Appl Phys 2010; 10: 1046-52.
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Watts PCP, Ponnampalam DR, Hsu WK, Barnes A, and Chambers B. The complex
permittivity of multi-walled carbon nanotube-polystyrene composite films in X-band. Chem
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*Submitted to Polymer Engineering and Science
186
Chapter 7
Broadband Dielectric Properties of Multi-walled Carbon Nanotube/Polystyrene
Composites*
7.1. Presentation of the Article
This paper is oriented to study the dielectric properties of MWCNT/polymer composites over the
broadband frequency range, i.e., 10-1
– 106 Hz. The dielectric properties inspected in this article
include real permittivity, imaginary permittivity and AC conductivity, which are analyzed in both
insulative and conductive regions over the whole frequency range. The broadband dielectric
properties presented in this article are of great significance from two aspects:
(1) This article can be used as an introductory section to understand the mechanisms behind
the broadband dielectric properties of CPCs. In other words, this article provides the
readers with general information about the dielectric spectroscopy of CPCs and helps the
researchers to design new morphologies for desired dielectric properties. For instance, the
innovative technique presented in chapter 8 to obtain enhanced broadband dielectric
properties was designed according to the information obtained in this article.
(2) As EMI shielding properties are linked to dielectric properties, obtaining the broadband
dielectric properties can provide the researchers with a notable insight to predict the
broadband EMI shielding properties of CPCs.
187
Broadband Dielectric Properties of Multi-walled Carbon Nanotube/Polystyrene
Composites
Mohammad Arjmand, Uttandaraman Sundararaj
Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Canada
7.2. Abstract
This study investigates the dielectric properties of multi-walled carbon nanotube
(MWCNT)/polystyrene composites over the broadband frequency range, i.e., 10-1 – 10
6 Hz. The
results showed that the real permittivity and imaginary permittivity increased remarkably with
increased MWCNT concentration. For instance, at 100 Hz, the real permittivity and imaginary
permittivity of the pristine PS was 2.71 and 0.01, respectively, which increased to 5.22×104 and
3.28×107 at 3.50 wt%, respectively. The increase of the real permittivity was related to the
formation of a large number of nanocapacitor structures, i.e., MWCNTs as nanoelectrodes and
polymer matrix as dielectric material, i.e., interfacial polarization. The increase in the imaginary
permittivity with MWCNT loading was attributed greater number of dissipating charges,
enhanced conductive network formation and boosted polarization loss arising from interfacial
polarization. It was also observed that the real and imaginary permittivities were frequency-
independent in the insulative region, whereas they decreased drastically with frequency in the
conductive region. The descending trend of real permittivity with frequency in the conductive
region was related to charge polarization relaxation; whereas, the reduction of imaginary
permittivity with frequency was attributed to lower Ohmic loss and polarization loss.
188
7.3. Introduction
Driven by the ever-growing demand for versatile microelectronics with increased
functionality, high performance and cost-effectiveness, the new and distinctive solution of
system-in-package (SiP) has been proposed to meet these requirements [1]. SiP is an assembly of
several types of chips, such as logic, memory and passive, in a package that performs as a unique
system [2-4].
In a typical SiP, discrete passives outnumber the active integrated circuits by several times
and occupy more than 70% of the area of printed circuit boards (PCBs) [3]. Among the passive
components, capacitors dominate in terms of numbers and occupied surface areas; therefore,
capacitors have become the major challenge in the development and miniaturization of SiPs.
Embedded capacitors have, thus, been introduced as a breakthrough in the size reduction and
performance enhancement of SiPs. Embedded capacitors have some other advantages over
currently used surface-mounted capacitors, such as decreased number of discrete capacitors,
decreased number of solder joints, and improved design options [4].
Polymers filled with ferroelectric particles have drawn great interest as embedded capacitors
due to inherent advantages, including process compatibility with PCBs, mechanical flexibility,
high adhesion strength and ability to be molded [5-9]. However, the current ferroelectric-
polymer composites fall significantly short of the growing requirements for advanced
applications. In order to achieve a satisfactory real permittivity, a large amount of ferroelectric
filler is required, which results in the reduction of adhesion strength and mechanical properties
[10, 11]. This poses challenges, as well as opportunities, for the development of novel embedded
capacitors. Accordingly, conductive filler/polymer composites (CPCs) have been proposed as
189
alternatives to address the drawbacks of ferroelectric/polymer composites [12]. High real
permittivity in CPCs is related to the formation of a large number of nanocapacitors, i.e.,
conductive nanofiller as nanoelectrode and polymer matrix as nanodielectric [13].
Different conductive fillers, such as carbon black, gold, silver and nickel nanoparticles, and
more recently carbon nanotubes (CNTs), have been used to fabricate CPCs for charge storage
applications [14-18]. Among the various conductive fillers, CNTs have been envisioned as
revolutionary conductive fillers for charge storage applications, due to their large surface area
and excellent electrical, thermal and mechanical properties. These fascinating properties are
great stimulation to inspect the dielectric properties of MWCNT/polymer composites for charge
storage applications. Furthermore, obtaining the broadband dielectric properties can provide the
researchers with a notable insight to predict broadband EMI shielding properties of CPCs [19].
Accordingly, this study is devoted to investigating the broadband dielectric properties of
MWCNT/polystyrene (PS) composites and detailing the mechanisms behind. Moreover, the
results presented in this article shed light onto the relationships between conductive network
formation, DC conductivity, AC conductivity and expected dielectric properties.
7.4. Experimental
7.4.1. Materials and Composite Preparation
Polystyrene (Styron® 610) with a density of 1.06 g/cm
3 and a melt flow index of 10.0 g/10
min (200 °C/5 kg) was kindly provided by Americas Styrenics LLC. The MWCNTs (NanocylTM
NC7000) were obtained from Nanocyl S.A. (Sambreville, Belgium). According to the
190
manufacturer, the MWCNTs were produced with the catalytic carbon vapor deposition (CCVD)
process and had an average diameter of 9.5 nm, a length of 1.5 μm and a surface area of 250-300
m2/g. Before processing, all the materials were dried at 50 °C for 4 hr under vacuum.
Nanocomposites with different concentrations of MWCNTs, i.e., 0.02, 0.10, 0.20, 0.30, 0.50,
1.00, 2.00 and 3.50 wt%, were produced through a solution mixing technique. In this technique,
nanocomposites with various MWCNT loadings were produced by mixing different volumes of
100 mg/ml PS/N,N-dimethylformamide (DMF) solution and 0.66 mg/ml MWCNT/DMF
suspension. Each mixture was stirred for 15 min and then ultrasonicated for 30 min in a
sonication bath (VWR, Model 150HT, 480 W, 50 Hz). The two mixtures were then combined
and stirred for an additional 10 min. Next, the suspension was dripped into a large amount of
methanol (MeOH), where the volume ratio of MeOH to DMF was approximately three to one.
Upon contact of the suspension with the MeOH, the PS chains retracted and precipitated
instantly, due to their insolubility in MeOH. The retracted chains entrapped the MWCNTs and
prevented them from reagglomeration. The final mixture was filtered and dried in a fume hood
for 16 hr and then transferred to a vacuum oven for 12 hr at 50 °C to remove the remaining
solvents.
The composites resulting from the solution mixing technique were then molded using a
Carver compression molder (Carver Inc., Wabash, IN) at 210 °C for 10 min under a pressure of
38 MPa. The compression molded samples had a thickness of 1.0 mm, width of 25.0 mm and
length of 42.0 mm.
191
7.4.2. Electrical and Dielectric Properties Measurements
Direct current (DC) conductivity measurements of the molded samples were conducted
employing two different setups. For the nanocomposites with conductivities lower than
10-2 Sm
-1, a Keithley 6517A electrometer connected to a Keithley 8009 test fixture (Keithley
Instruments, USA) was used. The measurements were performed at a frequency of 0.1 Hz. For
the samples with electrical conductivities more than 10-2 Sm
-1, the measurements were
conducted according to the ASTM 257-75 standards using a Loresta GP resistivity meter (MCP-
T610 model, Mitsubishi Chemical Co., Japan) connected to an ESP four-pin probe. The four-pin
probe eliminated the effect of contact resistance. The applied voltage was 10 V for all the DC
conductivity measurements. The dielectric properties of the nanocomposites were measured with
an impedance / gain-phase analyzer (Solartron SI 1260) in the frequency range of 10-1
– 10+6
Hz.
Prior to the measurements, the electrodes were painted on the samples with a silver paste.
7.4.3. Morphological Characterization
Light microscopy (LM) and transmission electron microscopy (TEM) techniques were
employed to investigate the dispersion and distribution of MWCNTs. LM in transmission mode
was carried out on thin sections of MWCNT/PS composites (1.00 wt%) with 5.0 µm thickness.
The samples were cut with a Reichert-Jung Ultramicrotome (Ultracut B model). The microtomed
layers were mounted on a glass slide and then cover slipped using a ProLong® Gold. A weight
was placed on the cover slip to assure that the thin sections were flat. The micrographs were
captured using 10x objective magnification on a Leica DMRXA2 microscope equipped with a
camera AndorTM
iXon 885. The entire cross-sectional area was imaged.
192
The TEM analysis of the nanocomposites was carried out on ultramicrotomed sample sections
using a Tecnai TF20 G2 FEG-TEM (FEI, Hillsboro, Oregon, USA) at a 200 kV acceleration
voltage with the standard single-tilt holder. The images were captured on a Gatan UltraScan
4000 CCD (Gatan, Pleasanton, California, USA) at 2048x2048 pixels. The samples were
ultramicrotomed to sections of ~ 70 nm at room temperature using a Leica EM UC6.
7.5. Results and Discussion
7.5.1. Morphological Analysis
In order to exploit the dielectric properties of MWCNT/polymer composites efficiently,
MWCNTs must get well dispersed and distributed in polymer matrix. In fact, well dispersion and
distribution contribute to efficient occurrence of charge polarization all across the composite.
Accordingly, morphological analyses of the made composites were performed to achieve an idea
about the states of MWCNT dispersion and distribution in PS matrix. Distribution is more of a
microscopic scale and is homogeneous dispersal of individual MWCNTs or their agglomerates in
the nanocomposite; dispersion is of nanoscopic scale and is disentanglements of MWCNT
agglomerates [20-22].
