ELECTRICAL PROPERTIES STUDY OF CARBON FILLERS IN
POLYMER NANOCOMPOSITES
by
Wilailak Chanklin
Master of Science in Petrochemical Technology, The Petroleum and Petrochemical College,
Chulalongkorn University, Thailand, 2009
A Dissertation Submitted in Partial Fulfillment
of the Requirements for the Degree of
Doctor of Philosophy
in the Graduate Academic Unit of Chemical Engineering Department
Supervisor: L.P. Felipe Chibante, Associate Professor, Chemical Engineering Department
Examining Board: Derek Lister, Professor, Chemical Engineering Department
Guida Bendrich, Professor, Chemical Engineering Department
Amirkianoosh Kiani, Professor, Mechanical Engineering Department
External Examiner: Cheol Park, Ph.D, NASA Langley Research Center
Hampton VA
This dissertation is accepted by the
Dean of Graduate Studies
THE UNIVERSITY OF NEW BRUNSWICK
September, 2016
©Wilailak Chanklin, 2016
ii
Abstract
The aim of this dissertation is to study the effect of various carbonaceous fillers on
the electrical, mechanical and thermal properties within polymer composites. Three types of
carbon fillers are selected; multi-walled carbon nanotube (MWCNT), carbon nanofibers (CNF)
and carbon black (CB). Two types of polymers, nylon (thermoplastic) and poly-
dimethylsiloxane (elastomer) are chosen as polymer matrix materials.
In the processing of carbon-based polymer composites, a melt mixing method via
extrusion is used to produced thermoplastic polymer composites; whereas, a solution mixing
method via sonication is used to fabricate elastomeric polymer composites. With these two
composite systems, the influence of filler type and loading on several composite properties is
studied. The characterization consists of evaluating four attributes: dispersion, electrical
resistivity, mechanical properties and thermal stability.
Finally, theoretical modeling is used to study electrical properties of these composites
parallel to the experimental observation. A statistical percolation theory (power law model) is
applied in terms of fillers concentrations to determine percolation threshold and compare with
experimental data.
iii
Acknowledgements
I would like to express my sincere gratitude and thanks to Dr. Felipe Chibante for his
intellectual guidance, support and patience throughout this research work in all these years. I
am always encouraged and inspired by his enthusiasm toward scientific research and his
insightful suggestions. I am grateful to receive this opportunity in working with him under the
exciting world of nanomaterials.
I would also like to extend my thanks to Professor Derek Lister, Professor Guida
Bendrich, Professor Amirkianoosh Kiani and Professor Enrique Barrera for serving on the
committee. Their time, their input and advice are invaluable in completing the dissertation.
I would like to express my deepest gratitude towards my handy-man Mr.Jaranyoot
Loawongkotr (Aui) for all his help, time, advice, encouragement, and especially his electrical
skills during my research work. Without his passion and guidance, this research would never
have been completed.
I would like to convey my thanks to my colleagues and friends from Applied Nano
Lab (ANL) during this work. They have been a great source of help and support through all
this work during the time far from home.
A sincere appreciation goes to all the staff and technicians in the Chemical
Engineering Department at the University of New Brunswick.
Finally, I would like to pronounce my immense gratitude to my family for their
understanding and support. Sincere thankfulness to my parents for letting me continue my
studies and always motivating me.
iv
Table of contents
Abstract .................................................................................................................................... ii
Acknowledgements ................................................................................................................ iii
Table of contents .................................................................................................................... iv
List of Tables ........................................................................................................................ viii
List of Figures .......................................................................................................................... x
Chapter 1 Introduction ....................................................................................................... 1
1.1 Motivation of this research ....................................................................................... 1
1.2 Research objectives .................................................................................................. 3
1.3 Summary of the Dissertation .................................................................................... 4
Chapter 2 Literature review ............................................................................................... 5
2.1 Introduction .............................................................................................................. 5
2.2 Percolation theory of electrical properties for the polymer composites ................... 6
2.2.1 Fundamental notation and terminology ............................................................... 6
2.2.2 Electrical conduction mechanism of polymer composites .................................. 8
2.2.3 Electrical transportation mechanism in polymer composites ............................ 11
2.3 Factors affecting the electrical conductivity of the polymer composites ............... 14
2.3.1 Carbon fillers reinforcement in the polymer composites .................................. 14
2.3.1.1 Carbon nanotubes ...................................................................................... 16
2.3.1.2 Carbon nanofibers ..................................................................................... 26
2.3.1.3 Carbon black .............................................................................................. 29
2.3.2 Processing and fabrication techniques of the polymer composites ................... 33
v
2.3.2.1 Solution blending ....................................................................................... 34
2.3.2.2 Melt blending ............................................................................................. 34
2.3.2.3 In-situ polymerization ............................................................................... 35
2.4 Electrical percolation models ................................................................................. 36
2.4.1 Statistical percolation models ............................................................................ 37
2.4.2 Thermodynamic percolation models ................................................................. 40
2.4.3 Geometrical percolation models ........................................................................ 41
2.4.4 Structure oriented percolation models ............................................................... 42
2.5 Properties of the polymer composites relevant to carbon filler materials .............. 44
Chapter 3 Experimental set up ......................................................................................... 50
3.1 Materials ................................................................................................................. 50
3.1.1 Polymer matrices ............................................................................................... 51
3.1.1.1 Thermoplastic – Nylon .............................................................................. 51
3.1.1.2 Elastomer – PDMS .................................................................................... 51
3.1.2 Carbon fillers ..................................................................................................... 52
3.1.2.1 Carbon nanotubes ...................................................................................... 52
3.1.2.2 Carbon black .............................................................................................. 54
3.1.2.3 Carbon nanofibers ..................................................................................... 54
3.2 Preparation method ................................................................................................ 55
3.2.1 Thermoplastic polymer composite .................................................................... 55
3.2.2 Elastomeric polymer composite ........................................................................ 57
3.3 Characterization techniques ................................................................................... 58
3.3.1 Electrical resistivity test ..................................................................................... 59
vi
3.3.1.1 Nylon composites ...................................................................................... 59
3.3.1.2 PDMS composites ..................................................................................... 60
3.3.2 Mechanical properties testing ............................................................................ 62
3.3.2.1 Nylon composites ...................................................................................... 64
3.3.2.2 PDMS composites ..................................................................................... 65
3.3.3 Field Emission Scanning Electron Microscopy (FESEM) ................................ 66
3.3.4 Scanning Electron Microscopy (SEM) .............................................................. 66
3.3.5 Transmission Electron Microscopy (TEM) ....................................................... 67
3.3.6 Thermogravimetric analysis (TGA) .................................................................. 67
3.4 Characterization results of materials ...................................................................... 68
3.4.1 Morphology of carbon fillers ............................................................................. 68
3.4.2 Elastomeric polymer composite conditions ....................................................... 73
Chapter 4 Role of nano-carbon fillers on electrical properties of polymer composites ..
........................................................................................................................... 78
4.1 Morphology analysis .............................................................................................. 78
4.2 Composition analysis ............................................................................................. 85
4.3 Electrical resistivity and percolation behavior analysis ......................................... 86
4.3.1 Percolation threshold analysis ........................................................................... 93
4.3.2 Comparison of experimental data with numerical model .................................. 96
4.4 Mechanical properties ............................................................................................ 99
4.5 Mechanical property predictions .......................................................................... 104
4.6 Thermal stability analysis ..................................................................................... 112
vii
Chapter 5 Prediction of power law model from PDMS reinforced with carbon
nanofiber polymer composites ............................................................................... 116
5.1 Morphology analysis ............................................................................................ 117
5.2 Prediction of power law model and electrical resistivity ..................................... 120
5.2.1 Influence of filler types on composite resistivity ............................................ 126
5.2.2 Influence of mixing conditions on composite resistivity ................................. 131
5.3 Mechanical properties .......................................................................................... 134
5.3.1 Influence of filler types on mechanical properties .......................................... 137
5.3.2 Influence of mixing conditions ........................................................................ 139
5.3.3 Mechanical properties prediction .................................................................... 141
5.4 Thermal degradation behavior.............................................................................. 145
Chapter 6 Conclusion and Future works ...................................................................... 149
6.1 Role of filler in thermoplastic polymer composites ............................................. 149
6.2 Application of power law model in elastomeric polymer composites ................. 152
6.3 Contributions to knowledge ................................................................................. 154
6.4 Future work .......................................................................................................... 155
6.4.1 Surface interactions between filler and polymer matrix .................................. 155
6.4.2 Analysis of polymer composites...................................................................... 156
6.4.3 Expansion of electrical conductivity model .................................................... 156
References ............................................................................................................................ 157
Appendices ........................................................................................................................... 191
Curriculum Vitae
viii
List of Tables
Table 1 Properties comparison between CNTs and other common reinforcing materials ..... 23
Table 2 Summary of carbon black morphology for different CB grades ............................... 31
Table 3 Examples of various polymer matrix-filler composites: c = percolation threshold and
t = critical exponent in the power law equation ........................................................ 49
Table 4 Physical properties of nylon and PDMS resin ........................................................... 51
Table 5 Properties of MWCNT C70P and C150P .................................................................. 53
Table 6 Properties of CB N234 and CNF ............................................................................... 54
Table 7 Specifications of a co-rotating twin-screw kneader ................................................... 56
Table 8 Temperature profiles of the extrusion process for various conductive fillers ........... 56
Table 9 Trials of sonication conditions for PDMS-based composites .................................... 75
Table 10 CNT-nylon composition under TGA measurement................................................. 85
Table 11 CNT-nylon composition under TGA measurement................................................. 86
Table 12 Summary of the percolation parameters for nylon composites ............................... 93
Table 13 Mechanical properties of CNT-nylon composites ................................................. 103
Table 14 Thermal stability of CNT-nylon composites as a function of CNT concentration 115
Table 15 Thermal stability of CB-nylon composites as a function of CB concentration ..... 115
Table 16 Mechanical properties of PDMS composites filled with various wt% of CNF ..... 137
Table 17 Mechanical properties of PDMS composites filled with 3 wt% of various fillers 138
ix
Table 18 Mechanical properties of PDMS composites filled with 3 wt% CNF by using
sonication and stirring method................................................................................ 141
Table 19 Thermal stability of CNF-PDMS composites as a function of CNF concentration
................................................................................................................................ 148
Table 20 Volume resistivity of CNF-PDMS composites at different conditions ................. 191
Table 21 Measured resistances of CNF-PDMS composites at various conditions ............... 193
Table 22 Measured electrical resistivity of CNT-nylon composites .................................... 194
Table 23 Measured electrical resistivity of CB-nylon composites ....................................... 195
Table 24 Measured electrical resistivity of CNF-PDMS composites ................................... 196
Table 25 Measured mechanical properties of CNT-nylon composites ................................. 197
Table 26 Measured mechanical properties of CNT-nylon composites (cont’) ..................... 198
Table 27 Measured mechanical properties of CNF-PDMS composites ............................... 199
Table 28 Calculated mechanical properties of CNF-PDMS composites (cont’) .................. 200
x
List of Figures
Figure 1 Conductivity ranges of conductors ............................................................................. 2
Figure 2 Differences between (a) volume and (b) surface electric current............................... 7
Figure 3 Plots of electrical (a) resistivity and (b) conductivity for the polymer composites as a
function of conductive filler content......................................................................... 10
Figure 4 Schematic demonstrations of equivalent electrical pathways .................................. 10
Figure 5 Schematic of carbon filler network in a polymer matrix .......................................... 12
Figure 6 Surface area to volume ratio (A/V) relations for various filler geometries .............. 15
Figure 7 Schematic structures of (a) SWCNTs and (b) MWCNTs ........................................ 17
Figure 8 Bonding and length in graphite structure (related to MWCNT formation).............. 18
Figure 9 TEM observations on graphitic carbon (a) SWCNTs and (b) MWCNTs with different
numbers of graphene layers ...................................................................................... 18
Figure 10 Number of patents and publications on CNTs-polymer composites ...................... 19
Figure 11 Graphene sheet of (a) SWCNTs formation and (b) chiralities of SWCNTs .......... 21
Figure 12 Schematic illustration of the arc discharge technique ............................................ 24
Figure 13 Schematic of the laser ablation process .................................................................. 25
Figure 14 Schematic of a CVD reactor ................................................................................... 26
Figure 15 Structures of CNF: (a) stacked-cup and (b) platelet ............................................... 27
Figure 16 Size comparison of (a) single-walled carbon nanotube (SWCNT), (b) multi-walled
carbon nanotube (MWCNT), (c) carbon nanofiber (CNF), (d) vapor-grown carbon
fiber (VGCF), and (e) carbon fiber (CF) .................................................................. 28
Figure 17 Size ranges of typical carbon black structural entities ........................................... 30
xi
Figure 18 Schematic descriptions of composites made of carbon blacks. (a) low structure (b)
intermediate structure (c) high structure ................................................................... 32
Figure 19 Molecular structure of (a) Nylon 6 and (b) PDMS ................................................ 50
Figure 20 Images of a co-rotating twin-screw kneader and a screw assembly ....................... 55
Figure 21 Experimental set up of CNF-PDMS composite fabrication ................................... 58
Figure 22 (a) Dimension of nylon composite samples, and (b) experimental setup for a 2-probe
electrical resistivity test ............................................................................................ 60
Figure 23 Experimental setup for a model 831 D 991 volume resistivity test fixture ............ 61
Figure 24 ASTM D412 Type D cutter (units are in mm) ....................................................... 63
Figure 25 Single-screw extruder (Brabender) for thin film extrusion; inset, a flat sheet die head
.................................................................................................................................. 65
Figure 26 Dog-bone shape specimen of PDMS-based composites for mechanical testing .... 66
Figure 27 Micrographs of CNT-C70P via (a) FESEM; (b) and (c) TEM .............................. 69
Figure 28 Micrographs of CNT-C150P via SEM at different magnifications........................ 70
Figure 29 FESEM images of CB N234 .................................................................................. 71
Figure 30 Micrographs of CNF Pyrograf III via (a) SEM;(b) and (c) TEM. NOTE:
* Image obtained from the manufacturer’s data sheet ............................................... 72
Figure 31 Compressive test of PDMS composites using a data acquisition circuit board ..... 73
Figure 32 Electrical resistance vs force applied for PDMS filled with 2 wt% CNF composites
.................................................................................................................................. 76
Figure 33 Volume resistivity of CNF-PDMS composites at 2 wt% under different sonication
conditions .................................................................................................................. 77
Figure 34 SEM images of neat nylon 6 under nitrogen fractured surfaces ............................ 79
xii
Figure 35 Tensile fractured surfaces of CNT-nylon composites at high magnification: (a) 3,
(b) 5, (c) 6, (d) 8, (e) 10 and (f) 12 wt% loading ...................................................... 80
Figure 36 Tensile fractured surfaces of CNT-nylon composites at low magnification: (a) 3,
(b) 5, (c) 6, (d) 8, (e) 10 and (f) 12 wt% loading ...................................................... 81
Figure 37 Tensile fractured surfaces of CNT-nylon composite at 5 wt% loading ................. 83
Figure 38 Tensile fractured surfaces of CB-nylon composites at (a) 15, (b) 20, (c) 30 and (d)
35 wt% loading ......................................................................................................... 84
Figure 39 Volume resistivity of nylon composites as a function of filler contents. ............... 87
Figure 40 Schematic of the percolation threshold of nylon composites with filler loadings of
(top) CNT and (bottom) CB ..................................................................................... 90
Figure 41 Schematic of CB and CNT conduction path within a test distance of volume
resistivity measurement ............................................................................................ 92
Figure 42 Log-log plot of resistivity as a function of (–c) with a linear fit for nylon
composites filled with CNT and CB ......................................................................... 94
Figure 43 Electrical resistivity modeling results of CNT-nylon and CB-nylon composites .. 98
Figure 44 Stress-Strain curve of CNT-nylon composites at various CNT loading .............. 100
Figure 45 Mechanical properties of CNT-nylon composites at various % loading (a) tensile
strength, (b) modulus, (c) toughness, and (d) elongation at break ......................... 102
Figure 46 Halpin-Tsai prediction and experimental results of modulus for CNT-nylon
composites at various %loading ............................................................................. 106
Figure 47 High magnification TEM micrographs of CNT-C70P representing the defects within
nanotube structure ................................................................................................... 107
xiii
Figure 48 Comparison of modulus between the experiment results and the Halpin-Tsai model
at various filler modulus values (Ef) ....................................................................... 108
Figure 49 Comparison of modulus between the experiment result and the Halpin-Tsai model
at various nylon modulus values (Em) .................................................................... 109
Figure 50 Comparison of modulus between the experiment result and the Halpin-Tsai model
at various aspect ratios of CNT (l/d)....................................................................... 110
Figure 51 Modified-Halpin-Tsai prediction and experimental results of modulus for CNT-
nylon composites at various % loading .................................................................. 111
Figure 52 TGA thermograph of CNT-nylon composites at a heating rate of 20C/min under
nitrogen flow; inset is a close-up look .................................................................... 113
Figure 53 TGA thermograph of CB-nylon composites at a heating rate of 20C/min under
nitrogen flow; inset is a close-up look .................................................................... 114
Figure 54 Tensile fractured surfaces of the CNF-PDMS composites under SEM at various
loadings(a) blank PDMS, (b) 1 wt%, (c) 2 wt%, (d) 3 wt%, (e) 4 wt% and (f) 5 wt%
................................................................................................................................ 119
Figure 55 Resistivity results of PDMS composites filled with CNTs and CNFs at 2 and 5 wt%
................................................................................................................................ 120
Figure 56 Electrical resistivity of CNF-PDMS composites as a function of CNF loadings. 122
Figure 57 Plot of log-log resistivity as a function of (–c) with a linear fit for CNF-PDMS
composites .............................................................................................................. 123
Figure 58 Electrical resistivity modeling results of CNF-PDMS composites ...................... 126
Figure 59 Volume resistivity of PDMS composites filled with 3 wt% CNTs, 3 wt% CNF and
15 wt% CB .............................................................................................................. 127
xiv
Figure 60 SEM images of PDMS composites filled with various carbon fillers at 3 wt% via
sonication method (a) CNT-C70P, (b) CNT-C150P, and (c) CNF ........................ 129
Figure 61 (a) SEM images of PDMS composites filled with 15 wt% CB and (b) images of
uncured PDMS composites filled with 20 wt% CB ............................................... 130
Figure 62 Volume resistivity of PDMS-CNT composites at various fabrication conditions 131
Figure 63 SEM images of PDMS composites filled with (a) 3 wt% of CNT-C70P via
mechanical stirring method, (b) 5 wt% of CNT-C70P via mechanical stirring method
and (c) 3 wt% of CNT-70P via sonication method................................................. 133
Figure 64 Stress-Strain curve of CNF-PDMS composites ................................................... 135
Figure 65 Mechanical properties of CNF-PDMS composites at various % loading ............ 136
Figure 66 Mechanical properties of PDMS composites filled with various fillers............... 138
Figure 67 Images of (a) CNT-C70P (TEM), (b) CNT-C150P (SEM), and (c) CNF (TEM) 139
Figure 68 Mechanical properties of CNF-PDMS composites using sonication and stirring
fabrication method .................................................................................................. 140
Figure 69 Halpin-Tsai prediction and experimental results of modulus for CNF-PDMS
composites at various % loading ............................................................................ 142
Figure 70 High magnification TEM micrographs of CNF (representing the defects within
nanotube structure) ................................................................................................. 143
Figure 71 Comparison of modulus of CNF-PDMS composites between the experiment and the
Halpin-Tsai model at (a) various filler’s modulus values (Ef), and (b) various filler’s
aspect ratio values (l/d) ........................................................................................... 144
Figure 72 Modified Halpin-Tsai prediction and experimental results of modulus for CNF-
PDMS composites at various % loading ................................................................ 145
xv
Figure 73 TGA thermograph of CNF-PDMS composites at a heating rate of 10C/min under
nitrogen flow ........................................................................................................... 147
Figure 74 Compressive test of CNF-PDMS composites using a data acquisition circuit board
................................................................................................................................ 192
Figure 75 JEOL 2011 transmission electron microscope (TEM) ......................................... 201
Figure 76 (a) FE-SEM model JEOL JSM6400 and (b) SEM model JEOL JSM6400 ......... 201
Figure 77 (a) TA Instruments Q600 Simultaneous TGA/DSC and (b) Instron 4465 machine
................................................................................................................................ 202
1
Chapter 1 Introduction
Composites are a class of engineering materials consisting of a mixture of two or more
components to produce a multiphase system with properties different from the constituents.
Carbon-filled polymer composites (or carbonaceous composites) are rigid conductive carbon
fillers introduced into softer polymers. It is generally introduced to improve mechanical and
electrical properties. The carbonaceous composites can be used in many applications such as
static dissipation (Maclaga & Fisher, 2001), electromagnetic shielding (Dhawan, Singh, &
Rodrigues, 2003), and radio frequency interference shielding (Heiser, King, Konell, & Sutter,
2004), where low to moderate conductivity is acceptable. In addition, the enhanced mechanical
properties can be useful in applications of aerospace and defense where weight and mechanical
properties are critical. Among the available fillers, carbon black and carbon nanotubes have
been used extensively due to their ability to impart high electrical conductivity to a polymer
matrix at relatively low filler content (Huang J. , 2002; Sanjines, Abad, Vaju, Smajda, Mionic,
& Magrez, 2011; Wang, Takei, Takahashi, & Javey, 2013).
1.1 Motivation of this research
Polymer composite development is currently increasing due to the growing of
commercial markets such as automotive, electronics, aerospace, marine, and sporting goods.
In composite materials where distinct phases are combined together for reinforcement, it has
also drawn great interest to the improvement and design for advanced material functionalities
and specific properties at various levels of scale; for instance; light weight, structural, thermal,
chemical, mechanical, and electrical properties.
2
Polymers are generally recognized as insulating materials and have been used in
numerous applications in place of metals, glass, wood, ceramics, or leather, whether or not
their insulating property has been required. However, the thought of using polymers in
applications where electrical conductivity is needed has turned attention toward developing
electrically conductive polymer materials. A wide range of polymers including thermoplastics,
thermosets and elastomers have been used to fulfill this concept.
There have been two major approaches to produce these materials:
1. Synthesizing novel polymer materials which are intrinsically electrical conductive;
2. Adding conductive materials (fillers) into an insulating polymer in order to obtain
a conductive material system, in which its conductivity can be tuned to various ranges (shown
in Figure 1).
Figure 1 Conductivity ranges of conductors
This research work aims to study the role of nano-carbon fillers on electrical
properties of polymers composites by the preparation of well characterized samples that are
relevant to industrial scale and with tuneable applications. A detailed study of the electrical
behavior of polymers composites was conducted using both computational and experimental
approaches.
Conductivity (S/cm)
Insulators Semiconductors Conductors
3
1.2 Research objectives
The overall goal of this research was to study the fundamental effects of different
nanostructures, processing conditions, and host matrices as it relates to electrical conductivity
in order to numerically derive the percolation threshold. Models typically account for filler
concentration, components’ conductivity, compatibility between fillers and polymer matrix,
filler aspect ratio, and filler orientation.
This research also aimed to fabricate and characterize polymer composites filled with
various carbon-based materials (multi-walled carbon nanotubes, carbon black, and carbon
nanofibers) as a potential candidate for the next generation of high strength, lightweight and
conductive polymer composites. One of the key challenges in processing of carbon-based
materials is efficient dispersion. A uniform distribution of these filler materials within the
polymer matrices and strong interaction between the components are critical for effective
improvement in composites properties. The major challenge for effective utilization of carbon
fillers is their tendency to aggregate due to intermolecular or van der Waals forces.
In this context, melt compounding (for thermoplastic composites) and solution mixing
(for elastomeric polymer composites) were utilized. The dispersion of the fillers within the
polymers was characterized using a scanning electron microscope. The electrical conductivity
of the polymer composites was characterized with standard two- and four-point probe methods.
As well, thermal conductivity of the composites was characterized. The mechanical properties
of the composites were characterized using a universal material testing system.
4
1.3 Summary of the Dissertation
Chapter 2 is focused on the review of existing literature and ongoing research in the
area of polymer composites with carbon-based fillers. Fundamental properties of each filler
type such as electrical and mechanical properties are discussed along with their applications.
In addition, mathematical modeling of the electrical conductivity of the composites is reviewed
and compared with experimental observation.
Chapter 3 provides detail of the experiments that were performed in this research work
as well as the characterization techniques used.
Chapter 4 and 5 present the results of the experimental investigation which were
discussed in sufficient detail.
Chapter 6 is dedicated to the key conclusions, and future work and some
recommendations are presented.
5
Chapter 2 Literature review
This chapter concisely presents an overview of published research and ongoing
research efforts in the area of carbon-based polymer composite materials. This review mainly
discusses the following:
- Background information on carbon-based fillers reinforcement in the polymer
composites: carbon nanotubes, carbon nanofibers, and carbon black
- Theory of percolation for electrical properties of the polymer composites
- Processing and fabrication techniques of the polymer composites
- Some properties of polymer composites relevant to carbon filler materials
2.1 Introduction
It has been shown that the demand of conductive materials for use in advanced
technology applications is growing (Harris, 2004; Jordan, Jacob, Tannenbaum, Sharaf, &
Jasiuk, 2005). To fully understand the usefulness of these materials, it is necessary to develop
fundamental knowledge of the factors that influence composite conductivity. This would
include studying the basic principles of composite conductivity and understanding how
different constituent material properties could change the conductivity values. This
information can be further applied to the development of new composites for use in various
applications.
One way to simplify the information is through the use of electrical conductivity
models, where their accuracies can be an advantage for several reasons. Models allow more
efficient materials design to target a specific conductivity range, which can reduce the costly
material used and time (Foygel, Morris, Anez, French, & Sobolev, 2005; Kim, Pfeifer, Park,
6
& Bandaru, 2011; Reza, 2014). Therefore, understanding the mechanisms that control
composite conductivity, while maintaining other properties, can help the research and the
industry to develop suitable and tunable conductive materials as the demand is forecasted to
increase.
2.2 Percolation theory of electrical properties for the polymer composites
Conventional polymeric materials lack suitable electrical, thermal, and mechanical
properties to satisfy the specific requirements for modern applications. The preparation of
advanced composites exhibiting better performance is currently required in several industrial
sectors (Thostenson, Ren, & Chou, 2001; Njuguna & Pielichowski, 2003; Chou, Gao,
Thostenson, Zhang, & Byun, 2010). A suitable design of multifunctional composites can be
achieved by choosing the appropriate synthetic polymers and fillers tailored to optimize the
polymer-filler interface. These polymer composites, preserving remarkable mechanical
properties of the matrix and exhibiting a sufficiently high electrical conductivity, have been
proposed for the dissipation of electrostatic charges, for electromagnetic shielding, electronic
packaging, sensors, and as structural parts in automotive and aerospace applications (Bauhofer
& Kovacs, 2009).
2.2.1 Fundamental notation and terminology
Before further discussion in detail on percolation theory, it is helpful to establish some
fundamental notation and terminology.
