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thesis entitled

EFFECTS OF FIBERS ON THE CURE CHARACTERISTICS
OF CARBON-REINFORCED EPOXY COMPOSITES

presented by

Cheryl Ann Schwalm

has been accepted towards fulfillment
of the requirements for

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EFFECTS OF FIBERS ON THE CURE CHARACTERISTICS

OF CARBON-REINFORCED EPOXY COMPOSITES

BY
Cheryl Ann Schwalm

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Chemical Engineering

1989

43570

ABSTRACT
EFFECTS OF FIBERS ON THE CURE CHARACTERISTICS
OF CARBON-REINFORCED EPOXY COMPOSITES

By
Cheryl Ann Schwalm

Effects of untreated and surface-oxidized carbon fibers on
epoxy-resin cures were experimentally investigated and
results were compared with the literature. DSC and FTIR
analyses showed no significant difference in extents of
cure and glass transition temperatures existed between neat
and carbon-reinforced epoxy resins. Reaction rates for neat
and carbon-reinforced epoxy resins were fit to a two-
equation cure-kinetic model. These two equations
represented the autocatalytic polymerization and diffusion-
controlled crosslinking reactions. Gelation times
increased and crosslinking rate constants decreased by ten
percent when the carbon-fiber concentration equalled 0.60.
Frequency factors decreased by 99 percent and activation
energies decreased by 35 percent with a carbon-fiber
concentration equal to 0.60. Carbon-fibers affected the
epoxy-resin cure reactions by restricting the molecular
mobility of reactants and forming chemical interactions

with epoxy molecules.

Dedicated to my father, Harold,
and my mother, Leona.

iii

ACKNOWLEDGEMENTS

I express my deepest gratitude to my family and friends,
for their endless love and encouragement. I acknowledge
the United States Naval Office and Michigan State
University Chemical Engineering department for financial

support. I wish to thank Dr. Martin Hawley, my advisor,
for his wisdom and guidance during the course of this
research. Appreciation is also extended to John DeLong,
Jinder Jow, and Mark Finzel for their knowledge and
suggestions. I want to thank Mike Rich and Javad Kalantar
for assistance with the experimental apparatus. In
conclusion, I would like to thank Dave Gagliardi, Carol
Kelly, and Allen Magolan for their moral support and
helpful ideas.

iv

LIST

LIST

LIST

I.

II.

TABLE OF CONTENTS

OF TABLES
OF FIGURES
OF NOMENCLATURE

INTRODUCTION

A. History

B. Advantages and Uses of Carbon-Reinforced
Epoxy Resins

C. Motivation of Thesis

D. Thesis Statement

BACKGROUND AND LITERATURE REVIEW
A. Carbon Fibers
1. Fabrication
2. Topography
a. Fiber Structure
b. Untreated Surface
c. Surface-Oxidized
B. Epoxy Resin
1. Time-Temperature-Transformation,
TTT, Diagrams -— A Model of the
Isothermal Cure Behavior
2. Cure Reactions
3. Cure Characteristics
a. Reaction Exotherm
b. Glass Transition Temperature
c. Cure-Kinetic Models
C. Reinforced Epoxy Composite
1. Types of Adhesion
2. Interphase Reactions
a. Glass-Epoxy
b. Carbon-Epoxy
'3. Cure Characteristics
a. Reaction Exotherm
b. Glass Transition Temperature
c. Cure-Kinetic Models
4. Mechanical Properties
D. The Role of Cure Kinetics in Composite
Manufacturing
1. Composite Cure
2. Laminate-Autoclave Curing

vii
ix

xiii

29
31
33
34
36
42
43
50
50
52
54
55
56
58
63
66

66
69

E. Instrumentation Overview
1. Differential Scanning Calorimeter, DSC

Theory

b. Analysis Techniques
2. Fourier Transform Infrared, FTIR,
Spectrometer

Theory

b. Analysis Techniques

III. EXPERIMENTAL STUDY
A. Sample Preparation
8. Experimental Instrumentation

1. DSC

2. FTIR Spectrometer
C. Experimental Procedure

1. DSC-Cured and DSC-Analyzed

2. Convectionally-Cured and FTIR-Analyzed
D. Experimental Results and Discussion

1. Carbon Fiber Experiments

a.
b.

2. Neat and Reinforced Epoxy-Resin Experiments

Carbon Fiber and Hardener Experiments
Carbon Fiber and Epoxy Experiments

a. Ultimate DSC Reaction Exotherm, Hut.

b. Initial FTIR-Spectroscopy Epoxy-Inten-

C.

d.
e.
f.

g.

sity Ratio
Full-Cure Time, t,(Isothermal Cure
Temperature, Tc)
Full-cure Extent of Cure, a(Tc)
Cure Kinetics
Glass Transition Temperature, T9 (T )
Reproducibility and Accuracy
(1) Hardener Addition
(a) Stoichiometric Variations
(b) Extent of Cure
(2) Fiber Impregnation
(3) Prevention of Environmental
Contamination
(4) Transmission- and Diffuse-Reflec-
.tance, DRIFT, FTIR Spectroscopy

IV. CONCLUSIONS

V. RECOMMENDATIONS
A. Problems and Suggestions
B. Further Research

APPENDICES

A. Maximum Exotherm Between Carbon Fibers and
Epoxy Matrix

8. TTT Diagram Transitions

C. DSC and FTIR-Spectroscopy Experimental Data

LIST OF REFERENCES

vi

73
73
74
76
77

77
79

86
86
94
94
97
99
99
102
105
106
109
109
112
112
115

117

125
131
149
155
155
156
156
157
159

161

167
174
174
177
181

183
186

190

LIST OF TABLES

Table 11.1. Comparison of high-strength and high-
modulus carbon fibers [17].

Table 11.2. Principal bond defects in carbon
fibers [22].

Table 11.3. Volatiles on surface-oxidized carbon-
fibers [22]: (a) composition versus temperature:

and (b) total and incremental amounts of desorbed

volatiles.

Table 11.4. Atomic percentages of constituents on
the carbon-fiber surface [8,31].

Table 11.5. Experimentally-determined ultimate
reaction exotherm, Hultl for an epoxy resin.

Table 11.6. Mijovic et a1. [44] cure-kinetic model
for a neat and 40% glass-reinforced epoxy resin.

Table 11.7. Composite manufacturing processes [2].

Table 111.1. Cure characteristics.

Table 111.2. Specimens for carbon-fiber experiments.

Table 111.3. Ultimate reaction exotherm, Mutt,
versus fiber weight fraction, wf.

Table 111.4. Total reaction exotherm, Hr, glass
transition temperature, T,, and full-cure time,
t,, versus cure temperature, Tc, for neat epoxy-
resin cures between 120'C and 250°C.

Table 111.5. Analysis of variance, ANOVA, of the
total reaction exotherm, H., for the following
sources of variation: (a) cure temperature, Tc;
and (b) fiber-weight fraction, wf.

Table 111.6. Gelation time, tgel, versus cure
temperature, Tc, and fiber-weight fraction, w,, for:
(a) untreated carbon-reinforced epoxy resin; and (b)
surface-oxidized carbon-reinforced epoxy resin.

vii

17

21

23

34

63

67

106

109

115

119

126

135

Table 111.7. Reation-rate constants, k1, kg,

and k3, as a function of cure temperature, Tc, and
fiber-weight fraction, w,, for: (a) untreated
carbon-reinforced epoxy resin: and (b) surface-
oxidized carbon-reinforced epoxy resin.

Table 111.8. Cure kinetic parameters for the neat
and: (a) untreated carbon-reinforced epoxy resin;
and (b) surface-oxidized carbon-reinforced epoxy
resin.

Table 111.9. Calculation of the entropy for: (a)
untreated carbon-reinforced epoxy resin: and (b)
surface-oxidized carbon-reinforced epoxy resin.

Table 111.10. Comparison of activation energy, EA,
for epoxy resins modeled with the autocatalytic
cure-kinetic equation in Equation 13.

Table 111.11. Extent of cure, a, after hardener
addition and fiber impregnation.

Table 111.12. FTIR-spectroscopy sample-preparation
errors.

Table C.1. DSC extent of cure, a, versus time, t,
for the neat, untreated carbon-reinforced, and
surface-oxidized carbon-reinforced epoxy resin
isothermally DSC-cured at 170°C, 200°C, and 220°C.