The process of MWCNT dispersion and distribution into polymer matrix comprises two steps:
1) wetting and infiltration of polymer melt into primary agglomerates and 2) dispersion and
distribution of MWCNTs by rupture and erosion mechanisms [20]. In the rupture mechanism,
large agglomerates are broken into smaller ones; whereas, the erosion mechanism includes
erosion of individual MWCNTs or bundles from the surface of large agglomerate. To obtain
good dispersion and distribution, all the mechanisms must take place efficiently at less than a
193
critical time, since prolonging the mixing process may lead to MWCNT breakage. Further details
on the mechanisms of MWCNT dispersion and distribution in polymer matrix can be found
elsewhere [20-23].
LM micrograph, shown in Figure 7-1, depicts a good view from the distribution state of
MWCNTs in PS matrix. Figure 7-1 demonstrates that large MWCNT agglomerates were
relatively well ruptured, eroded and distributed in the solution-mixed sample, thereby leading to
a good state of MWCNT distribution. Although some large MWCNT agglomerates are
observable, however the overall state of MWCNT distribution is satisfactory.
Figure 7-1: LM micrograph of MWCNT/PS composites with 1.00 wt% loading.
In order to obtain a good opinion from the dispersion state of MWCNTs, the TEM
micrographs of the made composites were taken. Figure 7-2(a) shows low-magnification TEM
image of MWCNT/PS composites; whereas, Figures 7-2(b) and (c) depict high-magnification
TEM images of MWCNT/PS composites in the polymer-rich and agglomerated areas,
respectively.
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Figure 7-2: TEM micrographs of the solution-mixed samples at (a) low magnification, (b) high
magnification (polymer-rich area) and (c) high magnification (agglomerated area).
As shown in Figure 7-2(a), no large agglomerate is observable in the solution-mixed sample.
The black arrows point to the MWCNT agglomerates. Figure 7-2(b) presents the dispersion of
MWCNTs in polymer-rich areas. It is obvious that the concentration of MWCNTs in the
polymer-rich area is considerable. This can be attributed to enhanced erosion of MWCNTs from
the surface of large or small agglomerates in the solution-mixed samples. Figure 7-2(c)
demonstrates the dispersion of the MWCNTs in the agglomerated areas. It can be seen that the
polymer melt infiltrated into agglomerates and disentangled them partially. However, the
agglomerated areas required much more time and energy to get thoroughly disentangled. In view
195
of the LM and TEM images, it can be inferred that MWCNT were relatively well dispersed and
distributed in the polymer matrix; therefore, they were prone to present notable dielectric
properties for MWCNT/polymer composites.
7.5.2. DC Conductivity
The new generation of microelectronics demands polymer-based capacitors with high real
permittivity and low imaginary permittivity. According to the percolation theory, a high real
permittivity with a low leakage current in CPCs can only be realized at filler loadings very close
to the percolation threshold [9, 13]. The insulator-conductor transition that occurs at the
percolation threshold precludes CPCs from being used as charge storage materials beyond the
percolation threshold. Therefore, determination of the percolation thresholds of CPCs is the first
step in their development for charge storage applications.
Figure 7-3 depicts the percolation curve (DC conductivity) of the solution-mixed samples.
The percolation curve of the MWCNT/PS composites can be divided into three distinct regions
in terms of electrical conductivity, i.e., the insulative region, the percolation region, and the
conductive region. In the insulative region, the MWCNTs loadings were very low with the
MWCNTs far from each other; thus, the PS matrix controlled the charge transfer. In this region,
the solution-mixed samples demonstrated conductivities ranging from 10-13
to 10-11
Sm-1
, which
were close to the conductivity of pure PS.
With increases in the MWCNT concentration, at a critical MWCNT concentration, i.e., called
the percolation threshold, the first conductive path formed, resulting in the insulator-conductor
196
transition. Employing the percolation theory [24, 25] led to the percolation threshold equal to
0.06 for the solution-mixed MWCNT/PS composites. This threshold is comparable to the lowest
percolation thresholds reported for MWCNT/PS composites in the literature, confirming good
dispersion and distribution of MWCNTs throughout the polymer matrix [26, 27]. In the
conductive region (MWCNT loadings far above the percolation threshold), the conductivity rose
with increased MWCNT concentration until a plateau was reached. The existence of the plateau
in the percolation curve of CPCs signified the formation of a three-dimensional conductive
network.
Figure 7-3: The percolation curve (DC conductivity) of the solution-mixed samples of the
MWCNT/PS composites.
7.5.3. AC Conductivity
In general, leakage current of a material in an alternating field originates from its electrical
conductivity. Accordingly, it is important to have a profound understanding of the electrical
conductivity in an AC field. Generally, AC conductivity is defined as following [28]:
197
( ) (7-1)
where AC AC conductivity, ɛ´ real permittivity, ɛʺ imaginary permittivity, angular frequency
and ɛ0 permittivity of free space. For CPCs, AC conductivity is expressed as follows [28-31]:
( ) (7-2)
where σDC is DC conductivity and A and s are parameters dependent on temperature, and
concentration and type of fillers. It is well known that σAC is the sum of all dissipative effects,
including Ohmic conduction (σDC) created by free charges as well as frequency-dependent
dielectric dispersion (A(ω)s). Of interest to note, DC conductivity, which originates from
resistive current, is usually independent of frequency and is industrially measured under a low-
frequency AC voltage, where the influence of capacitive currents is negligible.
To comprehensively investigate the dielectric behaviors, including AC conductivity, of the
MWCNT/PS composites over the broadband frequency range, it is necessary to study the
dielectric properties in both the insulative and conductive regions. Considering 0.06 as the
percolation threshold of the solution-mixed samples, the MWCNT loadings chosen for dielectric
spectroscopy were 0.02, 0.10, 0.50 and 3.50 wt%, which covered the whole insulative and
conductive regions for the made composites.
Figure 7-4 demonstrates the AC conductivity of the solution-mixed MWCNT/PS composites
over the broadband frequency range. It was observed that at low MWCNT concentrations
(insulative region), the AC conductivity had a strong ascending trend with frequency. Figure 7-4
shows that the AC conductivity of the composite holding 0.02 wt% MWCNT at 106 Hz was
around 10-5
S·m-1
, which was seven orders of magnitude greater than its DC conductivity. As a
198
matter of fact, at low filler loadings due to large insulative gaps between conductive fillers, the
DC conductivity (low-frequency AC conductivity) was very low. However, with frequency
increase, the role of capacitive currents highlighted, since high-frequency voltage facilitated
frequent development of capacitive currents in a time frame. This led to ascending trend of AC
conductivity as a function of frequency in the insulative region.
Figure 7-4: AC conductivity of the solution-mixed MWCNT/PS composites.
By increasing the MWCNT concentration, the effect of the DC conductivity increased and the
magnitude of the DC conductivity approached to that of AC conductivity at high frequencies. In
other words, due to well-established conductive network formation at high filler loadings, the
free electrons had the conquering role in generating the conductivity over the whole frequency
range. It can be observed that for MWCNT concentrations of 0.10, 0.50 and 3.50 wt%, which
were in the conductive region, the DC and AC conductivities were close to each other and
independent of frequency.
199
7.5.4. Charge Polarization Mechanisms in MWCNT/Polymer Composites
In general, charge polarization in MWCNT/polymer (nonpolar) composites originates from
three sources, namely 1) interfacial polarization, 2) MWCNT polarization, and 3) electronic
polarization of polymer. Interfacial (Maxwell–Wagner–Sillars) polarization is usually observed
in heterogeneous systems with phases with different conductivities, such as MWCNT/polymer
composites [32-34]. At the internal phase boundaries of polymer and MWCNTs, nomadic charge
carriers can be entrapped and give rise to charge polarization. As interfacial polarization takes
place at large scale (mesoscopic scale), it has usually been observed at low frequencies, due to its
large relaxation time with respect to electric field frequency at high frequencies
MWCNT polarization also contributes to the real permittivity of MWCNT/polymer
composites, particularly at high frequencies where interfacial polarization is weak. It is believed
that the crystallographic defects in MWCNT structures may act as polarized centers [14, 35]. For
instance, a defect in the armchair-type CNT, which can conduct electricity, can cause the
surrounding region to be semiconducting. Therefore, in the molecular structure of MWCNTs,
there may be two regions with different conductivities that induce charge polarization on the
molecular scale.
The electronic polarization of polymer matrix is the third side of the charge polarization
triangle in MWCNT/polymer composites. In the narrow insulative gaps between MWCNTs,
there may be a buildup of very high field strength, which is higher than the macroscopic field
strength by a factor of M (i.e., M is the ratio of the average size of the conducting MWCNT
aggregates to the average gap width) [36, 37]. This high field strength contributes considerably to
200
the electronic polarization of polymer matrix and, thus, real permittivity at high frequencies
(optical frequency) [19].
The electric dipole has a magnitude equals to strength of each charge times the separation
between charges. Considering the scale at which charges are polarized at different polarization
mechanisms, the degree of contribution of polarization mechanisms to real permittivity has the
following order: interfacial, atomic and electronic. It should be mentioned that with frequency
increase, the slow polarization mechanisms give up in turn, leaving the faster ones to contribute
real permittivity.
7.5.5. The Broadband Behavior of Real Permittivity
Figure 7-5 presents the real permittivity of the solution-mixed composites with different
MWCNT loading levels over the broadband frequency range. As shown in Figure 7-5, the real
permittivity increased tremendously with increased MWCNT concentration. For instance, at 100
Hz, the real permittivity of the pristine PS was 2.71, which increased to 6.00 and 5.22×104
at
0.02 and 3.50 wt%, respectively. The three distinct regions mentioned for the DC conductivity
percolation curve, namely the insulative, percolation and conductive regions, can be employed to
explain the evolution process of real permittivity with MWCNT concentration.
By adding a small amount of MWCNTs to the PS matrix (insulative region), some
nanocapacitor structures, i.e., MWCNTs separated by thin layers of polymer, were formed; and,
the real permittivity increased slightly relative to the pristine PS. In addition, the charge
polarization in the semiconductive MWCNTs also contributed to higher real permittivity at
201
greater MWCNT loadings. When MWCNT loading approached the percolation threshold
(percolation region), an abrupt growth in the real permittivity was observed. This increase can be
attributed to the formation of a large number of nanocapacitors, allowing the composite to store
the charge, i.e., interfacial polarization. As a matter of fact, as the percolation threshold was
approached, there was an increase in the number of nanoelectrodes (MWCNTs) and a decrease
in the thickness of nanodielectrics (PS layers between MWCNTs), both of which contributed to
the real permittivity. Beyond the percolation threshold (conductive region), despite the formation
of conductive paths, the real permittivity carried on growing with increased MWCNT
concentrations, since a great deal of MWCNTs were still wrapped with the PS matrix.