When a potential difference is applied between two electrodes, a current is created
while the displacement of charges is observed. The material offers resistance to flow of
charges, governed by Ohm’s law (Equation 2-1):
7
V = IR
Equation 2-1
where V is the potential difference (volt) between the electrodes, I is the current (ampere) or
displacement of charges between electrodes, and R is the resistance (ohm, ) of the material
to the flow of charges.
Depending on the position of the electrodes, the current can be mainly in the volume
or along the surface of the specimen; both configurations are present in Figure 2.
(a) (b)
Figure 2 Differences between (a) volume and (b) surface electric current
Resistance depends on sample size, electrode type and electrode size. To obtain an
intrinsic characteristic of the material, resistance is multiplied by a conversion factor leading
to a value of resistivity (Equation 2-2). Two different types of resistivity can be defined;
surface resistivity (in ohm/) and volume resistivity (in ohm-cm), which take into account the
geometry of the electrodes and the samples (Northrup, 1912).
e-
- - - -
+ + + + e-
- +
8
ρ = RmA
L
Equation 2-2
where is the resistivity (ohm-cm), Rm is the measured resistance (ohm), A is the cross-
sectional area in the length direction, and L is the distance between potential electrodes.
On the other hand, conductance is defined as the inverse or reciprocal of the electric
resistance and has the measurement unit of Siemens (S). Similarly, electrical conductivity ()
is the reciprocal of resistivity (Equation 2-3) which is the ability of a material to conduct an
electric current and has the unit of S/cm.
σ = 1
ρ
Equation 2-3
2.2.2 Electrical conduction mechanism of polymer composites
Different types of conductive fillers ranging from inorganic powders of metals to
carbonaceous fillers of carbon black, carbon nanotubes, carbon nanofibers, graphite have been
reported as potential candidates of reinforcements for electrical applications. The composite
conductivity containing different polymer-filler combinations results in different range of
application. This is because the conduction in a composite system is governed by complex
function of several parameters such as conductive filler’s loading and properties; the chemical
nature, molecular weight and viscosity of polymer; and the mixing and finishing process.
The electrical conductivity of conductive fillers and polymer resin mixtures can be
explained by using the percolation theory. Percolation theory was first studied by Broadbent
9
and Hammersley (Broadbent & Hammersley, 1957) and is developed to mathematically
describe a disordered media, where disorder is defined as a random variation in the degree of
connectivity. The formation of conductive paths when the filler concentration is higher than a
threshold or critical value.
In any insulating polymer matrix, a conductive filler material is added to obtain an
electrically active composite that facilitate charge transfer. Charge transfer in composite
materials occurs via conduction channels that get established by fillers contacts. A conduction
network is formed when electrons transfer from one point to another within the composite.
However, for the entire composite to be conducting, this conduction network has to expand
from one end to the other end of the composite. This can happen only when sufficient numbers
of fillers come into contact with another between two opposite ends of the composite. Thus,
electrical conduction of composite materials is a function of filler concentration (Liang, Ling,
Lu, & Liu, 2000).
By gradually filling conductive filler particles into insulating polymers, the variation
of electrical conductivity of composites can be divided into three distinct zones; insulation,
percolation, and conduction (Donnet, Bansal, & Wang, 1993), as shown in Figure 3. For a
better understanding of the relations linking the electrical properties with the geometrical and
physical characteristics of the composite, a schematic model of the structures obtained by
randomly mixing conducting cylinders inside an insulating cubic matrix is presented in Figure
4.
10
(a) (b)
Figure 3 Plots of electrical (a) resistivity and (b) conductivity for the polymer composites
as a function of conductive filler content
Figure 4 Schematic demonstrations of equivalent electrical pathways
In the first stage (Figure 4(a)), the electrical conductivity is very low since there are
only a few fillers causing large mean distance between particles. The electrical conductivity of
composites is close to that of the polymer matrices. However, it should be noted that some
Resi
stiv
ity
Filler content
Insulation
Zone
Percolation
ZoneConduction
Zone
Cond
ucti
vit
y
Filler content
Insulation
Zone
Percolation
ZoneConduction
Zone
Polymer
CNT
a b c d
Polymer
CNT
a b c d
11
large clusters connected by fillers are gradually formed in Figure 4(b) since there are some
fillers that are close to each other. Therefore, the electrical conductivity of composites
increases gradually due to tunneling effects among those neighboring fillers although there is
no complete conductive path formed by contacting fillers.
In the second stage, as the amount of fillers increases, the first complete electrically-
conductive path connected is formed across the entire composite (red path in Figure 4(c)).
According to the percolation theory, the presence of at least one electrical path gives the sharp
transition from the insulator behavior to the conductive one. Thus, the electrical conductivity
of composites exponentially increases in this stage. This process is termed the percolation
process, and the concentration of filler particles at this stage is called “percolation threshold”
(c) (Stauffer & Aharony, 1994).
In the final stage (Figure 4(d)), further addition of filler particles into the polymer
matrix progressively creates more electrically-conductive paths. When a percolation network
of filler is established in the polymer, a continuous path of conductive particles is formed; the
electron can travel from one surface through the material. Then, the electrical conductivity of
composites further increases gradually until leveling off occurs at a constant value.
2.2.3 Electrical transportation mechanism in polymer composites
It is found that the electrical conductive performances of the composites strongly
depend on the intrinsic response of the constituent materials (polymer resin and carbon fillers)
and on the correlate interactions which are governed by the interfacial properties. In a
percolating system, three different conduction regimes have been purposed based on the
distance of separation between filler particles (Medalia, 1986). The electrical resistive
phenomenon of materials is associated to two general types of resistances (Obitayo & Liu,
12
2012; Bao, Meguid, Zhu, & Weng, 2012; De Vivo, Lamberti, Spinelli, Tucci, Vertuccio, &
Vittoria, 2014): the intrinsic resistance of fillers (Rf) and the inter-tube resistances between
filler particles as schematically illustrated in Figure 5.
At low filler loading (well below percolation threshold), the mean distance between
filler particles appears to be larger than 10 nm. This separation does not permit the inter-
particulate tunneling to take place, where the composite conductivity is controlled by the
conductivity of the matrix. As the filler content increases (mean particle distance 10 nm),
conduction is assisted by the electric field based on quantum mechanical tunneling between
neighboring filler particles (Kirkpatrick, 1973; Ounaies, Park, Wise, Siochi, & Harison, 2003).
Figure 5 Schematic of carbon filler network in a polymer matrix
Due to the intrinsically good electrical conductivity of carbon fillers; however, the
conduction in the composites based on fillers random network is not correspondingly efficient.
The reason is due to the dominant role of the inter-tube resistances that is much higher than
the intrinsic resistance. Thus, great attention has been focused on the inter-tube phenomenon
(Paschen, Bussac, Zuppiroli, Minder, & Hilti, 1995).
RfRt
Rc
Polymer matrix
13
The inter-tube resistances are further divided into two types: the contact resistance
(Rc) and the tunneling resistance (Rt). The contact resistance is the resistance between filler
particles that are physically in contact in which the conduction takes place between these
particles through electron diffusion. The contact resistance has been showed to depend greatly
on the contact region and has large values variations (Yang, Anantram, Han, & Lu, 1999).
When there is a gap between the filler particles, conduction selectively occurs by a
tunneling mechanism. Tunneling is a relative phenomenon that is strongly influenced by the
distance between a pair of neighboring particles. This mechanism of electrical conduction
disappears gradually with increasing of the tunneling distance. Consequently, an increase of
the tunneling resistance or a decrease in electrical conductivity is observed (De Vivo, Lamberti,
Spinelli, Tucci, Vertuccio, & Vittoria, 2014; Spinelli, Giustiniani, Lamberti, Tucci, &
Zamboni, 2012). When the loading is sufficiently high, filler particles come closer into contact
and conduction occurs through the connecting paths established.
Considering that carbon fillers in a composite are randomly dispersed in the polymer
matrix, and the charge carriers choose the lowest resistance path possible through the
composite, a simple mathematic equation for the composite resistance (as shown in Equation
2-4) can be assumed to be the summation of the filler contact resistance without an insulating
film, and the resistance from its inherent properties, with account of amount of filler particles
presented:
Rcomposite = nRintrinsic + nRcontact
Equation 2-4
14
where Rcomposite is the composite resistance, n is the numbers of filler particle at the percolation
concentration, Rintrinsic is an intrinsic resistance of filler, and Rcontact is a contact resistance
between adjacent filler particles.
In addition, transport characteristics of the composite filled with conductive elements
are also dependent on many other parameters such as temperature, atmosphere, voltage
applied, and degree of dispersion (Mobius, 1996; Oana, Gunter, Leendert, & Gijsbertus, 2016).
2.3 Factors affecting the electrical conductivity of the polymer composites
Composite materials are the key interest in many fields of engineering applications.
Major advantages are their technological and ecological properties and potentials. One
essential property that limits the application-field of such composites is that the polymers are
non-electrically conductive. With an electrical resistivity more than 108 -cm, the polymer
cannot discharge static electric load. In order to attain an electrically conductive polymer,
electrical conductive fillers can be established in the material to form a continuous pathway or
percolation of the conductive fillers (Ezquerra, Connor, Roy, Kulescza, Fernandes-
Nascimento, & Balta-Calleja, 2001; Taipalus, Harmia, Zhang, & Friedrich, 2001; Brigandi,
Cogen, & Pearson, 2014).
2.3.1 Carbon fillers reinforcement in the polymer composites
Nanocomposites generally consist of a nanometer-scale phase in combination with
another phase. In term of nano-filler dimensionality, they can be classified into three systems:
one-dimensional (fiber), two-dimensional (platelet) and three-dimensional (sphere and
interpenetrating network).
15
A fundamental morphological characteristic in understanding the structure property
relation of composites is the surface area to volume ratio (A/V) of the addition fillers as seen
in Figure 6, where “d” is the particle or fiber diameter, “l” is the fiber or platelet length and “t”
is the platelet thickness (Hussain, Hojjati, Okamoto, & Gorga, 2006). The reduction of particle
diameter, platelet thickness, or fiber diameter from micrometer to nanometer changes the ratio
by three orders of magnitude. This increase in the interfacial area of nano-filler means that the
properties of the composites are dominated by the properties of the interface. In addition, the
increase in interfacial area makes the dispersion of nano-filler more difficult since the tendency
to agglomerate will be greater due to the larger contact surfaces (Thostenson, Li, & Chou,
2005).
One-dimensional Two-dimensional Three-dimensional
Figure 6 Surface area to volume ratio (A/V) relations for various filler geometries
Carbon fillers impart good conductivity to polymers and are consequently used at low
concentration in the manufacturing of conducting compounds. However, the use of a particular
carbon filler depends upon several factors such as the ability of the polymer to accept a certain
carbon filler concentration, the critical volume fraction at which the electrical percolation
occurs, the process ability of final composites, and the overall properties balance achieved at
the desired conductivity level (Paul & Robenson, 2008). Other properties, such as particle size,
l
lt
d d
l
l
lt
d d
l
l
lt
d d
l
A
V=
2
l +
4
d
A
V=
2
t +
4
l
A
V=
6
d
16
can have an effect on the electrical conductivity. It has been shown that for spherical particles,
smaller particle size will lower the percolation threshold (Clingerman, King, Schulz, &
Meyers, 2002; Du, Fischer, & Winey, 2005). It has been also studied that an aspect ratio (a
ratio of length to diameter, L/D) greater than one, as well as a broader range of aspect ratios
can lower the percolation threshold (Li, et al., 2007; Ayatollahi, Shadlou, Shokrieh, &
Chitsazzadeh, 2011; Pan & Li, 2013; Guo, et al., 2014).
2.3.1.1 Carbon nanotubes
Carbon nanotubes (CNTs) come in different types and they vary significantly
depending on the synthesis procedures. This section contains a brief introduction to carbon
nanotubes, sources of nanotubes, and some fundamental properties of nanotubes that are
critical to understanding in polymer composites.
Structure of carbon nanotubes
Carbon nanotubes are hollow long cylinders of covalently bonded carbon atoms
(Saito, Dresselhaus, & Dresselhaus, 1998; Hilding, Grulke, Zhang, & Lockwood, 2003; Kuilla,
Bhadra, Yao, Kim, Bose, & Lee, 2010). There are two basic types of CNTs that have high
structural perfection: (i) single-walled carbon nanotubes (SWCNTs), which consist of a single
graphene (a thin layer of carbon atoms arranged in a hexagonal honeycomb lattice) sheet
seamlessly wrapped into a cylindrical tube as shown in Figure 7(a) (Iijima, 1991; Iijima,
Ichihashi, & Ando, 1992; Bethune, et al., 1993); and (ii) multi-walled carbon nanotubes
(MWCNTs), comprised of up to several tens of concentric graphite sheets (layers of graphene
stacked on top of each other), discovered in 1991 by Iijima (Iijima, 1991; Iijima, Ichihashi, &
Ando, 1992) as illustrated in Figure 7 (b).
17
The diameter of a SWCNT is usually in the range of 0.5–2.0 nm, and the length can
be more than a micron (Bhushan, 2010). However, MWCNTs consist of numerous concentric
SWCNTs of varying diameter held together by weak van der Waals forces (Obitayo & Liu,
2012). The typical outer diameter of MWCNTs ranges from 3–30 nm (Qian, Dickey, Andrews,
& Rantell, 2000) with the interlayer spacing of approximately 0.34 nm between tubes (Iijima,
1991; Saito, Dresselhaus, & Dresselhaus, 1998; Terrones, 2004), as illustrated in Figure 8.
(a)
(b)
Figure 7 Schematic structures of (a) SWCNTs and (b) MWCNTs
Graphene sheet
Roll up
SWCNT
Graphite
(multiple graphene sheets)
Roll up
MWCNT
18
Figure 8 Bonding and length in graphite structure (related to MWCNT formation)
Figure 9 demonstrates the transmission electron microscopy (TEM) analysis on
crystal structures of SWCNTs (Zettle, 2015) and MWCNTs (Iijima, 1991) with five (left), two
(middle) and seven (right) graphene layers, respectively.
(a) (b) 6.7 nm 5.5 nm 6.5 nm
Figure 9 TEM observations on graphitic carbon (a) SWCNTs and (b) MWCNTs with
different numbers of graphene layers
Carbon atoms
Covalent bonds
Van der Waals
bonds
0.14 nm
0.34 nm
19
Numerous investigators have reported on remarkable physical and mechanical
properties for this form of carbon (Popov, 2004; Breuer & Sundararaj, 2004; Chun, Kuniharu,
Toshitake, & Ali, 2013; Liu & Kumar, 2014). From their unique electrical properties and
thermal conductivity (higher than diamond) to mechanical properties where the stiffness,
strength, and resilience exceed any current material, carbon nanotubes present tremendous
opportunities for the development of fundamentally new material systems. Figure 10 shows
the number of publications and patents in the area of carbon nanotubes and their polymer
composites since they were discovered (Moniruzzaman & Winey, 2006).
Figure 10 Number of patents and publications on CNTs-polymer composites
Each type of nanotubes holds particular properties, making them widely utilized in
different applications. Due to their nanoscale dimensions, nanotubes have large surface areas
which can enhance the interaction between the nanotubes and the polymer in the composites.
Year
1990 1992 1994 1996 1998 2000 2002 2004 2006
5000
4000
3000
2000
1000
0
Nu
mb
er o
f p
ub
lica
tio
ns/
pa
ten
ts
CNT article)
CNT patents
CNT/polymer articles
CNT/polymer patents
20
Electrical properties of carbon nanotubes
Carbon nanotubes possess unique electrical properties, where their properties have
been thoroughly explored both in theory and in experiment. CNTS possess higher electrical
conductivity than copper due to their low resistance and very few defects along their structure
(Mikitaev, Kozlov, & Zaikov, 2008). The electrical resistivity of CNTs was found to be as low
as 10-6 -m and can often be altered by modifying the structure of the nanotube lattice
(Meyyappan, 2005; Dervishi, et al., 2009). Numbers of studies have reported that CNTs exhibit
different electronic properties under different conditions. Understanding these behaviors
would be helpful in applying nanotubes in today’s design. CNTs can be either metallic or semi-
conducting depending on the diameter and the chirality (which describes the way the graphene
sheet is rolled, as shown in Figure 11). Chirality is the term used to define the twist of CNTs
and is directly related to electrical properties (Menon & Srivastava, 1997). Chirality of CNT
is defined by chiral vector (Equation 2-5) which is given as (Moniruzzaman & Winey, 2006):
Ch⃗⃗⃗⃗ ⃗=na1⃗⃗ ⃗+ma2⃗⃗ ⃗
Equation 2-5
where a1, a2 are the unit vectors of hexagonal lattice and n, m are the number of steps along
the unit vectors
The chiral vector (Ch) is expressed as the integers (n, m) and chiral angle (),
represented in Figure 11(a). It is the direction along which the graphene sheet is rolled up to
form a nanotube. This vector direction defines an orientation of carbon atoms around the tube
into three different basic patterns (Figure 11(b)): armchair (n = m and = 30), zigzag (n = 0
or m = 0 and = 0), and chiral (all others n, m and 0 30).
21
The electronic structure of MWCNTs is more complicated due to the various
coaxially arranged SWCNTs. Electron transport in MWCNTs is said to be similar to that of
the larger diameter SWCNTs because most of the electric current passing through a MWCNT
from the outside is mostly confined to the outermost cylindrical layer (Frank, Poncharal, Wang,
& De Heer, 1998). Thus, their physical properties are also complicated to predict.
(a)
(b) armchair
zigzag
chiral
Figure 11 Graphene sheet of (a) SWCNTs formation and (b) chiralities of SWCNTs
22
Mechanical properties of carbon nanotubes
Carbon nanotubes are unique for their approximately perfect cylindrical shape of
seamless graphite, nano-scale diameter, and high aspect ratio. These materials are found to be
much stronger than steel, with high flexibility and only one-sixth the weight of steel (Velasco-
Santos, Martínez-Hernández, Fisher, Ruoff, & Castano, 2003). CNTs have exceptional
mechanical properties and are among the stiffest and strongest fibers known (Harris, 2004;
Ogasaswara, Ishida, Ishikawa, & Yokota, 2004) due to the carbon-carbon chemical bond in a
graphene sheet (the covalent bonding between carbon atoms, as shown in Figure 8) (Robertson,
Brenner, & Mintmire, 1992; Dresselhaus, Dresselhaus, Charlier, & Hernández, 2004). Since
C-C bonds in the honeycomb lattice are one of the strongest bonds in nature, it is worthwhile
to explore the mechanical properties of CNTs (Meyyappan, 2005).
Young’s modulus is independent of chirality but depends on tube diameter. It is a
measure of how stiff or flexible a material is. CNTs are generally found to have a Young’s
modulus along the tube axis in the range of 300–1000 GPa, this is up to five times the stiffness
of SiC (Silicone Carbide-a semiconductor) fibers but with half the density. The Young’s
modulus of MWCNTs is normally higher than that of SWCNTs due to different nanotubes
diameters contained coaxially in the MWCNTs and also due to van der Waals forces acting
between the tubes (Terrones, 2004; Popov, 2004; Meyyappan, 2005).
Since carbon nanotubes have only a few defects in the structure they do not fracture,
even when they are bent severely (Dervishi, et al., 2009). The CNT elastic response to
deformation is also extraordinary. CNTs can be twisted and sustain large strain (elongation to
failure of 20–40%) in tension before fracture whereas most materials fail within 1% or less of
strain. Tensile strength is a measure of the amount of stress needed to pull a material apart.
23
The tensile strength of individual MWCNTs was measured up to 100 GPa (highest known
value so far) (Khare & Bose, 2005), this is about 20 times stronger than steel. Table 1 provides
a comparison on some properties of CNTs with other common reinforcement fibers.
Table 1 Properties comparison between CNTs and other common reinforcing materials
Fiber Diameter
(m)
Density
(g/cm3)
Tensile strength
(GPa)
Modulus
(GPa)
Carbon 7 1.66 2.4-3.1 120-170
S-glass 7 2.5 3.4-4.6 90
Aramid 12 1.44 2.8 70-170
Boron 100-400 2.5 3.5 400
Quartz 9 2.2 3.4 70
SiC fibers 10-20 2.3 2.8 190
CNTs 0.001-0.1 1.33 up to 50 up to 1000
Synthesis techniques for carbon nanotubes
Since the discovery of carbon nanotubes nearly a decade ago, there have been a
variety of techniques developed for large-scale and high quality products. The most widely
used methods are the electrical arc discharge, laser ablation, and chemical vapor deposition (
Thostenson, Ren, & Chou, 2001; Popov, 2004; Yogeswaran & Chen, 2008; Dervishi, et al.,
2009). For application of carbon nanotubes in composites, large quantities of CNTs are
required. In this section, brief review on the primary techniques for carbon nanotube
production is discussed.
In arc discharge method, carbon is vaporized in the presence of a catalyst (iron, cobalt,
boron, gadolinium) under an atmospheric of inert gas (helium or argon). This method generally
involves the use of two high-purity graphite rods as the anode and cathode that are separated
by a short distance (1-4 mm) inside a chamber, as illustrated in Figure 12. A current of about
24
50-100A is passed through the electrodes, and carbon atoms are ejected from the positive
electrode (anode) and deposited on the negative electrode (cathode). The resulting products
contain various graphitic structures that depend on the size of the graphite rods.
Figure 12 Schematic illustration of the arc discharge technique
In laser ablation technique (Figure 13), a powerful laser is used to ablate a carbon
target in a hot helium (He) or argon (Ar) atmosphere. As the graphite target inside a furnace is
heated up at about 1200C, a pulsed laser beam incident on the target starts to evaporate carbon
from the graphite. The carrier gas sweeps the carbon atoms from the high-temperature zone to
a cold copper collector on which they condense into nanotubes. This technique yields
nanotubes with number of layers varying from 4 to 24 and an inner diameter ranging between
1.5 and 3.5 nm. However, the laser ablation technique is very expensive since it involves high-
purity graphite rods and high-power lasers.
Both the arc-discharge and laser-ablation methods are limited in the volume of sample
produced in relation to the size of the carbon source (the anode in arc-discharge and the target
in laser-ablation). In addition, subsequent purification steps are necessary to separate the
Cathode Anode
Growing
CNTs
25
nanotubes from the undesirable by-products. These limitations have motivated the
development of gas-phase techniques by chemical vapor deposition, where nanotubes are
formed by the decomposition of a carbon-containing gas. This method is a continuous process
since the carbon source is continually replaced by the flowing gas. Moreover, the final purity
of the as-produced nanotubes is quite high, in which minimizing subsequent purification
processes.
Figure 13 Schematic of the laser ablation process
Chemical vapor deposition (CVD) is the most common technique of carbon
nanotubes production. This method involves the flow of a precursor hydrocarbon gas
(methane, ethylene, acetylene) or gases into a chamber that is heated at high temperature
(typically between 700C and 1000C) in the presence of catalytic substrate (Fe, Co, Ni). Once
the hydrocarbon gas decomposes into hydrogen and carbon, carbon atoms dissolve and diffuse
into the catalyst metal surface and rearrange themselves into a network of carbon atoms and
finally precipitate out in the form of CNTs. The length of nanotubes is mostly controlled by
the length of the hydrocarbon deposition time. One of the advantages of the CVD technique is
Furnace
Ar gas Graphite target
Laser beam Growing CNTsCopper
collector
26
that it can be scaled up for large scale and high-quality production of CNTs at a relatively low
cost. Figure 14 shows a schematic diagram of the CVD method exploiting the hydrocarbon
source in gas state.
Figure 14 Schematic of a CVD reactor
2.3.1.2 Carbon nanofibers
Carbon nanofibers (CNFs) have generated considerable interest due to their
exceptional mechanical, electrical and thermal properties. Also the low cost of CNFs compared
to CNTs (Thostenson, Li, & Chou, 2005) and availability in large quantities due to
advancement in production make them an attractive candidate as filler in polymer matrix.
CNFs are typically produced by two main approaches: (i) catalytic thermal chemical vapor
deposition where the growth mechanism has been proven as the deposition of the hydrocarbons
dissolved in the metal particle (a catalyst) and participated on the metal surface as graphitic
carbon, and (ii) electrospinning where the polymer nanofibers (as the precursors of CNFs) are
carbonized to form CNFs by a heat treatment of up to 1000C (Saito, Dresselhaus, &
Dresselhaus, 1998; Zhang, Aboagye, Kelkar, Lai, & Fong, 2014; Feng, Xie, & Zhong, 2014).
Furnace
Gas inlet Gas outletSample
27
Structure of carbon nanofibers
Carbon nanofibers are graphitic materials that are closely related to CNTs. They are
mainly differentiated from nanotubes by the orientation of the graphene planes. They can be
visualized as stacked-cup (Figure 15(a)) or platelet structure (Figure 15(b)), and are
intrinsically less perfect as they have graphitic edge terminations on their surface (Uchida,
Anderson, Minus, & Kumar, 2006; Feng, Xie, & Zhong, 2014).
(a) (b)
Figure 15 Structures of CNF: (a) stacked-cup and (b) platelet
Although CNFs are much smaller than conventional continuous or milled carbon
fibers, they are significantly larger than CNTs (van der Lee, van Dillen, Geus, de Jong, &
Bitter, 2006; Manafi & Badiee, 2008). The diameter of CNFs ranges from 50-500 nm; it
depends on the type of carbon fibers, while the diameter of CNTs is usually 1-30 nm. Slightly
larger fibers, diameter range of 100-200 nm, are also often called CNFs, even if the graphitic
orientation is approximately parallel to the axis. The compared illustration of various carbon-
based materials (Endo, Kim, Ezaka, Osada, Yanagisawa, & Hayashi, 2003) is shown below in
Figure 16.
28
Figure 16 Size comparison of (a) single-walled carbon nanotube (SWCNT), (b) multi-
walled carbon nanotube (MWCNT), (c) carbon nanofiber (CNF), (d) vapor-
grown carbon fiber (VGCF), and (e) carbon fiber (CF)
Properties of carbon nanofibers
The main advantage of CNFs over CNTs is that they give excellent dispersibility and
wetting properties within a polymer matrix. This provides the ability of CNFs to not form
oriented structures when compounded with polymer matrix; this is due to the nature of CNFs
that do not clump together and are not spread out like CNTs (Tibbetts, Lake, Strong, & Rice,
2007). One of the exciting applications of CNFs is their ability to conduct electrical current.
Although not as high as that of CNTs, the intrinsic resistivity of CNFs is 5x10-5 -cm. Due
to their chemical and mechanical properties, carbon nanofibers exhibit capability a number of
potential applications. The tensile strength of CNFs is between 2-7 GPa and the modulus is
up to 600 GPa with a density of 1.8 g/cm3, which are very close to those of CNTs (Miyagawa,
Rich, & Drzal, 2006; Poveda & Gupta, 2014).