Table 0.2. FTIR-spectroscopy epoxy-intensity peaks.

viii

139

142

144

146

159

163

186

188

LIST OF FIGURES

Figure 1.1. Conceptualization of the fiber-matrix
interphase.

Figure 11.1. Decomposition of polyacrylonitrile, PAN,
at 200°C under reduced pressure [11].

Figure 11.2. Dehydrogenation and denitrogenation
of polyacrylonitrile, PAN, [11].

Figure 11.3. A schematic model of the crystallite
columns in a carbon fiber. The S1, 82, and S3
represent voids, basal-plane boundary and
intercrystallite boundary, respectively [10].

Figure 11.4. A schematic model of the axial
hexagonal arrays of carbon atoms in a graphitic
basal plane [11].

Figure 11.5. A schematic three-dimensional
structural model of a carbon fiber [23].

Figure 11.6. Common graphitic basal-plane defects

on the carbon-fiber surface [22]: (a) hole defects:
(b) claw defects; and (c) twinning-line defects.
Note: A "twinning-line" is defined as a region in
which the defect causes a sequence of alternating
four- and eight-atom rings instead of the normal six-
atom hexagonal rings.

Figure 11.7. Volatiles from surface-oxidized carbon
fibers [8]: (a) composition versus temperature;
and (b) total amount desorbed versus temperature.

Figure 11.8. Schematic illustration of the potential
carbon-fiber surface groups [18].

Figure 11.9. Reaction of epichlorodyfrin and
bisphenol A, diphenyl propane A produces the epoxy
monomer, difunctional diglycidyl ether of bisphenol
A, DEGBA [33].

Figure 11.10. Typical cure schedule for an epoxy
resin.

ix

10

11

13

14

14

16

22

23

24

25

Figure 11.11. Schematic representation of a: (a)
branched polymer: and (b) crosslinked polymer [33].

Figure 11.12. Time-temperature-transformation, TTT,
diagram [36].

Figure 11.13. Representation of: (a) wetting of a
solid with a liquid: and (b) nonwetting of a solid
with a liquid. Note: 9 = contact angle.

Figure 11.14. Fiber-matrix adhesion between isolated
contact points on a carbon fiber.

Figure 11.15. Chemical reaction in the fiber-matrix
interphase between the carbon-fiber surface and epoxy
resin.

Figure 11.16. Illustration of a: (a) glass-silane
coupling-agent: and (b) the R groups covalently
bonding with the epoxy resin [2].

Figure 11.17. Experimental results reproduced from

Dutta et a1. [43]: (a) k, for a carbon-black

filled epoxy resin: (b) k2 for a carbon-black filled
epoxy resin: (c) k, for a glass-filled epoxy resin,

and (d) k; for a glass-filled epoxy resin.

Figure 11.18. A schematic of a laminate-fabrication
'sequence [62].

Figure 11.19. Nonuniformity in conventionally-cured
epoxy composite.

Figure 11.20. Illustration of the Michelson
Interferometer [28].

Figure 11.21. FTIR-spectroscopy analysis techniques:
a) transmission: b) single internal reflection, IRS:
and c) diffuse-reflectance, DRIFT [83].

Figure 111.1. The molecular structure of: (a) Dow
Epoxy Resin, DER 332 [90]; and (b) Diaminophenyl
sulfone, DDS [91].

Figure 111.2. Photograph of a prepregger machine
manufactured by the Research Tool Company.

Figure 111.3. A 500x photograph of a carbon-
reinforced epoxy composite with a fiber-weight
fraction, w,, of 0.60.

Figure 111.4. Cross-section of the DuPont 9900 DSC
cell [93].

32

44

46

48

51

60

71

72

78

80

87

89

92

95

Figure 111.5. Photograph of the DuPont thermal
analyzer, TA, and 9900 DSC.

Figure 111.6. Photograph of the Perkin-Elmer 1800
FTIR spectrometer.

Figure 111.7. Illustration of the Perkin-Elmer
diffuse-reflectance, PEDR, accessory [94].

Figure 111.8. Experimental DSC curves of: (a) the
ultimate reaction exotherm, Mutt, for an uncured
epoxy resin: (b) the total reaction exotherm, H,,
for an uncured epoxy resin: and (c) the glass
transition temperature, T“, for a fully-cured epoxy
resin.

Figure 111.9. FTIR-spectroscopy absorbance spectra
of: (a) an uncured epoxy resin: and (b) a cured
epoxy resin.

Figure 111.10. Total reaction exotherm, H,, versus
DSC-heating rate for an epoxy resin.

Figure 111.11. DSC analyses of the: (a) total
reaction exotherm, H1, versus the cure temperature,
Tc: and (b) the glass transition temperature, To!
versus T .

Figure 111.12. Illustration of the: (a) total
reaction exotherm, 8,, versus the log1o(glass
transition temperature, T,); and (b) log1o(residual
extent of cure, anid = 1 - a), versus the T9.

Figure 111.13. Illustration of the full-cure line.
The cure temperature, Tc, versus log time, t.

Figure 111.14. Time-temperature-transition, TTT,
diagram for a stoichiometric DER 332-DDS epoxy resin.

Figure 111.15. Full Cure extent of cure, a, versus
cure temperature, Tc, for the (a) DSC-cured and DSC-
analyzed untreated carbon-reinforced epoxy resin: (b)
DSC-cured and DSC-analyzed surface-oxidized carbon-
reinforced epoxy resin: and (c) convectionally-cured
and FTIR-analyzed surface-oxidized carbon-reinforced
epoxy resin.

Figure 111.16. Extent of cure, a, versus time, t,
for a: (a) DSC-cured and DSC-analyzed untreated
carbon-reinforced epoxy resin: and (b) DSC-cured and
DSC-analyzed surface-oxidized carbon-reinforced epoxy
resin.

xi

96

97

98

101

104

113

118

121

122

125

128

134

Figure 111.17. Reduced: (a) polymerization reaction
rate, on. 1, versus extent of cure, a, for the neat
epoxy res n: and (b) crosslinking reaction rate,
“3.82: versus a for the neat epoxy resin.

Figure 111.18. Logarithm of the rate constants,
k1, k2, and k3, versus inverse absolute cure
temperature, Tc, for: (a) untreated carbon-
reinforced epoxy resin: and (b) surface-oxidized
carbon-reinforced epoxy resin.

Figure 111.19. DSC analyses of fully-cured epoxy
resin at: (a) 170°C: (b) 190°C: (c) 200°C:
(d) 210°C: (e) zzo'c: (t) 230°C: and (g) 250°C.

Figure 111.20. Glass transition temperature, T,,
versus cure temperature, Tc, for: (a) untreated
carbon-reinforced epoxy resin: and (b) surface-
oxidized carbon-reinforced epoxy resin.

Figure 111.21. The extent of cure, a, versus time,
t, for a neat epoxy resin cured at 80°C.

Figure A.1. Chemical reaction of a carbon fiber and
an epoxy resin.

xii

137

138

153

158

158

179

LIST OF NOMENCLATURE

A - frequency factor

A(1184) - absorbance at 1184 cm'1 of fully-cured epoxy resin,

A(916) - absorbance at 916 cm" of fully-cured epoxy resin,

A°(1184) - absorbance at 1184 cm‘1 of unreacted epoxy resin,

A.(916) - absorbance at 916 cm'1 of unreacted epoxy resin,

A916 ¢_-1/A113‘ c_—1 - FTIR-spectroscopy epoxy intensity
ratio

(A916 c.-1/A,,,‘ c_-1)o - initial FTIR-spectroscopy epoxy
intensity ratio

ATR - attentuated total reflection

a. - molar absorption coefficient

B - ratio of hardener equivalents to epoxy-monomer
equivalents

B(v) - source intensity

C - proportionality constant

C, - hardener concentration

CA0 - initial hardener concentration

CE - epoxy-monomer concentration

C50 - initial epoxy monomer concentration

c - filler content

c. - molar concentration

DDS - diaminodiphenyl sulfone

xiii

 

DEGBA - diglycidyl ether of bisphenol A
DER 332 - Dow Epoxy Resin 332

DRIFT - diffuse reflectance

DSC - differential scanning calorimeter

dp - prepreg density

d; - water density
En - activation energy
E. - unreacted epoxy-monomer lattice energy

