ABSTRACT 
 
 
 
 
Title of Document: PROCESSING-STRUCTURE-
MICROSTRUCTURE- PROPERTY  
RELATIONSHIPS IN POLYMER 
NANOCOMPOSITES 
  
 Arun Kumar Kota, Doctor of Philosophy, 2007 
  
Directed By: Professor Hugh A. Bruck,  
Department of Mechanical Engineering 
 
 
The optimal development of polymer nanocomposites using carbon nanotube (CNTs) 
and carbon nanofiber (CNFs) fillers requires a complete understanding of processing-
structure-property relationships. The purpose of this understanding is to determine the 
optimal approach for processing polymer nanocomposites with engineered 
microstructures and enhanced material properties. In this research, two processing 
techniques were investigated: solvent processing and twin screw extrusion. The 
former is a batch process which employs mixing a polymer solution with a filler 
suspension using long mixing times and low levels of shear mixing. The latter is a 
continuous process that mixes polymer melts with solid nanoscale ingredients using 
high levels of shear mixing for a short mixing time. Previous studies conducted on 
polymer-CNT/CNF using these processes have focused mainly on processing-
microstructure and structure-property relationships using one technique or the other. 
  
This research focuses on understanding the processing-property relationships by 
comparing the structure-property relationships resulting from the two processes. 
Furthermore, the effect of ingredients and processing parameters within each process 
on microstructure and structure-property relationships was investigated. The 
microstructural features, namely, distribution of agglomerates, dispersion, alignment, 
and aspect ratio of the filler were studied using optical, scanning electron, confocal 
and transmission electron microscopy, respectively. The composition of the filler was 
determined using thermogravimetric analysis. The electrical, rheological, thermo-
oxidative and mechanical properties of the composites were also investigated. Many 
significant insights related to processing-structure-property relationships were 
obtained including:  (a) deagglomeration is a critical combination of the magnitude of 
shear rate and the residence time, (b) the structure-property relationships can be 
modeled using a new methodology based on the degree of percolation by representing 
the material as an interpenetrating phase composite, (c) annealing can re-establish 
interconnectivity and improve electrical properties, (d) the degree of dispersion can 
be resolved using thermogravimetric analysis, and (e) increasing extrusion speed 
inhibits thermal decomposition and begins to asymptotically increase strength and 
stiffness through reduction in aspect ratio and size of agglomerates. Finally, a new 
combinatorial approach was developed for rapidly determining processing-structure 
relationships of polymer nanocomposites. This dissertation has broad implications in 
the processing of high performance and multifunctional polymer nanocomposites, 
combinatorial materials science, and histopathology. 
 
  
 
 
 
 
 
 
 
 
 
 
PROCESSING-STRUCTURE-MICROSTRUCTURE- PROPERTY  
RELATIONSHIPS IN POLYMER NANOCOMPOSITES 
 
 
 
By 
 
 
Arun Kumar Kota 
 
 
 
 
 
Dissertation submitted to the Faculty of the Graduate School of the  
University of Maryland, College Park, in partial fulfillment 
of the requirements for the degree of 
Doctor of Philosophy 
2007 
 
 
 
 
 
 
 
 
 
 
Advisory Committee: 
Dr. H. A. Bruck, Associate Professor of Mechanical Engineering, Chair 
Dr. D. I. Bigio, Associate Professor of Mechanical Engineering 
Dr. S. R. Raghavan, Associate Professor of Chemical and Biomolecular Engineering 
Dr. A. Dasgupta, Professor of Mechanical Engineering 
Dr. S. D. Solares, Assistant Professor of Mechanical Engineering 
 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
? Copyright by 
Arun Kumar Kota 
2007 
 
 
 
 
 
 
 
 
 
 
 
 
 ii  
 
Dedication 
 
 
 
 
 
 
 
 
 
To the all pervasive Divinity that guided my  
search for Truth in Science 
 iii  
Acknowledgements 
 
I would like to express my deepest appreciation and gratitude to Dr. Bruck 
without whose guidance, support and encouragement this thesis would not have been 
possible. I admire Dr. Bruck?s constructive criticism of technical writing and his helpful 
remarks. I thank him for imparting me advice both on personal and professional fronts. I 
am indebted to him for guiding me in preparing for a career in academia. 
My sincere thanks and regards to all the professors at University of Maryland who 
have provided valuable suggestions and resources for my research. Special thanks to Dr. 
Bigio for helping me understand the mixing concepts associated with twin screw 
extrusion and to Dr. Raghavan for providing me with rheological concepts and a lot of 
guidance on the personal front. 
My warm regards to the program manager turned mentor turned friend, Dan 
Powell, for his help on both personal and professional fronts. 
I extend a warm thanks to my colleagues, Dan, Alan, Arvind and Bani, who have 
helped with their valuable suggestions and kept me company all along. I also extend a 
warm thanks to all the NASA interns, undergraduate students and friends for contributing 
innumerable hours of work towards the research. A special thanks to my house mates 
Isaac and Vikram for being very accommodating. 
I sincerely appreciate the help provided by all the staff at University of Maryland, 
especially by Howie in the machine shop and Penny in the main office.  
I love my parents and sister beyond expression for their support and 
encouragement at all times. 
 iv  
Table of Contents 
Dedication ...................................................................................................... ii 
Acknowledgements ......................................................................................iii 
Table of Contents......................................................................................... iv 
List of Tables ............................................................................................... vii 
List of Figures.............................................................................................viii 
1. Introduction............................................................................................ 1 
1.1 Background ....................................................................................................... 1 
1.1.1 Carbon Nanotubes and Carbon Nanofibers ................................................ 1 
1.1.2 Polymer-CNT/CNF Composites and their Applications ............................ 3 
1.2 Motivation for Research................................................................................... 4 
1.3 Research Objectives.......................................................................................... 6 
1.4 Dissertation Outline.......................................................................................... 7 
2. Literature Review .................................................................................. 9 
2.1 Polymer Nanocomposites : Processing............................................................ 9 
2.1.1 Solvent processing ...................................................................................... 9 
2.1.2 Melt mixing............................................................................................... 11 
2.1.3 In situ polymerization ............................................................................... 12 
2.1.4 Other methods........................................................................................... 13 
2.2 Processing ? Microstructure Relationships.................................................. 14 
2.3 Structure ? Property Relationships............................................................... 17 
2.3.1 Electrical Properties.................................................................................. 17 
2.3.2 Rheological Properties.............................................................................. 19 
2.3.3 Thermo-oxidative Properties .................................................................... 21 
2.3.4 Mechanical Properties............................................................................... 22 
2.4 Processing ? Property Relationships............................................................. 25 
2.5 Processing ? Structure Relationships: Extruded Polymer Composites..... 26 
2.5.1 Compositional Gradients for a Combinatorial Approach ......................... 27 
2.5.2 Residence Distributions as Measures of Mixing ...................................... 29 
3. Experimental Methods ........................................................................ 31 
3.1 Ingredients....................................................................................................... 31 
3.1.1 Polymer Matrix ......................................................................................... 31 
3.1.2 Fillers ........................................................................................................ 32 
3.1.2.1 Graphitized Multiwalled Carbon Nanotubes ........................................ 32 
3.1.2.2 Pyrograf III Carbon Nanofibers............................................................ 37 
3.1.2.3 Potassium Chloride ............................................................................... 42 
3.1.3 Solvents..................................................................................................... 42 
3.2 Processing of Polymer Nanocomposites........................................................ 43 
3.2.1 Solvent Processing.................................................................................... 43 
3.2.2 Twin Screw Extrusion............................................................................... 46 
 v  
3.2.2.1 Equipment & Peripherals...................................................................... 46 
3.2.2.2 Screw Design ........................................................................................ 53 
3.2.2.3 Procedure for Processing Polymer Nanocomposites ............................ 56 
3.2.3 Annealing the extruded PS-CNF composites ........................................... 59 
3.3 Characterization of Structure & Microstructure ........................................ 59 
3.3.1 Thermogravimetric Analysis: Composition.............................................. 59 
3.3.2 In-Situ Absorbance Measurement: Residence Distributions .................... 63 
3.3.3 Distribution, Dispersion, Aspect Ratio and Alignment: Microscopy....... 65 
3.4 Characterization of Properties ...................................................................... 67 
3.4.1 Electrical Conductivity ............................................................................. 67 
3.4.2 Rheological Properties.............................................................................. 67 
3.4.3 Thermo-oxidative behavior....................................................................... 69 
3.4.4 Mechanical Properties............................................................................... 69 
4. Results and Discussion......................................................................... 70 
4.1 Processing ? Microstructure Relationships.................................................. 70 
4.1.1 Microstructure of Solvent Processed PS ? MWCNT  Composites........... 70 
4.1.2 Microstructure of PS ? CNF Composites: Solvent Processed & Extruded ..  
 ................................................................................................................... 72 
4.1.3 Aspect Ratio of CNFs: Solvent Processed & Extruded............................ 75 
4.1.4 Alignment of CNFs: Extruded & Annealed PS-CNF Composites ........... 77 
4.1.5 Microstructure of Extruded PS ? CNF Composites: Influence of Screw 
Speed......................................................................................................... 79 
4.1.6 Porosity of Extruded PS ? CNF Composites ............................................ 80 
4.2 Structure ? Property & Processing ? Property Relationships.................... 80 
4.2.1 Solvent Processed PS ? MWCNT Composites......................................... 81 
4.2.1.1 Electrical Conductivity ......................................................................... 81 
4.2.1.2 Rheological Properties.......................................................................... 84 
4.2.1.3 Comparison of Electrical and Rheological Percolation........................ 89 
4.2.1.4 Effect of Solvent on Rheological Percolation....................................... 92 
4.2.1.5 Modeling as an Interpenetrating Phase Composite............................... 96 
4.2.2 PS ? CNF Composites: Solvent Processed & Extruded ......................... 104 
4.2.2.1 Electrical Conductivity: Solvent Processed........................................ 104 
4.2.2.2 Electrical Conductivity: Extruded & Annealed .................................. 106 
4.2.2.3 Rheological Properties: Solvent Processed......................................... 110 
4.2.2.4 Rheological Properties: Extruded & Annealed................................... 112 
4.2.2.5 Thermo-oxidative behavior: Solvent Processed & Extruded.............. 115 
4.2.2.6 Mechanical Properties: Extruded........................................................ 121 
4.3 Comparison of Solvent Processing and Extrusion: Summary.................. 128 
4.4 Processing ? Structure Relationships: A New Combinatorial Approach 129 
4.4.1 Prediction of the Compositional Gradient .............................................. 130 
4.4.2 CG Characterization Approach: Influence of Filler Size........................ 134 
5. Conclusions and Future Work.......................................................... 136 
5.1 Intellectual Contributions ............................................................................ 137 
5.2 Future Work.................................................................................................. 141 
 vi  
References.................................................................................................. 144 
 
 vii  
List of Tables 
 
Table 4.1 List of composites and material properties investigated for structure-property 
relationships. ? = Investigated, X= Not Investigated. ...................................................... 81 
Table 4.2 The power law fit parameters for the electrical conductivity of the PS-
MWCNT composites processed using THF and DMF solvents....................................... 83 
Table 4.3 Relationship between mass and volume fractions for PS-MWCNT composites.
........................................................................................................................................... 83 
Table 4.4 The power law fit parameters for the rheological properties of the PS-MWCNT 
composites processed using THF...................................................................................... 90 
Table 4.5 Normalized cross-correlation values for the normalized log of rheological 
parameters for PS-MWCNT nanocomposites processed with THF solvent when 
compared with the normalized log of the power law fits to the electrical conductivity 
measurements for THF processed PS-MWCNT nanocomposites and the fits to 
 *log& "log ?G  in figure 4.14. ....................................................................................... 91 
Table 4.6 Normalized cross-correlation values for the normalized log of rheological 
parameters for PS-MWCNT nanocomposites processed with DMF solvent when 
compared with the normalized log of the power law fits to the electrical conductivity 
measurements for DMF processed PS-MWCNT nanocomposites and the fits to 
 *log& "log ?G  in figure 4.16. ....................................................................................... 94 
Table 4.7 The degree of percolation calculated from the electrical conductivity 
measurements for each composition using the power law fit........................................... 97 
Table 4.8 Values of material properties determined from fitting experimental data for PS-
MWCNT composite with the new rheological models................................................... 102 
Table 4.9 The power law fit parameters for the electrical conductivity of the PS-CNF 
composites processed using DMF. ................................................................................. 105 
 viii  
List of Figures 
 
Figure 1.1 Structure of SWCNTs [2]................................................................................. 2 
Figure 1.2 Structure of MWCNTs [2]................................................................................ 2 
Figure 1.3 The inter-relationship of processing-structure/microstructure-property .......... 5 
Figure 2.1 An SEM image showing an isotropic dispersion of CNFs in PEEK matrix at 
15 wt.% loading [31]......................................................................................................... 15 
Figure 2.2 A TEM image showing alignment of MWCNTs in PC matrix at high draw 
down ratios [41]. ............................................................................................................... 17 
Figure 2.3 Establishing the percolation threshold through power law fits of electrical 
conductivity as function of weight fraction [48]............................................................... 19 
Figure 2.4 Storage modulus vs frequency for PMMA-SWNT composites [51]. ............ 20 
Figure 2.5 The (a) RTDs, and (b) RVDs at varying operating conditions. Note that the 
RVDs overlap, while the RTDs do not overlap [76]. ....................................................... 30 
Figure 3.1 Scanning electron micrograph showing the as-received MWCNTs with large 
agglomerations.................................................................................................................. 33 
Figure 3.2 Scanning electron micrograph showing a single agglomerate of MWCNTs. 34 
Figure 3.3 Scanning electron micrograph showing the individual MWCNTs, which are 
tens of nanometers in diameter. ........................................................................................ 34 
Figure 3.4 Spectrum of MWCNTs on the sample holder. ............................................... 35 
Figure 3.5 Spectrum of the sample holder only............................................................... 35 
Figure 3.6 Raman spectra of MWCNTs shows that they are graphitized........................ 36 
Figure 3.7 Raman spectra of graphite powder. ................................................................ 37 
Figure 3.8 Scanning electron micrograph showing the as-received CNFs. Note that most 
of the agglomerates are several tens of microns. .............................................................. 38 
Figure 3.9 The as-received CNF agglomerates at a higher magnification....................... 39 
Figure 3.10 The diameter of the as-received CNFs is on the order of 100micrometer. .. 39 
Figure 3.11 The as-received CNFs at a higher magnification. ........................................ 40 
Figure 3.12 Spectrum of the CNFs with the sample holder............................................. 40 
Figure 3.13 Spectrum of the sample holder only............................................................. 41 
Figure 3.14 Raman spectra of CNFs shows that they are distinctly different from 
MWCNTs.......................................................................................................................... 41 
Figure 3.15 The solvent processing experimental setup showing the sonication of filler 
suspension and dissolution of polymer in the same solvent. ............................................ 44 
Figure 3.16 The vacuum filtration setup to separate the polymer nanocomposite 
precipitate after solvent extraction.................................................................................... 45 
Figure 3.17 The Beuhler Pneumet I Hot Press................................................................. 45 
Figure 3.18 The twin screw extrusion facility overview ................................................. 47 
Figure 3.19 A schematic of the extrusion line with the loss-in-weight overhead feeders, 
optical probe and the automated extrudate collection system. ......................................... 47 
Figure 3.20 The interchangeable, electrically heated barrels showing the middle and end 
feed ports........................................................................................................................... 48 
Figure 3.21 Eight-to-round adapter that guides the flow from the screws into the die. .. 49 
Figure 3.22 Ceramic band heater to control the temperature of the die zone.................. 49 
Figure 3.23 The slit die with guillotine-edge arrangement.............................................. 49 
 ix  
Figure 3.24 The FACTS control system was used mainly to control the temperature and 
the screw speed of the extruder......................................................................................... 50 
Figure 3.25 The loss-in-weight over head feeders to feed powders and pellets. ............. 51 
Figure 3.26 The automated extrudate collection system.................................................. 51 
Figure 3.27 Chill roll........................................................................................................ 52 
Figure 3.28 Water bath..................................................................................................... 52 
Figure 3.29 Torque winder ............................................................................................... 53 
Figure 3.30 The twin screws when extracted out of the extruder. ................................... 53 
Figure 3.31 Low shear screw design................................................................................ 54 
Figure 3.32 High shear screw design ............................................................................... 55 
Figure 3.33 Extrudate exiting the slit die......................................................................... 57 
Figure 3.34 Automated collection of extrudate samples.................................................. 58 
Figure 3.35 The weight loss curves of the neat PS, neat MWCNTs and the neat CNFs. 61 
Figure 3.36 (a) Representative weight% and WLR profiles for PS- CNF composites. (b) 
Zoomed in view more clearly indicating the presence of a third peak. The weight percent 
remaining at the inflection point between the second and third peaks represents the 
loading of the filler in the composite. ............................................................................... 62 
Figure 3.37 The die zone with the optical probe mounted............................................... 63 
Figure 3.38 Representative normalized Residence Time Distribution (RTD)................. 65 
Figure 3.39 The RDA III parallel plate rheometer........................................................... 68 
Figure 3.40 The sample used for mechanical testing....................................................... 69 
Figure 4.1 Random, isotropic dispersion of MWCNTs at a 5wt.% loading. Note the 
continuous phase of percolated MWCNTs with a scaffold like structure. ....................... 71 
Figure 4.2 A macroscopic crack in the PS-MWCNT composites processed using (a) 
DMF and (b) THF reveals pull out of MWCNTs indicating poor adhesion between 
MWCNTs and PS ............................................................................................................. 71 
Figure 4.3 Surface of the (a) solvent processed and (b) extruded PS-CNF composites. 
While CNFs are present on the surface of the solvent processed composites, they tend to 
stay below the surface for the extruded composites. ........................................................ 73 
Figure 4.4 Cross-section of the (a) solvent processed and (b) extruded PS-CNF 
composites. While CNFs are randomly dispersed in the solvent processed composites, 
agglomerates are present in the extruded composites....................................................... 75 
Figure 4.5 Representative TEM images of (a) solvent processed and (b) extruded CNFs. 
Note the higher aspect ratio of the solvent processed CNFs (35:1) when compared to that 
of the extruded CNFs (25:1). ............................................................................................ 76 
Figure 4.6 Microstructure of the (a) extruded and (b) annealed PS-CNF composites. 
While the extruded composites show a preferential alignment of CNFs, the annealed 
composites show a relatively random distribution............................................................ 78 
Figure 4.7 Scanning electron micrographs of the extruded PS-CNF composites processed 
at a screw speed of  (a) 30 RPM showing the relatively bigger agglomerates of CNFs, and 
(b) 200 RPM showing the relatively smaller agglomerates of CNFs............................... 79 
Figure 4.8 Representative optical micrographs of extruded PS-CNF composites showing 
porosity in the (a) absence, and (b) presence of a vacuum pump..................................... 80 
Figure 4.9 Electrical conductivity of the PS-MWCNT composites solvent processed 
using THF and DMF at various MWCNT loadings with the corresponding power law fits.
........................................................................................................................................... 82 
 x  
Figure 4.10 (a) Storage modulus (G?) and (b) loss modulus (G?) of the solvent processed 
PS-MWCNT composites as a function of frequency. Data are shown for a range of 
MWCNT loadings. Note the plateau in G? at low frequencies for all of the MWCNT 
loadings indicating the presence of a pseudo-solid like phase in the composite formed by 
percolated MWCNTs........................................................................................................ 85 
Figure 4.11  Cross-over point of the G? and G? curves for the neat PS and the 12 vol.% 
MWCNT composites. While the neat PS shows a viscous response at lower frequencies, 
the 12 vol.% MWCNT composite shows a predominantly elastic response over the entire 
frequency range................................................................................................................. 86 
Figure 4.12 Complex viscosity (?*) as a function of (a) frequency (?), and (b) complex 
modulus (G*) for the PS-MWCNT composites processed with THF and tested at a 
temperature of 190?C. Data are shown for a range of MWCNT loadings. Note the plateau 
in complex viscosity in the high complex modulus regime.............................................. 87 
Figure 4.13 Inverse loss tangent as a function of frequency. Note the increase in inverse 
loss tangent with MWCNT loading. ................................................................................. 88 
Figure 4.14 The log-normalized values of storage modulus ( 'logG ) , loss modulus 
( "logG ), complex viscosity ( *log? ) and inverse loss tangent ( )"/'log( GG ), electrical 
conductivity ( c?log ) and the power law fit for electrical conductivity ( PLc?log ) as a 
function of the MWCNT loading at 190?C for THF processed composites. The 
rheological data were obtained from figures 4.10, 4.12 and 4.13 at a frequency of 0.1 
rad/s. The viscous rheological parameters, *"&?G , exhibit a gradual percolation rate, and 
hence a modified power law fit ( PLG ) *log& "log( ? ) was used. ................................... 90 
Figure 4.15 Complex viscosity (?*) as a function of complex modulus (G*) for the PS-
MWCNT composites processed with DMF and tested at a temperature of 190?C. Data are 
shown for a range of MWCNT loadings. Note the plateau in complex viscosity in the 
high complex modulus regime.......................................................................................... 93 
Figure 4.16 The log-normalized values of storage modulus ( 'logG ) , loss modulus 
( "logG ), complex viscosity ( *log? ) and inverse loss tangent ( )"/'log( GG ), electrical 
conductivity ( c?log ) and the power law fit for electrical conductivity ( PLc?log ) as a 
function of the MWCNT loading at 190?C for DMF processed composites. The 
rheological data was obtained at a frequency of 0.1 rad/s. Note that ?* and G? percolate 
similar to that predicted by the modified power law ( PLG )*log&"log(   ? ) for THF 
processed composites. However, G? and G?/G? percolate more gradually compared to c? . 
This is in contrast to that observed with the THF processed composites. ........................ 94 
Figure 4.17 Degree of percolation at various MWCNT loadings.................................... 96 
Figure 4.18 (a) Storage modulus (G?) and (b) loss modulus (G?) of the composites as a 
function of frequency. Data are shown for a range of MWCNT loadings. Note that the fits 
from the proposed rheological model match well with the experimental data............... 101 
Figure 4.19 Normalized rheological properties of the continuous phase of percolated 
MWCNTs indicating elastic-viscoplastic behavior with a crossover in behavior from 
elastic to viscoplastic at the normalized frequency of 1. ................................................ 103 
 xi  
Figure 4.20 Electrical conductivity of the PS-CNF composites solvent processed using 
DMF at various CNF loadings. The corresponding power law fits are also shown. ...... 105 
Figure 4.21 Electrical conductivity of the extruded and solvent processed PS-CNF 
composites at various CNF loadings............................................................................... 107 
Figure 4.22 Effect of annealing temperature on electrical conductivity of extruded PS-
CNF composites. The composites were annealed for 30 minutes. Note the lower 
percolation threshold at higher annealing temperature................................................... 108 
Figure 4.23 Effect of annealing time on electrical conductivity of extruded PS-CNF 
composites. The composites were annealed at 200?C. Note the lower percolation 
threshold at longer annealing times. ............................................................................... 109 
Figure 4.24 (a) Storage modulus (G?) and (b) loss modulus (G?) of the solvent processed 
PS-CNF composites as a function of frequency at a temperature of 190?C. Data are 
shown for a range of CNF loadings. Note the plateau in G? at low frequencies for all of 
the CNF loadings indicating the presence of a pseudo-solid like phase in the composite 
formed by percolated CNFs............................................................................................ 111 
Figure 4.25 (a) Storage modulus (G?) and (b) loss modulus (G?) of the extruded PS-CNF 
composites as a function of frequency at a temperature of 190?C. Data are shown for a 
range of CNF loadings. Note the lower values of G? and G? when compared with the 
solvent processed PS-CNF composites shown in figure 4.24. ....................................... 113 
Figure 4.26 Effect of annealing on the rheological properties of extruded PS-CNF 
composites. The composites were annealed for 30 mins................................................ 114 
Figure 4.27 (a) Weight percent loss profiles of PS-CNF composites at various CNF 
loadings. (b) WLR profile of the PS-CNF composites at various CNF loadings. The inset 
shows the peak WLR of the styrene-rich phase. (c) The decreasing magnitude of peak 
WLR of the styrene-rich phase with increasing CNF loading........................................ 117 
Figure 4.28 Average TPWLR of the styrene-rich phase of the PS-CNF composites 
processed via different techniques. Both the neat PS and the composites processed via 
solvent processing exhibit the least thermal stability and the extruded low porosity ones 
exhibit the highest thermal stability. The inset shows optical micrographs depicting the 
difference in porosity of the extruded composites.......................................................... 118 
Figure 4.29 Normalized relative TPWLR of the styrene-rich phase as a function of the 
extrusion screw speed. Note the approximately linear increase in TPWLR with increasing 
screw speed. .................................................................................................................... 119 
Figure 4.30 Normalized weight loss of CNFs as a function of time for the PS-CNF 
composites. Note that the rate of weight loss of CNFs increases with increasing levels of 
shear mixing.................................................................................................................... 121 
Figure 4.31 A representative stress-strain plot of the extruded PS-CNF composites.... 122 
Figure 4.32 Influence of CNF loading on the (a) tensile modulus, (b) tensile strength, 
and (c) % strain to failure of the extruded PS-CNF composites..................................... 124 
Figure 4.33 Influence of type of CNFs ? high density (HD) or low density (LD), filler 
feed port ? end or middle, and vacuum pump (VP) ? with or without, on the (a) tensile 
modulus, and (b) tensile strength of PS-CNF composites with 10 wt.% CNF loading, 
extruded at 200 RPM. ..................................................................................................... 126 
Figure 4.34 Influence of screw speed and flow rate on the (a) tensile modulus, and (b) 
tensile strength of PS-CNF composites with 10 wt.% CNF loading, extruded at 200 rpm. 
While flow rate does not affect the mechanical properties significantly, both modulus and 
 xii  
strength tend to increase with screw speed and begins to asymptotically reach a plateau at 
higher screw speeds. ....................................................................................................... 127 
Figure 4.35 Modeling the normalized RVD using a second order transfer function.  The 
peak of the experimental curve is slightly lower than that of the modeled curve because 
the optical probe measuring the absorbance reached its detection limit......................... 132 
Figure 4.36 The modeled normalized RVDs resulting from varying polymer flow rates 
and extruder screw speeds superimposed within reasonable error . ............................... 132 
Figure 4.37 The compositional gradient predicted via convolution correlates well with 
the experimental values obtained from thermogravimetric analysis for the PS-CNF 
composite. This confirms the validity of the non-destructive approach......................... 134 
Figure 4.38 The compositional gradient predicted via convolution correlates well with 
the experimental values obtained from thermogravimetric analysis for the PS-KCl 
composite. This indicates that the approach is independent of the size scale of the fillers.
......................................................................................................................................... 135 
 
 1  
1. Introduction 
 
 With the availability of new and improved processing and characterization 
techniques, researchers have become increasingly interested over the past decade in 
altering homogeneous materials by adding nanoscale fillers to create what are now being 
called nanocomposites. The unique high surface-to-volume ratios of the nanoscale fillers, 
combined with quantum mechanical and other nanoscale physical effects, have rendered 
the nanocomposites with properties that are significantly different from composites that 
are microstructured, and have unique structural characteristics that can also be possibly 
controlled by a given process in a different manner. Their significantly different 
properties have allowed and retain the potential for the development of novel materials, 
processes, phenomena by engineering composites at the nanoscale [1]. This may lead to 
new avenues in science and technology that require understanding in more detail the 
relationship between the processing of these nanocomposites, and their resulting structure 
and associated properties. 
 
