ABSTRACT
Title of Dissertation: CHARACTERIZATION OF PROPERTY -
STRUCTURE DEPENDENCIES FOR MULTI-
SCALE POLYMER COMPOSITES USING
EXTRUSION PROCESSES
Jason Robert Nixon
Directed by: Associate Professor David I. Bigio
Department of Mechanical Engineering
Multiscale reinforcement, using carbon microfibers and multi-walled carbon
nanotubes, of polymer matrix composites manufactured by twin-screw extru-
sion is investigated for enhanced mechanical and thermal properties with an
emphasis on the use of a diverging flow in the die for fluid mechanical fiber ma-
nipulation. Using fillers at different length scales (microscale and nanoscale),
synergistic combinations have been identified to produce distinct mechanical
and thermal behavior. Fiber manipulation has been demonstrated experimen-
tally and computationally, and has been shown to enhance thermal conductivity
significantly. Finally, a new physics driven predictive model for thermal con-
ductivity has been developed based on fiber orientation during flow, which is
shown to successfully capture composite thermal conductivity.
CHARACTERIZATION OF PROPERTY STRUCTURE
DEPENDENCIES FOR MULTI-SCALE POLYMER
COMPOSITES USING EXTRUSION PROCESSES
by
Jason Robert Nixon
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
2016
Advisory Committee:
Professor David I. Bigio, Chair/Adviser
Professor Hugh Bruck
Professor Avram Bar-Cohen
Professor Amir Riaz
Professor Isabel Lloyd
c© Copyright by
Jason Robert Nixon
2016
Contents
List of Figures v
List of Tables vii
Abbreviations viii
Symbols ix
1 Introduction 1
1.1 Polymer Composites . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Dissertation Outline . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Literature Review 8
2.1 Property Enhancement . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Adhesion and Dispersion . . . . . . . . . . . . . . . . . . . . . 9
2.3 Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Thermal Properties . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5 Processing Conditions . . . . . . . . . . . . . . . . . . . . . . 19
2.6 Microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.7 Multi-Filler Composites . . . . . . . . . . . . . . . . . . . . . . 24
3 Methods and Procedures 27
3.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.1 Polymer Matrix . . . . . . . . . . . . . . . . . . . . . . 27
3.1.2 Microscale Fillers . . . . . . . . . . . . . . . . . . . . . 28
3.1.3 Nanoscale Fillers . . . . . . . . . . . . . . . . . . . . . 28
3.1.4 Summary of Matrix and Filler Properties . . . . . . . . 29
3.2 Twin Screw Extrusion . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.1 Die Design . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.1.1 Die Residence Time . . . . . . . . . . . . . . 31
3.2.2 Screw Design . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.3 Extruder Control . . . . . . . . . . . . . . . . . . . . . 34
3.2.4 Material Feeders . . . . . . . . . . . . . . . . . . . . . 36
3.2.5 Material Collection . . . . . . . . . . . . . . . . . . . . 36
ii
Contents
3.2.5.1 Die A . . . . . . . . . . . . . . . . . . . . . 36
3.2.5.2 Die B-F . . . . . . . . . . . . . . . . . . . . 37
3.2.6 Pelletization . . . . . . . . . . . . . . . . . . . . . . . 37
3.3 Property Testing . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.1 Tensile Testing . . . . . . . . . . . . . . . . . . . . . . 38
3.3.2 Thermal Conductivity Testing . . . . . . . . . . . . . . 38
3.3.2.1 Calibration . . . . . . . . . . . . . . . . . . . 40
3.3.2.2 Single Blotter Testing . . . . . . . . . . . . . 41
3.3.2.3 Dual Blotter Testing . . . . . . . . . . . . . . 42
3.3.3 Optical Microscopy . . . . . . . . . . . . . . . . . . . . 43
3.3.3.1 Mounting and Polishing . . . . . . . . . . . . 43
3.3.3.2 Fiber Orientation Analysis . . . . . . . . . . 45
3.3.4 Statistical Analysis . . . . . . . . . . . . . . . . . . . . 46
4 Simulation 48
4.1 Theoretical Treatment . . . . . . . . . . . . . . . . . . . . . . . 49
4.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2.1 Method and Procedure . . . . . . . . . . . . . . . . . . 57
4.2.2 Characteristic Convergent Die . . . . . . . . . . . . . . 58
4.2.3 Characteristic Straight Die . . . . . . . . . . . . . . . . 61
4.2.4 Characteristic Diverging Die . . . . . . . . . . . . . . . 63
4.2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 64
5 Experiments 66
5.1 Long CMF Multiscale Study . . . . . . . . . . . . . . . . . . . 67
5.2 Short Fiber Diverging Die Study . . . . . . . . . . . . . . . . . 77
5.2.1 Long/Short CMF Comparison . . . . . . . . . . . . . . 78
5.2.2 Straight/Divergent Die Comparison . . . . . . . . . . . 85
5.3 Parametric Study . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.3.1 Effect on Fiber Orientation . . . . . . . . . . . . . . . . 92
5.3.2 Tensile Modulus . . . . . . . . . . . . . . . . . . . . . 94
5.3.3 Ultimate Tensile Strength . . . . . . . . . . . . . . . . 98
5.3.4 Thermal Conductivity . . . . . . . . . . . . . . . . . . 100
5.3.5 Rheological Argument . . . . . . . . . . . . . . . . . . 105
5.3.6 Summary of Statistical Analysis . . . . . . . . . . . . . 108
6 Predictive Model 111
6.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.1.1 Rule of Mixtures . . . . . . . . . . . . . . . . . . . . . 113
6.1.2 Halpin-Tsai Model . . . . . . . . . . . . . . . . . . . . 113
6.1.3 Nielsen Model . . . . . . . . . . . . . . . . . . . . . . 114
6.1.4 Cheng-Vachon Model . . . . . . . . . . . . . . . . . . 116
6.1.5 Agari-Uno . . . . . . . . . . . . . . . . . . . . . . . . 117
6.1.6 Filler Limitations . . . . . . . . . . . . . . . . . . . . . 117
6.2 Proposed Model . . . . . . . . . . . . . . . . . . . . . . . . . . 119
iii
Contents
7 Conclusions and Future Studies 128
7.1 Intellectual Contributions . . . . . . . . . . . . . . . . . . . . . 131
7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
A Property Summaries 136
Bibliography 143
iv
List of Figures
1.1 CNT diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Mixing mechanisms illustration. . . . . . . . . . . . . . . . . . 5
2.1 Fiber reinforcement visualization. . . . . . . . . . . . . . . . . 22
3.1 CoTSE setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2 Extruder dies: front. . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Extruder dies: rear. . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 Screw design. . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.5 ASTM D638-10 test specimen. . . . . . . . . . . . . . . . . . . 39
3.6 C-Therm TC-30 . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.7 TC-30 single blotter method. . . . . . . . . . . . . . . . . . . . 41
3.8 TC-30 Dual Blotter Method. . . . . . . . . . . . . . . . . . . . 42
3.9 Microscopy sample surface after polishing. . . . . . . . . . . . 44
3.10 Fiber orientation ellipse. . . . . . . . . . . . . . . . . . . . . . 45
3.11 Sample fiber orientation distribution . . . . . . . . . . . . . . . 46
4.1 Vincent and Agassant die illustration. . . . . . . . . . . . . . . 50
4.2 Normalized shear/extensional rate profile. . . . . . . . . . . . . 51
4.3 Characteristic fiber angle profile. . . . . . . . . . . . . . . . . . 54
4.4 Simulation: characteristic converging die. . . . . . . . . . . . . 59
4.5 Simulation: convergent die. . . . . . . . . . . . . . . . . . . . . 60
4.6 Simulation: characteristic straight die. . . . . . . . . . . . . . . 61
4.7 Simulation: straight die. . . . . . . . . . . . . . . . . . . . . . . 62
4.8 Simulation: characteristic diverging die. . . . . . . . . . . . . . 63
4.9 Simulation: divergent die. . . . . . . . . . . . . . . . . . . . . . 64
5.1 6 mm CMF, θ = 0◦, characteristic micrographs. . . . . . . . . . 67
5.2 6 mm CMF, θ = 0◦, mean tensile modulus. . . . . . . . . . . . 70
5.3 6 mm CMF, θ = 0◦, mean ultimate tensile strength. . . . . . . . 72
5.4 6 mm CMF, θ = 0◦, mean thermal conductivity. . . . . . . . . . 74
5.5 Short CMF characteristic micrographs. . . . . . . . . . . . . . . 79
5.6 Long CMF/short CMF tensile modulus comparison. . . . . . . . 80
5.7 Long CMF/short CMF ultimate tensile strength comparison. . . 81
5.8 Long CMF/short CMF thermal conductivity comparison. . . . . 82
5.9 Short CMF θ = 2.82◦ characteristic micrographs. . . . . . . . . 85
5.10 Straight/divergent tensile modulus comparison. . . . . . . . . . 87
v
List of Figures
5.11 Straight/divergent ultimate tensile strength comparison. . . . . . 88
5.12 Straight/divergent thermal conductivity comparison. . . . . . . . 89
5.13 Regression: tensile modulus Vn −Q interaction effect. . . . . . 95
5.14 Regression: tensile modulus Vµ − Vn − θ interaction effect. . . . 97
5.15 Regression: thermal conductivity Vµ main effect. . . . . . . . . 99
5.16 Regression: ultimate tensile strength Vn −Q interaction effect. . 100
5.17 Regression: thermal conductivity Vµ main effect. . . . . . . . . 102
5.18 Regression: thermal conductivity Q− θ interaction effect. . . . 104
6.1 Predictive model asymptotic behavior. . . . . . . . . . . . . . . 118
6.2 Vincent and Agassant die illustration. . . . . . . . . . . . . . . 120
6.3 Characteristic fiber angle profile. . . . . . . . . . . . . . . . . . 123
6.4 Modified Agari-Uno Matrix Coefficients. . . . . . . . . . . . . 126
vi
List of Tables
3.1 Manufacturer material properties. . . . . . . . . . . . . . . . . 29
3.2 Die dimension list. . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3 PBT processing conditions. . . . . . . . . . . . . . . . . . . . . 35
3.4 TC-30 calibration standards. . . . . . . . . . . . . . . . . . . . 40
3.5 Mounted sample polishing parameters. . . . . . . . . . . . . . . 44
4.1 Characteristic fiber orientation profile. . . . . . . . . . . . . . . 54
5.1 Fiber orientation regression model. . . . . . . . . . . . . . . . . 93
5.2 Tensile modulus regression model. . . . . . . . . . . . . . . . . 95
5.3 Ultimate tensile strength regression model. . . . . . . . . . . . . 98
5.4 Thermal conductivity regression model. . . . . . . . . . . . . . 101
6.1 Lewis-Nielsen model Vmax values. . . . . . . . . . . . . . . . . 115
6.2 Lewis-Nielsen model A values. . . . . . . . . . . . . . . . . . . 116
6.3 Die critical angle. . . . . . . . . . . . . . . . . . . . . . . . . . 121
A.1 Properties: lf = 6 mm, θ = 0◦. . . . . . . . . . . . . . . . . . . 137
A.2 Properties: lf = 100 µm, θ = 0◦. . . . . . . . . . . . . . . . . . 138
A.3 Properties: lf = 100 µm, θ = 1.41◦. . . . . . . . . . . . . . . . 139
A.4 Properties: lf = 100 µm, θ = 2.26◦. . . . . . . . . . . . . . . . 140
A.5 Properties: lf = 100 µm, θ = 2.82◦. . . . . . . . . . . . . . . . 141
A.6 Properties: lf = 100 µm, θ = 4.52◦. . . . . . . . . . . . . . . . 142
vii
Abbreviations
AlN Aluminum Nitride
BN Boron Nitride
ASTM American Society for Testing and Materials
Design
CMF Carbon MicroFiber
CNF Carbon NanoFiber
CNT Carbon NanoTube
CoTSE Co-rotating Twin-Screw Extruder
GF Short Glass Fiber
LDPE Low Densily Polyethylene
HDPE High Densily Polyethylene
MWNT Multi Walled Carbon NanoTube
PBT Poly (Butylene Terephthalate)
PC Poly (Carbonate)
PEEK Poly (Ether Ether Ketone)
PS Poly (Styrene)
PMC Polymer Matrix Composite
PMMA Poly (Methyl Methacrylate)
PES Poly (Ether Sulfone)
PET Poly (Ethylene Terephthalate)
SiC Silicon Carbide Die
SWNT Single Walled Carbon NanoTube
TSE Twin Screw Extruder
VGCF Vapor Grown Carbon Fiber
vol.% Percent by Volume
wt.% Percent by Weight
viii
Symbols
Ar Lewis-Nielsen Einstein coefficient.
Ar Aspect ratio.
C Integration constant.
df Fiber diameter.
E Tensile modulus.
hinlet Die inlet height.
houtlet die outlet height.
K Thermal conductivity.
Ke Effective thermal conductivity.
Kf CMF thermal conductivity.
Km Polymer matrix thermal conductivity.
Kr Ratio of CMF to matrix thermal conductivity.
L Die length.
lf Fiber length
N Screw speed.
Q Volumetric flow rate.
Vf Volumetric CMF concentration.
Vmax Maximum volumetric CMF concentration.
W Die width.
α˙ Extensional rate.
β Fiber path angle.
β0 Critical fiber path angle.
γ˙ Shear rate.
θ Die divergence angle.
µ Kinematic viscosity.
ν Dynamic viscosity.
ξ Fiber orientation w.r.t. die plane.
ξ Mean fiber orientation w.r.t. die plane.
ρ Density.
σu Ultimate tensile strength.
ix
Symbols
σy Yeild strength.
τ Time to fiber out.
φ Fiber orientation w.r.t. fiber path.
φ0 Initial fiber orientation w.r.t. fiber path.
x
Chapter 1
Introduction
Polymers have become ubiquitous in manufacturing due to their cost, availabil-
ity, performance, and weight. In comparison to metals and ceramics, polymers
are lighter, cheaper, easier to manufacture and machine, but do not match me-
chanical, thermal, or electrical performance. Depending on composition, poly-
mers can be brittle, ductile, crystalline, semi-crystalline, or amorphous. This
range of morphologies lends polymers many uses.
In order to reduce the performance gap, polymer matrix composites (PMCs)
are formed by reinforcing polymer matrices are with ceramic and/or metallic
fillers whose properties are typically orders of magnitudes greater than that of
the polymer matrix. Yet greater property improvements can be gained by us-
ing synergistic combinations of fillers at different length scales to reinforce the
polymer matrix through alternative mechanisms. Therefore, there is an impetus
to explore multiscale PMCs for a range of applications. This body of work is
1
Jason R. Nixon
concerned exclusively with carbon microfibers (CMFs) and multi-walled car-
bon nanotubes (MWNTs) compounded in a polybutylene terephthalate (PBT)
polymer matrix.
Unlike powdered fillers, which have no orientation, the fiber orientation within
the matrix is meaningful to PMC properties. Anecdotally, fibers act as load
bearing highways, carrying loading down their axis. However, fibers only frac-
tionally enhance performance when the load is applied at an oblique angle to
the fiber axis. This enhancement can be minimal to non-existent when the load
is applied diametrically, or orthogonally to the fiber axis. Therefore, manipulat-
ing the fibers into preferential orientations during the manufacture of PMCs is
highly desired based on the end product.
Twin screw extrusion is a continuous compounding and forming manufacturing
method that is used to form semi-infinite shapes with respect to the extrusion ori-
entation. Typically in twin screw extrusion, or more generally in any pumping
process process, fibers orient to nearly parallel with the extrusion orientation (in
the semi-infinite orientation of the shape) over time. For certain applications,
such as polymer heat exchangers, we desire fibers to be oriented obliquely or
transversely to the extrusion orientation, i.e. in the direction of the thickness,
such that fibers are contributing both to the extrusion orientation (longitudinally)
and through-thickness (transverse) thermal conductivity. However, by the high-
way analogy, fibers oriented in an oblique orientation are now not contributing to
the longitudinal strength. Therefore, some partial reorientation is best to achieve
2
Jason R. Nixon
the maximum transverse thermal conductivity while minimizing loss in strength
and stiffness in the longitudinal orientation.
In this dissertation, the central research focus is to characterize the improved
longitudinal tensile and through-thickness thermal properties for PBT/CMF/MWNT
composites manufactured using twin screw extrusion and the manipulation of
fiber orientation through fluid mechanical means, i.e. by use of a diverging die,
during the extrusion process.
1.1 Polymer Composites
Fillers are used to enhance the properties of a neat polymer. The continuous
phase, in this case a polymer matrix, is mixed with other materials, known
as fillers, that act as a discrete entities within the continuous polymer phase.
Fillers are selected to enhance one or more properties of the neat polymer ma-
trix. Fillers are categorically described by their dominant length scale; i.e. nano-
scale, micro-scale, etc, their dimensional approximation; zero-dimensional (par-
ticulates), one-dimensional (fibers), and two-dimensional (sheets and weaves);
and their composition. In this dissertation, a combination of nanoscale and mi-
croscale carbon one-dimensional fillers are the exclusive focus.
CMFs are composed of layered graphene cones, cups, and plates. They are
typically several micrometers in diameter, but can range from 50 µm to many
meters in length. However, these exceedingly high fiber lengths are limited to
3
Jason R. Nixon
other forms of composites manufacturing and are not considered in this disser-
tation. CMFs possess significantly greater mechanical and thermal properties
than that of neat polymers and are ideal for applications demanding increased
structural and thermal performances.
FIGURE 1.1: Single-walled carbon nanotube diagram.
Carbon nanotubes (CNTs), or more specifically single-walled CNTs (SWNTs),
have diameters in the range of several to tens of nanometers and are formed from
a single layer of graphene rolled into a cylinder and can take several forms de-
pending on the carbon atom organization (see Figure 1.1). SWNT structure has
been shown to greatly affect its measurable properties. By forming a cylinder
of concentrically organized SWNTs, MWNTs are formed. Both SWNTs and
MWNTs possess highly desirable properties including high electrical conduc-
tivity, high thermal conductivity, high mechanical strength, and low chemical
reactivity. CNTs have been properties have been shown to theoretically and
experimentally shown to exceed even CMF properties [1, 2, 3]. However, for
4
Jason R. Nixon
reasons discussed later, SWNTs and MWNTs remain expensive and difficult to
utilize in composites.
1.2 Mixing
For this dissertation, PMC manufacturing is performed using twin screw extru-
sion, a continuous compounding process that mixers fillers into a molten poly-
mer matrix, and then pumps that material through a die into the desired final
form. Inside the extruder, specially designed modular screws act to mix the
matrix and fillers together. Mixing is described by two mechanisms; dispersive
mixing and distributive mixing. The difference between these mechanisms is
illustrated in Figure 1.2.
FIGURE 1.2: Distributive and dispersive mixing [4].
5
Jason R. Nixon
Good distributive mixing leads to the ideal arrangement of fillers in space, which
in a simplistic sense is nearly equally spaced throughout the composite. Good
dispersive mixing leads to a reduction in the size of the filler, which could be
a bundles of fibers (e.g. the breakup of the bundle) or the erosion or rupture of
an agglomerated particle, much like the crumbling of dried mud. By changing
characteristics of the extrusion process like screw design and operating parame-
ters, different degrees of mixing can be achieved. In order to maximize property
improvements, both good dispersion and good distribution of the fillers is nec-
essary. However, care must also be taken to not subject the fillers and matrix to
excessive mixing, which can fracture fillers, thus leading to reductions in prop-
erty enhancement.
1.3 Research Objectives
The objectives of this research are as follows:
• Study processing-property-microstructure relationships for multiscale PMCs
using CMFs and MWNTs in a PBT matrix prepared by twin screw extru-
sion across a range of CMF concentrations, CMF lengths, MWNT con-
centrations, flow rates, and die angles and compare when possible.
– Characterize tensile modulus, ultimate tensile strength, and thermal
conductivity relationships with respect to input parameters using sta-
tistical analysis.
6
Jason R. Nixon
– Characterize property trade-offs when utilizing MWNTs.
• Develop procedure for fluid mechanical manipulation of fibers during
pumping to induced fiber reorientation using a diverging die.
– Identify property relationships and trade offs for reoriented fibers.
• Develop a predictive model based on existing property prediction models
and fluid mechanics to predict thermal conductivity. This model bridges
the gap between empirically identified relationships and the physical mech-
anisms driving this evolution.
1.4 Dissertation Outline
In the following chapters, the methods used to address research objectives in
§1.3 and the results obtained are be presented. Chapter 2 presents relevant poly-
mer processing and composites literature. Chapter 3 details the experimental
procedures used. Chapter 4 presents a theoretical introduction to fiber reorienta-
tion in a diverging flow as well as numerically simulated fiber orientation results
in a pumping flow. Chapter 5 presents and discusses microstructural and mate-
rial properties for laboratory compounded multiscale PMCs. Chapter 6 develops
a new model for the prediction of PBT/CMF/MWNT composite properties ex-
truded through a straight or diverging die. Chapter 7 summarizes new scientific
contributions and future work related to these studies. Appendix A tabulates
property values from Chapter 5.
7
Chapter 2
Literature Review
The following chapter presents a review of relevant scientific literature for mul-
tiscale PMC manufacturing and properties.
2.1 Property Enhancement
Reinforcement of polymer matrices using microscale and nanoscale fillers is the
subject of many research studies. The intent of this dissertation is to examine the
relationship between flow, microstructure, and resultant property enhancement
as a function of processing parameters during compounding and fillers.
8
Jason R. Nixon
2.2 Adhesion and Dispersion
Fillers are compounded into polymer matrices in order to achieve superior prop-
erties compared to neat matrix [1, 5, 6, 7]. However, simply ‘compounding’ is
not enough for property enhancement. Specifics of fiber dispersion, alignment,
aspect ratio(the ratio of fiber length to diameter), and interfacial stress transfer
all play a role in property enhancement [1, 8]. §2.6 addresses the effect of fiber
alignment. This section, as well as others, address fiber length.
Property enhancement is dominated by the degree of filler-matrix adhesion and
filler dispersion within the matrix under mechanical or thermal load [9, 10].
There must be considerable filler-matrix load transfer for property enhancement.
Fillers behave as structural defects when interfacial adhesion is low. These de-
fects produce local stress concentrations and ultimately lead to premature failure
under mechanical load. These defects produce local stress concentrations and
ultimately lead to premature failure [11, 12, 13]. Similarly, fillers act as thermal
barriers rather than conductors due to low interfacial adhesion under thermal
load.
Secondarily, local matrix morphology that is a distance from fibers also plays
a role in property enhancement. Both Potschke et al. [14] and Ding et al. [15]
observed this phenomenon in fiber pull-out experiments. After catastrophic fail-
ure, sheaths of matrix, tens of nm thick, extended from the fracture surface at
void sites previously occupied by CNFs. This suggests that the local interfa-
cial shear strength was much higher than otherwise expected. Assouline et al.
9
Jason R. Nixon
[16], Xie et al. [17], Sandler et al. [18] and Grady et al. [19] observed increased
local crystalinity in the interfacial region. Interface contact resistance, produced
from a decrease in interfacial thermal conductivity when thermal load is high,
inhibits heat flow, even in the presence of good adhesion. Islam and Pramila [20]
found that a microscopic interfacial contact resistance region reduced the effec-
tive thermal conductivity of the composite by up to 50% when the conductance
of the contact resistance zone was one to two orders of magnitude less than the
matrix. Nan et al. [21] demonstrated a correlation between interfacial resistance
thickness and fiber aspect ratio indicating effective thermal conductivity depre-
ciation. It is also important to keep in mind that local interfacial morphology
deviates from bulk morphology in polymer specific ways.
Dispersion also plays a role in property enhancement. Poor dispersion can lead
to both fiber re-agglomeration or lack of de-agglomeration. Under mechanical
load, fiber agglomerates will fail before their constituents due to a phenomena
known as fiber pull-out. Pull-out can occur under three possible conditions:
failure of the polymer-fiber interface, excessive shear stress in the matrix imme-
diately adjacent to the fiber, and failure at a fiber-fiber interface. The latter is
more likely to occur in agglomerates [22, 23]. Dispersibility has been found to
be related to the filler concentration of the composite. At high fiber concentra-
tions there is greater potential for agglomeration by way of entanglement and
reduced flow between closely packed fibers. In support, Machando et al. [24]
found that tensile properties were enhanced when SWNT concentrations was
less than 1 wt.%. At greater than W wt.% SWNT concentration, a decline in
10
Jason R. Nixon
enhancement was observed. Property depreciation is theorized to be a result of
decreased dispersibility at higher concentrations.
During melt-compounding, there is a correlation between increasing mixing en-
ergy and therefore the dispersive power of the mixer between increasing dis-
persion and decreasing fiber length. While many speculate that fiber length
maximization produces maximal tensile properties, reduced fiber length does
not necessarily result in property loss. Andrews et al. [25] showed that in-
creasing mixing energy reduced MWNT length by up to a factor of four (Ar =
1000 → Ar = 250). Yet those shortened MWNTs produced increased tensile
properties compared to longer MWNTs. From the other direction, Wang et al.