Ex - full-cure epoxy—polymer lattice energy

F(R;) - Kubelka-Munk function

F; - unreacted epoxy-monomer segmental mobility

Fx - full-cure epoxy-polymer segmental mobility

FTIR - Fourier transform infrared spectrometer

f - frequency

f. - epoxy-monomer functionality

f1(c) - function of filler content for the catalyzed
reaction rate

f2(c) - function of filler content for the autocatalyzed
reaction rate

g, - hardener functionality

H - reaction exotherm

HT - total reaction exotherm

Hut, - ultimate reaction exotherm

1(x) - interferogram intensity

ITCA - International Confederation for Thermal Analysis

i - reaction mechanism occurring chronologically during the

cure

xiv

K - overall reaction-rate constant
K' - initial reaction-rate constant

rate constant for the 1 reaction mechanism

53."
I l

catalyzed reaction-rate constant

3‘
I

autocatalyzed reaction-rate constant
kg - crosslinking reaction-rate constant
M - specimen weight

m - autocatalyzed-polymerization reaction order
m' - moles

m'o - initial moles

N - overall reaction order

n - catalyzed-polymerization reaction order
PAN - polyacrylonitrile

PEDR - Perkin-Elmer diffuse-reflectance

R - universal gas constant

R. - sample diffuse reflectance

r/R - normalized radius

SEM - scanning electron microscopy

8, - voids

32 - basal-plane boundary

8; - intercrystallite boundaru

s - scattering coefficient

T - absolute temperature

T, - internal transmittance

TEM - tunneling electron microscopy

Tc - cure temperature

T - glass transition temperature

T - unreacted glass transition temperature

go
T,,.l - gelled glass transition temperature
Tut. - ultimate reaction exotherm

TA - thermal analyzer

TTT - time-temperature-transformation

t. - full-cure time

t',[ - gelation time

VHT - vacuum heat treatment

w, - work of adhesion

w - absorption coefficient

w, - fiber-weight fractioni

XPS - x-ray photoelectron spectroscopy

x - mirror displacement

y - uniform sample thickness

a - extent of cure

a,.( - extent of cure at gelation

aa,d - residual extent of cure

oa,d1 - reduced polymerization reaction rate
a,,d2 - reduced crosslinking reaction rate
r, - epoxy resin surface free energy

12 - carbon fiber surface free energy

112 - epoxy-hardener surface free energy

9 - contact angle

6 - molar absorptivity

xvi

Chapter I

INTRODUCTION

In a carbon-reinforced epoxy composite, carbon fibers
act as the reinforcement and epoxy resin serves as the
matrix which holds the fibers. Carbon fibers have superior
mechanical properties, but are in a difficult to use form.
An epoxy resin has poor mechanical properties, but can
easily function as a structural element. The resultant
composite is a material with superior mechanical
properties, but in a form which can be easily handled

[1,2].

A. History

Fiber composites are neither new materials nor always
man-made. Wood is a fiber composite consisting of
cellulose chains embedded in a lignin matrix which has
existed for more than 350 million years -— since the
Middle-Devonian period of the Paleozoic era. What is new
and man-made are the realms of fiber composites which have

developed since the mid-twentieth century.

2

Laying groundwork for the study of composites, Herrick
[3] stated that the bond between a carbon fiber and an
epoxy resin is both physical and chemical. Since the
discovery that an enhanced carbon-fiber surface aids the
composite's mechanical integrity, the focus has shifted to
chemical bonding. For example, Drzal et al. [4] reported
that surface-oxidized carbon-reinforced composites have
improved interfacial-mechanical properties over untreated
carbon-reinforced composites. They implied that these
improved properties are the result of enhanced chemical
bonding between fiber and matrix. Fitzer et a1. [5] used
scanning electron microscopy, SEM, and wet chemical
analyses to probe the chemical nature of the carbon-fiber
surface. Their results suggested that both covalent and
hydrogen bonding occurred between the carbon fiber and

epoxy resin.

While the last decade has witnessed much fruitful
research, ”a priori" prediction of composite properties
based on fiber type, fiber-surface treatment, and resin
properties is not currently possible. Nevertheless,
manufacturers add surface-oxidized carbon fibers to

epoxy resins to form very useful composites.

 

3

8. Advantages and Uses of Carbon-Reinforced Epoxy Resins

Synergistic union of carbon fibers with an epoxy
resin creates a composite with strength and modulus values
in the direction of the oriented fibers which are
comparable to those of conventional materials, such as
steel and aluminum. Carbon-reinforced epoxy composites
also possess better thermal and electrical properties, less
tendency toward corrosion, reduced density, and lower
thermal expansion than conventional materials. Today,
carbon-reinforced epoxy composites are being used: (1) by
the aviation industry in wings and fuselages for aircrafts:
(2) in defense-related naval equipment such as ship masts,
hulls, and decks: (3) for recreational equipment, which
includes sailboats, motorboats, skis, bicycles, fishing
rods, bowling balls, golf clubs, and tennis rackets: and
(4) by the automobile industry for bumpers, distributor
caps, integrated front-end panels, leaf springs, and other

components.
C. Motivation of Thesis

All manufacturing processes are designed to produce a
desired product from starting materials through a
succession of physical and chemical treatments. During the
manufacture of a carbon-reinforced epoxy composite, carbon

fibers and epoxy resin undergo a number of physical

4
treatments. Fiber-surface treatments or resin
purification prepare them for chemical treatment. During
the chemical treatment, carbon fibers and epoxy resin are
combined and cured to form a carbon-reinforced epoxy
composite. This composite may undergo further physical
treatment, such as forming and trimming, before the final
desired product is obtained. The chemical treatment or
curing is the heart of any composite fabrication process,

the step that determines a successful process.

This study is to serve as an aid for manufacturing
high-performance composite materials. In the past, carbon-
reinforced epoxy-composite cures have been modeled with
neat, or fiberless, epoxy-resin cure kinetics. Today,
researchers [6] postulate that either physical or chemical
interactions exist in the region between the carbon fibers

and epoxy resin [7,8].

In this study, it will be determined whether more or
less epoxy molecules polymerize when carbon fibers are
added to the epoxy resin. Also the carbon-fiber effects on
thermal cure characteristics, such as the reaction exotherm
and glass transition temperature, will be considered.
Finally, this work will address carbon-fiber effects on

epoxy-resin cure kinetics.

 

D. Thesis Statement

A literature review is conducted to study the chemical
composition of the carbon fiber, epoxy resin, and fiber-
matrix interphase. A three-dimensional fiber-matrix
interphase concept has been developed by Sharpe [4]. He
stated that the interface is only part of the three-
dimensional fiber-matrix interphase. The interphase
extends between the bulk matrix through the interface to
the bulk fiber. This interphase is unlike either the bulk
matrix or fiberous material. Figure 1.1. illustrates a
schematic model of the fiber-matrix interphase in a fiber-

reinforced composite.

 

 

Interface

 

 

 

Figure 1.1. Conceptualization of the fiber-matrix
interphase.

6

The experimental study involves fabrication and curing
of carbon-reinforced epoxy-resins. A differential scanning
calorimeter, DSC, and a Fourier transform infrared, FTIR,
spectrometer are used to determine the carbon-fiber effects
on epoxy-resin cure characteristics. DSC should show an
increase in the reaction exotherm if additional epoxy
molecules react with carbon-fiber surface groups. FTIR
spectroscopy should show a decrease in the epoxy-intensity
ratio if additional epoxy molecules react with carbon-fiber
surface groups. Then, the cure data is fit to an
autocatalytic cure-kinetic and Arrhenius-temperature model.
Any thermal or kinetic differences between neat and carbon-
reinforced epoxy-resin cures is attributed to interactions

in the fiber-matrix interphase.

CHAPTER II

BACKGROUND AND LITERATURE REVIEW

Before the experimental study was performed, a review
of related literature was conducted. First, the chemical
structure of the carbon fiber and epoxy resin was
discussed. Next, the epoxy-resin cure was described and
several cure-kinetic models were evaluated. Finally, the
chemical nature of the fiber-matrix interphase and
experimental results from other composite characterization

studies were summarized.