1.1 Background 
1.1.1 Carbon Nanotubes and Carbon Nanofibers 
Two specific nanoscale fillers, Carbon Nanotubes (CNTs) and Carbon Nanofibers 
(CNFs), have been identified by materials scientists as having the greatest potential to 
revolutionize the technological landscape of the century ahead. CNTs can be categorized 
further as single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes 
(MWCNTs). SWCNTs are graphene sheets (hexagonal arrangement of sp2 hybridized 
 2  
carbon atoms) rolled into a cylinder and the ends closed by a hemi-fullerene with an 
appropriate diameter to form a nanotube as shown in figure 1.1 [2].  
 
Figure 1.1 Structure of SWCNTs [2] 
 
The nanoscale characteristics of these fillers are defined by their diameters, which range 
from less than a nanometer to few nanometers. MWCNTs are formed from concentric 
SWCNTs with diameter increase in range from a few nanometers to a few tens of 
nanometers as shown in figure 1.2 [2].  
 
Figure 1.2 Structure of MWCNTs [2] 
 3  
CNFs are similar in structure to MWCNTs, but have much larger diameters ? on the 
order of hundreds of nanometers ? and are formed from graphene layers arranged as 
stacked cones, cups or plates instead of perfect cylinders. CNTs and CNFs are unique due 
to their electronic structure and versatile properties like high adsorption, high mechanical 
strength, high electrical and thermal conductivity and low reactivity. These characteristics 
of CNTs and CNFs can further be translated to secondary structures with applications [1] 
in near-field microscope probes, field-emission based devices, chemical sensors, catalyst 
supports, gas storage, super-capacitors, nano-electronics and multifunctional or high-
performance composite materials.  
 
1.1.2 Polymer-CNT/CNF Composites and their Applications 
Polymer nanocomposites based on CNTs and CNFs are gaining importance in the 
global market due to their diverse applications. For example, compelling needs such as 
reduction of system mass, system-failure risks, and system complexity, while 
simultaneously imparting spacecraft and mission reconfigurability are demanding the 
development of high-performance and multifunctional polymer nanocomposites. Ever 
since the first polymer-CNT composites have been reported by Ajayan et al [3] in 1994, 
their fabrication has been increasingly reported with enhancements in mechanical, 
electrical, thermal and rheological properties. Isotropically-enhanced nanostructured bulk 
composites and directionally-enhanced composite films have the potential for utilization 
as space mission-enabling materials and in the civilian space arena. In specific, they can 
be used as light-weight aerospace structural panels, thin-walled space structures, EMI 
shielding and radiation shielding materials. Furthermore, they can also be used in 
 4  
sporting goods, automotive parts, electrostatic paints and heat sinks for electrical and 
electronic components [2]. 
While CNTs have been the primary focus of laboratory-scale research into the 
potential for property improvement in polymer composites, the considerably less 
expensive CNFs ($50/g for CNTs, $500/Kg for CNFs) have been more desirable for 
commercial production of polymer composites. However, the properties that have been 
characterized for polymer-CNF composites have not been as good as the polymer-CNT 
composites (e.g., approximately an order of magnitude difference in filler loadings for 
electrical percolation threshold and tensile modulus). As a consequence, there has been 
an additional need to compare the processing-structure-property relationships between 
polymer nanocomposites containing CNTs and CNFs for different processes in order to 
realize the potential seen in laboratory-scale research. 
 
1.2 Motivation for Research 
In order to enhance the desired material properties for truly and comprehensively 
realizing the application potential, it is important to understand how the processing and 
formulation (i.e., choice of composition and ingredients) of the polymer-CNT/CNF 
composites affects the structure and associated properties of these nanocomposites. Since 
CNTs are very expensive, we will use them only for small quantities of material 
produced via solvent processing, while larger quantities of considerably less expensive 
CNFs will be studied in both solvent and twin screw extrusion (TSE) processing. It is 
essential to understand the effect of various processing parameters on the structure of the 
polymer nanocomposites that in turn govern their properties. Establishing such 
 5  
processing-structure-property relationships also provides avenues to engineer the 
properties of the material to suit the demands of the application.  
With the above factors in view, the focus of this research is to fabricate polymer-
CNT/CNF material system using two different processes, an established laboratory-scale 
solvent processing technique and a more scalable, commercial twin screw extrusion 
(TSE) technique, and to characterize the processing-structure-property relationships (see 
figure 1.3).  
 
Figure 1.3 The inter-relationship of processing-structure/microstructure-property 
 
Since a majority of the processing-related research that has been conducted on 
polymer nanocomposites has focused on just small quantities of material produced via 
solvent processing to determine structure-property relationships, it will be important to 
see how the differences in the batch nature of the solvent processing and the continuous 
nature of the TSE technique affect the structure-property aspect of the relationships. It is 
also possible to use the continuous nature of the TSE technique to produce 
nanocomposites that are compositionally graded for rapid characterization of structure-
Ingredients 
Polymers, 
Nanoscale 
fillers Structure Gradient 
Architecture 
Microstructure 
Dispersion, 
Adhesion 
Property/ 
Performance 
Electrical 
Conductivity,  
Mechanical 
Strength, 
Rheological 
Properties 
Process 
Parameters 
Screw 
Speed, 
Channel Fill 
etc. 
 6  
property relationships in a combinatorial material science approach. Using the structure 
and property characterization, it will be possible to develop models to explain the 
fundamental physics governing of the structure-property relationships. 
 
1.3 Research Objectives 
The following list provides a detailed set of objectives for this research with 
polystyrene (PS) as the model polymer matrix: 
? Establish procedures to fabricate PS-MWCNT/CNF composites using the solvent 
processing (batch process) and twin screw extrusion (continuous process) techniques 
for further comparison by characterization. 
? Study the processing-microstructure relationships for the solvent processed PS-
MWCNT composites, solvent processed PS-CNF composites, and extruded PS-CNF 
composites and compare when applicable.  
? Establish the following structure-property and processing-property relationships for 
the PS-MWCNT/CNF composites produced by extrusion, compare them with the 
solvent processed, and explain them with the processing-microstructure relationships: 
i. Characterize electrical percolation and model electrical conductivity as 
a function of composition. 
ii. Characterize rheological percolation and relate it to electrical 
percolation by modeling the storage and loss moduli of 
interpenetrating phase composites using degree of percolation. 
iii. Characterize the thermo-oxidative behavior as a function of 
composition and the processing technique. 
 7  
iv. Characterize the mechanical properties as a function of composition 
and extrusion processing parameters. 
v. Establish the relation between the evolution of electrical, rheological, 
thermo-oxidative and mechanical properties of the composites and 
their microstructure. 
? Develop a convolution process model based on previously developed mixing models 
and an in-situ measurement technique in order to predict the compositional gradient 
produced by transient addition of nanoscale fillers into a twin screw extruder, and 
compare the compositional gradients with a posteriori characterization. Thus, develop 
a new approach to establishing processing-structure-property relationships in polymer 
nanocomposites via combinatorial materials science. 
 
1.4 Dissertation Outline 
In the following chapters of this dissertation, the methods used to address the 
above objectives and the results obtained will be presented. Chapter 2 contains a review 
of the processes used for producing polymer nanocomposites. While providing a detailed 
review of the research conducted to establish and understand the processing-
microstructure and structure-property relationships, it also delineates the deficiencies in 
the processing-property and processing-structure relationships in various polymer 
nanocomposites systems. Chapter 3 describes the ingredients used in this work, their 
properties, and experimental methods used to process and characterize the structure, 
microstructure and properties of the polymer nanocomposites. Chapter 4 presents and 
discusses in detail the results obtained by characterizing, the structure, microstructure and 
 8  
material properties of the PS-MWCNT and PS-CNF composites in context of the various 
relationships presented in chapter 2. Finally, chapter 5 summarizes the scientific and 
technical contributions of this work and presents the research issues that have potential 
for future investigation. 
 
 9  
2. Literature Review 
 
 
2.1 Polymer Nanocomposites : Processing 
Several processing methods are available for producing polymer nanocomposites, 
with both thermoplastic or thermoset polymer matrices and nanoscale fillers. Although 
the techniques are inherently different, all of them try to address issues such as 
deagglomeration of filler bundles and ropes, dispersion and alignment of the individual 
filler particles, and interfacial adhesion between the polymer matrix and the filler that 
directly affect the composite properties [4,5]. Similar to other nanoscale fillers, the 
effective utilization of CNTs and CNFs in composite applications depends strongly on 
the ability to disperse the CNTs individually and uniformly throughout the matrix without 
destroying their integrity or reducing their aspect ratio [6]. Furthermore, good interfacial 
bonding is required to achieve load transfer across the polymer-CNT/CNF interface [7]. 
Finally, the 3D architecture will determine the properties ? for example, skeleton-like for 
percolation, or well-aligned for high strength [8]. The three most common techniques ? 
solvent processing, melt mixing, and in situ polymerization are discussed in detail. 
However, new techniques, pre and post-processing techniques and combination of 
techniques have also been utilized. 
 
2.1.1 Solvent processing 
Solvent processing (also called solution blending) provides an advantage through 
low viscosities, which facilitate mixing and dispersion of the CNTs/CNFs. Solvent 
processing involves three major steps: (1) dispersing the CNTs/CNFs in a suitable 
 10  
solvent, (2) mixing with the polymer (at room temperature or elevated temperature), and 
(3) recovering the composite. There have been several variations of these three major 
steps to obtain the composite in the desired manner. For example, Du et al. [10] 
developed a versatile coagulation method that involves sonication of SWCNTs followed 
by mixing and stirring with poly-(methyl methacrylate) (PMMA) solution, and pouring 
the PMMA-SWCNT suspension into an excess of non-solvent to recover the composite. 
The precipitating polymer chains entrap the SWCNTs, thereby preventing the SWCNTs 
from bundling. A variant of recovering the composite is precipitation by cooling. This 
method has also been adapted to polyethylene (PE), where the PE-SWCNT suspension is 
heated to promote polymer solubility and then cooled to accomplish the precipitation 
[10]. When using solvent processing, CNTs/CNFs tend to agglomerate during slow 
solvent evaporation, leading to inhomogeneous distribution of the CNTs in the polymer 
matrix. The evaporation time was reduced by placing the polymer-CNT suspension on a 
rotating substrate (spin-casting) [11] or dropping the polymer-CNT suspension on a hot 
substrate (drop-casting) [12]. Many studies have used solvent processing with both 
thermoset and thermoplastic polymers. Biercuk et al. [13] dissolved epoxy in a well-
dispersed, ultrasonicated SWCNT suspension. The solvent was evaporated, and the 
epoxy was subsequently cured to form a nanocomposite. Safadi et al. [14] and Watts et 
al. [15] added MWCNTs to a solution of PS dissolved in toluene, and made composites 
both by film-casting and spin-casting. Aqueous solutions may also be used, depending on 
the polymer. An aqueous poly(vinyl alcohol) (PVA) solution was mixed with an 
electrostatically stabilized dispersion of CNTs in water, and was subsequently casted to 
form a composite film [16].  Qian et al. [17] made use of a simple solvent evaporation 
 11  
method assisted by high energy sonication to prepare polystyrene PS-MWCNT 
composite films. Solvent processing of polymer-CNF composites is not uncommon. For 
example, Yang et al [18] and zhang et al [19] prepared PS-CNF composites using toluene 
by sonication and magnetic stirring. In summary, solvent processing is a simple, yet 
versatile lab scale, batch process for preparing the polymer-CNT/CNF composites. 
 
2.1.2 Melt mixing 
Melt mixing of CNTs/CNFs with thermoplastic polymers using conventional 
processing techniques, such as extrusion, internal mixing, injection molding and blow 
molding, is particularly desirable, because of the speed and availability of these processes 
in the plastics industry. Nevertheless, there is still much to be learnt about the ability of 
CNTs/CNFs to withstand high magnitude of shear rates in the elongational flows and 
simultaneously about the optimal processing parameters that can provide isotropic 
dispersion of CNTs/CNFs. The widely used extrusion compounding is still the most 
convenient melt mixing technique and practical way to prepare filled polymer composites 
when nanoscale fillers are considered to replace microscale fillers for high-performance 
materials. However, mixing the nanoscale fillers with the polymer melt is more difficult 
than that of microscale fillers due to their strong tendency to agglomerate.  
Ferguson et al. [9] used a Buss Kneader for initial compounding, followed by 
injection molding to prepare composites of CNTs with various thermoplastics. Sandler et 
al. [4] dispersed MWCNTs in an epoxy by high speed stirring (2000 rpm) using a 
dissolver disk for 1 hour. They also investigated the effect of increased shear force by 
decreased the temperature of processing, thereby increasing the resin viscosity. Sennet et 
 12  
al. [20] and Potschke et al. [21] in two different work compounded polycarbonate (PC) 
with MWCNTs in a DACA co-rotating, intermeshing, conical twin screw 
microcompounder at 50-80 rpm with 250-265oC to investigate the affect of draw rate on 
the microstructure and properties of the composites. Mahfuz et al. [22] dry mixed Nylon6 
and MWCNTs and extruded in a single screw extruder and heat stabilized to form 
continuously drawn composite filaments. Kashiwagi et al. [23] prepared of MWCNTs 
with polypropylene (PP) composites in a Haake Polylab shear mixer at a temperature of 
190oC and screw speed of 20 rpm by mixing for 30 min to investigate the thermal 
stability and flame retardancy. Melt mixing of polymer-CNF composites to study the 
properties and microstructure was also extensively reported in literature. For example, 
small quantities of premixed PP and CNFs were fed to Haake Rheocord 90 twin screw 
extruder and extruded at a screw speed of 20 rpm followed by pelletization and fiber 
spinning [24] to study the morphology and mechanical properties of the composites. 
Andrews et al. [6] conducted an extensive study to investigate the microstructure, 
electrical, rheological and mechanical properties of composites of PS, PP, acrylonitrile-
butadiene-styrene (ABS) with MWCNTs and CNFs by processing them using a Haake 
Polylab shear mixer. In summary, unlike solvent processing, melt mixing is beneficial 
because it is free of solvents, which could possibly act as contaminants at the polymer-
filler interfaces. 
 
2.1.3 In situ polymerization 
In situ polymerization aims at bottom up synthesis of the entire composite 
structure by mixing the monomer and the nanoscale filler followed by polymerization. It 
 13  
is a method used for improving dispersion by better integration between the phases [18]. 
The main advantage is that reinforcement is obtained on a molecular scale. Tang and Xu 
[25] synthesized poly(phenylacetylene)-wrapped carbon nanotubes (PPA-CNTs), which 
were soluble in organic solvents, such as tetrahydrofuran, toluene, chloroform and 1,4-
dioxane. Fan et al. [26] synthesized conducting polypyrrole-coated carbon nanotubes 
(PPY-CNTs), and found that the magnetization of the composites is the sum of the two 
components, PPY and CNTs. Usually, most in situ polymerization works to prepare 
polymer composites are conducted in conjunction with pre and post-processing 
techniques. 
 
2.1.4 Other methods 
A combination of the above methods have also been used, along with pre and 
post-processing techniques, like purification, chemical treatment using surfactants, 
compatibilizers etc. Xie et al. [27] prepared PP-CNT composites compatibilized with 
maleic anhydride grafted styrene?(ethylene-co-butylene)?styrene copolymer by using a 
combination of ball milling and melt mixing. Jin et al. [28] coated MWCNTs by 
poly(vinylidene fluoride) (PVDF) and then melt-blended with PMMA. PVDF was found 
to be a compatibilizer that assists dispersion of MWCNTs in PMMA and served as an 
adhesive to increase their interfacial bond strength, hence greatly improving the 
mechanical properties of PMMA-MWCNT composites. Additionally, surfactants can be 
used as dispersing agents to improve the dispersion of CNTs in processing polymer-CNT 
composites. Gong et al. [29] used a non-ionic surfactant, polyoxyethylene-8-lauryl, as a 
processing aid for epoxy-CNT composites due to the strong interactions between carbon 
 14  
of CNTs and the hydrophobic segment of the surfactant via van der Waals forces, as well 
as epoxy and the hydrophilic segment of the surfactant via hydrogen bonding. The 
homogeneous dispersion of CNTs in epoxy improved the thermomechanical properties of 
the composites. Haggenmueller et al. [30] used a combination of solvent casting and melt 
mixing to disperse up to 8 wt.% SWCNTs in PMMA. Solvent cast composite film was 
broken into pieces and hot pressed into new films, which were again broken into smaller 
fragments and pressed again. This procedure was repeated as many as 25 times. The 
dispersion was found to improve as the number of steps was increased, with some of the 
films showing increased electrical conductivity. In summary, although the property 
enhancement observed with the combination of various methods, or with pre and post-
processing techniques is higher, the difficulty and time involved in processing makes 
them unsuitable for large-scale, continuous production. 
 
2.2 Processing ? Microstructure Relationships 
The influence of processing on the evolution of various aspects of microstructure, 
such as distribution, dispersion, alignment, agglomeration etc., was studied in great detail 
over the past decade with the availability of new and improved nanoscale characterization 
techniques.  
Du et al. [10] characterized the PMMA-SWCNT composites using optical 
microscopy and Raman imaging. They concluded that a macroscopic good dispersion is 
obtained when wet SWCNTs are used and macroscopic phase separation can be seen 
when dry SWCNTs are used. Furthermore, using scanning electron microscopy (SEM), at 
a 2 wt.% loading of SWCNTs in PMMA, they reported a filler network that impeded the 
 15  
motion of SWCNTs past one another. Sandler et al. [31] prepared well dispersed CNFs 
(see figure 2.1) in a thermoplastic poly(ether ether ketone) (PEEK) matrix via TSE at a 
loading of 15 wt.%.  
 
Figure 2.1 An SEM image showing an isotropic dispersion of CNFs in PEEK matrix at 
15 wt.% loading [31]. 
 
They reported that high intrinsic viscosity of thermoplastic matrices in general, has the 
dual advantage of increasing the shear applied to the aggregates (even breaking the 
individual CNTs/CNFs) and minimizing the opportunity for reaggregation. However, 
even extensive TSE does not lead to a complete break-up of the entanglements in 
commercially available catalytically-grown MWCNTs [32-34]; nanotube clusters were 
observed even at low filler loadings. Prolonged mixing times lead to an improved 
distribution of nanotube aggregates [33]. In contrast, nanotube weight fractions of up to 
30 wt.% of arc-grown as well as of CVD-grown MWCNTs were shown to disperse in 
PMMA [35] and PS [36] matrices, and the use of aligned, rather than entangled 
nanotubes, also appears to be advantageous [37]. Although filler dispersion can be aided 
 16  
by ball milling of the raw filler material prior to processing [38], this approach degrades 
the aspect ratio of individual particles significantly more than shear-intensive melt 
processing [39]. 
Processing of compounds under conditions involving both shear and elongational 
flows, such as injection-molding, can be used to induce alignment of the nanofiller [40]. 
Similarly, Kuriger et al. showed that flow-induced nanofiber alignment occurred during 
extrusion [39]; the degree of nanofiber alignment was improved by optimization of the 
extruder die geometry. Keeping the extruded strand under tension minimized die swell 
effects and the orientation of the filler was maintained. However, a decreasing degree of 
alignment with increasing nanofiber content was observed, most likely as a result of 
nanofiber-nanofiber interactions altering the flow field [39]. Similarly, drawing of 
composite extrudate was shown to induce significant nanotube alignment [36,20,41] (see 
figure 2.2) as did mechanical stretching of solid nanocomposites above the glass 
transition temperature [42,43], spin-casting of nanotube-polymer solutions [14], and the 
application of magnetic fields during in-situ polymerization [44]. 
In summary, although processing-microstructure relationships have been 
extensively studied in polymer nanocomposites, and there will continue to be a need for 
constantly studying them since they form the fundamental link between optimizing the 
processing parameters and realizing enhanced material properties through engineered 
microstructures. In specific, it would be very beneficial to compare the microstructure 
resulting from different processes for the same ingredients because it would assist in 
determining the appropriate process for preparing the material with the desired 
performance. 
 17  
 
Figure 2.2 A TEM image showing alignment of MWCNTs in PC matrix at high draw 
down ratios [41]. 
 