[26] found that mechanically reducing SWNT length by up to a factor of seven
(Ar = 725 → Ar = 100) not only increased dispersibility, but also improved
thermal conductance and electrical percolation onset concentration. Percolation
is defined as the threshold at which extremely large fiber networks form, dramat-
ically enhancing conductivity. Frusteri et al. [27] demonstrated similar results
for thermal conductance using three CMFs aspect ratios, Ar = 30, 500, 1000,
in a phase change material (PCM) matrix. These authors hypothesized that de-
creased length increased dispersibility, and therefore increased which resulted
in better load transference. However, at the microscale, there is evidence that
excessively shortened fibers result in mechanical property reduction [28]. It is
unlikely that critical fiber length, derived using continuum mechanics, is directly
applicable to nanoscale fibers.
11
Jason R. Nixon
Separate from process-induced dispersion and adhesion, significant work is cur-
rently focusing on the improvement of adhesion and dispersion from the per-
spective of the fiber [29, 30]. For nanoscale fibers, pre-treatment techniques
are often required to promote adhesion and dispersion [31, 32]. Pretreatments,
including functionalization and chemical treatment, are often used to improve
the wettability, roughness, and quality of the fiber surface [33]. Tiwari and
Bijwe [34] and Gong et al. [35] discuss the effectiveness of surface functional-
ization for adhesion enhancement. Surface functionalization is especially useful
for nanoscale carbon-based fibers that are typically chemically inert. However,
treatments could be used for any nanoscale filler. These treatments enhance sur-
face wettability, remove weakly bonded surface structures and contaminants,
allow for greater fiber-matrix entanglement, and increase fiber porosity, the
number of chemically active sites, and the number of potential nucleation sites.
Wang et al. [36] also found that mechanically shortened fibers has more chem-
ically active sites, which provided more opportunity for matrix-CNT bonding.
Secondary additives can also be included in the mixtures to enhance nanoscale
adhesion [37, 38].
For microscale fibers, with characteristic major dimensions three to five orders
of magnitude greater than nanoscale fibers, sufficient adhesion and dispersion
is easier to achieve by any compounding procedure. Consequently, microscale
fibers do not typically require secondary additives or modifications [39, 40].
12
Jason R. Nixon
2.3 Mechanical Properties
A body of authors have reported significant mechanical property enhancement
in microscale and nanoscale reinforced PMCs. Cho and Paul [41] increased the
concentration of organoclay in a nylon 6-organoclay nanocomposites and found
increased ultimate tensile strength and tensile modulus and decreased ductil-
ity as concentration increased. Carneiro et al. [42] found that increased vapor
grown carbon fibers (VGCF) concentration increased the tensile modulus and
yield strength, but decreased the impact strength when VGCF concentration was
varied from 0 wt.% to 20 wt.%. Bekyarova et al. [43] studied MWNT reinforce-
ment of an epoxy resin. The multiscale PMC had enhanced out-of-plane me-
chanical and electrical properties over the neat resin. Sandler et al. [39] observed
increased tensile modulus, bending modulus, yield strength, and ultimate tensile
strength for CNF concentrations below 15 wt.%. Ductility was maintained until
10 wt.% CNFs in poly(ether ether ketone)(PEEK). Above 10 wt.% CNFs, the
PMC became more brittle as the others had reported. Sandler et al. speculated
that as the CNF size decreased, CNF dispersion homogeneity increased, leading
to more matrix crystallization throughout the matrix.
Andrews et al. [23] found that high dispersion without fiber breakage was key
for achieving better properties for CNF and MWNT PMCs. While increasing
CNF concentration, at CNF concentrations below 15 vol.%, the tensile mod-
ulus increased while the ultimate tensile strength decreased. At higher CNF
concentrations, both the tensile modulus and ultimate tensile strength increase.
13
Jason R. Nixon
Overall, the removal of defects increased properties, and surface treatment im-
proved interfacial bonding. Poor adhesion led to fiber pull-out, which reduced
the effective mechanical properties.
While many reported improved ultimate tensile strength and reduced ductility,
there have also been cases where little improvement was observed. Lozano and
Barrera [44] found that with the addition of CNFs, ultimate tensile strength did
not improve significantly. However, increased brittleness was shown, which
could be attributed to the inability of the matrix to further crystallize when sub-
ject to deformation because of the molecular restrictions related to dispersion.
Lee et al. [45] claimed that a reduction of properties due to nanoscale fillers in-
dicated poor adhesion and dispersion. They used electrophoretic deposition to
deposit nanoscale reinforcements and found that good dispersion homogeneity
was achieved which lead to improved properties. Lastly, there have been reports
where fillers improved properties until a certain filler concentration, and then
begin to hinder the composite. Broza et al. [46] found that the tensile modulus,
ultimate tensile strength, and strain to failure increased when increasing CNT
concentration in a PBT matrix from 0.01 wt.% to 0.1 wt.%. However, when
CNT concentration was increased from 0.1 wt.% to 0.2 wt.%, the ultimate ten-
sile strength strength and the strain to failure of the nanocomposites decreased
slightly . Zeng et al. [47] added CNFs to poly(methyl methacrylate) (PMMA)
and found that there was an optimum concentration of CNFs between 5 wt.%
and 10 wt.% since beyond a 10 wt.% CNF concentration, the modulus began to
decline. Zeng et al. recognized, however, that this optimum concentration would
14
Jason R. Nixon
be a function is a function of fiber dimension and the degree of dispersion ho-
mogeneity.
Yesil et al. [48] studied CMF reinforced high-density polyethylene (HDPE),
polyethylene terephthalate (PET), and MWNT composites. They found that af-
ter an initial increase in tensile strength, the addition of microfibers and MWNTs
decreased the performance since there was a lack of compatibility with the poly-
mer phase beyond 30 wt.% concentration of PET.
In summary, the mechanical properties are altered with the addition of mi-
croscale and nanoscale fibers to a polymer matrix. Most groups have reported
improved properties, but recognize that there are likely a minimum or maximum
concentration that yield the greatest property enhancements. Furthermore, there
are intrinsic processing limitations that limit performance capability of com-
pounded PMCs. Above these limits, viscous forces and fiber interactions act to
erode and fracture fibers, reducing their effectiveness for PMC reinforcement.
2.4 Thermal Properties
Heat conduction is defined as the transfer of energy from more energetic to less
energetic particles through particle interactions [49]. Energy is related to the
translational motion, internal rotation, and vibrational modes of the molecules.
In solids, the transfer of energy is dominated by translation motion and lattice
vibrations [49]. PMC effective thermal conductivity is related to the number and
quality of matrix-filler interfaces, the quality of fibers, and the conductivity of
15
Jason R. Nixon
the matrix, for the the global exchange energy. Secondarily, the onset of thermal
percolation would produce yet better effective thermal conductivity. In order to
maximize thermal conductivity, fibers should ideal have a high aspect ratios and
be well dispersed [50, 51]. Again, by the highway analogy, a single continuous
highway is more effective than many short ones, presuming that the highway is
going in the direction you wish to travel.
Thermal property enhancement in polymer composites with CMFs and CNTs
has been predicted to be very high due to the thermal conductivity of the fillers
[52, 53]. For example, Hone et al. [51] examined epoxy-SWNT and epoxy-
VGCF thermal conductivity enhancement. They found an enhancement of 120%
at 1 wt.% SWNT and, 40% at 1 wt.% VGCF, and 110% at 2 wt.% VGCF. A
broad review of polymer and filler thermal conductivity values can be found
in [54]. Broadly, the thermal conductivity of many neat polymers have been
reported to be in the range of 0.1 W/mK to 1.0 W/mK.
Many authors have reported on the thermal conductivity of isolated CMFs.
PAN-based CMFs have demonstrated thermal conductivity between 8 W/mK
and 70 W/mK. Pitch-based CMFs have demonstrated thermal conductivity be-
tween 530 W/mK and 1100 W/mK. Metal fibers have been reported to be in the
range of 200 W/mK to 500 W/mK.
The measurement of the isolated thermal conductivity of a CNT has proven to
be a research domain of great interest. Using molecular dynamics simulations,
Berber et al. [52] predicted longitudinal thermal conductivity to be 6600 W/mK
at 25◦C for a pristine (defect free) CNT. Experimental results by Hone et al.
16
Jason R. Nixon
[55], Kim et al. [56], Yu et al. [57] established a wider range of 2800 W/mK to
6600 W/mK at 25◦C. While this value is unusually high, consideration of the
carbon-carbon bond structure and nearly defect free atomic structure, the value
is not surprising for an isolated CNTs [52]. Along the fiber axis, heat conduc-
tion is due to a phenomenon known as ballistic phonon transport. However,
this mechanisms is only available along the fiber axis, and it is therefore un-
surprisingly that the transverse heat flow of CNTs are reported as significantly
lower. Sinha et al. [58] experimentally demonstrated an effective conductivity
of 1.5 W/mK, three orders of magnitude less than axial conductivity.
From a structural perspective, Agarwal et al. [59] found that the effective con-
ductivity of highly aligned CNFs was greater than that of randomly aligned
CNFs. Hone et al. [51, 55], found that uniaxially aligned nanofiber structures
possessed a thermal conductivity of 250 W/mK, planar randomly aligned nanofiber
structures possessed thermal conductivity in the range of 30 W/mK to 70 W/mK,
and three-dimensional random nanofiber structures demonstrated even lower
thermal conductance. [60] showed similar results using molecular dynamics
simulations.
Wang et al. [26] explored the effect of CNT length on thermal conductivity and
found that mechanical shortening combined with surface treatment of the CNTs
enhanced thermal conductivity. Wang et al. hypothesized that shorter CNTs
had a richer surface chemistry and possessed improved dispersability, which is
supported by the work of Wang et al. [36]. Zimmer et al. [61] also explored
17
Jason R. Nixon
the thermal property enhancement using long MWNTs and short MWNTs. Re-
sults showed that, contrary to intuition but in support of previously discussed
works, the thermal conductivity long MWNTs was not improved over that of
short MWNTs, and that the long MWNTs acted more like insulators due to
phonon transport interference.
Frusteri et al. [27] examined CMFs of different lengths and loading’s mixed
with inorganic phase change materials. Results showed thermal conductivity en-
hancement increased linearly with loading, and that CMF length effected ther-
mal conductivity. Shorter CMFs produced higher thermal conductivity. The
authors speculated that this was because of the degree of homogeneity achieved
in the samples, where CMFs (6 µm diameter) of 200 µm length were better dis-
persed than the 3 mm and 6 mm mm CMFs. They also found that at a 7 wt.%
loading, the thermal conductivity quadrupled. Similar results were for shortened
fibers have already been discussed in §2.2.
Because effectiveness thermal conductivity has been found to be a function of
dispersion and adhesion, the reader is referenced back to §2.2 for a discussion
of interfacial thermal resistance, surface functionalization, etc.
Zhou et al. [62] examined thermal conductivity enhancement using surface treat-
ment of micro-SiC/DGEBA/EMI-2,4 and nano-SiC/DGEBA/EMI-2,4. Results
showed that surface treatment of the nano-SiC increased thermal conductivity.
Interestingly, Sun et al. [63] and Shenogin et al. [64] identified a competitive
relationship when functionalizing CNTs. While functionalization increases the
18
Jason R. Nixon
potential for adhesion, functionalization also damages the CNT structure. This
damage increases phonon transport interference, thus reducing the effective ther-
mal conductivity of the CNT.
While many have reported increased effective thermal conductivity, others have
found little improvement. Gojny et al. [65] concluded that low interfacial area
and weak interfacial adhesion promote thermal conductivity, which is in op-
position to the requirements of improved mechanical properties. Gojny et al.
theorized that poor adhesion acts to shield the fiber from the matrix, reducing
phonon transport interference along the fiber length. Therefore, CNTs, which
posses large interfacial areas and defect rich carbon structures, are not suitable
for thermal conductivity enhancement. However, it is possible that that interfa-
cial contact resistance, which was previously discussed in §2.2, was a dominant
mechanism rather than phonon transport resistance.
2.5 Processing Conditions
Twin-screw extrusion was used to compounding PMCs in this dissertations.
Twin-screw extrusion highly versatile method of melt-mixing capable of achiev-
ing a range of mixing qualities by changing configuration and operating param-
eters, which in turn effect the amount of shear stress and strain imparted to the
material during compounding. However, the design of screws and choice of
operating parameters remains somewhat of an art form and consequently the
subject of many experimental studies.
19
Jason R. Nixon
The shear stress seen by the material in the extruder is strongly dependent on
screw speed. Chen et al. [66] found that at higher shear rates, electrical conduc-
tivity at 1.5 wt.% CNT was comparable to conductivity at 2.5 wt.% CNT which
had been processed at a lower shear rate. However, while the higher shear rates
led to better dispersion and electrical conductivity, it also reduces the alignment
of the CNTs, reducing other properties. Villmow et al. [67] found that in a
PLA matrix, controlling for flow rate, a screw speed of 500 rpm yielded better
MWNTs dispersion when compared to 200 rpm and 100 rpm.
Vera-Agullo et al. [68] performed an extensive study on the dispersion of CNTs
and found that more aggressive screw designs increased dispersion, but also
increased CNT fracture. While less aggressive screw designs were found to suf-
ficiently disperse CNT agglomerates to form electrically conductive networks,
mechanical enhancement was only found using the most aggressive screw de-
signs. This relationship between dispersion and mixing intensity is fundamen-
tally demonstrated stated by Scurati et al. [69]s, who proposed a model of ag-
glomerate erosion and rupture based on the power input of the mixing process.
Gao et al. [70, 71] found that the degree of mixing is dependent on screw speed,
volumetric flow rate, specific throughput (volumetric flow rate divided by screw
speed). Pappas [72] and Fukuda [73] further explored this concept and char-
acterized the stress seen by the ingredients in an extruder. Pappas and Fukuda
found that specific throughput and screw speed effected the imparted stress on
the filler, where higher operating inputs produced imparted higher stress on the
20
Jason R. Nixon
filler. By varying processing conditions, the final structure and properties of the
PMC were altered significantly.
Acierno et al. [74] has shown that voids and gaseous inclusions have been shown
to reduce reduce property performance . At higher CNT loadings, the extent of
mechanical property improvement is limited by the high apparent viscosity of
the melt, which acts to limit the removal of gaseous inclusions, and the resulting
void defects [11]. Kuriger et al. [75] found that the number of voids increased
with the filler concentration, which is resultant from the extremely high appar-
ent viscosity near the filler in comparison to the bulk. Kota [3] found that by
pulling a vacuum on the melt during compounding, the porosity of the polymer
was significantly reduced and physical and electrical properties were greatly in-
creased.
2.6 Microstructure
As stated in §2.2, fiber alignment within the matrix produces anisotropic prop-
erties [29, 76]. We are primarily concerned with the average fiber orientation
of many fibers with respect to the applied load. Several bulk structure are com-
monly found in literature: unidirectionally aligned, in-plane randomly aligned,
and fully three-dimensional randomly aligned. A two-dimensional illustration
of these states is shown in Figure 2.1. Depending on the desired application,
different structure and structure orientation may be preferred.
21
Jason R. Nixon
FIGURE 2.1: Discontinuous fiber reinforcement, left to right: unidirectionally
aligned under longitudinal loading, unidirectionally aligned under transversely
loading, planar-randomly aligned.
Agarwal et al. [59] found that CMFs uniaxially aligned parallel to the applied
load greatly enhanced thermal conductivity. Agarwal et al. also found that in-
plane enhancement was up to 600% greater than uniaxially out-of-plane or ran-
dom structures, and that out-of-plane enhancement was little better than random.
Thostenson and Chou [77] found that the extrusion process and post-extrusion
drawing produced a uniaxial nanostructure in PS/CNT. These samples demon-
strated increased strength and increased stiffness when compared to a randomly
aligned PS/CNT samples, and demonstrated better load transfer capacity from
the PS to the CNTs. Kuriger et al. [75] found that the fiber alignment improves
with a longer time in the extruder, and that this had a significant effect on prop-
erties. By examining thermal conductivity, they found that highly aligned fiber
structures improved thermal conductivity most in the longitudinal direction.
Du et al. [78] performed an extensive study on the alignment and dispersion
of PMMA-SWNT and related it to mechanical, thermal, and electrical proper-
ties. While all the formulations/structures showed improvement over PMMA,
the electrical conductivity was greatly influenced by SWNT alignment, where
22
Jason R. Nixon
the aligned samples were 5 orders of magnitude lower in electrical conductivity
when compared to unaligned samples. This was a result of low SWNT contact
networking, which is necessary for electrical conductivity.
A number of authors have reported on process induced fiber orientation. Kuriger
et al. [75] and Rangari et al. [79] reported success in aligning fibers during extru-
sion. Jin et al. [80] and Haggenmueller et al. [81] reported success in producing
aligned structures using drawing. Highly aliened SWNT structures have also
been produced using magnetic fields [82, 83, 84]. In all cases, authors reported
significantly greater properties in-line with fibers then transversely.
While authors have reported on increased alignment uniformity using extrusion,
not all authors have reported such occurrence. Zeng et al. [47] and Potschke
et al. [85] found that nanoscale fibers were not necessarily aligned after extru-
sion. Sandler et al. [39] found that the alignment of CNFs further decreased
during injection molding.
Several groups have explored methods for creating random or out-of-plane aligned
filler structures. Vincent and Agassant [86] explored the use of diverging flow
to produce out-of-plane aligned fiber alignment.
Halpin and Kardos [87] showed that tensile strength and stiffness of three-
dimensional randomly oriented fibers could be approximated as isotropic.
23
Jason R. Nixon
The structure of fillers within the embedding polymer matrix greatly effects
PMC property anisotropy. Highly aligned fibers produce significant enhance-
ment in the orientation of the fillers, but little to no enhancement in other orien-
tations. Alternatively, randomly aligned filler structures tend to produce nearly
isotropic property enhancement, at the cost of reduced enhancement overall.
Manipulation of the structure at a microscale and nanoscale can produce en-
hancements in certain loading directions and reductions in others depending on
the preferred structural orientation.
2.7 Multi-Filler Composites
A number of studies have been conducted on PMCs compounded with two or
more different filler materials (ceramics, metals, etc.), length scales (microscale
and nanoscale), and/or dimensionalities (tubes, sheets, spheres, agglomerated
bodies, etc.). The goal of these studies was to identify combinations of fillers
that resulted synergistic PMC enhancement. PMCs containing multiple fillers
are broadly referred to as hybrid PMCs, while PMCs containing fillers of differ-
ent major length scales are referred to as multiscale PMCs.
Agarwal et al. [59] compounded CNFs and CMFs into PC and found that higher
thermal conductivity in PC/CMF/CNF samples than PC/CMF samples. Agarwal
et al. hypothesized that CNFs enhanced the interfacial adhesion between the PC
24
Jason R. Nixon
and CMF, leading to enhanced heat conduction through the fiber-matrix inter-
face. Lederer [88] explored filler-processing-property relationships of PBT/CM-
F/MWNT PMCs compounded by twin-screw extrusion. Lederer [88] found that
certain combinations of CMF and MWNT lead to enhancements in properties
over PBT/CMF alone for both tensile and thermal properties. For these PMCs,
CNT dispersion could become a significant issue, but was not directly measured.
Property improvements were not in general always synergistic and certain ra-
tios of CMFs and CNFs could result in property depreciation. Nie et al. [89]
investigated interfacial shear strength, longitudinal elastic modulus, and trans-
verse elastic modulus of epoxy/CMF/CNT PMCs a multiscale simulation. It was
found that elastic modulus of the CNT/epoxy was significantly enhanced over
neat epoxy, and that increasing CNT-epoxy adhesion also increased the effective
matrix properties. CMF properties changed little in the presence of CNTs. This
study rightly demonstrated that CNT adhesion is critical for property enhance-
ment.
As a note, the direct compounding of multiple fillers is not the only multiscale
PMC production method currently under considered. Another prominent tech-
nique is the synthesis of nanoscale features onto microscale fibers. By synthe-
sizing CNTs using CVD onto the surface of CMFs, Thostenson et al. [90] found
increased interfacial shear strength when compared to neat CMFs. This was
hypothesized to result from the enhanced surface area available for matrix ad-
hesion. Bekyarova et al. [43] studied SWNT and MWNT synthesis on CMFs
by electrophoretic deposition and found that the presence of MWNTs enhanced
25
Jason R. Nixon
electrical properties, did not effect tensile properties, and improved interfacial
shear stress when compared to neat CMFs. Similar work was also reported by
Lee et al. [91] and Qian et al. [92].
Multidimensional and multimaterial PMCs have also been examined in the lit-
erature. Xu et al. [93] examined the thermal conductivity of AlN spheres, AlN
whiskers, and SiC whiskers in epoxy, and found that the inclusion of spherical
and fibrous fillers of the same material produced the highest increase in thermal
conductivity. Furthermore, the inclusion of SiC whiskers could be used instead
of AlN whiskers to augment mechanical properties while the AlN particulates
enhanced the thermal properties
Lee et al. [94] studied the inclusion of a combination of Wollastonite and SiC
fibers, and boron nitride (BN) particles in HDPE. They found that at low con-
centrations, the combination of fiber and spherical fillers increased thermal con-
ductivity, but at higher filler concentrations the role of the fibrous material was
minimal. Research into the synergy between CNTs and graphene has also been
conducted by Zhang et al. [95], Zheng et al. [96], Li et al. [97]. However, CNT/-
graphene PMCs posed additional issues related to the dispersion and adhesion
to both the CNT and graphene fillers.
26
Chapter 3
Methods and Procedures
This chapter describes the equipment and procedures used in the experiments
conducted in this dissertation.
3.1 Materials
Three types of ingredient were utilized in this investigation: (1) polymer matrix,
(2) microscale filler, (3) nanoscale filler.
3.1.1 Polymer Matrix
Polybutylene terephthalate (PBT) was used as the polymer matrix throughout
all experiments presented in this dissertation. The PBT was supplied by Poly-
One Corporation and was sourced from Chang Chun Plastics Co. (Grade 1200
211D). Poly (butylene terephthalate) (PBT) is a semi-crystalline thermoplastic
27
Jason R. Nixon
which offers a good combination of thermal stability and mechanical properties
when compared to other polymers. [98] PBT is often used as an insulator for
electrical components in various industries and it is durable under harsh envi-
ronments, making it ideal for some applications. For this application, its rapid
crystallization made post-extrusion collection easier. The molecular weight of
the PBT is 28000. Its melting temperature is approximately 225◦C.
3.1.2 Microscale Fillers
Two lengths of CMF were used in this body of work: 6 mm (aspect ratio 800)
and 100 µm (aspect ratio 16). Both lengths of CMFs has a diameter of 7 µm
and were provided by Toho Tenax America, Inc. (Tenax-A HT C496 6mm
respectively and Tenax-A HT M100 100mu). 6 mm CMFs were mechanically
chopped and supplied as bundles. 100 µm CMFs were ball milled and supplied
as a loose powder. Both CMFs were recommended for use with PBT because
of surface adhesion compatibility. Although it would be ideal to use a wider
range of CMF lengths in the range of 200 µm to 500 µm, these CMFs were not
commercially available due to processability issues.
3.1.3 Nanoscale Fillers
PolyOne Corporation supplied a pre-compounded mixture containing 15 wt.%
MWNT and 85 wt.% PBT. Receiving the PBT/MWNT batch ensured consistent
28
Jason R. Nixon
and proper MWNT adhesion, dispersion, and distribution. Supplied MWNTs
were approximately 7 µm in length and 11 nm in diameter (aspect ratio 600).
3.1.4 Summary of Matrix and Filler Properties
Table 3.1 summarizes manufacturer specified material properties of the PBT and
fillers.
TABLE 3.1: Manufacturer specified material properties.
Property PBT CMF CMF MWNT
Density 1.31 g/cm3 1.82 g/cm3 1.82 g/cm3 1.50 g/cm3
Length - 100 µm 6 mm 7 µm
Diameter - 7 µm 7 µm 11 nm
Ten. Mod. 2.7 GPa 226 GPa 226 GPa -
Ult. Ten. Str. 42 MPa 4.41 GPa 4.41 GPa -
3.2 Twin Screw Extrusion
PMC samples were compounded using a co-rotating fully intermeshing twin-
screw extruder (CoTSE). Extrusion is a continuous melt-mixing process that
is commonly used in polymer processing, pharmaceutical, and food industries,
among many others. Continuous melt mixing produces consistent and well-
mixed product, although the choice of processing conditions and extruder design
remain somewhat of an art form.
29
Jason R. Nixon
The extruder used was a Coperion ZDSK 28 mm tri-lobal CoTSE, located in the
Advanced Manufacturing Laboratory at the University of Maryland, shown in
Figure 3.1. Each screw has an outer diameter of 28 mm and is 900 mm in long
from feed port to die. The resulting non-dimensional length to diameter ratio is
32.
FIGURE 3.1: Twin screw extruder setup in the Advanced Manufacturing Lab.
The extruder is comprised of eight zones: the intake block, five electrically
heated barrels, the connection block, and an electrically heated die zone. The
intake port receives material pellets (or powder) from above-mounted feeders.
Each barrel is individually electrically heat and can be water cooled if neces-
sary. The majority of the screws are housed within the barrels. Fillers are fed
into the extruder at the mixing port, located in the top of barrel three. A Welch
R1402 vacuum pumped is attached at the vacuum port located at barrel five.
Material was processed at a vacuum of 500 mmHG in order to remove volatiles
and gaseous inclusions. The connection block and die block proceed barrel five.
30
Jason R. Nixon
The connection block hosts ports for instrumentation such as a optical probes
or pressure transducers. For this dissertation, no additional instrumentation was
used and empty probe housings were secured into instrumentation ports to pre-
vent material from escaping.