A. Carbon Fibers

Appreciable interest in carbon fibers had originated
in 1880, when the incandescent lamp was created by Thomas
Edison [12]. He made carbon fibers by carbonizing natural
cellulose fibers, such as cotton or linen. In the 19505,
the Wright-Patterson Air Force Base had produced carbon
fibers from pyrolyzed viscose rayon [13]. A significant
breakthrough in carbon-fiber technology had occurred around
1965, when researchers discovered that they could form
high-strength carbon fibers. These high-strength fibers

were formed by subjecting mesophase petroleum pitch to a

8
continuous tensile stress at high temperatures. Today, the
most common carbon fibers used in composite technology are
those prepared by the carbonization of polyacrylonitrile,

PAN [14].

The basic goal in carbon-fiber development was to
produce a high density of graphitic basal planes which were
oriented parallel to the fiber axis [15,16]. A distinction
between carbon and graphite fibers should be made. Carbon
fibers were usually fabricated at temperatures of 1000°C to
1500°C and contain only 96% carbon [18,19]. 0n the other
hand, graphite fibers, were fabricated at temperatures up
to 2500°C and contain at least 99% carbon [20]. Graphite
fibers have a higher degree of orientation than carbon
fibers. Manufacturers primarily used carbon fibers in
composite fabrication: therefore, only carbon fibers were

tested in this study.

Both high-strength and high-modulus carbon fibers
exist. Table 1.1 lists several properties of commercial
high-strength and high-modulus carbon fibers [21]. The
difference between these two fibers was, simply, high-
strength carbon fibers have a higher tensile strength and
high-modulus carbon fibers have a higher Young's modulus.
In this study, only high-strength carbon fibers were

considered.

9

Table 11.1. Comparison of high-strength and high-modulus
carbon fibers [21].

 

 

Fiber Type High-Strength High-Modulus
Modulus (psi) 30.0 x 106 55.0 x 106
Tensile Stren (psi) 3.9 x 105 3.2 x 105
Density (g/ ) 1.8 1.9
Fiber Diameter (um) z 8 z 8

 

 

 

1. Fabrication

High-strength carbon fibers were formed by forcing the
polyacrylonitrile, PAN, precursor material through an
orifice. The chemistry of formation of the PAN precusor is
given in Figure 11.1. [14]. The degradation of PAN was
initiated by an impurity anion, X, (Figure II.1(b)) which
was derived from a cyclization to yield an impurity or
degradation product (Figure 11.1(a)). This initiation was
succeeded by a cyclization to yield an imine structure
(Figure 11.1(c)), which tautomerized into an enamine
structure (Figure 11.1(d)). Then, this enamine oxidized to
give the final pyridone structure (Figure II.1(e)). The
sequence of cyclized groups in the ladder structure
provided rigidity along the chain and maintains this
structure by extensive interchain bonding between the

polymer chains through C=0 and N-H groups.

10

a.
Vfiflf
X C" II .
b. (\p n
x’ NyCN/CN/CN
It
\ \ \ ,
X N N N N
If
X It I} it N".
OI

Figure 11.1. Decomposition of polyacrylonitrile, PAN, at
200°C under reduced pressure [14].

These fibers were then heated in an oxygenated
atmosphere at temperatures up to 400°C, and partially
graphitized in the presence of an inert gas at temperatures
up to 600°C, shown in Figure 11.2. When the temperature
reached 600°C, dehydrogenation occurred, and singular
hexagonal chains began to form small graphitic basal

planes.

11

Next, the temperature was increased from 600°C to
1500°C denitrogenation occurred [14]. During the
denitrogenation step, the small graphitic planes combined
to form larger graphitic basal planes and evolved volatiles
such as 3;, HCN, N33, co, coz, and N2 [3,7,14,18-21]. A
few of these volatiles remained as functional groups on the
carbon-fiber surface. These functional groups aided in
adhesion and were an important part of the fiber-matrix

interphase.

 

Figure 11.2. Dehydrogenation and denitrogenation of
polyacrylonitrile, PAN [11]. _

12

2. Topography

The carbon-fiber structure was very important when
considering the fiber effects on epoxy-resin cures.
Chemical constituents on the carbon-fiber surface were
responsible for adhering to the epoxy resin in the fiber-

matrix interphase.

a. Fiber Structure

The main structural units of the carbon fiber were
crystallitic columns. These crystallite columns contained
numerous arrays of graphitic basal planes oriented roughly
parallel to the carbon-fiber axis, as shown in Figure
111.3. The average length of the graphitic column was
estimated to be 12 basal arrays and the average graphitic

column is between 40 and 120 A [1,10].

Figure 11.4 shows that these basal planes were stacked
on top of each other in a regular abab...packing sequence
[11]. ‘Such a sequence meant that starting with one layer
(a) and using an axis normal to it as a reference, the
third layer (c) was similarly placed with respect to this
axis: whereas the second layer (b) was slightly shifted off
axis. The distance between two adjacent basal planes was

approximately 3.35 A.

13

 

f
i a
b x A
e 1
r s
52
53 ._

 

 

 

 

 

 

 

Figure 11.3. A schematic model of the crystallite columns
in a carbon fiber. The S1, 32, and S3 represent voids,
basal-plane boundary, and intercrystallite boundary,
respectively [10].

In these graphitic basal planes, the carbon atoms were
arranged in a near-ideal hexagonal matrix [22]. The
hexagonals in a graphitic basal plane have angles of 60'

between side faces, have carbon atoms at each of its

vertices, and were in parallel arrangement.

(a)

(b)

 

(C)

 

 

Figure 11.4. A schematic model of the axial hexagonal
arrays of carbon atoms in a graphitic basal plane [11].
Figure 11.5 [23] shows that a carbon fiber contained
three distinct regions, inner, middle, and outer. The
development and orientation in the inner layer was poor,
the crystallite columns were twisted and undulated. The

middle layer was better developed and highly ordered.

 

Figure 11.5. A schematic three-dimensional structural
model of a carbon fiber [23].

15

Diefendorf et al. [23] have used tunneling electron
microscopy, TEM, and described the outer untreated carbon-
fiber surface as being similar to an onion-skin structure.
Folding of the surface skin was caused by differences in
the thermal expansion coefficients of the poorly-ordered
fiber interior and the highly-ordered fiber exterior. Upon
cooling from the cure temperature, the outer carbon-fiber
surface cooled prior to the inner fiber layers. This
differential contraction placed the outer fiber surface in
compression and caused cracking and buckling of the carbon-

fiber surface.

b. Untreated Surface

Many macroscopic defects in carbon fibers were located
at the boundaries between single-crystal domains and within
non-basal plane regions of the surface. Significance of
the defects in the carbon-fiber surface comes from the fact
that the ideal graphite basal plane was inert. Thus,
chemical reactivity of a carbon-fiber was limited to these
basal-plane defect regions [24]. Figure 11.6 shows common
basal-plane defects. Table 11.1 lists the principal types
and causes of these defects in the carbon-fiber surface

[22].

16

 

Figure 11.6. Common graphitic basal-plane defects on the
carbon-fiber surface [22]: (a) hole defects: (b) claw
defects: and (c) twinning-line defects. Note: A
"twinning-line" is defined as a region in which the defect
causes a sequence of alternating four- and eight-atom
rings instead of the normal six-atom hexagonal rings.

17

Table 11.2. Principal bond defects in carbon fibers [22].

 

Types of Defects Causes of Defects

 

Edge Effects
Occurs wherever a C-C bond cannot be formed, due
to foreign atoms or molecules or misalignment of
carbon atoms.

Bond Isomerism Defects
Occurs when atoms become attached at carbon
atoms whose hybridization is sp3 in the carbon
hexagonal network, instead of the usual spz.

Chemical Effects
Incorporation of foreign atoms or molecules in
the carbon hexagonal network.

Radiation Damage Effects
Caused by bombardment with neutrons or other
high-energy radiation causing carbon atoms to
displace from their normal lattice position.

Gross Effects
Partly graphitized carbon, where only small
regions or crystallites of the carbon polymer
approximates the ideal graphite hexagonal
network: joined together by various kinds of
isomorphous carbon structures.

 

Since the untreated fiber-surface consisted of mainly
basal planes, X-ray photoelectron spectroscopy, XPS,
analyses of the bare, as-received, untreated carbon fiber
exhibited only a very small adsorption of oxygen after
exposure to air [24]. In an XPS study performed by Grant
et a1. [8], the untreated carbon-fiber surface was found
to consist of 92 atomic percent of carbon, 5 atomic percent
of oxygen and 2 atomic percent of nitrogen, and negligible

amounts of sodium and sulfur.