 
2.3 Structure ? Property Relationships 
2.3.1 Electrical Properties 
The electrical properties of the polymer composites are significantly higher than 
those of the neat polymer due to the excellent electrical properties and high aspect ratios 
of CNTs/CNFs. Composites containing conducting fillers in insulating polymers become 
electrically conductive when the filler content exceeds a critical value, known as a 
percolation threshold. The percolation threshold is characterized by a sharp jump in the 
conductivity by many orders of magnitude which is attributed to the formation of a three-
dimensional conductive network of the fillers within the matrix. The percolation 
threshold is typically determined by plotting the electrical conductivity as a function of 
the weight or volume fraction of nanotubes and fitting with a power law function (see 
 18  
figure 2.3). The high aspect ratios of the CNTs/CNFs allow them to form a conductive 
filler network at low loading, thereby resulting in a low percolation threshold. A wide 
range of values have been reported for percolation threshold and plateau conductivity of 
polymer-CNT/CNF composites, depending on the processing method, polymer matrix 
and nanotube type. A significant uncertainty in the results stems from the reports of 
percolation threshold in terms of volume fraction because the determination of the true 
volume fraction of the filler in the composites is not straightforward.  
Bai et al [45] found more than an 8-fold decrease in the threshold loading in 
epoxy-MWCNT composites when the MWCNT length was increased from 1 to 50 ?m. 
Well-dispersed nanotubes generally have higher aspect ratios than nanotube aggregates, 
so the percolation threshold decreases with better dispersion. Counter examples include 
work by Bryning et al. [46] where slight aggregation produces a lower percolation 
threshold by increasing the local interactions between nanotubes. When the nanotubes are 
highly aligned in the composites, there are fewer contacts between the tubes, which 
results in a reduction in electrical conductivity and a higher percolation threshold as 
compared to those in a composite with randomly oriented nanotubes. This topic has been 
extensively studied by Du et al. [47] using a series of PMMA-SWCNT composites where 
the degree of nanotube alignment was controlled by the melt fiber spinning conditions 
and quantified with the full width at half-maximum (FWHM) of the SWNT form factor 
scattering, where higher FWHM correspond to less SWNT alignment. Similar 
observations were made by other researchers [36,20,41] too. 
 19  
 
Figure 2.3 Establishing the percolation threshold through power law fits of electrical 
conductivity as function of weight fraction [48]. 
 
The percolation threshold reported for composites of polymer-CNF composites 
was usually higher than that of polymer-CNT composites. For example, Lozano et al [49] 
and Gordeyev et al [50] prepared PP-CNF composites via melt mixing and reported the 
percolation threshold to be 9 wt.% and 5 vol.% respectively.  
 
2.3.2 Rheological Properties 
The viscoelastic properties of polymer-CNT/CNF composites have both practical 
importance related to composite processing and scientific importance as a probe of the 
 20  
composite dynamics and microstructure. Figure 2.4 shows the typical response of storage 
modulus (G?) as a function of frequency for a polymer-CNT/CNF composite with good 
nanotube dispersion [51]. At high frequencies, the response is not sensitive to the filler 
loading, indicating that the short-range polymer dynamics are not influenced by the filler. 
At low frequencies, the rheological behavior progresses from a liquid-like response to a 
solid-like response (G? independent of w) as the filler loading increases. Similar, but less 
predominant trends are typical of loss modulus (G?). Applying a power law function to 
the appropriate rheological parameter as a function of the filler loading provides a 
rheological percolation threshold corresponding to the onset of solid-like behavior. 
 
Figure 2.4 Storage modulus vs frequency for PMMA-SWNT composites [51]. 
 
Potschke et al. [21] found that the rheological percolation threshold is strongly 
dependent on temperature. In their PC-MWCNT composite, the percolation threshold 
decreased from 5 to 0.5 wt % MWCNT upon increasing temperature from 170 to 280 ?C. 
They suggest that the superposition of the entangled polymer network and the combined 
nanotube-polymer network rather than the nanotube network alone dominates the 
 21  
rheological properties. In fact, in a set of PMMA-SWCNT composites, Du et al. [10] 
found that the rheological percolation threshold, 0.12 wt %, was smaller than the 
percolation threshold for electrical conductivity, 0.39 wt.%. In contrast, Wu et al. [52] 
reported that the rheological and electrical percolation thresholds are not significantly 
different from one another. 
 
2.3.3 Thermo-oxidative Properties 
The thermo-oxidative properties of the polymer-CNT/CNF composites have been 
studied to mainly identify their thermal stability and the changes imposed by the presence 
of CNTs/CNFs on the polymer phase. Mahfuz et al. [22] reported that the thermal 
decomposition temperature of composites of Nylon with very low mass fraction of 
MWCNTs is significantly higher than the neat Nylon. Furthermore, they also reported 
similar behavior in various other nanoparticle reinforced polymers [53,54]. Xu et al. [55] 
conducted a thorough work on the thermo-oxidative behavior of PS-CNF composites and 
concluded that temperature at peak weight loss rate increases more significantly at lower 
loadings than higher loadings of CNFs when compared with the neat PS. They also 
reported that the CNFs in the nanocomposites decompose at a lower temperature 
compared to the pristine CNFs. Chatterjee et al. [56] studied the thermal and thermo-
oxidative behavior of PP-CNF composites in nitrogen and air respectively. They reported 
that the degree of enhancement in thermal stability of the composites compared to the 
neat PP is more prominent in the presence of air, possibly due to the formation of a char 
layer that acts as a physical barrier between the uncombusted polymer and combustion 
zone. Similar observations about the increase in the thermal stability of the PP-CNF 
 22  
[57,58] and polyol-CNF composites were reported in literature and they were attributed 
to the restriction in the mobility of the macromolecules imposed by the CNFs. In contrast, 
a few reports on epoxy-CNF composites in literature indicate either no influence [59] on 
or a slight decrease [60] in the thermal stability with increasing CNF loading.  
 
2.3.4 Mechanical Properties 
The strength of discontinuously-reinforced composites typically depend on two 
structural characteristics: interfacial adhesion and dispersion. First, there should be a 
high degree of load transfer between the matrix and the discontinuous reinforcement such 
as the nanoscale fillers. When the interfacial adhesion between the phases is weak, the 
nanoscale fillers behave as holes or nanostructured flaws, inducing local stress 
concentrations and reducing the transfer of the CNT/CNF properties to the matrix 
material. Second, the CNTs and CNFs should be well dispersed. If poorly dispersed, the 
CNTs/CNFs will fail by separation of the bundle rather than by failure of the individual 
CNTs/CNFs themselves.  This may result in significantly reduced strength. 
The outstanding potential of the SWCNTs to adhere to polymer matrices has been 
evident from the super tough composite fibers fabricated by Dalton et al. [61]. By 
optimizing the coagulation spinning method, they spun several hundred meters of 
composite fibers of PVA-SWCNT composites at 60 wt. % loading, which had a tensile 
strength of 1.8 GPa, comparable to that of a spider silk. Wagner et al [62] found that the 
average interfacial stress required to remove a single MWCNT from the 
polyethylenebutene matrix is 47 MPa, which is about 10 times larger than the adhesion 
level between the same type of polymer and CNFs; this example demonstrates the 
 23  
importance of filler size on the interfacial strength. It suggests a good bonding between 
CNTs and polymer matrix. Therefore, efforts are underway to better understand the 
mechanism of interfacial adhesion at the molecular level to further optimize the interface 
in nanocomposite systems. 
To date, the main challenges have been to improve the dispersion of CNTs/CNFs 
in a polymer matrix when processing these nanocomposites. To maximize the advantage 
of CNTs/CNFs as effective reinforcements in high strength composites, they should not 
form aggregates and must be well dispersed to prevent slippage. However, the problem is 
that CNTs/CNFs easily agglomerate, bundling together and entangling, leading to many 
defect sites in the composites, and limiting the efficiency of CNTs/CNFs on polymer 
matrices. Salvetat et al. [63] studied the effect of dispersion of CNTs on the mechanical 
properties of polymer-CNT composites, and found that poor dispersion and rope-like 
entanglement of CNTs led to drastic weakening of the composites.  
To enhance the dispersion and improve mechanical properties, Gong et al. [29] 
used a non-ionic surfactant, polyoxyethylene-8-lauryl, and showed that with only 1 wt.% 
CNTs in the epoxy-CNT composites the elastic modulus increased by over 30%. Adding 
1 wt.% MWCNTs in the PS-MWCNT composite films by the solvent processing, results 
in 36% and 25% improvements in tensile modulus and break stress, respectively. 
Andrews et al. [6] prepared drawn isotropic petroleum pitch-SWCNT composite fibers 
with 5 wt.% SWCNTs. The tensile strength, modulus and electrical conductivity of these 
pitch composite fibers are enhanced by ~90, ~150 and ~340%, respectively, due to the 
orientation of the SWCNTs. In general, the stiffening effect of CNTs/CNFs appears to be 
more prominent in semicrystalline rather than amorphous thermoplastics, possibly due to 
 24  
the nucleation effects [31]. Although a linearly increasingly composite stiffness has been 
observed up to 15 wt.% of nanofibres [40], in many cases, a non-linear relationship is 
observed with increasing filler loading fraction. 
While there has been much effort to understand and control the adhesion and 
dispersion of CNTs/CNFs in polymer matrices, there are still a wide range of 
improvements in mechanical properties being reported in the literature. Safadi et al. [14] 
found that at less than 1 vol.% of MWCNTs, there is a 40% increase in strength of PS-
MWCNT composites. The modulus improved by a factor of 2 with respect to the neat 
polymer when 2.49 vol.% of CNTs were added. Tibbetts et al. [38] indicated that the 
addition of CNFs to a PP matrix had no effect on tensile strength, probably because of the 
increased brittleness of the polymer matrix, which resulted from PP?s inability to further 
crystallize on deformation, a behavior due to the molecular restrictions caused by the 
fiber dispersion. At 5 wt.% CNF loading, modulus and compressive strength of the spun 
PP increased by 50% and 100%, respectively. Comparable loading fractions of 
MWCNTs, rather than CNFs, in both solution-cast [14,17] and extruded PS films, 
produced a more pronounced stiffness enhancement, indicating that the crystalline quality 
of the nanoscale filler contributes to the overall performance of the nanocomposite. 
Similarly, comparisons of different types of filler in PA-12 composite fibres showed that 
well-dispersed CNTs produce a greater improvement in stiffness than CNFs, but that the 
type of nanotube also has an effect [37]. In addition, a direct comparison of aligned 
versus unoriented nanotubes showed a significant enhancement of the composite stiffness 
for the aligned nanotubes [36]. 
 25  
In summary, none of the polymer-CNT/CNF composites fabricated so far at low 
filler loadings demonstrated enormous increases in mechanical properties. Thus, in order 
to truly realize high performance composites using these nanoscale fillers, it is important 
to understand the fundamental reinforcement mechanisms via the structure-property 
relationships. Eitan et al [64] present a thorough micromechanics model of the polymer-
CNT/CNF composites suggesting that the high performance composites are possible only 
at high filler loadings. 
 
2.4 Processing ? Property Relationships 
Most of the polymer nanocomposites works reported in literature, some of which 
are reviewed in 2.1-2.3, were processed by a specific technique to establish the 
processing-microstructure and the structure-property relationships, without much 
emphasis on investigating the processing-property relationships, i.e., influence of the type 
of process or processing parameters on the resulting properties. In novel material 
development, establishing the processing-property relationships is as important as 
establishing the processing-microstructure and structure-property relationships. There 
have been very few investigations, however, that attempted to address the processing-
property relationships. Andrews et al. [6] compared the polymer-MWCNT composites 
that were processed by simple shear mixing with bench-scale extrusion and observed that 
extrusion aligns the MWCNTs, thereby increasing the electrical percolation threshold by 
at least an order of magnitude. Potschke et al [41] observed a similar decrease in 
electrical conductivity of extruded PC-MWCNT composites due to alignment at high 
draw down ratios. Furthermore, they reported a slight increase in the Young?s modulus 
 26  
and a slight decrease in % elongation to failure of the PC-MWCNT composites at high 
draw down ratios. However, they also report that similar behavior was observed in neat 
PC, thereby indicating that the observed property differences are mainly due to change in 
the microstructure of neat PC. Gallant et al. [65] quantitatively studied the burning rate in 
energetic microcomposites as a function of the screw speed and the screw design. Huang 
at al [66] prepared polydimethyloxane-MWCNT composites using a simple shear mixer 
and investigated the rheological properties of the composites as function of the mixing 
time. They reported that the viscosity of the composites exhibits an erratic behavior until 
a characteristic mixing time is reached when the dispersion of the MWCNTs in 
polydimethyloxane is reproducibly uniform. They claimed that the characteristic time, 
which is specific to each process, should be such that total energy supplied should be 
higher than van der Waals forces of attraction, which were reported to be ~10-4 J/m3. In 
summary, there is a significant need for thoroughly investigating the processing-property 
relationships of polymer nanocomposites. 
 
2.5 Processing ? Structure Relationships: Extruded Polymer 
Composites 
 
Conventional batch approaches to characterize the processing-structure-property 
relationships in polymer nanocomposites can be very time consuming. Approaches based 
on combinatorial materials science allow rapid characterization of both processing-
structure and structure-property relationships. The following sections provide a review of 
the research conducted to rapidly characterize compositional gradients (i.e., structure) via 
combinatorial approaches, especially suited to extrusion. 
 
 27  
2.5.1 Compositional Gradients for a Combinatorial Approach 
TSE process is ideally suited for producing continuous compositional gradients 
[31]. Operating a twin screw extruder at one steady condition and dynamically changing 
the ingredient input proportions to produce a new formulation results in the extrudate 
changing from the original composition to a second one. Due to the inherent back mixing 
in the extruder, an abrupt change in ingredient addition results in a more gradual change 
in the composition of the extrudate. In this way, the continuous nature of the process is 
especially well suited to combinatorially [67-69] produce polymer nanocomposites. In 
contrast, the batch process is incapable of producing a smooth continuous transition. It is 
also be possible to vary the screw configuration of the extruder to alter and optimize the 
characteristics of the gradient architecture. 
Gilman et al [31,70,71] produced extruded composites of Nylon6 or PS and 
purified organo-clay filler with specific emphasis on the combinatorial nature of the 
compositional gradients (CGs). They indicated that a single experiment can provide 
samples for in situ or a posteriori characterization over the entire compositional domain 
of interest. This significantly reduces the batch-to-batch variation and the time consumed 
in producing the samples at various compositions. Eidelman et al [72] produced thin film 
CGs of poly (L-lactic acid) with poly (D,L-lactic acid) using a three syringe pump 
system. Potyrailo et al [73] used a combinatorial extrusion system to generate polymeric 
CGs with two different material systems ? PP with model additives and PC with titanium 
dioxide filler. However, in order to develop the combinatorial approach the CGs should 
not only be produced, but also rapidly characterized. Eidelman et al. [72] developed an 
elaborate fourier transform infrared microspectroscopy technique that monitors the 
 28  
reflection-transmission spectra to obtain the composition. Potyrailo et al. [73] 
characterized the CGs in situ by using an optical probe signal that tracks the changes in 
color of the blend. However, all of the non-destructive in situ characterization approaches 
developed so far with optical probes are limited to low loadings of the filler in the 
composite. At higher loadings, especially of dark colored fillers, the optical probes tend 
to reach their saturation, i.e., detection limit. Furthermore, most of the prior works 
conducted to rapidly determine the CGs require a pre-calibration of the technique with 
known composition, thereby decoupling the processing from the evolution of the CG 
(i.e., structure).  
In order to rapidly characterize such CGs, the effect of the transient variations in 
the ingredients and the operating conditions for a given screw configuration must be 
modeled i.e., the processing-structure relationship has to be established. Typically, the 
compositional variation in a graded composite can be described using a power law 
relation as follows: 
      V=(x/t)p     (2.1) 
where V is the volume fraction of one phase, x is the distance along the graded region 
(known as the interlayer), t is the thickness of the interlayer, and p is the gradient 
exponent. However, it does not give a complete description of processing-structure 
relationship. In order to establish the processing-structure relationship, it is necessary to 
understand the mixing characteristics in the twin screw extruder. 
 
 
 
 29  
2.5.2 Residence Distributions as Measures of Mixing 
Since the flow in the extruder is highly non ideal due to channeling, back-mixing 
and stagnation, obtaining a complete knowledge of the flow patterns that govern mixing 
is impractical [74]. Conventionally, mixing in extruders is understood via residence time 
distribution (RTD), which is a measure of the how long the material takes to pass a given 
point [75]. The corresponding concept in the volume domain is called a residence volume 
distribution (RVD), i.e., it is a measure of the volume of the material that passes a given 
point. These distributions are typically expressed as normalized functions of time and 
volume in the following forms: 
    ( )( )
??
=
0
)(
dttf
tftf     (2.2)  
??
=
0
)(
)()(
dvvg
vgvg     (2.3) 
where,           Qtv ?=      (2.4) 
and )(tf  is the normalized RTD, )(vg  is the normalized RVD, Q is the throughput, t is 
time, v is volume, and f and g are the response functions associated with the amount of 
material that passes a given point in the extruder at the time, t, or along with a volume, v. 
In an earlier experimental work, Elkouss et al [76] confirmed that in an extruder with a 
fixed screw design, in spite of varying the polymer flow rates and extruder screw speeds, 
all the normalized RVDs superimpose (see figure 2.5) to form a single master curve, as 
long as the elastic effects were not predominant.  
 30  
 
(a) 
 
(b) 
Figure 2.5 The (a) RTDs, and (b) RVDs at varying operating conditions. Note that the 
RVDs overlap, while the RTDs do not overlap [76]. 
 
This indicates that as long as the Weissenberg number is less than one, the normalized 
RVD can be used as a characteristic of the process that is independent of processing 
conditions. 
 
 31  
3. Experimental Methods 
  
The ingredients, equipment and procedures used for processing and characterization 
of polymer composites are explained in the following sections. 
 
3.1 Ingredients 
There are three kinds of ingredients utilized in this research investigation: (1) 
polymer matrix, (2) fillers, and (3) solvents. Impact modified Polystyrene was chosen as 
the polymer matrix material because it is a regular commodity plastic that can easily be 
processed using both solvent processing and extrusion. The nanoscale fillers, multi-
walled carbon nanotubes and carbon nanofibers, were the primary motivation for this 
research investigation. An inexpensive, microscale filler, potassium chloride, was used to 
check the validity of the combinatorial approach developed across various size scales. 
Two different solvents, tetra-hydro furan and di-methyl formamide, were chosen because 
their potential for dissolving PS and dispersing the fillers. 
 
3.1.1 Polymer Matrix 
The impact modified Polystyrene (PS) (molecular weight ~ 150,000, 
polydispersity ~ 2.73) was obtained from Nova Chemicals Inc. It is a copolymer of 
styrene and butadiene and is used primarily in toys and product casings. While the 
styrene-rich phase provides the stiffness, the butadiene-rich phase provides the toughness, 
thereby improving its impact strength. The ease of processing with no pre-drying 
requirements makes PS a good model material for studying the processing-structure-
 32  
property relationships in polymer-CNT/CNF composites. The following is a list of 
properties of PS as provided by the manufacturer: 
 
  
 
3.1.2 Fillers 
3.1.2.1 Graphitized Multiwalled Carbon Nanotubes 
The graphitized Multiwalled CNTs (MWCNTs) were obtained from the 
University of Kentucky. The MWCNTs were vapor grown through the catalytic 
decomposition of a ferrocene?xylene mixture at 675?C in a quartz tube reactor and over 
quartz substrates, with a conversion of 25% of the total hydrocarbon feedstock [77]. The 
MWCNTs were further purified by annealing at 3000?C, i.e., graphitized, to remove the 
catalyst particles and microstructural defects as well as increase the thermal stability of 
the MWCNTs [78,79].  The manufacturer did not provide the properties, however some 
general characteristics of MWCNTs are as follows [1]: 
PS (Polystyrene,(C8H8C4H6)X) 
Vicat Softening Temperature: 91 C 
Electrical Conductivity: 10-20 S/m 
Specific Gravity: 1.04 
Recommended Melt Temperature: 190-230 C 
Thermal Decomposition Temperature: ~250 C 
Tensile Modulus: 2.0 GPa 
Tensile Strength:  16 MPa 
Elongation to failure: 15% 
 33  
MWCNT 
Diameter: 10-50 nm 
Length: 5-10 micrometer 
Tensile Modulus: 3-30 GPa for defective MWCNTs from a CVD process, 
and 1 TPa for defect-free MWCNTs from an electric arc process. 
Cost: $50,000/Kg 
 
The as-received MWCNTs were characterized using a scanning electron microscope 
(SEM) as shown in figures 3.1-3.3. The as-received MWCNTs were significantly 
agglomerated (~100 ?m). This can be expected due to the high van der Waals attractions 
in nanoscale fillers due to their high surface area. This is especially true with MWCNTs 
due to the delocalized electron cloud on their surface that allows induced dipoles easily. 
 
Figure 3.1 Scanning electron micrograph showing the as-received MWCNTs with large 
agglomerations. 
 34  
 
Figure 3.2 Scanning electron micrograph showing a single agglomerate of MWCNTs. 
 
 
 
 
Figure 3.3 Scanning electron micrograph showing the individual MWCNTs, which are 
tens of nanometers in diameter. 
 
The MWCNTs were also characterized using the x-ray fluorescence spectroscopy to 
study the elemental composition. Figure 3.4 below shows the spectrum of MWCNTs with 
 35  
the sample holder and figure 3.5 shows the spectrum of the sample holder only. 
Comparing the two images, it can be concluded that the sample does not contain any 
contaminants. 
 
Figure 3.4 Spectrum of MWCNTs on the sample holder. 
 
 
Figure 3.5 Spectrum of the sample holder only. 
 
 36  
Furthermore, the MWCNTs were characterized using Raman spectrometry to study the 
nature of chemical bonding (see figure 3.6). Typically, single-wall carbon nanotubes 
(SWCNTs) consist of three major types of Raman bands: the low frequency bands around 
160 ? 200 cm-1, intense peaks around 1500 ? 1600 cm-1, and bands around 1350 cm-1, 
which are due to defects in the nanotubes. Figure 3.7 shows the typical Raman spectra of 
graphite powder with a more intense peak around 2570 cm-1 and less intense peaks at 
1278 ? 1291 cm-1 and 1591 ? 1600 cm-1. Thus figure 3.6 indicates that the MWCNTs 
show the low frequency bands similar to SWCNTs and that the MWCNTs show strong 
indications of graphitization. Furthermore, the presence of several other peaks indicates 
that the MWCNTs may contain a few gross defects that were not removed upon 
graphitization. 
 
1285.41
1595.13
1811.94
1925.512028.75
2581.09
2870.17
2797.9
50010001500200025003000
Wavenumber cm-1
0.0
00
0.0
02
0.0
04
0.0
06
0.0
08
0.0
10
0.0
12
Ra
ma
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en
sit
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0.0
08
0.0
10
0.0
12
Ra
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en
sit
y
 
Figure 3.6 Raman spectra of MWCNTs shows that they are graphitized. 
 37  
2571.66
1595.40 1285.85
050010001500200025003000
Wavenumber cm-1
0.0
00
0.0
01
0.0
02
0.0
03
0.0
04
Ra
ma
n I
nt
en
sit
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0.0
00
0.0
01
0.0
02
0.0
03
0.0
04
Ra
ma
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en
sit
y
 
Figure 3.7 Raman spectra of graphite powder. 
 
3.1.2.2 Pyrograf III Carbon Nanofibers 
The Pyrograf?-III Carbon Nanofibers (CNFs) were obtained from Applied 
Sciences Inc.  The CNFs were vapor grown to be much smaller than the conventional 
continuous or milled carbon fibers (~10 ?m), but significantly larger than MWCNTs 
(~10 nm). Furthermore, the CNFs obtained were heat treated to remove the aromatics and 
partially organize the non-graphitic carbon. However, they still contain little quantities of 
iron catalyst and amorphous CVD carbon. CNFs are more affordable than the MWCNTs, 
and hence better suited for process development. The following is a list of properties and 
cost of the CNFs as provided by the manufacturer: 
 
 
 
 38  
CNF 
Diameter: 100-200 nm 
Length: 5-10 ?m 
Cost: $500/Kg 
 
The CNFs received were characterized using a scanning electron microscope (see figures 
3.8-3.11). Similar to the MWCNTs, it was observed that the as-received CNFs were 
significantly agglomerated (~100 ?m).  
 
Figure 3.8 Scanning electron micrograph showing the as-received CNFs. Note that most 
of the agglomerates are several tens of microns. 
 39  
 
Figure 3.9 The as-received CNF agglomerates at a higher magnification. 
 
 
 
 
 
Figure 3.10 The diameter of the as-received CNFs is on the order of 100micrometer. 
 
 40  
 
Figure 3.11 The as-received CNFs at a higher magnification. 
 
The CNFs were also characterized using the x-ray fluorescence spectroscopy to study the 
elemental composition. Figure 3.12 shows the spectrum of CNFs with the sample holder 
and figure 3.13 shows the spectrum of the sample holder only. Comparing the two 
spectra, it can be concluded that the sample does not contain copper, but contains iron, 
which is the catalyst used during the synthesis. 
 