3.2.1 Die Design
The die, mounted on the die block, forms the extrudate into the desired final
shape during pumping. All straight and divergent dies were designed with a
common die width W of 25.4 mm (1.0 in) and an inlet height hinlet of 1.0 mm.
Different divergence angles θ were created by varying the die length L from
25.4 mm to 50.8 mm (1 in to 2 in) and the outlet height houtlet from 1.0 mm to
5.0 mm. Table 3.2 provides a summary of the die geometries used in this body
of work.
TABLE 3.2: Die dimension list for all non-diverging and extruder diverging
dies.
Letter L hinlet houtlet θ
A 25.4 mm 1.0 mm 1.0 mm -
B 50.8 mm 1.0 mm 3.5 mm 1.41◦
D 50.8 mm 1.0 mm 5.0 mm 2.26◦
E 25.4 mm 1.0 mm 3.5 mm 2.82◦
F 25.4 mm 1.0 mm 5.0 mm 4.52◦
3.2.1.1 Die Residence Time
By control volume analysis, it is possible to calculate the mean residence time
of polymer within a die using throughput, polymer properties, and die geometry.
31
Jason R. Nixon
FIGURE 3.2: Extruder die front face (from left to right): straight compounding
die (A), divergent compounding die (E), strand die.
FIGURE 3.3: Extruder die rear face (from left to right): straight compounding
die (A), divergent compounding die (E), strand die.
The mean velocity of a particle in the die is defined as Equation 3.1.
vdie =
W · (hinlet + houtlet) · ρ
2Q
(3.1)
Alternatively, it is possible to define the mean die residence time, i.e. the amount
of time the die volume of material spends in the die, as Equation 3.2.
tdie = vdie · L (3.2)
32
Jason R. Nixon
3.2.2 Screw Design
Inside the CoTSE, two intermeshing screws synchronously rotate to mix mate-
rials. These screws are composed of modular screw elements that are affixed
to a central keyed shaft. These elements can be of the conveying and kneading
variety. Forward conveying elements pump material down-channel. A special
screw design, known as a pumping screw, is composed entirely of forward con-
veying elements. Conversely, reverse conveying elements pump material up-
channel. For these elements, the upstream melt pressure must overcome the
back-pressure generated by the reverse conveying element in order to pump ma-
terial forward. Reverse conveying elements are frequently used as end caps to
mixing sections in order keep material inside the mixing section for a longer
time. Kneading blocks, which are composed of a series of offset paddles, pro-
duce mixing. Mixing section configuration, paddle thickness (wide, medium,
and narrow), and paddle angle offset produce different amounts of mixing. Note
that although not used in this research, reverse kneading elements can also be
used. A variety of other types of screw elements are also available for special-
ist applications. Mixing section design is frequently varied in order to find the
ideal arrangement to maximize mixing while minimizing property depreciation
due to high stress. Screw element arrangement is critical for extrusion because
of the potential to dramatically alter properties.
The screw geometry used in this dissertation is shown in Figure 3.4.
33
Jason R. Nixon
FIGURE 3.4: Modular screw design used in this dissertation.
The screw shown in Figure 3.4 is divided into four sections, in order from first
to last: melting, conveying, mixing, and pumping. Material enter the melt sec-
tion through the intake block, is melted, and then conveyed downstream by the
conveying section where fillers are added through the feed port in barrel three.
The mixing section then kneads the material and fillers, dispersing fillers in the
matrix. After the mixing section, devolatilization in the pumping section re-
moves any gaseous contaminants in the material. The compounded melt is then
pumped to the screw tips, which are housed in the die zone. This pumping action
then forces the melt through the die.
3.2.3 Extruder Control
The ZDSK-28mm extruder is controlled by a FACTS MI 101 control system.
The control system has both manual and digital controls. This control unit was
used to set and monitor barrel and die temperatures, set screw speed, and mon-
itor motor amperage. To prevent damage to the extruder, drive amperage was
34
Jason R. Nixon
not allowed to exceed 15 amps, although the control system imposed a 20 amp
hard limit before emergency stop. Rheological properties, filler concentration,
processing conditions, and screw geometry all affect the drive load. If an excess
of material was fed into either feed port, if the material was highly elastic, or if
the screw geometry was too aggressive (quantity and placement of the kneading
elements) the drive could not achieve the necessary torque required to turn the
screws.
The standard temperature profile and screw speed set points for PBT are listed
in Table 3.3. Water cooling was not necessary for compounding PBT.
TABLE 3.3: Extruder set points for PBT.
Parameter Set Point
Flow rate 1.4 - 2.3 kg/hr
Screw Speed 200 rpm
Barrel 1 229◦C
Barrel 2 246◦C
Barrel 3 241◦C
Barrel 4 249◦C
Barrel 5 249◦C
Die Zone 235◦C
35
Jason R. Nixon
3.2.4 Material Feeders
To regulate material input to the extruder, two laboratory scale feeders were
used, one for material pellets and one for microfiber. Both feeders were secured
to a platform above the extruder extruder for access to the top-facing feed ports.
A K-Tron loss-in-weight twin-screw feeder was used to feed material pellets into
the extruder through the intake block. This feeder was connected to the extruder
feed port via a flexible tube and steel funnel. This feeder has a maximum limit
of 22.7 kg/hr.
Filler were fed into the feed port by a K-Tron Micro Feeder MT12 loss-in-weight
twin-screw feeder. Although this feeder is typically used for powders, it can
also be used for CMF bundles. Extensive validation was completed to verify the
feeder performance for fibers. This feeder has a maximum limit of 0.45 kg/hr.
3.2.5 Material Collection
Extrudate was collected in strips for property testing using the dies listed Ta-
ble 3.2 (Pg. 31) or in strands for pelletization.
3.2.5.1 Die A
Straight die samples were collected using a chilled roller system, which put the
strip under tension, rapidly cooled the sample, reduced surface non-uniformity,
and eased collection. The speed of the rollers could be set using an analog motor
36
Jason R. Nixon
controller, and was adjusted to match the rate of pumping. By setting the roller
speed greater than the pumping rate, the strip could be thinned.
3.2.5.2 Die B-F
Diverging die samples were collected using a metal conveyor belt in order min-
imize drawing prior to cooling, which could lead microstructural changes due
to internal flows generated during drawing. The speed of the conveyor was set
using an analog motor controller, and the speed was set to match the pumping
rate from the die.
3.2.6 Pelletization
Batched pellets were formed using the strand die and a Kilion Extruders Inc.
plastics pelletizer. During initial operation, strands were collected by hand and
drawn through a water bath to ensure cooling prior to pelletization and fed into
the pelletizer. Once fed, strands were automatically drawn into the pelletizer by
a friction pinch roller system. A spinning block then cut the strands down into
pellets of desired size which were ejected from the rear of the machine. The
draw rate of the pinch roller was set to match the extrusion rate. The collected
pellets were then dessicated as per neat PBT, and then used in the extruder to
achieve loadings greater than 15 wt.%.
37
Jason R. Nixon
3.3 Property Testing
3.3.1 Tensile Testing
Tensile tests were conducted using a Tinius Olsen H25K-T bench top univer-
sal testing machine with a 5000 lb load cell, located in the Modern Engineering
Materials Instructional Laboratory at the University of Maryland. An extension
rate of 2 mm/min was used. Samples were secured into this testing device by
two self tightening clamps which acted to pull the specimen apart. This plat-
form recorded the applied load and displacement in time and exported this data
as a tabulated data list. The native software also calculated the relevant ten-
sile material properties automatically, although it was necessary in some cases
to re-analyze the data to remove data artifacts like clamp slip. Using load/dis-
placement data, stress/strain data could be extracted, which in turn allowed for
tensile modulus, ultimate strength, and yield strength can be determined.
Tensile specimens manufactured and tested according to the ASTM D638-12
standard [99]. This standard specifies testing conditions and geometry in order
to produce reliable and repeated measures for tensile properties. The geometry
for a tensile specimen is shown in Figure 3.5.
3.3.2 Thermal Conductivity Testing
A C-Therm TC-30 modified transient plane source thermal measurement sys-
tem was used to measure effective thermal conductivity. The TC-30 measures
38
Jason R. Nixon
FIGURE 3.5: ASTM D638-10 type-IV tensile test specimen geometry.
thermal conductivity by applying a known current to the sensor’s spiral heating
element, which is is guarded to support one-dimensional heat transfer into the
sample, providing a small amount of heat. The applied current results in a rise in
temperature at the interface between the sensor and the sample, which induces
a change in the voltage drop of the sensor element. The rate of increase in the
sensor voltage is used to determine the thermal conductivity of the sample.
FIGURE 3.6: C-Therm TC-30 thermal conductivity measurement system.
39
Jason R. Nixon
Thermal conductivity is inversely proportional to the rate of increase in the tem-
perature at the point of contact between the sensor and the sample. The voltage
is used as a proxy for temperature. Voltage will rise more steeply when lower
thermal conductivity materials (e.g. foam) are tested. Conversely, the voltage
slope will be flatter for higher thermal conductivity materials (e.g. metal).
Thermal conductivity is calculated from the initial voltage V0, rate of change m
of the measured voltage in the testing window, and calibration coefficients C2,
C3, and C4 Equation 3.3. If the slope remains constant in the testing window,
a single blotter test (§3.3.2.2) test was used. If the voltage was demonstrated
non-linearity, a dual blotter test (§3.3.2.3, Pg. 42) procedure was used.
k =
C2
m
V0
− C4 + C3 (3.3)
3.3.2.1 Calibration
Full calibration was performed at the beginning of testing. Typically five cali-
bration standards, selected to span the expected conductivity range, were used
to generate the regression equation coefficients C2, C3, and C4. The standards
are listed below in Table 3.4.
TABLE 3.4: TC-30 calibration standard thermal conductivity at 20◦C in
W/m−K.
Material LAF20 Lexan HDPE Pyrex Macor
Conductivity 0.085 0.254 0.577 1.150 1.600
40
Jason R. Nixon
Once full calibration is completed, an HDPE calibration standard was tested
every ten samples to track calibration drift over time. Using this data, it was
possible to identify bad tests or to correct for small drifts in calibration.
3.3.2.2 Single Blotter Testing
FIGURE 3.7: Measured voltage plotted against root time for a single blot-
ter test. note the Initial non-linear behavior, followed by a constant rate
of change starting at approximately
√
t = 2. This curve was gener-
ated for sample D30-4. Using the calibration constants C1 = 0.001776,
C2 = −0.13, C4 = 0.0003332, the conductivity of this sample was calculated
to be 0.653 W/mK, a 262% increase over neat PBT.
For samples where the generated heat does not fully transverse the sample thick-
ness during testing, a single blotter test was used. For this procedure, a single
test was sufficient to calculate the thermal conductivity of the sample using the
rate of change of the voltage m with respect to root time from inside the testing
window, or from t = 4 (
√
t = 2) to t = 10 (
√
t = 3.16). An example of the
voltage curve generated during testing is shown in Figure 3.7. This procedure
is only valid when the voltage slope remains linear over the testing window. If
41
Jason R. Nixon
prior to t = 10, the voltage rate of change demonstrates time dependent behav-
ior, heat has fully transversed the thickness of the sample and begun moving into
the blotter. For these samples, a second test was performed in accordance with
the dual blotter testing method discussed in §3.3.2.3.
3.3.2.3 Dual Blotter Testing
FIGURE 3.8: Measured voltage plotted against root time for a dual blotter
test. Note the initial non-linear behavior, linear behavior, the divergence point,
and continued non-linear behavior as the heat passes through the sample and
into the blotter. A constant rate of change is extrapolated out from the diver-
gence point. This curve was generated using a glass microscope slide. Using
the calibration constants C1 = 0.001776, C2 = −0.13, C4 = 0.0003332, the
conductivity of this sample was calculated to be 0.797 W/mK.
For samples in which the conducted heat fully transverse the sample with the
testing window, a dual blotter method was used. For this, two tests were per-
formed, the first using a metal blotter and the second using a foam blotter. Be-
cause the thermal conductivity of the metal and foam bound the conductivity of
the composite, the rate of change of voltage will decrease for metal or increase
42
Jason R. Nixon
for foam. By overlaying these two voltage curves as shown in Figure 3.8, a
divergence point is identified and a constant rate of change at that point is as-
sumed to represent the true conductivity of the composite. This rate of change is
then used to calculate conductivity using Equation 3.3. A MATLAB code was
created to perform this analysis semi-automatically.
3.3.3 Optical Microscopy
For optical microscopy, samples were mounted in transparent epoxy and pol-
ished for imaging. These micrographs were then analyzed to extract fiber orien-
tation and distribution.
3.3.3.1 Mounting and Polishing
First, samples were mounted in 1.25 in diameter two part mounting cups a trans-
parent two part resin/hardener epoxy. Prior to curing, sample were placed in
a vacuum of 30 inHG for five minutes to remove air bubbles trapped in the
epoxy. The vacuum was then reduced to 15 inHG and the samples were al-
lowed to fully cure, which took approximately two hours. Post cure, mounted
samples were removed from mounting cups and polished using a MetPrep 4
semi-automatic polishing machine with neumatic powered head. Four polishing
pads were used for various times and head force, which are listed in Table 3.5.
The sample surface at the completion of each stage is shown in Figure 3.9.
43
Jason R. Nixon
TABLE 3.5: Mounted sample polishing pad grit, time, and head force. Pads
were used in order of increasing grit during polishing.
Paper [grit] 180 320 600 1200
Time [m:s] 1:30 3:00 6:00 24:00
Force [lbf] 8 8 8 14
(a) 180 grit. (b) 320 grit. (c) 600 grit. (d) 1200 grit.
FIGURE 3.9: Microscopy sample surface at 10X magnification after polishing
using the pads, time, and head force listed in Table 3.5. Fibers are indicated as
bright ellipses or circles (fiber cross section) in the image. Due to the thinness
of obliquely aligned fibers at their leading edge, cylindrical voids frequently
occur near the fiber edge due to fiber fracture
Samples were imaged using an Beuhler reflected light inverted microscope with
attached Infinity 2 microscope camera located in the Modern Engineering and
Materials Multi-Scale Measurements Laboratory at the University of Maryland.
All micrographs were taken using 10X magnification. Other magnifications, 5X,
20X, 40X, were available and used, but these micrographs were not included in
post-capture analysis. Micrograph images were captured using Infinity Capture
software. Analysis using MATLAB was performed on these images to extract
fiber orientation and distribution.
44
Jason R. Nixon
3.3.3.2 Fiber Orientation Analysis
Under the assumptions that fibers are approximately cylindrical along their axis
and circular on their face, fiber orientation can be calculated with respect to the
extrusion orientation (normal to the micrograph plan) using the major and minor
axis of the ellipses identified in the micrographs. An illustration of the mapping
of the measured ellipse onto the fiber is shown in Figure 3.10. The angle α is
calculated using Equation 3.4.
FIGURE 3.10: Illustration fiber orientation as a function of the ellipse formed
by the intersection of the cylindrical fiber and the cut plane where A is the
major axis, B is the minor axis which is equivalent to the fiber radius df , and
ξ is the angle between the fiber axis and the cut plane. The fiber diameter is
supplied by Toho Tenax of America as approximately 7 µm.
α = cos−1
(
B
A
)
(3.4)
Individual micrographs were collected into composite fiber orientation distribu-
tions for each condition. An example fiber orientation distribution, including the
Figure 3.9(d), is shown in Figure 3.11. While this distribution is approximately
45
Jason R. Nixon
resembles a χ2 distribution, this is coincidental and individual distributions tend
to less clearly form into a distinct form.
FIGURE 3.11: The distribution above presents the fiber orientation distribution
the condition Q = 1.81 kg/hr, Vµ = 23.6 vol.%, Vn = 1.8 vol.%, θ = 4.52◦.
This include the micrograph shown in Figure 3.9(d). The majority of fibers are
centered around approximately 70◦.
3.3.4 Statistical Analysis
In order to evaluate the effect of independent variables on measured properties,
multiple linear regression analysis was performed using MATLAB.
In 5.3, regression analysis was performed using four independent variables,
CMF concentration Vµ, MWNT concentration Vn, flow rate Q, and die angle
θ. A build-down approach was used while constructing the regression model.
Initially, all main effects, two-way interactions, three-way interactions, and four-
way interactions were considered. We then consider the highest order interac-
tion P-Values. We then remove the highest level effect with the greatest P-value
46
Jason R. Nixon
which is greater than 0.05. We then continue this process until only statistically
significant and marginal effects remain.
For each fitted regression model, assumptions were checked and validated in-
cluding linearity, normality, and scedasticity.
47
Chapter 4
Simulation
This chapter is divided into two sections: a theoretical examination of fiber
reorientation supplemented by the work of Vincent and Agassant [86] and a
computer simulation of CMF filled flow in a diverging channel during pumping.
The intention of these studies was to examine the potential for fluid mechanical
reorientation of CMFs during pumping as well as examine core characteristics
of the process in an ideal environment. This simulation investigation was per-
formed prior to experiments to qualitatively examine the interplay of divergence
angle, die length, and die inlet/out ratio.
48
Jason R. Nixon
4.1 Theoretical Treatment
Vincent and Agassant [86] analyzed the experimentally examined the behavior
of a single fiber in a diverging flow and developed a fluid mechanical description
of the fiber behavior. In this section, the description of fiber motion will be
examined and discussed as the basis for fiber orientation in a die during pumping
from an extruder.
Dies are characterized by an inlet height of hin, an outlet height of hout, and a
die length of L. From these, the die divergence angle θ can calculated using
Equation 4.1. All dies considered are constructed to be straight (θ = 0◦) or
diverging, i.e. hout ≥ hin, or θ ≥ 0◦. A list of die geometries (inlet height,
outlet height, and length) can be found in Table 3.2 (Pg. 31).
θ = tan
(
hout − hin
2L
)
(4.1)
Figure 4.1 illustrates the die and relevant angles within.
Fibers are considered to be passive with respect to the flow. They are also as-
sumed to be ellipsoidal approximations of cylinders described by their by their
major axis lf (fiber length) and minor axis rf (fiber radius). Fibers are assumed
to have a circular cross section.
Vincent and Agassant provide a solution to the Stokes flow in a diverging chan-
nel. Using this solution, they calculated fiber angle φ with respect to fiber path
based on the initial fiber angle φ0 for a fiber traveling on the streamline defined
49
Jason R. Nixon
FIGURE 4.1: Illustration the die and relevant angles for the Vincent and Agas-
sant die flow.
by the angle β. In this solution, the shear rate γ˙ and extensional rate α˙ in an
unperturbed diverging channel flow are defined as:
γ˙ = −A (cos (2β) + sin (2θ))
ρ2
(4.2)
α˙ = −A sin (2β)
ρ2
(4.3)
A =
Q
h (sin (2θ)− 2θ cos (2θ)) (4.4)
where Q is the inlet volumetric flow rate and h is the channel height at the
fiber centroid. At large divergence angles β, both shear rate and extensional
rate demonstrate non-linear behavior. However, in the range of die angles con-
sidered in this thesis, between 0◦ to 5◦, by the small angle approximation, the
extensional rate is approximately linear over the channel arc. The normalized
shear rates, across a sample die angle is shwon in Figure 4.2.
50
Jason R. Nixon
FIGURE 4.2: Normalized shear and extensional rates across the profile of a
θ = 4.52◦ die operating at 4 lb/hr. Shear and extensional rates are respectively
normalized by their absolute maximum values. This plot demonstrates the
behavior of the rates across channel. Because of normalization, the intercept
point is not not represented. The critical die angle for this channel is 2.02◦.
The time rate of change of the fiber angle is defined as:
dφ
dt
= r (α˙ sin (2φ) + γ˙ cos (2φ)) + γ˙ (4.5)
where the geometric factor r is defined as:
r =
l2f − r2f
l2f + r
2
f
(4.6)
For the 100 µm CMFs used in this dissertation, r = 0.9902. The behavior
of a single fiber in the flow depends on the path angle β of the flow. When
β < β0, where β0 is some critical angle, the fiber is observed to asymptotically
converge to an equilibrium position that is approximately normal to the fiber
51
Jason R. Nixon
path orientation. When β > β0, the fiber will behave as if in shear and converge
asymptotically to an orientation nearly tangential to the fiber path. The critical
angle β0 in flow is defined as Equation 4.7.
cos (2β0) = r
2 cos (2θ) +
√
(1− r2) (1− r2 cos2 (2θ)) (4.7)
This result implies that in the die pumping process, even with optimal fiber
reorientation, near the edges of the sample, fibers will be mostly longitudinally
aligned while fibers near the center of the sample will be more aligned in the
through-thickness direction.
Three solutions to the diverging channel in the creeping flow regime are pre-
sented for various bounds of the fiber path angle: β = 0, β < β0, and β > β0.
β = 0 : φ = tan−1
(
Cρ−2r
)− τ
2
(4.8)
β < β0 : φ =
X + Y + (X − Y )Cρ−2Y/α˙
γ˙
(
1 + Cρρ−2Y/α˙
) − τ
2
(4.9)
β > β0 : φ = tan
−1
(
X
γ˙
− Y
′
γ˙
tan
(
Y ′ log (ρ)
α˙
+ C
))
− τ
2
(4.10)
where τ , X , Y , and Y ′ are defined by:
τ = cos−1
(
α˙√
α˙2 + γ˙2
)
or τ = sin−1
(
γ˙√
α˙2 + γ˙2
)
(4.11)
X = r
√
α˙2 + γ˙2 (4.12)
52
Jason R. Nixon
Y =
√
ρ2α˙2 + (r2 − 1) γ˙2 (4.13)
Y ′ =
√
(1− r2) γ˙2 − r2α˙ (4.14)
C is an integration constant based on the fiber orientation at the inlet of the
die channel. Using the fiber path angle β, the fiber path orientation φ can be
transformed into the fiber planar orientation by α = φ + β. Figure 4.3 demon-
strates the idealized orientation (again, these equations assume a passive fiber
which does not act upon the flow) across a vertical section at the die outlet, as
one would observe when performing optical microscopy (§3.3.3). This demon-
strates that there is indeed a core of highly aligned (with respect to the through
thickness direction) fibers, while fibers more towards the walls of the die tend to
be more aligned in the longitudinal direction. However, this is not necessarily
an explicitly negative consequence as the outer shell of the sample may help the
sample retain tensile properties while the core increases thermal conductivity.
53
Jason R. Nixon
FIGURE 4.3: Fiber angle α plotted against normalized fiber path angle β/θ.
The local fiber angle increase near the critical path angle is a geometric artifact
arising from the examination of a vertical section of the channel rather than an
arc. Fibers which are closer to the critical path experience a greater time in the
die, and are thus are slightly more orientated to their infinity time orientation
than fibers near β0/2. The generating conditions for these profiles are listed in
Table 4.1.
TABLE 4.1: Characteristic fiber orientation profile input parameters for pro-
files presented in Figure 4.3.
θ 1.41◦ 4.52◦
hin 1 mm 1 mm
hout 5 mm 3.5 mm
L 25.4 mm 50.8 mm
lf 100 µm 100 µm
df 7 µm 7 µm
β0 0.24◦ 2.02◦
The work of Vincent and Agassant [86] is a central framework that demonstrates
the effectiveness of fiber reorientation during a pumping process. However, by
these calculations, we see that zoned structure forms, where near the center of
54
Jason R. Nixon
the flow, fibers are oriented towards normal to the flow path, and near the die
walls, oriented closely to the flow path.
55
Jason R. Nixon
4.2 Simulation
Prior to experimental work fiber reorientation in convergent, straight, and di-
verging channels was simulated and qualitatively examined. The study of fiber
orientation in the die of a pumping device is critical to the fluid mechanical
manipulation of fiber orientation.
During pumping, as discussed in §4.1, a number of factors effect fiber orienta-
tion. These system inputs include flow rate, filler volume fraction filler geome-
try, the flow regime, i.e. shearing and extensional flows, the geometric specifi-
cation of the flow geometry. Similar results using injection molding have been
demonstrated by Gupta and Wang [100]. Furthermore, post pumping processes,
such as drawing, have also been shown to have an effect on fiber orientation
[101, 102].
Simulation of fiber orientation during pumping through a die was performed
using Autodesk’s Moldflow software, which uses the Fulgar-Tucker model to
approximate the fiber orientation using a high order tensor approximation. The
core of this simulation is the Fulgar-Tucker (FT) model, a tensor valued approx-
imation of the fiber orientations probability backed by laboratory experiment
[103, 104]. Results gathered from these simulations can then be used to make
predictions about final fiber orientation.
56
Jason R. Nixon
4.2.1 Method and Procedure
Initially, three dies were studied: a convergent die, a straight die, and a diver-
gent die. Two system parameter were varied: volumetric flow rate and volumet-
ric filler concentration. Convergent dies are nearly ubiquitously used in Fused
Deposition Modeling (FDM) printing processes, which is itself a small scale
extrusion pumping process, as well in screw extrusion processes. Straight dies
are also frequently used in extrusion processes. Through straight and diverging
dies, fibers become oriented nearly parallel to the sheet plane, parallel to the
extrusion orientation [105].
Three values of flow rate and three values of CMF concentration were tested, for
a total of nine conditions per die, for a total of twenty-seven conditions. Three
values of CMF concentration were chosen: 0 vol.%, 10 vol.%, and 20 vol.%.
For flow rate, the volumetric rates corresponding to lbh3, lbh3, and lbh5 were
used (using the material properties of PBT).