 

18

c. Surface-Oxidized

Manufacturers have added oxidized functional groups to
the carbon-fiber surface to enhance the adhesion of the
carbon fiber and epoxy resin. These oxidizing treatments
were performed by wet-chemical methods with either sodium
hypochlorite or nitric acid. Drzal et al. [25] have
described the oxidizing treatments through a two part
mechanism: First, the weak, outer fiber layer was removed:

second, the functional surface groups were added.

Oxidizing treatments changed the surface of the
untreated carbon fiber by [7,25]: (1) increasing the
surface area, (2) increasing the surface rugosity, (3)
reducing the tensile strength, (4) changing the chemical
functionality or reactivity, (5) removing the original
surface layer, and (6) changing the surface energy. A
chemically and structurally new region was created, much
different from the onion-skin structure of the untreated

carbon fiber.

The constituents on a surface-oxidized carbon-fiber
surface have been investigated by using wet-chemical
analyses. Donnet et al. [11] have performed chemical
reactions with the carbon-fiber surface groups and showed
that oxidative treatments add carboxylic acids, lactones,

carbonyls, and hydroxyls to the carbon-fiber surface.

19
Boehm et al. [20] have performed similar wet chemical
analyses on surface-oxidized carbon fibers. Their results
showed equivalent amounts of free carboxyl groups, lactones
with structures similar to that of fluorenscein or to a
lactol of a formyl-carboxylic acid, phenolic hydoxyl

groups, and carbonyl groups.

Several researchers [6—8,18,21] have used XPS to
identify the chemical constituents on the carbon-fiber
surface. Kozlowski et al. [21] have performed XPS analyses
on carbon fibers and detected the presence of keto-enol
type groups and carboxyl-ester groups. Denison et al. [18]
have used XPS and determined that carboxyl, carbonyl, and
hydroxyl groups present on the carbon-fiber surface. Grant
et al. [8] have found carboxylic and carbonyl groups to be
the most prevalent functionalities present, with small

amounts of phenolic and lactone functionalities.

Thomas et al. [6] have used XPS and concluded that
the carbon-fiber surface chemisorbed nitrogen. Other
surface XPS studies have shown that nitrogen in the form of
cyano or amino groups and trace impurities due to the
manufacturing process, such as silicon, sodium, and iron

were present on the carbon-fiber surface [7].

In spite of these past efforts, Sellitte et al. [27]

believed the structure of the oxidized carbon-fiber surface

20
was not well understood due to the analyses used. They
claimed the wet-chemical and XPS analyses were not
sufficiently sensitive to detect minor chemical structural
differences which were important in understanding fiber-
matrix adhesion. They characterized the surface-oxidized
carbon fibers with attenuated total reflection, ATR, FTIR,
spectroscopy. Their results yield similar carbon-fiber
constituents: phenols, hydroxyls, carboxyls, and
carbonyls. Unfortunately, the ATR-FTIR spectroscopy
analysis of carbon fibers was not fully reliable either,
because spectra were distorted by the severe scattering

phenomena and high absorbance of the carbon fibers [27-29].

To determine the constituents on the surface-oxidized
carbon fibers, Grant et al. [8] have performed desorption
studies in which carbon fibers were thermally heated under
a vacuum. The zero-order reduction of their mass data is
listed in Table 11.3 (a) and plotted in Figure 11.7 (a).
These data showed that the most abundant volatile removed
after 60 minutes at 150°C was carbon-monoxide. This
implied many C=0 groups were present on the carbon-fiber
surface or the most prevalent carbon-fiber surface groups
were carbonyls and carboxyls. Other carbon-fiber surface
components were hydrogen, methane, amine, water, nitrogen,
and carbon dioxide. Quantification of the total amounts of
volatiles desorbed are listed in Table 11.3 (b) and plotted

in Figure 11.7 (b).

 

21

Table 11.3. Volatiles on surface-oxidized carbon-fibers
[22]: (a) composition versus temperature: and (b) total
and incremental amounts of desorbed volatiles.

 

 

 

 

 

 

 

 

 

 

 

 

 

75°C 150°C 177°C 204°C
vn'r/ VHT/ vn'r/ VHT/
130 min 60 min 90 min 90 min
(mole %) (mole %) (mole %) (mole %)
H2 13 6 28 14
CH‘ 3 2 6 "
NH; 6 15 27 11
H20 25 18 14 -
C0 28 42 6 28
N2 12 8 9 -
C02 13 9 10 35
b.
Treatment Incremental Total Monolayer
Amount Amount Capacity
(monolayers) (monolayers) (moles/gm)
75°C VHT
130 min 1.6*10'2 1.6*10'2 2.61*10‘5
150°C VHT
60 min 4.6 4.62 2.61%‘10'6
177°C VHT
90 min 3.8*10'2 4.62 3.43*10°6
204°C VHT I
90 min 1.1*10'3 4.63 3.43*10'6

 

 

 

 

Note: VHT a vacuum heat treatment.

22
100

 

o—o H20
. H CO
H N2
80‘ o—o C02
‘ I—c H2

H NHJ

Mole 7.

 

 

 

 

' ' l ' r ' r V r ' ' r
70 90 HD 130 150 I70 190 2‘0
Temperature. °C

 

 

Monolayer Desorbed

 

 

 

 

 

 

 

O f. r r

0 so 160 1:50 200
Temperature. 'C

 

Figure 11.7. Volatiles from surface-oxidized carbon fibers
[8]: (a) composition versus temperature: and (b) total
amount desorbed versus temperature.

Grant et al. [8] quantified the elements in the
surface-oxidized carbon-fiber surface as 85 atomic percent
of carbon, 11 atomic percent of oxygen, 3.5 atomic percent
of nitrogen, 1.0 atomic percent of sodium, and negligible
amounts of sulfur. A comparison of the surface elements on
untreated and surface-oxidized carbon fiber is given in
Table 11.4. Based on the findings presented in this

section, a schematic illustration of the potential carbon-

fiber surface is constructed in Figure 11.8.

23

Table 11.4. Atomic percentages of constituents on the
carbon-fiber surface [8,31].

 

 

Element Untreated Surface-Oxidized
C 92.0 85.0
0 5.0 10.0
N 2.0 3.5
S <0.2 <0.5
Na 1.0 1.0

 

 

Figure 11.8. Schematic illustration of the potential
carbon-fiber surface groups [18].

 

24

B. Epoxy Resin

Epoxy resins are commonly used in high-performance
fiber composites because of their strength, chemical
resistance, toughness, and low thermal expansion on curing
[32-34]. An epoxy resin is a thermoset composed of polymer

chains which are formed from epoxy monomers:

o
/ \

R - HC - CH2
In this study, a diglycidyl ether of bisphenol A, DGEBA,
epoxy monomer was cured. Figure 11.9 shows how the DGEBA
epoxy monomer can be formed by condensing an excess of
epichlorohydrin with bisphenol A, diphenylol propane A

[33].

/o\ as that
CH3

3 0H
/0\ |
H2C —- cue"2 o——<3—.|:—<}-—ocuzcncn2
X

mg

T"°
O—O-f-O—ocuzuc — CHCHZCI

0%

Figure 11.9. Reaction of epichlorodyfrin and bisphenol A,
diphenyl propane A produces the epoxy monomer, difunctional
diglycidyl ether of bisphenol A [33].

25

Thermosetting epoxy monomers have been polymerized
with hardeners such as amines or anhydrides under the
application of heat and pressure as shown in Figure 11.10.
Under reduced pressure, the cure temperature was increased
and maintained at a level such that the liquid epoxy resin
polymerized and underwent a sudden and irreversible
transformation to an elastic gel. After gelation, the
epoxy resin was subjected to a higher cure temperature and
the pressure was released. During this post-cure stage,
the epoxy resin crosslinked and transformed from an elastic
gel to a hard, brittle glass. Unlike thermoplastic resins
which melt when re-exposed to either heat or pressure,
thermosetting epoxy resins cannot reliquidify under further

applications of heat and pressure [33].

 

O-O Pressure I 85 psi: vacuum I 28 In Hg.
H Pressure - 100 psi; vacuum - not

A

 

g

Cure Temperature, T.,°C
i

J

A

 

 

 

O
1

260 ' 360

time, t, min

C
an.
O
0

Figure 11.10. Typical cure schedule for an epoxy resin.