Figure 7-5: Real permittivity, as a function of frequency, of the solution-mixed samples at
different MWCNT concentrations.
In view of Figure 7-5 and the percolation threshold of the solution-mixed samples, it can be
claimed that the real permittivity was almost independent of frequency in the insulative region,
whereas it varied with frequency in the conductive region. For instance, the real permittivity of
202
the solution-mixed samples at 0.02 wt% (insulative region) was frequency-independent;
however, at 3.50 wt% (conductive region), the real permittivity demonstrated a decaying trend in
the low frequency range (10-1
– 3×100 Hz), then was constant up to 2×10
4 Hz, and finally
showed another decaying trend above 2×104 Hz.
In order to predict the dielectric behaviors of CPCs as a function of frequency, it is imperative
to understand the charge polarization mechanisms over the whole frequency range. In CPCs, the
dependency of real permittivity on frequency relies on the presence of nanocapacitor structures.
At low MWCNT concentrations (insulative region), due to the lack of a large amount of
nanocapacitor structures, the real permittivity was constant over the whole frequency range;
whereas, the abundance of nanocapacitor structures close to or above the percolation threshold
(conductive region) led to the frequency-dependent real permittivity (Figure 7-5).
The very high real permittivity of the MWCNT/PS composites close to or above the
percolation threshold in the low frequency range originated from low-frequency dispersion
(LFD) mechanism (Figure 7-5) [38, 39]. LFD has similar mechanism as interfacial polarization,
but occurs at lower frequencies. In LFD mechanism, due to sufficiently low frequencies,
nomadic charge carriers with low drift velocity also found sufficient time to move towards
internal interfaces and pile up. This led to very large real permittivities. It was observed that LFD
declined sharply with frequency, which can be related to the LFD relaxation phenomenon.
In the intermediate frequency range, the real permittivity resulted from interfacial
polarization. In the interfacial polarization mechanism, only charge carriers with high drift
velocity got enough time to pile up at the interfaces in each half cycle of alternating electric field.
These charge carriers were able to keep pace with alternating field over a wide frequency band.
203
This led to a constant real permittivity in the intermediate frequency range, until interfacial
relaxation happened. It was interesting to observe that with increases in MWCNT concentration,
the interfacial relaxation occurred at lower frequencies. This can be related to reduced relaxation
time of MWCNT/PS composites with higher MWCNT loadings, which arose from reduced
thicknesses of nanodielectrics and enhanced capacity of nanocapacitors. In the high frequency
range, the real permittivity showed a descending trend with frequency due to interfacial
relaxation. With the decay of the interfacial polarization in the high frequency range, the roles of
the MWCNT polarization and PS polarization found more importance.
7.5.6. The Broadband Behavior of Imaginary Permittivity
Imaginary permittivity is representative of energy dissipation within a dielectric and is
considered as a critical factor whether a material is appropriate for charge storage or not. CPCs
functioning as charge storage materials are needed to show a low imaginary permittivity (leakage
current). Imaginary permittivity is composed of two components; namely Ohmic loss and
polarization loss. Ohmic loss arises from DC conduction and represents the dissipation of
electrical energy by mobile charge carriers moving throughout the dielectric material.
Polarization loss originates from the friction accompanying the orientation of electric dipoles in
each half cycle of an AC field. Therefore, it can be said that the polarization loss, as a portion of
imaginary permittivity, has a direct relationship with real permittivity. In other words, the higher
the real permittivity of a dielectric, the greater is the momentum generated by charge
polarization, and thus the higher is the dissipation of energy to come over the momentum to
reorient the dipoles in each half cycle of alternating field.
204
As shown in Figure 7-6, the imaginary permittivity was very low at MWCNT concentrations
far below the percolation threshold; however, it increased tremendously as the MWCNT
concentration approached the percolation threshold. For instance, it was observed that at 100 Hz,
the imaginary permittivity of 0.02 wt% MWCNT/PS composite was 0.01, which increased to
3.28×107 at 3.50 wt% loading. Several factors constitute the direct relationship between
imaginary permittivity and MWCNT concentration. Firstly, increase in MWCNT content
accompanies with increase in the amount of dissipating nomadic charges and formation of
conductive networks in the composites. In fact, at enhanced conductive network formation, the
electrons had greater mean free paths in which to move according to the direction of the electric
field in each half cycle and, consequently could dissipate more electrical energy [19]. Moreover,
large amount of energy can be dissipated by free charges at the contact spots between MWCNTs.
The boosted polarization loss originating from interfacial polarization at filler loadings close to
or above the percolation threshold is another important factor contributing to imaginary
permittivity.
It was also observed that the imaginary permittivity was independent of frequency in the
insulative region; however, it was highly sensitive to frequency in the conductive region. As
depicted in Figure 7-6, the imaginary permittivity of conductive samples showed several orders
of magnitude reduction by sweeping the whole frequency range. The descending trend of
imaginary permittivity with frequency in the conductive region can be attributed to the reduced
available times for free electrons to sweep the network in each half cycle of alternating field, i.e.,
lower Ohmic loss. In addition, with frequency increase, the interfacial polarization relaxation
occurs, which is associated with lower polarization loss due to incomplete dipole reorientation.
205
Figure 7-6: Imaginary permittivity, as a function of frequency, of the solution-mixed samples at
different MWCNT concentrations.
7.6. Conclusions
Characterization techniques, such as LM and TEM showed that MWCNTs were well
dispersed and distributed all across the composites, contributing to better exploitation of
MWCNT electrical properties for charge storage applications. Comparing the DC and AC
conductivities results showed that the AC conductivity was highly sensitive to frequency in
insulative region, whereas it was almost constant with frequency in the conductive region. The
DC and AC conductivities in the conductive region at high frequencies were close to each other.
The dielectric spectroscopy showed that the real and imaginary permittivities increased
tremendously as the MWCNT concentration approached the percolation threshold. The increase
in the real permittivity was related to the formation of a large number of nanocapacitors
(MWCNTs as nanoelectrodes and PS as nanodielectrics). The increase in the imaginary
206
permittivity was attributed to greater number of dissipating charges, enhanced conductive
network formation and boosted polarization loss arising from interfacial polarization.
It was also found that the real and imaginary permittivities were almost constant with
frequency in the insulative region, while they descended drastically with frequency in the
conductive region. The descending trend of real permittivity with frequency was related to
charge polarization relaxation. The reduction of imaginary permittivity with frequency in the
conductive region was attributed to the reduced available times for free electrons to sweep the
network (lower Ohmic loss) and also lower polarization loss due to interfacial polarization
relaxation.
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*Submitted to Polymer
210
Chapter 8
Novel Composites of Copper Nanowire/PVDF with Superior Dielectric
Properties*
8.1. Presentation of the Article
This article introduces CuNW as a competent substitution for MWCNT to be employed in
CPCs for charge storage applications. The CPCs used for charge storage applications are
required to present high real permittivity and low imaginary permittivity. In order to obtain high
real permittivity, highly conductive fillers are greatly acknowledged. The limited electrical
conductivity of MWCNTs prompted us to investigate the dielectric properties of CuNW/polymer
composites, due to superior electrical conductivity of CuNWs to MWCNTs. However,
unavoidable oxide layer formation on the surface of CuNWs sounds as a barrier to exploit the
electrical conductivity of CuNWs. Nonetheless, in this study the oxide layer formation was
innovatively employed as a benefit to decay the conductive network formation to reduce the
imaginary permittivity. As a matter of fact, high conductivity of fresh core of CuNWs combined
with the presence of oxide layer on their surfaces led to novel composites with superior dielectric
properties.
211
Novel Composites of Copper Nanowire/PVDF with Superior Dielectric
Properties
Aline Bruna da Silva1, Mohammad Arjmand
2, Uttandaraman Sundararaj
2,
Rosario E. S. Bretas1
1Department of Materials Engineering, Universidade Federal de São Carlos, São Carlos, Brazil
2Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Canada
8.2. Abstract
Novel copper nanowire (CuNW)/poly(vinylidene fluoride) (PVDF) nanocomposites with high
dielectric permittivity and low dielectric loss were prepared by coagulation technique followed
by melt compression. Their dielectric properties over the broadband frequency range, i.e. 101 –
106 Hz, were compared with multi-walled carbon nanotubes (MWCNT)/PVDF nanocomposites
prepared by the same technique. It was observed that the CuNW/PVDF nanocomposites showed
higher dielectric permittivity, lower dielectric loss and thus significantly lower dissipation factor
than of the MWCNT/PVDF nanocomposites. For instance, at filler concentrations of 0.8 and
1.5v% and at a frequency of 20 Hz, the MWCNT/PVDF nanocomposites presented dissipation
factors of 2.4103 and 1.310
4; whereas the CuNW/PVDF nanocomposites showed the
dissipation factors significantly lower and equal to 2.0 and 3.9, respectively. This behavior was
ascribed to a higher conductivity of the fresh core of CuNWs relative to MWCNTs, which
provided the composites with greater amount of mobile charge carriers participating in the
interfacial polarization (higher dielectric permittivity). Moreover, the presence of oxide layer on
the CuNW surfaces decayed the conductive network formation leading to a low dielectric loss.
212
8.3. Introduction
Polymer nanocomposites with high dielectric permittivity have found great attention to store
electrical energy and have a high potential for a broad range of applications, such as
communications devices, actuators, artificial muscles, charge-storage capacitors systems, etc [1-
3]. Easy processability of the polymer matrix combined with high dielectric permittivity of the
filler draws a promising future for these nanocomposites. Nonetheless, the low dielectric
permittivity of the polymer matrix still constitutes a challenge to obtain a versatile polymer
composite with a high dielectric permittivity (high-k polymer composite).
The most traditional method to increase this permittivity is, thus, to disperse a high-k
insulating ceramic powder into the polymer matrix to form a composite [4]. However, to meet
the demanding requirements for new generation of electronics a large amount of ceramic is
usually required, resulting in loss of flexibility and mechanical strength. Another strategy is to
produce percolative composites using conductive or semi-conductive fillers. As the volume
fraction of the conductive fillers increases to the vicinity of the percolation threshold, these
composites can present an abrupt increase in dielectric permittivity [1, 5, 6], while retaining the
polymer matrix flexibility. When the concentration of the conductive filler is close to the
percolation threshold, a large amount of conductive fillers approximates to each other but still
remains insulated by thin layers of dielectric material, forming a great deal of nanocapacitors
(conductive nanofiller as nanoelectrode and polymer matrix as nanodielectric) [1, 6-8].