Figure 3.12 Spectrum of the CNFs with the sample holder 
 41  
 
Figure 3.13 Spectrum of the sample holder only. 
 
Furthermore, the CNFs were characterized using Raman spectrometry to study the nature 
of chemical bonding. The CNFs exhibited several peaks uncharacteristic of the 
MWCNTs indicating that they are significantly different in nature (see figure 3.14). This 
could be possibly due to the existence of several microstructural defects in CNFs. 
1282.64
1921.36
1630.56
2882.04
3214.39
0500100015002000250030003500
Wavenumber cm-1
0.0
00
0.0
01
0.0
02
0.0
03
0.0
04
0.0
05
0.0
06
Ra
ma
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en
sit
y
0.0
00
0.0
01
0.0
02
0.0
03
0.0
04
0.0
05
0.0
06
Ra
ma
n I
nt
en
sit
y
 
Figure 3.14 Raman spectra of CNFs shows that they are distinctly different from 
MWCNTs. 
 
 42  
CNFs of two different bulk densities, low density (LD) and high density (HD), 
were used. While both of them exhibited similar agglomerates, elemental composition 
and chemical bonding, they differed in their aspect ratio. The average aspect ratio of the 
CNF LD and CNF HD were 50: 1 and 25:1, respectively. 
 
3.1.2.3 Potassium Chloride 
Technical grade potassium chloride (KCl) microparticles were obtained from 
NAVSEA-IHMD. This material was screened through a U.S. sieve size #60 
corresponding to screen openings of 250 ?m. The material passing through the 250 ?m 
screen was used. KCl was used as a dummy filler to check the validity of the 
combinatorial approach developed across various size scales. Furthermore, it is 
inexpensive and allows quick characterization of the composition via thermal 
decomposition because the decomposition temperatures of PS and KCl are significantly 
different unlike PS and MWCNTs or CNFs.  
 
3.1.3 Solvents 
Research grade N,N di-methyl formamide (DMF) and tetra-hydro furan (THF) 
were obtained from Fisher Scientific. They were suggested to be good dispersants for 
MWCNTs [46,80] and hence used in this work study the effect of solvent on the material 
properties. The following are a few properties of DMF and THF as obtained from the 
manufacturer: 
 
 
 43  
 
DMF (C3H7NO) THF (C4H8O) 
Specific Gravity: 0.94 
Boiling Point: 153?C 
Specific Gravity: 0.89 
Boiling Point: 66?C 
 
 
3.2 Processing of Polymer Nanocomposites 
The polymer nanocomposites were processed using two different techniques: 
solvent processing and twin screw extrusion to compare the effect of processing on the 
structure-property relationships. Each of these techniques will be discussed in detail in 
the following sections. 
 
3.2.1 Solvent Processing 
The purpose of solvent processing is to create samples equivalent to the extruded 
version by using a minimum amount of MWCNTs/CNFs in a lab-scale, batch process. 
Known amounts of the filler and PS were measured to obtain the desired loading of filler 
in the composite. The desired solvent is added to two different beakers containing PS and 
the filler to make a 1 wt.% suspension and 5 wt.% solution respectively. The suspension 
of filler in the solvent is sonicated in an VWR 75D sonicator for ~2 hours. During the 
sonication the beaker is covered with a lid or an aluminum foil to avoid evaporation of 
the solvent. This is particularly essential for solvents with high vapor pressure such as 
THF. Simultaneously, in a separate beaker PS was dissolved in the solvent by stirring as 
shown in figure 3.15. The filler suspension was then mixed with the PS solution and 
allowed to stir covered for ~2 hours. As noted in an earlier work [46], it was observed 
 44  
that periodic addition of solvent produced better dispersion. Subsequently, the solvent 
was allowed to evaporate leaving behind the polymer nanocomposite. 
 
Figure 3.15 The solvent processing experimental setup showing the sonication of filler 
suspension and dissolution of polymer in the same solvent. 
 
THF evaporates easily due to its high vapor pressure, but DMF usually requires solvent 
extraction. For solvent extraction, the mixture of filler suspension and the PS solution 
was gradually added into stirred water (non-solvent for PS) until all the polymer 
nanocomposite precipitates. The solvent extraction should be done gradually because it 
allows for the solvent (THF or DMF) to diffuse into the non-solvent phase leaving behind 
the polymer nanocomposites precipitate. The resultant mixture is filtered using a water 
aspirator-based vacuum filtration, as shown in figure 3.16, to obtain the precipitate. The 
PS-filler composite is then placed on a watch glass and dried in a vacuum oven for 12-24 
hours at 100?C for the solvent to evaporate from the composite. Finally, the dried 
composite is hot-pressed into a 30 mm diameter disc specimen for electrical and 
rheological property characterization using a Beuhler Pneumet I hot press (see figure 
Sonication of 
MWCNTs/CNFs Dissolution of PS 
 45  
3.17) at a temperature of 150?C under a pressure of 85 psi. Samples with various mass 
fractions of filler in PS were prepared by this method.  
 
Figure 3.16 The vacuum filtration setup to separate the polymer nanocomposite 
precipitate after solvent extraction. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3.17 The Beuhler Pneumet I Hot Press 
 
 
 
Ram Control 
On/Off switch 
Cooling Fins Heater 
Pressure  
Gauge 
 46  
3.2.2 Twin Screw Extrusion 
TSE is a type of melt mixing process that is utilized to manufacture a number of 
consumer and industrial goods, from snack foods and medical tubing to plastic pellets 
and military propellants. The process is a continuous type in that the twin screw extruder 
will produce a product as long as the ingredient supply is maintained. Because this type 
of process has so many advantages over batch type, it has found widespread utility across 
diverse industries. For most however the advantages are universal: economy, quality, 
environment, flexibility, and safety. Some of these advantages illustrate why the twin 
screw extruder shows great promise for producing functionally graded materials.  
Furthermore the continuous process yields a more consistent product thus 
improving overall quality. There is significantly less variation in material, and the 
efficiency of mixing is better than batch methods. The process lends itself to on-line 
analysis allowing for the quick detection of anomalous conditions or material 
automatically diverting it to waste. 
 
3.2.2.1 Equipment & Peripherals 
For this research investigation, the TSE facility in the polymer processing 
laboratory at the University of Maryland was used. A laboratory scale Werner & 
Pfleiderer model ZDSK-28 twin screw extruder with co-rotating, fully-intermeshing 
screws was the focal point of the experimental set-up. The extruder and the related 
peripherals are shown in figures 3.18 and 3.19. 
 47  
 
 
 
Figure 3.18 The twin screw extrusion facility overview 
 
 
Figure 3.19 A schematic of the extrusion line with the loss-in-weight overhead feeders, 
optical probe and the automated extrudate collection system. 
1 
2 
3 
4 
5 
6 
7 
8 
9 
1 Extruder hood  4 Optical probe 7 Extruder 
2 System control box  5 Feeder  8 Sample collecting 
3 Feeder control box  6 Die   9 Adjustable height table 
 
1 2 3 4 5 
 48  
The extruder consisted of a main feed throat, called the ?end port?, followed by 
five interchangeable sections, commonly referred to as the ?barrel zones? and the ?die 
zone? at the end to which the extrusion die was connected as shown in figures 3.19 and 
3.20. The barrel zone 3 was called the ?middle port?. The middle port had an opening at 
the top that could be used either for feeding filler from the overhead feeders or 
devolatilization (i.e., removing the volatiles). When the middle port was used for 
devolatilization, the filler was fed along with the polymer through the end port. A Walsh 
R1402 vacuum pump was used to remove the air entrained with the nanoscale filler and 
other volatiles such as vapors from the extrudate. All the barrel zones were heated 
electrically and water-cooled such that five different temperature zones, one per barrel 
zone, were possible. The temperature can be controlled from ambient to ~300?C. The 
twin screws run through the barrel zone and the die zone. 
 
Figure 3.20 The interchangeable, electrically heated barrels showing the middle and end 
feed ports. 
 
The die zone, which was at the end of the barrel zones, consisted of an eight-to-
round adapter (see figure 3.21). This adapter houses the screw tips (i.e., end of the 
 49  
screws) and directs the flow from the figure eight of the barrel to a round hole that 
comprises the die entrance. The adapter was designed to accommodate a wide variety of 
extrusion dies, the hardware that forms the final shape of the extruded product. The 
temperature of the adapter was controlled using a ceramic band heater figure 3.22. 
 
Figure 3.21 Eight-to-round adapter that guides the flow from the screws into the die. 
 
Figure 3.22 Ceramic band heater to control the temperature of the die zone. 
 
The die was attached to the eight-to-round adapter. The slit die used in this work 
is 2.5 cm wide and 1 mm thick (see figure 3.23). The die is designed with a guillotine-
edge arrangement that allows control over the thickness of the extrudate. This die was 
used to fabricate ribbon-like extrudate. 
 
Figure 3.23 The slit die with guillotine-edge arrangement. 
 50  
The twin screw extruder was controlled by a FACTS MI-101 control system (see 
figure 3.24). The FACTS MI-101 is a versatile data acquisition and control system 
specifically designed for extrusion line applications. The system has a broad range of 
capabilities including digital I/O and analog inputs, temperature and speed loop control, 
and PID loops that can be mixed and matched or cascaded together to provide complete 
extruder control. The system?s configuration for different products may be stored as user 
defined product codes, allowing the user to change the entire system at the touch of a 
button to run a different product. 
 
Figure 3.24 The FACTS control system was used mainly to control the temperature and 
the screw speed of the extruder. 
 
The TSE facility contains three loss-in-weight feeders (see figure 3.25) to feed the 
polymer pellets or powder. The loss-in-weight control for solids allows strict feed rate 
control and verification of feeder stability. One is a pellet feeder and the other two are 
powder feeders. Only one of the two powder feeders was used at a time. All the feeders 
were a laboratory scale twin screw type; a type that exhibited better accuracy than the 
single screw or vibrating tray varieties. While one of the powder feeders could accurately 
 51  
feed at high flow rates (>0.5 Kg/h), the other could accurately feed at lower flow rates 
(<0.25 Kg/h). The lower feed rates were especially suitable when using expensive fillers. 
A KCM control system was used to integrate and operate the feeders. The feeders rest on 
a mobile feeder platform that was designed to allow the feeders to be used with any of the 
extruders in the polymer processing laboratory. The feeders were connected to the feed 
port of the extruder with a finely polished stainless steel pipe.  
 
Figure 3.25 The loss-in-weight over head feeders to feed powders and pellets. 
 
During the course of the present work, the extrudate collection system was 
automated using a chill roll, water bath and a torque winder. Figure 3.26 shows a 
schematic of the automated extrudate collection system. 
 
Figure 3.26 The automated extrudate collection system. 
 52  
The chill roll (see figure 3.27) contains a top roller and two bottom rollers. The top roll 
and one of the bottom rollers are driven by a motor. The speed of the rollers is adjusted in 
accordance with the speed at which the extrudate comes out of the die. The rollers are 
cooled from inside with cooling water. It is also provided with sprinklers for additional 
cooling. The extrudate enters the chill roll upon exiting the die and is cooled. The 
extrudate passes over the top roller and between the bottom rollers before it is immersed 
in the water bath. 
 
Figure 3.27 Chill roll 
 
The water bath (see figure 3.28) consists of a steel trough with three rollers fixed to it. 
The trough, when filled with water, allows for the immersion and hence cooling of the 
extrudate. The extrudate upon exiting the bottom of the chill roll enters the water trough 
below the rollers and is conveyed further to the torque winder. 
 
Figure 3.28 Water bath 
 53  
The torque winder (see figure 3.29) contains a roller that is driven by a motor and used to 
wind up the extrudate into a roll. The torque on the torque winder can be adjusted and is 
set such that the extrudate is maintained under tension at all places. This ensures a 
smooth surface of the extrudate. 
 
Figure 3.29 Torque winder 
 
 
3.2.2.2 Screw Design  
A twin screw extruder is mainly classified by the diameter of the screw and 
direction of rotation of one screw with respect to the other. In this work, co-rotating, 
intermeshing screws with a nominal diameter of 28 mm were used. The overall length to 
diameter ratio was greater than 26, which results in more options for screw element 
combinations to control the mixing and transport processes. Figure 3.30 shows the image 
of the screws.  
 
Direction of Flow 
Figure 3.30 The twin screws when extracted out of the extruder. 
 
 54  
The design of the screw plays a very important role in determining the degree of 
mixing achieved in the extruder. The geometry used for the screws is highly flexible in 
that individual element pairs of different shapes can be added together to result in 
specialized combinations for different material formulations. The screw designs used in 
this work contained three different zones ? the melting zone, the conveying zone and the 
mixing zone. The conveying zone was in place to allow for the polymer relaxation, 
thereby, not decomposing the polymer chains at extremely high shear rates. Two different 
screw designs, one with a relatively low shear design (see figure 3.31) and another with a 
relatively high shear design (see figure 3.32) were used to investigate the influence of 
screw design on the structure-property relationships of the polymer nanocomposites.   
 
Figure 3.31 Low shear screw design 
 55  
 
Figure 3.32 High shear screw design 
 
The low shear screw design was configured such that the polymer could be fed 
through the end port and the filler could be fed through the middle port. In the low shear 
screw design, the polymer melted in the melting zone after entering the extruder the end 
port, got conveyed through the conveying zone, and subsequently the melt got mixed in 
the mixing zone with the filler that was introduced through the middle port. On the other 
hand, the high shear screw design was configured such that both the polymer and the 
filler could enter through the end port and a vacuum pump could be connected to the 
middle port for devolatilization. In the high shear screw design, the polymer and filler 
entered through the end port with simultaneous melting and solid mixing, followed by 
conveying in the conveying zone and eventually melt mixing in the mixing zone. 
 56  
Compared to the low shear screw design, the residence time of the polymer and the filler, 
together, is longer in the high shear screw design. Furthermore, the number of shear 
elements such as kneading blocks and the reverse elements that occur during the polymer 
and filler transport is higher for the high shear screw design. 
 
3.2.2.3 Procedure for Processing Polymer Nanocomposites  
Processing the nanocomposites via TSE consists of melting the polymer, mixing 
the polymer melt with nanoscale filler in the twin screw extruder, extruding the 
nanocomposites through the die, and collecting the extrudate using the peripheral 
equipment. The following describes in the detail the various steps in the process. 
Before the extruder is turned on, the feeder system has to be set up in the desired 
manner.  The feeder system is calibrated to feed the desired material. The feeders are 
filled with the desired amounts of the polymer and the filler. The outlet of the feeder is 
connected to the desired feed port of the extruder and the aptness of the connection is 
ensured to avoid any polymer or filler spill. Following the feeder setup, the Facts Inc. 
control system, and the vent for exhaust gases are turned on. The barrel zones and the die 
zone are heated to the desired temperature. The temperatures of the barrel zones and the 
die zone depend on the polymer being used and is obtained from the manufacturer?s 
specification of the recommended melt temperature for extrusion. For PS, the following 
temperature profile is used ? barrel zone 1 at 375?F, barrel zone 2 at 425?F, barrel zone 3 
at 425?F, barrel zone 4 at 425?F, barrel zone 5 at 425?F, and die zone at 325?F. The 
cooling water supply is turned on to ensure temperature control of the barrel zones. 
Furthermore, it is ensured that the feed zone does not get heated up too high to avoid 
 57  
clogging the feed port due to softened polymer pellets. The desired screw speed is set and 
the extruder is turned on. The screw speeds used in this investigation ranged from 30 
RPM to 200 RPM. Using the KCM feeder control unit, the desired feed rate of the 
polymer is set. The feed rates used in this work range from ~0.5 Kg/hr to ~2 Kg/hr. The 
screw speed and feed rate for a given polymer are set based on an insight into the degree 
of channel fill [81] and the maximum torque that can be achieved by the extruder motor 
for a given screw design. The pressure starts building up in the extruder as the screw 
channels gradually get filled up. Eventually, the extrudate comes out of the die (see figure 
3.33).  
 
Figure 3.33 Extrudate exiting the slit die. 
 
The initial extrudate may include the polymer and filler in the extruder from a previous 
run and must be purged. After the polymer melt attains a steady flow, the nanoscale 
fillers were added at the desired flow rate through the desired feed port, i.e., end port of 
middle port an impulse or step input. The experiments with impulse input of the CNFs 
were conducted to obtain the residence distributions as described in 3.3.2. The 
experiments with step input of the CNFs were conducted to establish the processing-
microstructure and structure-property relationships as described in 4.1 and 4.2.2. 
Experiments with step input of CNFs and KCl were also conducted to demonstrate the 
 58  
combinatorial approach as described in 4.4. In the step input experiments, the flow rate of 
the filler is chosen to produce the desired loading of filler in the composite. 
The extrudate from TSE is collected using the peripheral equipment ? chill roll, 
water bath and torque winder. The cooling water system is turned on and the extrudate is 
fed to the chill roll followed by the water bath and the torque winder. The speed of the 
chill roll and the speed of the rollers of the torque winder are controlled until the 
extrudate is steadily collected, as a roll, with uniform cross-section. Figure 3.34 shows a 
snap shot from steady collection of extrudate. Notice the PS roll wound up on the roller 
of the torque winder. The thickness of the extrudate could be tuned by varying the speed 
of the chill roll. 
 
Figure 3.34 Automated collection of extrudate samples 
 
Experiments with step input of filler were conducted with and without a vacuum pump 
connected to the middle port for devolatilization. This resulted in composites with 
varying porosity, as described in 4.1.6, that were studied to determine the influence of 
 59  
porosity on material properties. Furthermore, as mentioned in 3.2.2.2, step input 
experiments were also conducted with high shear and low shear screw designs to 
investigate the influence of screw design on the structure-property relationships of the 
polymer nanocomposites. 
 
3.2.3 Annealing the extruded PS-CNF composites 
The extruded PS-CNF composites at various CNF loadings were further annealed 
to investigate the influence of annealing on their microstructure, electrical and 
rheological properties. The composites were placed on a steel plate and heated to a 
temperature well above the softening point of PS (90?C), up to the recommended melt 
temperature (~210?C) in an inert atmosphere. In essence, it was ensured that there was no 
imposed stress on the PS-CNF composite, such as that imposed during the shear flow 
through the die. This led to relaxation of the percolated network of CNFs as described in 
4.1.4 and improvement in electrical properties as described in 4.2.2.2. 
 
3.3 Characterization of Structure & Microstructure 
3.3.1 Thermogravimetric Analysis: Composition 
Composition of the filler in the composites is the important structural parameter 
that has to be determined not only to establish the structure-property relationships, but 
also as a quality check for the processing related material losses. Determining the KCl 
loading in the PS-KCl composites was relatively easier because the thermal 
decomposition temperatures of PS and KCl are significantly different. Hence, it was easy 
to combust PS completely without affecting the KCl. Knowing the initial weight ( ow ) of 
 60  
the PS-KCl composite and the final weight ( fw ) after the combustion of PS, the KCl 
loading can determined as, 
o
f
w
wKClWt ?= 100.%     (3.1) 
However, it is more complicated for the PS-MWCNT and PS-CNF composites because 
the combustion of CNFs and MWCNTs starts before the complete combustion of PS. 
Thus a more sophisticated technique like thermogravimetric analysis (TGA), with 
controllable temperature ramp and continuous weight monitoring, is required to 
determine the loading of MWCNTs and CNFs in the composites.  
In this work, a Cahn TG 2131 TGA was used to determine the loading of 
MWCNTs and CNFs in the composites. In all the TGA tests conducted, the initial weight 
of the composite sample was consistently maintained to be ~100 mg. The weight 
fluctuations experienced by the empty sample holder were subtracted from the raw TGA 
data before analyzing the weight loss of the sample. Figure 3.35 shows the 
thermogravimetric response of the neat ingredients i.e., neat PS, neat MWCNTs and neat 
CNFs, in the temperature range of 25-1000oC at a temperature ramp of 10oC/minute in an 
air atmosphere. It is evident that the PS shows two distinctly different weight losses and 
decomposes completely by 550oC. While the former weight loss corresponds to the 
styrene-rich phase, the latter corresponds to the butadiene-rich phase. The two-stage 
combustion of PS in an air atmosphere is in agreement with an earlier work by Castaldi et 
al [82]. The neat MWCNTs start to decompose around 750oC. The neat CNFs start to 
decompose around 600oC and are nearly completely consumed by 1000oC.  
 61  
0
20
40
60
80
100
0 200 400 600 800 1000
Temperature (oC)
W
eig
ht
% 
Re
ma
ini
ng
MWCNT
CNF
PS
 
Figure 3.35 The weight loss curves of the neat PS, neat MWCNTs and the neat CNFs. 
 
Consequently, the TGA of the PS-MWCNT and PS-CNF composites was 
conducted in an air atmosphere using the following temperature profile ? hold isothermal 
at room temperature for 10 minutes, ramp at 10oC/minute up to 600oC and hold 
isothermal for 30 minutes at 600oC. Figure 3.36 shows the representative weight percent 
and weight loss rate (WLR) profiles obtained when the PS-CNF composites were studied 
using the TGA procedure described above. The two distinct weight losses corresponding 
to PS and the third weight loss corresponding to the CNFs are evident. The three 
corresponding peaks in WLR are also distinct. The behavior of PS-MWCNT composites 
was very similar to the PS-CNF composites except the higher decomposition temperature 
of MWCNTs. The loading of the MWCNTs or CNFs in the composite was determined 
from the weight percent remaining at the time corresponding to the point of inflection 
between the second and third peaks of the WLR curve (i.e., when the second derivative of 
weight percent is zero). This is a rigorous and consistent technique to characterize the 
materials of unknown composition produced via combinatorial approaches [31]. 
 62  
0
20
40
60
80
100
0 1000 2000 3000 4000 5000
Time (sec)
W
eig
ht 
Pe
rc
en
t (
%
)
-5
0
5
10
15
20
W
LR
 (m
g/m
in)
Wt% WLR
 
(a) 
 
0
10
20
30
0 1000 2000 3000 4000 5000
Time (sec)
W
eig
ht 
Pe
rc
en
t (
%
)
-5
0
5
10
W
LR
 (m
g/m
in)
Wt% WLR
 
 (b) 
Figure 3.36 (a) Representative weight% and WLR profiles for PS- CNF composites. (b) 
Zoomed in view more clearly indicating the presence of a third peak. The weight percent 
remaining at the inflection point between the second and third peaks represents the 
loading of the filler in the composite. 
 
 63  
 Although TGA is a precise and accurate technique to determine the loading of the 
filler in the composite, it is also a time consuming and destructive. Hence, it is less 
suitable for determining the compositional gradients of polymer nanocomposites. 
 
3.3.2 In-Situ Absorbance Measurement: Residence Distributions 
As described in 2.5.2, residence distributions are a convenient measure of the 
average mixing occurring in extrusion due to channeling, back-mixing and stagnation. In 
this work, a Cuda I-150 optical probe was used to obtain the residence time distribution 
of the extrusion process. The optical probe was mounted in the die zone as shown in 
figure 3.37.  
 
Figure 3.37 The die zone with the optical probe mounted. 
 
While the PS melt is white, the MWCNTs/CNFs are black in appearance. An impulse 
input of the filler material would result in a gradual change in the color and hence the 
absorbance of the melt. The optical probe tracked the changes in absorbance of the melt, 
thereby tracking the amount of material flowing past a stationary point. The maximum 
output signal of the optical probe had a voltage of 1V DC. The intensity of the optical 
Slit Die 
Optical Probe 
 64  
probe was adjusted to produce an output signal between 0.44V DC and 0.46V DC when 
neat PS melt passes beneath the probe during the extrusion process. The curve obtained 
by tracking the change in the optical absorbance of the melt as a function of time after an 
impulse input of the filler material is the residence time distribution (RTD). The optical 
probe data was acquired by an automated data acquisition system at a frequency of 10 Hz 
and filtered using a low-pass butterworth filter to avoid any noise from electrical 
interference. By trial and error, the best filtering parameters were obtained to be a cutoff 
frequency of 0.02 Hz, filter order of 1 and no decimation (i.e., decimation factor of 1). 
Furthermore, in order to compare the RTDs resulting from different processing 
conditions, they were normalized (i.e., the area under the RTD curve was set to unity) as 
given by equation (2.2). Figure 3.38 shows a normalized RTD resulting from the TSE 
process. The impulse input of the filler is followed by a brief delay time (tD) following 
which there is a sharp increase in the absorbance of the melt. The end time (tE) marks the 
flow of the entire input amount of the filler past the optical probe. For any given time 
interval (t0), the area under the curve represents the amount of material with that flowed 
past the optical probe. The mean residence time is defined as the time at which half of the 
total amount of material flowed past optical probe. The mean residence times of the filler 
in the extruder when fed through the middle port and the end port were found to be ~5 
minutes and ~15 minutes respectively. Furthermore, the normalized RTDs can be 
converted to normalized residence volume distributions (RVDs) as given by equations 
(2.3) and (2.4). The normalized RVDs thus obtained were modeled as a series of perfect 
batch mixers, and convoluted with a step input to predict the compositional gradient as 
described 4.4.1. Since this technique is rapid and non-destructive when compared to the 
 65  
TGA, it is suitable for combinatorial approaches to fabricate and characterize polymer 
nanocomposites. 
 