 

26
1. Time-Temperature—Transformation, TTT, Cure Diagrams -—

A Model of the Isothermal Cure Behavior

As Figure 11.10 shows, isothermal curing of epoxy
resin was an important part of the cure process. The time
and temperature necessary to transfer the liquid epoxy
resin into a glass-like material must be known. A typical
time-temperature-transformation, TTT, diagram is shown in
Figure 11.11. This diagram delineated five different
regions of state encountered during an isothermal epoxy-
resin cure: ungelled glass, gelled glass, liquid, gelled
rubber, and char [35].

A fully-cured epoxy resin underwent two cure stages:
gelation and vitrification. Gelation signified the
transformation from a liquid to a gel state and is shown by
the isoconversion gelation line in the TTT diagram.
Vitrification signified the transformation from a gel to a
glassy state and is shown by the 'S'-shaped line in the TTT

diagram.

27

 

gsiéuao CHAR
BER REVMIFICAUON
hm

mama ON
/ mu. an: we onmmanou

 
    
   
 

LIQUID OELLED GLASS

 

 

UNGELLED GLASS

 

 

 

time
Figure 11.11. Time-temperature-transformation, TTT,
diagram.

The relationship between the extent of cure, a, at
gelation and vitrification during isothermal cures formed
the basis of the TTT diagram. This model demonstrated that
gelation and vitrification depend on the cure kinetics, as
well as the physical parameters of the epoxy resin, i.e.,
the Tg'ult, the T9 of the unreacted epoxy resin, T90, and
the T, of the gelled epoxy resin, Tg,gel°

1n the glassy state, large-scale molecular motion did
not occur. Rather, atoms moved around their equilibrium
positions in an irregular crystal lattice. If the cure
temperature, Tc, remained below T90, reactive species were
immobilized in the ungelled glassy state and the epoxy

resin remained unreacted and processable.

28
1f the isothermal Tc exceeded the Tg',,[, the epoxy
resin gelled. In the gelled-glass state, flow
characteristics of the epoxy resin were inhibited by
interchain forces originating from either secondary forces

or chemical bonds.

If the Te remained between the T9,,,l and Tg'ult, the
epoxy resin stayed in a liquid state prior to gelation. 1n
the liquid state, polymer chains moved freely and molecules

easily slid past one another when a force was applied.

If the Te exceeded the Tg'ult, the epoxy resin gelled
and became rubber-like. The local freedom of motion of the
polymer chains was not restricted enabling epoxy polymers
to slide past one another causing the epoxy resin to
exhibit elastic properties which were associated with
typical rubbers [33]. Theoretically, in this gelled-rubber
state, the epoxy-resin cure can proceed to completion.
Unfortunately, completion of the cure reaction rarely

occurred due to thermal degradation.

Thermal degradation usually occurred at temperatures
near the T9,ult° Thermal degradation was characterized by
two processes, devitrification and revitrification.
Devitrification marked the glass-to-rubber transformation

and corresponded to a decrease of T9. Revitrification

 

 

29
marked a rubber-to-glass transformation and lead to the

formation of char [36].

The full-cure line in Figure 11.12 represented the
conditions at which the maximum reaction has occurred or
the maximum epoxy monomers have reacted. At these
conditions, the ultimate reaction exotherm, Holt, and
Tg'u[t were reached. Manufacturers strive to achieve full-
cure conditions because at full cure, the material

properties were optimized.

This section has shown that transition states of an
epoxy resin were dependent on both the Tc and t. The Tc and
t helped determine the epoxy-resin cure kinetics and the
final physical properties. By developing and using TTT
diagrams, manufacturers were able to predetermine the final

epoxy-resin properties.

2. Cure Reactions

1n the following, cure reactions responsible for the
~phase transitions in the TTT diagram were discussed.
During cure, the polyfunctional epoxy monomers were
polymerized with a hardener and transformed into a
crosslinked macromolecular structure. The most common

hardeners were difunctional or tetrafunctional amines.

30
The polymerization reactions can be described with two
reactions. The first reaction involved an epoxy monomer
and the hydrogen of a primary amine to form a branched

secondary amine [37-39]:

0 H on
/ \ I |

R-ca-CH2 + R—NH2 ———> R-N-CRHCH2 (1)
Hydrogen-donor groups, such as moisture or impurities,
catalyzed this epoxy-amine reaction. The hydrogen-donor
group attracted the oxygen atom of the epoxy leaving the
carbon atoms with a slightly positive charge. Then a
nitrogen atom on the nucleophillic hardener reacted with a
carbon atom on the epoxy. The product was a secondary

amine, which contained a hydroxyl group.

The other polymerization reaction was autocatalyzed by
the hydroxyl of the secondary amine. The secondary amine

reacted with another epoxy monomer to form [37,39]:

/\ II | I
R-CH-cn2 + R-NCRHCH2 ———> R-N- c-RHCH2

2

O H OH H OH

[ ] (2)
Here, the nucleophillic nitrogen attacked another carbon
atom of an epoxy extending the polymer chain and formed a
tertiary amine which contained an additional hydroxyl

group.

31
At gelation, the onset of the diffusion-controlled
crosslinking reaction caused a reaction-rate decrease.
This reaction-rate decrease was attributed to: (1) the
increase in viscosity imposed on the system due to lack of
diffusional transport to a reaction site: and (2) the
difficulty of forming bonds due to steric hinderance of the

polymerization products. The crosslinking reaction,

0 on -—cn——
/ \ | |
R-cn-CH2 + -—CH—- ———> oclzRHCH2 (3)
0H

involved the reaction between epoxy and hydroxyl groups on

either a secondary or tertiary amine [37,39].

Researchers [34,37,40] have generally agreed that
there is no large selectivity in the reaction of a primary
amine with an epoxy group over a secondary amine. They
also have found no evidence to support an etherification

reaction between two epoxies:

O O

/ \ / \
R-CH-cn2 + R-CH-CH2 -——> (R-O-CHZ-O)n (4)

3. Cure Characteristics

The polymerization reactions, shown in Equations 4 and

5, caused the linear polyfunctional epoxy monomers to form

 

 

32
branched polymers [32] as shown in Figure II.12(a). After
40 to 60 percent of the epoxy monomers have reacted [33],
gelation occurred. At gelation, the cure reactions shifted
from chemical control to diffusion control and the reaction
rate decreased. The diffusion-controlled crosslinking
reactions, shown in Equation 6, caused the branched
polymers to form network polymers as illustrated in Figure

II.12(b).

Figure 11.12. Schematic representation of a: (a) branched
polymer: and (b) crosslinked polymer [33].

Experimenters [2,36,41] have found that optimum
properties were attained when a stoichiometric epoxy resin

was cured. According to Chan et al. [41], gelation

33
occurred at a well-defined and calculatable stage during
cure. Consider a stoichiometric epoxy resin which
contained a mixture of epoxy monomers, A, with a
functionality of f, and hardener, B, with a functionality

of g,. The extent of cure at gelation, 09.1: was given by

ag.i=[(f.'1)(9.'l)]"’2: (5)
where f, - epoxy monomer functionality
g, - hardener functionality

Beyond the gelation point, the cure proceeded to form
an infinite network possessing the dimensions of the
reaction vessel with increased crosslink density and
increased glass transition temperature, T9 [41]. When the
Tg equaled the cure temperature, Tc, vitrification
occurred. Vitrification, as described by Enns et a1. [36],

was the transformation from a viscous gel to a glass.
a. Reaction Exotherm

The reaction exotherm was the heat literated during an
epoxy-resin cure. Two reaction exotherms have been
discussed and studied in the literature, the ultimate
reaction exotherm, Halt, and the total reaction exotherm,
H1. The Hut, for an epoxy resin was the heat literated when
all epoxy monomers have reacted. The MT was the heat
literated during an isothermal cure. Unlike the H,, the

Hal. was usually determined with dynamic temperature scans.

34
Experimental Hut, for stoichiometric epoxy resins are
shown in Table 11.5. The average experimental Hut, was
25.3 cal/mol. Studies have shown that the maximum
obtainable H, was only 85 to 90 percent of the Hut:
[22,34,42].

Table 11.5. Experimentally-determined ultimate reaction
exotherm, Hultl for an epoxy resin.