1 101 102 103 104
Diameter (nm)
(a) (b) (c) (d) (e)
29
In summary, CNFs are one of the nano-structured forms of elongated graphite but are
cheaper and possess better dispersibility together with network forming abilities compared to
CNTs. Moreover, the intrinsic electrical conductivity of CNF is higher than that of CB
although it has a lower conductivity than that of CNT. It has been found that CNFs have
displayed better composite characteristics than either of CB or CNT due to their excellent
processability features, which are observed to be lacking in CNT and CB. Continuous
conducting networks can be formed when coupled with compatible polymers, especially the
polar polymers. This has been used in the synthesis of composites with electrical, thermal and
mechanical applications. But the disadvantage of CNFs lies in obtaining purer forms of CNFs,
for which preprocessing steps are proposed in making efficient composites for electrical as
well as mechanical devices.
2.3.1.3 Carbon black
Carbon black (CBs) is virtually pure elemental carbon in the form of colloidal
particles that are produced by either incomplete combustion (furnace black) or thermal
decomposition (thermal black) of gaseous or liquid hydrocarbons under controlled conditions.
Its physical appearance is that of a black, finely divided pellet or powder. The most common
manufacturing process is the furnace black process that uses heavy aromatic oils as feedstock;
whereas, the thermal black process uses natural gas (Huang, 2002; Brigandi, Cogen, &
Pearson, 2014).
Structure of carbon blacks
Because carbon black is a commercial product with specific properties, its
manufacturer is geared toward generating a substance of high purity and uniform quality.
Carbon blacks are composed almost exclusively of elemental carbon (> 97%) arranged in a
30
particulate structure (Huang, 2002). Imperfect graphite layers orient around growth centers to
form primary particles as seen in Figure 17(red). Deposition of elemental carbon forms primary
particles.
Figure 17 Size ranges of typical carbon black structural entities
The deposition of elemental carbon from the vapor continues as individual primary
particles collide and stick to one another. The contacting of primary particles fuses together
into grapelike clusters (termed as aciniform aggregates) as presented in Figure 17(dark-blue).
The diameter of primary particles may range from 10 nm to approximately 500 nm; aggregates
are usually less than 1 m. Clusters of aggregates may form and are called agglomerates
(Figure 17(black)). The formation of agglomerates continues after the deposition of carbon has
ended. Carbon blacks are usually highly agglomerates with 10 to 1000 aggregates per
agglomerate (Watson & Valberg, 2001). Most carbon blacks are classified and assigned a grade
number based on surface area and structure measurements.
The utility and ultimate economic value of carbon black is determined through a
complex mix of carbon chemistry, surface energy and particle physics (MDI, 2010). The most
important properties are surface area, primary particle size and structure. For example, surface
Primary particle
15-300 nm
Aggregate
85-500 nm
Agglomerate
1 nm-1 m
31
area influences the ability of carbon black to absorb UV radiation where structure influences
the ease or difficulty of dispersion and electrical conductivity properties. It is the balance of
surface area and structure that determines the utility of the particular grade of carbon black.
Table 2 shows the morphology of different grades of carbon blacks (Long, Nascarella, &
Valberg, 2013).
Table 2 Summary of carbon black morphology for different CB grades
Carbon black
grade
Primary particle
size* (nm)
Aggregate size*
(nm)
Surface area
(m2/g)
N110 27 93 143
N220 32 103 117
N234 31 109 120
N326 41 108 94
N330 46 146 80
N339 39 122 96
N351 50 159 75
N375 36 106 105
N550 93 240 41
N660 109 252 34
N774 124 265 30
N990 403 593 9
* Measured by TEM
Depending on the degree of aggregation two different structures of carbon black are
categorized. A high structured CB may have about 200 particles per aggregate with
considerable branching and chaining; whereas a low structured CB is known to have around
30 particles per aggregate (Balberg, 2001). A high structure CB has higher conductivity than
that of a low structure CB due to the presence of strong attractive forces between particles.
However, this is a disadvantage in dispersing CBs to form composites since more energy of
32
separation between the aggregates is required to obtain homogeneous dispersion (Medalia,
1986; Bourrat, 1993). Although a high degree of dispersion is not desirable for high electrical
conductivities, it helps to have homogeneity in producing composites with strong mechanical
properties. Figure 18 demonstrates the schematic of carbon black at different structures. The
lower structures tend to contain more spherical particles; whereas in the high structure carbon
black, the gap width between agglomerates is much smaller than the low structure carbon
black.
(a) (b) (c)
Figure 18 Schematic descriptions of composites made of carbon blacks. (a) low structure
(b) intermediate structure (c) high structure
Properties of carbon blacks
The intrinsic electrical properties of CB aggregates depend on many factors such as
the electrical conductivity and the size of the individual particles, the level and nature of
impurities on the surface of the graphene layers, the degree of contact between the particles of
the same aggregate and between the particles of different aggregates, and the packing factor or
density (Sanjines, Abad, Vaju, Smajda, Mionic, & Magrez, 2011).
33
Carbon black reinforced composites were the first generation of conducting polymer
composites developed due to their excellent polymer-filler and filler-filler adhesion
characteristics (Zhang, Dehghani-Sanij, & Blackburn, 2007). Because of the low intrinsic
conductivities of carbon blacks compared with that of other carbonaceous fillers (such as CNTs
and CNFs) and the lack of 3-dimensionality in their structure, they were observed to lack the
ability to produce high strength materials, except in cases of high filler loading (Sanjines,
Abad, Vaju, Smajda, Mionic, & Magrez, 2011). However, with electrical conductivity values
ranging from 1 to 104 S/m of CB, it is efficiently used as a conducting filler in many polymer
composite systems and applications; for examples, graded semiconductor in optoelectronic
applications, conducting electrodes, solid electrolytes for batteries, anti-reflection coating,
room temperature gas sensors, and electrical switching devices (Bigg, 1984; Lan, Leng, Liu,
& Du, 2008).
2.3.2 Processing and fabrication techniques of the polymer composites
The performance of a composite requires optimization of many factors such as nature
of materials (conductive filler and polymer), processing techniques, experimental conditions,
distribution of fillers within the matrix, strength of interaction between filler and polymer.
Challenges of homogeneous dispersion in solvent and supporting media, alignment of filler in
the load directions, and interconnectivity with matrix must be considered in order to obtain
composites with enhanced properties. Therefore, the processing techniques for manufacturing
polymer-based composites become an important issue and must be carefully designed.
Currently, there are three main types of sample preparation methods that would
partially overcome the problems in dispersion and adhesion: solvent solution mixing, melt
mixing and in-situ polymerization (Viswanathan, Laha, Balani, Agarwal, & Seal, 2006).
34
2.3.2.1 Solution blending
This is a common method for fabrication polymer composites since it provides
advantage through low viscosity; which facilitates the mixing and dispersion of fillers (Safadi,
Andrews, & Grulke, 2002). In general, solution blending involves three major steps:
Step1: Disperse fillers in a suitable liquid medium or solvent with or without energy
processes such as magnetic stirring, shear mixing and ultrasonication
Step 2: Mix the suspension with the polymer either at room temperature or certain
temperature
Step 3: Recover the composite by precipitating or casting at room temperature or a
heated environment to evaporate the solvent and curing
However, the minimum sonication conditions (time and power) that produce filler
degradation are yet to be determined and will certainly depend on filler concentration and
initial filler length distribution (Beruto, Capurro, & Marro, 2005; Kabir, Saha, & Jeelani,
2007). High-power ultrasonication for a long period of time tends to shorten the filler length
and reduce the aspect ratio, which is harmful to composite properties. Scale-up is also another
concern with solution blending because residual solvent must be recovered.
2.3.2.2 Melt blending
Melt blending is the most common technique used to disperse conductive fillers into
polymer matrix (Potschke, Dudkin, & Alig, 2003; Sandler, et al., 2004). This method uses high
temperature (above the softening point of the polymer) and high shear forces to disperse fillers
in a polymer matrix and is most compatible with current industrial practices. However, relative
to solution blending, melt blending is generally less effective at dispersing conductive fillers
in polymers and is limited to lower concentrations due to the high melt viscosities of the
35
composites at higher loadings. Dispersion is the most important consideration in the
preparation of conductive polymer composites. Shearing forces affect the dispersion during
compounding due to their actions on filler agglomerates at the interface and break them into
primary aggregates (Potschke, Bhattacharyya, Janke, & Geoering, 2003; Alig, et al., 2012).
The compounding devices should have high shearing forces to offer greater energy for mixing.
Many types of plastic compounding equipment are commonly used in the industry, such as
intensive dry mixers, internal intensive batch mixers, two-roll mills, and extruders. The weak
van der Waals forces between the agglomerates can be easily overcome allowing dispersion.
2.3.2.3 In-situ polymerization
This fabrication strategy starts by dispersing fillers in monomer followed by
polymerization of the monomers. Functionalized fillers can improve the initial dispersion of
fillers in liquid (monomer or solvent), and consequently in composites. Furthermore, in situ
polymerization methods enable covalent bonding between functionalized fillers and the
polymer matrix using various condensation reactions (Kaminsky, Zhao, et al., 2005; Funck, &
Wiemann, 2006; Funck & Kaminsky, 2007). However, as the polymerization progresses the
viscosity of the reaction medium increases. This extent of in situ polymerization reactions
might be limited. The benefits of in-situ polymerization are the ability to form composites with
polymers that are not easily solution blended or melt compounded.
36
2.4 Electrical percolation models
The first mathematical approach on percolation theory was developed by Broadbent
and Hammersley (Broadbent & Hammersley, 1957). They showed that the percolation process
is the consequence of geometrical phase transition in a random medium and, interestingly, the
change in transport and physical properties of the system follows a universal power law (or a
scaling law). Studying the properties of networks above the percolation threshold has been of
secondary importance; therefore, an increased availability of functional experimental data
motivates not only the prediction of the percolation threshold but also the properties of
networks above the percolation threshold.
Numerous percolation models have been proposed to explain the electrical
conductivity of composite systems comprised of conductive and insulating materials
(McCullough, 1985; Sevick, Manson, & Ottino, 1988; Debondt, Feroyen, & Deruyttere, 1992).
These percolation models can be divided into statistical, thermodynamic, geometrical, and
structure-oriented subdivisions (Lux, 1993). Each class predicts the electrical conductivity
based on distinct approaches. All of the models have several common features such as size and
geometry of filler, amount and distribution of filler in insulating matrix, interaction between
conducting and insulating components, and mixture preparation method.
Due to the limited characterization techniques of the polymer composite samples,
only the statistical percolation model proposed by Kirkpatrick and Zallen as known as the
power law model or the scaling law will be applied to predict the electrical phenomenon of the
filled polymer composites in this research. However, brief explanation of other models will be
discussed with their limitations and dependent parameters.
37
2.4.1 Statistical percolation models
The statistical percolation models have occupied the majority of the literature about
the electrical percolation phenomenon (Hsu, Holtje, & Barkley, 1988; Stauffer & Aharony,
1994). These models typically predict the conductivity based on the probability of particle
contacts within the composite. Two of the early percolation models often referenced are the
models originally proposed by Kirkpatrick (Kirkpatrick, 1973) and Zallen (Zallen, 1983). The
model was proposed by a power law (or scaling law) equation as follows:
σ = S |p - pc|q
Equation 2-6
where is the property studied, S is the proportional constant, p is the occupation probability,
pc is a percolation threshold, and q is a critical exponent.
It is not possible to give an analytical form for the constant S because of lack of
knowledge about the cluster size distributions (size and shape) in most systems. However, this
model can be extended to the prediction of the electrical behavior for polymer composites since
it generally deals with the number and properties of clusters.
Specifically in this study, is referred to as the electrical resistivity of the composite,
is the filler concentration (wt%). Therefore, Equation 2-6 can be rearranged as:
ρ = ρ0( -
c)
-t
Equation 2-7
38
where is the electrical resistivity of the composite, 0 is a scaling constant, is weight
percentage of the filler, c is weight percentage of the filler at percolation or percolation
threshold, and t is a critical exponent.
Once the parameters 0, t, and c are established by curve-fitting, the electrical
resistivity predictions can be made. The universal values of t that have been commonly used
are approximately 1.3 for two-dimensional systems and approximately 2.0 for three
dimensional systems (Kirkpatrick, 1973; Balberg & Bozowski, 1982). However, for CNT-
polymer composites, the broad range of t values fitted from experimental measurements, as
well as the differences for values obtained by different simulations clearly indicates that the
critical exponent is not universal. Instead, it has been indicated that values of the critical
exponent obtained from experiments for three-dimensional percolating systems can be ranged
from below 2 to 10 for CNTs. The values of t were found generally between 1.3 and 4.0 for
MWCNTs (Bauhofer & Kovacs, 2009). Other experimental and theoretical studies have also
showed that the percolation threshold is dependent on the morphology of conductive fillers
such as sizes, shapes, aspect ratio, and orientation (Kirkpatrick, 1973; Balberg, 2012).
A similar form to a statistical model is proposed by McLachlan (McLachlan, Chiteme,
Heiss, & Wu, 2003; McLachlan, et al., 2005), as given in Equation 2-8. This model includes
the calculation for the conductivity of the constituent materials, the percolation threshold, and
a critical exponent. The value of the critical exponent is determined experimentally, and
typically ranges between 1.5 and 3.1 (Balberg, 1987; McLachlan & Suati, 2007).
39
(1-)(ρm1 t⁄ - ρ
h1 t⁄ )
ρm1 t⁄ + (
1 - c
c
) ρh
1 t⁄ +
(ρm1 t⁄ - ρ
l1 t⁄ )
ρm1 t⁄ + (
1 - c
c
) ρl
1 t⁄ = 0
Equation 2-8
where is the volume fraction of filler, c is the percolation threshold, h is the filler resistivity,
l is the polymer resistivity, m is the composite resistivity and t is the critical exponent. This
model is usable for composites containing two fillers because it is claimed for its applicability
for composites consisting of a highly conductive material embedded in a poorly conducting
material.
Bueche (Zallen, 1983; Lux, 1993) tried to explain the S-shaped conductivity curves
of the binary mixtures, which contain conductive particles in an insulating matrix, based on
the concept of polymer gelation:
ρ = ρ
m ρ
f
(1 - Vf) ρf + Vf ωg ρm
Equation 2-9
where is the resistivity of the mixture, m is the resistivity of the insulating material, f is the
resistivity of the conductive material, Vf is the volume fraction of the conductive phase in the
mixture, g is the weight fraction of the conductive phase in an infinite cluster (a function of
the number of contacts per particle and the probability of contact).
However, Zallen discussed the parallel relation of the original percolation problem
and presented that the calculated values from Bueche’s equation did not match the
experimental data. It was reported that this model was able to account for the different jumps
40
in conductivity, only when the correct value for the maximum number of contacts per particle
was chosen.
2.4.2 Thermodynamic percolation models
The thermodynamic models allow the prediction of composite conductivity based on
the interactions between the polymer and the filler material. This is specifically done by the
use of interfacial tension and the surface energies of the constituents.
Mamunya, et al. (Mamunya, Davidenko, Prundar-Tudor, & Lebedev, 1995;
Mamunya, Davidenko, & Lebedev, 1997) studied the composite conductivity as a function of
filler volume fraction in different polymers in which the influence of other factors on the
conductivity was evaluated. These factors included the filler and polymer surface energies and
the polymer melt viscosity. The prediction results presented that the percolation behavior was
dependent on the interaction between polymer and filler in addition to the size and amount of
the filler material. At all points above the percolation threshold, the composite conductivity
was related to Equation 2-10:
log σm = log σc + (log σF - log σc) ( -
c
F - c
)
k
Equation 2-10
with
and
k = K∙
c
( - c)
0.75
K = A - B ∙ γpf
41
where m is the composite conductivity, c is the conductivity at the percolation threshold (c),
F is the conductivity at the maximum packing fraction (F), is the volume fraction of filler,
pf is the interfacial tension with p as the surface energy of the polymer and f is the surface
energy of the filler, and A and B are the constants.
The Mamunya model fitted well for a number of different polymers filled with carbon
black, however it was not extended to include other types of fillers.
2.4.3 Geometrical percolation models
According to the research of Lux (Lux, 1993), the geometrical percolation models
were originally proposed to predict the conductivity of sintered mixtures of conducting and
insulating powders. The major assumption is that during the sintering process, the insulating
material is deformed into cubic particles and the conductive particles are arranged in a regular
manner on the surfaces of the insulating particles. The main parameters used in evaluating the
conductivity of the mixture are the diameters of the non-sintered particles or the edge length
of the sintered particles.
A well-known model in this class is the one proposed by Malliaris and Turner
(Malliaris & Turner, 1971). This model predicted the volume percolation concentration by two
equations; the first one calculated the percolation threshold of the network formation (VA), and
the second applied to the volume fraction at the end of the conductivity increase (VB).
F = 0.65 ∙ c
1 3⁄ γ
pf = γ
p + γ
f - γ
p∙ γ
f
0.5
42
VB = 100 [1
1 + θ
4∙
D
d ]
Equation 2-11
VA = 0.5 Pc VB
Equation 2-12
These equations include the diameters of the conductive (d) and insulating (D)
particles, the probability for the occurrence of long bands of conductive particles (Pc) where
the following values are given: Pc = 1/3 for hexagonal array; Pc = 1/2 for cubic array; Pc = 2/3
for triangle array, and the arrangement of the conductive particles on the surface of the
insulating particles () where the following values are given: = 1.11 for hexagonal
arrangement; = 1.27 for cubic arrangement; = 1.375 for triangle arrangement. However,
comparison between the experimental data and the predicted values of percolation threshold
using this model did not match up accurately in the conductive binary mixtures.
2.4.4 Structure oriented percolation models
The structure oriented models are based on the physical construction of the final
composites. The electrical conductivity of the composite materials is often affected by
structural properties such as the aspect ratio and the orientation of fillers. These properties are
typically a result of the processing techniques employed to produce the composites. The
alignment of the fillers can significantly result in the different conductivity values depending
on the direction of measurement.
43
A model proposed by Nielsen (Lux, 1993; Clingerman, King, Schulz, & Meyers,
2002) related the conductivity of a composite to the aspect ratio (l/d) and the coordination
number of the filler. The equations used in Nielson’s model are as follows:
σc = σpoly 1 + AB
f
1 - Bφf
Equation 2-13
with and
where f is the volume fraction of filler, c is the composite conductivity, poly is the polymer
conductivity, f is the filler conductivity, m is the maximum packing fraction, A is a function
of aspect ratio and orientation, and B is essentially equal to 1 for polymer systems.
This model was used to describe the electrical conductivity, the thermal conductivity,
and the modulus of metal-polymer systems. However, it was found that the equation was
marginally accurate for thermal conductivity estimation and it was completely ineffective in
predicting the electrical conductivity (Lux, 1993; Clingerman, King, Schulz, & Meyers, 2002).
In conclusion of the review on conductivity models, the models were proposed from
diverse modeling techniques; from quantum mechanics for discrete molecular structure to
continuum micro-mechanics for continuous mechanical structure of nanocomposites. It is
noteworthy that among available analytical models, the percolation-based equation originally
developed by Kirkpatrick and Zallen or power law model has shown to be the most applicable
to various polymer composite systems. Due to its simplistic formula that could provide
excellent numerical simulations to estimate the composite conductivity.
B =
σfσpoly - 1
σfσpoly + A
φ ≈ 1 + (1 -
m
m
2)
f
44
2.5 Properties of the polymer composites relevant to carbon filler materials
The results of numerous studied have indicated that the effects of conductive particles
on the electrical, mechanical and other properties of the composites are strongly dependent on
the dispersion state of filler particles and the interactions between filler and polymer matrix.
In this section, some related literature research works are summarized.
Meincke et al. (Meincke, Kaempfer, Weickmann, Friedrich, Vathauer, & Warth,
2004) fabricated composite of MWCNT in polyamide-6 (PA6) using a co-rotating twin screw
extruder. At 12.5 wt% the modulus almost doubled from 2.6 GPa to 4.2 GPa. However, at such
a high loading the ductility decreased from 40% to 4%. The percolation threshold of this
composite was found to be 4 to 6 wt%. Liu et al (Liu, Phang, Shen, Chow, & Zhang, 2004)
also made composite of MWCNT-nylon6 (PA6) by a simple melt mixing method. The mixing
was performed using a Brabender twin screw mixer at 250C for 10 min. The composite films
observed a significant increase in modulus from 400 MPa to 1200 MPa with the addition of
2 wt% nanotubes. The yield strength was improved from 18% to 47%; however, the elongation
at break slightly decreased from 150% to 100% with no decrease in toughness. These
impressive results were attributed to a good dispersion and adhesion of the nanotubes.
Peoglos et al. (Peoglos, et al., 2007) found an electrical percolation threshold between
2.5 and 5 wt% for PA6-MWCNT for compression molded plates of composites prepared by a
Plasti-Corder laboratory kneader operated at 240C, 60 rpm, and 15 min. The results indicated
an electrical volume resistivity of 104 -cm (4 wt% MWCNT) and 103 -cm (5 wt%
MWCNT) for PA6-MWCNT composites prepared by masterbatch dilution. Various
MWCNTs filled with four different types of nylon12 (PA12) were prepared in a DACA micro-
compounder at 210C with a mixing speed of 250 rpm for 5 min (Socher, Krause, Boldt,
45
Hermasch, Wursche, & Potschke, 2011). The electrical percolation thresholds of the
investigated CNTs varied between 0.7 to 5 wt%.
Kanbur Y. and Kucukyavuz Z. (Yasin & Zuhal, 2009) analyzed the effect of different
processing types and varying carbon black contents on mechanical properties and electrical
conductivity. Polypropylene-CB composites were prepared via two different melt blending
techniques, injection molding and compression molding. The results showed that injection
molded samples had better mechanical properties than the compression samples. This was due
to the orientation of the polymer chain in the direction of applied force for samples prepared
by injection molding. The decrease in percent deformation at break of the samples was caused
by the addition of CB, which restricted the motion of polymer chains. Moreover, increasing
the amount of CB revealed an increase of the thermal stability of composites. In the subject of
composites, it had been observed that mechanical stiffness and strength increased at the cost
of ductility with reinforcement. Incorporation of carbon fillers in most cases made the materials
brittle and, hence, decreased the toughness. Tchoudakov et al. (Tchoudakov, Breuer, & Narkia,
1996) also observed the melt blended composite system of CB reinforced in PP had a
percolation threshold between 2-4 wt% whereas nylon-6 had 25 wt%. This was because a
sufficiently good interaction of CB and nylon reduced the contact between CB particles until
a higher concentration was reached. The effects of structure and processing time on electrical
conductivity were also studied by Bigg (Bigg, 1984) using different grades of carbon black;
namely Ketjenblack (highly porous), Vulcan black (medium porosity, high structure) and
Acetylene black (low porosity). The conductivity of highly porous CB composites was
concluded to be less sensitive to processing time than that of those made of high structure CB
(low porosity).
46
In addition, the electrical conductivity of CBs, CNTs, and GNP (graphite nano-
platelets) fillers in a PC (polycarbonate) matrix was determined by Via et al. (Via, King, Keith,
& Bogucki, 2012). All of the experimental results exhibited the typical percolation phenomena,
where at low filler concentrations the composite displayed electrical conductivities comparable
to that of the polymer. Above the percolation threshold, the composite had an electrical
conductivity up to 16 orders of magnitude higher than that of the polymer. The percolation
thresholds of PC composites reinforced with CNT, CB, and GNP were 1.2, 2.4, and 4.6 volume
percent (approximately 2.5, 5, 8 wt%), respectively. Similar results were observed by King et
al. (King, Via, King, Miskioglu, & Bogucki, 2011). The composite with 8 wt% CB in PC had
a good combination of properties for semi-conductive applications. The electrical conductivity
was 122 -cm with the modulus, ultimate tensile strength, and strain at ultimate tensile
strength of 2.8 GPa, 61 MPa, and 3.4%, respectively.
Some investigations showed the effects of the structure and molecular weight of a
polymer matrix. (Sumita, Kayaki, & Miyasaka, 1986; Huang, Wu, & Grossman, 2000; Huang
& Wu, 2000). For an amorphous polymer, conductive particles were dispersed uniformly in
the matrix, and high electrical conductivity was achieved when the concentration of the
conductive fillers reached the percolation threshold. For crystalline polymers, the conductive
particles would be ejected from the crystalline regions during crystallization and concentrated
in the amorphous region. In this case, the percolation threshold would decrease accordingly.
The study on the molecular weight effect showed that an increase in molecular weight led to
an increase in percolation concentration. This was because the high molecular weight polymers
were more difficult to spread on the conductive fillers and slowed the formation of conducting
networks.
47
Zeng et al. (Zeng, Saltysiak, Johnson, Schiraldi, & Kumar, 2004) used twin-screw
extrusion followed by melt spinning to produce PMMA-CNF composite systems in the form
of films and threads. Modulus was observed to be increased by 80% at 5 wt% loading of CNF
but without any increase in the tensile strength. However, increasing the loading to 10%
resulted in a substantial decrease in the modulus which was further explained to be due to the
issues with dispersion and decrease in the fiber-polymer wetting when the concentration of the
fiber particles was increased. Improvement of mechanical (tensile and flexural strengths) and
electrical properties of epoxy by addition of the CNFs with different filler contents was also
studied by Shokrieh et al. (Shokrieh, Esmkhani, Vahedi, & Shahverdi, 2013). Different weight
fractions of CNF were added to the polymer by an in-situ method. The maximum improvement
in tensile strength and flexural strength at 0.25 wt% CNF in epoxy resin was 23% and 10%,
respectively. However, higher filler content was required to increase the Young’s modulus and
flexural modulus of 15.6% and 10%, respectively, using 1 wt% CNF. By adding more CNFs
to epoxy, the strain-to-failure was found to reduce due to the agglomerate of CNF particles.
The percolation threshold was determined at 0.5 wt% CNF.
Finnegan and Tibbetts (Finnegan & Tibbetts, 2001) also demonstrated the advantage
of CNFs over CBs in their ability to form uniform dispersions in a polymer matrix by studying
PS-CB and PS-VGCNF composites prepared by solvent casting. Greatly improved in
conductivities of the composites made from CNFs were observed as compared to those of CBs
at the same filler loading. This was attributed to the availability of CNFs in very high aspect
ratios, which resulted in low percolation thresholds. Moreover, Tibbetts et al. (Tibbetts, Lake,
Strong, & Rice, 2007) reviewed a comprehensive study of electrical transport properties of
VGCNF polymer systems in various systems. Their work claimed that it was not essential to
48
have a higher degree of orientation of the fibers inside the polymer matrix to achieve higher
conductivities, as they observed a decrease in the conductivity of the composite when the
orientation changed from random to unidirectional. Xu et al. (Xu, Donahoe, & Pittman Jr.,
2004) synthesized VGCNF-vinyl ester composites using different compounding techniques of
mechanical stirring and mixing with roller blades (Brabender). The results showed very low
percolation thresholds of 2-3 wt%.
So far, more than 200 publications report on the electrical percolation threshold of
different polymer composite systems. The variation can be of many parameters such as filler
type and grade, synthesis method, treatment and dimensionality as well as polymer type and
dispersion method. Table 3 summarizes some example of various polymer composites with
different fillers and their preparation method.