Figure 3.38 Representative normalized Residence Time Distribution (RTD). 
 
3.3.3 Distribution, Dispersion, Aspect Ratio and Alignment: Microscopy 
To characterize the microstructural features, several microscopy techniques, 
optical microscopy, confocal microscopy, scanning electron microscopy (SEM), and 
transmission electron microscopy (TEM), were employed. Each technique is beneficial in 
characterizing a particular microstructural feature. The following is a list of 
microstructural features of interest and the associated microscopy techniques used in this 
research to study them: 
1. Distribution of Agglomerates (optical) 
Fraction of 
CNTs in a given 
time interval 
Dt  
Ot  
Et  
 66  
2. Dispersion of MWCNTs/CNFs (SEM) 
3. Aspect ratio CNFs (TEM) 
4. Alignment of CNFs (confocal) 
 
The macroscopic distribution of agglomerates of CNFs and MWCNTs and the 
porosity in the composites was characterized using a Leica optical microscope. Since the 
as-prepared surface of the extruded composites did not exhibit any features (see 4.1.2),  it 
had to be polished with 800 grit and 1200 grit size SiC polishing papers followed by 3 
?m, 1 ?m and 100 nm diamond suspensions to expose the porosity and the agglomerates. 
The dispersion of MWCNTs or CNFs and the morphology of the PS-MWCNT 
and PS-CNF composites were examined using a Quanta FEG 200 scanning electron 
microscope (SEM). The surface and the cross-section of the nanocomposites were 
imaged as-prepared and after polishing. While imaging composites with low MWCNT 
loadings under the SEM, it was observed that using a low energy electron beam (~5 kV) 
circumvented the charge accumulation on the surface. However, the composites with low 
CNF loadings had to be coated with gold in order to avoid the charge accumulation.  
In order to characterize the aspect ratio of the CNFs in the composites processed 
via solvent processing or extrusion, the CNFs were separated from the PS matrix by 
refluxing the PS-CNF composites with THF in the absence of shear (stirring, sonication 
etc.), followed by further dilution. A drop of the dilute CNF suspension was mounted on 
a grit and characterized using the Jeol TEM to measure the aspect ratio of the CNFs. 
The alignment of the CNFs in the composites was evaluated using a laser 
confocal microscope (Carl Zeiss Model LSM510). The confocal microscope utilizes 
coherent laser light and collects reflected light exclusively from a single plane with a 
 67  
thickness of 100 nm (a pinhole sits conjugated to the focal plane and rejects light out of 
the focal plane). A red laser (? = 633 nm) was used as the coherent light and images were 
taken with an Epiplan-Neofluar 100x/1.30 oil-pool objective. A filter (Rapp 
Optoelectronic LP385) was used to limit the lower spectra of reflected light. One hundred 
two-dimensional images (optical slices with 512 pixels x 512 pixels), with scan size 92.1 
x 92.1 ?m, were taken at a spacing of 100 nm by moving the focal plane. Images were 
further analyzed using the NIH Image software program. 
 
3.4 Characterization of Properties 
3.4.1 Electrical Conductivity 
The electrical conductivity of the composites was measured in accordance with 
ASTM D4496. Samples of a known cross-sectional area and thickness were placed 
between copper electrodes and the DC resistance was measured using an Agilent 34401A 
precision digital multimeter. The surfaces of the sample in contact with the electrodes 
were coated with silver paint in order to reduce discrepancies arising from micro-
roughness. It was ensured that the surface area of the electrodes exceeded the cross-
sectional area of the discs. 
 
3.4.2 Rheological Properties 
Dynamic rheological measurements were performed on a Rheometrics RDAIII 
rheometer (see figure 3.39 below) using 2.5 cm parallel plates. Sample discs of 2.5 cm 
diameter were placed between the plates with due care given to the sensitive transducer 
of the instrument. The oven was then heated to the desired temperature under a nitrogen 
 68  
atmosphere to avoid degradation of PS. The melt rheology was conducted at temperatures 
of 170, 180, 190, 200 and 210?C with a gap of about 1 mm between the plates. After 
attaining the desired temperature, the plates were further pushed together by 
approximately 0.1 mm to ensure that the sample completely fills the volume between the 
plates. Any additional material overhanging the plates was trimmed using a metal spatula. 
The storage modulus, loss modulus and complex viscosity were measured as functions of 
frequency (0.01 ? 100 rad/s) within the linear viscoelastic regime (less than 0.5% strain) 
of the sample. Before recording each frequency sweep, the sample was equilibrated at the 
test temperature usually for a period of 30 min. Three different samples were tested at 
each loading of the filler. 
      
Figure 3.39 The RDA III parallel plate rheometer. 
 
 
 
 69  
3.4.3 Thermo-oxidative behavior 
In addition to determining the loading of the filler, the thermo-oxidative behavior 
of the composites was also studied using the TGA. In specific the temperature at and 
magnitude of the peak weight loss rate corresponding to the styrene rich phase and the 
weight loss of the filler were studied as function of the type of process and the extrusion 
processing parameters. 
 
3.4.4 Mechanical Properties 
For the mechanical tests, samples were prepared according to the ASTM D-638 
?Standard Test Method for Tensile Properties of Plastics? (see figure 3.40) and the 
prescribed test procedure was followed. A Tinius Olsen load frame with a 25 KN load 
cell was used.  The sample was loaded as close to parallel as possible to crosshead 
motion to reduce shear stress. The grips were approximately 100 mm apart to provide a 
suitable gage length for strain measurement. Samples were preloaded to approximately 4 
lbf to reduce the error in strain measurement. The tests were conducted at 5 mm/min. 
After the test was complete, the data was saved and then reduced using the gauge length 
and the cross-sectional area of the sample to obtain stress-strain curves. 
 
Figure 3.40 The sample used for mechanical testing. 
 
 
 70  
 
4. Results and Discussion 
 
 
4.1 Processing ? Microstructure Relationships 
The microstructure of solvent processed PS-MWCNT, solvent processed PS-CNF 
and extruded PS-CNF composites was studied using one or more of optical, confocal, 
scanning and transmission electron microscopy and compared when applicable. 
 
4.1.1 Microstructure of Solvent Processed PS ? MWCNT  Composites  
The as-received agglomerates of MWCNTs (see figure 3.2) were sonicated and 
mixed with the PS using the solvent processing technique described in 3.2.1. An SEM 
image of the surface of the solvent processed PS-MWCNT composite with 5 wt.% 
MWCNT loading is shown in figure 4.1. The surface revealed a random, isotropic 
dispersion with two distinctly different kinds of MWCNTs ? non-interacting MWCNTs 
that are reinforcing the polymer matrix and percolated MWCNTs that form a scaffold-
like structure. It was also observed that the diameter of the processed MWCNTs ranged 
from 30-50 nm and the length ranged from 2-5 ?m thereby indicating no evidence of tube 
breakage. The loading of MWCNTs is qualitatively consistent with the volume fraction 
calculations (see 4.2.1.1). Furthermore, the significant increase in electrical (see 4.2.1.1) 
and rheological (see 4.2.1.2) properties is due to the scaffold-like characteristics of the 
continuous phase of percolated MWCNTs. 
 71  
 
Figure 4.1 Random, isotropic dispersion of MWCNTs at a 5wt.% loading. Note the 
continuous phase of percolated MWCNTs with a scaffold like structure. 
 
The microstructure of the PS-MWCNT composites with 5 wt.% loading prepared 
using two different solvents, DMF and THF, was also compared. SEM images of a 
macroscopic crack initiated by shearing the composite are shown in figure 4.2.  
 
 
 
 
Figure 4.2 A macroscopic crack in the PS-MWCNT composites processed using (a) 
DMF and (b) THF reveals pull out of MWCNTs indicating poor adhesion between 
MWCNTs and PS. 
 
10 ?m 
Percolated 
MWCNTs 
 72  
Both images show that the MWCNTs are pulled out as the crack propagates, thereby 
providing some potential insight into the interfacial adhesion between the MWCNTs and 
the PS. These results indicate that there is a low level of interfacial adhesion associated 
with the use of solvents, which could have a deleterious effect on the macroscopic 
mechanical behavior. 
 
4.1.2 Microstructure of PS ? CNF Composites: Solvent Processed & Extruded 
In order to understand the effect of the mixing mechanism on the dispersion of 
CNFs, the microstructure of the solvent processed PS-CNF composites was studied and 
compared with the extruded ones. Figure 4.3 shows the SEM images of the surface of the 
solvent processed and extruded PS-CNF composites with 5 wt.% CNF loading.   
 
      (a) 
5 ?m 
 73  
 
 (b) 
Figure 4.3 Surface of the (a) solvent processed and (b) extruded PS-CNF composites. 
While CNFs are present on the surface of the solvent processed composites, they tend to 
stay below the surface for the extruded composites. 
 
It is evident from the figures that the CNFs are present on the surface of the solvent 
processed composites, but depleted on the surface of the extruded composites. The 
depletion of CNFs at the surface was consistently observed in spite of varying operating 
conditions in the extrusion process. Such filler phase segregation at the surface of the 
extruded composites was observed in earlier works too [24]. It can be attributed to the 
alignment of the CNFs imposed by the shear flow in the die. Since the shear rate (or 
velocity gradient) is maximum at the die wall, which is in contact with the surface of the 
extrudate, the likelihood of alignment of CNFs is more at the surface of the extrudate. To 
align in the direction of the flow, the CNFs rotate around their center of mass, thereby 
staying below the surface. 
5 ?m 
 74  
Since the surface of the extruded composites did not offer sufficient information 
about the dispersion of CNFs, the cross-section was studied and compared with that of 
the solvent processed composites. Figure 4.4 shows the SEM images of the cross-section 
of the solvent processed and extruded PS-CNF composites with 5 wt.% CNF loading. It 
is evident from the figures that the solvent processed composites show a random 
dispersion of CNFs and the extruded composites show agglomerates of CNFs with an 
average size of 50 ?m. The dispersion of CNFs in the solvent processed PS-CNF 
composites is similar to the dispersion of MWCNTs in the solvent processed PS-
MWCNT composites.  
 
 
 
(a) 
20 ?m 
 75  
 
 (b) 
Figure 4.4 Cross-section of the (a) solvent processed and (b) extruded PS-CNF 
composites. While CNFs are randomly dispersed in the solvent processed composites, 
agglomerates are present in the extruded composites. 
 
 
 
4.1.3 Aspect Ratio of CNFs: Solvent Processed & Extruded 
The aspect ratio of CNFs in the solvent processed and extruded PS-CNF 
composites was measured as described in 3.3.3 to determine the effect of processing on 
the mechanical degradation of the filler. Figure 4.5 shows a representative TEM image 
each of the CNFs separated from the solvent processed and the extruded PS-CNF 
composites. It was found from 120 such measurements that the average aspect ratio of the 
solvent processed CNFs was 35:1 and that of the extruded CNFs was 25:1. The lower 
aspect ratio of the extruded CNFs indicates that the magnitude of shear rate in extrusion 
(attrition) is higher than that in solvent processing (sonication).  
20 ?m 
CNF Agglomerate 
 76  
 
(a) 
 
 
 (b) 
Figure 4.5 Representative TEM images of (a) solvent processed and (b) extruded CNFs. 
Note the higher aspect ratio of the solvent processed CNFs (35:1) when compared to that 
of the extruded CNFs (25:1). 
 
However, as discussed in 4.1.2, the extruded composites exhibit agglomerates of CNFs, 
while the solvent processed ones exhibit random dispersion of CNFs. This can be 
attributed to the lower residence time in extrusion (5-10 minute) when compared to that 
in solvent processing (2-4 hour). An important conclusion can be drawn from these 
2 ?m 
2 ?m 
 77  
observations: deagglomeration is a critical combination of both the magnitude of shear 
and the residence time. 
 
4.1.4 Alignment of CNFs: Extruded & Annealed PS-CNF Composites 
 
As will be discussed in 4.2.2.1, the electrical properties of the solvent processed 
PS-CNF composites were better than those of extruded ones. Furthermore, annealing the 
extruded composites as described in 3.2.3 improved the electrical properties, as will be 
discussed in 4.2.2.2. In order to understand the microstructural changes associated with 
the improvement in electrical properties, the extruded and annealed PS-CNF composites 
were characterized using confocal microscopy. Confocal microscopy was chosen over 
SEM or TEM in order to obtain the configuration of CNFs at various depths below the 
surface, without disturbing the surface. Representative images of the unannealed and 
annealed PS-CNF composites with 10 wt.% CNF loading can be seen in figure 4.6.  
 
 
(a) 
 
Extruded FFT 
 
10 ?m 
 78  
 
 
(b) 
Figure 4.6 Microstructure of the (a) extruded and (b) annealed PS-CNF composites. 
While the extruded composites show a preferential alignment of CNFs, the annealed 
composites show a relatively random distribution. 
 
The image of the unannealed composite tends to indicate a preferential alignment 
of the CNFs. In order to better assess the level of alignment, the Fourier transform of the 
image was obtained. An anisotropic pattern was obtained that is elongated normal to the 
apparent alignment direction in the image. Thus, it is clearly evident that the CNFs are 
preferentially aligned, presumably due to the shear flow through the die. In contrast, the 
image of the annealed composite exhibits a relatively random distribution of the CNFs, 
and the corresponding Fourier transform has a more isotropic pattern An important 
conclusion about the processing-microstructure relationships can be drawn from these 
observations: confocal microscopy indicates that annealing restores a random 
distribution of CNFs, which implies the re-establishment of interconnectivity of CNFs 
that is necessary for the improvement in electrical properties. 
 
 
10 ?m 
Annealed FFT 
 79  
4.1.5 Microstructure of Extruded PS ? CNF Composites: Influence of Screw Speed 
In order to investigate the influence of screw speed on the size and distribution of 
the CNF agglomerates, the extruded PS-CNF composites were polished and characterized 
with the SEM. Figures 4.7a and 4.7b show the surface of the extruded PS-CNF 
composites, processed at the minimum (30 RPM) and the maximum (200 RPM) screw 
speed respectively, with agglomerates of CNFs that were exposed by polishing. It is 
evident from the images that the agglomerates in the composites processed at 30 RPM are 
relatively bigger than those processed at 200 RPM. While the composites processed at 30 
RPM show an average agglomerate size of ~100 ?m with an aspect ratio of 2:1, the 
composites processed at 200 RPM show an average agglomerate size of ~30 ?m with an 
aspect ratio of 1:1. An important conclusion about the processing-microstructure 
relationships can be drawn from these observations: increasing screw speed, which 
corresponds to increased shear rate, reduces the aspect ratio and size of the 
agglomerates, but does not disperse them into individual CNFs. 
        
 (a)      (b) 
Figure 4.7 Scanning electron micrographs of the extruded PS-CNF composites processed 
at a screw speed of  (a) 30 RPM showing the relatively bigger agglomerates of CNFs, and 
(b) 200 RPM showing the relatively smaller agglomerates of CNFs. 
 
50 ?m 
2:1 
50 ?m 
1:1 
 80  
4.1.6 Porosity of Extruded PS ? CNF Composites 
The porosity of the extruded PS-CNF composites, caused by the air entrained in 
the CNFs, was controlled by using a vacuum pump as described in 3.2.2.3 in order to 
study the effect of porosity on material properties. The qualitative distribution of pores in 
the PS-CNF composites, with and without a vacuum pump in the extrusion line, was 
characterized using optical microscopy as shown in figure 4.8. It is evident that using the 
vacuum pump reduces porosity in the composites, but does not eliminate it completely. 
    
        (a)           (b) 
Figure 4.8 Representative optical micrographs of extruded PS-CNF composites showing 
porosity in the (a) absence, and (b) presence of a vacuum pump. 
 
4.2 Structure ? Property & Processing ? Property Relationships 
The material properties of the solvent processed PS-MWCNT, solvent processed 
PS-CNF and extruded PS-CNF composites were studied as a function of their structure 
(i.e., composition) and compared when applicable. Furthermore, the affect of processing 
parameters, within a type of process, on the properties was also studied. Table 4.1 gives 
an overview of the properties investigated. ??? or ?X? indicate that the property was 
investigated or not investigated, respectively. 
 
1 mm 1 mm 
 81  
Table 4.1 List of composites and material properties investigated for structure-property 
relationships. ? = Investigated, X= Not Investigated. 
 Solvent Processed 
PS-MWCNT 
Solvent Processed 
PS-CNF 
Extruded 
PS-CNF 
Electrical ? ? ? 
Rheological ? ? ? 
Thermo-oxidative X ? ? 
Mechanical X X ? 
 
 
4.2.1 Solvent Processed PS ? MWCNT Composites 
4.2.1.1 Electrical Conductivity 
Figure 4.9 shows the experimentally determined electrical conductivity ( c? ) of 
PS-MWCNT composites, processed using DMF and THF, as a function of the MWCNT 
loading. Each data point on the plot represents the average of measurements on 6-8 
different samples, and the scatter in the data was within 5% of this average value. The 
conductivity of neat PS is ~10-20 S/m. Upon adding the MWCNTs, the conductivity of the 
composites increased by 20 orders of magnitude approaching a value of 1 S/m. At low 
loadings of MWCNTs, closer to the onset of percolation, the composites processed using 
DMF exhibit higher electrical conductivity than those processed using THF. The 
conductivity data are classically interpreted by a percolation model, which gives the 
following power law expression for conductivity as a function of particle volume fraction 
?:   
    ????? )( cPSPLc A ?+=     (4.1) 
Here, PLc?  is the conductivity of the composite predicted by the power law fit, 
PS?  is the electrical conductivity of the neat PS, A  is a constant based on the 
interconnectivity of the MWCNTs, c?  is the percolation threshold and ?  is the critical 
 82  
exponent. The percolation threshold corresponds to the formation of a CNT network that 
allows electron transport by tunneling or electron hopping along CNT interconnects. 
1.E-20
1.E-17
1.E-14
1.E-11
1.E-08
1.E-05
1.E-02
1.E+01
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Volume Fraction MWCNTs
 ???? 
(S/
m)
THF (experiment)
DMF (experiment)
THF (power law)
DMF (power law)
 
Figure 4.9 Electrical conductivity of the PS-MWCNT composites solvent processed 
using THF and DMF at various MWCNT loadings with the corresponding power law fits.  
 
The conductivity data for PS-MWCNT composites in figure 4.9 were fit using equation 
(4.1) and the best fit parameters are listed in table 4.2. For the curve fit, mass fractions 
( w ) were converted to volume fractions (values in table 4.3) using the simple rule of 
mixtures as shown in equation (4.2).  
)( fillerPSfiller
PS
w
w
???
??
?+=    (4.2) 
Here, PS?  is the density of PS and filler?  is the density of the filler, i.e., MWCNTs. The 
power law fits to the electrical conductivity data of both the DMF and THF-processed 
composites yielded a normalized cross-correlation coefficient of 1.00. 
 83  
Table 4.2 The power law fit parameters for the electrical conductivity of the PS-
MWCNT composites processed using THF and DMF solvents. 
 
 
 
 
 
 
 
Table 4.3 Relationship between mass and volume fractions for PS-MWCNT composites. 
 
 
 
 
 
 
 
From figure 4.9, it can be seen that percolation begins near a volume fraction of 
0.017 in the DMF processed composites and 0.019 in the THF processed ones. Beyond 
this point, there are distinct differences in the percolation behavior depending on the 
solvent used. The composites that are solvent processed with DMF percolate more 
rapidly than those processed with THF as described by the critical exponents 1.5 and 1.9 
respectively. However, the choice of solvent does not appear to affect the conductivity of 
the fully-percolated composite, which in both cases is ~ 1 S/m. This value is reached at 
about 8 vol.% MWCNTs. Thus, the interconnectivity of MWCNTs is only slightly better 
using DMF than THF. An important conclusion can be drawn about the processing-
property relationships in solvent processed PS-MWCNT composites from these 
observations: the difference in the percolation thresholds for the two solvents indicates 
that the choice of solvent does not have a significant effect on electrical properties. 
 
 
Power law 
parameter 
THF (?c) DMF (?c) 
A 16 16 
?c 0.019 0.017 
? 1.9 1.5 
Mass  
Fraction 
Volume  
Fraction 
0.01 0.02 
0.03 0.05 
0.05 0.08 
0.07 0.12 
 84  
4.2.1.2 Rheological Properties 
The structure-property relationships for solvent processed PS-MWCNT 
composites were further investigated for their dynamic melt rheological properties to 
compare with those of the solvent processed PS-CNF composites that will be discussed in 
4.2.2.3. Figures 4.10-4.13 show the various rheological parameters obtained from the 
THF processed PS-MWCNT composites. Figures 4.10a and 4.10b show the storage 
modulus G? and the loss modulus G? as functions of frequency. Data collected over a 
temperature range of 170?C-210?C have been shifted using the time-temperature 
superposition principle to extend the frequency range, and are reported at the median 
temperature of 190?C. Both G? and G? increase with MWCNT loading.  
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
0.01 0.1 1 10 100 1000
Frequency, ?  (rad/s)
Sto
ra
ge
 M
od
ulu
s, G
' (P
a) 
 
0 vol. %
2 vol. %
5 vol. %
8 vol. %
12 vol. %
 
 
 (a) 
 85  
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
0.01 0.1 1 10 100 1000
Frequency, ?  (rad/s)
Lo
ss 
M
od
ulu
s, G
'' (
Pa
)  
0 vol. %
2 vol. %
5 vol. %
8 vol. %
12 vol. %
 
 
Figure 4.10 (a) Storage modulus (G?) and (b) loss modulus (G?) of the solvent processed 
PS-MWCNT composites as a function of frequency. Data are shown for a range of 
MWCNT loadings. Note the plateau in G? at low frequencies for all of the MWCNT 
loadings indicating the presence of a pseudo-solid like phase in the composite formed by 
percolated MWCNTs. 
 
More importantly, at loadings exceeding 2 vol.%, G? reaches a plateau at low frequencies 
indicating that the percolated MWCNTs may be forming a pseudo-solid like network 
with strong interactions between polymer and particles [83,84]. 
Evidence of the formation of a pseudo-solid like network of percolated MWCNTs 
can also be seen in Figure 4.11, where the variation of G? and G? with frequency is 
compared for the neat PS sample and for the composite with the highest MWCNT 
loading of 12 vol. %. While the neat PS melt shows a typical transition from elastic to 
viscous behavior (G? > G?) at a critical frequency of 13 rad/s, the composite shows a 
predominantly elastic response (G? > G?, plateau in G?) over the entire frequency range. 
(b) 
 86  
1.E+03
1.E+04
1.E+05
1.E+06
1 10 100
Frequency, ?  (rad/s)
G'
, G
'' (
Pa
)
12 vol.% G'
12 vol.% G''
0 vol.% G''
0 vol.% G'
 
Figure 4.11  Cross-over point of the G? and G? curves for the neat PS and the 12 vol.% 
MWCNT composites. While the neat PS shows a viscous response at lower frequencies, 
the 12 vol.% MWCNT composite shows a predominantly elastic response over the entire 
frequency range. 
 