Material profiles (material and simulation parameters) in Moldflow are pre-
defined in the Moldflow material library. Simulations in Moldflow rely on both
experimentally determined material properties and simulation specific parame-
ters Therefore, a different material profile was chosen for each CMF concen-
tration. PBT material profiles were chosen at 0 vol.%, 10 vol.%, and 20 vol.%.
The grade of PBT used was selected to most close reflect the measured and
manufacturer specified properteis of the PBT used throughout the dissertation.
57
Jason R. Nixon
In each simulation, fiber orientation tensor value is tracked. The simulation so-
lution provides the value at each mesh node [103, 104] After simulation, the
fiber orientation tensor is interpolated between nodes and extracted as a graphic.
Because this parameter is a tensor field, individual fibers and local fiber prop-
erties cannot be tracked. Additionally, complex fiber interaction phenomenon
such as breakage or networking cannot be modeled using this technique.
4.2.2 Characteristic Convergent Die
Figure 4.4 shows a characteristic convergent die fiber orientation color plot at
20 vol.% and lbh5.
The qualitative results are coded such that: black indicates that a fiber is parallel
to the fiber path while white indicates that the fiber is perpendicular to the fiber
path As the grey scale color increase from black to white, fibers are orienting
away from the fiber path. In the simulation, the orientation ranges from zero
to one, where zero indicates that the fiber is perpendicular to its path, and one
corresponds to a parallel fiber with respect to path.
58
Jason R. Nixon
FIGURE 4.4: Characteristic converging die color map (at 20 vol.% and lbh5).
There are several ubiquitous features between all convergent die simulations.
First, fibers tend to be highly aligned with respect to path prior to and in the die.
This is resultant from 1) the shear flow through this channel and 2) from from
the decreasing die height and subsequent increase in speed of the fiber during
pumping. By the design of the simulation, fiber orientation results immediately
after the die are meaningless.
59
Jason R. Nixon
FIGURE 4.5: Convergent die conditions. Columns from left to right: lbh3,
lbh4, and lbh5. Rows from top to bottom: 10 vol.% and 20 vol.%.
With increasing CMF concentration, increasing fiber alignment is found with
decreasing flow rate. As the flow rate increases, a core of decreased alignment
forms in the center with higher relative alignment between the liquifer bound-
aries and the core of de-alignment. At flow rate increases, the region of lower
alignment extends further towards the wall. This behavior is occurs at all CMF
concentrations. Increasing CMF concentration leads to increased fiber align-
ment. This is becomes clear when comparing 10 vol.% and 20 vol.% at lbh5.
At higher CMF concentration, the core de-aligned core increases in size over
comparable flow rates.
60
Jason R. Nixon
4.2.3 Characteristic Straight Die
Figure 4.6 shows a characteristic straight die fiber orientation color plot at 20 vol.%
and lbh5.
FIGURE 4.6: Characteristic straight die color map (at 20 vol.% and lbh5).
At the dies inlet, fibers are highly aligned. Once the die, fibers tend to de-align
before the end of the die. At the die inlet, there is core of high fiber alignment.
Near the wall, fiber alignment is low. This result is unexpected, given that a shear
flow acts to align fibers with respect to path. However, this behavior is likely
explained by the relatively short length of the straight channel. Given a higher
channel length, it is expected that fibers would again align with path, resulting
in the characteristically aligned pattern that is see in literature and experiments
within this dissertation.
61
Jason R. Nixon
FIGURE 4.7: Straight die conditions. Columns from left to right: lbh3, lbh4,
and lbh5. Rows from top to bottom: 10 vol.% and 20 vol.%.
Controlling for flow rate, increasing CMF concentration correlates with increased
fiber alignment pre-die and further penetration of a high alignment core in the
die. CMF concentration also correlates to increasing fiber alignment pre-die and
in-die. There is little noticeable effect of flow rate at 10 vol.%. At 20 vol.%, in-
creasing flow rate leads to higher fiber alignment prior to, but little noticeable
change in the actual straight zone of, the die. Comparison between 10 vol.%
and 20 vol.% shows that the global fiber orientation pre-die is much greater in
the 20 vol.% than 10 vol.%. Additionally, at 20 vol.%, the vorticies present in
the corner as a result of the right angle produces much higher fiber alignment at
20 vol.% than 10 vol.%. It is also likely that the instantaneous transition from
large die height to the channel height leads to adverse conditions shortly after
fibers enter the die.
62
Jason R. Nixon
4.2.4 Characteristic Diverging Die
Figure 4.8 shows a characteristic diverging die fiber orientation color plot at
20 vol.% and lbh5.
FIGURE 4.8: Characteristic divergent die color map (at 20 vol.% and lbh5).
Prior to the die, fibers are shown to close align with respect to path. This is a
result of the high shear in this region and the many converging flow paths. Sec-
ond, immediately after entering the die, the fibers rapidly de-align with respect
to path.
63
Jason R. Nixon
FIGURE 4.9: Divergent die conditions. Columns from left to right: lbh3, lbh4,
and lbh5. Rows from top to bottom: 10 vol.% and 20 vol.%.
At 10 vol.% and 20 vol.%, increasing flow rate correlates to increasing pre-die
fiber alignment. At the outlet, a core of low alignment with higher alignment
near the boundary forms. With increasing flow rate, fiber alignment in the core
increases. , indicating that lower flow rates result in a decreased fiber align-
ment. In each condition, the placement, size, and intensity of the highly aligned
shell varies. This is a result of the interplay between extensional and shear flow
mechanisms present in the channels as discussed in §4.1.
4.2.5 Summary
Across all geometries, fiber orientation preceding the die does not significantly
effect the fiber orientation in the die. Immediately prior to the die channel, shear
rate increases, leading to an increase in fiber alignment.
64
Jason R. Nixon
In the convergent die, high fiber alignment (fiber is nearly parallel with the fiber
path) is observed throughout the die. Both increasing CMF concentration and
increasing flow rate were found to increase alignment in-die. For higher flow
rates, a banded structure was found across the die inlet, such that center align-
ment was slightly less aligned than near the die walls.
In the straight die, fibers were found to enter the die highly aligned, followed
by rapid de-alignment between the fiber and path. As with the convergent die,
a core of high alignment was observed in the center of the die. Increasing CMF
concentration and flow rate resulted in increased alignment and greater down-
channel penetration of high alignment into the die. Die channel length greatly
affects the rate and orientation of the final fiber orientation. However, from a
practical standpoint, the flow profile of the melt in a straight die would lead to
increased stress over the convergent die, and thus greater fiber-fiber interactions.
In aggregate, fibers in the the divergent die were found to be nearly perpendic-
ular to the flow path. As identified by Vincent and Agassant [86], in addition
to the extensional effects that reduce fiber alignment near the center of the die
the die, shear-like effects near the wall resulted in more aligned fibers. The use-
fulness of the diverging die lies in its ability to de-align fibers towards the die
outlet, resulting in fibers aligned towards the through-thickness direction of the
sheet rather than the axial direction that is currently found in CMF loaded die
flow.
65
Chapter 5
Experiments
This chapter is divided into three sections corresponding to a progression of ex-
periments examining multiscale composite properties. First, long CMF 6 mm
multiscale composite properties θ = 0◦ are presented and basic trends in multi-
scale property behavior with respect to CMF concentration and MWNT concen-
tration are discussed in §5.1. These results are representative of classic pumping
(i.e. fibers aligned strongly in the flow orientation). Second, in §5.2, short
CMF 100 µm multiscale composite properties θ = 0◦ and θ = 2.82◦ are pre-
sented and compared to long CMF properties. Basic trends between straight
and diverging die composite properties are discussed. Finally in §5.3, a para-
metric study across CMF concentration, MWNT concentration, flow rate, and
die angles is conducted. This data was analyzed using multiple regression anal-
ysis and included data from §5.2. Trends between independent parameters on
physical properties are discussed.
66
Jason R. Nixon
5.1 Long CMF Multiscale Study
(a) 10 wt.% CMF. (b) 15 wt.% CMF.
(c) 20 wt.% CMF. (d) 25 wt.% CMF.
(e) 30 wt.% CMF.
FIGURE 5.1: 6 mm CMF characteristic micrographs samples compounded at
0 wt.% MWNTs, θ = 0◦, 4 lb/hr, and 200 rpm. Fibers are indicated by bright
circular or ellipsoidal profiles against the darker matrix. Fiber orientation was
not found to be effected by MWNT concentration.
67
Jason R. Nixon
Micrographs in Figure 5.1 are characteristic of fiber orientation at different CMF
concentrations. Fibers are indicated as bright circular or ellipsoidal cross sec-
tions on the darker polymer matrix background. MWNT concentration was not
found to significantly effect observable microscale structure. Visual inspection
of these micrographs indicates that fibers are well-aligned with the axis of ex-
trusion (normal to the micrograph plane). Fiber orientation analysis indicates
that the fibers are aligned within 10◦ of the extrusion axis. Fiber orientation
was determined using the angle analysis tools discussed in §3.3.3. Sources of
variance in this analysis include micrograph resolution, sample flatness during
mounting, and small perturbations in flow during extrusion. At the resolution
given, a single pixel of resolution error can lead to a degree or more of error
in the fiber angle calculation. Visual inspection also indicates the onset fiber
exfoliation and premature fracture at CMF concentrations exceeding 25 wt.%
CMF. This is evidenced by the regular and circular fiber cross sections found
in Figure 5.1(c) as compared to the non-uniformed and ragged fiber cross sec-
tion in Figure 5.1(e). These ragged cross sections are likely a results of two
mechanisms. First, due to the high CMF aspect ratio (Ar = 600), high CMF
stiffness, and moderately aggressive screw geometry, it is very likely that CMFs
are fracturing during compounding. This theory is also demonstrate in observed
tensile properties later in this section. Fractures occurring at an oblique angle
with respect to the fiber axis plane will create non-circular cross sections. Dur-
ing fracture, it is likely that small fiber fragments are released and further broken
up, much as a spherical agglomerated filler is broken down into small particles
by dispersive mixing, leading to the small CMF elements found in high CMF
68
Jason R. Nixon
loading micrographs.
69
Jason R. Nixon
(a) Organized by MWNT concentration.
(b) Organized by CMF concentration.
FIGURE 5.2: 6 mm CMF mean tensile modulus percent increase for samples
compounded at θ = 0◦, 1.81 kg/hr, and 200 rpm. The tensile modulus of neat
PBT is 2.42 GPa. The maximum tensile modulus increase, 508% (14.66 GPa),
is observed at 25 wt.% CMF and 0 wt.% MWNT. Error bars represent one
standard deviation of the measured data.
70
Jason R. Nixon
Inspection of Figure 5.2(a) shows that tensile modulus generally increases lin-
early with respect to CMF concentration, with the exception that between 15 wt.%
and 20 wt.% CMF, there is a significant drop in stiffness before the linear trend
resumes. This is likely due to additional fiber damaged incurred during the pel-
litization and remelting of the 15% CMF/PBT batch. In general, the stiffest
samples are found using only CMF. The introduction of MWNTs appears to
dramatically reduce the overall stiffness of the composite by up to 100%. The
stiffest material possible occurs using 25 wt.% CMF, and is nearly 500% stiffer
than neat PBT. Purely CMF loaded composites also demonstrate a characteristic
lack of increase in tensile modulus from 25 wt.% to 30 wt.%. It is also important
to note that with a non-zero MWNT concentration, the lack of tensile modulus
increase from 25 wt.% to 30 wt.% CMF is not present in any case. In the case
of 0% MWNT, this is likely the second onset of process induced fiber damage,
the first of which occurs between 15 wt.% CMF and 20 wt.% CMF and which
was dodged by introducing the CMF/PBT batching process. In another study,
a second CMF/PBT batching process was performed 25 wt.% CMF to exam-
ine the potential of incorporating up to 40 wt.% CMF. The diminishing return
of tensile modulus increase was observed to cease, but no more increase was
gained either. It is theorized that at this level of loading, so much fiber damage
has been incurred due to the higher loading and two-run batching process that it
was not possible to exceed the 30 wt.% limit without the use of a larger TSE.
71
Jason R. Nixon
(a) Organized by MWNT concentration.
(b) Organized by CMF concentration.
FIGURE 5.3: 6 mm CMF mean ultimate tensile strength percent increase for
samples compounded using θ = 0◦ at 1.81 kg/hr and 200 rpm. The measured
ultimate tensile strength of neat PBT is 49.0 MPa. The maximum ultimate ten-
sile strength percent increase, 78% (87.2 MPa), is observed at 30 wt.% CMF
and 1.0 wt.% MWNT. Error bars represent one standard deviation of the mea-
sured data.
72
Jason R. Nixon
For ultimate tensile strength of long fiber composites shown in Figure 5.3, the
maximal improvement, controlling for MWNT concentration, is found at 30 wt.%
CMF. While not present in all MWNT concentration, linearly increasing trends
were observed at 0.0 wt.% MWNT (R2 = 0.912), 1.5 wt.% MWNT (R2 = 0.863),
and 2.0 wt.% MWNT (R2 = 0.960). In general, it appears that in the presence
of MWNTs, greater than 15 wt.% CMF is needed for the composite ultimate
tensile strength to exceed the ultimate tensile strength of neat PBT. The vari-
ance in measured ultimate tensile strength, as evidenced by the significant stan-
dard deviations observed, could lie in the testing specimen preparation or in the
composites themselves, in which locally non-favorable microstructures lead to
premature failure.
73
Jason R. Nixon
(a) Organized by MWNT concentration.
(b) Organized by CMF concentration.
FIGURE 5.4: 6 mm CMF mean thermal conductivity percent increase for sam-
ples compounded at θ = 0◦, 1.81 kg/hr, and 200 rpm. The measured ther-
mal conductivity of neat PBT is 0.18 W/mK. The maximum long CMF ther-
mal conductivity percent increase, 200% (0.54 W/mK) is observed at 25 wt.%
CMF, and 30 wt.% CMF and 2.0 wt.% MWNT. Error bars represent one stan-
dard deviation of the measured data.
74
Jason R. Nixon
For 0 wt.% MWNT, there is a linear trend from 0 wt.% CMF to 25 wt.% CMF
(R2 = 0.949), followed by a drop off at 30 wt.% CMF, consistent with the at-
trition limit. At loadings at or below 15 wt.% CMF, the inclusion of MWNTs
acts to increase the thermal conductivity at lower MWNT concentration (up to
1.0 wt.% MWNT) followed by a decrease again. At MWNT concentrations
above 1.5 wt.% MWNT, it was found the inclusion of MWNTs universally acted
to decrease the thermal conductivity of a composite with equivalent LCMF but
no MWNT loading.
This is thought to be a result of several possible mechanisms. First, the inclusion
of MWNTs into the polymer matrix acts to increase the apparent viscosity. This
effect combined with increased fiber-fiber interactions at higher loadings may
result in more fiber fracture during compounding, leading to shorter paths for
improved thermal conduction between thermal interface barrier present between
CMFs and the matrix material. Second, at higher MWNT loadings, MWNT
are likely agglomerating, leading to reductions in over thermal conductivity im-
provement. Third, at higher MWNT loadings, there are potentially more ther-
mal resistance barriers in the polymer matrix between the MWNTs and polymer
matrix [106]. Longitudinal tensile modulus and ultimate tensile strength are
universally enhanced by the presence of CMFs. In general, MWNTs appear
to reduce the tensile modulus and ultimate tensile strengths, except at 15 wt.%
CMF and 30 wt.% CMF, where 0.5 wt.% MWNT is found to improve the mod-
ulus and strength. These two CMF concentrations, 15 wt.% and 30 wt.% CMF
are extruder loading limits related to the screw geometry, screw dimensions, and
75
Jason R. Nixon
fibers. It is possible that the onset of CMF concentration induced fiber damage
and MWNT concentration are correlate to synergistic mechanical enhancement.
Transverse thermal conductivity is not enhanced significantly by the presence
of MWNTs, except again at 15 wt.% CMF at 0.5 wt.%, 1.0 wt.%, and 2.0 wt.%
MWNT at 30 wt.% CMF and 2 wt.% MWNT. Again, the highest improvement
is found at the loadings in which the most fiber damage occurs. Therefore,
it is possible that the inclusion of MWNTs may produce synergistic property
enhancement with shorter fibers over longer fibers.
Due to the extreme length of long CMFs (6 mm), short CMFs will be used in-
stead in subsequent sections. While a reduction in properties is expected due
to reduced fiber length (literature indicates that for both thermal and tensile im-
provement, longer fibers are preferred over short fibers), the shorter length scale
of fiber is needed due to geometric constrains in dies with non-zero divergence
angle. Furthermore, this may capitalize on the apparent benefit of shorter CMFs
and MWNT concentration observed in this section.
76
Jason R. Nixon
5.2 Short Fiber Diverging Die Study
In this section, the effect of two die angles, θ = 0◦ (A) and θ = 2.82◦ (E) was
examined across the range of CMF concentrations, 10 wt.%, 15 wt.%, 20 wt.%,
25 wt.%, and 30 wt.% and MWNT concentrations, 0 wt.% and 2 wt.%. Flow
rate, screw speed, and vacuum pressure were controlled at 1.81 kg/hr, 200 rpm,
and 500 mmHG. A total of new 20 conditions were studied in this section. New
short CMF results are compared against long CMF results in §5.1. Basic trends
comparing straight and diverging dies are discussed, as well as the relationship
between long CMF and short CMF properties.
New results are tabulated in Table A.2 (θ = 0◦) and Table A.5 (θ = 2.82◦) .
77
Jason R. Nixon
5.2.1 Long/Short CMF Comparison
This section compares short 100 µm CMF and long 6 mm CMF multiscale com-
posite property results to establish the relatively small reduction in properties
when reducing fiber length.
Analysis of micrographs for short CMF micrographs, which are characteristi-
cally represented in Figure 5.5 shows that, again, only a statistically insignifi-
cant portion of the fibers imaged are oriented out of the extrusion orientation.
Comparison shows between 0 wt.% MWNT and 2 wt.% MWNT again shows
no detectable difference. At 25 wt.% and more intensely in 30 wt.%, fiber dam-
age is clear, matching the trend observed in long CMF micrographs shown in
Figure 5.1.
78
Jason R. Nixon
(a) 10 wt.% CMF. (b) 15 wt.% CMF.
(c) 20 wt.% CMF. (d) 25 wt.% CMF.
(e) 30 wt.% CMF.
FIGURE 5.5: Short CMF characteristic micrographs (θ = 0◦).
79
Jason R. Nixon
FIGURE 5.6: Comparison of 6 mm CMF and 100 µm CMF tensile modulus
percent increase, compounded at θ = 0◦ at 1.81 kg/hr and 200 rpm. The mea-
sured tensile modulus of neat PBT is 2.42 GPa. The maximum short CMF
tensile modulus increase, 420% (12.58 GPa), is observed at 25 wt.% CMF and
2 wt.% MWNT. Error bars represent one standard deviation of the measured
data.
Using short CMFs, for both 0 wt.% and 2 wt.% MWNT concentrations, stiffness
linearly increases with respect to CMF concentration (R2 = 0.908 and R2 = 0.943
respectively) from 0 wt.% to 25 wt.% CMF, From 25 wt.% to 30 wt.% CMF, and
an appreciable decrease in properties in tensile modulus increase occurs. Again,
this is likely related to extruder geometry and filler geometry limits that occur
between 25 wt.% and 30 wt.%. The presence of short CMFs universally in-
creases the tensile modulus of the composites. Comparison between long CMF
and short CMF tensile modulus, controlling for MWNT concentration, shows
that at 0 wt.% MWNTs, short CMF tensile moduli are approximately 30% lower
than long CMF moduli, and at 2 wt.% SCMF moduli are approximately 45%
80
Jason R. Nixon
greater long CMF tensile moduli. By using short CMF, MWNTs increase ten-
sile modulus rather than decreasing it.
FIGURE 5.7: Comparison of 6 mm CMF and 100 µm CMF ultimate tensile
strength percent increase, compounded at θ = 0◦ at 1.81 kg/hr and 200 rpm.
The measured ultimate tensile strength of neat PBT is σu = 49 MPa. The
maximum short CMF ultimate tensile strength increase, 50% (75.6 MPa),
is observed at 25 wt.% CMF and 0 wt.% MWNT. Error bars represent one
standard deviation of the measured data.
The presence of MWNTs universally reduces the ultimate tensile strength of
the composite. Linear trend is observed is observed between CMF concentra-
tion and ultimate tensile strength, although this trend is not statistically signif-
icant. At 0 wt.% MWNT and 2 wt.% MWNT concentrations, comparison be-
tween short CMF and long CMF conditions shows that ultimate tensile strength
is comparable. 25 wt.% MWNT remains an exception to this trend. It is possible
that this variation is related to processing variance, or potentially to the onset of
fiber damage due to extruder loading with respect to fiber size.
81
Jason R. Nixon
FIGURE 5.8: Comparison of 6 mm CMF and 100 µm CMF thermal conduc-
tivity percent increase, compounded at θ = 0◦ at 1.81 kg/hr and 200 rpm. The
measured thermal conductivity of neat PBT is 0.180 W/mK. The maximum
short CMF thermal conductivity increase, 148% (0.466 W/mK), is observed at
25 wt.% CMF and 0 wt.% MWNT. Error bars represent one standard deviation
of the measured data.
Figure 5.8 shows that the thermal conductivity of both 0 wt.% and 2 wt.% sam-
ples have a relatively linear increase in thermal conductivity from 0 wt.% to
25 wt.%: (R2 = 0.927) and (R2 = 0.959) respectively, followed by a decrease
from 25 wt.% to 30 wt.%. The greatest increase in thermal conductivity is found
at 25 wt.%: 94% for 0 wt.% and 79% for 2 wt.%. For any SCMF concentration,
thermal conductivity was found to be lower with the presence of nanotubes than
without.
Comparison of thermal conductivity between short CMF and long CMF con-
ditions, controlling for MWNT concentration, shows that trend wise that at
10 wt.%, thermal conductivity’s are not different, but from 15 wt.% to 30 wt.%,
82
Jason R. Nixon
PBT-SCMF samples posses greater conductivity than long CMF samples. The
difference between SCMF and LCMF increases with increasing CMF concen-
tration. In general, samples with MWNTs tend to under-perform samples with
not MWNT concentration.
For short CMF and long CMF composites at 0 wt.% MWNT concentration, it
has been shown, and is theoretically consistent, that the tensile modulus and
strengths are reduced in short CMF composites when compared to long CMF
conditions [28, 107]. Structural reinforcement in highly aligned fibrous fillers
requires long load-carrying paths for reinforcement (assuming high quality fiber
surface finish, sufficient polymer-fiber adhesion, equal distribution of load within
the fiber, ideal fiber morphology, etc.). Short paths results in more loading being
carried in the matrix as well as more fiber-matrix-fiber load transitions. Further-
more, stress imbalance at the fiber tips, which is normally diminished over long
fiber lengths, is more prominent in short CMF conditions. as well as stress im-
balance near the fiber tips. Over longer lengths, this imbalance diminishes over
the length of the fiber. For shorter fibers, this imbalance can play significant
effects in the reinforcement of the composites. Similarly, for thermal properties,
longer fibers reduces the number of polymer-fiber interface interference’s that
must be overcome, leading to improved thermal conduction. However, the ef-
fect of CMF length in the presence of MWNTs has not been previously studied.
It is interesting that MWNT reinforcement actual increases stiffness when com-
paring short CMF to long CMF, and helps to reduce the difference in ultimate
83
Jason R. Nixon
tensile strength. However, it should also be noted that there is a significant re-
duction in ultimate tensile strength at 2 wt.% MWNT across all CMF loadings.
84
Jason R. Nixon
5.2.2 Straight/Divergent Die Comparison
(a) 10 wt.% CMF. (b) 15 wt.% CMF.
(c) 20 wt.% CMF. (d) 25 wt.% CMF.
(e) 30 wt.% CMF.
FIGURE 5.9: Short CMF characteristic micrographs (θ = 2.82◦).
In all micrographs, fiber reorientation from the extrusion orientation to some
oblique alignment is evidenced by the ellipsoidal cross section of the fiber faces.
While some property increase depreciation when switching from long CMFs to
85
Jason R. Nixon
short CMFs were seen in §5.2.1, the move from short to long CMFs was neces-
sary in order to maximize the reorientability of CMFs, which was limited geo-
metrically by CMF length and die height. However, as will be discussed in more
detail later, these short CMF orientation demonstrates a banded structure in the
sample, such, when examining the transverse cross section, the bottom third and
top third of fibers tended towards a flow axis alignment while the middle third of
fibers tended towards an oblique orientation. Furthermore, a source of variance
which could not be accounted for were small amounts of drawing during sam-
ple collection which could effect the short fibers more dramatically than long
fibers. Again, no apparent difference was observed between 0 wt.% MWNT
and 2 wt.% MWNT concentrations. From these micrographs, it appears that the
number of fibers oriented out of plane increases from 10 wt.% to 25 wt.% CMF.
However, at 30 wt.% CMF, the number of reoriented fibers appears to decrease.
This could be indicative of the onset of an interaction mechanism preventing
fibers from freely reorienting.
86
Jason R. Nixon
FIGURE 5.10: Comparison of tensile modulus percent increase at θ = 0◦ and
θ = 2.82◦, compounded at 1.81 kg/hr and 200 rpm using 100 µm CMFs. Error
bars represent one standard deviation of the measured data.