The effective dielectric permittivity of the conductive filler/polymer composite (CPC) can be
several orders of magnitude higher than of the insulating polymer matrix. Furthermore, lower
percolation threshold of CPCs relative to traditional composites leads to lower costs and easier
213
processability [7]. The high dielectric permittivity in CPCs is not a direct consequence of the
intrinsically high-k fillers, but is due to huge increase in interfacial polarization, i.e., an effective
increase of electrode surface area due to contiguity of conductive filler near the percolation
threshold [6, 8-10]. However, high dissipation factors above the percolation threshold arising
from conductive network formation preclude the use of CPCs with high filler loadings for charge
storage applications [5, 7].
Many studies have focused on developing CPCs with low dissipation factors; some strategies
are available to prevent the direct contact between the conductive particles, such as coating the
surface of the conductive filler with a thin insulating layer [11, 12], using surface-oxidized metal
particles [13], incorporating a secondary ferroelectric filler as barrier layer [14, 15] or aligning
the conductive filler [16]. All these techniques require further processing or they have an adverse
effect on the dielectric permittivity of the made composites.
In this study, we present a novel copper nanowire/poly(vinylidene fluoride) (CuNW/PVDF)
nanocomposite with higher dielectric permittivity and lower dissipation factor than the multi-
walled carbon nanotube (MWCNT)/PVDF nanocomposite obtained by similar technique. PVDF
was chosen as the matrix because it is a semi-crystalline polymer that has extensive applications
due to its thermal stability, chemical resistance, pyro and piezoelectric properties, high
permittivity and relatively low dissipation [1, 5, 17]. MWCNT/polymer nanocomposites were
chosen for comparison due to their superior electrical and dielectric properties, originating from
the extraordinary electrical properties together with giant surface area of MWCNTs.
CuNWs are susceptible to oxidation due to a very large surface area, which has made them
inappropriate for many electrical applications. The goal of this work was to use this weakness as
214
a benefit, producing novel CuNW/PVDF nanocomposites in which the oxide layer on the surface
of the CuNWs plays the role of an insulating barrier. In other words, the oxide layer as insulating
barrier is prone to avoid direct contact between the fillers above the percolation threshold
reducing the dissipation factor. The resultant high dielectric permittivity and low dissipation
factor of these innovative nanocomposites make them particularly attractive for technological
applications as storage energy materials.
8.4. Experimental
8.4.1. Materials
The PVDF Kynar® 1000HD was purchased from Arkema Inc. The density and melt flow rate
are 1.78 g/cm3 and 1.1g/10 min (at 230 C/5.0 kgf), respectively. The dielectric permittivities are
10.5 and 7.0 at 100 Hz and 1 MHz according to IEC 60250, respectively. The MWCNTs
(NanocylTM
NC7000) were obtained from Nanocyl S.A. (Sambreville, Belgium). According to
the manufacturer, the MWCNTs were produced with the catalytic carbon vapor deposition
(CCVD) process and had an average diameter of 9.5 nm, a length of 1.5 μm and a surface area of
250-300 m2/g. The synthesis of CuNWs was an in-house technology, in which CuNWs were
synthesized through AC electrodeposition of Cu in porous aluminum oxide (PAO) templates.
Afterwards, CuNWs were liberated from Al electrodes, collected in 150 ml methanol and bath
sonicated for 30 min. Next, the nanowires were collected by filtration in nylon membranes (0.45
mm pore size) and dried for 2 hr under vacuum. The synthesized nanowires had averages
diameter and length of 30 nm and 1.5 µm, respectively. Details of the synthesis and liberation are
215
described in a previous work [18, 19]. Figure 8-1 shows micrographs of MWCNT (as-received)
and synthesized CuNW.
Figure 8-1: TEM micrographs of (a) as-received MWCNT (NC7000), (b) synthesized CuNW.
8.4.2. Mixture Preparation
The PVDF Kynar® 1000HD and MWCNTs (Nanocyl
TM NC7000) were dried at 50 °C for 4 hr
under vacuum. The MWCNT/PVDF and CuNW/PVDF nanocomposites were produced by
solution mixing technique. PVDF was dissolved into DMF at 80 ºC under continuous stirring to
obtain a solution with concentration of 0.1 g/ml. Meanwhile, MWCNTs and CuNWs were also
dispersed into DMF under sonication at room temperature for 30 min. The concentrations of
MWCNT and CuNW suspensions were 0.00033 and 0.00500 g/ml, respectively. Cooling down
the PVDF/DMF solution to room temperature, the MWCNT/DMF and CuNW/DMF suspensions
were mixed with PVDF/DMF solution separately using magnetic stirring for 5 min.
Subsequently, the suspensions were dripped into methanol (non-solvent to PVDF), where the
volume ratio of DMF to methanol was 1:3. Upon contact of the suspension with the methanol,
216
the PVDF chains retracted and precipitated instantly, due to their insolubility in methanol. The
retracted chains entrapped the fillers and prevented them from reagglomeration.
The mixtures were then filtered and placed in an evaporation dish for 24 hr in a fume hood.
Next, the MWCNT/PVDF nanocomposites were dried at 80 ºC for 24 hr in a vacuum oven;
whereas, the CuNW/PVDF nanocomposites were dried for 96 hr at room temperature under
vacuum. Finally, the MWCNT/PVDF and CuNW/PVDF nanocomposites with the
concentrations between 0.4v% and 1.5v% were produced by the compression molding of the
prepared materials at 200 ºC for 10 min under pressure of 35 MPa.
8.4.3. Characterization
Characterizations of the MWCNT and CuNW were carried out by scanning electron
microscopy (SEM) and transmission electron microscopy (TEM) techniques using a XL 30 FEG
and a CM120 microscope operating at 120kV, both from Philips, respectively. For those
analyses, diluted solutions of MWCNT and CuNW were prepared by sonication in methyl
alcohol for 15 min with subsequent dripping on copper grids. The average diameter of both
fillers was measured using the Image-Pro® Plus 4.5 software. The oxidation of CuNWs was
studied by wide-angle x-ray diffraction (WAXD), using a Rigaku diffractometer, model Ultima
IV, with CuK radiation (= 1.542 Å), operated at 40 kV and 40 mA.
The morphology of the nanocomposites was also characterized by the SEM and TEM
techniques employing the above-described microscopes. For the SEM analysis the samples were
cryo-fractured using liquid nitrogen, while for the TEM analysis the samples were prepared by
217
cryo-ultramicrotomy. Direct current (DC) conductivity was measured by two different setups
with 90 V as applied voltage. For the samples with conductivities lower than 10-2
S·m-1
, a
Hiresta UP (MCP-HT450 model) resistivity meter connected to an URS probe ring was used; for
the samples with electrical conductivities higher than 10-2
S·m-1
, a Loresta GP resistivity meter
(MCP-T610 model) connected to an ESP four-pin probe was used. Both instruments were from
Mitsubishi Chemical Co., Japan. The broadband dielectric properties were measured using an
impedance/gain-phase analyzer (Solartron SI 1260) in the frequency range of 101 and 10
6 Hz.
Prior to the measurements, electrodes of silver were painted on the samples.
8.5. Results and Discussion
8.5.1. Oxidation of CuNWs
Luo et al. [20] demonstrated that the oxidation reaction of CuNW synthesized by AC
electrodeposition in PAO templates can be divided in two stages, in which the degree of
oxidation is determined by the presence of Cu, Cu2O and CuO. Before oxidation the CuNW
presents only metallic Cu and Cu2O; after stage 1 the composition of CuNW consists of Cu2O
and CuO and after stage 2 oxidized CuNWs present only CuO.
As shown in Figure 8-2, the WAXD analyses of the CuNW powder displayed diffraction
peaks at 2θ values of 43.2˚, 50.4˚ and 74.1˚ corresponding to (111), (200) and (220) planes of Cu
[21], respectively. The diffraction at 61.4° corresponds to the (220) crystalline planes of the
cubic phase of Cu2O [22] and the peaks at 2θ values of 35.5˚, 38.7˚, 48.8˚, 58.2˚, 61.5˚, 66.2˚ and
81.2˚ correspond to the (002), (-111), (111), (200), (-202), (202), (-113), (-311), (310), (313)
crystalline planes of CuO, respectively [23]. Therefore, it can be claimed that the CuNWs used in
218
this work were partially oxidized (with oxidation being in stage 1) and had possibly a non-
conductive shell (oxide layer) and a conductive core (fresh copper).
Figure 8-2: WAXD diffractogram of the CuNW.
8.5.2. Morphological Characterization of the Nanocomposites
Figure 8-3 shows the SEM micrographs of the solution-mixed MWCNT/PVDF and
CuNW/PVDF nanocomposites, both at concentration of 1.5v%. These images revealed a
segregated structure for both types of nanocomposites. The segregated structure has been
reported by other researchers, and led to CPCs with lower percolation threshold [24, 25]. In fact,
to obtain a low percolation threshold, a non-uniform distribution of nanofiller network is
preferred [26, 27]. In this way, conductive fillers just occupy some preferred areas to make a
conductive network, thereby resulting in lower percolation threshold.
219
Figure 8-3: SEM images: a) MWCNT/PVDF nanocomposites; b) CuNW/PVDF nanocomposites,
both with 1.5v% of filler.
The segregation could be the result of weak interactions between the nanofillers and the
PVDF chains, which prevents significant incorporation of the fillers. As a matter of fact, when
the suspension of conductive filler/PVDF/DMF was dripped into methanol, the polymer chains
precipitated instantly and the coagulated chains captured the conductive fillers and prohibited
them from reagglomeration. The vivid networks of conductive filler without any significant
agglomerates, seen in Figure 8-3, confirm this idea. However, due to inhomogeneous dispersion
of conductive filler in suspension, the polymer chains created some filler-free areas during the
coagulation. This led to the morphology of segregated structure for both MWCNT/PVDF and
CuNW/PVDF composites. Comparing both structures, it is observed that the MWCNT/PVDF
composite was formed by segregated structures smaller than the CuNW/PVDF composites; this
can be ascribed to higher affinity of MWCNT to PVDF chains, and in consequence better
dispersion and distribution of MWCNTs in PVDF matrix.
220
TEM micrograph of MWCNT/PVDF shows that MWCNT were well dispersed in PVDF
matrix. Individual MWCNTs are easily observable without creating any significant agglomerate.