Differences in rheological response upon addition of MWCNTs can also be noted 
in the complex viscosity ?*. It can be seen from figure 4.12a that the neat PS melt shows 
a newtonian plateau in ?* at low frequencies. On the other hand, the ?* curves for non-
zero  MWCNT loadings do not show a plateau over the frequency range, indicative of 
elastic behavior in the PS-MWCNT composites due to interactions between the 
MWCNTs. As the loading of MWCNTs increases, a percolated network forms and the 
composite develops a finite yield behavior. Correspondingly, a plot of ?* vs. the complex 
modulus G* exhibits divergence at loadings above 2 vol.%, as shown in figure 4.12b 
[85].  
13 rad/s 
 87  
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
0.1 1 10 100
Frequency, ?  (rad/s)
Co
mp
lex
 V
isc
osi
ty,
 ????*
 (P
a-s
) 
0 vol.%
2 vol.%
5 vol.%
8 vol.%
12 vol.%
 
(a) 
 
  
(b) 
Figure 4.12 Complex viscosity (?*) as a function of (a) frequency (?), and (b) complex 
modulus (G*) for the PS-MWCNT composites processed with THF and tested at a 
temperature of 190?C. Data are shown for a range of MWCNT loadings. Note the plateau 
in complex viscosity in the high complex modulus regime. 
 88  
 
The asymptotic complex modulus increases from 13800 Pa at an MWCNT loading of 5 
vol. % to 30300 Pa at 12 vol. %. In addition, while neat PS exhibits a plateau in complex 
viscosity in the low complex modulus regime, the diverging curves of PS-MWCNT 
composites exhibit complex viscosity plateaus, ranging from 1700 Pa-s at 5 vol. % to 
2400 Pa-s at 12 vol. %, in the high complex modulus regime. 
Additional insight into the interaction between the MWCNTs and the PS matrix 
can be obtained from the inverse loss tangent (G?/G?), which is a measure of the damping 
characteristics or firmness of the material [86]. As shown in figure 4.13, the inverse loss 
tangent increases with MWCNT loading, especially at low frequencies. This indicates a 
hindrance to energy dissipation and relaxation of the polymer chains due to the 
percolation of the MWCNTs. 
0
1
10
0.1 1 10 100
Frequency, ?  (rad/s)
In
ve
rse
 L
oss
 T
an
ge
nt,
 (ta
n ????
)-1
0 vol.%
2 vol.%
5 vol.%
8 vol.%
12 vol.%
 
Figure 4.13 Inverse loss tangent as a function of frequency. Note the increase in inverse 
loss tangent with MWCNT loading. 
Increasing  
pseudo-solid like 
behavior 
 89  
4.2.1.3 Comparison of Electrical and Rheological Percolation 
The inter-relationship between electrical and rheological properties in terms of the 
structure-property relationships of PS-MWCNT composites was also investigated to 
understand the difference in using these properties to establish percolation of MWCNTs. 
A closer examination of the low frequency (0.1 rad/s), microstructure sensitive regime of 
figures 4.10-4.13 shows an increase in all the rheological parameters with MWCNT 
loading for the THF processed composites. As expected from previous research 
investigations [14,84], the parameter whose absolute values are most sensitive to particle 
loading is the storage modulus G?, which increased by more than 2 orders of magnitude 
upon adding MWCNTs. Over the same range of MWCNT loadings, the absolute values 
of ?*, G?, and G?/G? each increased by about an order of magnitude. 
Similar to the electrical percolation threshold, rheological percolation threshold is 
correlated with the onset of power law dependence of a rheological property on the 
volume fraction. However, there is no agreement on which quantity to use in this regard: 
for example, while Du et al [51] report the percolation based on G?, Kharchenko et al [83] 
report the percolation based on G?/G?. In order to understand which rheological 
parameter describes percolation better, the normalized-log values of various directly 
measured ( logG?  and logG??) and derived rheological parameters( log *?  and 
log( / )G G? ?? ) are plotted in figure 4.14, and compared with the normalized-log values of 
electrical conductivity ( c?log ) and the power law predictions of electrical conductivity 
( PLc?log ). In addition, a power law of the form described by equation (4.1) was used to 
 90  
fit the G? and ?* data (fit parameters in table 4.4) and the normalized log-values of the 
modified power law predictions ( PLG )*log&"log(   ? ) are also plotted in figure 4.14. 
 
Figure 4.14 The log-normalized values of storage modulus ( 'logG ) , loss modulus 
( "logG ), complex viscosity ( *log? ) and inverse loss tangent ( )"/'log( GG ), electrical 
conductivity ( c?log ) and the power law fit for electrical conductivity ( PLc?log ) as a 
function of the MWCNT loading at 190?C for THF processed composites. The 
rheological data were obtained from figures 4.10, 4.12 and 4.13 at a frequency of 0.1 
rad/s. The viscous rheological parameters, *"&?G , exhibit a gradual percolation rate, and 
hence a modified power law fit ( PLG ) *log& "log( ? ) was used. 
 
Table 4.4 The power law fit parameters for the rheological properties of the PS-MWCNT 
composites processed using THF. 
 
 
 
 
 
 
 
Power law 
parameter 
THF (  *log& "log ?G ) 
A 16 
?c 0.019 
? 7 
0.E+00
1.E-01
2.E-01
3.E-01
4.E-01
5.E-01
6.E-01
7.E-01
8.E-01
9.E-01
1.E+00
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Volume Fraction MWCNTs
No
rm
ali
ze
d L
og
(pr
op
ert
y)
log G'
log (G'/G'')
      ??
log G''
      ?
      ?
(log G''& PL
c
log ?*)
log
log
log
c
PL
'G
"g G
*g?
)"/'l g( GG
c?g
PL
c?log
PLG ) *log& "log( ?
 91  
An inspection of figure 4.14 reveals that "logG  and *log?  exhibit a percolation 
behavior that is far more gradual when compared to 'logG  and "/'log GG  and c?log . 
Quantitative comparisons between fits were made using normalized cross-correlation 
coefficient values (table 4.5). Both "logG  and *log?  seem to match well with 
PLG )*log&"log(   ?  yielding normalized cross-correlation coefficients of 0.97 and 0.98 
respectively, as opposed to 0.86 and 0.87 respectively when compared with PLc?log . At 
lower loadings of MWCNTs, closer to the electrical percolation threshold, "/'log GG  
matches better with PLc?log  when compared to 'logG . At higher loadings, both 'logG  
and "/'log GG  match well with PLc?log . Overall, comparing 'logG  and "/'log GG  
with PLc?log  yielded normalized cross-correlation coefficients of 0.95 and 0.98 
respectively, as opposed to 0.92 and 0.84 respectively when compared with 
PLG )*log&"log(   ? . 
Table 4.5 Normalized cross-correlation values for the normalized log of rheological 
parameters for PS-MWCNT nanocomposites processed with THF solvent when 
compared with the normalized log of the power law fits to the electrical conductivity 
measurements for THF processed PS-MWCNT nanocomposites and the fits to 
 *log& "log ?G  in figure 4.14. 
Rheological 
Parameter 
Power law 
( PLc?log ) 
Power law 
(  *log& "log ?G ) 
G' 0.95 0.92 
G'/G'' 0.98 0.84 
G'' 0.86 0.97 
?? 0.87 0.98 
 
It can be noted that while G? and G? are directly measured rheological parameters, 
?* and G?/G? are derived rheological parameters that have physical significance in terms 
 92  
of the flow and firmness of the nanocomposites. An important conclusion can be drawn 
from figure 4.14: to report rheological percolation, G? is a good choice among the 
directly measured rheological parameters, and G?/G? is a good choice among the derived 
rheological parameters due to the steep increase in their values at low MWCNT loadings. 
Microstructurally, this indicates that the elastic load transfer and electrical conductivity 
are far more sensitive to the onset of percolated MWCNTs than the viscous dissipation 
mechanisms as quantified by the change in the power law exponent. 
 
4.2.1.4 Effect of Solvent on Rheological Percolation 
In order to study the influence of solvent on rheological percolation, the variation 
of ?* with G* obtained from the DMF-processed composites (figure 4.15) was compared 
with that obtained from the THF-processed ones (figure 4.12b). In figure 4.15, the 
asymptotic complex modulus increases from 11600 Pa at 5 vol. % MWCNTs to 37500 Pa 
at 12 vol. %. Comparing with figure 4.12b, the G* value at 12 vol. % is 25% greater for 
the DMF-processed composites as compared to the THF ones. The diverging curves of 
the DMF-processed composites exhibit complex viscosity plateaus similar to those 
observed with THF ones and their values range from 1350 Pa-s at an MWCNT loading of 
5 vol. % to 2300 Pa-s at 12 vol. %. However, the complex viscosity plateau for the fully 
percolated (12 vol.%) composites does not vary significantly with the choice of solvent. 
 
 93  
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+03 1.E+04 1.E+05 1.E+06
Complex Modulus, G* (Pa)
Co
mp
lex
 V
isc
osi
ty,
 ????*
 (P
a-s
)
0 vol.%
2 vol.%
5 vol.%
8 vol.%
12 vol.%
 
Figure 4.15 Complex viscosity (?*) as a function of complex modulus (G*) for the PS-
MWCNT composites processed with DMF and tested at a temperature of 190?C. Data are 
shown for a range of MWCNT loadings. Note the plateau in complex viscosity in the 
high complex modulus regime. 
 
Next, the normalized log-values of various rheological parameters and electrical 
conductivity obtained from the DMF-processed composites (figure 4.16) were compared 
with those obtained from the THF-processed ones (figure 4.14) using the normalized 
cross-correlation coefficients (table 4.6).  
2300 Pa-s 
2200 Pa-s 
1350 Pa-s 
11
60
0 P
a 
32
80
0 P
a 
37
50
0 P
a 
 94  
 
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Volume Fraction MWCNTs
No
rm
ali
zed
 L
og
(p
ro
pe
rty
)
G'
G'/G"
G"
??
?
?
G''-
pow er law
pow er law
THF
pow er law??
 
Figure 4.16 The log-normalized values of storage modulus ( 'logG ) , loss modulus 
( "logG ), complex viscosity ( *log? ) and inverse loss tangent ( )"/'log( GG ), electrical 
conductivity ( c?log ) and the power law fit for electrical conductivity ( PLc?log ) as a 
function of the MWCNT loading at 190?C for DMF processed composites. The 
rheological data was obtained at a frequency of 0.1 rad/s. Note that ?* and G? percolate 
similar to that predicted by the modified power law ( PLG )*log&"log(   ? ) for THF 
processed composites. However, G? and G?/G? percolate more gradually compared to c? . 
This is in contrast to that observed with the THF processed composites. 
 
Table 4.6 Normalized cross-correlation values for the normalized log of rheological 
parameters for PS-MWCNT nanocomposites processed with DMF solvent when 
compared with the normalized log of the power law fits to the electrical conductivity 
measurements for DMF processed PS-MWCNT nanocomposites and the fits to 
 *log& "log ?G  in figure 4.16. 
Rheological 
Parameter 
Power law 
( PLc?log ) 
Power law 
(  *log& "log ?G ) 
G' 0.88 0.95 
G'/G'' 0.94 0.89 
G'' 0.76 0.98 
?? 0.77 0.99 
'logG
"logG
*log?
)"/'log( GG
c?log
PL
c?log
PLG ) *log& "log( ?
 95  
 
Figure 4.16 reveals that in DMF-processed composites, "logG  and *log?  exhibit a 
percolation behavior that is more gradual when compared to 'logG , "/'log GG  and 
PL
c?log . Both "logG  and *log?  seem to match well with 
PLG )*log&"log(   ?  yielding 
normalized cross-correlation coefficients of 0.98 and 0.99 respectively, as opposed to 
0.76 and 0.77 respectively when compared with PLc?log . This behavior is similar to that 
observed in the THF processed composites. However, in the DMF-processed composites, 
unlike the THF-processed ones, both 'logG  and "/'log GG  increase more gradually 
when compared with PLc?log  yielding normalized cross-correlation coefficients of 0.88 
and 0.94 respectively, as opposed to 0.95 and 0.89 respectively when compared with 
PLG )*log&"log(   ? . This indicates that DMF influences the electrical conductivity more 
than the elastic behavior of the composites, unlike THF. Thus, an important conclusion 
can be drawn about the processing-property relationships in solvent processed PS-
MWCNT composites from these observations: the choice of solvent has a slight effect on 
the differences between rheological and electrical percolation. All of these results are 
consistent with previous investigations [87] on the effect of solvents on electrospinning 
of PS, where the conductivity of the PS solutions with DMF was found to be 2.4 ?S/cm, 
compared to ~0 ?S/cm with THF, and the surface tension was found to be 34.339 mN/m 
with DMF, compared to 24.735 mN/m with THF. 
 
 
 
 96  
4.2.1.5 Modeling as an Interpenetrating Phase Composite 
In order to gain further insight into the relationship between electrical and 
rheological percolation, the PS-MWCNT composite is considered as a combination of 
two phases: a continuous PS phase reinforced by non-interacting MWCNTs, and a 
continuous phase consisting of a pseudo-solid like network of percolated MWCNTs, as 
identified in 4.1.1. In order to quantify the distribution of MWCNTs among the phases, 
the degree of percolation ( )(C ? ) is proposed as: 
)(
)()(C
PLPT
c
PL
c
??
???
0=     (4.3) 
where )(PLPTc ?? 0 is the value of electrical conductivity according to the power law fit 
when the percolation threshold is 0 vol. % (i.e., instantaneous percolation). Thus, the 
degree of percolation reflects the offset in the connectivity of the MWCNTs that begins 
above the percolation threshold. The degree of percolation )(C ?  as a function of volume 
fraction can be seen in figure 4.17.  
0.0
0.2
0.4
0.6
0.8
1.0
0 0.2 0.4 0.6 0.8 1
Volume Fraction MWCNTs
De
gr
ee
 of
 P
er
co
lat
ion
 
Figure 4.17 Degree of percolation at various MWCNT loadings. 
 
 97  
The )(C ?  based on the power law model converges to the theoretical maximum above a 
volume fraction of 0.6, which is close to the classical theoretical maximum packing 
fraction for cylinders of 0.79 where full percolation of the microstructure would have to 
occur. This indicates that the degree of percolation obtained from the power law fit can 
provide a physically reasonable prediction of the distribution of MWCNTs among the 
interpenetrating phases. The degree of percolation corresponding to each of the 
compositions that was characterized is shown in table 4.7.  
Table 4.7 The degree of percolation calculated from the electrical conductivity 
measurements for each composition using the power law fit. 
 
 
 
 
 
 
By using a linear rule-of-mixtures formulation commonly employed for 
predicting the properties of interpenetrating phase composites [88,89], the product of the 
degree of percolation and the volume fraction can be used to quantify the contribution of 
each phase to the  dynamic rheological properties of the composite: )(C ??  for the 
continuous phase consisting of a pseudo-solid like network of percolated MWCNTs and 
)(C ???1  for the continuous phase of PS reinforced by non-interacting MWCNTs. 
Accordingly, the storage modulus, G?, and the loss modulus, G??, can each be represented 
as a function of the degree of percolation, )(C ? , frequency, ?, and MWCNT volume 
fraction, ?, as shown in equations (4.4)-(4.9). The relationships in equations 4.4-4.9 are 
obtained from classical formulae used for describing the rheological response of 
Mass  
Fraction 
Volume  
Fraction 
Degree of  
Percolation 
0.01 0.02 0.00 
0.03 0.05 0.42 
0.05 0.08 0.62 
0.07 0.12 0.75 
 98  
polymers, including the effect of non-interacting particles and the viscoelastic behavior of 
a solid [90-94]. The continuous phase of percolated MWCNTs is modeled using a 
frequency-dependent behavior of a elastic-viscoplastic solid observed in clay suspensions 
[90], while the unpercolated MWCNTs are modeled by using the classical Nielsen 
formula that introduces the concept of maximum packing using a generalized Kerner 
equation [94]. 
)(
))(()()(/ 1)(/1
)()(/ 1)(/1
))(1(                  
 )()0()()),(,('
'
''
''
''
''
5.
''
?
???????
????
??
?
?
?
????????
PS
PSRMWCNT
PSRMWCNT
PSRMWCNT
PSRMWCNT
c
PMWCNT
c
PMWCNT
c
PMWCNTPMWCNTPMWCNT
G
AGG
GG
AGG
GGA
C
GCCG
??
?
?
?
?
?
??
?
?
?
?
?
???
?
???
?
+
??
???
?
???
?
+
?+
?+
+??
?
?
?
?
?
?
?
?
?
?
?
?
?
?
???
?
???
?+
???
?
???
??+=
           (4.4) 
)( 
))(()()(/ 1)(/1
)()(/ 1)(/1
))(1(                  
 )()0()()),(,(''
''
''''
''''
''''
''''
5.
''''
?
???????
????
??
?
?
?
????????
PS
PSRMWCNT
PSRMWCNT
PSRMWCNT
PSRMWCNT
c
PMWCNT
c
PMWCNT
c
PMWCNTPMWCNTPMWCNT
G
AGG
GG
AGG
GGA
C
GCCG
??
?
?
?
?
?
??
?
?
?
?
?
???
?
???
?
+
??
???
?
???
?
+
?+
?+
+??
?
?
?
?
?
?
?
?
?
?
?
?
?
?
???
?
???
?+
???
?
???
??+=
           (4.5) 
where, 
2
2
'
1
)(
?
?
?
?
?
?
?
?
???
?
???
?+
???
?
???
?
=
p
c
PS
p
c
PSp
PSPS GG
?
?
?
?
?    (4.6) 
 99  
2
''
1
)0()(
?
?
?
?
?
?
?
?
???
?
???
?+
=
q
c
PS
PSPSG
?
?
???    (4.7) 
    ?( ?(?)) = 1 + (1- ?m)?(?)/?m2   (4.8) 
         ?(?) = )C/()C( ??? ?? 1    (4.9) 
and the following constants are determined by applying equations (4.4)-(4.7) to the 
experimental melt rheology data: 
)0('PMWCNTG   = storage modulus of the continuous phase of percolated MWCNTs as 
0??  
)(' ?PMWCNT?  = real part of complex viscosity for the continuous phase of percolated 
MWCNTs as ???  
'
RMWCNTG   = effective storage modulus of the MWCNT reinforcement in the 
continuous PS phase 
p
PSG   = plateau modulus of neat PS 
)0(''PMWCNTG  = loss modulus of the continuous phase of percolated MWCNTs as 
0??  
)('' ?PMWCNT?   = imaginary part of complex viscosity for continuous phase of percolated 
MWCNTs as ???  
''
RMWCNTG   = effective loss modulus of the MWCNT reinforcement in the continuous 
PS phase 
)0(PS?   = viscosity of neat PS as 0??  
 100  
p,q,  = power law indices 
c
PS? ,
c
PMWCNT?  = critical frequencies related to the relaxation of neat PS and percolated 
MWCNTs 
A  = shape and orientation factor of reinforcement 
?M      = maximum theoretical volume fraction of non-interacting MWCNTs 
Thus, the degree of percolation obtained from the electrical conductivity measurements 
provides a means of distinguishing the effect of percolated and unpercolated MWCNTs. 
This essentially results in a modification of the Nielsen equation for unpercolated 
suspensions to include the effects of percolation.  
The fits to the experimental data obtained from using the new rheological models 
and the degree of percolation can be seen in figure 4.18. These results indicate good 
correlation between the fits and the experimental data, and verify the appropriateness of 
the new rheological models for capturing the formation of the interpenetrating phase 
composite from the percolation of the MWCNTs. Thus, the new rheological models 
permit, for the first time, determination of the properties of the continuous phase 
consisting of a pseudo-solid like network of percolated MWCNTs. These values can be 
seen in table 4.8. The continuous phase of percolated MWCNTs exhibits an elastic solid 
like behavior at low frequencies with a complex modulus, 
( ) ( )2"2'* )0()0()0( PMWCNTPMWCNTPMWCNT GGG += = 360 kPa, and then transitions at higher 
frequencies to a viscoplastic solid like behavior with a complex viscosity,  
( ) ( )2"2'* )()()( ?+?=? PMWCNTPMWCNTPMWCNT ??? = 6 kPa-s/rad.  
 101  
 
 
  
 
 
Figure 4.18 (a) Storage modulus (G?) and (b) loss modulus (G?) of the composites as a 
function of frequency. Data are shown for a range of MWCNT loadings. Note that the fits 
from the proposed rheological model match well with the experimental data. 
 
  0 vol. % 
  2 vol. %  
  5 vol. % 
  8 vol. % 
12 vol. % 
(b) 
G?
 (P
a) 
0.1                          1                          10                         100 
? (rad/s) 
1.E+06        
1.E+05        
1.E+04              
1.E+03        
1.E+02        
1.E+01        
G?
 (P
a) 
1.E+06        
1.E+05        
1.E+04              
1.E+03        
1.E+02        
1.E+01        
0.1                          1                          10                         100 
? (rad/s) 
? (rad/s) 
0.1                         1                         10                       100 
(a) 
  0 vol. % 
  2 vol. %  
  5 vol. % 
  8 vol. % 
12 vol. % 
 102  
 
Table 4.8 Values of material properties determined from fitting experimental data for PS-
MWCNT composite with the new rheological models 
 
 
Simultaneously, it is possible to isolate the effects of the non-interacting MWCNTs that 
reinforce the PS. The reinforcing MWCNTs behave like an elastic solid with an effective 
complex modulus, ( ) ( )2"2'* )0()0()0( RMWCNTRMWCNTRMWCNT GGG += = 208 kPa.  
The frequency response at low and high frequencies provides direct insight into 
the nature of the continuous phase of percolated MWCNTs. The normalized complex 
modulus, )0(*/)(* GG ? , and the normalized complex viscosity, )0(*/)(* ??? , seen in 
figure 4.19 are consistent with the frequency independent modulus of an elastic solid at 
low frequencies and frequency independent viscosity of a viscoplastic solid at high 
frequencies. This behavior is indicative of a scaffold-like microstructure that exhibits a 
stick-slip friction mechanism at higher frequencies.  
Constant Value 
)(' ?PMWCNT?  4 kPa-s/rad 
)0('PMWCNTG  350 kPa 
'
RMWCNTG  200 kPa 
p
PSG  100 kPa 
)('' ?PMWCNT?  5 kPa-s/rad 
)0(''PMWCNTG  80 kPa 
''
RMWCNTG  60 kPa 
)0(PS?  10 kPa-s/rad 
P 0.70 
Q 0.55 
c
PS?  12 rad/s 
c
PMWCNT?  80 rad/s 
 A 1000 
?M 0.65 
 103  
This aspect of the research has a very important implication: it provides a new 
methodology for quantifying the continuous phase formed by the percolation of 
nanostructures in polymer nanocomposites through the properties obtained using 
equations (4.4)-(4.9). It can be applied to functionalized nanostructures being developed 
for [95,96]: (a) controlling the percolation of the nanostructures through self-assembly, 
(b) enhancing their interaction with the continuous reinforced polymer phase, (c) 
enhancing the cohesion between nanostructures. This is possible because the continuous 
reinforced polymer phase stabilizes the state of the continuous phase of percolated 
nanostructures, which is similar in principle to the stabilization of proteins using 
formalin-fixed, paraffin-embedded tissue blocks for histopathology. 
 
Figure 4.19 Normalized rheological properties of the continuous phase of percolated 
MWCNTs indicating elastic-viscoplastic behavior with a crossover in behavior from 
elastic to viscoplastic at the normalized frequency of 1. 
 
 
??? */*
?/?c 
 104  
4.2.2 PS ? CNF Composites: Solvent Processed & Extruded 
In order to further investigate the effects of processing on the structure-property 
and processing-property relationships in polymer nanocomposites, CNFs were used 
instead of MWCNTs to allow for larger quantities of less expensive but structurally and 
chemically similar nanoscale ingredients to be used in a commercial scale twin screw 
extruder.  To rigorously investigate the effects of processing, the effect of the CNF 
ingredients on the structure-property relationships for solvent processed nanocomposites 
had to also be investigated as previously outlined in Table 4.1. 
 