49
Table 3 Examples of various polymer matrix-filler composites: c = percolation threshold
and t = critical exponent in the power law equation
Polymer Filler Dispersion
method c
(wt%) t
Resistivity
@ c (-cm) Reference
Epoxy MWCNT Stirring 0.011 2.04 1010
(Kovacs, Velagala,
Schulte, & Bauhofer,
2007)
Epoxy MWCNT Stirring 0.6 2.9 109 (Yuen, et al., 2007)
EBA CB Melt
mixing 8 3.47 107
(Mdarhri, Brosseau,
Zaghrioui, & Aboudi,
2012)
PA MWCNT Melt
mixing 4-6 - 106-1011
(Meincke, Kaempfer,
Weickmann,
Friedrich, Vathauer,
& Warth, 2004)
PA CB Melt
mixing 5-10 - 105-1012
(Meincke, Kaempfer,
Weickmann,
Friedrich, Vathauer,
& Warth, 2004)
PC MWCNT Melt
mixing 1.44 2.1 1010
(Potschke, Dudkin, &
Alig, 2003)
PDMS MWCNT Solvent
casting 4 2.52 105
(Lu, Lu, Bermak, &
Lee, 2007)
PDMS MWCNT Stirring 3 4.7 109
(Rizvi, Cochrane,
Biddiss, & Naguib,
2011)
PE MWCNT Stirring 2.2 1.4 1010
(Rizvi, Cochrane,
Biddiss, & Naguib,
2011)
HDPE CB Melt
mixing 1.5-3 - 105-109 (Yuan & Wu, 2010)
PMMA SWCNT Stirring 0.17 1.3 105 (Skakalova, Dettlaff,
& Roth, 2005)
PP VGCF Melt
mixing 9-18 - 109
(Breuer &
Sundararaj, 2004)
PP CB Melt
mixing 6.2 1.93 106
(Zois, Apekis, &
Omastova, 2001)
PP CNF Melt
mixing 1-2 1.75-2 103-104 (Paleo, et al., 2010)
PS MWCNT Melt
mixing 1.2 2.5 108
(Mdarhri, Brosseau,
Zaghrioui, & Aboudi,
2012) Acronyms: EBA (ethylene butyl acrylate), PA (polyamide), PC (polycarbonate), PE (polyethylene), HDPE (high-density polyethylene),PET
(polyethylene terephthalate), PP (polypropylene), PMMA (polymethyl methacrylate), PDMS (polydimethylsiloxane), PS
(polystyrene),VGCF (vapor-grown carbon fiber)
50
Chapter 3 Experimental set up
This chapter discusses the experimental work undertaken in this research. It consists
of four sections. In the first section, all materials used are described in detail. In the second
section, sample preparation procedures of two different polymer composites are reported. In
the third section, all characterization techniques used are explained in detail. Finally, in the
fourth section, some preliminary results of the materials analyzed are summarized.
3.1 Materials
Materials used in this research were chosen based on their widespread use. Nylon 6
was selected as it is commonly used in a number of applications for thermoplastic polymer
composites; whereas Poly-dimethylsiloxane (PDMS) was chosen as the elastomeric polymer
composite due to its excellent mechanical properties such as elasticity, high extensibility, and
chemical inertness. Figure 19 illustrated the molecular structure (the repeating unit) between
nylon 6 (contains amide groups, CONH) and PDMS (consists of linear siloxane backbones,
[–Si–O–]n). Additionally, different carbon fillers were selected based on their abilities to
convey high electrical conductivity to the composites while still maintaining a relatively low
cost. All materials were used as received without further purification.
(a) (b)
Figure 19 Molecular structure of (a) Nylon 6 and (b) PDMS
51
3.1.1 Polymer matrices
3.1.1.1 Thermoplastic – Nylon
The thermoplastic polymer resin of choice was polyamide 6 (PA6, Nylon 6 – fiber
grade BS700A) obtained from Nylene Canada Inc. Nylon is one of the most widely used
engineering thermoplastics, as it comes with decent material properties such as a high strength
and stiffness, as well as excellent chemical and abrasion resistance, and excellent load bearing
capability. Major applications of nylon are found in the fiber sector and in the automotive,
aviation, and electrical or electronics industries. Table 4 summarizes some of the properties
for nylon 6 pellet, as received.
3.1.1.2 Elastomer – PDMS
Poly-dimethylsiloxane (PDMS) is an organo-silicon compound, also known as
silicone rubber, and is the most widely used silicone rubber in the electronic packaging field
due to its flexibility property. The PDMS used was Sylgard 184 Silicone Elastomer that
consists of a base elastomer (Part A) and a curing agent (Part B) and was purchased from Dow
Corning, USA. The ratio of Part A to Part B is 10:1. Some of the properties of PDMS are listed
in Table 4.
Table 4 Physical properties of nylon and PDMS resin
Property Nylon 6 PDMS
Specific gravity 1.13-1.15 1.03
Moisture content 0.12 wt% -
Tensile strength 78 MPa 6.7 MPa
Melting point 215°C -
Electrical resistivity 5×1012 -cm 2.9×1014 -cm
Thermal conductivity 0.24-0.28 W/m.K 0.27 W/m.K
52
3.1.2 Carbon fillers
Carbon fillers impart good conductivity to polymers and are consequently used at low
concentration in the manufacturing of conducting compounds. However, the use of a particular
carbon filler depends upon several factors, such as the ability of the polymer to accept a certain
concentration, the critical concentration at which the electrical percolation occurs, the process
ability of the final composites, and the overall mechanical properties balance achieved at the
desired conductivity level. Three different carbon fillers were used in this study: carbon
nanotubes (CNT), carbon black (CB), and carbon nanofiber (CNF).
3.1.2.1 Carbon nanotubes
Multi-walled carbon nanotubes (MWCNT) are obtained from Bayer Material Science,
Germany. Two grades of MWCNTs were used, C70P and C150P. According to the
manufacturer, the carbon nanotubes were produced by the catalytic carbon vapor deposition
(CCVD) process with high defects and high aspect ratio. This method is generally used for
bulk production and controlled growth of nanotubes (Mittal, Dhand, Rhee, Park, & Lee, 2015).
In this method, synthesis of CNTs take place due to the decomposition of a mixture of
hydrocarbon gases (such as methane and ethylene) or volatile carbon compounds present in
the chamber onto metallic substrate, where metallic nanoparticles behave as catalyst and
nucleation sites in the growth process of carbon nanotubes at temperatures of 500-1000C and
under atmospheric pressure. The selection of catalyst and preparation of substrate decides the
type and quality of the nanotubes produced. Usually, Fe, Ni, Co nanoparticles are used as a
catalyst.
53
The difference between the two grades of nanotubes used in this research is that the
new grade of CNT-C70P is more easily incorporated than CNT-C150P as reflected by its
greatly reduced bulk density of 45–95 kg/m3. With regard to their other properties as shown in
Table 5, the two Baytubes grades are virtually the same with high purity of 95 wt%.
Another content of 5 wt% is counted as the impurities on the surface and inside the
core of nanotubes during synthesis and processing of CNTs (Tam, Nghia, Quynh, Khoi, &
Minh, 2008; Ge, et al., 2008; Remy, et al., 2015). These impurities may include the amorphous
carbon, catalysts, catalyst supports, and carbon nanoparticles. It is unavoidable that the as-
received CNTs are contaminated by catalyst residues, and it is impossible to entirely remove
the metals without destroying the structural entity of the CNTs since some of the metal particles
are protected by graphitic shells.
Table 5 Properties of MWCNT C70P and C150P
Property C70P C150P
Outer mean diameter ~13 nm 13-16 nm
Inner mean diameter ~4 nm 4 nm
Length >1 m 1->10 m
Bulk density (powder) 45-95 kg/m3 130-150 kg/m3
Specific gravity 1.6–1.9 1.6–1.9
Surface area 117 m2/g 220 m2/g
54
3.1.2.2 Carbon black
Carbon black (CB) has been used for decades as a convenient and cheap additive for
thermoplastics as well as for rubbers. Its largest uses are as a reinforcing agent in vehicle tires
and rubber automotive products. Other common everyday products that often contain carbon
black include inks, paints, plastics, and coatings. The carbon black of choice was CB N234
that was obtained from Columbian Chemicals, USA. It consists mainly of elemental carbon
and the properties are given in Table 6.
3.1.2.3 Carbon nanofibers
The carbon nanofibers (CNF) were supplied by Pyrograf Products Inc, USA. Pyrograf
III (PR-24-HHT) grade has a unique structure referred to as stacked cup carbon nanotubes
(SCCNT). It also has a minimal chemical vapor deposited (CVD) layer of carbon on the surface
of the fiber over a graphitic tubular core with heat-treating to 3000C. The properties of the
CNF are given in Table 6 as reported by the manufacturer.
Table 6 Properties of CB N234 and CNF
Property CB N234 CNF
C-Purity 99 wt% -
Outer mean diameter 30-50 nm 60-150 nm*
Length - 30-100 m
Density 20-380 kg/m3 ** 32-320 kg/m3 ***
Specific gravity 1.7–1.9 2
Surface area 120 m2/g 35-45 m2/g
Iron - <100 ppm
* Fiber average diameter, ** Bulk density of powder, *** Apparent density
55
3.2 Preparation method
The preparation procedures are divided into two parts due to the difference in polymer
matrix nature. The melt mixing method was used for thermoplastic composites while solution
mixing was used for elastomeric composites.
3.2.1 Thermoplastic polymer composite
The composites with different concentrations of CNTs and CBs were prepared using
a melt mixing method via a 25 mm co-rotating twin-screw kneader (Type: ZK 2542 D) from
Dr. Collin GMBH, Germany (Figure 20). This is a system of two intermeshing screws rotating
in the same direction. The rotation in a co-rotation system provides a gentle plastification at
high throughput while maintaining homogeneous shearing of the melt. Furthermore the
stripping of both flanks provides an improved self-cleaning effect.
Figure 20 Images of a co-rotating twin-screw kneader and a screw assembly
56
The specifications of the kneader used in this research are showed in Table 7. The
twin-screw extruder includes 8 thermal zones starting from the hopper and ending at the die.
The temperature profile of the extruder was set as presented in Table 8, considering the
processing conditions recommended by the Nylene supplier.
Table 7 Specifications of a co-rotating twin-screw kneader
Type Specification
Screw diameter 2 25 mm
Screw length 42 (L/D)
Heating zones 8
Drive power 16 kW
Nylon pellets were fed in the main feeder (gravimetric hopper, zone 1) while feeding
the carbon filler into the side stuffer (gravimetric feeder) located in zone 3 at various percent
loadings. Extrusion conditions were kept constant at 100 rpm of screw speed and 2 kg/hr of
the main feeder. The extruded composite was cooled immediately in a 1-m long water bath.
The extrudate was then pelletized using a stand pelletizer (CSG 171/2) and approximately 4
kg of each sample was collected.
Table 8 Temperature profiles of the extrusion process for various conductive fillers
Filler
Temperature profile (°C)
Zone
1
Zone
2
Zone
3
Zone
4
Zone
5
Zone
6
Zone
7
Zone
8
Main
feeder
Side
feeder Mixing Die
CNT 215 230 245 260 260 260 245 230
CB 250 265 280 280 280 290 285 270
57
3.2.2 Elastomeric polymer composite
A sonication technique was used to disperse carbon fillers into an elastomer resin, as
it generates some important effects in the liquid medium such as transient cavitation and
acoustic streaming. Acoustic cavitation involves the formation, growth, pulsating and
collapsing of tiny bubbles, producing transient (in the order of micro-seconds) micro-hot spots.
The strong impact coupling with local high temperatures can also enhance the wettability
between polymer and filler particles; thus it is able to break the agglomerating bodies by
damaging the van der Waals forces between the particles and make them disperse
homogeneously in the liquid medium (Kabir, Saha, & Jeelani, 2007).
The electrically conductive PDMS composites were prepared via a horn sonicator (24
kHz, 500 Watts). Ultrasound sonication is a form of vibration that provides energy for the
agglomerated fillers to escape from the surrounding resisting force. For the production of CNF-
PDMS composites, different weight fractions of CNFs (1, 2, 3, 4, and 5 wt%) were mixed with
PDMS-based resin in chloroform solvent through the procedures illustrated in Figure 21.
First, a specific weight of CNFs was sonicated with chloroform while mixing PDMS
with chloroform by stirring. To prevent a temperature increase, the sonication process was
carried out in an ice bath and was stopped at regular interval of 10 minutes. Consequently, the
temperature during the dispersion process was held at less than 40C. On the next step,
removing part of the solvent by evaporation produced a viscous gel-like, which, was then
mixed with the curing agent in the ratio of 1:10 (curing agent to PDMS-based). The resulting
gel-like liquid was evacuated in a vacuum chamber to remove any bubbles in the mixture, and
was cast by a pressed-mold to the desired thickness and dimension. The casting was cured in
58
an oven at 100ºC for 2 hours and the final CNF-PDMS composites appeared completely black
to give a flexible conductive PDMS composite sheet.
Figure 21 Experimental set up of CNF-PDMS composite fabrication
3.3 Characterization techniques
The properties enhancement of the composites due to the addition of carbon fillers
was characterized, including: electrical resistivity test, mechanical properties test, microscopic
test and thermogravimetric analysis. Several ASTM techniques were used to analyze the
composite materials; however, in some cases, ASTM standards were unavailable. Thus,
common techniques throughout the literature were utilized for the remaining tests. The general
description of the experimental setups used in this study, as well as the conditions and
parameters of each experiment, are described in the following sections.
PDMS/A
&
Chloroform
Sonication
220 min
CNF
&
Chloroform
Stirring
40 minPDMS/CNF
mixture
Sonication
220 min
MixingPDMS/CNF
gel-like
mixture
Curing
&
CastingPDMS/CNF
composite
Evaporation
59
3.3.1 Electrical resistivity test
In order to perform the electrical (volume) resistivity measurements, it would have
been desirable to use the actual standard ASTM D4496-87. This standard involves DC
resistance or conductance of moderately conductive materials, where the volume resistivity is
in the range of 1 to 107 -cm. The specifications and measurement setup for this standard were
found to be rather complicated and difficult. An alternative method was therefore developed
and used. Nevertheless, it still contains the same main principles.
To assure the accuracy of resistivity measurements, the possible decay of measured
resistance values with time was assessed. It was noted that the resistance readings fluctuated
minimally within the one minute observation. Therefore, data recording was delayed by 15
seconds on all samples to allow sufficient time for the signals to stabilize.
In this study, two configurations of volume resistivity measurement set up were used
due to the differences in polymer types and shapes of the final samples. Besides, the specimen
was cleaned with isopropy alcohol and kept under room conditions for 3 hours prior to the
measurements.
3.3.1.1 Nylon composites
The resistivity apparatus of the extruded samples (the sample dimension is shown in
Figure 22) was designed to measure the volumetric longitudinal or in-plane resistivity. This
test consisted of the 2-point probe connected with Keysight 34460A (Figure 22) in order to
investigate the effect of filler loading on electrical property. To eliminate the contact resistance,
conductive silver ink was coated and used as electrodes with a constant distance of 5 cm. The
60
resistance was then measured five times at five different locations along the extruded sample,
and the average value was used to calculate the resistivity.
(a) (b)
Figure 22 (a) Dimension of nylon composite samples, and (b) experimental setup for a 2-
probe electrical resistivity test
3.3.1.2 PDMS composites
The model 831 D991 test fixture is designed specially to test material in accordance
with ASTM D991 “Rubbery property: the volume resistivity of electrically conductive and
antistatic products”. This technique is used to evaluate the electrical behavior of rubber
products. This test method is useful in predicting the behavior of such products having
resistance up to approximately 100 M. The D991 test fixture utilizes the measurement of
current through a material and the voltage drop across a section of the material to calculate the
volume resistivity in -cm. It can measure specimens from 10-102 mm wide to 127-152 mm
long; however, the standard size was designed for 76 mm by 127 mm with 1 mm thickness.
The test fixture was connected with either a Keithley 2400 source meter or a Keysight
34460A, where the voltage source was used to apply a potential across both sides of the test
specimen causing current to flow through the specimen. The voltage drop across a section of
Sample
Current
Source
Volt
meter
61
the specimen was measured. The ammeter was used to measure the current from the voltage
source, shown in Figure 23.
Figure 23 Experimental setup for a model 831 D 991 volume resistivity test fixture
Using the following calculation from the D991 test method, the volume resistivity of
the material can be determined by Equation 3-1:
ρv=
Vwd
iL
Equation 3-1
where v is the volume resistivity (-cm), V is the potential difference across potential
electrodes (B-B’), i is the current through specimen (A-A’), w is the width of specimen
(constant at 7.62 cm), d is the thickness of specimen (constant at 0.1 cm), and L is the distance
between potential electrodes (constant at 6.35 cm).
62
3.3.2 Mechanical properties testing
The mechanical behavior of materials is an important property to study because it
provides quantitative analysis of how a material will perform under loading conditions. There
are several different types of tests that can be used to characterize the mechanical behavior of
a material. The stress-strain relationship of the material is characterized by measuring the
response of the material as a load is applied. The idealized relationship for stress (Equation
3-2) and strain (Equation 3-3) is relatively simple but becomes more complicated when taking
into account the real systems.
Stress ():
σ = F
A
Equation 3-2
where F is the applied force on the sample (N), A is the cross-sectional area through which the
force is applied (mm2), and is stress (MPa).
Strain ():
ε = ∆l
l0
Equation 3-3
where l is the changes of sample length (mm), l0 is the original length of the sample which is
referred as the gauge length (mm), and is strain (mm/mm)
63
One of the main motivations behind the development of reinforced composites is to
produce flexible materials with enhanced mechanical properties. Mechanical properties
including modulus, tensile strength and toughness were determined as a function of filler
loading using a tensile testing Instron 4465. In this work, tensile property tests were performed
at room temperature with a relative humidity of 50%. The samples were first cut using a dog-
bone shape cutter according to ASTM standard D412 (Type D, Figure 24).
Figure 24 ASTM D412 Type D cutter (units are in mm)
Three specimens from each percent loading were tested. The sample specimen was
held between the two pneumatically operated grips and subjected to a fixed load of 100 N with
a constantly fixed drawing rate of 20 mm/min. The gauge length was the distance between the
upper and the lower grip, which was fixed for all tests at 35 mm. During the experiment, a
uniaxial loading was continually applied on the specimen until failure occurred.
The initial slope obtained from the stress-strain curve was used to calculate the
modulus (Equation 3-4) while tensile strength was determined from the maximum stress at
yield (Equation 3-5). Lastly, the toughness was determined from the area under the stress-
strain curve.
64
Modulus:
Modulus=Applied Stress (σ)
Strain (ε)=
FA0
∆ll0
Equation 3-4
Tensile strength:
Tensile strength = Maximum applied force
Original cross-section area =
Fmax
A0
Equation 3-5
3.3.2.1 Nylon composites
In this study, nylon composites filled with CB were not tested because of their
inability to form the dog-boned shape specimens. Instead, a nylon matrix filled with CNT was
characterized for its mechanical properties. The reinforced pellets were extruded as a thin film
(a thickness of 0.5 mm) via a single-screw extruder (Brabender) coupled with a flexible flat
sheet die head, Figure 25. The screw speed was fixed at 30 rpm and a temperature profile for
all 5 heating zones was set as followed: 250C-270C-280C-300C-320C. The composite
films were cut into a dog-boned shape (according to ASTM standard D412) specimen
immediately after extrusion.
65
Figure 25 Single-screw extruder (Brabender) for thin film extrusion; inset, a flat sheet
die head
3.3.2.2 PDMS composites
The samples were directly cut from a molded sheet of PDMS-based samples using a
dog-bone shape cutter according to ASTM standard D412, as shown in Figure 26.
66
Figure 26 Dog-bone shape specimen of PDMS-based composites for mechanical testing
3.3.3 Field Emission Scanning Electron Microscopy (FESEM)
In order to investigate the morphological character of the carbon nano-materials, a
Hitachi model SU-70 FESEM at the University of New Brunswick is used. The samples are
loosely dispersed on conductive tape to preserve the as-prepared morphology as much as
possible. Images are acquired at different magnifications to show both the agglomeration of
the carbon particles and the surface topology of the individual carbon tubes. All images are
acquired using an acceleration voltage of 2 kV for better resolution of the surface features.
3.3.4 Scanning Electron Microscopy (SEM)
The dispersion and adhesion of the conductive fillers in the polymer matrix were
studied using a JEOL JSM6400 digital scanning electron microscope at the University of New
Brunswick. An electron beam (1 kV, 0.14 nA) was used to obtain micrographs of fracture
surfaces of the composite materials and the images were collected at various magnifications.
The fractured surface after performing the mechanical testing on the Instron testing machine
33
100
3 16
6.5
6.5
67
and/or the cryogenic surface (under liquid nytrogen) of the samples were analyzed. Since the
polymeric materials were non-conducting, a very thin layer (~5 nm) of gold coating was
sputtered onto the sample before mounting on the machine.
3.3.5 Transmission Electron Microscopy (TEM)
Transmission electron microscopy was used to depict particle size and structural
characteristics of the carbon conductive fillers. A JEOL 2011 transmission electron microscope
was used for this analysis. Samples were prepared by sonicating a small amount of carbon
filler in ethanol for 3 minutes; they were then micro-pipetted onto a carbon grid and left to dry
overnight.
3.3.6 Thermogravimetric analysis (TGA)
Thermogravimetric analysis (TGA) is an experimental technique that measures the
weight changes that occur as a specimen is heated. This method can be used to determine the
thermal stability of a material as well as the presence of volatile components in a sample. A
TA Instruments Q600 Simultaneous TGA/DSC was used to perform these tests. Samples
(10-15 mg) were placed into a ceramic sample dish after tarring. Subsequently, the samples
were then heated to 600-800C at 20C/min under nitrogen condition.
68
3.4 Characterization results of materials
3.4.1 Morphology of carbon fillers
FESEM and TEM of CNT-C70P were performed on the as received dry powders. The
appearance of the agglomerates was observed as bird nest structures, Figure 27(a). Due to the
synthesis process of CNT materials, they are usually provided in a strongly agglomerated state.
The nanotubes are held together by physical entanglements in these agglomerates, due to the
structural defects during their growth and the van der Waals interactions between them. These
agglomerates also resulted from the entanglement of CNTs, which caused significant
obstruction toward achieving a homogeneous dispersion of nanotubes in a composite.
Apart from the agglomeration of nanotubes, Figure 27(b) and Figure 27(c) also
showed the variation in diameter and size of the nanotubes as received. Moreover, the black
spots from TEM images of CNT-C70P in Figure 27(b) can be attributed to the impurities
during synthesis and processing of CNTs, as described in Section 3.1.2.1.
69
(a)
(b) (c)
Figure 27 Micrographs of CNT-C70P via (a) FESEM; (b) and (c) TEM
The morphology of CNT-C150P (as a dry powder form) was obtained from the
manufacturer. According to the supplier, this grade of CNT was bulkier, due to its higher
density, than CNT-C70P. Thus, higher agglomerate sizes and particle clumps were observed
(Figure 28).
70
Figure 28 Micrographs of CNT-C150P via SEM at different magnifications
Carbon black (N234) structure was observed under FESEM as shown in Figure 29. It
can be seen that CB is composed of primary particles fused into aggregates. The spherical-like
structure of CB is clearly present with approximately 30–100 nm of an aggregate size. The
aggregates of CB with considerable branching and chaining of prime particles can be referred
to as a high-structure black (Huang J. , 2002). A high-structure black has stronger attractive
forces between these aggregates, which mean the dispersion process should provide more
energy to separate them.
71
Figure 29 FESEM images of CB N234
The morphology of carbon nanofibers (Figure 30(a)) was similar to that of the carbon
nanotubes (Figure 27(a)) because they were both produced by a similar method. Besides,
carbon nanofibers also have a high aspect ratio and hollow core; however, the core of the
graphitic layers in carbon nanofibers had various different internal structures. Figure 30(b)
visibly demonstrated the stacked cups or coins conformation of these nanofibers. This
morphology had large reactive edges on the inside and outside, increasing the surface area of
the fiber and the available space for further chemical functional groups modification.
Depending on the application demands, carbon nanofibers can be created with different
diameters and morphology. In addition, the TEM micrographs at lower magnifications of
carbon nanofibers shown in Figure 30(c) revealed that CNF is much bigger than CNT; thus,
the dispersion of carbon nanofibers is expected to be simpler than that of carbon nanotubes.
72
(a)*
(b) (c)
Figure 30 Micrographs of CNF Pyrograf III via (a) SEM;(b) and (c) TEM.
NOTE: * Image obtained from the manufacturer’s data sheet
73
3.4.2 Elastomeric polymer composite conditions
The PDMS composites prepared in this research were in the collaboration with
another project related to piezoresistive materials for pressure sensor application; thus it was
necessary to characterize a suitable condition for optimum piezoresitivity (changes of electrical
resistance versus force applied) of the samples.
In this section, a compressive piezoresistance analysis (performed by another member
in the Applied nanotechnology research group) of various preparation conditions was
investigated under a data acquisition circuit board with a constant compression rate of 20
mm/min (the measurement setup is shown in Figure 31). The samples were connected via a
constant 1 k resistor to maintain the 5 volts source (the limitation of power supply to a circuit
board). The measurement was sampled with a 16-bit DAQ board and conducted until the load
reached 100 N. All PDMS samples were fixed at 2 wt% CNF loading under a continuous-cycle
mode of sonication. The high CNF loading (> c) was chosen so that a sufficient current could
be detected.
Figure 31 Compressive test of PDMS composites using a data acquisition circuit board
74
Since CNF particles tend to entangle and clump together, in most cases it is quite
difficult to disperse these particles in the polymer matrix. Agglomerated particles act as defects
and can cause damage to the polymer performances. Thus, the improved properties are mainly
dependent on the distribution of filler particles inside the matrix. Sonication not only disperses
fillers but also destroys the filler structure via cutting; thus optimizing a suitable sonication
condition is required. The parameters studied are listed in Table 9 as follows:
- Sonication time: since sonication cannot be done for an indefinite period of time so
optimum time for the ultrasound sonication must be adequately controlled in order to achieve
the maximum conductivity as well as maintain the overall properties.
- Power amplitude and output control level: the amount of energy input to the liquid
medium (solvent) is proportional to the amplitude (percentage of the actual horn sonicator
power). If there is not enough energy given to the composite mixture, the CNFs agglomerate
cannot escape the resisting force within its clusters; thus the aid for dispersion is limited.
However, if too much energy is applied to a CNF cluster, the frequency of collision between
each single CNF will be increased. Hence the dispersion mechanism may be adversely affected
by excessive energy given to the CNFs.
- Amount of solvent: an appropriate volume of solvent used in the mixing process is
essential since it aims to ensure the attainment of proper viscosity to evenly disperse CNFs in
the PDMS matrix and maintain the stability of CNFs in the solution.