 

 

 

 

 

 

Experimenter(s) Resin Hut. Error
cal/mol
Klute et al.[43] DGEBA-amine 26.0 11.2
Prime [37] DGEBA-amine 25.0 10.94
Dutta et al.[44] DER 332-amine 25.8 11.0
Horie et al.[43] DER 332-amine 24.5 10.65
Sourour et al.[40] DER 332-DDS 26.1 10.70
This study DER 332-DDS 24.6 10.75
Average 25.3
—

 

b. Glass Transition Temperature

Many researchers [33,40,43,45,46] have investigated
the network structures of epoxy resins by studying their
glass transition temperature, T,. The T9 has been defined
as the temperature at which the epoxy resin changes from an
elastic gel to a hard, brittle glass. A shift in T9
depended upon: (1) the crosslinking effect, and (2) the

hardener effect.

A number of studies have related the degree of

crosslinking, Me, to the shift in T9. By averaging the

35

results, a rough estimate of Mc has been made [47]:

T9 - Tgo a 3.9.9.993 (6)
x,

where T,o - unreacted T,

DiBennedetto [48] has expanded this equation by relating

the extent of cure, a, to the shift in T,:

T. - I o = ( E £3. - 2,11; 1 - o : (7)
Too (1'(1'Fx/Fu)°a)

 

where E. - unreacted epoxy-monomer lattice energy,

full-cure epoxy-polymer lattice energy,

, unreacted epoxy-monomer segmental
mobility, and

F, - full-cure epoxy-polymer segmental
mobility.

"II!!!
x
I

Bidstrup et al. [48] have DSC-cured DER 332-DDS epoxy resin
and used DiBennedetto's equation to model the T, versus a
data. Their estimated values for E,/Em, F,/F,, and T,o
were 0.30, 0.18, and 293°K, respectively. Good agreement
was found between the theoretical model and their

experimental DSC data.

The hardener effect has been described as follows
[47]. As Equation 3 shows, the T, was a function of the a.
From the previous section, Equation 1 showed that the a,,l
was dependent on the functionality of the hardener.
Therefore, since the number of crosslinks directly affected
the T,, the hardener functionality either increased or

decreased the T,.

 

36

Addabo et al. [49] have stated that as the cure
temperature, T,, approached the T,, vitrification occurred.
Vitrification caused the network segments to immobilize and
cure reactions to cease. Barton [33] had found that
vitrification slows, but does not halt, the cure reactions.
Prolonged isothermal cure below the ultimate glass
transition temperature, T,,,lt, resulted in a T, greater
than the T,. The T,,,l, was the maximum obtainable T, and
occurs when all the epoxy monomers have reacted.
Experimenters [32,41] have found that epoxy resins which
were isothermally cured below their T,,,[, have a T,

approximately 10°C higher than the T,.

The T, was an important physical property of an epoxy
resin. Manufacturers optimized cure schedules to produce
epoxy resins with high glass transition temperatures. By
understanding the epoxy resin cure, particularly the cure
kinetics, prediction of the extent of cure or glass

transition temperature was possible.

c. Cure-Kinetic Models

The two epoxy-resin cure reactions, polymerization and
crosslinking, have been modeled with various cure-kinetic
models. A cure-kinetic model should be selected based on
how well the model describes the cure reactions. Some

cure-kinetic models accurately described the epoxy cure,

37
while others have major deficiencies. In this section,

several cure-kinetic models were evaluated.

Kinetic rate expressions describing the epoxy-resin
cure have been discussed in the literature [40,33,50,51].
Some of these proposed models were semiempirical in nature,
while others were based upon the detailed chemical
mechanism of the epoxy-resin cure. In general, the cure
kinetics of an epoxy resin have been modeled in two ways:
(1) nth-order kinetics: and (2) autocatalyzed reaction

kinetics.

In an early investigation by Acitelli et al. [52],
they fit their epoxy-resin cure data to an nth-order
equation,

sis-Ku-a)": (8)

dt

where K a overall reaction-rate constant,

a s extent of cure, and

N - overall reaction order.
Their cure-kinetic model assumed the following: (1)
identical cure kinetics over the entire reaction: (2) the

same reaction occurs prior to and subsequent to gelation,

and (3) the cure reaction is diffusion-controlled.

Newer findings have shown that the identical cure

kinetics are not held over the entire reaction and the

 

38
epoxy-resin cure was not diffusion controlled until after
gelation occurred. Therefore, this model did not accurately

model the epoxy-resin cure.

In a study conducted by Hagnauer et al. [53],
polymerization was assumed to be the predominant reaction
during early stages of the epoxy-resin cure. Their data

was described by the following third-order expression,

$9.- = Kc.c.2: V (9)
dt
where K = z §'(QE° + g,° ,
CE. CA.2
K' = [do/dt ],
a->0
CE = epoxy-monomer concentration,
C, = hardener concentration,
C,° 2 initial epoxy-monomer concentration, and
C,° = initial hardener concentration.

This kinetic expression gave the initial reaction rate as
the maximum reaction rate since the rate of conversion was

proportional to the unreacted epoxy-monomer concentration.

In a typical epoxy cure, the maximum reaction rate
occurred at an a between 0.30 and 0.40. The model from
Hagnauer et al. also neglected to describe the different
transitions the epoxy resin undergoes during cure and
yielded unrealistic overall reaction orders of 0.5 and 2.1
[53]. It was concluded that no nth-order kinetic models

have accurately described the epoxy-resin cure.

39

The epoxy-resin cure occurred by two simultaneous
polymerization reactions. The first cure reaction was
initiated and catalyzed by the hydrogen-donor groups, such
as impurities or moisture. The second cure reaction was
autocatalyzed by the hydroxyl groups present in the
reaction products of the first polymerization reaction
[54]. An expression which described these cure kinetics

for a stoichiometric epoxy-resin is [43,55,56]:

fig - (k1 + kzo')(1 - a"): (10)
dt
where k, 2 catalyzed polymerization reaction rate
constant,
k2 - autocatalyzed polymerization reaction rate
constant,
m - autocatalyzed polymerization reaction order,
and

n - catalyzed polymerization reaction order.

The rate constants, k1 and k2, obey an Arrhenius

temperature model:

k, = A exp( -E,/RT ): (11)

where i - reaction mechanism occurring
chronologically during the cure,

A - frequency factor,

EA = activation energy,

R a universal gas constant,
T - absolute temperature.

Dutta and Ryan [43] and Mijovic et al. [44], have used
Equation 10 and Equation 11 to model the epoxy-resin rate
constants, k1, and k2. Their experimental data fit this

cure-kinetic model well.

 

40
Sourour et al. [40] have generalized Equation 10 to
include non-stoichiometric epoxy resins and assumed that
the reaction orders, m and n, are equal to one. Their rate

equation for an epoxy resin is:
da=(k1+kz)(1-a)(B-a)r° (12)
dt

where B 8 ratio of hardener equivalents to epoxy-
monomer equivalents.

This model assumed that: (1) the exclusive reactions are
the polymerization reactions: (2) the concentration of
hydrogen-donor groups are constant throughout the reaction:
(3) the concentration of the hydrogen-donor groups is
negligible compared to the epoxy monomer and hardener
concentrations: and (4) gelation and vitrification occur
simultaneously. Unfortunately, this model was not valid
during the later stages of cure, where the reaction

mechanism is diffusion-controlled.

Further investigations of epoxy-resin cures were
conducted by Loos and Springer [57-60]. They used DSC and
found two exothermic maxima in the reaction rate, dH/dt,
versus time data. They concluded these exothermic peaks
were caused by the polymerization and crosslinking
reactions. They felt that their data could not be
correlated by a single equation. Therefore, they used the

following two equations to describe their data:

 

41

fig - (k1 + kza)(1 - a)(B - a) for a < a,,l and (13)

dt

fig = k3(1 - a) for a > a,,l, (14)

dt

where k,- crosslinking reaction rate constant, and

a'.l 3 0030

Their cure-kinetic model assumed the following: (1) the
rate constant, k3, can be correlated to an Arrhenius type
equation: (2) the model is consistent with initial and
final stages of cure: and (3) the a at gelation, a,,l,

equal to 0.3.

Careful analysis of Loos et al. experimental data
showed that their epoxy resin was partially cured prior to
DSC curing [42]. This explained why their value for a,,,
was only 0.3. According to Prime [32] gelation for epoxy

resins occurred at an a between 0.50 and 0.80.