It is worth noting that the observable lengths of MWCNT in the TEM micrograph do not present
the whole length of MWCNTs due to curvy structure of this nanomaterial. The TEM micrograph
of CuNW/PVDF shows that CuNWs were relatively well-dispersed in the polymer matrix;
however, bundles of CuNWs are also discernible. This can be related to high van der Waals
forces between CuNWs and also their low affinity to PVDF matrix.
Figure 8-4: TEM images of: a) MWCNT/PVDF nanocomposites; b) CuNW/PVDF
nanocomposites, both with 1.5v% of filler.
8.5.3. DC and AC Conductivity
In general, energy dissipation within a dielectric in an alternating field is related to its
electrical conductivity. Accordingly, it is important to have a profound understanding of the
electrical conductivity in an AC field. Generally, the AC conductivity * is calculated from the
dielectric permittivity and dielectric loss according to the relation: ( ) ,
where o is vacuum permittivity (8.854×10-12
F/m), is angular frequency and ɛ´ and ɛ are
221
dielectric permittivity and dielectric loss, respectively [28]. This equation shows that the real part
of AC conductivity is proportional to dielectric loss and occurs due to flow of charges through
the dielectric material (DC conduction). The imaginary part of AC conductivity is engaged with
dielectric permittivity and does not pass through the dielectric material, but is generated to
compensate for the charges which are polarized within the dielectric material (dielectric
dispersion).
For CPCs, AC conductivity is expressed as follows [28-30]:
( ) (8-1)
where σDC is DC conductivity and A and s are parameters dependent on concentration and type of
fillers, temperature and morphology of CPCs. It is well known that σAC is the sum of all
dissipative effects, including Ohmic conduction (σDC) created by free charges as well as
frequency-dependent dielectric dispersion (A(ω)s). Dielectric dispersion in CPCs originates from
interfacial, dipolar and/or electronic polarization mechanisms depending on the frequency range,
molecular structure of conductive filler and polymer matrix and morphology of CPCs [31].
Given the frequency range focused in this study, i.e., 101 to 10
6 Hz, interfacial polarization
played the main role in developing the dielectric properties of the MWCNT/PVDF and
CuNW/PVDF nanocomposites. Interfacial polarization is broadly observed in heterogeneous
systems with phases with different conductivities or dielectric permittivities, such as CPCs [32,
33]. Interfacial polarization takes place because of the accumulation of mobile charges at the
interface of unlike phases with different electrical conductivities or permittivities. As interfacial
polarization occurs at large scale (mesoscopic scale), it has usually been observed at low
frequencies, due to its large relaxation time with respect to electric field frequency at high
222
frequencies [8, 32]. It is notable to declare that the dipolar polarization occuring in the PVDF
matrix also contributes slightly to the dielectric properties of conductive filler/PVDF
nanocomposites over the freqyency range of study.
Figure 8-5 and Figure 8-6 present the DC conductivity and AC conductivity of the
MWCNT/PVDF and CuNW/PVDF nanocomposites, respectively. The electrical percolation
thresholds (c) of both nanocomposites were obtained by fitting the data to the power law
equation for electrical conductivity [34]. The percolation thresholds obtained from the
percolation theory were 0.13v% and 0.27v% for the MWCNT/PVDF and CuNW/PVDF
nanocomposites, respectively. This result can be related to the higher aspect ratio of MWCNTs,
which gives rise to higher probability of MWCNTs contacting each other, i.e., lower percolation
threshold.
Figure 8-5 and Figure 8-6 show a continuous increase in the AC conductivity of both
nanocomposites, with the increase of the amount of filler. This increase can be related to the
formation of further conductive paths (higher DC conductivity), and also larger dielectric
dispersion arising from the development of interfacial polarization. It was also observed that both
DC and AC conductivities of the MWCNT/PVDF nanocomposites were higher than of the
CuNW/PVDF nanocomposites, although Cu has higher intrinsic conductivity than MWCNT. It
seems that the oxide layer on the surface of CuNWs avoided the direct contact between them
leading to a lower electrical conductivity.
Pure PVDF and nanocomposites with low filler content displayed AC conductivity highly
dependent on frequency, indicating an insulating behavior. However, as the filler content was
increased, the AC conductivity became independent of frequency, indicating the formation of a
223
complete conductive network. In fact, in the insulative region and at low frequency range, due to
large insulative gaps between the conductive fillers, the AC (DC) conductivity was very low.
Nevertheless, with frequency increase, the role of dielectric dispersion arising from interfacial
polarization increased leading to a rise in AC conductivity. It is also evident that at high filler
loadings, the AC conductivity of the MWCNT/PVDF nanocomposite was independent of
frequency, showing the conquering role of Ohmic conduction and well-established conductive
network formation. Nonetheless, the CuNW/PVDF nanocomposites at high filler loadings still
demonstrated an ascending trend with frequency. We believe that the presence of oxide layer on
the surface of CuNWs precluded the direct contact between CuNWs averting the formation of a
well-established conductive network. Therefore, the dielectric dispersion still played an
important role in contributing to AC conductivity at high frequencies.
(a) (b)
Figure 8-5: a) DC conductivity as a function of volume concentration, and linear fitting of the
data to the power law equation for electrical conductivity; b) AC conductivity of the
MWCNT/PVDF nanocomposites as a function of frequency.
224
(a) (b)
Figure 8-6: a) DC conductivity as a function of volume concentration, and linear fitting of the
data to the power law equation for electrical conductivity; b) AC conductivity of the
CuNW/PVDF nanocomposites as a function of frequency.
8.5.4. Dielectric Permittivity and Dielectric Loss
The ability of dielectric materials to store energy is attributed to polarization, i.e. electric
field-induced separation and alignment of electric charges, which can result in an increase in
capacitance. As mentioned before, considering the frequency range of study (101 – 10
6 Hz),
interfacial polarization is the conquering polarization mechanism in developing the dielectric
properties of the MWCNT/PVDF and CuNW/PVDF nanocomposites.
Figure 8-7 (a) and (b) shows the dielectric permittivity of the MWCNT/PVDF and
CuNW/PVDF nanocomposites as functions of filler content and frequency. It is evident that the
dielectric permittivity grew drastically as the filler content was increased. This increase can be
related to the formation of nanocapacitor structures, conductive nanofiller as nanoelectrode and
225
polymer matrix as nanodielectric, experiencing interfacial polarization. The electric dipole has a
magnitude equals to strength of each charge times the separation between charges. Considering
the scale at which the charges are polarized in interfacial polarization, i.e. mesoscopic scale, the
interfacial polarization creates a large dipole momentum. Moreover, increase in conductive filler
content is associated with the formation of an abundance of nanocapacitor structures. Thus, the
high dielectric permittivity at filler loadings close to or above the percolation threshold can be
related to the presence of a large number of nanocapacitor structures together with large dipole
momentum of interfacial polarization.
It can be observed that at high filler loadings (conductive region), the dielectric permittivity
declined tremendously with frequency for both types of nanocomposites. For instance, the
dielectric permittivities of 1.5v% MWCNT/PVDF and 1.5v% CuNW/PVDF nanocomposite
were 618 and 1189 at 20 Hz, which decreased to 46 and 18 at 106
Hz, respectively. This is due to
the large retardation time of interfacial polarization with respect to the electric field frequency at
high frequencies (relaxation phenomenon) [1, 8]. In fact, with frequency increase, the electric
field is too fast not to let the free electrons pile up at the interface. However, in the insulative
region, due to absence of interfacial polarization, the dielectric permittivity was independent of
frequency.
226
(a) (b)
Figure 8-7: Dielectric permittivity (´): (a) MWCNT/PVDF nanocomposite; (b) CuNW/PVDF
nanocomposites.
It is interesting to observe that CuNW/PVDF nanocomposites presented higher dielectric
permittivity than MWCNT/PVDF nanocomposites. As shown in Figure 8-7, at filler
concentrations of 0.4, 0.8 and 1.5v% and at a frequency of 20 Hz, the MWCNT/PVDF
nanocomposites exhibited dielectric permittivities of 91, 290 and 618, respectively, while the
dielectric permittivities of the CuNW/PVDF nanocomposites were 230, 577 and 1189,
respectively. The higher dielectric permittivity of CuNW/PVDF nanocomposites can be related
to the higher conductivity of CuNWs compared to MWCNTs. The higher conductivity of
CuNWs provided the composites with greater amount of mobile charge carriers participating in
the interfacial polarization leading to larger dielectric permittivity. Thus, the CuNW/PVDF
nanocomposites presented superior dielectric permittivity to MWCNT/PVDF nanocomposites.
227
Figure 8-8 shows the dielectric loss () as functions of filler content and frequency for both
types of nanocomposites. It can be seen that the dielectric loss rose significantly with filler
content. The increase of dielectric loss with filler content can be attributed to enhanced Ohmic
loss and polarization loss. At higher filler contents, the amount of dissipating nomadic charges is
higher. Moreover, increase in filler content is associated with the developed conductive network
formation in which the electrons have greater mean free path to move in each half cycle of
alternating field, thereby dissipating more electrical energy [7, 35]. All these phenomena lead to
higher Ohmic loss, which is linked to dissipation of energy in phase with alternating field. In
addition, the augmented polarization loss arising from interfacial polarization is another
significant factor increasing the dielectric loss at higher filler contents.
(a) (b)
Figure 8-8: Dielectric loss () :(a) MWCNT/PVDF; (b) CuNW/PVDF nanocomposites.
228
The dielectric loss displayed a frequency-independent behavior in the insulative region, but it
dropped drastically with frequency in the conductive region. The decaying trend of dielectric loss
with frequency can be ascribed to reduced Ohmic loss and polarization loss. As a matter of fact,
frequency increase accompanies with reduced available times for free electrons to travel
throughout the conductive network in each half cycle of alternating field, i.e. reduced Ohmic
loss. Furthermore, due to interfacial polarization relaxation, the interfacial charge polarization
decays with frequency leading to lower dipole momentum and polarization loss.