75
Table 9 Trials of sonication conditions for PDMS-based composites
Condition Time
(min)
Power
amplitude (%)
Output
control (level)
Relative dispersion
energy
Solvent
(ml)
1 240 60 6 2.88104 200
2 230 70 8 3.36104 200
3 210 70 8 1.12104 200
4 210 70 8 1.12104 300
5 230 70 8 3.36104 300
It is expected that the observed piezoresistive phenomenon is caused by the formation
of conductive paths and the degeneration of a network sequentially (Tiwana, Redmond, &
Lovell, 2012; Stassi, Cauda, Canavese, & Pirri, 2014). Initially, the composites contain
numerous conductive CNF particles embedded in an insulating matrix and are essentially not
in contact with randomly oriented; yielding a high resistance as current flows across the
thickness dimension of the material. As compressive force increases, the elastic polymer
matrix deforms to the extent that the CNF particles are forced to re-orientate themselves and
thereby lateral expand of the matrix. This forms a large surface area for electric fields to be
generated and allows electron hopping (Mott, 1987; Hussain, Choa, & Niihara, 2001; Beruto,
Capurro, & Marro, 2005; Qu & Wong, 2007; Abyaneh & Kulkarni, 2008).
Figure 32 shows the change of resistance under compressive forces ranging from 5 to
100 N for PDMS reinforced with 2 wt% CNF. All composites’ conditions reveal the
conductivity improvement upon compression, as can be seen by the change in electrical
resistance in the scale of orders of magnitude. Clearly, low values of electrical resistance of
2.5107 -cm can be measured in condition 3, 4 and 5; however the responsive detection of
76
samples were found at a high load applied of 30-45 N. Thus, these states were not considered
as a suitable condition for pressure sensor application.
Based on the results of condition 2/5 and 3/4, it can be deduced that a higher volume
of solvent can reduce the initial resistance of the composite samples under the same relative
energy. This might be due to the dispersability and stability of the CNF dispersion in a PDMS
matrix, causing more electrons to transfer through the sample (Huang & Terentjev, 2012).
However, at the same volume of solvent (200 ml), a low relative energy resulted in a lower
resistance (better conductive ability) but a poorer force response.
Figure 32 Electrical resistance vs force applied for PDMS filled with 2 wt% CNF
composites
5
6
7
8
9
0 10 20 30 40 50 60 70 80 90 100
log r
esis
tan
ce (
)
Force (N)
Condition 1
Condition 2
Condition 3
Condition 4
Condition 5
77
In addition, the slopes of each sample curve obtained in Figure 32 were determined.
Obviously, the composite prepared by condition 1 and 2 exhibit rapid decreases in resistance
at 20 and 30 N with very high slope of 0.221 and 0.282 compared to condition 3-5 of 0.085.
However, a lower load applied of 20 N under an acceptable range of the resistance was desired
since the application of this CNF-PDMS composite requires low-force sensitivity. Therefore,
condition 1 was chosen as an optimum condition for the experiment of PDMS-based
composites in this research.
The volume resistivity of each sample under these various conditions was also
measured using the technique described in section 3.3.1.2. The results are illustrated in Figure
33. Obviously, condition 1 provides the composite with the least resistivity and variation value;
this supported the conclusion made earlier.
Figure 33 Volume resistivity of CNF-PDMS composites at 2 wt% under different
sonication conditions
0
50
100
150
200
250
300
350
1 2 3 4 5
Vol
resi
stiv
ity (
-c
m)
Condition
78
Chapter 4 Role of nano-carbon fillers on electrical properties of polymer
composites
To complement the studies, a variety of experimental data was acquired. The data
included electrical resistivity and percolation threshold studies, mechanical properties, and
dispersive properties of carbon fillers on polymer matrices. The most relevant results of nylon
composites are discussed below whereas more details of the results are attached in Appendix
B and Appendix C.
In general, conventional polymeric materials are flexible and have mechanical
resistance but low electrical conductivity. For some specific applications, a material with
suitable electrical conductivity is needed; thus, conducting polymeric composites were
fabricated to overcome this problem. Due to the uniqueness of physical, thermal and electrical
properties that are present in carbon fillers beyond other available conventional materials, they
are attractive for the engineering applications as reinforcing materials. Incorporating carbon
fillers with polymer materials to improve their properties makes them more valuable, as they
become electrically conductive while keeping their interesting properties.
4.1 Morphology analysis
To analyze the dispersion state of carbon fillers in polymer composites, cross-
sectional fractured surfaces of the composites were characterized. Extruded neat nylon 6
samples were cryogenically fractured in liquid nitrogen and examined under the electron
microscope at various magnifications. SEM examination in Figure 34 shows that neat nylon
resin experiences brittle fracture with a rough and slight grainy surface indicating extensive
deformation prior to failure (Mahmood, Islam, Hameed, & Saeed, 2013).
79
Figure 34 SEM images of neat nylon 6 under nitrogen fractured surfaces
The SEM micrographs of fractured CNT-nylon composites at various loadings are
illustrated in Figure 35. As clearly observed, carbon nanotube dispersion is present as the bright
dots and lines indicating the ends of broken nanotubes after fracture. Due to the absence of
carbon nanotube aggregates or clusters in all samples of different filler content, this
observation can be represented as a good dispersion and distribution of nanotube fillers in
nylon matrix.
At low filler loading (Figure 36(a)), individual carbon nanotubes are visible.
However, rough fractured surfaces are also observed at higher nanotube loadings (Figure 36(e)
and Figure 36(f)) due to an embrittlement of the composites with increasing carbon nanotube
content. The SEM images also display the reduction of empty space (black background of
nylon resin surface) as nanotube concentrations increased, indicating more condensed and
compacted area of carbon nanotube distribution. This good distribution of carbon nanotube
promotes CNT-to-CNT interactions through surface contact (or tunneling); thus, it should
increase the electrical conductivity of the composite, as will be further discussed.
80
(a) (b)
(c) (d)
(e) (f)
Figure 35 Tensile fractured surfaces of CNT-nylon composites at high magnification:
(a) 3, (b) 5, (c) 6, (d) 8, (e) 10 and (f) 12 wt% loading
81
(a) (b)
(c) (d)
(e) (f)
Figure 36 Tensile fractured surfaces of CNT-nylon composites at low magnification:
(a) 3, (b) 5, (c) 6, (d) 8, (e) 10 and (f) 12 wt% loading
1 m
Broken ends of CNT
2 m
1 m 2 m
1 m 1 m
82
Since the dimensions of CNT fillers are very small, no definite evidence for the carbon
nanotube pull-out and no holes in nylon matrix were observed. Therefore, it may be concluded
that the failure is mostly due to the fracture where the CNTs are strongly embedded in nylon
matrix. This typical breakage phenomenon of CNT upon tensile stretching indicates a strong
interfacial adhesion between the CNT and the nylon matrix (Zhang, Shen, Phang, & Liu, 2004;
Rangari, Yousuf, Jeelani, Pulikkathara, & Khabashesku, 2008; Mahmood, Islam, Hameed, &
Saeed, 2013), leading to enhancement in mechanical properties of composites as a
consequence of increased load transfer between the two components in the system.
Another interesting effect was observed under close inspection of SEM images, as
presented in Figure 37. Two points of view can be postulated: (i) stretching of nylon fibers
within its resin or (ii) bridging of nanotubes interconnecting lumps in the nylon matrix. Since
nylon 6 used in this research is a spinning-grade resin, it is likely to stretch out to less than 1
m in diameter. Another possible notion arises from the strong interfacial adhesion between
the CNT filler and the polymer matrix. It might be described that carbon nanotubes are
stretched out with a curved and tapered end while another end of the tube is still strongly
embedded in the polymer resin (Sahoo, Cheng, Cai, Li, & Chan, 2009). The lumps diameter
in Figure 37(right) is observed to be much larger than the diameter of individual carbon
nanotubes (10-20 nm); thus, the connection of polymeric lumps might come from the nanotube
bundles that are wrapped by polymer. Similar observations were also made by Zhang et al.
(Zhang, Shen, Phang, & Liu, 2004) and Liu et al. (Liu, Phang, Shen, Chow, & Zhang, 2004).
However, further investigation is required to clarify this phenomenon.
83
Figure 37 Tensile fractured surfaces of CNT-nylon composite at 5 wt% loading
On the other hand, Figure 38 shows SEM micrographs of impact fractured surfaces
of nylon composites containing various carbon black loadings. As expected, a nano-size of
highly structured carbon blacks is aggregated together and the aggregates also detach from
each other. At low concentration of carbon black (Figure 38(a)), individual particles of the
filler homogeneously distributed within the nylon matrix are evident. In the case of carbon
black in nylon matrix, its particles tend to pack together and close contact between the
aggregations is observed. This increasing of carbon black concentrations causes many primary
CB particles to form primary aggregates with considerable branching and chaining; thus a few
small clusters are noticed (indicating by the white-dot clumps as circled in Figure 38(b) and
Figure 38(c)). The dispersion of carbon blacks reasonably well obtains in the polymer matrix
when the carbon black content increases; although there are still aggregated particles forming
clusters. Moreover, these clusters could possibly effect to the reduction in mechanical
properties of the overall composites.
5 m 1 m
84
(a) (b)
(c) (d)
Figure 38 Tensile fractured surfaces of CB-nylon composites at (a) 15, (b) 20, (c) 30 and
(d) 35 wt% loading
1 m 1 m
2 m 2 m
85
4.2 Composition analysis
The filler content in polymer composites is an important factor influencing the
electrical conductivity; therefore, it is crucial to verify the actual filler concentration as it will
effect the modeling estimation. To validate the weight percentage of carbon fillers (CNT and
CB) in the polymer matrix and also confirm that fillers are distributed throughout the matrix
on the microscopic scale. Thermogravimetric analysis (TGA) experiments were performed on
the nanocomposite pellets as well as the unfilled polymer. In TGA, the weight is measured as
the sample is heated at a constant rate through its degradation temperature. Carbon fillers are
thermally stable at much higher temperatures than the nylon matrix. After pyrolysis of the
matrix, the residual mass can be utilized to calculate the weight percentage of carbon fillers in
the composite. At 580C (after pyrolysis), the nylon is completely decomposed, and the
residual weight of carbon fillers can be taken as the weight percentage of fillers within the
composite. Table 10 and Table 11 show the calculation results for the different compositions.
Table 10 CNT-nylon composition under TGA measurement
%wtset Residue (%) %wtmeasured % Difference
0 0.73 - -
3 3.99 3.26 9
5 5.28 4.55 9
6 6.32 5.58 7
8 9.41 8.68 8
10 10.4 9.62 4
12 14.2 13.4 12
86
Table 11 CNT-nylon composition under TGA measurement
%wtset Residue (%) %wtmeasured % Difference
0 0.73 - -
15 17.0 16.3 8
20 20.9 20.2 1
30 33.6 32.9 10
35 37.0 36.3 4
As shown in the tables above, the specimens show residual weight corresponding to
their compositions where the deviation is within the acceptable range. This result can confirm
good control and precise sample preparation by the extrusion machine used.
4.3 Electrical resistivity and percolation behavior analysis
Nylon composites filled with CNT and CB were characterized for their DC electrical
resistivity using 2-probe measurement. Among these composites, only the ones with higher
concentration of carbon fillers could be measured accurately. For the materials containing less
than 3 wt% of CNTs and 15 wt% of CBs, no measurable resistance could be recorded due to
the limitation of the instrument. The electrical resistivity results (calculated by Equation 2-3)
of CNT-nylon and CB-nylon composites in terms of weight percent loading have been plotted
in Figure 39.
It can be clearly seen that both sample sets demonstrate the percolation transition at
which a conductive path was formed in the composite causing the materials to become a
conductor. According to many researches on the electrical properties of polymer composites
(Balberg, 2001; Meincke, et al., 2004; Seung, et al., 2009; Potschke, et al., 2010; Alig, et al.,
2012), the resistivity value of the composite does not change much at low filler content or
87
below the percolation threshold. In most cases, it approaches to the resistivity of the polymer
bulk. However, near the point of percolation threshold, significant transition in the composite
resistivity (several orders of magnitude) can be observed due to the formation of continuous
electron paths or conducting networks. When filler content increases beyond the threshold, the
resistivity has gained a strong dependence on the filler content resulting in less changes in
composite resistivity.
Figure 39 Volume resistivity of nylon composites as a function of filler contents.
Additionally, it is obvious that the differences in filler structures and shapes have
significant effect on the resistivity of the composites. One noticeable difference is that, at the
same resistivity value, the composites containing CNTs contains less filler than do CB-nylon
composites. For example, materials with resistivity values lower than 104 -cm can be
88
regarded as electrically conductive (Mikitaev, Kozlov, & Zaikov, 2008). In case of the CNT-
filled composites, it starts at 6 wt% whereas for the CB-filled composites it starts at 18 wt%.
This result indicates that a conductive network is closely related to the structure and
dispersibility of the fillers. As demonstrated in Figure 36(c) for 6 wt% CNT and Figure 38(b)
for 20 wt% CB, CB-filled composite showed several clumps of the conductive filler while
individual tubes can be observed for CNT-filled composites. This revealed that the more
uniform the distribution of the fillers is, the more easily and effectively the conductive network
can be formed at lower filler content. Thus, a continuous conductive network was generated
efficiently at lower loading for CNTs than CBs, since CNT particles were dispersed uniformly
on the nanometer scale (Du, Scogna, Zhou, Brand, Fischer, & Winey, 2004; Du, Fischer, &
Winey, 2005; Lee, Cho, Jeon, & Youn, 2007; Hilarius, Lellinger, Alig, Villmow, Pegel, &
Potschke, 2013; Chen, Pan, Wang, Liu, & Zhang, 2015).
Moreover, the aspect ratio of the fillers also plays an important role in the electrical
properties of the polymer composites. It is well known that the aspect ratio of CNTs is typically
in the range of 100-1000 (Potschke, Dudkin, & Alig, 2003; Cheng, et al., 2010; Kasgoz, Akin,
& Durmus, 2015). This is a hundred times greater than that of the conventional carbon fillers
(carbon black and carbon nanofiber) used to enhance the electrical conductivity in polymer
materials (Foygel, Morris, Anez, French, & Sobolev, 2005). Therefore, the low-loading
content of CNTs is enough for tube-tube interactions in composites to reach the point where a
conductive path can be created allowing the electrons to flow through the composites. As a
result of CNT configuration, only the outer layer contributes to the electron transport that gives
the composite its electrical properties (Norkhairunnisa, Azizan, Mariatti, Ismail, & Sim, 2011).
89
Incorporation of conductive fillers in an insulating polymer matrix can make the
composite conducting through the formation of continuous conduction networks. In general,
variation of electrical conductivity or resistivity with filler concentration is sigmoidal curve
(S-shaped), as shown in Figure 3. This curve consists of three parts; the initial region is where
the filler concentration is less than percolation threshold. The second part is where only a few
continuous conducting networks are formed (Kim, Pfeifer, Park, & Bandaru, 2011; Kim, Park,
Kapadia, & Bandura, 2013). When a small concentration of filler is added, there is an abrupt
decrease in resistivity. In this region, slight change in filler concentration causes significant
decrease on resistivity in which the system changes from insulating to conducting. The third
part is where the change in resistivity becomes marginal.
Generally, the formation of a conducting network in an insulating matrix depends on
the characteristics of the conducting filler as well as the matrix polymer. As previously
demonstrated in Figure 39, CNT-nylon exhibited a sharp decrease in the resistivity between 1
and 3 wt% loading (from 1014 -cm to 7.26106 -cm). This is about 8 orders of magnitude
decrease in electrical resistivity with only 3 wt% loading of CNT. The significant drop in the
resistivity confirms that the percolation threshold has been reached and the composites are in
the conductive range beyond this concentration. However, a higher loading of CB fillers
between 10 and 15 wt% is required to induce the percolation to be visible (from 1014 -cm to
3.14104 -cm). An additional increase of 5 wt% in CB concentration decreased the resistivity
from 3.14104 to 415 -cm at 20 wt%. A further increase in CB contents beyond this point
reveals only a marginal decrease in resistivity of the composites and is almost constant for
carbon black content above 30 wt%. This indicates that the percolation threshold is already
exceeded. Once the carbon black conducting networks are extensively formed above the
90
percolation threshold, further addition of CB particles has little or no contribution to the
resistivity.
Figure 40 schematically explains the electrical behavior of the composite in terms of
the characteristic and orientation of different conductive fillers used in this nylon matrix. At
low loading of CNT-filled composites, the conductive filler is distributed randomly in various
orientations due to the effectively high aspect ratio of nanotubes. The relative tube-tube
interactions can occur when the distance between the tubes is very close. The conductive tube
network creates the electrical conducting path that allows the electrons to tunnel through the
tube channels by electron hopping (Wu, Masaharu, Natsuki, & Ni, 2006; Via, King, Keith, &
Bogucki, 2012). With the addition of 3 wt% (Figure 40(top)), carbon nanotubes inclusions
become in contact and significantly reduce the electrical resistivity of the composite materials.
Figure 40 Schematic of the percolation threshold of nylon composites with filler loadings
of (top) CNT and (bottom) CB
0 wt % 3 wt% 12 wt%
Increasing of MWCNT loading
0 wt% 15 wt% 35 wt%
Increasing of CB loading
91
However, the conductive carbon black particles do not result in electron tunneling at low filler
loading due to the three-dimensional structure of the fillers. As the filler loading increases, the
filler agglomerates and forms cluster of CB aggregates in certain regions. The filler clusters
started to contact each other at 15 wt% loading (Figure 40(bottom)) and the electron tunneling
effect could take place, reducing the resistivity of the composite. Therefore, it can be deduced
that a higher weight percent of CB particles is required, compared to CNTs, for the conductive
fillers to have direct contact with each other and create conducting networks.
A simple model considering the filler geometry can be schematically demonstrated in
Figure 41. With the assumptions that CB particles are perfectly sphere and directly contacted
together; whereas CNT particles are straight and randomly dispersed in a matrix at an angle of
45 end-to-end connection, a simple calculation of the numbers of filler particles to create the
conducting path within the composite can be made. Base on the information of average filler
sizes obtained from the manufacturer (CB diameter of 35 nm, and 13 nm diameter with 1 m
length for CNT), the amount of filler particles that can be participated across the test distance
of 5 cm were determined (the sample calculation is shown below) to be 1.43106 and 7.07104
particles for CB and CNT, respectively. It is obvious that greater amount of CB particles is
needed in order to allow electric charges transfer across the composite lengthwise.
For CB:
5 cm (test distance)
35 nm (diameter 1 CB particle⁄ ) = 1.43×10
6 CB particles
For CNT:
5 cm (test distance)
1 μm cos45(length 1 CNT particle⁄ ) = 7.07×10
4 CNT particles
92
Figure 41 Schematic of CB and CNT conduction path within a test distance of volume
resistivity measurement
In addition, a linear circuit diagram can be used to estimate the composite resistance
from each filler type based on the geometric relation. The conducting path behaves similarly
to a network of resistors connected in series where each filler is a resistor by itself, and the
mathematical expression is shown in Equation 2-4. With the concept of contact resistance
between filler particles alone, great resistance from CB-filled composite can be expected to
appear due to the summation of many CB resistors within the conducting network where CB
presents 20 times more CB particles/resistors than CNT. Moreover, the inherent resistance of
CB is about 100 higher than CNT based on the literature review as describes in Section 2.3.1.
Therefore, the resistance of CB-filled composites can be evaluated to be 2000 times higher
than that of CNT-filled composite once the percolation exists. In order to support this
argument, an experimental confirmation can be made. At 16 wt% loading of both fillers, the
composite resistivity is estimated to be approximately 102 -cm for CNT-nylon composite and
105 -cm for CB-nylon composite (from Figure 39). It can be seen that CB-filled composites
presents approximately 1000 times more resistive. Thus, the simple geometric model proposed
93
in this research can be used to quantify the percolating resistance the polymer composite
systems with good agreement.
4.3.1 Percolation threshold analysis
The statistical power law expression derived from percolation theory: ρ = ρ0(-
c)
-t
in Equation 2-7 is used to fit the resistivity (v) data at filler loading above the percolation
threshold (>c). The percolation threshold and the critical exponent were obtained by plotting
the log of the electrical resistivity as a function of the log of (–c) with varying c (Figure 42)
until the best linear fit was obtained. The results achieved from the fit function present a
correlation factor (R2) of greater than 99% and Table 12 summarizes all of related percolation
parameters including: percolation threshold (c) and critical exponent (t).
Table 12 Summary of the percolation parameters for nylon composites
Sample c
(wt%)
Critical exponent
t R2
CNT-nylon 2.95 3.18 0.998
CB-nylon 16.3 1.44 0.990
The relatively low electrical percolation threshold obtained from CNT-nylon samples
(3.0 wt%) is attributed to the geometrical characteristics such as high aspect ratio and high
surface area as well as the uniform dispersion of nanotube particles in the polymer matrix.
These attractive properties of CNT facilitate the formation of conducting networks and thus
transform the insulating polymer to a conducting composite at low content (Ma, Siddiqui,
Marom, & Kim, 2010). According to many reports on the electrical percolation threshold of
polymer-CNT composites, the experimental values vary between 0.05 and 6 wt% (Sandler,
94
Kirk, Kinlorch, Shaffer, & Windle, 2003; Meincke, Kaempfer, Weickmann, Friedrich,
Vathauer, & Warth, 2004; Zhang, Rastogi, Chen, Lippits, & Lemstra, 2006; Kodgire,
Bhattacharyya, Bose, Gupta, Kulkarni, & Misra, 2006; McLachlan & Suati, 2007; Logakis, et
al., 2009; Krause, Potschke, & Hausler, 2009; Spitalsky, Tasis, Papagelis, & Galiotis, 2010;
Zhu, Zang, & Jiao, 2014); more articles are used in Table 3. Thus, these results are in good
agreement with the percolation values found in literatures. The variation is possibly related to
the dispersion degree, geometry, surface treatment and alignment of CNTs, the properties of
the polymer matrix, and the processing technique used to produce the polymer composites. It
has been found that the well-dispersed CNTs gave rise to 50 times higher conductivities that
the entangled ones (Bauhofer & Kovacs, 2009).
Figure 42 Log-log plot of resistivity as a function of (–c) with a linear fit for nylon
composites filled with CNT and CB
y = -3.18x + 5.23
R² = 0.9978
y = -1.44x + 3.50
R² = 0.9904
0
1
2
3
4
5
6
7
-1.5 -1 -0.5 0 0.5 1 1.5
log r
esis
tivit
y (
-c
m)
log (-c)
CNT-nylon CB-nylon Linear (CNT-nylon) Linear (CB-nylon)
95
On the other hand, the formation of continuous conducting paths or network in nylon
matrix percolates at a greater CB concentration of 16 wt% because CB particles tend to form
agglomerate structure and clusters within the composite. It has been found in the literature that
the electrical percolation threshold generally appears at about 5-20 wt% for the composites
filled with carbon black (Yui, Wu, Sano, Sumita, & Kino, 2006; Hu, et al., 2014; Jose, Susana,
Enrique, Javier, & Maritza, 2015; Chen, et al., 2015; Deniz, Sousa, Arlindo, Sakamoto, &
Fuzari Jr, 2015).
The exponent t calculated in this study is found to be 3.18 and 1.44 for CNT-filled
and CB-filled composites, respectively. Generally, the critical exponent t reflects the
dimensionality or the connectivity of the composite system, with the theoretical values falling
between 1.3 to 2.0 for two-dimension and three-dimensions, respectively (Stauffer & Aharony,
1994; Sahimi, 1994). The experimental t value from CNT-nylon composite shows large
deviation to the theoretical one. This is because CNTs are not ideally dispersed as an individual
tube in the polymer matrix (as observed in Figure 35 and Figure 36); instead, they are entangled
and form bundles.
Similar deviations from the universality of percolation exponents in conducting
composites have been found in the range from 2 to 10 (Balberg & Bozowski, 1982; Carmona,
Prudhon, & Barreau, 1984; Mamunya, Davydenko, Pissis, & Lebedev, 2002; Kanapitsas, et
al., 2008; Li & Zhang, 2010; Spitalsky, Tasis, Papagelis, & Galiotis, 2010; Balberg, 2012;
Behbahani, Motlagh, Ziaee, & Nikravan, 2015); more examples are tabulated in Table 3.
Various factors such as physical properties of the constituents and method of synthesis can
contribute to this non-universality. The source of this non-universality in t values is not well
understood, although some studies have attributed it to the complex tunneling transport
96
processes in the real composites (Balberg, 1987; Keblinski & Cleri, 2004; Bao, Meguid, Zhu,
& Weng, 2012).
However, it is notable that the critical exponent t obtained from CB-nylon composite
(1.44) appeared close to the universal value of 2 as well as with other experimental values
reported for CB filled polymer systems (Zois, Apekis, & Omastova, 2001; Balberg, 2001;
Cheng, et al., 2010; Da Silva, Kanda, & Nagashima, 2012). The closer the t to the universal
value, the closer the conducting network dimensionality. In this case, CB randomly dispersed
in nylon matrix almost as a 3-D network due to their aggregates (as shown in Figure 38).
Another interesting interpretation can be taken from the t results or the slope. It is
clear that CNT-nylon composite shows higher slope than CB-nylon one. This represents the
effective of filler geometry to the conductivity. The higher slope of CNT means that for a small
change in filler concentration, the change in composite conductivity is more pronounced in
CNT than that of CB composite.
4.3.2 Comparison of experimental data with numerical model
Once the experimental portion was completed, the results were compared and
analyzed according to the statistical model described previously in the literature survey. This
study is aimed to investigate the applicability of a numerical model to accurately predict the
electrical resistivity of carbon-based polymer composites. In order to simulate the electrical
resistivity over the percolation threshold in terms of weight percentage of fillers, the power
law model took the following forms:
For CNT-nylon composites, ρ = 1.71×105(- 2.95)-3.18 Equation 4-1
For CB-nylon composites, ρ = 3.16×103(- 16.3)-1.44 Equation 4-2
97
Theoretically, the value of 0 (a scaling constant) should approach the resistivity of
the conductive filler itself. However, the scaling constant in this study was much higher than
expected. This might be due to the existing contact resistance between the fillers or their
clusters in the system, which effectively causes the addition in resistivity of the fillers
themselves (Ounaies, Park, Wise, Siochi, & Harison, 2003; Bao, Meguid, Zhu, & Weng, 2012;
Oana, Gunter, Leendert, & Gijsbertus, 2016).
Figure 43 shows the experimental results compared to the values predicted by the
statistical model. It can be seen that the power law model successfully exhibits good agreement
between the results and the calculations for both nylon composite systems with the bulk of data
at higher carbon filler loadings (>c). The results also support the electrical resistivity
characteristic of the reinforced composites and the morphology observation that the
theoretically predicted value of c strongly depends on the carbon particle sizes and structures.
The polymer composites filled with large aspect ratio and nanoscale dimension of carbon
nanotubes show lower c. This result is qualitatively similar to that of many researchers
(Nakamura, Nishizawa, Motohira, & Yanagida, 1994; Hussain, Hojjati, Okamoto, & Gorga,
2006; Zhou, Wang, Zhang, & Zhang, 2006; Potschke, et al., 2010; Sanjines, Abad, Vaju,
Smajda, Mionic, & Magrez, 2011; Kasgoz, Akin, & Durmus, 2015), where the value of c can
be extremely low in composites consisting of highly anisotropic fillers such as thin cylinders.