Tensile modulus at θ = 2.82◦, as graphed in Figure 5.10 with short CMF θ = 0◦,
controlling for MWNT concentration, is approximately linear from 0 wt.% to
30 wt.% CMF (R2 = 0.926 at 0 wt.% MWNTs and R2 = 0.797 at 2 wt.% MWNTs).
Across the CMF range, there is no statistically significant difference between
tensile modulus with 0 wt.% MWNTs and 2 wt.% MWNTs. The maximum in-
crease in tensile modulus was observed at 30 wt.% CMF of 410%. Interestingly,
no loading limit between 25 wt.% and 30 wt.% CMF, as seen in §5.1 and §5.2.1,
was observed for θ = 2.82◦ conditions. At concentrations at and below 20 wt.%,
there is a small but statistically significant difference between the tensile mod-
ulus θ = 0◦ and θ = 2.82◦ conditions, without or with MWNTs. From 10 wt.%
to 25 wt.% CMF, θ = 0◦ conditions still tend to have greater tensile modulus
87
Jason R. Nixon
than θ = 2.82◦ conditions. This result is consistent with the theory that fibers
are being reoriented away from the extrusion axis (which is parallel to the axis
of tensile loading), and that fibers which are oriented off the loading axis con-
tribute less to the measured tensile modulus. At 30 wt.%, once the loading limit
is reached, θ = 2.82◦ conditions dramatically out perform θ = 0◦ conditions,
and nearly reach the maximum tensile modulus properties measured for θ = 0◦
conditions at 25 wt.% CMF.
FIGURE 5.11: Comparison of ultimate tensile strength percent increase at
θ = 0◦ and θ = 2.82◦, compounded at 1.81 kg/hr and 200 rpm using 100 µm
CMFs. Error bars represent one standard deviation of the measured data.
The ultimate tensile strength of θ = 2.82◦, graphed against equivalent θ = 0◦
conditions, is presented in Figure 5.11. At θ = 2.82◦, ultimate tensile strength
is shown to follow an linear trend from across CMF concentration for 0 wt.%
MWNT. Ultimate tensile strength does not vary significantly across CMF con-
centration for 2 wt.% MWNT. At 0 wt.% MWNT, ultimate tensile strength is
88
Jason R. Nixon
adversely affected the diverging die at low CMF concentrations, but converges
linearly (R2 = 0.959) to θ = 0◦ properties at higher CMF concentrations. For
2 wt.% MWNT conditions, little improvement in ultimate tensile strength was
observed for any CMF loading. This poor performance is attributed to both CMF
reorientation and the adverse effect of MWNTs on polymer matrix ultimate
tensile strength. Interestingly, the highest ultimate tensile strength occurs at
30 wt.% CMF for θ = 2.82◦, performing 30 wt.% better than 25 wt.% CMF for
θ = 0◦. Again, no loading limit is observed for ultimate tensile strength between
25 wt.% and 30 wt.% CMF. It is worth nothing that the degree of fiber reorien-
tation may not be consistent across specimens, thus the variation in θ = 2.82◦
conditions may in part be due to this variations in pumping and collection.
FIGURE 5.12: Comparison of thermal conductivity percent increase at θ = 0◦
and θ = 2.82◦, compounded at 1.81 kg/hr and 200 rpm using 100 µm CMFs.
Error bars represent one standard deviation of the measured data.
Comparison between 0 wt.% and 2 wt.% MWNT shows that from 10 wt.% to
89
Jason R. Nixon
15 wt.% CMF, thermal conductivity is approximately equivalent between condi-
tions. However, beyond 15 wt.% CMF, thermal conductivity of 0 wt.% MWNT
thermal conductivity drops significantly while the thermal conductivity of 2 wt.%
MWNT conditions continues to rise linearly (R2 = 0.945). Unlike θ = 0◦ con-
ditions,the presence of MWCNTs acts to improve thermal conductivity. In both
MWCNT loading conditions, no loading limit is found between 25 wt.% and
30 wt.%. The largest increase in thermal conductivity of 121% is found at
30 wt.% and 2 wt.%. This serves to indicate that MWNT concentration is en-
hancing thermal conductivity by, in a rough analogue to CMF concentration,
MWNT reorientation.
Comparison of θ = 0◦ and θ = 2.82◦ conditions indicates that tensile modulus
is marginally diminished with increasing die angle. Ultimate tensile strength
demonstrates different trends in the absence of presence of MWNTs. With
0 wt.% MWNT, ultimate tensile is decreased with increasing die angle at lower
CMF concentrations, but come to near equality at higher CMF concentrators. At
2 wt.% MWNTs, ultimate tensile strength remains universally low and does not
follow a clear trend. At 0 wt.% MWNT, thermal conductivity demonstrates a de-
creasing trend with increasing CMF concentration, and demonstrates an increas-
ing trend with respect to CMF concentration at 2 wt.% MWNT. These trends in-
dicate, and are verified by optical microscopy, that reorientation of CMFs acts to
marginally decrease longitudinal tensile properties while increasing transverses
thermal properties. This prompts a further study into the effects of flow rate and
a further investigation of die angle on the properties of reoriented multiscale
90
Jason R. Nixon
composites, which is performed in the next section.
91
Jason R. Nixon
5.3 Parametric Study
A parametric study was conducted using three new die geometries across a range
of flow rates, CMF concentrations, and MWNT concentrations. Statistical anal-
ysis was performed, including both new results as well as results from §5.2.
This analysis generated statistical predictive models and highlighted significant
trends between independent parameters and measured properties. A description
of the linear regression analysis methodology is in §3.3.4.
Three new die angles are used: θ = 1.41◦ (B), θ = 2.26◦ (D), and θ = 4.52◦
(F). Results for θ = 0◦ (A) and θ = 2.82◦ (E) are included in statistical anal-
ysis. Again, five CMF concentrations, 10 wt.%, 15 wt.%, 20 wt.%, 25 wt.%,
30 wt.%. and two MWNT concentrations, 0 wt.% and 2 wt.%, were used. Three
flow rates were used, 1.36 kg/hr, 1.81 kg/hr, and 2.26 kg/hr. This new paramet-
ric axis was introduced to examine the effect of varying shear rate on measured
properties. Previously, results were obtained only using 1.81 kg/hr. Excluding
previous results, this introduces 90 new conditions, for a total of 110 conditions
including previous results. Screw speed and vacuum pressure were controlled
at 200 rpm and 25 inHG. New results are tabulated in Table A.3 (θ = 1.41◦),
Table A.4 (θ = 2.26◦), and Table A.6 (θ = 4.52◦).
5.3.1 Effect on Fiber Orientation
Qualitative analysis of did not yield significant insight into the relationship be-
tween CMF concentration, MWNT concentration, flow rate, and die angle or
92
Jason R. Nixon
any obvious interacting effects. Main effects, as well as individual interactions
were examined using a multiple linear regression model. All interaction effects
with the exception of CMF concentration with MWNT concentration VµVn were
found to be non-significant. Furthermore, a systematic study conducted includ-
ing and not including flow rate indicated that flow rate plays no significant role
in fiber orientation. The remaining multiple linear regression model is shown in
Equation 5.1, and the coefficients and P -values of these parameters is tabulated
in Table 5.1.
αˆ (Vµ, Vn, θ) = β0 + β1Vµ + β2Vn + β3θ + β4VµVn (5.1)
TABLE 5.1: Fiber orientation regression model parameters.
Effect Coefficient P-Value
Intercept 54.30 0.0000
Vµ 4.93E−5 0.9899
Vn -0.8300 0.1573
θ 0.7334 0.0000
VµVn 0.0671 0.0165
The main effect of die angle θ and the interaction between CMF concentration
and MWNT concentration were the only statistically significant effects identi-
fied. Both CMF and MWNT concentration were found to be conditional upon
the interaction effect. The adjusted correlation coefficient of this data was be
R2 = 0.3222. This model is based on the average median fiber distribution of
multiple images per condition, so additional power could be gained from in-
cluding the median value of individual images. However, this introduces non-
uniformity in the median variance at lower CMF concentrations because of the
93
Jason R. Nixon
relative sparsity of fibers per image when compared to the high CMF concen-
trations, where fibers are sufficiently densely packed to allow for more accurate
measurement within a single image. Overall, the adjusted regression coefficient
R2 = 0.3222 indicates that the inferential model does not explain much of the
fiber orientation variance. While the source of variance could lie in physical phe-
nomenon, it more likely lies in the measurement of fiber analysis. The analysis
of a two-dimensional micrograph does not yield significant information about
the three-dimensional structure of a characteristic space.
5.3.2 Tensile Modulus
One statistically significant two-way interaction effect, MWNT concentration
on flow rate (P = 0.0002), and one significant three way interaction effect, the
effect of MWNT concentration on the CMF concentration and flow rate in-
teraction (P = 0.0047), were found with an adjusted correlation coefficient of
R2 = 0.670. The regression model is defined in Equation 5.2 and Table 5.2.
Eˆ (Vµ, Vn, Q, θ) =β0 + β1Vµ + β2Vn + β3Q+ β4θ + β5VµVn
+ β6Vµθ + β7Vnθ + β8VnQ+ β9VµVnθ
(5.2)
94
Jason R. Nixon
TABLE 5.2: Tensile modulus regression model parameters.
Effect Coefficients P-value
Intercept -0.3231 0.5463
Vµ 0.1118 0.0000
Vn 1.5367 0.0000
Q 0.1190 0.1939
θ 0.3472 0.0130
VµVn -0.0520 0.0001
Vµθ -0.0150 0.0042
Vnθ -0.2842 0.0042
VnQ -0.2452 0.0002
VµVnθ 0.0132 0.0047
FIGURE 5.13: Predicted tensile modulus (line) using Equation 5.2 plot-
ted against observed values (markers) demonstrating the two-way interac-
tion between MWNT concentration and flow rate. Flow rate is controlled
(1.81 kg/hr).
The effect of MWNT concentration with respect to flow rate, shown in Fig-
ure 5.13, on tensile modulus is complex. At 0 wt.% MWNT concentration, in-
creasing flow rate acts to marginally increase composite stiffness. This appears
to indicate that while the fibers are being reoriented out of plane with respect to
95
Jason R. Nixon
the load bearing direction, the effect is on stiffness is marginal. However in the
presence of MWNTs, fibers are reoriented dramatically out of plane because of
the increased shear rate from the presence of MWNTs, it appears that the fibers
are oriented more out of plane, leading to reduced stiffness.
At 0 wt.% MWNTs, increasing die angle at low CMF concentrations (Vµ ≤ 20 wt.%)
leads to an increase in tensile modulus with respect to die angle. At higher CMF
concentration (Vµ ≥ 25 wt.%), increasing die angle leads to a decrease in ten-
sile modulus. At all CMF concentrations , increasing CMF concentration leads
to a greater tensile modulus at θ = 0◦. By visual inspection, while these trends
are apparent, observed data is still very loosely distributed about the predicted
trend. At 2 wt.% MWNT, the mean stiffness at θ = 0◦ is nearly 100% lower than
with 0 wt.% MWNT. At 2 wt.% MWNT, CMF conditions which are increasing
at 0 wt.% MWNT are now decreasing. Physically, this could be mechanistically
attributed to, in the case of 2 wt.% MWNTs, the effect of CMF concentration
overcomes the effect of CMF orientation (which is proportional to die angle),
while at 0 wt.% MWNTs, the effect of CMFs concentration is overcome by the
effect of CMF orientation.
96
Jason R. Nixon
(a) MWNT Concentration: 0 wt.%.
(b) MWNT Concentration: 2 wt.%.
FIGURE 5.14: Predicted tensile modulus (line) using Equation 5.2 plotted
against observed values (markers) demonstrating the three-way interaction be-
tween CMF concentration, MWNT concentration, and die angle. Flow rate is
controlled (1.81 kg/hr).
97
Jason R. Nixon
5.3.3 Ultimate Tensile Strength
One statistically significant two-way interaction effect between MWNT concen-
tration and flow rate P = 0.0217, and one main effect of die angle P = 0.0000
were found for ultimate tensile strength. CMF concentration was not found
to be statistically significant, but was found to be trending towards significant
P = 0.0921. The regression model for ultimate tensile strength is defined in
Equation 5.3 and Table 5.3. Note that the value of the intercept, i.e. the neat
ultimate tensile strength percent increase, is approximately zero. This model
has an adjusted correlation coefficient of R2 = 0.8632, indicating that a signifi-
cant amount of measured ultimate tensile strength variance is explained by the
regression model. Remaining variance could be a result of processing variance
and sample preparation before testing.
σˆu (Vµ, Vn, Q, θ) = β0 + β1Vµ + β2Vn + β3Q+ β4θ + β5VnQ (5.3)
TABLE 5.3: Ultimate tensile strength regression model parameters.
Effect Coefficients P-value
Intercept -0.0052 0.2241
Vµ 0.0105 0.0921
Vn -0.2151 0.4121
Q -0.0609 0.0113
θ -0.0807 0.0000
QVn -0.0072 0.0217
The only statistically main effect, die angle, is plotted in Figure 5.15. Physically,
increasing die angle θ leads to increased fiber angle ξ within the central third of
the extruded sample, which is the segment that thermal and tensile testing was
98
Jason R. Nixon
performed on. As fiber angle increases, these obliquely aligned contribute less
to the ultimate tensile strength of the composite. This is true in the absence
and presence of MWNTs. However, the presence of MWNTs acts to weaken
the polymer matrix. This is evidenced by the relatively bi-modal distribution of
ultimate tensile strength based on the presence or absence of MWNTs, which is
shown in Figure 5.16.
FIGURE 5.15: Predicted ultimate tensile strength (line) using Equation 5.3
plotted against observed values (markers) demonstrating the main effect of
CMF concentration. CMF concentration (20 wt.%) and flow rate (1.81 kg/hr)
are controlled. Note the bi-modal effect of MWNT concentration on ultimate
tensile strength.
The result of MWNT concentration on flow rate is shown in Figure 5.16. In
the absence of MWNTs, increasing flow rate leads to up to a 25% increase in
ultimate strength at 2.27 kg/hr from 1.36 kg/hr. However, 2 wt.% MWNTs, the
origin of the predicted ultimate tensile strength reduced by approximately 40%
from 0 wt.% MWNT as well as demonstrates a decreasing trend with respect
99
Jason R. Nixon
to increasing flow rate rather than an increasing trend as is for 0 wt.% MWNT.
This is a likely indication, fibers are taken more out of plane with increasing
flow rate in at 2 wt.% MWNT. This result follows closely with the results shown
in Figure 5.13 for tensile modulus. This is highly evidenced by the nearly bi-
modal distribution of measured ultimate strength in Figure 5.16. This a result of
the weakening of the polymer matrix by the inclusion of MWNTs.
FIGURE 5.16: Predicted ultimate tensile strength (line) using Equation 5.3
plotted against observed values (markers) demonstrating the two way interac-
tion effect between MWNT concentration and flow rate. CMF concentration
(20 wt.%) is controlled.
5.3.4 Thermal Conductivity
One statistically significant main effect, CMF concentration (P = 0.0000), and
one three way interaction effect, the effect of MWNT concentration on the in-
teraction between flow rate and die angle (P = 0.0120), were found with an
100
Jason R. Nixon
adjusted correlation coefficient of R2 = 0.834. The remaining three indepen-
dent independent parameters and three interaction effects were marginal. The
regression model, including statistically significant effects and marginal effects,
is defined in Equation 5.4.
kˆ (Vµ, Vn, Q, θ) =β0 + β1Vµ + β2Vn + β3Q+ β4θ + β5VnQ
+ β6Vnθ + β7Qθ + β8VnQθ
(5.4)
TABLE 5.4: Thermal conductivity regression model parameters.
Effect Coefficient P-value
Intercept 0.7800 0.0078
Vµ 0.0388 0.0000
Vf -0.3761 0.0632
Q -0.0785 0.2635
θ -0.3710 0.0002
VnQ 0.0845 0.0899
Vnθ 0.2673 0.0001
Qθ 0.0829 0.0006
VnQθ -0.0421 0.0120
101
Jason R. Nixon
FIGURE 5.17: Predicted thermal conductivity (line) using Equation 5.4 plotted
against observed values (markers) demonstrating the interaction between CMF
concentration and MWNT concentration. Flow rate (1.81 kg/hr) and die angle
(2.25◦) are controlled.
Physically, the action of CMF concentration is clear. As CMF concentration is
increased, there are more fibers available to transfer heat. However, while not
indicated as statistically significant, there is a clear effect of MWNT concentra-
tion on thermal conductivity. At 2 wt.% MWNTs, there is up to an 50% increase
in thermal conductivity while controlling for all other parameters. This indicates
that either the CMFs have been reoriented to a more favorable orientation, or that
the MWNTs, or morphological changes brought on by the presence of MWNTs,
are now carrying a portion of the heat load. While not examined, it is likely that
MWNTs orientation is also effected during flow, and by the equations given by
Vincent and Agassant [86], MWNTs should be much more effected than the
102
Jason R. Nixon
CMFs due to aspect ratio. It is likely that this is the source of thermal conduc-
tivity between 0 wt.% MWNT and 2 wt.% MWNT concentration.
103
Jason R. Nixon
(a) MWNT Concentration: 0 wt.%.
(b) MWNT Concentration: 2 wt.%.
FIGURE 5.18: Predicted thermal conductivity (line), using Equation 5.4, plot-
ted against observed values (markers) demonstrating the three-way interaction
effect of MWNT concentration, flow rate, and die angle. CMF concentration
(20 wt.%) is controlled. Comparison of Figure 5.18(b) (0 wt.% MWNT) and
Figure 5.18(a) (2 wt.% MWNT) indicate that MWNT concentration changes
the interaction between flow rate and die angle.
104
Jason R. Nixon
The differing interaction between flow rate and die angle as a function of MWNT
concentration shown in Figure 5.18 could be the result of two potential mech-
anisms. In the absence of MWNTs, increasing flow rate improves thermal
conductivity increase, such that increasing die angle at 2.27 kg/hr increases
thermal conductivity, but increasing die angle decreases thermal conductivity
at 1.36 kg/hr and 1.81 kg/hr. However, in the presence of MWNTs, all three
flow rates demonstrate increasing thermal conductivity with increasing die an-
gle. First, it is possible that MWNTs themselves are carrying a portion of the
thermal load. Second, it is possible that the MWNTs influence the matrix rheol-
ogy and therefore the flow of CMFs in the die as well as assisting to damp out
secondary flows which act to reorient fibers during collection. In the absence of
MWNTs, it is likely that the increasing flow rate, while decreasing the die resi-
dence time, (see §3.2.1.1, Pg. 31), increases the magnitude of velocity gradients
acting on the fibers.
5.3.5 Rheological Argument
The effect of MWNT concentration on thermal conductivity, or more loosely to
tensile modulus or ultimate tensile strength, can be attributed to several mecha-
nisms. First, the presence of MWNT concentration increases the apparent vis-
cosity of the melt. Second, by this increased viscosity, fiber damage during
processing is more likely, which in turn results in shorter fibers which may be
easier to reorient, or alternatively more difficult to orient from the random state
in the die zone. However, this would be balanced by reduced carrying capacity
105
Jason R. Nixon
of the fibers due to lower fiber lengths. Third, CNTs alter the matrix morphol-
ogy, leading to increased conductivity through the matrix.
A number of authors have conducted rheological and dynamic mechanical prop-
erties of nanocomposites. Valendtino et al. [108] examined viscosity, loss mod-
ulus, and the loss tangent as a function of MWNT concentration in LDPE and
HDPE up to 5 wt.% MWNTs. They found that the viscosity of neat HDPE
was on the order of 5 · 103 Pa·s at low frequencies and demonstrated shear thin-
ning behavior starting at 10 rad/s. At 0.5 wt.% and 1.0 wt.% MWNTs, little
difference in viscosity was observed except for a slight increase. However, at
2.5 wt.% MWNTs, a significant increase in viscosity, almost one and a half or-
ders of magnitude at low frequencies, as well as a change in the shear thinning
behavior over the full range of frequencies was observed. At frequencies above
100 rad/s, the viscosity’s of neat and loaded melts were observed to converge.
Yet more increase in viscosity and change in shear thinning behavior were ob-
served at 5.0 wt.%. For reference, these composites were prepared by micro-
twin-screw-extrusion. Potschke et al. [109] also observed similar increased in
viscosity as well as the MWCNT dependence of viscosity increase. Ahmad et al.
[110] investigated the effect of surface treatment on viscosity increase and found
that pristine CNTs demonstrated the greatest viscosity, which treated CNTs still
demonstrated viscosity increase over neat polymer, but not as much as pristine
CNTs.
Valendtino et al. and Potschke et al. [111] theorized that, because of the ap-
proximately comparable length scale between polymer chains and MWNTs, the
106
Jason R. Nixon
network of polymer chains interacts with that of the MWNT network (or par-
tial networks), leading to increased viscosity. Potschke et al. also observed an
onset in dramatically increased rheological properties at some certain threshold
MWNT concentration, which was identified as the ’percolation threshold con-
centration,’ at which extensive MWNT networks formed. This relationship was
found to be strongly related to temperature, as Potschke et al. observed the onset
of percolation at 5.0 wt.% at 170◦C and 0.5 wt.% at 280◦C, which they theorized
related to the network density as a function of temperature during compound-
ing. McNally et al. [112] explored similar structures in PE and found that the
percolation onset was much higher, at 7.5 wt.%. McNally et al. identified three
mechanisms for this increase: (1) PE coats the MWNTs, this reducing the ef-
fectiveness of electrical transmission; (2) twin screw extrusion may improve the
coating of MWNTs over other preparation tools; and (3) the geometry of the ex-
truder die induces alignment of the MWNTs during extrusion, thus reducing the
number of contact points. Extending this rationale, it is possible that the flow in-
duced orientation produces an anisotropically percolated networks. This could
support the thermal conductivity results in §5.3.6 when comparing straight die
to increasing divergences with and without MWNTs.
As stated previously, the effect of MWNT concentration on viscosity could lead
to several effects during pumping through a die. First, because the viscosity is
increased and the shear thinning profile is changed, the apparent viscosity in
the melt is likely to be increased. This would could lead to a reduction in the
reorientability of the fibers during extrusion. However, the theory presented by
107
Jason R. Nixon
Vincent and Agassant would seem to imply that this is not the case. From obser-
vation during extrusion, it is clear that the melt is more viscous during extrusion,
and therefore more resistant to minute reorientation’s induced by pulling on the
extrudate after pumping through the die. By this mechanism, reorientation that
occurred during extrusion would be less likely to be undone during collection
than extrudate without MWNTs. However, by the same mechanism, the fibers
would likely be more difficult to reorient during extrusion.
Finally, during compounding, the amount of stress encountered in the extruder is
related to the shear rate and the viscosity of the melt. By changing the apparent
viscosity of the melt by the inclusion of MWNTs (given that during compound-
ing any flow induced alignment would be constantly agitated by the mixing sec-
tion), it is possible that the fibers fracture during mixing, leading to a reduced
aspect ratio.
5.3.6 Summary of Statistical Analysis
Multiple regression analysis was conducted on measured fiber orientation ξˆ,
mean tensile modulus Eˆ, mean ultimate tensile strength σˆu, and mean thermal
conductivity Kˆe of composite samples produced using die angles of θ = 0◦ (A),
θ = 1.21◦ (B), θ = 2.26◦ (D), θ = 2.82◦ (E), and θ = 4.52◦ (F). Four indepen-
dent input variables were used, CMF concentration Vµ, MWNT concentration
Vn, flow rate Q, and die angle θ. In §5.3, regression models were generated,
108
Jason R. Nixon
and statistically significant effects and interactions were discussed. In this sec-
tion, the statistically significant main and interactions effects for tensile modu-
lus, Equation 5.5, ultimate tensile strength, Equation 5.6, thermal conductivity,
Equation 5.7, and are summarized.
Eˆ = β8VnQ+ β9VµVnθ + Eˆmarginal (5.5)
σˆu = β4θ + β5VnQ+ σˆu,marginal (5.6)
kˆ = β1Vµ + β8VnQθ + kˆmarginal (5.7)
Two interactions were observed for tensile modulus. Without MWNTs, increas-
ing flow rate has little effect on stiffness, with a mean tensile modulus increase
of approximately 250% controlling for all other parameters. However, with
MWNTs, controlling for all parameters, stiffness is reduced from 50% up to
100% as compared to no MWNTs and demonstrates a decreasing trend with
increasing flow rate. This is indicative of increase fiber reorientation in the pres-
ence of MWNTs with increasing flow rate. The second interaction, the relation-
ship of MWNT concentration on the interaction between die angle and CMF
concentration is complex. In the absence of MWNTs, increasing die angle at
low CMF concentrations (Vµ ≤ 20 wt.%) leads to an increase in tensile modulus
with respect to die angle, while the inverse is true at higher CMF concentrations.
At 2 wt.% MWNT, the inverse of 0 wt.% MWNT trends are true. This behavior
is likely due to the effect of fiber-fiber interaction on reorientation as die angle
increases.
109
Jason R. Nixon
Increasing die angle leads to an decreased ultimate tensile strength. This is con-
sistent with fibers being reoriented more out of plane as fiber angle increases
due to a greater die angle, leading to less CMFs contributing to the strength of
the composite. MWNTs significantly reduce the overall strength of the compos-
ite. At 0 wt.% MWNT concentration, increasing flow rate marginally increases
ultimate tensile strength. At 2 wt.% MWNT, increasing flow rate decreases ulti-
mate tensile strength. This is again consisted with the theory, in the presence of
MWNTs, increasing flow rate takes more fibers out of plane, leading to reduced
ultimate tensile strength.