As shown in Figure 8-8, it was surprisingly observed that the dielectric loss in CuNW/PVDF
nanocomposites was considerably lower than the MWCNT/PVDF nanocomposites, which is
significantly desirable for charge storage applications. At filler concentrations of 0.4, 0.8 and
1.5v%, the MWCNT/PVDF nanocomposites exhibited dielectric losses of 541, 7105 and
8.1106, respectively, while the dielectric losses of the CuNW/PVDF nanocomposites were
1020, 1142 and 4620, respectively, both at a frequency of 20 Hz. The lower dielectric loss of the
CuNW/PVDF nanocomposites is ascribed to the presence of oxide layer on the surface of
CuNWs avoiding the formation of a conductive network. In other words, oxide layer reduced the
Ohmic loss through shrinking the available free path of nomadic charges by decaying the
conductive network formation. It is worthwhile to mention that although polarization loss in the
CuNW/PVDF nanocomposite was higher (due to higher dielectric permittivity); however, the
Ohmic loss played the dominant role in enhancing the dielectric loss.
The dielectric permittivity and dielectric loss are related to each other with the term
dissipation factor, which is of great importance in industry since it includes the effects of both
dielectric permittivity and dielectric loss.
229
(8-2)
The lower the dissipation factor of a dielectric material, the better is its performance for charge
storage applications. Figure 8-9 depicts the dissipation factors of the MWCNT/PVDF and
CuNW/PVDF nanocomposites as functions of filler content and frequency. It can be observed
that the dissipation factors of the CuNW/PVDF nanocomposites are orders of magnitude lower
than the MWCNT/PVDF nanocomposite. For instance, at filler concentrations of 0.4, 0.8 and
1.5v% and at a frequency of 20 Hz, the MWCNT/PVDF nanocomposites presented dissipation
factors of 5.9, 2.4103 and 1.310
4, while the CuNW/PVDF nanocomposites showed the
dissipation factors significantly lower and equal to 4.5, 2.0 and 3.9, respectively. As a matter of
fact, high conductivity of fresh core of CuNWs (high dielectric permittivity) combined with the
presence of oxide layer on their surfaces (low dielectric loss) led to novel composites with
superior dielectric properties and reduced dissipation factors.
230
(a) (b)
Figure 8-9: Dissipation factor (tan ) as function of the frequency: (a) MWCNT/PVDF
nanocomposites; (b) CuNW/PVDF nanocomposites.
Figure 8-10 shows a scheme of the oxide layer formation on the outer surface of CuNWs.
This layer avoids the direct contact between the nanowires leading to very low energy losses.
The fresh core of the CuNWs provides the composite with high interfacial polarization.
Therefore, it can be claimed that we have used the formation of oxide layer, which is usually
assumed as a weakness for electronic applications, as a benefit to improve the dielectric
properties. This combined with high conductivity of fresh core of CuNWs draws a promising
future for CuNW/polymer composites as charge storage materials.
231
Figure 8-10: Scheme of core-shell structured CuNW, composed of a non-conductive shell (oxide
layer) and a conductive core (fresh copper), showing the blocking of the charge carriers at
internal interfaces of the individual CuNW.
8.6. Conclusions
The dielectric properties of the CuNW/PVDF and MWCNT/PVDF nanocomposites, prepared
by coagulation technique followed by compression molding, were compared. It was observed
that the dielectric permittivity and dielectric loss increased drastically with conductive filler
content for both types of nanocomposites. The ascending trend of dielectric permittivity with
filler content was ascribed to the formation of an abundance of nanocapacitor structures, i.e.
conductive nanofiller as nanoelectrode and polymer matrix as nanodielectric. The increase of
dielectric loss with filler loading was attributed to enhanced Ohmic loss and polarization loss
arising from conductive network formation and developed interfacial polarization, respectively.
The results also showed that the dielectric permittivity and dielectric loss declined with
frequency for both types of nanocomposites, which was attributed to polarization relaxation and
reduced Ohmic loss and polarization loss, respectively.
232
Comparing the dielectric properties of the MWCNT/PVDF and CuNW/PVDF
nanocomposites showed that the CuNW/PVDF nanocomposites presented higher dielectric
permittivity, lower dielectric loss and consequently significantly lower dissipation factor than of
the MWCNT/PVDF nanocomposites. Higher dielectric permittivity of the CuNW/PVDF
nanocomposite was attributed to greater intrinsic conductivity of fresh core of CuNWs relative to
MWCNTs, thereby providing the nanocomposites with more free charges taking part in
interfacial polarization. Lower dielectric loss in the CuNW/PVDF nanocomposites was ascribed
to the presence of oxide layer on the surface of CuNWs averting the direct contact between
CuNWs. In conclusion, it can be claimed that high conductivity of fresh core of CuNWs
combined with the presence of oxide layer on their surfaces led to novel composites with
superior dielectric properties.
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Chapter 9
Summary, Conclusions and Future Work
9.1. General Background and Project Objectives
In the current competitive market of electronics, companies are taking effort to produce
lighter weight and smaller electronic devices with enhanced functionality and design options.
Accordingly, conductive filler/polymer composites (CPCs) have attracted great attention to
satisfy these requirements, due to their tunable electrical conductivity, light weight, low cost,
corrosion resistance and easy processability [1, 2]. CPCs are made by incorporating conductive
filler into a polymer matrix. Conventional polymers such as polycarbonate (PC), polystyrene
(PS) and poly(vinylidene fluoride) (PVDF) are insulative; however, adding conductive fillers to
these polymer matrices can provide them with wide a range of conductivities through the
formation of a conductive network.
The ability to regulate the conductive network formation in CPCs enables them to present a
wide spectrum of conductivity, and to perform as insulative, semi-conductive or conductive
materials. The level of electrical conductivity defines the applications in which CPCs can be
used. Charge storage, ESD protection and EMI shielding are the major applications of CPCs,
requiring low, medium and high electrical conductivity, respectively.
Accordingly, this dissertation aimed to create unique morphologies of nanocomposites by
manipulating mixing methods and processing conditions employing different nanofillers, and
then relating the obtained morphologies to the final electrical properties, i.e., electrical
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conductivity, electromagnetic interference (EMI) shielding and dielectric properties. In order to
perform do this, multi-walled carbon nanotube (MWCNT) was selected as the conductive filler,
due to its extraordinary electrical properties and increasing industrial usage; and PC, PS and
PVDF were employed as the polymer matrices.
In this dissertation, controlling the conductive network formation was the key aspect in
designing the morphology of CPCs for electrical applications. Improving the conductive network
formation enhances electrical conductivity and EMI shielding; whereas, deteriorating the
conductive network formation decreases the leakage current, thereby improving dielectric
properties [1-4]. Having the knowledge of controlling the conductive network formation enables
the manufacturers to employ cost-effective materials and proper processing conditions to attain
the desired properties. In this dissertation, two distinct techniques were employed to manipulate
the conductive network formation to improve the electrical properties including:
Aligning the conductive filler (MWCNT) using an injection molding machine
Changing the type of conductive filler (substituting MWCNTs with copper nanowires
(CuNWs))
This dissertation was directed to scrutinize the influence of the above-mentioned techniques
on electrical properties of CPCs. These techniques were manipulated to tailor the conductive
network formation to improve electrical conductivity and EMI shielding or dielectric properties.
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9.2. Electrical Behaviors of CPCs and the Mechanisms Behind
Prior to exploring the influence of the above-mentioned techniques on the electrical properties
of CPCs, some studies were implemented on MWCNT/polymer composites to obtain a general
understanding of the realm of CPCs and their electrical behaviors. These studies investigated the
electrical behaviors of MWCNT/polymer composites, as typical CPCs, as functions of MWCNT
loading and composite thickness, and were used to describe the mechanisms behind the behavior.
9.2.1. Volume Resistivity
Volume resistivity is the reciprocal of electrical conductivity and defined as the electrical
resistance through a cube of a material. When expressed in ohmcm, it would be the electrical
resistance through a one-centimeter cube of a material. Volume resistivity is considered to be an
important factor when dealing with the bulk of materials, such as EMI shielding and charge
storage. Volume resistivity of materials is a property which spans a very wide range. The
resistivity of insulators is typically more than 1014
Ωcm, that of semi-conductive materials
covers the range 1014
to around 1 Ωcm, and for semi-metals and metals it is less than 1 Ωcm.
The results showed that the volume resistivity of MWCNT/polymer composites decreased
with increase in MWCNT content due to formation of conductive network. Generally speaking,
the descent of volume resistivity with MWCNT concentration can be better described by the
percolation curve (volume resistivity versus MWCNT content curve). The percolation curve of
CPCs can be divided into three distinct regions: 1) the region far below the percolation threshold
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(insulative zone), (2) the region where percolation occurs (percolation zone) and (3) the region
far above the percolation threshold (conductive zone).
In the insulative region, the MWCNTs are far from each other and the polymer matrix
restricts the conductance, due to its insulative properties. By raising the filler loading further, the
fillers get closer and ultimately at a critical concentration range called the percolation threshold,
the first conductive network forms, which lets the current pass through. In the percolation region,
where percolation occurs, the free electrons in conductive filler will increasingly play the role of
charge carriers due to direct contact between MWCNTs; thus, the resistivity of nanocomposite
diminishes by several orders of magnitude. After percolation, as the filler concentration
increases, the clusters initiate connections with each other to form a 3-D network which leads to
further decrease in resistivity. Nevertheless, in the conductive region, the constriction resistance
of contact spots between MWCNTs leads the resistivity to decrease marginally. In fact, a
considerable amount of current dissipates at the contact spots between the conductive fillers
leading to a plateau in the percolation curve at high MWCNT concentrations.
9.2.2. EMI Shielding
Electronic devices inherently irradiate electromagnetic (EM) waves. As these waves can
interfere with the operation of other electronics, related agencies have applied regulations to
shield the EM waves. In order to perform effective shielding, electronics should be enclosed with
appropriate conductive shields. CPCs are promising candidates to shield electronics, due to their
low weight, low cost, and easy processability that improve design options and reduce or
eliminate the seams and penetrations in electronics’ enclosures.
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Conventional polymers, due to their insulative nature, are inherently transparent to incident
EM waves. However, CPCs due to presence of interacting mobile charge carriers in conductive
filler can shield the EM wave efficiently. EMI shielding in CPCs comprises three distinct
mechanisms; namely reflection, absorption and multiple-reflection. When an EM wave strikes a
medium with unlike intrinsic impedance from the space in which EM wave is propagating, a
portion of EM wave is reflected off from the shielding material surface; a portion of EM wave
penetrates through the material, which is attenuated through absorption mechanism; and the
remaining portion is transmitted out the material. The lower the power of the transmitted wave,
the higher is the efficiency of shielding material.