Another interesting observation can be made out of Figure 43. The prediction model
shows that the ultimate resistivity of CB-filled composite will never be below 10 -cm;
although, it estimates only at 20 -cm when 50 wt% CB is added. The poor performance in
electrical conductivity of the CB-filled composites compared to the CNT-filled is governed by
two main reasons: (i) the poor contact of CB particles due to their spherical shape along with
98
a low aspect ratio of unity makes it difficult for them to form conducting networks in the
matrix, and (ii) the inherently lower conductivity of CB than CNT. This prediction result
benefits many advantage designs in electronic applications.
Figure 43 Electrical resistivity modeling results of CNT-nylon and CB-nylon composites
0
2
4
6
8
10
12
14
0 10 20 30 40 50 60
log re
sist
ivit
y (
-c
m)
Filler content (wt%)
CNT-nylon Power law-CNT
CB-nylon Power law-CB
99
4.4 Mechanical properties
Polymer systems are widely used in various applications due to their unique attributes
such as ease of production, light weight, and often ductile nature. However, polymers have
lower strength and modulus than metals and ceramics. When carbon fillers are used as
reinforcing agents in the polymer composites, the mechanical properties of composites are
hypothesized to improve with the filler weight percent loading. Several factors can be
contributed to the mechanical properties of polymer composites, such as the matrix
morphology, the filler orientation and distribution, and the interaction at matrix-filler interface
(Moniruzzaman, Chattopadhyay, Billups, & Winey, 2007). Among these requirements,
dispersion of the fillers is a critical issue in achieving uniform mechanical stress distribution.
In order to completely understand the mechanical behavior of polymer composites under
tensile loading, stress-strain curves have been obtained. In this study, nylon-filled with carbon
black composites were not included in the discussion because of their inability to form the dog-
bone shaped specimens.
The low density, high aspect ratio, and extraordinary mechanical properties of carbon
nanotubes (with tensile strength up to 50 GPa and modulus up to 1000 GPa) (Wu & Shaw,
2006; Spitalsky, Tasis, Papagelis, & Galiotis, 2010), these make them particularly attractive
for reinforcement in composite materials. However, many challenges exist in achieving good
improvement in mechanical properties. In general, the mechanical properties of CNTs-polymer
composites are substantially superior to those of the neat polymer matrix. This is probably due
to the dispersion of high strength CNTs nano-fillers throughout the polymeric matrix that
exhibit strong interaction between nanotubes and polymer matrix. However, addition of the
rigid filler materials tends to produce composites that are brittle and break at a lower strain
100
than does the base polymer (Thostenson, Ren, & Chou, 2001; Otero, Martinez, Oller, &
Salomon, 2012; Zang, Zhu, & Jiao, 2015).
Typical stress-strain curves for nylon loaded with CNT at concentrations ranging
from 3–12 wt% are plotted in Figure 44. The curves exhibit a linear elastic region, followed
by yield (a point of plateau) and a plastic deformation region before break. As shown in the
graph, stress is proportional to strain with a constant proportionality at the initial portion of the
curve (up to 5% strain), leading to a linear relationship between stress and strain values that
can be explained by Hooke’s law.
Figure 44 Stress-Strain curve of CNT-nylon composites at various CNT loading
The mechanical properties versus carbon nanotube loading are summarized in Figure
45. The graphs demonstrate that incorporation of carbon nanotube fillers in nylon matrix can
0
20
40
60
80
100
120
140
160
180
0 10 20 30 40 50 60 70 80
Str
ess
(MP
a)
Strain (%)
Nylon
3%
5%
6%
8%
10%
12%
101
considerably increase both the tensile strength and modulus, which make nylon tougher and
more resistant to deformation. This behavior is consistent with the experiments previously
reported in the literature for CNT-nylon composites (Zhang, Shen, Phang, & Liu, 2004;
Bradford, Wang, Zhao, Maria, Jia, & Zhu, 2010; Wang, et al., 2011) where the incorporation
of CNTs with a very large fracture strain to thermoplastics can either lead to an improvement
of their toughness or to a small reduction in tensile ductility (Liu, Phang, Shen, Chow, &
Zhang, 2004; Baji, Mai, Wong, Abtahi, & Du, 2010). Moreover, the standard deviation of all
results obtained is minimal (within 5% range); this is probably due to a uniform and stable
dispersion of the reinforcing filler in the polymer resin (Jordan, Jacob, Tannenbaum, Sharaf,
& Jasiuk, 2005; Bao & Tjong, 2008; Alig, et al., 2012).
In Figure 45(a), a slight increase can be observed in tensile strength (7.83% improved)
at 3 wt% of CNT. This small change is probably because only small nanotube networks might
have just formed at this level. The effect of carbon nanotube content on the composite strength
becomes significant as the filler loading increases where the tensile strength was measured to
be 94.3 MPa (21% improved) and 150 MPa (92% improved) at 5 and 10 wt% CNTs,
respectively. An enhancement of 113% was possible with the addition of 12 wt% CNT; the
measured tensile strength was increased from 78 MPa to 166 MPa. This improvement in tensile
strength is expected to be due to the strong interaction between CNTs and polymer chains
where the nanotubes can achieve their potential as fillers with extremely high strength. As
described in the surface fracture results (Section 4.1) that no pull-out of CNTs from the nylon
surface can be observed, indicating a good interfacial adhesion between the fillers and the
polymer matrix.
102
(a) (b)
(c) (d)
Figure 45 Mechanical properties of CNT-nylon composites at various % loading (a)
tensile strength, (b) modulus, (c) toughness, and (d) elongation at break
The effect of carbon nanotube concentrations on the modulus (Figure 45(b)) of the
composites is obtained from a linear relation of the stress-strain curve (at 3-4% strain). It is
revealed that CNTs have significant impact on the modulus of composites. The modulus
increases significantly with CNT loading at higher levels. With the addition of 3wt% CNT, the
modulus was enhanced to 1.55 GPa with an improvement of 3.3% over the neat nylon resin.
Further filling of CNTs into the composite has facilitated the increment of the modulus. For
composite having 6 wt% of carbon nanotubes, the modulus was increased to 2.0 GPa from 1.5
0
50
100
150
200
0 5 10 15
Ten
sile
yie
ld s
tren
gth
(MP
a)
CNT content (wt%)
0
1
2
3
4
5
0 5 10 15
Mo
du
lus
(GP
a)
CNT content (wt%)
0
1
2
3
4
5
0 5 10 15
Tou
gh
nes
s (M
J/m
3)
CNT content (wt%)
0
20
40
60
80
0 5 10 15
Str
ain
(%
)
CNT content (wt%)
103
GPa for neat nylon and showed an improvement of 33%. An improvement of 153% was found
from the addition of 12 wt% CNTs at the modulus of 3.8 GPa.
Toughness of materials depends on both the maximum stress attained and also on
strain at which the composite breaks. In composite materials the addition of reinforced-filler
can increase the strength and stiffness. However, this also affects the overall flexibility of the
composites in which reducing the toughness of the material can be observed (Figure 45(c)).
The elongation at break is an indicator for the toughness of the materials and is strongly
affected by nanotube loading. A drastic decrease in elongation at break with increasing CNT
content (Figure 45(d)) can be observed. The reduction in materials’ toughness is caused by the
brittle character of carbon nanotubes that may cause the stiffness of the composites to rise.
Table 13 is the summary of the mechanical properties of the carbon nanotube based composites
with its improvement.
Table 13 Mechanical properties of CNT-nylon composites
Sample Tensile strength Modulus Toughness
(MJ/m3)
Elongation
at break
(%) MPa % Improved GPa % Improved
Nylon 78* - 1.5* - - -
3 84.1 7.83 1.55 3.27 4.05 67.0
5 94.3 20.9 1.87 24.5 2.91 33.0
6 103 32.0 1.99 32.7 2.39 27.1
8 127 62.8 2.46 63.9 2.20 20.0
10 149 91.6 2.77 84.6 1.88 18.0
12 166 113 3.79 153 1.36 11.1
* Values obtained by the manufacturer
It is found that the random alignment of CNT fillers in a nylon matrix can act as imperfections
and consequently lead to lower strain-to-failure values, indicating an increase in brittleness
104
(Muller, Krause, Kretzschmar, & Potschke, 2011; Geneviene, David, & Pascal, 2013);
however, more evidence is required to explain this argument.
4.5 Mechanical property predictions
The reinforcing effect of the fillers in composite materials depends on various filler
parameters such as shape, aspect ratio, modulus, volume fraction, interfacial adhesion, surface
characteristics and orientation (Fornes & Paul, 2003; Anoukou, Zairi, Nait-Abdelaziz, Zaoui,
Messager, & Gloaguen, 2011; Faraz, Besseling, Korobko, & Pichen, 2014). Many factors
could potentially influence the mechanical properties of the final composites where a better
understanding on the effects of each filler property is needed. Several models have been
proposed to describe this reinforcing effect and predict the mechanical properties of reinforced
composites; for example, the models of Halpin-Tsai, and Nielsen, and Mori-Tanaka (Tucker
& Liang, 1999; Gojny, Wichmann, Kopke, Fiedler, & Schulte, 2004; Ramakrishna, Lim, Inai,
& Fujihara, 2006; Li, et al., 2007; Pizzutto, Suave, Bertholdi, Pezzin, Coelho, & Amico, 2011;
Aziz, Rashid, & Salleh, 2013).
The Halpin-Tsai model as a semi-empirical equation has been widely used to
numerically estimate the modulus of various reinforced composite materials. This model
accounts for the constituent properties, concentrations of each constituent, as well as aspect
ratio and orientation of the filler (Ayatollahi, Shadlou, Shokrieh, & Chitsazzadeh, 2011; Faraz,
Besseling, Korobko, & Pichen, 2014). The model assumes a uniform distribution and random
orientation of the reinforcements within the host polymer, and no imperfection in the host
matrix where the filler-matrix interfaces are perfectly bonded (Kanagaraj, Varanda, Zhil'tsova,
Oliveira, & Simoes, 2007; Balakrishnan & Saha, 2011; Shadlou, Ahmadi-Moghadam, &
Taheri, 2014). For unidirectional and discontinuous filler composites, the Halpin-Tsai model
105
predicts the composite modulus in both the longitudinal direction (L) and the transverse
direction (T) using Equation 4.3 to Equation 4.6 as show below:
Ec= Em [3
8(
1+2 L
1-L
)+
5
8(
1+2 T
1-T
)]
Equation 4-3
in which
L
= Ef Em⁄ - 1
Ef Em⁄ + 2
Equation 4-4
T
= Ef Em⁄ - 1
Ef Em⁄ + 2
Equation 4-5
= lf
df
Equation 4-6
where E is the modulus, is the volume fraction of filler, l and d are the length and the average
diameter of the reinforcements. The subscripts c, m and f refer to composite, matrix and filler,
respectively. In Equation 4.6, is a shape parameter depending on filler geometry, orientation
and loading direction (Mohapatra, Mohanty, & Nayak, 2011).
To analyze the capability of the Halpin-Tsai model, the length and diameter of carbon
nanotubes were taken as 1 μm and 13 nm (values obtained from the manufacturer shown in
106
Table 5). The modulus of nanotubes was taken as 1 TPa (1000 GPa) and the modulus of neat
nylon was 1.5 GPa. Volume fractions () of the filler were calculated using the rule of mixture:
= (wf ρ
f⁄ )
(wf ρf
⁄ )+ ((1-wf) ρm
⁄ )
Equation 4-7
where wf is the weight fraction of CNT, f is the density of filler (1.75 g/cm3), and m is the
density of nylon (1.14 g/cm3).
The modulus of the predicted values was compared with the experimental results as
graphically illustrated in Figure 46.
Figure 46 Halpin-Tsai prediction and experimental results of modulus for CNT-nylon
composites at various %loading
A significant difference (90-270%) between the experimental results and the theoretical
predictions can be observed, where the Halpin-Tsai model overestimates the results by a large
0
2
4
6
8
10
0 5 10 15
Mod
ulu
s (G
Pa)
CNT content (wt%)
Experiment
Halpin-Tsai model
107
margin. Moreover, the difference between experimental results and model’s prediction
becomes high at higher filler concentration.
The large discrepancies are expected to be due to the underlying assumptions of the
model, in which uniform distribution of reinforcement and no provision for any imperfection
in the matrix were made. The miscibility between CNT and its matrix of nylon was clearly
detected and discussed in the morphology results of Section 4.1.1, where the homogeneous
dispersion of nanotubes was observed; thus, an assumption of uniform distribution is
applicable. The difference is consequently expected to be due to the imperfection of nanotube
in the polymer composite, since defects play a crucial role in the properties of nano-structure
materials (Charlier, 2002; Blase, & Roche, 2007; Terrones, et al., 2010; Charlier, Dresselhaus,
Jorio, Filho, & Saito, 2010). However, it is difficult to identify accurately and quantitatively
the type of defects. Figure 47 illustrates the possible structure defects of carbon nanotubes used
in this study, showing significant distortions and curvature imperfections.
Figure 47 High magnification TEM micrographs of CNT-C70P representing the defects
within nanotube structure
108
In order to obtain the best fit between the experimental data and the predicted model,
material properties variations were carried out. The parameters Halpin-Tsai include the
modulus of carbon nanotube and pure matrix, the volume fractions of CNT and the aspect ratio
of nanotubes.
At constant aspect ratio of CNT (l/d = 76.9) and modulus of neat nylon (1.5 GPa), the
modulus of the nanotubes was varied to 500, 200, 100, and 50 GPa. The calculated predictions
are presented in Figure 48(a). It can be clearly observed that the predicted modulus becomes
closer to the experimental values as the intrinsic modulus of the carbon nanotube is reduced.
Although carbon nanotubes are expected to have high strength and stiffness (modulus) as a
result of their molecular structure (Popov, 2004; Andrews & Weisenberger, 2004; Mittal,
Dhand, Rhee, Park, & Lee, 2015), the actual value used in fitting the prediction model can be
lower or higher than that obtained from the manufacturer.
Figure 48 Comparison of modulus between the experiment results and the Halpin-Tsai
model at various filler modulus values (Ef)
0
1
2
3
4
5
6
7
0 5 10 15
Mod
ulu
s (G
Pa)
CNT content (wt%)
Experiment Ef = 500
Ef = 200 Ef = 100
Ef = 50
109
Though there was no purification or treatment of nanotubes used in this composite fabrication,
the structural imperfection of the tubes can possibly cause the ability to transfer load applied
within the composite samples (Balakrishnan & Saha, 2011).
Further investigation was to estimate a suitable modulus value of neat nylon since it
theoretically influences the prediction of modulus using the Halpin-Tsai model. The modulus
of the matrix (Em) was varied from 1 to 3 GPa at constant aspect ratio of nanotube (l/d = 76.9)
and modulus (100 GPa). The results were plotted and depicted in Figure 49. A similar trend
with the effect of filler modulus can be obtained.
Figure 49 Comparison of modulus between the experiment result and the Halpin-Tsai
model at various nylon modulus values (Em)
Another parameter affecting the model is the aspect ratio of carbon nanotubes
(Miyagawa, Rich, & Drzal, 2006; Ayatollahi, Shadlou, Shokrieh, & Chitsazzadeh, 2011). The
fixed values of 100GPa and 1 GPa were selected for the modulus of nanotube and nylon,
respectively. The values for the apparent aspect ratio ranges of 50 to 100 were varied, and the
1
2
3
4
5
6
7
0 5 10 15
Mod
ulu
s (G
Pa)
CNT content (wt%)
Experiment Em = 3
Em = 2 Em = 1.5
Em = 1
110
results are shown in Figure 50. It can be noted that a linear increase of modulus with CNT
concentrations is observed where the estimated composite modulus is slightly influenced by
the change in nanotube aspect ratio. The difference becomes less effective (only 1-3.5%) at
l/d value of 80 in the ranges of low CNT loading (3-10 wt%). However, at high nanotube
content of 12 wt%, the predicted values exhibit a large difference of 40%.
Figure 50 Comparison of modulus between the experiment result and the Halpin-Tsai
model at various aspect ratios of CNT (l/d)
In conclusion, the fitting values chosen are 100 GPa, 1 GPa and 80 for filler modulus,
matrix modulus and filler aspect ratio, respectively. Figure 51 shows the comparison of
experimental and predicted values of modulus of CNT-nylon composites with corrective fitting
parameters. It is observed that the modulus of nylon was found to increase with the CNT
concentration. The modified-fitting predictions exhibited close correlation between
experimental and theoretical results up to 10 wt% of CNT reinforcement with the deviation of
less than 3.5%. However, the maximum deviation was found to be 39.7% for 12 wt% of CNT.
1
2
3
4
0 5 10 15
Mod
ulu
s (G
Pa)
CNT content (wt%)
Experiment l/d = 50
l/d = 80 l/d = 100
l/d = 150 l/d = 200
111
Figure 51 Modified-Halpin-Tsai prediction and experimental results of modulus for
CNT-nylon composites at various % loading
1
2
3
4
5
6
7
8
9
0 5 10 15
Mo
du
lus
(GP
a)
CNT content (wt%)
Experiment
Halpin-Tsai
Modified Halpin-Tsai
112
4.6 Thermal stability analysis
Polymer degradation may occur if the materials are exposed to relatively high
temperatures for a long time. Therefore, it is crucial to understand the degradation behavior
and the thermal stability of the composites under accelerated testing at elevated temperatures,
since it is important in determining the reliability of the selected composite materials in
extreme environments. In order to investigate the thermal stability of the CNT-nylon and CB-
nylon composites, TGA measurements were carried out from ambient temperature to 600C
under a flowing nitrogen atmosphere.
The addition of fillers to nylon polymer restricted the mobility and hindered the
molecular rearrangement of the polymer chains. The TGA results for nylon filled with CNT
and CB composites are shown in Figure 52 and Figure 53, respectively. It can be seen that
nylon and its filler composites display single step degradation. Clearly, reinforcing nylon
matrix with carbon nanotubes and carbon blacks can increase the initial decomposition
temperature (onset temperatures, Tonset). The weight loss during the degradation stage up to
100C is attributed to the presence of moisture in the sample surface and to the volatile
substances contained in the resin (Ehrenstein, Riedel, & Trawiel, 2004; Mdarhri, Brosseau,
Zaghrioui, & Aboudi, 2012). As expected, the residual weight of the filled composites is higher
than the neat polymer resin. Additionally, the remaining quantity after degradation of pure
nylon resin at 550C also shows traces amount of chars remaining ( 1 wt%).
113
Figure 52 TGA thermograph of CNT-nylon composites at a heating rate of 20C/min
under nitrogen flow; inset is a close-up look
The initial decomposition temperature (Tonset) of neat nylon was measured to be
419C. Obviously the onset temperatures of reinforced composites raised and shifted to a
higher value as the filler loading increases. This enhancement is due to the synergistic effect
of the high thermal conductivity of the fillers resulting in a greater flow of heat throughout the
sample (Teh, Mariatti, Wagiman, & Beh, 2008; Kong, Mariatti, Rashid, & Busfield, 2012).
The filler aggregates act as a barrier that prevents the degradation diffusion from the bulky
polymer into the gas phase. In addition, the entrapment of the polymer delays the thermal
degradation process, reducing the mobility of the polymer around the fillers and improving the
thermal stability of the composites.
0
10
20
30
40
50
60
70
80
90
100
0 100 200 300 400 500 600
Wei
gh
t (%
)
Temperature (C)
Nylon 3 wt% 5 wt% 6 wt% 8 wt% 10 wt% 12 wt%
30
40
50
60
70
420 440 460 480 500
114
Figure 53 TGA thermograph of CB-nylon composites at a heating rate of 20C/min under
nitrogen flow; inset is a close-up look
As listed in Table 14 and Table 15, Tonset for 12 wt% CNT-nylon composite was
443C (24C greater than pure nylon resin); while Tonset for 15 wt% CB-nylon composite was
435C (16C greater than pure nylon resin). Differences in the thermal stability between CNT-
nylon and CB-nylon composites (8C different) were attributed to the differences in dimension
and aspect ratio of the fillers. This could be due to the higher thermal conductivity of CNTs
that facilitates heat dissipation within the matrix which prevents the local accumulation of heat.
Aspect ratio plays an important role in determining both thermal stability and conductivity of
the composites. It has been reported that fillers with higher aspect ratio can form bridges among
the neighboring particles and create conductive networks. This causes the conductive network
to facilitate phonon and electron transfer, which leads to high thermal stability and conductivity
of the reinforced composites (Norkhairunnisa, Azizan, Mariatti, Ismail, & Sim, 2011).
0
10
20
30
40
50
60
70
80
90
100
0 100 200 300 400 500 600
Wei
gh
t (%
)
Temperature (C)
Nylon 15 wt% 20 wt% 30 wt% 35 wt%
40
50
60
70
420 430 440 450 460 470 480
115
Table 14 Thermal stability of CNT-nylon composites as a function of CNT concentration
Loading
(%)
Tonset
(°C)
Weight at Tonset
(%) Tonset
(°C)
0 419 99.5 -
3 435 99.8 16
5 439 99.5 20
6 440 99.8 21
8 441 99.8 22
10 441 99.8 22
12 443 99.8 24
Table 15 Thermal stability of CB-nylon composites as a function of CB concentration
Loading
(%)
Tonset
(°C)
Weight at Tonset
(%) Tonset
(°C)
0 419 99.5 -
15 435 99.8 16
20 430 99.8 11
30 432 99.8 13
35 431 99.8 12
116
Chapter 5 Prediction of power law model from PDMS reinforced with carbon
nanofiber polymer composites
Materials play key role in every field of technology, such as medical, sensors, and
computing, to make a living more comfortable. There is always a critical need to use new
materials with improved properties; however, understanding the relationship between
structures and the properties of existing materials are essential. The properties enhancement
can be tailored by combining two or more materials according to the requirements (Rahman,
Ali, Zahrani, & Eleithy, 2011).
In Chapter 4, the relationship between the electrical properties and the composite
systems of thermoplastic filled with CNT and CB are well described by the power law
equation. This chapter presents the validation of that numerical model in a different composite
system where an elastomeric polymer matrix filled with carbon nanofiber are applied. The
excellent properties from the nanofiber filler provides an excellent source of composite
materials for various engineering applications.
Polydimethyl-siloxane (PDMS) is by far one of the most important elastomeric
polymers that has been receiving considerable attention due to its unique properties, such as
high transparency, gas permeability, good electric insulation, low surface free energy,
excellent weather resistance and low toxicity (Chaudhry & Billingham, 2001; Mark, 2004; Xu,
Pang, Zhu, Zhang, & Feng, 2010; Park, Sim, Jeoung M.G., Seo, & Kim, 2013). Although pure
PDMS has good thermal stability, it still has poor mechanical properties due to an inherent
weak interaction between PDMS chains and is not able to meet the practical requirement
during application. In order to improve the overall performance of PDMS composites, a variety
117
of reinforcing fillers has been introduced into PDMS matrix by different means (Chen D. , et
al., 2015). There are several challenges to obtain good polymer composites using various
fillers; such as achieving uniform dispersion in the polymer matrix and good adhesion at the
polymer-filler interface. Several methods have been used to improve dispersion of fillers
within solutions or polymer matrices; including sonication, modification of composite
processing methods, and functionalization of filler surface (Rizvi, Cochrane, Biddiss, &
Naguib, 2011).
5.1 Morphology analysis
Generally, morphology and distribution of the loading particles in polymeric matrices
have an important effect on the overall property improvement of PDMS composites. Scanning
electron microscopy was used to investigate the surface morphology of the tensile fractured
surface and the distribution of carbon nanofibers in a PDMS matrix. Analysis of the
morphology of these CNF-PDMS sheets provides valuable information on their interaction
within the polymer and help in better understanding of enhancement in mechanical properties.
Figure 54 shows the SEM micrographs of CNF-PDMS composites at various filler loadings.
The microscopic images reveal uniform and homogeneous dispersions of carbon nanofibers
within the PDMS matrix, where individual nanofibers can be seen. This observation is possibly
due to the fiber length, which is in the order of a micrometer of carbon nanofiber. The
appearance of theses individual carbon nanofibers throughout the sample qualitatively exhibits
the formation of continuous percolative paths in the composite samples. The images were
observed at several regions along the specimen and no major air voids existed within the
specimen. It can be noted that numerous filler particles were embedded in the PDMS matrix,
where a good interface adhesion between PDMS resin and nanofibers was achieved.
118
At low filler content in Figure 54(b) and Figure 54(c), no obvious signs of fiber
agglomeration or preferential orientation were visibly noticed. It is quite conceivable that more
contact points took place between the nanofibers as CNF content increased, where the
nanofibers could have become closer to each other. Few clusters of carbon nanofibers were
detected at higher loading as presented in Figure 54(d) and the sizes of filler aggregations in
PDMS matrix became large, as shown in Figure 54(f). However, it has been suggested that the
formation of a conductive network does not necessarily need a very good distribution and
dispersion (Du, Fischer, & Winey, 2005). Hence, the occurrence of slight aggregations and
also improper distribution at high CNF loadings could have diminished the space between the
nanofibers or created direct contact between them and led to more conductivity (Kabir, Saha,
& Jeelani, 2007). Another interesting observation can be drawn from these SEM images; as
the filler loading increased, the distance between carbon nanofiber particles seemed to shorten
and the space between nanofibers became narrow. This likely implied that the strong
interaction between PDMS matrix and carbon nanofibers had been reached.
119
(a) (b)
(c) (d)
(e) (f)
Figure 54 Tensile fractured surfaces of the CNF-PDMS composites under SEM at various
loadings(a) blank PDMS, (b) 1 wt%, (c) 2 wt%, (d) 3 wt%, (e) 4 wt% and (f) 5
wt%
120
5.2 Prediction of power law model and electrical resistivity
Because this work was done under the collaboration with another project, a
preliminary experiment was conducted to evaluate and relate the effect of filler geometry in a
different type of polymer. The variation of different filler dimension but same one-dimensional
shape was expected to be small. As depicted in Figure 27(b) and Figure 30(c), the filler shapes
of CNTs and CNFs are similar; however, CNFs are almost 10 times larger than CNTs in
diameter. Therefore, the dispersion of CNFs in polymer matrix can be expected to be easier.
The initial experiments of PDMS composites filled with CNTs and CNFs were carried
out at 2 and 5 wt%. Sample preparation followed the steps described in Section 3.2.2, and the
resistivity results are shown in Figure 55. It can be seen that these two PDMS systems act
similarly with slightly effect from the different of filler dimension and size.
Figure 55 Resistivity results of PDMS composites filled with CNTs and CNFs at 2 and 5
wt%
0
0.5
1
1.5
2
2.5
2 3 5
log r
esis
tivit
y (
-c
m)
Filler content (wt%)
CNF-PDMS
CNT-PDMS
121
The linear resistor circuit was applied once again to calculate the numbers of filler
particles across the thickness distance in the four-point probe measurement (a thickness of
PDMS sheet is 2 mm). The calculation below shows that less CNF particles is required to fulfill
the percolating path at a given distance due to the fact that CNF particles are bigger than CNTs.