4.2.2.1 Electrical Conductivity: Solvent Processed 
Figure 4.20 shows the experimentally determined electrical conductivity ( c? ) of 
solvent processed PS-CNF composites, processed using DMF, as a function of the CNF 
loading. Each data point on the plot represents the average of measurements on 6-8 
different samples, and the scatter in the data was within 5% of this average value. The 
conductivity of neat PS is ~10-20 S/m. However, the detection limit of our measurements 
was ~10-8 S/m. Hence, all electrical conductivity values, which were below the detection 
limit, were assumed to be equal to 10-8 S/m. Upon adding the CNFs, the conductivity of 
the composites increased by 8 orders of magnitude approaching a value of 1 S/m with 10 
wt.% CNF loading. Similar to the PS-MWCNT composites, the conductivity data of the 
PS-CNF composites were fit using the power law of the form shown in equation (4.10):  
    ??? )( cPSPLc wwA ?+=     (4.10) 
Here, PLc?  is the conductivity of the composite predicted by the power law fit, PS?  is the 
electrical conductivity of the neat PS (assumed to be 10-8 S/m), A  is a constant based on 
 105  
the interconnectivity of the CNFs, cw  is the percolation threshold and ?  is the critical 
exponent. The data were modeled in terms of weight fractions instead of volume fractions 
because the density of CNFs is unknown. The best fit parameters are listed in table 4.9.  
1.E-08
1.E-06
1.E-04
1.E-02
1.E+00
0 2 4 6 8 10
Wt% of CNFs
El
ec
tri
ca
l C
on
du
cti
vit
y, 
???? 
(S
/m
)
Experiment
Power Law
 
Figure 4.20 Electrical conductivity of the PS-CNF composites solvent processed using 
DMF at various CNF loadings. The corresponding power law fits are also shown. 
 
Table 4.9 The power law fit parameters for the electrical conductivity of the PS-CNF 
composites processed using DMF. 
 
 
 
 
 
 
It must be noted that the percolation threshold of the solvent processed PS-CNF 
composites is 3 wt.%, compared to 1 wt.% of the PS-MWCNT composites. Furthermore, 
the plateau in electrical conductivity was seen at ~10 wt.% for PS-CNF composites, 
compared to ~5 wt.% for the PS-MWCNT composites. However, the value of the peak 
electrical conductivity seems to asymptotically reach 1 S/m in both cases. From these 
Power law 
parameter 
DMF (?c) 
A 0.002 
wc 3 
? 3 
 106  
results a very important conclusion can be drawn about the effect of ingredients on 
structure-property relationships: the differences in percolation threshold and the plateau 
in electrical conductivity can be attributed to the lower aspect ratio of CNFs (~30:1) 
when compared with MWCNTs (~100:1). 
 
4.2.2.2 Electrical Conductivity: Extruded & Annealed 
The effect of processing on the structure-property relationships of the PS-CNF 
composites was further studied by comparing the electrical properties of the extruded 
polymer nanocomposites before and after annealing. Figure 4.21 shows the 
experimentally determined electrical conductivity ( c? ) of the solvent processed and 
extruded PS-CNF composites as a function of CNF loading. It is evident that the extruded 
composites exhibit a higher percolation threshold of 7 wt.%, compared to 3 wt.% of the 
solvent processed composites. At 10 wt.%, the extruded composites show an electrical 
conductivity of ~5 x 10-4 S/m, which is 3 orders of magnitude lower than ~0.8 S/m of the 
solvent processed composites. As described in 4.1.4, the higher percolation threshold and 
lower conductivity of the extruded composites can be attributed to the preferential 
alignment of CNFs, presumably due to the shear flow through the die.  
 107  
1.E-08
1.E-06
1.E-04
1.E-02
1.E+00
0 3 6 9 12 15
Wt% of CNFs
El
ec
tri
ca
l C
on
du
cti
vit
y, 
???? 
(S
/m
)
Extruded
Solvent Processed
 
Figure 4.21 Electrical conductivity of the extruded and solvent processed PS-CNF 
composites at various CNF loadings. 
 
Furthermore, it was observed that the electrical conductivity of the extruded PS-
CNF composites changed significantly upon annealing. Figure 4.22 shows the influence 
of annealing temperature on the electrical conductivity of the extruded PS-CNF 
composites. The conductivity data for composites annealed at 170 and 200?C for 30 min 
are presented. It is evident that conductivity can be recovered by annealing at high 
temperatures. In the absence of annealing, i.e., for the as-extruded composites, a 
percolation threshold of 7 wt.% was observed with appreciable conductivities at 10 wt.% 
and 15 wt.% CNF loading. Annealing at 170?C for 30 min did not change the percolation 
threshold, but increased the conductivity by ~2 orders of magnitude. Annealing at 200?C 
for 30 minutes lowered the percolation threshold to 3 wt.% by imparting appreciable 
conductivities to the composite with 5 wt.% and 7 wt.% CNF loading. It was also 
observed that the choice of annealing temperature is crucial: higher than the softening 
point of PS (~ 150?C), but well below its thermal degradation temperature (~ 250?C). It 
 108  
must be noted that all the electrical conductivity measurements were made at room 
temperature.  
1.E-08
1.E-06
1.E-04
1.E-02
1.E+00
0 3 6 9 12 15
Wt% of CNFs
El
ec
tri
ca
l C
on
du
cti
vit
y, 
???? 
(S
/m
)
Extruded
Annealed at 170 C
Annealed at 200 C
 
Figure 4.22 Effect of annealing temperature on electrical conductivity of extruded PS-
CNF composites. The composites were annealed for 30 minutes. Note the lower 
percolation threshold at higher annealing temperature. 
 
Figure 4.23 shows that in addition to annealing temperature, the annealing time 
also has an effect on the electrical conductivity of the PS-CNF composites. The 
conductivity data for composites annealed for 3 min and 30 min at 200?C are presented. 
It is evident that conductivity can be recovered by annealing for longer time. Annealing 
for 3 min at 200?C lowered the percolation threshold to 5 wt.% and increased the 
conductivity by ~2 orders of magnitude. Annealing for 30 minutes at 200?C lowered the 
percolation threshold to 3 wt.% by imparting appreciable conductivities to the composite 
with 5 wt.% and 7 wt.% CNF loading. 
 109  
1.E-08
1.E-06
1.E-04
1.E-02
1.E+00
0 3 6 9 12 15
Wt% of CNFs
El
ec
tri
ca
l C
on
du
cti
vit
y, 
???? 
(S
/m
)
Extruded
Annealed for 3 min
Annealed for 30 min
 
Figure 4.23 Effect of annealing time on electrical conductivity of extruded PS-CNF 
composites. The composites were annealed at 200?C. Note the lower percolation 
threshold at longer annealing times. 
 
From these results an important conclusion can be drawn about the effect of 
processing on structure-property relationships: as described in 4.1.4, annealing re-
establishes the interconnectivity of preferentially aligned CNFs in the extruded 
composites (see figure 4.6), thereby enhancing the electrical conductivity. The increase in 
electrical conductivity with increasing annealing temperature and annealing time suggests 
that the phenomenon is diffusion controlled. However, nanocomposites are typically non-
Brownian systems due to their high matrix viscosity and the extended geometry of the 
filler particles [83,97-99]. Nevertheless, while translational diffusion may be limited, the 
particles may still be able to rotate and re-orient, even under non-Brownian conditions. 
Annealing at higher temperatures will promote such re-orientation because of the 
decrease in matrix viscosity and the increased thermal diffusivity. It is evident from 
figures 4.22 and 4.23 that the nanocomposites with higher particle loadings recover their 
conductivity after annealing at lower temperatures and for shorter times. At higher 
 110  
loadings, the particles are sufficiently close to each other that they can re-form 
interconnects quite easily. However, at lower loadings, the particles need to re-orient 
and/or diffuse appreciable distances to form a link with their nearest neighbors. Similar 
reorganization under quiescent conditions at high temperatures (after shear, for example) 
was reported for clay particles in polymer/clay nanocomposites [98,99]. A further driving 
force for the re-orientation of clay particles was postulated to arise from strong attractive 
interaction between particles [99]. This may be a factor in the PS-CNF composites too, 
since it is known that CNFs experience stronger van der Waals interactions than clay 
particles due to their highly conductive nature.  
 
4.2.2.3 Rheological Properties: Solvent Processed 
The solvent processed PS-CNF composites were investigated for their dynamic 
rheological properties. Figure 4.24 shows the storage modulus G? and the loss modulus 
G? of the DMF processed PS-CNF composites as functions of frequency. Both G? and G? 
increase with CNF loading. At 3 wt.% loading of CNFs and above, G? reaches a plateau 
at low frequencies indicating that percolated CNFs may be forming a pseudo-solid like 
network with strong interactions between polymer and particles [83,84]. Similar, but less 
predominant effects are observed in G?.  
 111  
1.E+00
1.E+02
1.E+04
1.E+06
0.01 0.1 1 10 100
Frequency, ? (rad/sec)
St
or
ag
e M
od
ulu
s, 
G'
 (P
a)
0 wt%
3 wt%
5 wt%
7 wt%
10 wt%
 
 
 
1.E+00
1.E+02
1.E+04
1.E+06
0.01 0.1 1 10 100
Frequency, ? (rad/sec)
Lo
ss
 M
od
ulu
s, 
G"
 (P
a)
0 wt%
3 wt%
5 wt%
7 wt%
10 wt%
 
 
Figure 4.24 (a) Storage modulus (G?) and (b) loss modulus (G?) of the solvent processed 
PS-CNF composites as a function of frequency at a temperature of 190?C. Data are 
shown for a range of CNF loadings. Note the plateau in G? at low frequencies for all of 
the CNF loadings indicating the presence of a pseudo-solid like phase in the composite 
formed by percolated CNFs. 
 
(a) 
(b) 
 112  
Thus, the rheological percolation threshold qualitatively matches well with the 
electrical percolation threshold of the solvent processed PS-CNF composites. In addition, 
comparing figures 4.10 and 4.24, it is evident that the rheological behavior of the solvent 
processed PS-MWCNT and PS-CNF composites is similar, but the values of G? and G? 
are consistently higher for the former. From these results, an important conclusion can be 
drawn about the effect of ingredients on the structure-property relationships: due to the 
higher aspect ratio of MWCNTs when compared to the CNFs, the rheological properties 
are higher for the PS-MWCNT composites. 
 
4.2.2.4 Rheological Properties: Extruded & Annealed 
The extruded PS-CNF composites were investigated for their dynamic rheological 
properties to compare with those of the solvent processed composites. Figure 4.25 shows 
the storage modulus G? and the loss modulus G? of the extruded PS-CNF composites as 
functions of frequency. Comparing figures 4.24 and 4.25, it is evident that the rheological 
behavior of the extruded and solvent processed PS-CNF composites is similar. Both G? 
and G? increase with CNF loading and at 3 wt.% loading of CNFs and above, G? reaches 
a plateau at low frequencies indicating that percolated CNFs may be forming a pseudo-
solid like network with strong interactions between polymer and particles [83,84]. 
Similar, but less predominant effects are observed in G?. However, the values of G? and 
G? of the extruded composites are consistently lower than solvent processed composites 
at all loadings. This can be attributed to the lower aspect ratio of CNFs in the extruded 
composites when compared to the solvent processed composites as described in 4.1.3. 
 113  
1.E+00
1.E+02
1.E+04
1.E+06
0.01 0.1 1 10 100
Frequency, ? (rad/s)
St
or
ag
e M
od
ulu
s, 
G'
 (P
a)
0 wt%
3 wt%
5 wt%
7 wt%
10 wt%
 
 
 
1.E+00
1.E+02
1.E+04
1.E+06
0.01 0.1 1 10 100
Frequency, ? (rad/s)
Lo
ss
 M
od
ulu
s, 
G'
 (P
a)
0 wt%
3 wt%
5 wt%
7 wt%
10 wt%
 
 
Figure 4.25 (a) Storage modulus (G?) and (b) loss modulus (G?) of the extruded PS-CNF 
composites as a function of frequency at a temperature of 190?C. Data are shown for a 
range of CNF loadings. Note the lower values of G? and G? when compared with the 
solvent processed PS-CNF composites shown in figure 4.24. 
 
(a) 
(b) 
 114  
Furthermore, similar to electrical conductivity, annealing the extruded PS-CNF 
composites resulted in increased rheological properties. However, the increases in the 
rheological properties were not as significant as the electrical conductivity. Figure 4.26 
shows the effect of annealing on the inverse loss tangent as a function of CNF loading. 
Inverse loss tangent, which represents the firmness of the material, shows a modest 
increase after annealing. In addition to the direct evidence provided by microscopy (see 
4.1.4), this corroborates the re-establishment of connections between the CNFs that were 
lost during processing. It should be noted that the rheological data in figure 4.26 were 
obtained at 200?C by annealing for 30 mins. Indeed, it is then understandable that the 
differences in rheology at 200?C are modest compared to the differences in electrical 
conductivities of unannealed and annealed composites conducted at room temperature.  
0.1
1
10
0 3 6 9 12 15
Wt% of CNFs
Inv
er
se
 Lo
ss
 Ta
ng
en
t, G
'/G
"
Extruded
Annealed at 200 C
 
Figure 4.26 Effect of annealing on the rheological properties of extruded PS-CNF 
composites. The composites were annealed for 30 mins. 
 
 115  
4.2.2.5 Thermo-oxidative behavior: Solvent Processed & Extruded 
To understand the effects of processing on the thermo-oxidative behavior of the 
polymer phase and the filler phase in the PS-CNF composites, thermo gravimetric 
analysis was conducted at various CNF loadings in an unmixed, extruded and solvent 
processed state. For extruded PS-CNF composites, the effects of porosity, screw speed 
and screw design were also studied. The detailed experimental procedure was described 
in 3.3.1 and 3.4.3. 
Figures 4.27a and 4.27b show the representative weight percent and weight loss 
rate (WLR) profiles respectively of the PS-CNF composites at various CNF loadings. 
The magnitude of the peak WLR of the styrene-rich phase as a function of the CNF 
loading can be seen in figure 4.27c. In contrast to the results reported in [55], figures 
4.27a and 4.27b indicate that there is no significant effect of CNF loading on any of the 
three temperatures at peak weight loss rate (TPWLR) of the solvent processed or 
extruded PS-CNF composites. However, the magnitude of the peak WLR corresponding 
to the styrene-rich phase was found to quadratically decrease with CNF loading. This is 
consistent with the quadratic reduction in the WLR that is predicted by the simple 
combustion model [100] for an isotropic solid structure, such as a sphere or a cube, as its 
size is reduced (which is equivalent to a reduction in the volume fraction of the polymer). 
Thus, the reduction of the peak WLR of the composite is consistent with increasingly 
replacing the weight of PS with CNFs. The peak WLR decreases quadratically from 15.7 
mg/min for neat PS to 0 mg/min for neat CNFs. 
 
 
 
 116  
 
 
0
20
40
60
80
100
0 2000 4000 6000 8000
Time (sec)
W
eig
ht
 P
er
ce
nt
 (%
) 7 wt%
5 wt%
3 wt%
1 wt%
0 wt%
 
(a) 
 
 
 
0
3
6
9
12
15
18
0 2000 4000 6000 8000
Time (sec)
W
LR
 (m
g/m
in) 7 wt%5 wt%
3 wt%
1 wt%
0 wt%
  
(b) 
 
 117  
11
13
15
17
0 1 2 3 4 5 6 7 8
Wt% of CNF
Pe
ak
 W
LR
 of
 St
yr
en
e-r
ich
 Ph
as
e (
mg
/m
in)
 
(c) 
Figure 4.27 (a) Weight percent loss profiles of PS-CNF composites at various CNF 
loadings. (b) WLR profile of the PS-CNF composites at various CNF loadings. The inset 
shows the peak WLR of the styrene-rich phase. (c) The decreasing magnitude of peak 
WLR of the styrene-rich phase with increasing CNF loading. 
 
 In order to understand the effect of processing on the thermo-oxidative behavior 
of the polymer phase in the composites, the TPWLR corresponding to the styrene-rich 
phase was compared for the solvent processed, low porosity extruded and high porosity 
extruded composites. Since there was no significant effect of CNF loading on the 
TPWLR, the average of all the TPWLR corresponding to the styrene-rich phase at the 
loadings studied was assumed to be a representation of the processing effects. Figure 4.28 
shows the average TPWLR of neat PS and the PS-CNF composites corresponding to the 
styrene-rich phase as a function of the processing technique. It is evident that the solvent 
processed composites exhibit the lowest TPWLR, while the low porosity extruded 
composites exhibit the highest TPWLR. The neat PS results tend to indicate that the 
0.002 x2-0.357x+15.7 
 118  
solvents contaminate the PS thereby enhancing its combustion. Thus, an important 
conclusion can be drawn regarding the effect of processing on the thermal properties of 
the polymer phase of PS-CNF composites: extrusion is a slightly more desirable process 
than solvent processing for enhancing the thermal stability of the polymer phase by 
avoiding contamination from solvents. In addition, the decrease in TPWLR of PS-CNF 
composites in comparison to neat PS indicates that the presence of CNFs, which are 
thermally more conductive, tends to enhance the combustion by improving the rates of 
heat transfer. Within the TSE process, the removal of porosity through the use of a 
vacuum pump tends to marginally enhance the thermal stability.  
 
Figure 4.28 Average TPWLR of the styrene-rich phase of the PS-CNF composites 
processed via different techniques. Both the neat PS and the composites processed via 
solvent processing exhibit the least thermal stability and the extruded low porosity ones 
exhibit the highest thermal stability. The inset shows optical micrographs depicting the 
difference in porosity of the extruded composites. 
 119  
Further insight into the effects of extrusion processing conditions on the thermo-
oxidative behavior of the polymer phase of the composites was obtained by studying the 
TPWLR of the styrene-rich phase as a function of the extruder screw speed, which 
corresponds to the magnitude of shear rate (see figure 4.29).   
0
0.2
0.4
0.6
0.8
1
0 30 60 90 120 150 180 210
Screw Speed (RPM)
No
rm
ali
zed
 R
ela
tiv
e T
PW
LR
 of
 th
e S
tyr
en
e-
ric
h P
ha
se
 
Figure 4.29 Normalized relative TPWLR of the styrene-rich phase as a function of the 
extrusion screw speed. Note the approximately linear increase in TPWLR with increasing 
screw speed.  
 
The TPWLR of the styrene-rich phase is normalized to vary between 0 and 1 to identify 
the qualitative trend clearly. It indicates an approximately linear increase in TPWLR with 
screw speed. This can be attributed to the increase in agglomerate size at a screw speed of 
30 rpm when compared to 200 rpm due to lower shear rates, as discussed in 4.1.5. Thus, 
an important conclusion can be drawn about the effects of processing on the 
microstructure of the PS-CNF composite: increasing the surface area of the 
agglomerated and dispersed CNFs in the polymer possibly inhibits the initiation of 
thermal decomposition. This provides additional evidence that the use of solvents is 
 120  
affecting the thermal decomposition of PS in a deleterious manner (see figure 4.27) since 
the dispersion of the CNFs, which is better in solvent processed PS-CNF composites (see 
figure 4.4), should be enhancing the thermal stability. 
In order to investigate the effects of the solvent and extrusion processing on the 
thermo-oxidative behavior of the CNFs, the normalized weight loss of CNFs in the 
composites (i.e., the normalized weight loss after the time corresponding to the point of 
inflection between the second and third peaks of the WLR curve) was studied as a 
function of time and compared with unmixed ingredients (i.e., unprocessed PS and CNF). 
Figure 4.30 shows that the CNFs in solvent processed composites decompose at a 
substantially faster rate than the TSE processed ones. It can also be seen that the CNFs in 
both processes exhibit a faster decomposition rate relative to the unmixed material. 
Increasing the degree of shear in the TSE process i.e., changing from a low shear to a 
high shear screw design (see 3.2.2.2), slightly increases the rate of thermal 
decomposition. Given that the solvent processed PS-CNF composites show a random 
dispersion of CNFs (see figure 4.4), the thermo-oxidative behavior of the TSE processed 
material tends to indicate a microstructure in which the CNFs are better dispersed than 
the unmixed ingredients, but not dispersed as well as the solvent processed composites. 
Agglomerations in the extruded composites are clearly evident in the micrographs seen in 
figure 4.7. Thus, an important conclusion about characterizing the effect of processing on 
the microstructure of PS-CNF composites can be made: the combination of figures 4.7 
and 4.30 indicates that the TGA measurements can provide insight into the degree of 
dispersion resulting from the processing of the composites in a manner that is 
complimentary to conventional microscopy techniques. 
 121  
 
Figure 4.30 Normalized weight loss of CNFs as a function of time for the PS-CNF 
composites. Note that the rate of weight loss of CNFs increases with increasing levels of 
shear mixing. 
 
4.2.2.6 Mechanical Properties: Extruded 
To further investigate the structure-property and processing-property relationships 
for extruded PS-CNF composites, the tensile modulus, tensile strength, and % strain to 
failure of the PS-CNF composites extruded using the high shear screw design (see 
3.2.2.2) were measured using the procedure described in 3.4.4. Figure 4.31 shows a 
representative stress-strain plot of the extruded PS-CNF composites. The stress-strain 
behavior seen in figure 4.31 is typical of most glassy polymers. Neat PS is a brittle 
polymer with a less than 1% strain to failure. The presence of polybutadiene in 
polystyrene results in toughening above the yield strain. The toughening is usually 
 122  
attributed to the generation and growth of crazes [101]. This explains the higher % strain 
to failure (~8%) of the PS observed in figure 4.31. 
0
2
4
6
8
10
12
14
16
18
0 0.02 0.04 0.06 0.08
Strain
St
re
ss
 (M
Pa
)
 
Figure 4.31 A representative stress-strain plot of the extruded PS-CNF composites. 
 
Figure 4.32 shows the tensile modulus, tensile strength and the % strain the 
failure as functions of CNF loading. The tensile modulus shows a linear increase from 1.9 
GPa for the neat PS to 3.1 GPa for the extruded PS-CNF composite with ~10 wt.% CNF 
loading. The tensile strength shows a linear increase from 16 MPa for the neat PS to 25 
MPa for the extruded PS-CNF composite with ~10 wt.% CNF loading. The % strain to 
failure shows a linear decrease from 12% for the neat PS to 2% for the extruded PS-CNF 
composite with ~10 wt.% CNF loading. In summary, at 10 wt.% CNF loading, the tensile 
modulus increased by 62%, tensile strength increased by 54% and % strain to failure 
decreased by 85% compared to the neat PS. While the increase in tensile modulus and 
 123  
tensile strength is due to the higher mechanical properties of CNFs, the decrease in % 
strain to failure is due to the brittle nature of the CNFs.  
y = 0.1258x + 1.9752
R2 = 0.98
1.7
1.9
2.1
2.3
2.5
2.7
2.9
3.1
3.3
3.5
0 2 4 6 8 10
Wt% of CNFs
Te
ns
ile
 M
od
ul
us
 (G
Pa
)
 
(a) 
 
y = 0.953x + 15.829
R2 = 0.9724
10
14
18
22
26
0 2 4 6 8 10
Wt% of CNFs
Te
ns
ile
 S
tre
ng
th
 (M
Pa
)
`
 
(b) 
 124  
y = -0.0089x + 0.0977
R2 = 0.8502
0%
5%
10%
15%
20%
25%
0 2 4 6 8 10
Wt% of CNFs
% 
St
ra
in
 to
 F
ail
ur
e
 
 (c) 
Figure 4.32 Influence of CNF loading on the (a) tensile modulus, (b) tensile strength, 
and (c) % strain to failure of the extruded PS-CNF composites. 
 