To study the shielding mechanisms of CPCs accurately, the contributions of absorption and
reflection to EMI shielding as functions of MWCNT concentration and material thickness were
investigated. It was observed that the values of both reflection and absorption increased with
increase in MWCNT concentration. The ascent in reflection with MWCNT loading is attributed
to higher amount of interacting mobile charge carriers on the surface of CPCs. However, the
ascending trend of absorption with MWCNT loading is more complicated to explain and is
attributed to higher imaginary permittivity (Ohmic loss) and real permittivity (polarization loss)
of the MWCNT/polymer composites [1, 2].
Real permittivity in MWCNT/polymer composites arises from the formation of a large
number of nanocapacitors, i.e., MWCNTs acting as electrodes and insulative polymeric layer
acting as dielectric material, and also presence of structural defects (polarization centers) in
MWCNTs [5-7]. Increasing MWCNT concentration results in an increase in both the number of
nanocapacitors and polarization centers, leading to higher real permittivity (charge polarization).
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In addition, increasing MWCNT concentration is accompanied with a reduction in the thickness
of insulative polymeric gaps between MWCNTs leading to greater electronic polarization of
polymeric layer. Hence, there is a direct relationship between MWCNT loading and the
polarization loss in AC field and shielding by absorption.
Imaginary permittivity of MWCNT/polymer composites originating from Ohmic loss also
contributes significantly to shielding by absorption, where energy is dissipated by movement of
the nomadic charge carriers along the MWCNTs. Increasing MWCNT concentration is
associated with an increase in the number of dissipating mobile charge carriers leading to higher
imaginary permittivity; and therefore, higher shielding by absorption. Moreover, as additional
networks are formed, the electrons have a greater mean free path in which to move according to
the direction of electric field in each half cycle and, consequently, could dissipate more electrical
energy, i.e. higher Ohmic loss.
Multiple-reflection is the third mechanism of shielding representing internal reflections inside
a conductive barrier. This mechanism usually occurs in materials with large interfacial areas,
such as filler-polymer systems. Multiple-reflection has a negative influence on overall EMI
shielding, since its resultant is an increment in transmitted wave. Multiple-reflection can be
ignored if the shield’s thickness is larger than the shield’s skin depth [3]. The skin depth is the
distance inside the conductive material at which the wave power decreases to of its incident
value and is defined as √ , where f is the wave frequency, μ is shield’s magnetic
permeability and σ is the shield’s electrical conductivity. As multiple-reflection cannot be
measured independently, its influence is inherent in shieldings by reflection and absorption. In
our samples, particularly at high shielding values, multiple-reflection can be ignored.
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9.2.3. Broadband Dielectric Spectroscopy of CPC
Generally, charge polarization in MWCNT/polymer composites arises from three sources,
namely 1) interfacial polarization, 2) MWCNT polarization, and 3) polymer polarization.
Interfacial polarization usually occurs in heterogeneous systems with phases with different
conductivities or real permittivities, such as MWCNT/polymer composites [8]. At the internal
phase boundaries of polymer and MWCNTs, nomadic charge carriers can be trapped and cause
charge polarization. As electric dipole has a magnitude equal to strength of each charge times the
separation between charges, the contribution of interfacial polarization to dielectric permittivity
can be orders of magnitude larger than other types of polarization, since the charge carriers are
separated over a considerable distance, i.e., at the mesoscopic scale. It is worthwhile to mention
that interfacial polarization diminishes greatly with increased frequency, due to the large
retardation time of interfacial polarization with respect to the electric field frequency at high
frequencies (relaxation phenomenon) [9].
MWCNT polarization also contributes to the real permittivity of MWCNT/polymer
composites, particularly at high frequencies where interfacial polarization is weak. It is believed
that the crystallographic defects in MWCNT structures may behave as polarized centers [10]. For
instance, a defect in the armchair-type CNT, which can conduct electricity, can cause the
surrounding region to be semiconducting. Therefore, in the molecular structure of MWCNTs,
there may be two regions with dissimilar conductivities that induce charge polarization on the
molecular scale.
The electronic polarization of polymer matrix also contributes to real permittivity, particularly
at high frequencies. In the narrow insulative gaps between MWCNTs, there may be a buildup of
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very high field strength, which is higher than the macroscopic field strength by a factor of M (i.e.,
M is the ratio of the average size of the conducting MWCNT aggregates to the average gap
width) [11]. This high field strength contributes significantly to the electronic polarization of
polymer matrix and, thus, real permittivity.
Real and imaginary permittivities of CPCs over the broadband frequency range are functions
of many parameters, including conductive filler and polymer matrix features, content of filler,
interaction of conductive filler and polymer matrix, frequency range, etc [12, 13]. The results
demonstrated that the real permittivity rose considerably, specifically at low frequencies, as the
MWCNT concentration approaches the percolation threshold or beyond. As a matter fact, huge
real permittivities close to or above the percolation threshold arose from the formation of a large
number of nanocapacitor structures experiencing interfacial polarization, i.e., MWCNTs as
nanoelectrodes and polymer matrix as dielectric material. It was also observed that the real
permittivity was frequency-independent in the insulative region (concentrations below the
percolation threshold); however, it was a strong function of frequency in the conductive region.
This phenomenon was related to relaxation phenomenon of interfacial polarization occurring at
higher frequencies. As a matter of fact, the accumulated charges at the interface did not adapt
themselves to increased frequency, resulting in the relaxation phenomenon.
Likewise, the results showed that the imaginary permittivity was very low at MWCNT
concentrations far below the percolation threshold; nonetheless, it increased considerably
(several orders of magnitude) as the MWCNT concentration approached the percolation
threshold. High imaginary permittivity at MWCNT concentrations close to or above the
percolation threshold was attributed to two mechanisms: (1) increase in the amount of interacting
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nomadic charges in the composite due to growth in the content of MWCNTs, and (2) the
formation of conductive network in the composite which provided the nomadic charges with
greater mean free path in which to move in each half cycle of alternating field. It was also
observed that imaginary permittivity was frequency-independent in the insulative region;
whereas it showed a very strong descending trend with frequency in the conductive region.
9.3. Effects of MWCNT Alignment, Induced by Injection Molding, on Volume Resistivity
and EMI Shielding
In order to explore the effects of MWCNT alignment, induced by an injection molding
machine, on the electrical properties of the injection molded MWCNT/PS composites, a series of
injection molding experiments were carried out on a 5.00 wt% MWCNT/PS composites using a
two-level, four-factor factorial design to study the impact of four processing parameters, i.e.,
mold temperature, melt temperature, injection/holding pressure and injection velocity on the
volume resistivity of the molded composites. An injection molding machine (Boy 12A) was used
to inject the MWCNT/PS nanocomposite melt into a rectangular cavity. The cavity was fed with
an edge gate and had dimensions of 22.86 × 10.16 × 2.0 mm.
The results showed a decrease of about ten orders of magnitude in the volume resistivity by
adding 5.00 wt% MWCNT, compared with pure PS. Interestingly, depending on the processing
conditions, differences in the volume resistivity up to six orders of magnitude was observed in
the thickness direction of the nanocomposites. The results revealed that the melt temperature
followed by the injection velocity had the greatest influence on MWCNT alignment and volume
resistivity, while the influences of mold temperature and injection pressure were unimportant. In
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other words, the composites produced at lower melt temperature and higher injection velocity
underwent higher shear rate, and thus presented greater MWCNT alignment. It was also
observed that the greater MWCNT alignment was associated with inferior conductive network
formation and higher volume resistivity.
To investigate the influence of MWCNT alignment on electrical properties at different
MWCNT concentrations, we used the results obtained from the experimental design of 5.00 wt%
MWCNT to select three processing conditions with the maximum possible variation in MWCNT
alignment, i.e., volume resistivity. In other words, knowing the considerable influence of melt
temperature and injection velocity on MWCNT alignment and volume resistivity of
MWCNT/PS nanocomposites, three different injection molding experiments (from sixteen
experiments in the experimental design) were employed to make samples with various MWCNT
alignments at different MWCNT concentrations. The selected injection molding experiments
were performed by manipulating just the melting temperature and injection velocity. The
samples made at different processing conditions were used to investigate the effects of MWCNT
alignment on the electrical properties of MWCNT/PS composites at different MWCNT
concentrations. To have a better comprehension of the effects of MWCNT alignment on the
electrical properties, the electrical properties of the injection molded samples were compared
with those of the compression molded samples, where MWCNTs were determined to be
randomly distributed.
The results displayed that the injection molded (MWCNT-aligned) samples showed a higher
volume resistivity and percolation threshold than the compression molded (randomly distributed
MWCNTs) samples. Using the Raman spectroscopy in conjunction with volume resistivity
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results, it can be claimed that the greater the alignment of MWCNTs, the higher are the
resistivity and percolation threshold of MWCNT/polymer composites. We contend that the
alignment of MWCNTs reduced the probability of MWCNTs being connected with each other,
which gave rise to a higher volume resistivity and percolation threshold.
It was also observed that the injection molded samples showed inferior EMI shielding than
the compression molded samples in the X-band frequency range (8.2 – 12.4 GHz). Moreover, the
results demonstrated that the higher MWCNT alignment corresponded to lower EMI shielding.
As there is an inverse relationship between MWCNT alignment and MWCNT connectivity, it
can be interpreted that greater MWCNT connectivity in the compression molded samples caused
higher EMI shielding. The obtained results are in agreement with researchers who believe that
EMI shielding does not require filler connectivity; nevertheless, it rises with filler connectivity
[2, 14].
To obtain more in-depth knowledge about the effect of MWCNT alignment on EMI shielding,
the impacts of MWCNT alignment on shielding by reflection and absorption were investigated.
We observed that at different MWCNT concentrations, the shielding by reflection of the
compression molded and injection molded samples were almost identical. This similarity was
described by the fact that the MWCNT surface projection normal to the incoming EM wave had
comparable area regardless of whether the MWCNTs were aligned or not. However, the
shielding by absorption was extremely sensitive to MWCNT alignment. The inverse relationship
between MWCNT alignment and conductive network formation says that the shielding by
absorption may be a strong function of MWCNT connectivity. To verify this hypothesis, the
effects of MWCNT alignment on real and imaginary permittivities were studied.
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It was interesting to observe that the real permittivity of the compression molded samples was
higher than injection molded samples in the X-band frequency range. This was attributed to
larger electronic polarization of polymer matrix in the compression molded samples. In fact, in
narrow insulative gaps between MWCNTs, very high field strength may build up, which is
higher than the macroscopic field strength by a factor of M (i.e., M is the ratio of the average size
of the conducting MWCNT aggregates to the average gap width) [15]. This high field strength
contributes significantly to the electronic polarization of the polymer matrix. Since the
possibility that MWCNTs neighbor each other in the compression molded samples was greater,
the insulative gaps of the polymer were thinner, resulting in a higher electric field and greater
electronic polarization of the polymer matrix. Therefore, the compression molded samples
showed greater real permittivity than injection molded samples. In conclusion, it can be claimed
that higher polarization of the polymer matrix in the compression molded samples played a
significant role in greater polarization loss and enhanced absorption.