For thermal conductivity, two significant effects were observed. First, TC in-
creases with increase CMF concentration. Furthermore, the presence of MWNTs
acts to increase thermal conductivity nearly 50% more than without. The second
effect is the differing interaction between flow rate and die angle as a function
of MWNT concentration. In the absence of MWNTs, increasing flow rate im-
proves thermal conductivity increase, such that increasing die angle at 5 lb/hr
increases thermal conductivity, but increasing die angle decreases thermal con-
ductivity at 3 lb/hr and 4 lb/hr. However, in the presence of MWNTs, all three
flow rates demonstrate increasing thermal conductivity with increasing die an-
gle. These effects in composite appear to indicate that MWNTs again improve
the reorientation of CMFs which may be related to the increase in apparent vis-
cosity of the melt, leading to improved transverse thermal conductivity, and that
MWNTs may be acting to improve the matrix thermal conductivity as well.
110
Chapter 6
Predictive Model
6.1 Background
The prediction of thermal conductivity in composite materials is a complex sub-
ject. A review of the fundamental prediction models is provided by Progel-
hof et al. [113], Tavman and Akinci [114], Shen et al. [115], and tangentially
by Zimmer et al. [116]. An ideal model must incorporate discrete phase mor-
phology, discrete phase structure embedded in the continuous phase, local and
global distributions of the discrete phase, and discrete phase volumetric fraction
for number of distinct discrete phases. Examining each of these characteris-
tics more closely allows us to examine the parametric space that is necessary to
cover for these models.
Discrete phase morphology presents a difficult challenge in that 0-D phases (i.e.
powders), 1-D phases (i.e. fibers), and higher dimensional discrete phases (i.e.
111
Jason R. Nixon
sheets, weaves, etc.) each interact differently within the continuous phase as
well as with each other. Furthermore, the scale of the filler can introduce ad-
ditional interactions. For example, MWNTs have proven to be very useful for
creating electrically conductive networks without a polymer due to the higher
number of connections in a well dispersed composite, whereas CMFs have been
shown to be better for mechanical enhancement due to their load bearing capac-
ity.
The structure of the discrete phase or phases also plays a significant role in
property enhancement. Uniaxially aligned cylindrical fillers have been shown
to produce great enhancement in the longitudinal direction, but little to nega-
tive enhancement in the transverse orientation. Likewise, thermal conductivity
was found to be enhanced, but electrical conductivity was not found to signif-
icantly improve due to few interconnects within the discrete phase. Discrete
phase structure has been found to be more dominant in erode-able 0-D materials
as well as 1-D and greater materials. Furthermore, with even 1-D structures,
uni-axially aligned, planar-aligned, and randomly aligned structures are possi-
ble, each with different property anisotropy in different orientations.
In the following sections, a review of well-known and seminal predictive models
will be discussed beginning with the rule of mixtures and leading into more
commonly used models like the Lewis-Nielsen and Halpin-Tsai models. Each
of these models, a two phase system is considered with matrix conductivity Km
and filler conductivity Kf . The ratio of Kf to Km is denoted as Kr. At the end
of this section, a review of the asymptotic behavior will be discussed.
112
Jason R. Nixon
6.1.1 Rule of Mixtures
The parallel model and series models (also known as the rule-of-mixtures and
the inverse rule-of-mixtures respectively) describes the transference of a heat in
layers parallel and in series to heat flow. These models give the effective upper
(parallel) and lower (series) bounds of the effective thermal conductivity Ke.
For an N -phase system, the general effective thermal conductivity equation is
given by the following equation:
Kne =
N∑
i=1
kni Vi (6.1)
where n = 1 produces the parallel conduction model and n = −1 produces the
serial conduction model. The geometric mean model effective thermal conduc-
tivity is given by:
Ke =
N∏
i=1
kVii (6.2)
6.1.2 Halpin-Tsai Model
The Halpin-Tsai model, presented in Halpin and Kardos [117], utilizes an anal-
ogy between in plane heat flow (defined in Equation 6.1) where n = 1 and
boundary conditions to the transverse transport of heat. The Halpin-Tsai model
assumes fibers of uniform cross section arranged in parallel. The effective trans-
verse heat flow coefficient is given by:
Ke = Km
[
1 + ζηVf
1− ηVf
]
η =
Kr + 1
Kr − ζ ζ = 1 (6.3)
113
Jason R. Nixon
The geometry reinforcement parameter ζ varies according to filler morphology
and structure. The Halpin-Tsai model can also be applied to properties other
than thermal conductivity, for which other values of ζ are appropriate. A value
of ζ = 1 was chosen because of the analogous relationship between transverse
thermal conductivity and longitudinal shear modulus and because of an assumed
circular fiber cross section. Alternative choices of the geometry reinforcement
parameter can be found in Halpin and Kardos [117]. Aside from the geometry
reinforcement parameter, The Halpin-Tsai model is a function of only the matrix
conductivity Km, filler conductivity Kf , and matrix volume fraction Vf .
6.1.3 Nielsen Model
The Lewis-Nielsen model, [118, 119, 120], is a modification of the Halpin-Tsai
model (see §6.1.2) to incorporate to filler shape and structure (i.e. orientation).
kc = Km
(
1 + ABVmax
1−BψVmax
)
(6.4)
B =
Kr − 1
Kr + A
ψ = 1 + Vf
(
1− Vmax
V 2max
)
where A = Ke − 1, Ke is the Einstein coefficient, and Vmax is the maximum
packing factor. A list of Einstein coefficients is list in Table 6.2, and a list of
maximum packing fractions is tabulated in Table 6.1. The maximum packing
fraction was determined from the geometric solution to a packing problem. For
114
Jason R. Nixon
the Lewis-Nielsen model, the packing fraction limit is explicitly defined, Vf :
0 ≤ Vf ≤ Vmax.
It is clear that the Nielsen model incorporates many of the parameters one would
wish to see in a predictive model (maximum packing, filler morphology, filler
structure, etc.), it has been shown in some studies to accurately predict thermal
conductivity [94, 106, 115] and in others to under predict thermal conductivity
[59, 121]. In studies that matched well, divergence was still found at relative
higher loadings.
TABLE 6.1: Lewis-Nielsen model values for Vmax.
Shape Type of packing Vmax
Spheres Hexagonal close 0.7405
Spheres Face centered cubic 0.7045
Spheres Body centered cubic 0.6000
Spheres Simple cubic 0.5240
Spheres Random close 0.6370
Spheres Random loose 0.6010
Fibers Uniaxial hexagonal close 0.9070
Fibers Uniaxial simple cubic 0.7850
Fibers Uniaxial random 0.8200
Fibers Three-dimensional random 0.5200
115
Jason R. Nixon
TABLE 6.2: Lewis-Nielsen model values for A.
Shape Heat Flow A
Cubes Any 2.00
Spheres Any 1.50
Spherical aggregates Any -
Random rods (Ar = 2) Any 1.58
Random rods (Ar = 4) Any 2.08
Random rods (Ar = 6) Any 2.80
Random rods (Ar = 10) Any 4.93
Random rods (Ar = 15) Any 8.38
Uniaxial fibers Parallel 2Ar
Uniaxial fibers Perpendicular 0.5
6.1.4 Cheng-Vachon Model
The model proposed by Cheng and Vachon [122] is probabilistic approximation
of a discontinuous phase in a unit cell. This model was developed for particle-
filled and fiber-filled composites, but is insensitive to the morphology and struc-
ture of the filler. The transverse conductivity of the composite is given by:
1
Ke
=
1√
ACD2
ln
(
D + E
D − E
)
+
1−B
Km
(6.5)
A = Km −Kf B =
√
3Vf
2
C = −4
√
2
3Vf
D =
√
Km − AB E = B
√
AC
2
116
Jason R. Nixon
Note that this model is only valid from Vf ≤ 66.6 vol.%. When Kr > 100,
the effective thermal conductivity can be approximated by the second term of
Equation 6.5; that is Ke ≈ Km/ (1−B).
6.1.5 Agari-Uno
Agari and Uno [123] derived a semi-empirical model based on the generalization
of parallel and serial conduction mechanisms (see Equation 6.1) which capture
the effects of filler-filler contact and the fillers effect on the matrix state.
ln (Ke) = VfCf ln (Kf ) + (1− Vf ) ln (CmKm) (6.6)
Cm andCf are experimentally determined constants of order unity. Cm is a mea-
sure of the effect of the filler on the morphology of the polymer (i.e. increased
crystallinity, crystal size, thermal interference, etc.). Values of Cm ≈ 1 indicate
that the matrix is not significantly effected by the fillers, which is the case of
CMFs. Cf measures the ease of the filler to form conductive networks.
6.1.6 Filler Limitations
All predictive models, with the exception of the rule of mixtures, asymptotically
convergences to a constant effective thermal conductivity as the ratio of the filler
thermal conductivity to the matrix thermal conductivity is Kr > 50. Figure 6.1
plots the behavior some of the models listed above at a 20 vol.% CMF and .
It should be noted that the convergence behavior to the asymptote varies for
117
Jason R. Nixon
each model. Furthermore, the asymptotic value of thermal conductivity varies
greatly, ranging from Ke = 1.25Km up to nearly Ke = 3.65Km. Physically,
this limitation arises from heat transfer capacity of the matrix. Regardless of the
fiber heat conduction, the interference between the matrix and fiber, as well as
the neat conductivity of the matrix, becomes the limiting factor in heat transfer.
This demonstrates the need for an improved matrix material, given that the fiber
conductivity is somewhat arbitrary beyond Kr > 50.
FIGURE 6.1: A selection of the predictive models listed in §6.1 are plotted
against the filler/matrix thermal conductivity ratio at a fixed volumetric con-
centration of 20 vol.% CMF. With the exception of the rule of mixtures, all
models converge to some asymptotic value of effective thermal conductivity
around approximately Kr = 50. The ratio of effective conductivity to matrix
conductivity (Ke/Km) for Kr = 2000 is listed beside the model name in the
plot legend.
118
Jason R. Nixon
6.2 Proposed Model
The newly developed model combines fiber orientation predictions made by
Vincent and Agassant [86] with the semi-empirical predictive model proposed
by Agari and Uno [123]. A thorough discussion of those equations is performed
in §4.1 and §6.1.5. A brief summary of the relevant formulas from Vincent and
Agassant’s work are presented in this section, followed by new contributions
combining these works and fitting them to experimental data from §5.3.
The Agari-Uno model well captures the physical effects of MWNT and CMF
concentration rather than probabilistic models which tend to average out the ef-
fect of fillers into a continuum approximation and do not accurately capture fiber
orientation. However, by introducing the Agassant and Vincent fiber orientation
model, we gain a more accurate representation of the effects of CMF orientation
on effective CMF thermal conductivity and the effects of MWNT concentration
on the effective thermal conductivity which is not seen in previously discussed
models.
An illustration of the die flow system is shown in Figure 6.2.
The shear rate γ˙ and extensional rate α˙ are defined by Equation 6.7.
γ˙ = −A (cos (2β) + sin (2θ))
ρ2
α˙ = −A sin (2β)
ρ2
(6.7)
A =
Q
h (sin (2θ)− 2θ cos (2θ))
119
Jason R. Nixon
FIGURE 6.2: Illustration the die and relevant angles for the Vincent and Agas-
sant die flow.
The time rate of change of the fiber angle is defined as:
dφ
dt
= r (α˙ sin (2φ) + γ˙ cos (2φ)) + γ˙ (6.8)
r =
l2f − r2f
l2f + r
2
f
For the 100 µm fibers used in this dissertation, r = 0.9902. As stated previously,
the behavior of a fiber depends on the path angle β. When β < β0, fibers
asymptotically converge to an equilibrium position that is approximately normal
to the fiber path orientation. When β > β0, the fiber will behave like a fiber in
shear and asymptotically converge to an orientation tangential to the fiber path.
The value of the critical angle in the unperturbed flow is defined by Equation 6.9.
β0 = r
2 cos (2θ) +
√
(1− r2) (1− r2 cos2 (2θ)) (6.9)
120
Jason R. Nixon
The critical angle β0, calculated using Equation 4.7, as well as the fraction of
the die height that is within the critical angle, for each die angle is tabulated in
Table 6.3.
TABLE 6.3: Die critical angle.
Die θ β0 β0/θ
A 0.00◦ - -
B 1.42◦ 0.24 16.9%
D 2.27◦ 0.59 26.0%
E 2.82◦ 0.89 31.6%
F 4.52◦ 2.02 44.9%
Vincent and Agassant provide three solutions to the Stokes flow problem based
on the fiber path angle β: β = 0, β < β0, and β > β0.
β = 0 : φ = tan−1
(
Cρ−2r
)− τ
2
(6.10)
β < β0 : φ =
X + Y + (X − Y )Cρ−2Y/α˙
γ˙
(
1 + Cρρ−2Y/α˙
) − τ
2
(6.11)
β > β0 : φ = tan
−1
(
X
γ˙
− Y
′
γ˙
tan
(
Y ′ log (ρ)
α˙
+ C
))
− τ
2
(6.12)
where τ , X , Y , and Y ′ are defined by:
τ = cos−1
(
α˙√
α˙2 + γ˙2
)
or τ = sin−1
(
γ˙√
α˙2 + γ˙2
)
(6.13)
X = r
√
α˙2 + γ˙2 (6.14)
Y =
√
ρ2α˙2 + (r2 − 1) γ˙2 (6.15)
Y ′ =
√
(1− r2) γ˙2 − r2α˙ (6.16)
121
Jason R. Nixon
C is an integration constant based on the fiber orientation at the inlet of the
die channel. Using the fiber path angle β, the fiber path orientation φ can be
transformed into the fiber planar orientation by ξ = φ+ β. One consequence of
using this model is that, while flow rate does appear in the shear and extension
rate calculation, the form of the flow solutions is such that flow rate cancels.
Therefore, the propose predictive model to be developed will not capture the
effect of flow-rate on the solution. Because the fiber orientation is given over
the entire channel width, we will assume that the mean of the fiber orientation
ξ¯ is representative of the effective fiber orientation across the thickness. The
average fiber orientation is calculated using Equation 6.17.
ξ¯ =
1
2θ
∫ θ
−θ
ξ (β) dβ (6.17)
It should be noted that using the orientation model by Vincent and Agassant
has several limitations. First, the calculation by Vincent and Agassant does not
take into account shear dependency on viscosity, and so while it is likely that
the viscosity across the channel does vary, this effect is not captured. Secondly,
the effect of fiber-fiber interaction is not accounted for, so the results that come
from this orientation prediction more than likely highly optimistic.
Now that the orientation of fibers across the thickness of a sample has been iden-
tified, we now want to connect this orientation model with a predictive model.
For this, we choose the Agari-Uno model discussed in §6.1.5. MWNT concen-
tration is handled within the properties of the matrix.
122
Jason R. Nixon
FIGURE 6.3: Fiber angle α plotted against normalized fiber path angle β/θ.
We now propose the modified Agari-Uno model, which will incorporate infor-
mation about the MWNT concentration, CMF concentration, and the fiber ori-
entation profile across the die. Again, the classic Agari-Uno model is defined
as:
ln (Ke) = VfCf ln (Kf ) + (1− Vf ) ln (CmKm) (6.18)
In this formulation, the coefficient Cm captures the MWNT concentration, Cf
captures the CMF orientation which is functionally dependent on die angle, flow
rate, and fiber shape, and Vf captures the effect of increasing CMF concentra-
tion. These input parameters should well capture the parametric space explored
in §5.3. Due to the relative simplicity of the model, we must assumed that fibers
are well distributed throughout the composite, and that local variance in fiber
123
Jason R. Nixon
orientation is averaged out over the bulk of the composite.
To begin, we make two assumptions. First, that the effective CMF thermal con-
ductivity is dependent on the average fiber orientation.
Kf = Kf,0 +Kf,ξ
(
1 + sin
(
ξ¯ − 90◦)) (6.19)
This assumption presents us with both a benefit and a challenge. First, this re-
lationship more accurately takes into account that while CMFs have a measured
conductivity, that conductivity is fully utilized by the composite due to finite
length and interface resistance. By taking this assumption into account, we can
reasonably show that the effective conductivity Kf of the CMF with respect to
the composite is dependent on the mean fiber orientation ξ¯, the initial effective
conductivity of longitudinally aligned CMFs Kf,0, and the additional conduc-
tivity benefit for fibers aligned in the transverse orientation Kf,ξ. Note that Kf,ξ
is functionally dependent on interfacial resistance and fiber length, and since
these were not directly accounted for in this study will be assumed to be some
constant.
Next, we make the assumption that Cm is also dependent on the mean fiber
orientation ξ¯ and will take the form shown in Equation 6.20.
Cm = Cm,0 + Cm,ξ
(
1 + sin
(
ξ¯ − 90◦)) (6.20)
where Cm,0 is calculated at a die angle of θ = 0◦ and Cm,ξ is some constant
124
Jason R. Nixon
representing MWNT concentration. It should be noted again that this model
does not capture the effect of flow rate. While flow rate does appear in the rate
calculations performed by Vincent and Agassant, these rates are treated as ratios
in later reorientation calculations and are lost. In the following examination of
the applicability of this model, we will then treat data as if flow rate was not a
factor.
During fitting, Cf = 1 was found in all cases. The Kf was determined to
be of the form Kf = 3 + 7
(
1 + sin
(
ξ¯ − 90◦)). By this result, if CMFs are
in a fully transverse orientation (ξ = 90◦), the effective CMF thermal con-
ductivity is 10 W/mK, which is approximately 55 times more conductive than
PBT (0.18 W/mK). While this is still dramatically less than the manufacturer
specified CMF thermal conductivity, it is still near the asymptotic limit after
which increasing CMF thermal conductivity will provide negligible benefits. At
0 wt.% MWNT concentration, Cm = 1.6, and at 2 wt.% MWNT concentration,
Cm = 1.4 + 1.3
(
1 + sin
(
ξ¯ − 90◦)). This result is important so far as it is
now clear that the benefit of MWNT concentration increasing with increasing
die angle, which was not seen for the θ = 0◦ for either short CMFs or long
CMFs. The fitted against the experimentally determined Cm values are plotted
in Figure 6.4. Fitted values of Cm correlate very well with the experimentally
identified values.
Correlation analysis was performed to examine the modified Agari-Uno model
predicted thermal conductivity as compared against the measure thermal con-
ductivity. A coefficient of determination R2 = 0.7358 was found. Further
125
Jason R. Nixon
FIGURE 6.4: Experimental (marker) compared against fitted (line) Cm values.
Note that at 0 wt.% MWNTs, the matrix coefficient is not effected by the die
angle by means of the fiber orientation. However, at 2 wt.% MWNT, it is
clear that the introduction of MWNTs has a very beneficial effect on thermal
conductivity.
analysis shows that while the model captures the basic trends and is accurate
to thermal conductivity which has been average across flow rates, its inability to
capture the effect of flow rate is increasing the variance in the model. However,
the modified Agari-Uno model sufficiently well captures the orientation depen-
dent CMF thermal conductivity as well as the empirically the effect of MWNT
concentration, and produces results which correlate well to measured thermal
conductivity. It is worth noting that the θ = 2.82◦ condition is dramatically un-
der predicted by the modified Agari-Uno model. However, this is unsurprising
given that this was also an outlying condition in the regression analysis per-
formed in §5.3. Finally, the procedure for calculating the modified Agari-Uno
model does not accurately capture the depreciation in properties observed from
15 wt.% to 20 wt.% for one-run composites, or from 25 wt.% to 30 wt.% for
126
Jason R. Nixon
two-run composites.
The final procedure for generating the modified Agari-Uno model is as follows.
1. Calculate the mean fiber orientation parameter ξ (β) from the Stokes flow
solutions to a diverging channel flow using Equation 6.10, Equation 6.11,
and Equation 6.12. This also requires the calculation of the shear and
extension rates, as well as the critical path angle for the die.
2. Average the fiber orientation ξ (β) across the width of the die to generate
the mean fiber orientation ξ¯.
3. Calculate the effective thermal conductivity using Equation 6.18 and re-
lationships for Kf and Cm (Equation 6.19 and Equation 6.20). For now,
constants in these relationships must be determined from the θ = 0◦ con-
dition and at least one other non-zero divergence angle.
127
Chapter 7
Conclusions and Future Studies
Although a significant amount of work concerning the compounding and man-
ufacturing of multiscale PMCs has been performed including process-structure
relationships and the synergistic benefits of fillers at multiple length scales, there
has not been an effort to date to manipulate fiber orientation in the die of an ex-
truder during the extrusion process and thereby select the best fiber structure
for a given application. In order to address this issue, work in this dissertation
focused on measuring the tensile and thermal properties of twin screw com-
pounded PBT/CMF/MWNT multiscale composites whose fiber microstructure
had been manipulated using a diverging flow in the die. A physics driven model,
informed by statistical analysis and existing predictive models, was developed
to predict the properties of these PMCs.
The research issues addressed in this work answered several questions related
to fiber orientation in two-dimensional semi-infinite forms. The result of this
128
Jason R. Nixon
work is an advancement of microstructural and capability understanding of mul-
tiscale PMCs using CMFs and MWNTs. This work has more comprehensively
explored the relationship of manipulating fiber orientation into the through-
thickness orientation by fluid mechanical means, leading to enhanced heat trans-
fer properties in the transverse orientation with some reduction of mechanical
properties in the sheet planes. Furthermore, the benefit of MWNTs have now
been realized for this application, which was not seen in preceding studies con-
cerning this compounding method and constituents.
Centrally, a parametric study of short microfiber multiscale PMCs was con-
ducted over a range of CMF concentrations, MWNT concentrations, flow rates,
and die angle, the last three of which contribute to the reorientation of CMFs
during pumping through the die. For each of the properties measured, tensile
modulus, ultimate tensile strength, and thermal conductivity, different trends
and interactions between the input parameters were measured.
For tensile modulus, without MWNTs, increasing flow rate has little effect on
stiffness, with a mean tensile modulus increase of approximately 250% con-
trolling for all other parameters. However, with MWNTs, controlling for all
parameters, stiffness is reduced from 50% to 100% as compared to no MWNTs
and demonstrates a decreasing trend with increasing flow rate. This is indica-
tive of increase fiber reorientation in the presence of MWNTs with increasing
flow rate. This behavior is likely due to the effect of fiber-fiber interaction on
reorientation as die angle increases. It is important to note that these results
did not behave in a particularly linear fashion, and the mechanical properties
129
Jason R. Nixon
for θ = 2.82◦ demonstrate behavior very much out of line with respect to any
other die angle in the trends. This was reflected in the relatively poor correlation
coefficient of R2 = 0.670. In the future, it may be beneficial to explore around
the θ = 2.82◦ region to determine if this is a type of sweet spot for property
enhancement.
Ultimate tensile strength was found to follow the most obvious trends. Increas-
ing die angle leads to an decreased ultimate tensile strength. This is consistent
with fibers being reoriented more out of plane as fiber angle increases due to a
greater die angle, leading to less CMFs contributing to the strength of the com-
posite. MWNTs significantly reduce the overall strength of the composite. It
would be beneficial in the future to explore the ultimate strength of these com-
posites in order to using different lengths to improve mechanical load transfer,
as well as to explore the potential for increased fiber damage with increasing
viscosity due to MWNT concentration.
For thermal conductivity, two significant effects were observed. First, thermal
conductivity increases with increase CMF concentration. Furthermore, the pres-
ence of MWNTs acts to increase thermal conductivity nearly 50% more than
without. In the absence of MWNTs, increasing flow rate improves thermal con-
ductivity increase. However, in the presence of MWNTs, all three flow rates
demonstrate increasing thermal conductivity with increasing die angle. These
effects in composite appear to indicate that MWNTs again improve the reorien-
tation of CMFs, leading to improved transverse thermal conductivity, and that
MWNTs may be acting to improve the matrix thermal conductivity as well. This
130
Jason R. Nixon
is likely related to both fiber damage due to increased viscosity as well as the
increase in viscosity either aiding the reorientation of fibers or preventing the
aligning fibers int he first place during pumping throught he die.
Between all parameters, it is clear that fiber reorientation leads to improved
transverse properties at the cost of longitudinal tensile properties. Furthermore,
these trends were used to inform a physics based model developed from the flow
solutions to the Stokes flow in a diverging channel and the predictive Agari-Uno
model.
7.1 Intellectual Contributions
Through this research effort, the following specific intellectual contributions
were made for PBT/CMF/MWNT multiscale composite compounding and prop-
erties.
• The capability of fiber reorientation towards a semi-transverse orientation
during pumping through a diverging die flow has been computationally
and experimentally demonstrated systematically across a range of CMF
concentration, MWNT concentrations, flow rates, and die angels.
– The utility of MWNTs for enhanced through thickness heat trans-
fer has been realized in multiscale composites as observed by direct
transverse heat transfer improvement with MWNT presence when
controlling for all other inputs.
131
Jason R. Nixon
∗ The utility of purely CMF concentration was found to be limited
in a diverging die flow without the addition of MWNTs. With
the addition of 2 wt.% MWNTs, heat transfer was observed to
increase by up to 50% controlling for other variables.
• A parametric study investigating CMF concentration, MWNT concentra-
tion, flow rate, and die angle was performed.
– In general, increasing CMF and MWNT concentrations improved
thermal conductivity and tensile properties. For a zero-divergence
die, MWNT concentration as not found to have a significant benefit
to longitudinal tensile properties or transverse thermal conductivity.