Figure 4.32a provides an important insight into the reinforcing effects of CNFs on 
the tensile modulus of extruded PS-CNF composites: by extrapolating the linear trend of 
the tensile modulus to a 100 wt.% CNF loading, the limiting tensile modulus for the 
CNFs was estimated to be ~15 GPa. This value is similar to other recent investigations 
[71] into the mechanism of carbon nanomaterials reinforcement in polymer 
nanocomposites. However, it is significantly lower than the expectations of carbon 
nanomaterials [102,103]. This discrepancy may be due to the previously discussed 
agglomerates of CNFs (see 4.1.2 and 4.1.5) that act as masses of ?springs?, thereby 
reducing the effective modulus of the CNFs. Furthermore, the existence of agglomerates 
could promote crack propagation while preventing the nanocomposites from realizing the 
full enhancement in mechanical properties. 
 125  
 In addition, the effect of various extrusion processing parameters on the tensile 
modulus and tensile strength was also studied. Figure 4.33 shows the influence of the 
type of CNFs ? high density (HD) or low density (LD), filler feed port ? end or middle,  
and a vacuum pump (VP) ? with or without, on the tensile modulus and tensile strength 
of extruded PS-CNF composites with 10 wt.% CNF loading, extruded at 200 RPM. It is 
evident that the LD CNFs result in higher modulus and strength than the HD CNFs. This 
can be attributed to the higher aspect ratio of LD CNFs when compared to HD CNFs (see 
3.1.2.2) that results in higher surface area and hence better load transfer. The choice of 
filler feed port, which corresponds to the residence time in the extruder, does not indicate 
any effect on mechanical properties. The increase in residence time in feeding the filler 
through the end port when compared to the middle port is less than 10 minutes. The 
results indicate that such a small increase in residence time is not sufficient to improve 
the mixing significantly. Correspondingly, no appreciable change in the mechanical 
properties was observed.  
2.0
2.4
2.8
3.2
Processing Parameter
Te
ns
ile
 M
od
ulu
s (
GP
a)
Middle Port, no VP, HD
Middle Port, no VP, LD
End Port, no VP, LD
End Port, with VP, LD
 
(a) 
 126  
14
18
22
26
Processing Parameter
Te
ns
ile
 S
tre
ng
th
 (M
Pa
)
Middle Port, no VP, HD
Middle Port, no VP, LD
End Port, no VP, LD
End Port, with VP, LD
 
 (b) 
Figure 4.33 Influence of type of CNFs ? high density (HD) or low density (LD), filler 
feed port ? end or middle, and vacuum pump (VP) ? with or without, on the (a) tensile 
modulus, and (b) tensile strength of PS-CNF composites with 10 wt.% CNF loading, 
extruded at 200 RPM. 
On the other hand, using a vacuum pump in-line further improved the modulus and 
strength. The vacuum removed the air entrained in the CNFs, thereby reducing the 
porosity in the composites (see figure 4.8) and increasing the modulus and strength. 
Figure 4.34 shows the influence of screw speed and flow rate on the tensile 
modulus and tensile strength of PS-CNF composites with 10 wt.% CNF loading. Two 
different flow rates ? 1 and 2 lb/hr, and five different screw speeds ? 30, 60, 90, 150, 200 
RPM were employed. While there was no significant effect of flow rate on the 
mechanical properties, increasing screw speed, which corresponds to increased 
magnitude of shear rate, increased the modulus and strength. This is due to the 
redistribution of higher aspect ratio agglomerates into lower aspect ratio ones, as 
described in 4.1.5. 
 
 127  
2.0
2.4
2.8
3.2
0 50 100 150 200
Screw Speed (RPM)
Te
ns
ile
 M
od
ulu
s (
GP
a) 1 lb/h 2 lb/h
 
(a) 
12
14
16
18
20
22
24
26
0 50 100 150 200
Screw Speed (RPM)
Te
ns
ile
 S
tre
ng
th
 (M
Pa
) 1 lb/h 2 lb/h
 
 (b) 
Figure 4.34 Influence of screw speed and flow rate on the (a) tensile modulus, and (b) 
tensile strength of PS-CNF composites with 10 wt.% CNF loading, extruded at 200 rpm. 
While flow rate does not affect the mechanical properties significantly, both modulus and 
strength tend to increase with screw speed and begins to asymptotically reach a plateau at 
higher screw speeds. 
From Figure 4.34, a conclusion may be drawn concerning processing-property 
relationships for extruded PS-CNF composites: both modulus and strength begin to 
 128  
asymptotically reach a plateau value at higher screw speeds indicating that increasing 
the magnitude of shear rate does not provide a complete solution to obtaining optimal 
mechanical properties. 
 
4.3 Comparison of Solvent Processing and Extrusion: Summary 
With the results described in 4.2.2, it is possible to begin constructing an idea of 
the differences between solvent processing and extrusion. For the aforementioned physics 
of the processing effects on the material, the results are qualitatively indicating the 
following: 
 
Characteristics & Mechanism 
 
 
 
 
   
            
 
 
 
 
Microstructure 
 
 
 
 
 
Properties 
 
 
 
 
 
 
 
 
Solvent Processing 
? Batch (small quantities) 
? Ultrasonic energy couples with 
agglomerates to cause separation 
through agitation or bursting of 
microbubbles through cavitation. 
? Polymer and filler mixed in a low shear 
environment after sonication, for a long 
time, in a less viscous medium. 
 
 
? Good dispersion on micro and nanoscale 
resulting in low percolation threshold. 
Resultant filler aspect ratio is higher. No 
induced alignment. 
 
 
? Higher rheological and electrical 
properties, but lower thermo-oxidative 
properties. 
? Continuous (large quantities)  
? Breakup of agglomerates at higher shear 
rates. Possible separation of agglomerates 
through attrition at low degree of screw 
channel fills. 
? Polymer and filler mixed in a high shear 
environment, in a more viscous medium. 
 
 
 
? Good distribution on microscale, poor 
dispersion on nanoscale resulting in high 
percolation threshold. Resultant filler 
aspect ratio is lower. Induced alignment. 
 
 
? Lower rheological and electrical 
properties, but higher thermo-oxidative 
properties. 
 
TSE 
 129  
4.4 Processing ? Structure Relationships: A New Combinatorial 
Approach 
 
The processing-structure relationship in extruded PS-CNF composites has also 
been examined for establishing a new approach to develop polymer nanocomposites via 
combinatorial materials science. The new combinatorial approach is a direct outcome of 
the transient processing conditions of extrusion that permits for a high throughput, 
continuous method to process PS-CNF composites for rapid structure-property 
characterization. However, in this research it was essential to establish the relationship 
between the mixing in extrusion (i.e., processing) and the resulting compositional 
gradient (i.e., structure).  
As described in 2.5.1, although there has been significant research to develop and 
characterize compositional gradients (CGs), they are either a posteriori techniques 
[104,105] or limited to low loadings of the filler in the composite [73]. At higher 
loadings, especially of dark colored fillers, the optical probes tend to reach their 
saturation, i.e., detection limit. Furthermore, most of the prior works conducted to rapidly 
determine the CGs require a pre-calibration of the technique with known composition, 
thereby decoupling the processing from the evolution of the structure. In order to address 
these issues, a non-destructive approach, based on the residence distribution (see 3.3.2) 
representing the mixing in the extrusion process was adopted. The nature of the approach 
allows rapid characterization of the CG compared to a time-consuming and destructive 
approach such as thermogravimetric analysis. 
 
 
  
 130  
4.4.1 Prediction of the Compositional Gradient 
In general, the response )(ty , from a linear, continuous, time-invariant system 
described by )(t? with input signal, )(tu , can be predicted using the convolution integral 
[106]: 
??? dutty t )()()(
0?
??=     (4.12) 
In the extrusion context, equation (4.12) can be transformed into the volume domain as,  
?
?
?=
0
')'()'(?)( dvvHvvgvC     (4.13) 
where, )(? vg  is a characteristic of the process that is independent of processing 
conditions, )(vH is the Heaviside function representing the step input of the filler and 
)(vC is the response to the step input of the filler, i.e., the CG, assuming that the melt 
absorbance is linearly proportional to composition of the filler. This assumption is valid 
at low compositions of the filler where Rayleigh static light scattering principles predict 
that the scattered intensity of light scales linearly with number of particles [107,108], i.e., 
composition of the filler. 
In order to establish the processing-structure relationship and predict the CG, the 
characteristic of the process that is independent of the processing conditions has to be 
identified. As described in 2.5.2, leveraging the efforts of Elkouss et al [76], the master 
curve ( )(? vg ) obtained by modeling the normalized residence volume distributions 
(RVDs) can be used as a characteristic of the process in equation (4.13) to obtain the CG. 
The normalized RVDs, obtained experimentally using the in situ optical probe (see 
3.3.2), can be modeled in various ways [109-113] to obtain the master curve ( )(? vg ). 
 131  
Without loss of generality, the applicability of the approach can be demonstrated by 
modeling the normalized RVDs using simple empirical equations based on transfer 
functions that represent a series of perfect batch mixers [114,115]. A second order 
transfer function that corresponds to the mixing occurring in the screw and the die zones 
of the extruder was used. In the Laplace domain, it can be represented as,  
2
2
)()( as
easG svd
+=
?
 `    (4.14) 
where, dv  is the delay volume and a   is the shape factor. The inverse transform gives the 
model in the volume domain as, 
)(2 )()( dvva
d evvavg
???=     (4.15) 
Figure 4.35 shows a representative normalized RVD that was obtained experimentally 
and the curve obtained by modeling it with the normalized form of equation (4.15), as 
shown in equation (2.3).  The peak of the experimental curve is slightly lower than that of 
the modeled curve because the absorbance of the optical probe reached its saturation i.e., 
detection limit. The same argument explains why the peak was flatter than what would be 
expected.  This is especially true with dark fillers such as CNFs and CNTs. This 
phenomenon was not observed in an earlier work using the same experimental setup with 
bright fillers [104,105]. 
 132  
0
4
8
0 0.1 0.2 0.3 0.4 0.5
Volume (l)
No
rm
ali
ze
d A
bs
or
ba
nc
e
Experimentally obtained from Optical Probe
2nd OrderTransfer Function Model
 
Figure 4.35 Modeling the normalized RVD using a second order transfer function.  The 
peak of the experimental curve is slightly lower than that of the modeled curve because 
the optical probe measuring the absorbance reached its detection limit. 
 
In addition, to leverage the earlier efforts by Elkouss et al [76], the absence of 
predominant elastic effects has to be verified. It was done by experimentally obtaining 
the normalized RVDs for the PS-CNF composites at varying polymer flow rates and 
extruder screw speeds for a fixed screw design. These normalized RVDs were modeled 
as described above and it was observed that all the curves superimposed within 
reasonable error as shown in figure 4.36. 
 
Figure 4.36 The modeled normalized RVDs resulting from varying polymer flow rates 
and extruder screw speeds superimposed within reasonable error . 
 
Polymer Flow 
Rate (Kg/h) 
Screw Speed 
(RPM) 
0.5 30 
1 40 
1 60 
1.5 45 
1.5 60 
1.5 90 
2 60 
2 90 
 
 133  
For the resulting master curve ( )(? vg ) of PS-CNF composites, lvd 052.0=  and 
130 ?= la . Using equation (4.13), the convolution of )(? vg with a Heaviside step function 
of magnitude k, predicts the CG as, 
?=
v
dvvgkvC
0
)(?)(      (4.16) 
Figure 4.37 compares the CG of PS-CNF composites ranging from an initial volume 
fraction of 0 to a final volume fraction of 0.06 i.e., 6=k , experimentally characterized 
using a TGA, with that theoretically predicted by equation (4.16). The weight fraction 
characterized by the TGA was converted to volume fraction using equation (4.2).  
An important conclusion can be drawn from figure 4.37 about the characterization 
of processing-structure relationships for extruded PS-CNF composites: the experimental 
measurements correlate well with those predicted by convolution thereby validating the 
non-destructive approach. This approach has significant implications in combinatorial 
techniques utilizing CGs. It allows rapid characterization of the CGs when compared to 
the time consuming and destructive tests like thermogravimetric analysis. With this 
approach, the amount of filler that is needed to achieve a CG containing all volume 
fractions between 0 and 0.06 was only 15 g, which was achieved by operating the PS 
feeder steadily at a rate of 2 lb/hr and the CNF feeder at 0.2 lb/hr for 10 minutes. 
Extending the operation of the CNF feeder beyond this time resulted in steady-state 
production of the PS-CNF composites with a volume fraction of 0.06 at a rate of 0.016 
l/min. 
 134  
0
2
4
6
0 0.1 0.2 0.3 0.4
Volume of the Extrudate (l)
Vo
l%
Experimental
Convolution Model
 
Figure 4.37 The compositional gradient predicted via convolution correlates well with 
the experimental values obtained from thermogravimetric analysis for the PS-CNF 
composite. This confirms the validity of the non-destructive approach. 
 
 
4.4.2 CG Characterization Approach: Influence of Filler Size 
Due to the expensive nature of nanoscale ingredients, it is desirable to apply the 
CG characterization approach to inexpensive microscale ingredients, such as bright 
colored KCl, and assess their suitability as ?dummy? fillers. Figure 4.38 compares the CG 
of PS-KCl composites ranging from an initial volume fraction of 0 to a final volume 
fraction of 0.18 i.e., 18=k , experimentally characterized using a TGA, with that 
predicted by equation (4.16). Here, it must be noted that the master curve ( )(? vg ) used in 
equation (4.16) was that obtained from modeling the normalized RVDs for the PS-CNF 
composites. In spite of that the experimental results correlated well with those predicted 
by convolution. Thus it can be concluded that the size scale of the fillers tested does not 
affect the evolution of CGs, thereby indicating that the transient effects of the mixing 
 135  
process are independent of the size of the filler. This would imply that the normalized 
RVD resulting from the microscale and nanoscale filler is the same. Therefore the 
following conclusion can be drawn about the influence of the size scale of ingredients on 
the processing-structure relationships: inexpensive microscale ingredients can be used to 
conduct impulse or step experiments to verify the absence of predominant elastic effects 
and to establish appropriate processing conditions for obtaining desired CGs instead of 
using more expensive nanoscale ingredients.  
0
3
6
9
12
15
18
0 0.1 0.2 0.3 0.4
Volume of the Extrudate (l)
Vo
l%
Experimental
Convolution Model
using the RVD
obtained from CNFs
 
Figure 4.38 The compositional gradient predicted via convolution correlates well with 
the experimental values obtained from thermogravimetric analysis for the PS-KCl 
composite. This indicates that the approach is independent of the size scale of the fillers. 
 
 
 136  
5. Conclusions and Future Work 
 
 
Although a significant amount of research has been conducted to establish the 
structure-property relationships of polymer-CNT/CNF composites, there have been very 
few efforts to address the effect of processing on the structure-property relationships. In 
order to address this issue, this work focused on comparing the processing-microstructure 
and structure-property relationships of PS-MWCNT and PS-CNF composites produced 
via solvent processing and twin screw extrusion. The processing-property relationships 
were also investigated for the extruded composites. In addition to batch processing, a 
combinatorial approach to establishing the processing-structure-property relationships of 
PS-CNF composites was demonstrated. 
 The research issues addressed in this work answered several fundamental 
questions related to developing polymer nanocomposites with enhanced material 
properties. They resulted in advancing the understanding of the influence of the type of 
process and processing parameters on the electrical, rheological, thermo-oxidative and 
mechanical properties of the PS-MWCNT and PS-CNF composites. This helps in 
engineering the properties and performance of these composites by appropriate choice of 
the type of process and the processing parameters. The microstructural characterization 
led to a better understanding of how the properties of the PS-MWCNT and PS-CNF 
composites evolved as a function of distribution of the agglomerates, and dispersion, 
alignment and aspect ratio of the filler. The non-destructive approach based on the 
convolution of process models to predict the compositional gradients allowed for more 
rapid characterization of processing-structure relationships in polymer nanocomposites 
developed via a combinatorial approach. 
 137  
5.1 Intellectual Contributions 
 
 Through this research effort, the following specific intellectual contributions were 
made that directly affect the development and characterization of polymer 
nanocomposites:  
? New methodology to quantify the limiting rheological properties of percolated 
nanostructures [116]: In all the works reported to date, the increase in electrical 
conductivity and rheological parameters of polymer-CNF/MWCNT composites were 
each reported or modeled independently as a function of the particle percolation. 
There have been no reports of a physical and quantitative relationship between the 
increase in electrical conductivity and the rheological parameters, both of which 
fundamentally depend on the extent of particle percolation. In order to address this 
issue, an interpenetrating phase polymer nanocomposite formed by percolation of 
MWCNTs in PS-MWCNT composites was quantitatively characterized. This was 
accomplished by treating the PS-MWCNT composite as a combination of two phases: 
a continuous PS phase reinforced by non-interacting MWCNTs, and a continuous 
phase consisting of the pseudo-solid like network of percolated MWCNTs. The 
distribution of MWCNTS among the continuous phases was determined from the 
degree of percolation of MWCNTs correlated to power-law fits of the electrical 
conductivity with and without a percolation threshold. Subsequently, the dynamic 
rheological properties (the storage modulus and loss modulus) of the PS-MWCNT 
composites were interpreted as a function of the degree of percolation, in addition to 
the concentration of MWCNTs and frequency using a modified Nielsen?s model. This 
methodology, for the first time, allows the determination of limiting rheological 
 138  
properties of the pseudo-solid like network of percolated MWCNTs. Simultaneously, 
it was possible to isolate the effect of non-interacting MWCNTs reinforcing the PS 
from the percolated MWCNTs. Hence, this methodology has important implications 
in quantifying the properties of percolated nanostructures not only in polymer 
nanocomposites, but also in self-assembly, tissue fixation etc. 
? Novel approach to assess the degree of dispersion using thermogravimetric 
analysis [117]: Traditionally thermogravimetric analysis was used to study the 
composition of composite systems, identify the purity of fillers, and to establish the 
thermal and thermo-oxidative behavior of polymer nanocomposites. In this work, the 
normalized thermo-oxidative decomposition of the CNFs resulting from different 
processes (solvent processing and twin screw extrusion) and processing conditions 
(high and low shear screw design) was studied in detail. It was observed that the 
normalized thermo-oxidative decomposition of the CNFs correlated well with the 
qualitative degree of dispersion of the CNFs obtained from scanning electron 
microscopy. Hence, a novel thermogravimetric analysis-based approach was 
demonstrated that can characterize the degree of dispersion of the filler in composites 
that complements conventional microscopy techniques. This approach has three 
significant advantages over conventional microscopy techniques: (1) it does not 
require a contrast difference between the filler and the matrix, (2) it is not limited to 
probing small areas at a time and gives a bulk measurement of the degree of 
dispersion, and (3) it is more quantitative. 
 
 139  
? Novel approach to rapidly and non-destructively characterize compositional 
gradients resulting from transient extrusion [118]: In the past few years there has 
been an increased interest in rapidly characterizing the composition and properties of 
composites with CGs resulting from transient extrusion. However, the current state-
of-art characterization techniques for determining the composition in compositional 
gradients are either a posteriori techniques or limited to low loadings of the filler in 
the composites. Furthermore, most of the prior works conducted to rapidly determine 
the CGs require a pre-calibration of the technique with known composition, thereby 
decoupling the processing from the evolution of the structure. In this work a novel 
convolution approach based on normalized residence volume distributions was 
developed and demonstrated to overcome the above drawbacks. The nature of the 
approach allows rapid characterization of the CG compared to a time-consuming and 
destructive approach such as thermogravimetric analysis. Since the approach does not 
decouple processing from the evolution of the structure, it can be used to precisely 
estimate the quantity of expensive nanoscale fillers required to produce the 
compositional gradient, before conducting the experiments. Furthermore, it was also 
shown that the approach is independent of the size scale of the filler. Hence, 
inexpensive microscale fillers can be used instead of more expensive nanoscale fillers 
to conduct experiments to establish the appropriate processing conditions for 
obtaining desired compositional gradients. 
? Advanced understanding of mechanical property enhancement in polymer 
nanocomposites and associated limitations: In this work, the effect of CNF 
composition and extrusion processing parameters on the tensile strength and tensile 
 140  
modulus of the polymer nanocomposites has been thoroughly investigated. Although 
increasing the composition of CNFs increases the mechanical properties of the 
composites, similar enhancements at higher concentrations (more than ~10 wt.%) 
have also been demonstrated by using less expensive carbon microfibers. Thus, the 
effectiveness of using CNFs is limited to lower concentrations (less than ~10 wt.%). 
Furthermore, at lower concentrations, it was observed that increasing the extrusion 
shear rate leads to an asymptotic plateau in mechanical properties. At higher shear 
rates, microscopy showed that the CNFs deagglomerate, but also suffer from a 
reduction in aspect ratio, thereby losing their effectiveness to enhance the mechanical 
properties. Since deagglomeration is a function of both the magnitude of shear rate 
and the residence time, it is desirable to use a lower shear rate and an extended 
residence time in order to retain the aspect ratio of CNFs, thereby increasing their 
effectiveness to reinforce the polymer matrix. As evidenced by microscopy in this 
work, further improvement of the mechanical properties of polymer nanocomposites 
is possible by improving the interfacial adhesion. In summary, the insights discussed 
above advance the understanding of how to better enhance the mechanical properties 
of polymer nanocomposites. 
? Improved selection of the process to obtain the desired properties [117,119,120]: 
In this work, the influence of different processes on the electrical, rheological and 
thermo-oxidative properties of polymer nanocomposites was studied. The following 
conclusions were drawn to improve the selection of the type of process that can be 
used to obtain the desired properties: (1) Flow induced shear stresses in the die during 
extrusion align the nanoscale fillers and reduce the electrical conductivity. Upon 
 141  
annealing the extruded composites, the aligned nanoscale fillers are relaxed and 
regain their interconnectivity, and hence the electrical conductivity of composite is 
improved. Thus, in order to obtain better electrical conductivity of polymer 
nanocomposites, a combination of extrusion and annealing is desirable. (2) Solvent 
processing is more desirable to obtain better rheological properties than the extruded 
ones because of the lower reduction in aspect ratio of the nanoscale fillers in solvent 
processing when compared to extrusion. (3) Extrusion is more desirable to obtain 
better thermal stability of the composites when compared to solvent processing 
because the absence contamination of from solvents. (4) As long as the nanoscale 
fillers can be dispersed randomly, the choice of solvent does not have a significant 
affect on the electrical and rheological properties of the polymer nanocomposites. 
 
5.2 Future Work 
 
During the course of this research investigation, some interesting research issues 
have been uncovered that affect the development of polymer nanocomposites needing 
further investigation. The following is a list of these issues: 
1. Characterize the mechanical properties of the extruded polymer nanocomposites in 
both axial and transverse directions. This will provide a better understanding of the 
nanoscale filler alignment on the mechanical properties of the polymer 
nanocomposites. 
2. Characterize the molecular weight and crystallinity of the polymer as a function of 
the type of process and processing parameters. This will provide insight to decouple 
 142  
the affect of filler loading from the changes in the properties of the polymer phase 
itself. 
3. Process composites with varying residence time and magnitude of shear rate. Since it 
has been concluded in this work that deagglomeration is a strong function of both the 
residence time and the magnitude of shear rate, it would be appropriate to find the 
critical combination of the two parameters that would lead to optimal material 
properties. While the residence time can be varied by modifying the screw design, the 
magnitude of shear rate can be varied by modifying the screw speed. 
4. Process and characterize the properties of hierarchically structured composites for 
multifunctionality. In the present work, the composites were made using only one 
filler to enhance the properties. By studying multi-component and multi-scale 
systems, significant enhancement in more than one property, for example, both 
electrical and mechanical properties, can be achieved to address multifunctionality. 
5. Tailor the expanse of the compositional gradient by varying the screw design. 
Although the entire treatment of the combinatorial approach developed in this work 
assumes a fixed screw design, it is not difficult to extend it to varying screw designs. 
Assuming the absence of predominant elastic effects, every new screw design tested 
requires only a single impulse experiment to experimentally obtain the normalized 
residence volume distribution that can be modeled to obtain the master curve. 
Subsequently, the compositional gradient for the new screw design can be predicted 
by using equation. 
6. Process and characterize polymer-CNF composites with other polymer systems. 
Polymers, such as Nylon, are qualified for different applications than PS. They may 
 143  
also offer better interfacial adhesion between the polymer matrix and the CNFs 
resulting in better mechanical properties. 
7. Process and characterize composites of polymers with CNFs functionalized both at 
the ends and the sidewalls. While the end functionalization can be utilized to cross-
link the CNFs with another, thereby creating a continuous fiber-like structure, the 
sidewall functionalization can be used to improve the adhesion to the polymer matrix. 
This could potentially result in ultrastrong nanocomposites that can be deployed in 
space flight applications. 
8. Characterization of diseased tissues in histopathological specimens: The new 
technique for characterizing limiting properties in polymer nanocomposites can be 
extended to histopathology by investigating a new approach to characterizing the 
degree of percolation for networks of non-conductive diseased tissues, such as 
confocal microscopy techniques, that would replace the electrical conductivity 
measurements. The concentration of diseased cells would also need to be calibrated 
against the level of mechanical degradation in the percolated network of diseased 
cells and the isolated diseased cells that are quantified using the new technique. 
  
 
 
 144  
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