For CNT:
2 cm (test distance)
1 μm cos45(length 1 CNT particle⁄ ) = 7092 CNT particles
For CNF:
2 cm (test distance)
30 μm cos45(length 1 CNF particle⁄ ) = 472 CNF particles
Based on literature search in Section 2.3.1; however, the inherent resistivity of CNF was found
to be 10 times less than that of CNT (10-4 -cm for CNT and 10-3 -cm for CNF). Thus, it can
be said that CNF is 10 times more resistive than CNT, but there is 1/10th the numbers of their
particles presented to create the conducting network. With the advantage of a simple linear
mathematical model presented in Equation 2-4, the composite resistivity (Rcomposite) can be
estimated to be relatively closed values between CNF-PDMS and CNT-PDMS systems. This
finding reveals that CNF and CNT exhibit similar conducting network within PDMS matrix.
Therefore, incorporating the percolation parameter (the dimensionality-t value of 3.18) from
CNT-nylon system is expected to be an effective tool to predict the percolation threshold for
CNF-PDMS system. With the information of resistivity at 2 and 5 wt% CNF filled with PDMS
as well as the application of power law model, the percolation concentration of CNF-PDMS
composite was calculated to be 0.9 wt%.
122
Next, the experiments of 1 to 5 wt% CNF loading were extended. The behavior of a
classical percolating system for PDMS composites is shown in Figure 56. The figure clearly
shows that a low conducting region with resistivity on the order of that of the insulating matrix
is well separated from a high-conducting region with resistivity close to that of the composites.
In this case, the resistivity is strongly dependent on carbon nanofiber content. In general, the
percolation threshold is characterized by a sharp decrease in the electrical resistivity. This
major drop in resistivity can be attributed to the formation of a continuous pathway which
allows charges to travel a macroscopic distance through the polymer composites.
Figure 56 Electrical resistivity of CNF-PDMS composites as a function of CNF loadings.
The resistivity of pure PDMS is approximately 1014 -cm (as obtained from the
manufacturer); adding 1 wt% CNF can effectively decreased the resistivity of the composites
by 10 orders of magnitude. This can be regarded as the formation of the percolative paths of
the conducting network throughout the polymer matrix (Sandler, Kirk, Kinlorch, Shaffer, &
0
5
10
15
0 1 2 3 4 5
log re
sist
ivit
y (
-c
m)
CNF content (wt%)
123
Windle, 2003; Kim, Pfeifer, Park, & Bandaru, 2011; da Silva, Kanda, & Nagashima, 2012;
Chu, Kim, Sohn, & Lee, 2013). Upon further increase of the CNF content, a levelling off was
observed and the electrical resistivity only showed a slight decrease at 2 to 5 wt%. This small
decrease in resistivity after the percolation concentration may be attributed to the better contact
between the continuous electrical paths, since a small potential barrier allows charge
conduction (Balberg, 2001; Da Silva, Kanda, & Nagashima, 2012).
Regarding to the literature review, different researchers have looked into the
percolation behavior of different composite systems. This study compares the experimental
percolation values with the prediction of power law model based on a completely different
system. The fitting parameters are evaluated in order to understand the electrical behavior. The
critical concentrations and exponents of the CNF-PDMS composites are determined by linear
fitting of log-log plots from the power law equation; a result is illustrated in Figure 57.
Figure 57 Plot of log-log resistivity as a function of (–c) with a linear fit for CNF-PDMS
composites
y = -2.86x + 2.72
R² = 0.998
0
1
2
3
4
5
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
log r
esis
tivit
y
log (-c)
124
The experimental values of c and t for composites are 0.83 wt% and 2.86,
respectively. It can be seen that the percolation threshold from the predicted calculation and
the experiment are very close (0.90 and 0.83 wt% from model and experiment, respectively).
The critical exponent t generally reflects the dimensionality of the system, with a theoretical
value between 1.5 and 2.0 for three-dimension networks (Andrade Jr., Auto, Kobayashi,
Shibusa, & Shirane, 1998; Bauhofer & Kovacs, 2009; Kassim, Achour, Costa, & Lahjomri,
2014); however, there is a slight different between the critical exponent values of 3.18 and 2.86
from model and experiment, respectively. It can be pointed out that the exponents differ
according to the different of resistivity measurements between 2-point and 4-point method.
In addition, the critical exponent t found in this research slightly exceeds the universal
value. According to the model described by Balberg (Balberg, 1987), a random distribution of
fillers in an insulating medium presumably corresponded to the resistor networks that exhibit
diverging distribution of the high resistance values where a large range of tunneling is observed
(McLachlan, Chiteme, Heiss, & Wu, 2003). Several mathematical models can be used to
describe the DC electrical conductivity of the composites but frequently do not fit accurately
the experimental data. This is due to the fact that they must contain several factors which affect
the electrical conductivity of the composite systems, such as the shape and size of the particles
inclusions, and the interaction between the filler and the host matrix. In principle, percolation
theory assumes that the conductive particles contact directly in conductive networks and there
is no contact resistance among conductors (Liang, Ling, Lu, & Liu, 2000), where the resistivity
of composites is mainly determined by the resistivity of conductive fillers. However, it has
been found that the electrical conduction in polymer composites occurs by electron hopping
between adjacent conductors and the conductive paths are formed through the composites.
125
These conduction networks are hypothesized to be the results of quantum tunneling effects
where the distance between neighboring conductive particles is sufficient for the electron
hopping to occur (Ounaies, Park, Wise, Siochi, & Harison, 2003; Balberg, Azulay, Toker, &
Millo, 2004; Foygel, Morris, Anez, French, & Sobolev, 2005; Rahman & Servati, 2012; Bao,
Meguid, Zhu, & Weng, 2012). In quantum tunneling, there is an evidence of existing contact
resistance within the conductive path, where electron conduction occurs between two fibers
through the inter-tube gap and also through the fibers themselves. Thus, the tunneling effects
and the contact resistance could be the main reasons that increased the fitting values since the
nanofibers do not physically form a contacted network.
In summary, the resistivity prediction by power law model is validated to explain the
conduction mechanism for a different perspective. Knowledge of the percolation study
essentially helps in designing a composite material. The prediction relationship can be
expressed as shown in Equation 5.1 and Figure 58. This is in good agreement with the
experimental results for CNF-PDMS composites for filler contents above the percolation
threshold.
For CNF-PDMS composites, ρ = 531.2(- 0.83)-2.86 Equation 5-1
126
Figure 58 Electrical resistivity modeling results of CNF-PDMS composites
5.2.1 Influence of filler types on composite resistivity
Electrically conductive polymer composites containing carbon fillers have recently
received considerable attention because of their high conductivity, low weight loss, and ease
of processing (Zhang, Dehghani-Sanij, & Blackburn, 2007; Battisti, Skordos, & Partridge,
2010). Four different commercially available carbon-based materials were studied with regard
to their dispersibility. The electrical resistivity of PDMS composites containing CNT-C70P,
CNT-C150P, CNF, and CB under similar sonication conditions was investigated to
comprehend the effect of filler structures. The electrical volume resistivity at fixed filler
concentrations (3 and 15 wt%) are shown in Figure 59, showing 41.3, 70.1, and 53.4 -cm for
C70P, C150P, and CNF composites, respectively. However, the electrical resistivity of PDMS-
CB was over the measurable limit of the instrument, even when a very high loading of 15 wt%
was introduced.
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6
log
re
sist
ivit
y (
-c
m)
CNF content (wt%)
CNF-PDMS
Power law-CNF
127
These results point out that carbon-based materials can exhibit strong variations in
their electrical properties depending on the dispersibility of fillers (Figure 60) within the same
matrix material.
Figure 59 Volume resistivity of PDMS composites filled with 3 wt% CNTs, 3 wt% CNF
and 15 wt% CB
The use of C70P carbon nanotubes with their high aspect ratio as well as their lower
agglomeration leads to a lower value of electrical resistivity than that of the bulkier C150P
carbon nanotubes and the stacked-cup carbon nanofibers particles. Technologically, building
a conductive network within an insulation matrix does not necessary require well distributed
filler but it needs well dispersed fillers or homogeneous arrangement of fillers in the polymer
composites (Reza, 2014). This expectation is given by the reduced number of electron filler-
filler hops required to cross a given distance. Generally, the conductive fillers should be located
of 5-10 nm apart in order to allow the electric charges to circulate or tunnel. It has also been
reported that the conductive tunneling behavior is the most effective contribution of CNTs in
polymer composites when compared with spherical fillers or sub-micrometer fibers (Andrews
0
20
40
60
80
100
CNT C70P CNT C150P CNF CB
Volu
me
resi
stiv
ity (
-c
m)
> 106
-cm
128
& Weisenberger, 2004; Du, Scogna, Zhou, Brand, Fischer, & Winey, 2004; Zhang, Rastogi,
Chen, Lippits, & Lemstra, 2006; Seung, Jong, Sheong, Seoung, Kyeong, & Jae, 2009).
129
(a)
(b)
(c)
Figure 60 SEM images of PDMS composites filled with various carbon fillers at 3 wt%
via sonication method (a) CNT-C70P, (b) CNT-C150P, and (c) CNF
0.5 m
5 m
1 m5 m
5 m1 m
130
When CB was added into PDMS matrix under the same processing manner the
electrical resistivity could not be measured (out of 100 M range) even at the high loading of
up to 15 wt%. Figure 61(a) illustrates the fractured surface of PDMS filled with 15 wt% CB.
(a)
(b)
Figure 61 (a) SEM images of PDMS composites filled with 15 wt% CB and (b) images of
uncured PDMS composites filled with 20 wt% CB
It can be noticed that CB particles are separated from each other and tend to pack together to
form large agglomerates. This fact is one of the reasons that electrical resistivity was out of the
5 m1 m
131
detectable range because CB clusters do not contact each other and a conducting network is
not formed. Therefore, higher amounts of CB particles are required to produce a neighboring
conductive particles effect; for example, nearly 40 wt% of CB was needed to create the
conductive paths that reduced the resistivity of SBR (Styrene Butadiene Rubber) filled with
carbon black composites (Wan, Xiong, Yu, & Wen, 2005). In addition, at higher loading of
carbon black, it was observed that the curing had not occurred, as can be seen in Figure 61(b).
5.2.2 Influence of mixing conditions on composite resistivity
The mixing method is one of the most effective factors influencing the dispersion and
distribution of fillers in the polymer matrix. It is expected that uniform dispersion of fillers
within the polymer matrix results in the best electrical properties. Figure 62 compares the
electrical resistivity of PDMS-CNT C70P composites by two different solution mixing
methods; mechanical stirring and sonication.
Figure 62 Volume resistivity of PDMS-CNT composites at various fabrication conditions
0
10
20
30
40
50
60
70
80
Volu
me
resi
stiv
ity (
-c
m)
C70P 3 wt%
Stirring
C70P 5 wt%
Stirring
C70P 3 wt%
Sonication
132
These mixing methods are commonly used in the lab with easy operation and cleaning. It is
obvious that the sonication process provides lower electrical resistivity than the stirring method
even when the CNT content is raised to almost double.
The decrease in electrical resistivity via sonication method may be attributed to
having smaller aggregates and better dispersion of CNTs as further illustrated by the SEM
analysis under tensile fractured samples in Figure 63. The process condition of mechanical
stirring showed a lot of tightly entangled CNTs, which are observed as the bright dots
throughout PDMS matrix. These dots are ascribed to the ends of the broken CNTs owing to
their high conductivity. The micrographs reveal that mechanical stirring caused clumping of
the CNT content. There isolated CNT-rich regions along with a dominant matrix that would
be largely un-reinforced or resin-rich. Since CNTs are much entangled and bundled together
due to their strong attractive forces originating from entanglements and high van der Waals
interaction, the use of higher shear forces is required in order to break up their entanglements
during the mixing process (Liu F. , Sun, Sun, & Yeow, 2014). The sonication method
significantly exhibits uniform dispersion of CNTs in the whole PDMS matrix without
significant agglomeration, Figure 63(c).
133
(a) (b)
(c)
Figure 63 SEM images of PDMS composites filled with (a) 3 wt% of CNT-C70P via
mechanical stirring method, (b) 5 wt% of CNT-C70P via mechanical stirring
method and (c) 3 wt% of CNT-70P via sonication method
5 m 5 m
5 m
134
5.3 Mechanical properties
The mechanical properties and the performance of composites largely depend on the
inherent property of the filler added, the polymer used, and the interfacial interaction between
the polymer and the filler. However, there are many challenges to achieving improvements in
mechanical properties. The requirement for a good composite is good filler dispersion,
alignment and interfacial load transfer. Dispersion of the filler is a critical issue in achieving
uniform force distribution. A good interface with adhesion between the filler and the matrix is
also important for efficient load transfer.
The tensile properties of neat and filled PDMS composites were determined and the
stress-strain curves of CNF-PDMS composites in the range of 0-5 wt% loading are plotted in
Figure 64. The plot exhibits typical two-region stress-strain curves. The first region is more
linear with a smaller slope in which a small stress applied would produce a large strain or
deformation, causing a rubber or elastomer behavior of the composites. The second region is
reached after the deformation at a certain value (80-90% strain). Beyond this point, larger
stress is required to produce the same amount of strain or elongation. The increased force
required for deformation is due to the slipping of polymer chains, which absorbs some of the
mechanical work applied. Therefore, the composites in the second region behave harder than
in the first region; this is typically referred to as the work hardening effect (Liu, Sun, & Chen,
2009). Continuously increasing the force applied will reach the maximum stress that the
specimens can support without breaking. The maximum stress is defined as the tensile strength
and the maximum strain is called the elongation at break.
135
Figure 64 Stress-Strain curve of CNF-PDMS composites
The influence of CNF loading on the mechanical performance of PDMS composites
is illustrated in Figure 65 and summarized in Table 16. Significant improvement of CNF-
PDMS composites over neat PDMS is clearly demonstrated in the results of tensile strength,
modulus, overall toughness, and elongation at break. Due to the proposed application of these
CNF-PDMS composites as piezoresistive sensors, it is unlikely that strains greater than 30%
will be seen. Thus, the modulus values obtained in this study were calculated within the range
of 30% strain. Clearly, there is reinforcement as evidenced by considerable improvements in
tensile strength and modulus of the composites with the CNF loading. With the addition of 1
wt% of CNF, 8 % increase in tensile strength and a 22 % increase in the modulus are achieved.
Increase in the tensile strength indicates that CNFs are acting as reinforcement in the polymer
matrix by transferring load from the polymer to the fillers (Lee & Khang, 2012). Addition of
CNF leads to an increase in the modulus of the composites.
0
1
2
3
4
5
6
7
8
9
0 50 100 150 200
Str
ess
(MP
a)
Strain (%)
PDMS
PY1%
PY2%
PY3%
PY4%
PY5%
136
Figure 65 Mechanical properties of CNF-PDMS composites at various % loading
The area under the stress-strain curve can be used to obtain the value of absorption
energy before the fracture occurs. This is referred to as the materials’ toughness which, is
defined as the total energy needed to break the specimen. Toughness depends on both the
maximum stress attained and the strain at which the composite breaks. It can be seen in Figure
64 that as the CNF content increased from 1 wt% to 5 wt%, the areas under the stress-strain
curves increased. This suggests that the toughness of the composites increased moderately
owing to the addition of CNFs. In composite materials, the addition of CNFs increases the
stiffness and strength but affects the flexibility and thus reduces the toughness of the materials.
0
2
4
6
8
10
0 1 2 3 4 5 6
Str
ess
(MP
a)
CNF loading (wt%)
(a) Tensile strength
0
0.5
1
1.5
2
2.5
0 1 2 3 4 5 6
Str
ess
(MP
a)
CNF loading (wt%)
(b) Modulus
0
100
200
300
400
500
0 1 2 3 4 5 6
Tou
gh
nes
s (k
J/m
3)
CNF loading (wt%)
(c) Toughness
0
50
100
150
200
250
0 1 2 3 4 5 6
Str
ain
(%
)
CNF loading (wt%)
(d) Elongation at break
137
Table 16 Mechanical properties of PDMS composites filled with various wt% of CNF
Sample
Tensile strength Modulus Toughness Elongation
at break
(%) MPa %
Improved MPa
%
Improved kJ/m3
%
Improved
0 5.61 - 0.90 - 312 - 184
1 6.04 7.71 1.10 22.2 331 6.08 183
2 6.64 18.4 1.30 44.4 372 19.1 183
3 6.70 19.4 1.40 55.6 378 21.1 180
4 6.93 23.5 1.60 77.8 395 26.7 178
5 7.74 37.9 1.90 111.1 450 44.1 176
5.3.1 Influence of filler types on mechanical properties
In order to explain the effect of filler types on the mechanical properties, the
mechanisms contributing to these properties were studied. One of the main properties that
ensure proper functionality of the composites is the load transfer. The interfacial strength
between conductive fillers and the polymer matrix is of crucial importance, since the
reinforcement strongly depends on the load transfer from matrix to filler. Figure 66 and Table
17 summarize the mechanical properties of three different fillers (CNF, CNT-C70P, and CNT-
C150P) at 3 wt% loading under the same processing conditions described in Section 3.2.2.
Clearly, CNT-C70P demonstrates the highest tensile strength and modulus among the
three. This can be due to a stronger interface bonding between the filler and the matrix, which
leads to better load transfer, as well as to uniform dispersion of CNT-C70P, which supports
this enhancement in mechanical properties. Moreover, it has been reported that cylindrical
particles with smaller diameter build stronger interfacial interactions with the polymer matrix
(Manoharan, Sharma, Desai, Haque, Bakis, & Wang, 2009; Ayatollahi, Shadlou, Shokrieh, &
Chitsazzadeh, 2011).
138
Figure 66 Mechanical properties of PDMS composites filled with various fillers
Table 17 Mechanical properties of PDMS composites filled with 3 wt% of various fillers
Sample UTS
(MPa)
%
Improved
Max.
Strain
(%)
%
Decreased
Modulus
(MPa)
%
Improved
PDMS 5.62 - 184 - 0.9 -
CNF 6.70 19.3 180 2.16 1.4 55.6
C70P 8.10 44.2 169 8.15 2.1 133
C150P 6.65 18.4 163 11.4 1.7 88.9
This is also in good agreement with the TEM images in Figure 67. Obviously, CNT-
C70P has the smallest diameter compared to CNT-C150P and CNF particles; therefore, higher
0
2
4
6
8
10
PDMS
blank
CNF C70P C150P
Str
ess
(MP
a)
(a) Tensile strength
0
1
2
3
PDMS
blank
CNF C70P C150P
Str
ess
(MP
a)
(b) Modulus
0
50
100
150
200
250
PDMS
blank
CNF C70P C150P
Str
ain
(%
)
(c) Elongation at break
139
tensile strength, modulus, and toughness in the composites reinforced with CNT-C70P could
be reached.
(a) (b) (c)
Figure 67 Images of (a) CNT-C70P (TEM), (b) CNT-C150P (SEM), and (c) CNF (TEM)
The decrease of elongation at break in PDMS composites filled with CNT-C70P is
more pronounced. This might be attributed to the ductile to brittle transition of the composites
when the aspect ratio of fillers increases. A higher number of CNT-C70P particles in the
composites can effectively reduce mobility of the polymer chains, which leads to more brittle
behavior. However, more evidence is needed to confirm this argument since the aspect ratio
of CNT-C70P is the lowest among the fillers studied here.
5.3.2 Influence of mixing conditions
It is well known that good dispersion and good interfacial adhesion are the basic
requirements for matrix reinforcement in a composite. According to the morphology results, a
high sonication power is more efficient at dispersing CNTs than mechanical stirring; however,
the tensile strength and modulus showed the opposite effect. For the well dispersed and
homogeneously distributed fillers via the sonication method, the measured mechanical
140
properties of the composites are lower than those of the composites prepared by the stirring
method. The results are revealed in Figure 68 and Table 18.
Figure 68 Mechanical properties of CNF-PDMS composites using sonication and stirring
fabrication method
The stirring method showed improvement of 68.3% and 166.7% of tensile strength
and modulus over the neat PDMS. Generally, it would be imagined that conductive fillers have
to be well dispersed in the polymer matrix to achieve the desired properties. Thus, much effort
is usually spent in sample preparation to disintegrate the initial agglomerates in which most of
the fillers are produced.
0
2
4
6
8
10
12
PDMS blank 3%, sonic. 3%, stir.
Str
ess
(MP
a)
(a ) Tensile strength
0
1
2
3
PDMS blank 3%, sonic. 3%, stir.
Str
ess
(MP
a)
(b) Modulus
0
50
100
150
200
250
PDMS blank 3%, sonic. 3%, stir.
Str
ain
(%
)
(c) Elongation at break
141
Table 18 Mechanical properties of PDMS composites filled with 3 wt% CNF by using
sonication and stirring method
Sample
Tensile
strength
(MPa)
%
Improved
Elongation
at break
(%)
%
Improved
Modulus
(MPa)
%
Improved
PDMS
blank 5.61 - 184 - 0.9 -
CNF 3%,
sonication 8.10 44.2 169 8.15 2.1 133
CNF 3%,
stirring 9.45 68.3 178 3.28 2.4 167
5.3.3 Mechanical properties prediction
The elastic modulus of a reinforced composite can be predicted by the Halpin-Tsai
equations. The modulus of CNF-PDMS composites are evaluated in the same manner as
described in Section 4.5.
The length and diameter of carbon nanofibers were fixed at 30 μm and 60 nm. The
modulus of nanofibers was taken as 250 GPa and the modulus of pure PDMS was 1 MPa
(0.001 GPa). In Figure 69, a large difference (170-840 %) between the experimental results
and the theoretical predictions can be observed, where the model overestimates the results by
a large margin. This large margin prediction by Halpin-Tsai model has been observed in many
studies (Pizzutto, et al., 2011; Mohapatra, Mohanty, & Nayak, 2011; Shadlou, Ahmadi-
Moghadam, & Taheri, 2014; Arun & Kanagaraj, 2015).
142
Figure 69 Halpin-Tsai prediction and experimental results of modulus for CNF-PDMS
composites at various % loading
The large deviation can be expected to be due to the assumptions of the model, in
which uniform distribution and perfect bonding between filler and matrix were made
(Kanagaraj, Varanda, Zhil'tsova, Oliveira, & Simoes, 2007; Montazeri, Javadpour, Khavandi,
Tcharkhtchi, & Mohajeri, 2010; Shokrieh, Mosalmani, & Omidi, 2014). The dispersion of
CNFs within a PDMS matrix was discussed in the morphology results of Section 5.1, where
good distribution with few clusters of nanofibers was observed. The agglomerates of carbon
nanofiber may cause the interaction between the filler and matrix to be less effective (Zhang,
Tan, Wang, Tan, & Li, 2014). Moreover, Figure 70 reveals imperfections of nanofibers used
in this research, where defects and broken edges of CNFs exist. These imperfections may cause
randomness of nanofiber in the composites, resulting in less arranged distribution of fibers
(Afrooz, Ochsner, & Rahmandoust, 2012; King, Klimek, Miskioglu, & Odegard, 2015).
0
2
4
6
8
10
12
0 1 2 3 4 5
Mod
ulu
s (M
Pa)
CNF content (wt%)
Experiment
H-T
143
Figure 70 High magnification TEM micrographs of CNF (representing the defects within
nanotube structure)
Since the modulus of pure PDMS obtained from experiment and supplier are slightly
different, this value was fixed at 1 MPa as received from the experiment. The filler’s modulus
and aspect ratio were further considered in order to analyze their effects on the prediction.
At the fixed values of aspect ratio of CNF (l/d = 500) and the modulus at PDMS (1
MPa), the modulus of nanofiber was varied at 250, 100, 50, 10, 1 and 0.1 GPa. The predictions
are presented in Figure 71(a). It can be seen that the predicted modulus becomes closer to the
experimental values as the intrinsic modulus of carbon nanofiber decreases. As per the
dimension of CNF, the maximum and minimum aspect ratio was calculated to be 500 and 700,
respectively. Figure 71(b) shows the effect of aspect ratio on the composites’ modulus as a
function of nanofiber content. It can be observed that the reduction of aspect ratio slightly
influences the predicted values of composites’ modulus, in which the deviation between
experimental and modeling values are in good agreement.
144
(a) (b)
Figure 71 Comparison of modulus of CNF-PDMS composites between the experiment
and the Halpin-Tsai model at (a) various filler’s modulus values (Ef), and (b)
various filler’s aspect ratio values (l/d)
The fitting values were calculated and chosen as 0.1 GPa, 0.001 GPa (1 MPa) and 500
for filler’s modulus, matrix’s modulus and filler’s aspect ratio, respectively. Figure 72 shows
the comparison of experimental and predicted values of modulus of CNF-PDMS composites
with corrective fitting parameters. One important finding from this modeling is that the only
factor that effectively influences the composites’ modulus is the intrinsic modulus of carbon
nanofiber. However, with fixing numbers, the modified prediction exhibited close agreement
between experimental and theoretical results, with a deviation of less than 8%.
0
2
4
6
8
10
12
0 1 2 3 4 5
Mo
du
lus
(MP
a)
CNF content (wt%)
Experiment Ef = 250
Ef = 100 Ef = 50
Ef = 10 Ef = 1
Ef = 0.1
1
1.5
2
2.5
0 1 2 3 4 5
Mo
du
lus
(MP
a)
CNF content (wt%)
Experiment l/d = 500
l/d = 600 l/d = 700
145
Figure 72 Modified Halpin-Tsai prediction and experimental results of modulus for
CNF-PDMS composites at various % loading
5.4 Thermal degradation behavior
The superior thermal stability of silicone elastomers has made them attractive
candidates for use at elevated temperatures. Because of its excellent thermal stability, PDMS
has been consider for application as adhesives for high temperature service, packing for
chromatographic columns, and lubricants (Deshpande & Rezac, 2002). To succeed in these
high temperature applications, the thermal degradation of the composite materials must be
understood.
The addition of filler to silicone rubber restricted the mobility of the siloxane chains
and hindered the molecular rearrangement of the PDMS chain. TGA results for the composites
filled with 1, 3 and 5 wt% CNFs are shown in Figure 73. The tests were conducted, at the same
procedure as described in Section 3.3.6 for nylon composites, under nitrogen condition at a
constant heating rate of 10C/min.
0
2
4
6
8
10
12
0 1 2 3 4 5
Mod
ulu
s (M
Pa)
CNF content (wt%)
Experiment H-T Modified H-T
146
A single weight loss step apparently obtained since the PDMS samples were tested in
an inert atmosphere. The weight loss during the initial decomposition stage was attributed to
the presence of moisture on the sample surface and to the volatile substances contained in the
PDMS resin (Kong, Mariatti, Rashid, & Busfield, 2012). The remaining residue after
decomposition of silicone rubber at 800C was due to the traces of silica in the PDMS matrix
(Camino, Lomakin, & Lageard, 2002; Lewicki, Liggat, & Patel, 2009). It can be noted in
Figure 73 that an apparent weight loss appears between 450 and 700 C.