We also observed that the imaginary permittivity of the injection molded samples was lower
than that of the compression molded samples and the level of this difference increased
tremendously with increase in MWCNT concentration. The higher imaginary permittivity of the
compression molded samples was ascribed to the enhanced conductive network formation, i.e.,
there was enhanced MWCNT network formation in the compression molded samples. At
enhanced conductive network formation, the electrons have a greater mean free path in which to
move according to the direction of electric field in each half cycle of alternating field, and
consequently, can dissipate more electrical energy. Greater electrons’ mean free path at lower
MWCNT alignments can be related to improved MWCNT network formation, leading to larger
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conduction current. Thus, it can be concluded that the greater electrical energy loss by free
electrons in each half cycle of alternating field in the compression molded samples, due to
greater electrons’ mean free path, contributed considerably to higher shielding by absorption.
Since the electrical conductivity and EMI shielding of the compression molded samples were
greater than those of the injection molded samples, it can be concluded that in order to obtain
high electrical conductivity and EMI shielding in injection molding process, the mold and
processing conditions should be designed in such a way to obtain random distribution of
MWCNTs.
9.4. Effects of MWCNT Alignment, Induced by Injection Molding, on Dielectric Properties
The materials used for charge storage applications are required to present high real
permittivity with a low leakage current, i.e., imaginary permittivity. High real permittivity with a
low leakage current in CPCs can only be attained at filler contents very close to the percolation
threshold [16]. The enhanced real permittivity observed in CPCs near the percolation threshold
arises from the formation of a large number of nanocapacitors, i.e., conducting clusters isolated
by thin layers of polymer. These nanocapacitors entitle CPCs to store large amount of charges.
Nevertheless, the insulator-conductor transition that occurs in CPCs at the percolation threshold
leads to a drastic variation in the volume resistivity and imaginary permittivity; thereby it
prevents employing CPCs as charge storage materials above the percolation threshold. Hence,
there is a very narrow concentration window near the percolation threshold for high aspect ratio
fillers, such as MWCNTs, to regulate the dielectric properties.
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In this dissertation, MWCNT alignment was introduced as an innovative technique to improve
the dielectric properties and to broaden the narrow concentration window used to regulate the
dielectric properties. Actually, the dielectric properties results used to justify the effects of
MWCNT alignment on EMI shielding were analyzed for another scenario, i.e., charge storage
applications. Comparing the percolation curve of the compression molded and injection molded
samples showed that the sharp decline in the volume resistivity of the injection molded samples
around the percolation threshold was muted in comparison to that of the compression molded
samples. Therefore, it can be asserted that the MWCNT alignment can provide a wider
concentration window around the percolation threshold to regulate the dielectric properties.
Wider insulator-conductor transition window decreases the challenges and risks in manipulating
CPCs around the percolation threshold to obtain the preferred dielectric properties.
We observed that the imaginary permittivities of the injection molded samples were
significantly lower than those of the compression molded samples. Lower imaginary permittivity
of the injection molded samples relative to the compression molded samples was related to
inferior network formation and lower Ohmic loss arising from MWCNT alignment. Nonetheless,
MWCNT alignment showed an adverse influence on the real permittivity. This was also related
to a lower chance of MWCNTs neighboring each other leading to a poorer electronic
polarization of polymer matrix.
Therefore, MWCNT alignment reduced both real and imaginary permittivities; however,
charge storage materials are required to present high real permittivity and low imaginary
permittivity. Hence, it is necessary to evaluate the overall impact of MWCNT alignment on the
dielectric properties. Hence, the dissipation factors (imaginary permittivity/real permittivity) of
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the compression molded and injection molded samples at different MWCNT concentrations were
compared with each other. The results showed that injection molded samples presented lower
dissipation factor than compression molded samples, thereby improving dielectric properties. In
other words, the positive effect of the MWCNT alignment on reducing the dissipative energy
dominated its adverse effect on decreasing the capacitive energy. In brief, this study shows that
injection molding process, as an industrial technique, can be creatively employed to improve the
dielectric properties of MWCNT/polymer composites for charge storage applications.
9.5. Novel CuNW/PVDF Nanocomposites for Charge Storage: Comparison of its Dielectric
Properties with MWCNT/PVDF Nanocomposite
The CPCs used for charge storage applications are needed to present high real permittivity
and low imaginary permittivity. In order to attain a high real permittivity, highly conductive
fillers are greatly appreciated, since greater amount of nomadic charges would be available for
charge polarization. The limited electrical conductivity of MWCNTs was the stimulation to
investigate the dielectric properties of CuNW/polymer composites, due to superior electrical
conductivity of CuNWs to MWCNTs.
Highly conductive CuNWs are prone to provide enhanced charge polarization. However,
unavoidable oxide layer formation on the surface of CuNWs acts as a barrier and significantly
reduces the electrical conductivity of CuNWs. Unavoidable oxide layer formation on the surface
of CuNWs, which has always been a disadvantage for electronics applications, was innovatively
employed as an advantage to decay the conductive network formation and reduce the imaginary
permittivity. In fact, the oxide layer around CuNWs has the potential to avoid the direct contacts
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between CuNWs leading to inferior conductive network formation (lower energy loss). On the
other hand, the fresh core of CuNWs can provide the composite with considerable free charges
for interfacial polarization. The results showed that high conductivity of fresh core of CuNWs in
combination with the presence of oxide layer on their surfaces caused CuNWs to show superior
dielectric properties relative to MWCNTs.
9.6. Recommendations
Processing conditions, composite morphology and composite components are the three key
factors to be manipulated to obtain the desired electrical properties. In other words, obtaining
preferred electrical properties in CPCs is possible by tailoring the processing conditions and
composite morphology using proper conductive fillers. Given these factors, the following
subjects are recommended for future work:
Developing a comprehensive model to include the effects of alignment, dispersion,
conductivity of filler and wave frequency on electrical properties of CPCs. The starting
point for this model can be the equations developed for electrical properties of conductive
monolithic materials. It should be noted that in employing these equations for CPCs the
effects of real permittivity and charge polarization should be embedded.
Studying the influence of MWCNT alignment on the broadband EMI shielding and
dielectric properties of MWCNT/polymer composites. In this dissertation, the influence of
alignment on the electrical properties of MWCNT/polymer composites was just studied
over the X-band (8.2 – 12.4 GHz). Broadband spectroscopy of electrical properties will
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provide further information about the EMI shielding mechanisms and their relationship
with real and imaginary permittivities.
Comparing the EMI shielding and dielectric properties of CPCs holding MWCNTs and
CuNWs over the X-band. This investigation can give further information about the
mechanisms behind the relationship between intrinsic conductivity of filler and EMI
shielding for high-frequency applications.
Investigating the effect of degree of CuNW oxidation on the electrical properties of
CuNW/polymer composites.
Manipulating the structure of MWCNTs in order to obtain desired electrical properties in
MWCNT/polymer composites, i.e., doping MWCNTs to improve electrical conductivity
and EMI shielding or creating structural defects to improve the dielectric properties.
Incorporating secondary ferroelectric filler such as BaTiO3, as insulating barrier, to
deteriorate conductive network formation and improve the dielectric properties of
MWCNT/polymer composites. Next, injection molding of the made composites to
examine the impacts of both MWCNT alignment and barrier layer in improving the
dielectric properties for charge storage applications.
Investigating the influence of novel nanofillers, such as exfoliated nanographene, on the
electrical properties of CPCs.
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Employing injection-compression molding to produce CPCs with high electrical
conductivity and EMI shielding. In this way, we can combine the benefits of injection
molding, as a mass production technique, and compression molding to get random
distribution of MWCNTs. As shown in the thesis, unavoidable MWCNT alignment in
injection molding process has an adverse effect on electrical conductivity and EMI
shielding.
Incorporating MWCNTs into a blend with the following features to obtain enhanced
dielectric properties: a blend with one dispersed phase and one continuous phase; the
MWCNTs should have higher affinity to dispersed phase. Accordingly, we can obtain
high real permittivity originating from MWCNT within dispersed phase and low
imaginary permittivity due to lack of a conductive network throughout the composite.
The MWCNT concentration should be low enough to not let any network form in the
continuous phase.
It was mentioned that in conductive monolithic materials, the reflection loss is a function
of whereas the absorption loss is a function of , where is electrical
conductivity and is magnetic permeability. It is known that EM wave is composed of
two components; namely electric field and magnetic field. Thus, it is important to employ
a hybrid system of filler to shield both electric field and magnetic field. We recommend
using a hybrid system of a conductive filler and a magnetic filler. As listed in Table 2-3,
silver has higher electrical conductivity and nickel has higher magnetic permeability
relative to copper. This provides an opportunity to investigate the electrical properties of
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composites comprising silver or nickel nanowires or their hybrid system. It is highly
recommended that the fillers used in hybrid composites have aspect ratios of the same
order of magnitude. The information obtained from this study can shed more light on the
relationships between filler intrinsic properties and electrical properties of composites.
Investigating the hybrid system of MWCNT and CuNW (CuNW is more conductive and
MWCNT has higher aspect ratio and surface area) to obtain enhanced dielectric
properties. It should be regarded that both electrical conductivity and surface area are
important factors in the final dielectric properties.
Studying the effects of foaming on dielectric properties due to its impact on decaying the
conductive network formation [17]. Foaming, like alignment, is a novel way to improve
dielectric properties, and to widen the typically narrow concentration window used to
regulate dielectric properties.
Injection molding of CuNW/polymer composites to take advantage of the influence of
oxidative layer on the surface of CuNWs together with CuNW alignment on the dielectric
properties.
Covering the surface of MWCNTs with an oxidative layer, such as polymer layer or
surfactant to decrease imaginary permittivity for charge storage applications.
Investigating the rheological properties of injection molded samples versus
compression molded samples. This will provide more information on the effects of
MWCNT alignment on viscosity and shear rate, which can be an important factor on
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aspect ratio loss and developed morphology in injection molded samples. Investigating
this concept is important due to significant impact of MWCNT aspect ratio on electrical
properties. (MWCNT aspect ratio is decreased by more sever processing.)
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