However, post-reorientation, increasing both CMF and MWNT con-
centration was beneficial.
– The specific main and interaction effects between input parameters
were statistically examined and empirical insights were gained.
• A new physics based model was developed using on the fiber reorientation
model by Vincent and Agassant and the Agari-Uno predictive model.
– This model successfully captures the effect of fiber reorientation,
CMF concentration, and MWNT concentration on properties.
• Investigated and identified a processing work-around to reach up to 30 wt.%
(22 vol.%) CMF concentration as well as processing limitations at these
high loadings.
132
Jason R. Nixon
7.2 Future Work
During the course of work, future research avenues were identified.
1. Confocal Microscopy. Using an optically transparent polymer matrix, use
confocal microscopy to visualize the three-dimensional fiber structure.
Currently, planar optical microscopy does not sufficiently capture fiber
orientation information to meaningfully correlate to measured physical
properties, nor can make an accurate assessment of fiber damage at high
loadings. Using a volumetric visualization approach, more insight into the
effect of structure on properties can be derived.
• Entropic Characterization. Continue the development of entropic
characterization of fiber filled PMCs. Early in this dissertation, en-
tropy measures for analyzing the distribution of fibers in planar mi-
crographs were developed. However, as previously stated, planar
microscopy does not sufficiently capture the 3D fiber structure, and
so entropy analysis was removed. However, with a volumetric rep-
resentation of the fiber structure, entropy could be employed more
meaningfully to gain insight into structure-property relationships.
2. Post-Extrusion Fiber Manipulation. Explore the potential to apply sec-
ondary fluid mechanical manipulation using rollers or other techniques
to further reorient fibers in the center and edges of the sheet. The flow
solutions of Vincent and Agassant [86] show that fiber orientation near
133
Jason R. Nixon
the edges of the die will always demonstrate low reorientation. There-
fore, investigating the capability of secondary reorientation by mechani-
cal manipulation may yield yet more fiber reorientation into the through-
thickness orientation.
3. Effect of MWNTs on Viscosity. Investigate the effect of MWNT inclusion
on the viscosity of the polymer matrix. Authors have already show that
the inclusion of MWNTs in a randomly aligned state both increase the vis-
cosity of the polymer matrix as well as changes the shear-dependency of
viscosity. However, it has also been shown that by aligning the MWNTs,
this increase is somewhat diminished. Therefore, in order to understand
the effects of matrix viscosity and the complex nature of the MWNT-shear
dependency on CMF reorientation, it would be beneficial to conduct rhe-
ological study on these melts in order to identify their contribution to the
observed increase in thermal conductivity and other properties with and
without the contribution of MWNTs.
4. Effect of Matrix Morphology. Investigate the effect of matrix properties,
i.e. viscosity, on fiber manipulation. Low shear rates near the center of
the dies flow may lead to reduced reorientability due to viscosity shear
dependency. By examining another matrix with low viscosity or a more
preferential shear rate dependency, there is potential for increased fiber
reorientability.
5. Alternative Matrix. Reach higher total physical properties by using a ma-
trix with higher neat properties. CMF/MWNT concentration effects in
134
Jason R. Nixon
different matrices are expected to be different than those determined in
this body of work. However, as demonstrated in §6.1.6, beyond a filler/-
matrix property ratio of 50, the utility of Filler contribution dramatically
decreases. Therefore, the use of a matrix with higher neat properties is
imperative to increased performance.
6. Higher CMF concentration.Investigate the potential for further property
increases by increasing CMF and MWNT concentration. Due to fiber-
fiber interaction during mixing, it is likely that a non-intermeshing twin
screw extruder is necessary due to its exceedingly higher free volume as
compared to an intermeshing twin screw extruder like the one used in this
work.
• Explore the effect of high CMF (Vµ > 19.4 vol.%) concentration the
freedom of fiber reorientation in the die.
7. In-Situ Cross Linking. Investigate compounding with a low molecular
weight polymer matrix to reduce fiber damage during the processing.
During this process, add an agent which increases the cross linking, in-
creasing the polymer molecular weight after fillers have been sufficiently
compounded in.
135
Appendix A
Property Summaries
The following appendix tabulates the mean µ, standard deviation σ, percent
difference mean from neat %µ calculated using Equation A.1, and percent dif-
ference standard deviation %σ calculated using Equation A.2 values presented
in Chapter 5.
%µ =
µ− µneat
µneat
(A.1)
%σ =
σ
σneat
(A.2)
136
Jason R. Nixon
TABLE A.1: Physical properties for lf = 6 mm, θ = 0◦. Each property is
arranged into three columns: measured mean, standard deviation, and percent
increase. Statistics were calculated using eight samples on average.
PBT Vµ Vn Q Tensile Modulus Ultimate Strength Thermal Conductivity
wt.% wt.% wt.% kg/hr GPa % MPa % W/mK %
100% 0% 0.0% 1.81 2.41 0.13 - 49.0 2.2 - 30.7 6.1 -
100% 0% 0.5% 1.81 1.87 0.13 -22% 11.0 4.6 -77% 7.2 0.1 -76%
99% 0% 1.0% 1.81 2.48 0.52 3% 39.7 10.4 -19% 28.0 0.1 -9%
99% 0% 1.5% 1.81 - - - - - - - - -
98% 0% 2.0% 1.81 - - - - - - - - -
90% 10% 0.0% 1.81 5.67 0.76 135% 51.8 6.9 6% 39.9 8.9 30%
90% 10% 0.5% 1.81 4.36 0.53 81% 36.0 15.5 -26% 30.4 7.8 -1%
89% 10% 1.0% 1.81 6.36 0.61 164% 63.0 9.6 28% 49.7 7.6 62%
89% 10% 1.5% 1.81 3.68 0.37 53% 28.8 5.0 -41% 23.7 7.1 -23%
88% 10% 2.0% 1.81 3.72 0.24 55% 24.9 6.7 -49% 22.6 6.4 -26%
85% 15% 0.0% 1.81 7.61 1.28 216% 65.0 7.7 33% 52.6 8.0 71%
85% 15% 0.5% 1.81 7.88 1.13 227% 71.9 3.1 47% 49.8 18.7 62%
84% 15% 1.0% 1.81 7.95 1.09 230% 66.9 13.1 37% 49.0 0.7 60%
84% 15% 1.5% 1.81 5.05 0.46 110% 44.6 4.9 -9% 41.5 6.1 35%
83% 15% 2.0% 1.81 4.58 0.73 90% 30.9 9.3 -37% 28.1 9.2 -9%
80% 20% 0.0% 1.81 10.67 1.11 343% 71.1 0.9 45% 51.5 13.8 68%
80% 20% 0.5% 1.81 4.22 0.64 75% 23.9 10.2 -51% 20.1 11.0 -35%
79% 20% 1.0% 1.81 5.17 0.37 114% 44.1 6.1 -10% 38.8 8.1 27%
79% 20% 1.5% 1.81 4.99 0.44 107% 40.6 6.1 -17% 38.5 6.5 25%
78% 20% 2.0% 1.81 5.70 0.32 137% 41.9 7.0 -14% 38.2 8.6 24%
75% 25% 0.0% 1.81 14.65 2.41 508% 79.5 10.7 62% 55.2 8.2 80%
75% 25% 0.5% 1.81 5.36 0.42 123% 53.0 11.9 8% 46.2 11.2 51%
74% 25% 1.0% 1.81 5.88 0.63 144% 45.3 9.6 -8% 41.7 9.4 36%
74% 25% 1.5% 1.81 7.96 1.83 231% 50.6 14.5 3% 46.1 12.2 50%
73% 25% 2.0% 1.81 8.76 0.41 264% 53.7 14.1 10% 46.0 15.9 50%
70% 30% 0.0% 1.81 13.17 0.83 447% 75.7 6.2 54% 66.0 7.0 115%
70% 30% 0.5% 1.81 10.87 1.75 351% 87.4 8.1 78% 63.9 8.8 108%
69% 30% 1.0% 1.81 10.58 1.09 339% 78.9 11.9 61% 70.7 5.3 130%
69% 30% 1.5% 1.81 9.68 1.07 302% 66.4 7.4 36% 62.8 8.0 105%
68% 30% 2.0% 1.81 10.62 1.08 341% 55.3 7.7 13% 50.6 9.6 65%
137
Jason R. Nixon
TABLE A.2: Physical properties for lf = 100 µm, θ = 0◦. Each property is
arranged into three columns: measured mean, standard deviation, and percent
increase. Statistics were calculated using eight samples on average.
PBT Vµ Vn Q Tensile Modulus Ultimate Strength Thermal Conductivity
wt.% wt.% wt.% kg/hr GPa % MPa % W/mK %
90% 10% 0% 1.81 6.51 0.19 170% 59.3 3.17 21% 0.257 0.001 43%
85% 15% 0% 1.81 7.28 0.27 202% 64.2 3.06 31% 0.346 0.007 92%
80% 20% 0% 1.81 8.48 0.44 252% 73.0 2.82 49% 0.387 0.002 115%
75% 25% 0% 1.81 9.11 0.44 278% 73.5 3.90 50% 0.446 0.010 148%
70% 30% 0% 1.81 11.13 0.42 362% 68.1 4.36 39% 0.423 0.017 135%
88% 10% 2% 1.81 4.46 0.35 85% 23.0 1.81 -53% 0.274 0.027 52%
83% 15% 2% 1.81 4.99 0.35 107% 32.3 3.25 -34% 0.328 0.016 82%
78% 20% 2% 1.81 5.57 0.43 131% 41.7 3.81 -15% 0.349 0.035 94%
73% 25% 2% 1.81 5.66 0.71 135% 38.7 0.85 -21% 0.412 0.070 129%
68% 30% 2% 1.81 5.88 0.80 144% 57.8 5.05 18% 0.405 0.027 125%
138
Jason R. Nixon
TABLE A.3: Physical properties for lf = 100 µm, θ = 1.41◦. Each property is
arranged into three columns: measured mean, standard deviation, and percent
increase. Statistics were calculated using eight samples on average.
PBT Vµ Vn Q Tensile Modulus Ultimate Strength Thermal Conductivity
wt.% wt.% wt.% kg/hr GPa % MPa % W/mK %
90% 10% 0% 1.36 3.83 0.18 59% 54.9 2.25 12% 0.360 0.010 100%
85% 15% 0% 1.36 5.42 0.95 125% 57.8 2.41 18% 0.387 0.025 115%
80% 20% 0% 1.36 8.07 0.51 235% 55.9 4.21 14% 0.396 0.036 120%
75% 25% 0% 1.36 10.97 0.40 355% 47.0 1.56 -4% 0.425 0.015 136%
70% 30% 0% 1.36 9.33 0.72 287% 44.1 2.40 -10% 0.441 0.011 145%
90% 10% 0% 1.81 5.49 0.07 128% 47.0 9.31 -4% 0.351 0.039 95%
85% 15% 0% 1.81 6.12 0.17 154% 51.0 7.07 4% 0.392 0.009 118%
80% 20% 0% 1.81 8.94 0.18 271% 52.4 3.70 7% 0.405 0.010 125%
75% 25% 0% 1.81 12.53 0.17 420% 53.9 5.70 10% 0.423 0.020 135%
70% 30% 0% 1.81 9.30 0.76 286% 52.9 5.69 8% 0.436 0.004 142%
90% 10% 0% 2.27 6.46 0.53 168% 52.9 0.50 8% 0.389 0.006 116%
85% 15% 0% 2.27 7.71 0.64 220% 54.9 3.43 12% 0.405 0.001 125%
80% 20% 0% 2.27 8.53 0.36 254% 59.8 6.93 22% 0.418 0.058 132%
75% 25% 0% 2.27 9.21 0.60 282% 60.8 7.59 24% 0.446 0.063 148%
70% 30% 0% 2.27 8.87 0.53 268% 51.9 4.48 6% 0.486 0.020 170%
88% 10% 2% 1.36 6.46 0.35 168% 16.2 4.43 -67% 0.364 0.025 102%
83% 15% 2% 1.36 6.99 0.78 190% 15.2 4.77 -69% 0.396 0.025 120%
78% 20% 2% 1.36 7.33 0.31 204% 16.2 4.55 -67% 0.445 0.010 147%
73% 25% 2% 1.36 5.64 0.31 134% 19.6 3.92 -60% 0.473 0.020 163%
68% 30% 2% 1.36 4.34 0.05 80% 20.1 5.39 -59% 0.434 0.019 141%
88% 10% 2% 1.81 5.74 0.78 138% 32.3 3.04 -34% 0.342 0.037 90%
83% 15% 2% 1.81 6.51 0.27 170% 29.4 1.85 -40% 0.391 0.021 117%
78% 20% 2% 1.81 6.94 0.24 188% 28.4 5.88 -42% 0.405 0.042 125%
73% 25% 2% 1.81 5.54 0.64 130% 29.9 1.96 -39% 0.427 0.034 137%
68% 30% 2% 1.81 4.43 1.21 84% 33.3 4.41 -32% 0.436 0.017 142%
88% 10% 2% 2.27 3.57 0.24 48% 24.5 1.96 -50% 0.389 0.059 116%
83% 15% 2% 2.27 4.29 0.31 78% 20.6 6.47 -58% 0.437 0.011 143%
78% 20% 2% 2.27 5.11 0.05 112% 20.1 5.88 -59% 0.459 0.008 155%
73% 25% 2% 2.27 4.39 0.36 82% 23.0 1.47 -53% 0.475 0.029 164%
68% 30% 2% 2.27 3.76 0.17 56% 25.0 4.41 -49% 0.513 0.020 185%
139
Jason R. Nixon
TABLE A.4: Physical properties for lf = 100 µm, θ = 2.26◦. Each property is
arranged into three columns: measured mean, standard deviation, and percent
increase. Statistics were calculated using eight samples on average.
PBT Vµ Vn Q Tensile Modulus Ultimate Strength Thermal Conductivity
wt.% wt.% wt.% kg/hr GPa % MPa % W/mK %
90% 10% 0% 1.36 6.41 0.22 166% 33.8 5.39 -31% 0.353 0.020 96%
85% 15% 0% 1.36 7.37 0.34 206% 42.1 0.98 -14% 0.378 0.014 110%
80% 20% 0% 1.36 7.95 0.68 230% 51.0 3.92 4% 0.387 0.055 115%
75% 25% 0% 1.36 8.24 0.36 242% 54.4 3.11 11% 0.419 0.027 133%
70% 30% 0% 1.36 9.21 0.72 282% 52.4 2.26 7% 0.437 0.006 143%
90% 10% 0% 1.81 7.18 0.37 198% 49.5 9.70 1% 0.333 0.020 85%
85% 15% 0% 1.81 7.71 0.17 220% 51.5 1.71 5% 0.365 0.013 103%
80% 20% 0% 1.81 10.27 0.26 326% 52.9 7.74 8% 0.396 0.001 120%
75% 25% 0% 1.81 11.09 0.59 360% 54.4 1.06 11% 0.432 0.010 140%
70% 30% 0% 1.81 10.89 0.17 352% 55.9 3.05 14% 0.464 0.020 158%
90% 10% 0% 2.27 5.69 0.40 136% 55.9 0.99 14% 0.329 0.013 83%
85% 15% 0% 2.27 6.99 0.22 190% 57.3 0.21 17% 0.356 0.046 98%
80% 20% 0% 2.27 7.90 0.70 228% 60.8 3.39 24% 0.396 0.016 120%
75% 25% 0% 2.27 9.11 0.34 278% 64.7 6.86 32% 0.443 0.057 146%
70% 30% 0% 2.27 10.22 0.12 324% 62.2 2.94 27% 0.506 0.017 181%
88% 10% 2% 1.36 5.06 0.91 110% 26.5 7.13 -46% 0.328 0.099 82%
83% 15% 2% 1.36 6.70 0.29 178% 33.3 3.43 -32% 0.427 0.026 137%
78% 20% 2% 1.36 7.76 0.02 222% 37.2 3.92 -24% 0.472 0.046 162%
73% 25% 2% 1.36 10.03 0.51 316% 27.0 4.41 -45% 0.509 0.033 183%
68% 30% 2% 1.36 12.19 0.24 406% 2.9 0.51 -94% 0.540 0.062 200%
88% 10% 2% 1.81 5.47 0.27 127% 17.6 0.49 -64% 0.394 0.030 119%
83% 15% 2% 1.81 7.52 0.32 212% 10.3 3.43 -79% 0.441 0.017 145%
78% 20% 2% 1.81 7.25 0.02 201% 0.0 3.92 -99% 0.504 0.012 180%
73% 25% 2% 1.81 6.94 0.25 188% 1.5 4.41 -97% 0.590 0.048 228%
68% 30% 2% 1.81 11.09 0.10 360% 8.8 0.51 -82% 0.556 0.047 209%
88% 10% 2% 2.27 4.27 0.17 77% 12.7 6.86 -74% 0.385 0.025 114%
83% 15% 2% 2.27 4.77 0.29 98% 7.8 0.98 -84% 0.437 0.049 143%
78% 20% 2% 2.27 5.71 0.46 137% 2.5 4.41 -95% 0.497 0.034 176%
73% 25% 2% 2.27 5.98 0.02 148% 10.3 5.39 -79% 0.544 0.084 202%
68% 30% 2% 2.27 5.62 0.12 133% 22.5 0.49 -54% 0.567 0.040 215%
140
Jason R. Nixon
TABLE A.5: Physical properties for lf = 100 µm, θ = 2.82◦. Each property is
arranged into three columns: measured mean, standard deviation, and percent
increase. Statistics were calculated using eight samples on average.
PBT Vµ Vn Q Tensile Modulus Ultimate Strength Thermal Conductivity
wt.% wt.% wt.% kg/hr GPa % MPa % W/mK %
90% 10% 0% 1.81 7.33 0.41 204% 32.3 2.05 -34% 0.220 0.001 22%
85% 15% 0% 1.81 8.44 0.31 250% 36.8 3.94 -25% 0.290 0.007 61%
80% 20% 0% 1.81 9.01 0.67 274% 51.9 2.96 6% 0.315 0.002 75%
75% 25% 0% 1.81 9.98 0.46 314% 71.1 3.46 45% 0.394 0.010 119%
70% 30% 0% 1.81 10.80 0.99 348% 91.1 8.73 86% 0.425 0.017 136%
88% 10% 2% 1.81 4.24 0.41 76% 38.2 1.81 -22% 0.391 0.012 117%
83% 15% 2% 1.81 4.55 0.60 89% 35.8 3.25 -27% 0.412 0.021 129%
78% 20% 2% 1.81 5.40 0.54 124% 28.9 3.81 -41% 0.479 0.052 166%
73% 25% 2% 1.81 5.95 0.13 147% 38.7 0.85 -21% 0.466 0.070 159%
68% 30% 2% 1.81 5.30 0.74 120% 46.1 5.05 -6% 0.553 0.027 207%
141
Jason R. Nixon
TABLE A.6: Physical properties for lf = 100 µm, θ = 4.52◦. Each property is
arranged into three columns: measured mean, standard deviation, and percent
increase. Statistics were calculated using eight samples on average.
PBT Vµ Vn Q Tensile Modulus Ultimate Strength Thermal Conductivity
wt.% wt.% wt.% kg/hr GPa % MPa % W/mK %
90% 10% 0% 1.36 7.62 0.31 216% 49.0 5.52 0% 0.266 0.024 48%
85% 15% 0% 1.36 8.24 0.35 242% 48.5 4.35 -1% 0.286 0.013 59%
80% 20% 0% 1.36 8.92 0.54 270% 43.1 9.31 -12% 0.326 0.006 81%
75% 25% 0% 1.36 8.72 0.00 262% 34.8 9.80 -29% 0.344 0.042 91%
70% 30% 0% 1.36 8.10 0.68 236% 36.3 5.39 -26% 0.367 0.072 104%
90% 10% 0% 1.81 7.76 0.27 222% 55.9 4.63 14% 0.306 0.012 70%
85% 15% 0% 1.81 8.05 0.87 234% 45.6 7.74 -7% 0.346 0.043 92%
80% 20% 0% 1.81 8.29 0.31 244% 41.2 6.37 -16% 0.378 0.027 110%
75% 25% 0% 1.81 8.53 0.50 254% 37.7 0.87 -23% 0.401 0.048 123%
70% 30% 0% 1.81 8.82 0.69 266% 44.6 6.30 -9% 0.405 0.027 125%
90% 10% 0% 2.27 7.09 0.36 194% 51.0 5.43 4% 0.367 0.006 104%
85% 15% 0% 2.27 8.19 0.10 240% 52.4 3.39 7% 0.398 0.010 121%
80% 20% 0% 2.27 9.21 0.53 282% 54.4 3.48 11% 0.434 0.018 141%
75% 25% 0% 2.27 10.46 0.27 334% 53.4 5.88 9% 0.466 0.020 159%
70% 30% 0% 2.27 11.38 0.53 372% 55.9 0.49 14% 0.502 0.022 179%
88% 10% 2% 1.36 4.68 0.62 94% 11.8 9.31 -76% 0.385 0.020 114%
83% 15% 2% 1.36 5.21 0.03 116% 0.0 5.39 -99% 0.437 0.025 143%
78% 20% 2% 1.36 5.93 0.34 146% 9.8 6.49 -80% 0.486 0.030 170%
73% 25% 2% 1.36 6.24 0.39 159% 14.2 5.88 -71% 0.549 0.024 205%
68% 30% 2% 1.36 6.60 0.22 174% 15.7 1.47 -68% 0.590 0.016 228%
88% 10% 2% 1.81 4.39 0.63 82% 16.2 6.86 -67% 0.423 0.011 135%
83% 15% 2% 1.81 5.11 0.14 112% 9.3 5.49 -81% 0.464 0.020 158%
78% 20% 2% 1.81 5.66 0.10 135% 2.9 4.58 -94% 0.515 0.030 186%
73% 25% 2% 1.81 6.34 0.03 163% 0.5 8.37 -99% 0.562 0.015 212%
68% 30% 2% 1.81 6.96 0.04 189% 5.9 7.10 -88% 0.607 0.022 237%
88% 10% 2% 2.27 4.19 0.14 74% 11.8 0.98 -76% 0.445 0.015 147%
83% 15% 2% 2.27 4.84 0.05 101% 9.3 3.43 -81% 0.482 0.037 168%
78% 20% 2% 2.27 5.35 0.50 122% 4.4 5.70 -91% 0.518 0.033 188%
73% 25% 2% 2.27 6.22 0.54 158% 13.7 6.69 -72% 0.556 0.010 209%
68% 30% 2% 2.27 6.24 0.90 159% 17.6 9.54 -64% 0.599 0.072 233%
142
Bibliography
[1] J. Coleman, U. Khan, W. Blau, and Y. Gunko. Small but strong: A re-
view of the mechanical properties of carbon nanotubepolymer compos-
ites. Carbon, 44(9):16241652, 2006.
[2] T. Villmow, P. Potschke, S. Pegel, L. Haussler, and B. Kretzchmar. Influ-
ence of twin-screw extrusion conditions on the dispersion of multi-walled
carbon nanotubes in poly(lactic acid) matrix. Polymer, 49(16):35003509,
2008.
[3] A. Kota. Processing-Structure-Microstructure-Property Relationships in
Polymer Nanocomposites. PhD thesis, University of Maryland, 2007.
[4] Z. Tadmor and C. G. Gogos. Principles of Polymer Processing. Wiley-
Interscience, 2006.
[5] F. Li, H. Cheng, S. Bai, G. Su, and M. S. Dresselhaus. Tensile strength
of single-walled carbon nanotubes directly measured from their macro-
scopic ropes. Applied Physical Letters, 77(20):3161–3163, 2000.
[6] D. A. Walters, L. M. Ericson, M. Casavant, J. Liu, D. T. Colbert, K. A.
Smith, and R. E. Smalley. Elastic strain of freely suspended single-wall
carbon nanotube ropes. Applied Physical Letters, 74(25):3803–3805,
1999.
[7] J. P. Salvetat, J. M. Bonnard, N.H. Thomson, A.J. Kuklik, L. Forro,
W. Benoit, and L. Zuppiroli. Mechanical properties of carbon nanotubes.
Applied Physics A Materials Science and Processing, 69(3):255–260,
1999.
143
Bibliography
[8] Y. Li. Effect of addition of carbon nanofibers and carbon nanotubes
on properties of thermoplastic biopolymers. Polymer, 52(10):23102318,
2011.
[9] Z. Spitalsky, D. Tasis, K. Papagelis, and C. Galiotis. Carbon nan-
otube/polymer composites: Chemistry, processing, mechanical and elec-
trical properties. Progress in Polymer Science, 35(3):357401, 2010.
[10] M. Sanchez-Garcia, J. Lagaron, and S. Hoa. Effect of addition of carbon
nanofibers and carbon nanotubes on properties of thermoplastic biopoly-
mers. Composites Science and Technology, 10(7):1095–1105, 2011.
[11] M. Moniruzzaman and K. Winey. Polymer nanocomposites containing
carbon nanotubes. Macromolecules, 39(16):51945205, 2006.
[12] J. Salvetat, A. Kulik, J. Bonard, G. Briggs, T. Stockli, K. Metenier,
S. Bonnamy, F. Beguin, N. Burnham, and L. Forro. Elastic modulus of
ordered and disordered multi-walled carbon nanotubes. Advanced Mate-
rials, 11(2):161–165, 1999.
[13] O. Breuer and U. T. Sundararaj. Big returns from small fibers: a review of
polymer/carbon nanotube composites. Polymer Composites, 25(6):630–
645, 2004.