The initial decomposition temperature (Tonset) of pure PDMS was observed at 495C
with 4.5 % weight loss. Incorporation of carbon nanofiber obviously increased the onset
temperature where the decomposition temperature shifted to higher values. The presence of
only 1 wt% of carbon nanofiber effectively enhanced the thermal stability of PDMS
composites, in which the Tonset was shifted 10C higher than the unmodified PDMS matrix.
The increase of decomposition temperature (from 10C to 30C higher than the original PDMS
matrix) with addition of carbon nanofibers is more pronounced at higher filler concentration,
as presented in Table 19.
147
Figure 73 TGA thermograph of CNF-PDMS composites at a heating rate of 10C/min
under nitrogen flow
The temperature at 20% weight loss (T20%) can be used to describe the quantitative
difference among the composite materials. The addition of CNF in PDMS matrix visibly
improved the thermal stability of composites, as shown in Table 19. The T20% of PDMS filled
with 1 wt% CNF increases 8.5C compared to pure PDMS. It increases continuously with the
increasing of CNF loading and reaches 15C when CNF loading is 5 wt%. In addition, the
residue at 800C of the PDMS composites was evaluated and presented in Table 19.
The weight loss is the result of polymer thermal decomposition, mainly caused by the
breakdown of the main chains in PDMS matrix and the generation of volatile decomposition
products (Yang, et al., 2005; Kashiwagi, et al., 2005; Zhao, Zhang, Wu, & Bai, 2016). The
dispersed CNF particles and their interconnected networks act as barriers that can hinder the
30
40
50
60
70
80
90
100
0 100 200 300 400 500 600 700 800
Wei
gh
t (%
)
Temperature (C)
PDMS
CNF 1%
CNF 3%
CNF 5%
148
movement of polymer chains and reduce the movement rate of those volatile decomposition
products. Since carbon nanofibers do not decompose under inert condition, so the weight loss
comes only from PDMS decomposition. The formation of nanofiber networks in a PDMS
matrix can effectively prevent the movement capability of polymer chains and volatile
decomposition products and decrease the rate of thermal decomposition of composites (Chen
D. , et al., 2015).
This effect is further enhanced with the addition of CNFs, which results in
improvement of the composite thermal stability. When CNF content increases, the distance
between nanofiber particles becomes shorten and a CNF network is formed gradually, as
shown in Figure 54. The CNF network relatively increases the difficulty of movement of
polymer chains and volatile decomposition products, so it decreases the rate of thermal
decomposition of composites (Yang J. , et al., 2005; Zhao, Wu, & Bai, 2015).
Table 19 Thermal stability of CNF-PDMS composites as a function of CNF concentration
CNF
(wt%)
Tonset
(°C)
Weight at Tonset
(%) Tonset
(°C)
T20%
(°C) T20%
(°C)
Weight at 800C
(%residue )
0 495 95.5 - 528 - 31
1 505 98 10 536 8 33
3 513 96 18 540 12 35
5 527 97 32 543 15 36
The high thermal conductivity of carbon nanofibers can be expected to be another
reason of the thermal stability improvement in the thermal stability of the PDMS composites
since the composite thermal stability is commonly governed by the filler content. This high
thermal conductivity of nanofibers helps facilitate a greater heat flow and dissipation
throughout the composite (Kong, Mariatti, Rashid, & Busfield, 2014).
149
Chapter 6 Conclusion and Future works
The overall goal of this research was to study the effect of carbon fillers on the
electrical, mechanical and thermal properties of the polymer composites. The impact of filler
loading on the properties of the composites were investigated.
6.1 Role of filler in thermoplastic polymer composites
In general, polymeric materials are flexible but have low electrical conductivity. In
some specific applications, a flexible material with desired electrical conductivity is needed
such as in antistatic packaging, sensors, and batteries. In order to overcome the natural
properties of these insulating matrices, electrical conductive polymer composites were
fabricated. The modified materials exhibit excellent combinations of mechanical properties,
ease of processability and remarkable electrical properties.
Thermoplastic polymer (nylon) composites were prepared with two different types of
conductive filler (CNT and CB). The composites were continuously processed by the melt
compounding technique with a co-rotating twin-screw extruder under the same operating
conditions. The geometrical effects of carbon constituents on conductive network pathways
and composite properties were explored; however, the constituents were used as received
without surface modification or pre-treatment.
The morphology of the composites was analyzed under SEM and TEM microscopes.
The investigation on the dispersion state clearly illustrated that CNTs were generally well
dispersed and only occasional aggregates were found at higher concentration. Moreover, it was
found that filler shape and structure were noticeably affecting the features on its fracture
surface and significantly affected its conductivity.
150
One of the main objectives in this research was to determine the effects of different
fillers’ shape on the electrical conductivity of composites. The conductivity characterizations
of nylon-filled composites were measured by a drastic transition in conduction. By increasing
the filler concentration, a phenomenon explained by the percolation theory was observed when
the first continuous chains of linked conductive filler particles were present. The outstanding
electrical properties improvement of nylon composites were determined at 2.0 and 14.8 wt%
of the percolation threshold for CNT and CB composites, respectively. Additional increase of
the conductive filler concentration above its percolation point showed slight enhancement in
the electrical conductivity of the composites. Obviously, composites containing CNTs favor
the conductive pathways through an insulating matrix at much lower percolation threshold than
CB due to their unique size and geometry. The high aspect ratio of CNTs, compared to an
approximately spherical shape in case of CB fillers contributed to the efficiency of the
conducting network. Moreover, the effects of CB aggregation were able to noticeably reduce
the formation of the conductive path in the polymer matrix.
The conductivity has been explained based on the percolation theory, in which good
agreement between experimental and theoretical values above percolation thresholds was
presented. Experimental work provided relations between composite conductivity and filler
concentration in order to approximately estimate the desired conductivity ranges in specific
applications. The percolation parameter values were calculated and fitted with the prediction
models as:
ρ = 5.96×106( - 2.0)-4.81 for CNT-nylon, and
ρ = 1.09×104( - 14.8)-1.91 for CB-nylon
151
The different filler contents can lead to different effects on other desired composite
properties such as processability and mechanical properties. A significant observation from the
extrusion process was that a higher temperature profile was required during CB-based
composites preparation. This led to higher mixing energy requirements but produced a material
that could not be fabricated into testing specimens. However, composites filled with CNTs
resulted in mechanical enhancement. This was due to the reinforcement effect of their fibrous
shape, which imparted outstanding mechanical properties. The tensile strength and modulus of
the composites essentially increased with increasing CNT content but elongation at break
showed a different trend. Adding more conductive filler does increase the composite
conductivity significantly but it was found to lower the elongation at break, indicating that the
composite becomes brittle or less ductile. Therefore, it is important to achieve the desired
conductivity properties while still maintaining some ductile behavior.
The enhancement of interfacial interaction between carbon fillers and nylon matrix
was further examined with the application of TGA. It was found that addition of the conductive
fillers influenced the degradation of the polymer chains, since different particle sizes have
different effects on thermal degradation behavior. The analysis indicated that the thermal
decomposition temperature of CNT-nylon was improved at a higher rate than that of CB-nylon
composite. This is due to the extremely high thermal conductivity of 1000 W/m.K for CNT
(compared to 10 W/m.K for CB) that helped CNT to conduct the heat out of nylon resin better
than CB. This lower thermal stability of CB in the polymer matrix consequently caused a
higher operating temperature in the extrusion process and led to the inability of mechanical
properties measurement. Moreover, the differences of the initial degradation temperatures
between nylon and its composite were calculated. This also supported the previous finding
152
where a much lower concentration of CNTs was consumed. It was found that every 1 wt% of
CNT addition exhibited 2C improvements in the composites’ thermal degradation at 5 %
weight loss (T95); while, it showed 1C improvement with every 1 wt% of CB added. This
indicated that more thermal energy was required in order to break the bonds between CNTs
and the polymer matrix; thus, improvement of the thermal stability was more pronounced in
CNT-nylon composites.
Based on the data reported in this work, CNTs can be especially classified as high
performance fillers since they allow preparation of thermoplastic polymer composites with
much enhanced properties. However, lack of mass production and high-cost of CNTs
($100/lb compared to $10/lb for CB) effectively prevent them from extending industrial
consuming in the low-cost composite formulations and commercial applications.
6.2 Application of power law model in elastomeric polymer composites
When an electrically conducting phase is dispersed in sufficient quantity in a polymer
resin, a conductive composite is formed. The unique properties of the composites make them
technologically superior to or more cost effective than conventional materials. Although some
information is available regarding the effects of different types of polymer, it must be realized
that the relationship cannot be made precisely due to several reasons: (i) generally, different
polymers contain different ingredients and another assortment of base formulae may result in
different relative effects, (ii) different mixing techniques and conditions result in different
dispersibility of fillers, and (iii) the interaction between fillers and polymers are different due
to their different compatibility, which may substantially affect the overall composite
properties.
153
The overall goal on the area of elastomeric polymer composites in this research was
to investigate the capability of a statistical power law model on the prediction of composite
conductivity. An effort was made to understand the effect of filler addition on the electrical,
mechanical and thermal stability properties of the reinforced composites. The fabrication
procedure of the elastomeric polymer composites was optimized to achieve the best properties
from the addition of one-dimensional conductive fillers. A solution mixing process via
sonication was employed to disperse CNFs throughout PDMS resin.
Since the compatibility of polymer matrix with conductive fillers affects the
composite conductivity, as a guide to the performance of polymer composites, the dispersion
state of the fillers inside the polymer matrix was studied. Through SEM micrographs, PDMS
composites demonstrated a uniform dispersion of CNF fillers where individual fibers can be
observed. The presence of the individual fibers possibly provide more conductive pathways
for electron transfer leading to higher conductivity.
A percolation model of Kirkpatrick (or power law model) was used to estimate the
change of resistivity in terms of carbon nanofiber contents. The results agreed well with the
experimental data where the percolation parameters and a percolation threshold of 0.83 wt%
were calculated and fitted with the prediction model as:
ρ = 531.2(- 0.83)-2.86 for CNF-PDMS composite, and
Experimental results revealed that reinforcement by carbon nanofibers gave
remarkable improvements in the mechanical properties of PDMS composites over the neat
polymer resin. The mechanical behavior under tensile loading conditions displayed an
increasing trend in stress-strain curves with increasing filler concentration. However, such
154
enhancements made the composite material brittle and the samples broke at lower strain values
than the neat polymer matrix.
The thermal property improvements in polymer composites are influenced by many
factors such as filler aspect ratio, thermal conductivity, orientation, dispersion, and the
interfacial thermal resistance between filler and polymer matrix. The experimental results
demonstrated an increasing tendency of the thermal degradation temperatures as the carbon
nanofiber increased. Since CNFs and CNTs have similar thermal conductivity of 1000
W/m.K, similar enhancements were found especially at low % loading. An increase in thermal
stability is generally attributed to the high thermal stability of the fillers and restriction of
polymer chain movement imposed by the fillers. Based on the composites’ thermal degradation
temperature at 5 % weight loss (T95), it indicated that every 1 wt% of CNF addition into the
PDMS matrix exhibited 5.3C improvement. Thus, more heat can be transferred in the PDMS
matrix due to the flexibility of its polymer chain.
6.3 Contributions to knowledge
In summary, the major contributions of this research to the field of polymer
composites are as following:
- A comprehensive study on electrical, mechanical and thermal properties of CNT-
nylon and CNF-PDMS composites was conducted.
- Study the existence of electrical conductivity model for thermoplastic and
elastomeric polymer composites containing carbon filler with varying concentrations.
155
- The percolation threshold for electrical conductivity of various polymer composites
were determined, which allowed a predictive tool to determine tunable electrical conductivity
for a given particular application.
6.4 Future work
While significant amount of work was done and the goals set forth at the beginning
of this study were accomplished, there are still some areas that would benefit from additional
study. These areas include alternative characterization of the composite samples and the
expansion of this work to include a broader range of polymer matrices and exploring other
conductive fillers beside carbon. The observations of this research combined with further
experimentation and analysis could prove valuable development and application of composite
materials.
6.4.1 Surface interactions between filler and polymer matrix
One of the most interesting areas that should be targeted for additional experimental
work is the study of the surface interactions between the filler particles and the matrix materials
and how it specifically effects the electrical conductivity. Although there were significant
improvements in electrical, mechanical, and thermal properties of the composites with the filler
materials used in this research, there is still need for more work to efficiently disperse the fillers
in the polymer composites in order to utilize their unique intrinsic properties. Different
fabrication methods such as chemical modification or in-situ polymerization methods can be
applied. Additionally, use of more commercial polymer resins (both thermoplastic and flexible
elastomeric polymers) in making conductive polymer composites could be further studied to
add knowledge to the polymer composites for other electronics applications.
156
6.4.2 Analysis of polymer composites
One difficulty that arose in the characterization of the polymer composite samples
was the inability to measure the composite conductivity at low filler loading. Due to the
capability of the instrument used, which is on the limit of mega-ohm range, a higher resistance
measurement device is needed. Moreover, it was found that there are multiple factors affecting
properties of the polymer composites, additional characterization techniques can be further
investigated systematically, such as thermal conductivity, viscoelastic behavior analysis and
rheological properties. On the other hand, more experimental work is needed for making
samples of composites loaded with spherical conductive particles of carbon black as well as
carbon naonotubes and carbon nanofibers in order to achieve a complete comparison between
the modeling results and the experimental data.
6.4.3 Expansion of electrical conductivity model
In this research, a significant amount of experimental work was completed in order to
explain the electrical conductive behavior of the polymer composites. However, additional
work can be done to describe the conduction mechanism in the polymer composites by the
application of other conductivity models, such as the models based on thermal and orientation
characteristics. Further characterizations are required to incorporate the composite information
into those models. Moreover, an improvement to the electrical conductivity model toward the
development of a new model can be further studied.
157
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191
Appendices
Appendix A Optimizing the CNF-PDMS composites conditions
Table 20 Volume resistivity of CNF-PDMS composites at different conditions
Condition Rmeasured Rmeasured
()
v
(-cm)
v,avg
(-cm) SD
Value Unit
1 0.8539 kW 853.9 102.5 103.3 3.35
0.8525 852.5 102.3
0.8269 826.9 99.22
0.9028 902.8 108.3
0.8696 869.6 104.4
2 1.717 kW 1717 206.0 195.6 13.2
1.758 1758 210.9
1.529 1529 183.5
1.512 1512 181.4
1.637 1637 196.5
3 2.539 kW 2539 304.7 317.3 9.91
2.580 2580 309.6
2.661 2661 319.3
2.705 2705 324.6
2.734 2734 328.1
4 1.437 kW 1437 172.5 207.1 21.7
1.681 1681 201.7
1.776 1776 213.2
1.826 1826 219.1
1.908 1908 229.0
5 1.737 kW 1737 208.5 221.2 10.7
1.803 1803 216.4
1.817 1817 218.1
1.887 1887 226.5
1.971 1971 236.5
192
Figure 74 Compressive test of CNF-PDMS composites using a data acquisition circuit
board
193
Table 21 Measured resistances of CNF-PDMS composites at various conditions
Force
(N) Resistance ()
Condition 1
Resistance ()
Condition 2
Resistance ()
Condition 3
Resistance ()
Condition 4
Resistance ()
Condition 5
5 8.03107 1.61108 2.29107 1.78107 2.29107
10 8.03107 1.61108 2.29107 1.78107 2.29107
15 6.03107 1.61108 2.29107 1.78107 2.29107
20 4.71106 1.61108 2.29107 1.78107 2.29107
25 1.98106 1.01108 1.29107 1.78107 2.29107
30 1.23106 3.90106 3.07106 1.78107 2.29107
35 1.02106 2.26106 1.58106 1.14107 1.11107
40 7.73105 1.90106 1.29106 1.98106 3.40106
45 6.36105 1.48106 1.05106 8.63105 2.12106
50 4.35105 1.20106 9.02105 3.88105 1.34106
55 3.70105 8.28105 6.91105 2.88105 1.04106
60 3.15105 6.34105 5.96105 2.35105 7.62105
65 2.82105 4.49105 5.16105 2.21105 6.96105
70 2.64105 3.55105 4.61105 2.04105 6.74105
75 2.57105 3.16105 3.98105 1.87105 5.78105
80 2.18105 2.46105 3.74105 1.67105 4.94105
85 2.15105 2.22105 3.54105 1.70105 4.81105
90 1.99105 1.99105 3.84105 1.58105 4.72105
95 1.93105 2.01105 3.69105 1.54105 4.69105
100 1.95105 1.96105 3.10105 1.49105 3.95105
194
Appendix B Raw data: electrical resistivity results
Table 22 Measured electrical resistivity of CNT-nylon composites
Sample Dia. Leng. Rmeasured Rmeasured
()
v
(-cm)
v,avg
(-cm) SD
(cm) (cm) Value Unit
3 wt% 0.17 5 1.5 G 1.5109 6.81106 7.26106 3.21105
0.17 1.6 1.6109 7.26106
0.17 1.7 1.7109 7.72106
0.17 1.6 1.6109 7.26106
0.16 1.8 1.8109 7.24106
5 wt% 0.14 5 11 M 1.1107 3.39104 3.14104 2.60103
0.14 11 1.1107 3.39104
0.13 11 1.1107 2.92104
0.15 8 8.0107 2.83104
0.15 9 9.0107 3.18104
6 wt% 0.2 5 1.2 M 1.2106 7.54103 8.67103 931.9
0.2 1.4 1.4106 8.80103
0.2 1.3 1.3106 8.17103
0.2 1.6 1.6106 1.01104
0.2 1.4 1.4106 8.80103
8 wt% 0.17 5 207 k 2.1105 940.7 906.1 50.6
0.17 180 1.8105 817.1
0.17 206 2.06105 935.2
0.17 203 2.03105 922.5
0.17 202 2.02105 917.0
10 wt% 0.13 5 143 k 1.43105 380.6 369.2 8.2
0.13 140 1.40105 372.7
0.13 137 1.37105 364.7
0.17 79 7.9104 359.6
0.17 82 8.2104 372.2
12 wt% 0.22 5 11.26 k 1.13104 85.6 83.6 8.2
0.21 10.48 1.05104 72.6
0.21 11.23 1.12104 77.8
0.23 10.87 1.09104 90.3
0.23 11.04 1.10104 91.7
195
Table 23 Measured electrical resistivity of CB-nylon composites
Sample Diameter Length Rmeasured Rmeasured
()
v
(-cm)
v,avg
(-cm) SD
(cm) (cm) Value Unit
15 wt% 0.2 5 42.44 M 4.24107 2.67105 2.38105 2.30104
0.2 38.68 3.87107 2.43105
0.2 39.96 4.00107 2.51105
0.2 33.95 3.39107 2.13105
0.17 47.59 4.76107 2.16105
20 wt% 0.24 5 41.56 k 4.16104 376.0 415.0 36.6
0.22 52.44 5.24104 398.7
0.24 45.94 4.59104 415.6
0.24 52.45 5.24104 474.6
0.22 53.93 5.39104 410.0
30 wt% 0.2 5 15.20 k 1.52104 95.5 90.6 5.54
0.2 14.97 1.50104 94.1
0.2 15.03 1.50104 94.4
0.19 14.88 1.49104 84.4
0.19 14.96 1.50104 84.8
35 wt% 0.19 5 4.26 k 4.26103 24.2 26.3 1.77
0.19 4.75 4.75103 26.9
0.19 4.88 4.88103 27.7
0.19 4.93 4.93103 28.0
0.19 4.34 4.34103 24.6
196
Table 24 Measured electrical resistivity of CNF-PDMS composites
Sample Rmeasured Rmeasured
()
v
(-cm)
v,avg
(-cm) SD
Value Unit
1 wt% 0.7173 M 7.17105 8.61104 8.37104 2.24103
0.6699 6.70105 8.04104
0.7052 7.05105 8.46104
0.6881 6.88105 8.26104
0.7073 7.07105 8.49104
2 wt% 0.8539 k 853.9 102.5 103.3 3.35
0.8525 852.5 102.3
0.8269 826.9 99.2
0.9028 902.8 108.3
0.8696 869.6 104.4
3 wt% 0.4327 k 432.7 51.9 53.4 1.57
0.4300 430.0 51.6
0.4555 455.5 54.7
0.4458 445.8 53.5
0.4591 459.1 55.1
4 wt% 0.1403 k 140.3 16.8 16.3 0.50
0.1399 139.9 16.8
0.1341 134.1 16.1
0.1334 133.4 16.0
0.1309 130.9 15.7
5 wt% 0.0919 k 91.9 11.0 10.8 0.36
0.0917 91.7 11.0
0.0929 92.9 11.1
0.0870 87.0 10.4
0.0864 86.4 10.4
197
Appendix C Raw data: mechanical properties results
Table 25 Measured mechanical properties of CNT-nylon composites
Sample Maximum load (kN) Maximum Displacement (mm)
Measured Avg SD Measured Avg SD
3 wt% 0.05051 0.05047 0.00200 22.25 23.46 1.29
0.05244 23.33
0.04845 24.81
5 wt% 0.05751 0.05659 0.00152 12.09 11.56 0.46
0.05742 11.28
0.05484 11.32
6 wt% 0.0612 0.06180 0.00167 16.03 15.07 0.91
0.06368 14.22
0.06051 14.97
8 wt% 0.07491 0.07621 0.00172 7.08 7.01 0.49
0.07816 7.46
0.07556 6.49
10 wt% 0.09179 0.08966 0.00188 5.97 6.30 0.35
0.08897 6.66
0.08823 6.28
12 wt% 0.09778 0.09965 0.00169 4.18 3.87 0.29
0.10106 3.83
0.10011 3.61
198
Table 26 Measured mechanical properties of CNT-nylon composites (cont’)
Sample Tensile strength (MPa) Maximum Strain (%) Toughness (kJ/m3)
Calculated Avg SD Calculated Avg SD Calculated Avg SD
3 wt% 84.18 84.11 3.33 63.6 67.04 3.67 3985 4050 81.91
87.40 66.7 4142
80.75 70.9 4023
5 wt% 95.85 94.32 2.53 34.5 33.04 1.30 2857 2911 144.8
95.70 32.2 2801
91.40 32.3 3075
6 wt% 102.0 103.0 2.78 45.8 43.07 2.60 2486 2392 129.0
106.1 40.6 2245
100.9 42.8 2445
8 wt% 124.9 127.0 2.87 20.2 20.03 1.40 2201 2201 98.50
130.3 21.3 2300
125.9 18.5 2103
10 wt% 153.0 149.4 3.13 17.1 18.01 0.99 1981 1876 91.19
148.3 19.0 1814
147.1 17.9 1834
12 wt% 163.0 166.1 2.81 11.9 11.07 0.82 1308 1361 49.12
168.4 10.9 1405
166.9 10.3 1370
199
Table 27 Measured mechanical properties of CNF-PDMS composites
Sample Maximum load (kN) Maximum Displacement (mm)
Measured Avg SD Measured Avg SD
PDMS 0.02196 0.02245 0.00104 66.78 64.43 2.17
0.02174 62.49
0.02364 64.03
1 wt% 0.02285 0.02418 0.00119 66.69 64.08 2.75
0.02452 64.34
0.02516 61.21
2 wt% 0.02752 0.02657 0.00136 65.63 63.91 1.51
0.02718 62.82
0.02501 63.27
3 wt% 0.02691 0.02680 0.00171 65.59 63.04 2.21
0.02846 61.85
0.02504 61.69
4 wt% 0.02797 0.02772 0.00156 63.17 62.42 2.84
0.02605 64.80
0.02913 59.28
5 wt% 0.03014 0.03095 0.00146 60.28 61.49 2.10
0.03264 63.92
0.03008 60.28
200
Table 28 Calculated mechanical properties of CNF-PDMS composites (cont’)
Sample Tensile strength (MPa) Maximum Strain (%) Toughness (kJ/m3)
Calculated Avg SD Calculated Avg SD Calculated Avg SD
PDMS 5.490 5.61 0.26 190.8 184.1 6.21 305.3 312.0 6.96
5.435 178.5 319.2
5.910 182.9 311.5
1 wt% 5.713 6.04 0.30 190.5 183.1 7.85 342.4 331.0 10.2
6.130 183.8 328.1
6.290 174.9 322.6
2 wt% 6.880 6.64 0.34 187.5 182.6 4.31 379.4 371.8 9.74
6.795 179.5 360.8
6.253 180.8 375.1
3 wt% 6.728 6.70 0.43 187.4 180.1 6.31 388.6 378.0 9.48
7.115 176.7 374.9
6.260 176.3 370.4
4 wt% 6.993 6.93 0.39 180.5 178.3 8.10 400.8 395.5 4.91
6.513 185.1 391.1
7.283 169.4 394.6
5 wt% 7.535 7.74 0.37 172.2 175.7 6.00 460.1 449.8 9.84
8.160 182.6 440.5
7.520 172.2 448.7
201
Appendix D Figures of instruments used in this research
Figure 75 JEOL 2011 transmission electron microscope (TEM)
(a) (b)
Figure 76 (a) FE-SEM model JEOL JSM6400 and (b) SEM model JEOL JSM6400
202
(a) (b)
Figure 77 (a) TA Instruments Q600 Simultaneous TGA/DSC and (b) Instron 4465
machine
Curriculum Vitae
Candidate’s full name: Wilailak Chanklin
Universities attended:
2008–2009: Exchange student at University of New Brunswick, Canada.
2007–2009: Master of Science in Petrochemical Technology, The Petroleum and
Petrochemical College, Chulalongkorn University, Thailand.
Master research under the topic of “Hydrophobic–modified cellulose fibers and
cellulose microfibrils as reinforcements for bio-composites”
2003–2007: Bachelor of Engineering, Chemical Engineering, Burapha University,
Thailand.
Bachelor research under the topic of “A studying of alcohol types influential for
production and properties of biodiesel from palm oil”
Conference Proceeding: W. Chanklin, L. Shuzhao and H. Xiao “Hydrophobic–modified
cellulose fibers and cellulose microfibrils as reinforcement for biocomposites”, Society of
Plastics Engineers Annual Technical Conference (ANTEC) 2009
Conference Attending and Presentations:
2013: Canadian Chemical Engineering Conference (Oral presentation), Fredericton,
New Brunswick, Canada
2012: Graduate Research Conference (Oral presentation), University of New
Brunswick, Fredericton, New Brunswick, Canada
2012: Material Research Societies Fall Meeting and Exhibits, Boston, Massachusetts,
USA
2011: Material Research Societies Fall Meeting and Exhibits (Poster presentation),
Boston, Massachusetts, USA
2011: Chemical Engineering Graduate Student Association Conference (1st place
award Poster Presentation), University of New Brunswick, Fredericton, New Brunswick,
Canada
2010: Chemical Engineering Graduate Student Association Conference (2nd place
award Poster Presentation), University of New Brunswick, Fredericton, New Brunswick,
Canada
2010: Material Research Societies Fall Meeting and Exhibits, Boston, Massachusetts,
USA
2008: AUTO21 Conference as a HQP (High Quality Personal), Ontario, Canada