[14] P. Potschke, T. D. Fornes, and D. R. Paul. Rheological behavior of mul-
tiwalled carbon nanotube/polycarbonate composites. Polymer, 43(11):
3247–3255, 2002.
[15] W. Ding, A. Eitan, F. T. Fischer, X. Chen, D. A. Dikin, and R. Andrews.
Direct observation of polymer sheathing in carbon nanotube polycarbon-
ate composites. Nano Letters, 3(11):1593–1596, 2003.
[16] E. Assouline, A. Lustiger, A. H. Barber, C. A. Cooper, E. Klein,
E. Watchel, and H. D. Wagner. Nucleation ability of multiwall carbon
nanotubes in polypropylene composites. Journal of Polymer Science:
Part B, 41:520–527, 2003.
144
Bibliography
[17] X. L. Xie, K. Aloys, X. P. Zhou, and F. D. Zeng. Ultrahigh molecu-
lar mass polyethylene/carbon nanotube composites - crystallization and
melting properties. Journal of Thermal Analysis and Calorimetry, 74:
317–323, 2003.
[18] J. Sandler, G. Broza, M. Nolte, K. Schulte, Y.-M. Lam, and M. S. P.
Shaffer. Crystallization of carbon nanotube and nanofiber polypropylene
composites. Journal of Macromolecular Science: Part B, 42(3-4):479–
488, 2003.
[19] B. P. Grady, F. Pompeo, R. L. Shambaugh, and D. E. Resasco. Nucle-
ation of polypropylene crystallization by single-walled carbon nanotubes.
Journal of Physical Chemisty: Part B, 106:106, 2002.
[20] R. Islam and A. Pramila. Thermal conductivity of fiber reinforced com-
posites by the fem. Journal of Composite Materials, 33(18):1699–1715,
1999.
[21] C.-W. Nan, R. Berringer, D. R. Clarke, and H. Gleiter. Effective thermal
conductivity of particulate composites with interfacial thermal resistance.
Journal of Applied Physics, 82:6692–6699, 1997.
[22] A. Kothari, K. Jian, J. Rankin, and B. Sheldon. Comparison between
carbon nanotube and carbon nanofiber reinforcements in amorphous sil-
icon nitride coatings. Journal of the American Ceramic Society, 91(8):
27432746, 2008.
[23] R. Andrews, D. Jacques, M. Minot, and T. Rantell. Fabrication of carbon
multi-wall nanotube/polymer composites by shear mixing. Macromolec-
ular Materials and Engineering, 287(6):395403, 2002.
[24] M. A. Lopez Machando, V. Valenti, J. Biagiotti, and J. M. Kenny.
Thermal and mechanical properties of single-walled carbon nanotube-
spolypropylene composites prepared by melt processing. Carbon, 43:
1499–1505, 2005.
145
Bibliography
[25] R. Andrews, D. Jacques D. L. Qian, and T. Rantell. Multi-wall carbon
nanotubes: synthesis and application. Accounts of Chemical Research,
35(12):1008–1017, 2002.
[26] S. Wang, R. Liang, B. Wang, and C. Zhang. Dispersion and thermal
conductivity of carbon nanotube composites. Carbon, 47:53–57, 2009.
[27] S. Frusteri, V. Leonardi, S. Vasta, and G. Restuccia. Thermal conductivity
measurement of a pcm based storage system containing carbon fibers.
Applied Thermal Engineering, 25(11):16231633, 2005.
[28] J. L. Thomason and M. A. Vlug. Influence of fiber length and concentra-
tion on the properties of glass fibre-reinforced polypropylene: 1. tensile
and flexural modulus. Composites: Part A, 27A:477–484, 1996.
[29] X.-L. Xie, Y.-W. Mai, and X.-P. Zhou. Dispersion and alignment of car-
bon nanotubes in polymer matrix: A review. Material Science and Tech-
nology, 49:89–112, 2005.
[30] P.-C. Ma, N. A. Siddiqui, G. Marom, and J.-K. Kim. Dispersion and func-
tionalization of carbon nanotubes for polymer-based nanocomposites: A
review. Composites: Part A, 41:1345–1376, 2010.
[31] D. Tasis, N. Tagmatarchis, V. G eorgakilas, and M. Prato. Soluble carbon
nanotubes. Chemistry-A European Journal, 9(17):4000–4008, 2003.
[32] D. Tasis, N. Tagmatarchis, A. Bianco, and M. Prato. Chemistry of carbon
nanotube. Chemical Reviews, 106:1105–1136, 2006.
[33] M. Sharma, S. Gao, E. Madar, H. Sharma, L. Y. Wei, and J. Bijwe. Car-
bon fiber surfaces and composite interphases. Composites Science and
Technology, 102:35–50, 2014.
[34] S. Tiwari and J. Bijwe. Surface treatment of carbon fibers: a review.
Procedia Technology, 14:505–512, 2014.
146
Bibliography
[35] X. Gong, J. Liu, S. Baskaran, R. D. Voise, and J. S. Young. Surfactant-
assisted processing of carbon nanotube/polymer composites. Chemistry
of Materials, 12(4):1049–1052, 2000.
[36] S. Wang, Z. Liang, B. Wang, C. Zhang, and Z. Raman. Precise cutting
of single walled carbon nanotubes. Nanotechnology, 17:055301–055306,
2007.
[37] H. Y. Kordkheili, M. Farsi, and Z. Rezazadeh. Physical, mechanical and
morphological properties of polymer composites manufactured from car-
bon nanotubes and wood flour. Composites: Part B, 44:750–755, 2013.
[38] C. Unterwger, J. Duchoslav, D. Sifter, and C. Furst. Characterization
of carbon fiber surfaces and their impact on the mechanical properties
of short carbon fiber reinforced polypropylene composites. Composites
Science and Technology, 108:41–47, 2015.
[39] J. Sandler, P. Werner, M. Shaffer, V. Demchuck, V. Altsadt, and A. Win-
dle. Carbon-nanofibre-reinforced poly(ether ether ketone) composites.
Composites: Part A, 33(8):1033–1039, 2002.
[40] T. Kashiwagi, E. Grulke, J. Hilding, R. Harris, W. Awad, and
J. Douglas. Thermal degradation and flammability properties of
poly(propylene)/carbon nanotube composites. Macromolecular Rapid
Communication, 23(13):761–765, 2002.
[41] J. Cho and D. Paul. Nylon 6 nanocomposites by melt mixing. Polymer,
42(3):1083–1094, 2001.
[42] O. Carneiro, J. Covas, C. Bernardo, G. Caldeira, D. Hattum, J. Ting,
R. Alig, and M. Lake. Production and assessment of polycarbonate com-
posites reinforced with vapour-grown carbon fibres. Composites Science
and Technology, 58(3-4):401–407, 1998.
[43] E. Bekyarova, E. Thostenson, A. Yu, H. Kim, J. Gao, J. Tang, H. Hahn,
T. Chou, M. Itkis, and R. Haddon. Multiscale carbon nanotube-carbon
147
Bibliography
fiber reinforcement for advanced epoxy composites. Langmuir, 23(7):
39703974, 2007.
[44] K. Lozano and E. V. Barrera. Nanofiber-reinforced thermoplastic com-
posites. i. thermoanalytical and mechanical analyses. Journal of Applied
Polymer Science, 79(1):125–133, 2001.
[45] S. Lee, O. Choi, W. Lee, J. Yi, B. Kim, J. Byun, M. Yoon, H. Fong,
E. Thostenson, and T. Chou. Processing and characterization of multi-
scale hybrid composites reinforced with nanoscale carbon reinforcements
and carbon fibers. Composites: Part A, 45(4):337–344, 2011.
[46] G. Broza, M. Kwiatkowska, Z. Roslaniec, and K. Schulte. rocessing and
assessment of poly(butylene terephthalate) nanocomposites reinforced
with oxidized single wall carbon nanotubes. Polymer, 46(16):58605867,
2005.
[47] J. Zeng, B. Saltysiak, W. Johnson, D. Schiraldi, and S. Kumar. Processing
and properties of poly(methyl methacrylate)/carbon nano fiber compos-
ites. Composites: Part B, 32(2):173–178, 2004.
[48] S. Yesil, O. Koysuren, and G. Bayram. Effect of microfiber reinforce-
ment on the morphology, electrical, and mechanical properties of the
polyethylene/poly(ethylene terephthalate)/carbon nanotube composites.
Polymer Engineering and Science, 50(11):20932105, 2010.
[49] F. Incropera, D. Dewitt, T. Bergman, and A. Lavine. Fundamentals of
Heat and Mass Transfer. John Wiley Sons, Inc., 2007.
[50] M. Bryning, D. Milkie, M. Islam, J. Kikkawa, and A. Yodh. Thermal con-
ductivity and interfacial resistance in single-wall carbon nanotube epoxy
composites. Applied Physics Letters, 87(16909):1–3, 2003.
148
Bibliography
[51] J. Hone, M. C. Llaguno, A. T. Johnson, B. Batlogg, Z. Benes, and J.E.
Fischer. Thermal properties of carbon nanotubes and nanotube-based ma-
terials. Applied Physics A Materials Science and Processing, 74(3):339–
343, 2002.
[52] S. Berber, Y. Kwon, and D. Tomanek. Unusually high thermal conduc-
tivity of carbon nanotubes. Physical Review Letters, 84(20):4613–4616,
2000.
[53] J. Che, T. Cagin, and W. Goddard. Thermal conductivity of carbon nan-
otubes. Nanotechnology, 11(2):65–69, 2000.
[54] Z. Han and A. Fina. Thermal conductivity of carbon nanotubes and their
polymer nanocomposites: a review. Progress in Polymer Science, 36:
914–944, 2011.
[55] J. Hone, M. Whitney, C. Piskoti, and A. Zettl. Thermal conductivity
of single-walled carbon nanotubes. Physical Review B, 59(4):25142516,
1999.
[56] P. Kim, L. Shi, A. Majumdar, and P. L. McEuen. Thermal transport mea-
surements of individual multiwalled nanotubes. Physical Review Letters,
87(21):215502/1–4, 2001.
[57] C. Yu, L. Shi, Z. Yao, D. Li, , and A. Majumdar. Thermal conductance
and thermopower of an individual single-wall carbon nanotube. Nano
Letters, 5:1842–1846, 2005.
[58] S. Sinha, S. Barjami, G. Iannacchione, A. Schwab, and G. Muench. Off-
axis thermal properties of carbon nanotube films. Journal of Nanoparticle
Research, 7:651–657, 2005.
[59] S. Agarwal, M. Masud, K. Khan, and R. Gupta. Thermal conductivity
of polymer nanocomposites made with carbon nanofibers. Polymer Engi-
neering and Science, 48(12):24742481, 2008.
149
Bibliography
[60] R. S. Prasher, X. J. Hu, Y. Chalopin, N. Mingo, K. Lofgreen, S. Volz,
F. Cleri, and P. Keblinski. Turning carbon nanotubes from exceptional
heat conductors into insulators. Physical Review Letters, 102(105901):
1–4, 2009.
[61] M. Zimmer, Q. Cheng, S. Li, J. Brooks, R. Liang, B. Wang, and C. Zhang.
Comparative characterization of multi-scale carbon fiber composites with
long and short mwcnts at higher weight fractions. Journal of Nanomate-
rials, 2012(532080):1–9, 2012.
[62] T. Zhou, X. Wang, G. Mingyuan, and X. Liu. Study of the thermal con-
duction mechanism of nano-sic/dgeba/emi-2,4 composites. Polymer, 49
(21):46664672, 2008.
[63] Y.-P. Sun, K. Fu, Y. Lin, and W. Huang. Functionalized carbon nan-
otubes: properties and applications. Accounts of Chemical Research, 35
(12):1096–1104, 2002.
[64] S. Shenogin, A. Bodapati, L. Xue, R. Ozisik, and P. Keblinski. Effect
of chemical functionalization on thermal transport of carbon nanotube
composites. Applied Physics Letters, 85(12):2229–2231, 2004.
[65] F. Gojny, M. Wichmann, B. Fiedler, I. Kinloch, A. Windle W. Bauhofer,
and K. Schulte. Evaluation and identification of electrical and thermal
conduction mechanisms in carbon nanotube/epoxy composites. Polymer,
47(6):20362045, 2006.
[66] G. Chen, Y. Li, and H. Shimizu. Ultrahigh-shear processing for the prepa-
ration of polymer/carbon nanotube composites. Carbon, 45(12):2334–
2340, 2007.
[67] T. Villmow, P. Potschke, S. Pegel, L. Haussler, and B. Kretzchmar. Influ-
ence of twin-screw extrusion conditions on the dispersion of multi-walled
carbon nanotubes in poly(lactic acid) matrix. Polymer, 49(16):35003509,
2008.
150
Bibliography
[68] J. Vera-Agullo, A. Gloria-Pereira, H. Varela-Rizo, J. Gonzalez, and
I. Martin-Gullon. Comparative study of the dispersion and functional
properties of multiwall carbon nanotubes and helical-ribbon carbon
nanofibers in polyester nanocomposites. Composites Science and Tech-
nology, 69(10):1521–1532, 2009.
[69] A. Scurati, D. L. Feke, and I. Manas-Zloczower. Analysis of the kinet-
ics of agglomerate erosion in simple shear flows. Chemical Engineering
Science, 60(23):6564–6573, 2005.
[70] J. Gao, G. Walsh, D. Bigio, R. Briber, and M. Wetzel. Residence time
distributions model for twin-screw extruders. AIChE Journal, 45(12):
2541–2549, 1999.
[71] J. Gao, G. Walsh, D. Bigio, R. Briber, and M. Wetzel. Mean residence
time analysis for twin screw extrusion. Polymer Engineering and Science,
40(1):227–237, 2000.
[72] W. Pappas. Characterization and comparison of stress history in various
sized twin-screw extruders using residence stress distributions. Master’s
thesis, University of Maryland, 2011.
[73] G. Fukuda. A new scale-up approach through the evaluation of stress his-
tory within a twin-screw extruder. Master’s thesis, University of Mary-
land, 2014.
[74] D. Acierno, P. Scarfato, E. Amendola, G. Nocerino, and G. Costa. Prepa-
ration and characterization of pbt nanocomposites compounded with dif-
ferent montmorillonites. Polymer Engineering and Science, 44(6):1012–
1018, 2004.
[75] R. Kuriger, M. Alam, D. Anderson, and R. Jacobsen. Processing
and characterization of aligned vapor grown carbon fiber reinforced
polypropylene. Composites: Park A, 33(1):53–62, 2002.
151
Bibliography
[76] R. S. Ruoff and D. C. Lorents. Mechanical and thermal properties of
carbon nanotubes. Carbon, 33(7):925–930, 1995.
[77] E. T. Thostenson and T.-W. Chou. Aligned multi-walled carbon
nanotube-reinforced composites: processing and mechanical character-
ization. Journal of Physics D: Applied Physics, 35(16):77–80, 2002.
[78] F. Du, J. E. Fischer, and K. I. Winey. Coagulation method for prepar-
ing single-walled carbon nanotube/poly(methyl methacrylate) compos-
ites and their modulus, electrical conductivity, and thermal stability. Jour-
nal of Polymer Science: Part B, 41(24):3333–3338, 2003.
[79] V. K. Rangari, M. Yousuf, S. Jeelani, M. X. Pulikkanthara, and V. N.
Khabashesku. Alignment of carbon nanotubes and reinforcing effects
in nylon-6 polymer composite fibers. Nanotechnology, 19(145703):1–9,
2008.
[80] L. Jin, C. Bower, and O. Zhou. Alignment of carbon nanotubes in a
polymer matrix by mechanical stretching. Applied Physics Letters, 73:
1197, 1998.
[81] R. Haggenmueller, H. H. Gommans, A. G¿ Rinzler, J. E. Fischer, and
K. I. Winey. Aligned single-wall carbon nanotubes in composites by melt
processing methods. Chemical Physics Letters, 330:219–225, 2000.
[82] T. Kimura, H. Ago, M. Tobita, S. Ohshima, M. Kyotani, and M. Yumura.
Polymer composites of carbon nanotubes aligned by a magnetic field.
Advanced Materials, 14(19):1380–1383, 2002.
[83] E. S. Choi, J. S. Brooks, D. L. Eaton, M. S. Al-Haik, M. Y. Hussaini,
H. Garmestani, D. Li, and K. Dahmen4. Enhancement of thermal and
electrical properties of carbon nanotube polymer composites by magnetic
field processing. Journal of Applied Physics, 94(9):6034, 2003.
152
Bibliography
[84] T. Takahashi, K. Yonetake, K. Koyama, and T. Kikuchi. Polycarbonate
crystallization by vapor-grown carbon fiber with and without magnetic
field. Macromolecular Rapid Communications, 24(13):763–767, 2003.
[85] P. Potschke, A. Bhattacharyya, and A. Janke. Carbon nanotube-filled
polycarbonate composites produced by melt mixing and their use in
blends with polyethylene. Carbon, 45(5-6):965–969, 2004.
[86] M. Vincent and J. F. Agassant. Experimental and theoretical study of
short-fibre orientation in diverging flows. Rheological Acta, 24(6):603–
610, 1985.
[87] J. C. Halpin and J. L. Kardos. Strength of discontinuous reinforced com-
posites 1. fiber reinforced composites. Polymer Engineering and Science,
18(6):496–504, 1978.
[88] A. C. Lederer. Characterization of physical properties of multi-scale poly-
mer composites under various processing conditions. Master’s thesis,
University of Maryland, 2012.
[89] J. Nie, Y. Jia, P. Qu, and Q. Shi. Carbon nanotube/carbon fiber multi-
scale composite: influence of interfacial strength on mechanical proper-
ties. ournal of Inorganic and Organometallic Polymers and Materials,
21:937–940, 2011.
[90] E. T. Thostenson, W. Z. Li, D. Z. Wang, Z. F. Ren, and T. W. Chou.
Carbon nanotube/carbon fiber hybrid multi-scale composites. Journal of
Applied Physics, 91(9):6034–6066, 2002.
[91] S.-B. Lee, O. Choi, W. Lee, J.W Yi, B.-S. Kim, J.-H. Byun, M.-K.,
H. Fong, E. T. Thostenson, and T.-W. Chou. Processing and character-
ization of multi-scale hybrid composites reinforced with nanoscale car-
bon reinforcements and carbon fibers. Composites: Part A, 42:337–344,
2011.
153
Bibliography
[92] H. Qian, A. Bismarck, E. S. Greenhalgh, G Kalinka, and M. S. P. Shaffer.
Hierarchical composites reinforced with carbon nanotube grafted fibers:
The potential assessed at the single fiber level. Chemical Materials, 20:
1862–1869, 2008.
[93] Y. Xu, D. D. L. Chung, and C. Mroz. Thermally conducting aluminum
nitride polymer-matrix composites. Composites: Part A, 32:1749–1757,
2001.
[94] G.-W. Lee, M. Park, J. Kim, J. I. Lee, and H. G. Yoon. Enhanced thermal
conductivity of polymer composites with hybrid fillers. Composites: Part
A, 37:727.734, 2006.
[95] S. Zhang, S. Yin, C. Rong, P. Huo, Z. Jiang, and G. Wang. Synergistic ef-
fects of functionalized graphene and functionalized multi-walled carbon
nanotubes on the electrical and mechanical properties of poly(ether sul-
fone) composites. Macromolecular Nanotechnology, 49:31253134, 2013.
[96] Z. Zheng, Z. Wang, Q. Feng, F. Zhang, Y. Du, and C. Wang. Prepara-
tion of surface-silvered graphene-cnts/polyimide hybrid films: Process-
ing, morphology and properties. Materials Chemistry and Physics, 138:
350–357, 2013.
[97] W. Li, A. Dichiara, and J. Bai. Carbon nanotubegraphene nanoplatelet hy-
brids as high-performance multifunctional reinforcements in epoxy com-
posites. Composites Science and Technology, 74:221–227, 2013.
[98] A. Arostegui and J. Nazabal. Compatibilization of a polybutylene tereph-
thalate/polyethylene octene copolymer blends with different amounts of
an epoxy resin. Journal of Applied Polymer Science, 91(1):260–269,
2004.
[99] ASTM D638-10. ASTM Internationals, 2010.
154
Bibliography
[100] M. Gupta and K. Wang. Fiber orientation and mechanical properties of
short-fiber-reinforced injection-molded composites: simulated and exper-
imental results. Polymer Composites, 14(5):367–382, 1993.
[101] M. L. Shofner, K. Lozano, F. J. Rodriguez-Macias, and E. V. Barrera.
Nanofiber-reinforced polymers prepared by fused deposition modeling.
Journal of Applied Polymer Science, 89(11):3081–3090, 2003.
[102] A. Bagsik and V. Schoppner. Mechanical properties of fused deposition
modeling parts manufactured with ultem9085. In Society of Plastic En-
gineers Annual Technical Conference 2011, 2011.
[103] S. G. Advani and C. L. Tucker III. The use of tensors to describe and
predict fiber orientation in short fiber composites. Journal of Rheology,
31(8):751–784, 1987.
[104] S. G. Advani and C. L. Tucker III. Closure approximations for three-
dimensional structure tensors. Journal of Rheology, 34(4):367–386,
1990.
[105] H. L. Tekinalp, V. Kunc, G. M. Vlez-Garca, C. E. Duty, L. J. Love, A. K.
Naskar, C. A. Blue, and S. Ozcan. Highly oriented carbon fiberpolymer
composites via additive manufacturing. Composites Science and Tech-
nology, 105:144–150, 2014.
[106] C. Guthy, F. Du, S. Brand, K. Winey, and J. Fischer. Thermal conductiv-
ity of single-walled carbon nanotube/pmma nanocomposites. Journal of
Heat Transfer, 129(8):10961099, 2007.
[107] S.-Y. Fu and B. lauke. Effects of fiber length and fiber orientation distri-
butions on the tensile strength of short-fiber-reinforced polymers. Com-
posites Science and Technology, 56:1179–1190, 1996.
[108] O. Valendtino, M. Sarno, N. G. Rainone, M. R. Nobile, P. Ciambelli,
H. C. Neizert, and G. P. Simon. Influence on the polymer structure and
155
Bibliography
nanotube concentration on the conductivity and rheological properties of
polyethylene/cnt composites. Physica E, 40:2440–2445, 2008.
[109] P. Potschke, T. D. Fornes, and D. R. Paul. Rheological behavior of mul-
tiwalled carbon nanotube/polycarbonate composites. Polymer, 43:3247–
3255, 2002.
[110] A. A. Ahmad, A. A. Al-Juhani, S. Thomas, S. K. De, and M. A. Atieh.
Effect of modified and unmodified carbon nanotubes on the rheological
behavior of high density polyethylene nanocomposites. Journal of Nano-
materials, 2013:1–12, 2013.
[111] P. Potschke, M. Abdel-Goad, I. Alig, S. Dudkin, and D. Lellinger. Rhe-
ological and dielectrical characterization of melt mixed polycarbonate-
multi-walled carbon nanotube composites. Polymer, 45:8863–8870,
2004.
[112] T. McNally, P. Potschke, P. Halley, M. Murphy, D. Martin, S. E. J. Bell,
G. P. Brennan, D. Bein, P. Lemoine, and J. P. Quinn. Polyethylene multi-
walled carbon nanotube composites. Polymer, 46:8222–7232, 2005.
[113] R. C. Progelhof, J. L. Throne, and R. R. Ruetsch. Methods for predic-
tion the thermal conductivity of composite systems: a review. Polymer
Engineering and Science, 16(9):615–625, 1976.
[114] I. H. Tavman and H. Akinci. Transverse thermal conductivity of fiber
reinforced polymer composites. International Communication of Heat
and Mass Transfer, 27(2):253–261, 2000.
[115] M.-X. Shen, Y.-X. Cui, J. He, and Y.-M. Zhang. Thermal conductivity
model of filled polymer composites. International Journal of Minerals,
Metallurgy and Materials, 18(5):623–631, 2011.
[116] M. Zimmer, X. Fan, J. Bao, B. Wang, C. Zhang, and J. Brooks. Through-
thickness thermal conductivity prediction study on nanocomposites and
156
Bibliography
multiscale composites. Materials Sciences and Applications, 3:131–138,
2012.
[117] J. C. Halpin and J. L. Kardos. The halpin-tsai equations: a review. Poly-
mer Engineering and Science, 16(5):344–352, 1976.
[118] L. Nielsen. Thermal conductivity of particulate-filled polymers. Journal
of Applied Polymer Science, 17:3819–3820, 1973.
[119] T. Lewis and L. Nielsen. Dynamic mechanical properties of particulate-
filled polymers. Journal of Applied Polymer Science, 14:1449, 1970.
[120] L. Nielsen. The thermal and electrical conductivity of two-phase systems.
Industrial Engineering and Chemistry Fundamentals, 13:17–20, 1974.
[121] S. Wang and J. Qui. Enhancing thermal conductivity of glass fiber/poly-
mer composites through carbon nanotubes incorporation. Composite:
Part B, 41:533–536, 2010.
[122] S. C. Cheng and R. I. Vachon. The prediction of the thermal conductiv-
ity of two and three phase solid heterogeneous mixtures. International
Journal of Heat and Mass Transfer, 12:249–264, 1969.
[123] Y. Agari and T. Uno. Estimation of thermal conductivities of filled poly-
mers. Journal of Applied Polymer Science, 32:5705–5712, 1986.
157