This concludes the literature review of the cure-
kinetics models. Equations 13 and 14 were selected to
model this study's experimental data and a,,l was

calculated from Equation 1.

42

C. Reinforced Epoxy Composite

The subject of this study is carbon-reinforced epoxy
composites. In previous sections, the chemical structure
of carbon fibers and epoxy resin was reviewed. In this
section, the region between carbon fibers and epoxy resin,

the fiber-matrix interphase, was addressed.

The fiber-matrix interphase extended from the edge of
the bulk fiber material to the edge of the bulk matrix
material [1]. The "edge" of a material was defined as the
point at which the local properties begin to differ from
those of the bulk material. Figure 1.1 shows three
different regimes which were found in a carbon—reinforced
composite: (1) the bulk epoxy matrix: (2) the interphase
region, which includes the fiber-matrix interface: and (3)

the carbon fiber.

Cured commercial carbon-reinforced epoxy composites
usually have a fiber weight fraction, w,, between 40 and 70
percent [61,62]. Since the carbon-fiber diameter was
between 7 and 8 A [63,64]: average fiber to fiber distances
were on the order of several microns. Drzal et al. [1]
stated that the carbon-reinforced epoxy-composite
interphase was on the order of tenths of microns: and

Garton et al. [65] reported that the interphase was between

43
0.20 and 0.40 microns. Thus, the fiber-matrix interphase

could be 10 percent of the composite material.

1. Types of Adhesion

Physical and mechanical properties of carbon-
reinforced epoxy composites depended on the structure and
properties of the fiber-matrix interphase. Each interphase
was specific to the particular fiber-matrix system used.
However, there were generalities that apply to all systems.
According to Hull [66], the fiber-matrix adhesion could

result from any one of the following mechanisms.

(1) Physical Absorption or Wetting

Physical absorption or the wetting of the carbon-fiber
surface by the epoxy resin was critical to achieve a high
degree of adhesion bonding at the fiber-matrix interphase
[67]. Physical attraction was best understood by
considering the wetting of a solid carbon-fiber surface by
the liquid epoxy resin. Figure 11.13(a) shows that wetting
occurred when the contact angle between the carbon fiber
and epoxy resin approached zero. Figure 11.13(b) shows
that nonwetting occurred when the contact angle was greater
than 90°, which caused the epoxy resin to ball up and run

off the carbon-fiber surface [68].

       

44
a. b.
Wetting Nonwetting
e < 90°C 9 > 900,
In
\-
\I
Figure 11.13. Representation of: (a) wetting of a solid 3

with a liquid: and (b) nonwetting of a solid with a liquid
[68]. Note: 6 = contact angle.

Wetting was explained in the terms of two theoretical
equations, the Dupre equation for thermodynamic work of
adhesion, W,, and Young's equation for surface free energy.
The Dupre equation represented the work necessary for an

epoxy resin to wet a carbon fiber [68],

WA ' T1 + 72 ' 7123 (11) X

where r, = epoxy resin surface free energy,
r2 - carbon fiber surface free energy, and
112 = epoxy-hardener surface surface free
energy.

   
 
 

The W, represented a physical bond resulting from highly
localized intermolecular dispersion forces which, in an
ideal situation, can allow for very strong adhesion bet
the carbon fiber and epoxy resin. The Young's equation

related these surface free energy terms as follows:

r1 = 712 + 12 cose: (16)

where 8 a contact angle.

45
An epoxy resin with a surface energy of 43 mJ/mz readily

wets carbon fibers with a surface free energy of 70 mJ/mz.

Schultz et al. [69] have performed wet chemistry and
reverse gas-chromatography analyses on untreated, surface-
oxidized, and coated carbon fibers. Coated carbon fibers
were common commercial carbon fibers in which a protective
coating of epoxy resin was applied to the fiber surface.
Their results showed better fiber-matrix adhesion in
carbon-reinforced epoxy composites containing the coated
carbon-fibers. They claimed that acid-base interactions
between the carbon-fiber and epoxy resin caused this

increased adhesion.

Although the surface free energy was important in the
initial wetting of the carbon fiber by the epoxy resin,
initial free surface energies might not be important
factors in the final bond between the carbon fiber and
epoxy resin. Wetting was adversely affected by [70,71]:
(a) a contaminated carbon-fiber surface, which reduces the
effective surface area: (b) the occurrence of shrinkage
stresses during cure which leads to rearrangement of the
carbon-fiber surface: or (c) the overlapping of the carbon
fibers, preventing the epoxy resin from completely wetting
the carbon fibers. Figure II.14 illustrates how two carbon
fibers averted the epoxy resin from wetting isolated

contact points.

46

sea-vs

Figure 11.14. Fiber-matrix adhesion between isolated
contact points on a carbon fiber.

(2) Interdiffusion

The union of carbon fibers and epoxy resin could form
by the diffusion of the epoxy polymers into the carbon-
fiber surface. The strength of this union depended upon
the amount of molecular entanglement and the type of
bonding between the atomic constituents of the intertwined
polymers. Interdiffusion has occurred with many resins,
but because the epoxy polymers were large, the effect of
molecular entanglement with the carbon-fiber surface was
small [72]. Schultz et al. [69] have verified that the
dispersion forces or interdiffusion of the epoxy resin and
carbon-fiber surface played an insignificant role on

adhesion in the fiber-matrix interphase.

47

(3) Electrostatic Attraction

Electrostatic attraction results from forces caused by
a difference in electrostatic charge between the atoms or
molecules of the carbon fiber and epoxy resin. Again, this
attraction should not have a significant effect between the

carbon fibers and epoxy polymers [72].

(4) Chemical Bonding

Many researchers [1,2,5,20,21] have felt that chemical
bonding was an important factor in the adhesion between a
carbon fiber and epoxy resin. Prior to chemical bonding,
the epoxy monomer wet the carbon-fiber surface as
previously described. Next, a chemical bond could form
between a carbon-fiber surface group and an epoxy monomer
in the fiber-matrix interphase as illustrated in Figure

II.15.

48

 

Site at which H2 could Graphitic basal plane: Site at which H20 could
chemically bond (60). chemically bond (14).

Figure 11.16. Chemical reaction in the fiber-matrix
interphase between the carbon-fiber surface and epoxy
resin.

(5) Mechanical Adhesion

During carbon-reinforced epoxy composite cures,
mechanical interlocking of the two surfaces contributed to
adhesion between the carbon fibers and epoxy resin. The
epoxy resin formed as a brittle glass-like material around
the carbon fibers. If adhesion was solely from mechanical
interlocking when the composite was stressed, the carbon
fiber should pull from the epoxy resin leaving no signs of

a cohesive failure.

49

Drzal et al. [7] have studied untreated and surface-
oxidized carbon-reinforced epoxy composites. After
stressing the composites, they have used an ultramicrotome
to prepare samples for examination with a transmission
electron microscope, TEM. Their results indicated that the
failure in an untreated carbon-reinforced composite was
cohesive, and failure in a surface-oxidized carbon-
reinforced resin was interfacial.

ReseaEChers [4,31] have hypothesized that onion-skin
layers fracture under the residual stresses while cooling
down from fiber-processing temperatures. This tendency of
the onion-skin layer to break up into small particles and
easily pull from the fiber-matrix interface appeared to
correlate with failure at the carbon-fiber surface. This
result suggested that the onion-skin layer of the untreated
carbon-fiber surface was the weakest link in the fiber-

matrix interphase.

Electron micrographs [23] of surface-oxidized carbon-
reinforced epoxy composites have illustrated that the
fracture surfaces follow the contours of the carbon fiber.
That is, the fracture surfaces have propagated through the
fiber-matrix interphase. The fiber-matrix interphase in
surface-oxidized carbon-reinforced epoxy resins appeared to
be the weakest link in the composite. They have concluded

that fiber-matrix adhesion was of chemical nature, not the

 

50
result of mechanical adhesion between the fiber and matrix

[3,7].

In addition to these five mechanisms, phenomena such
as Van der Waals forces, hydrogen bonding, or other low
energy forces might be involved with joining a fiber to the
matrix. In this study, the effect of fiber-matrix adhesion
on the epoxy-resin cure characteristics was considered.

How the epoxy-resin cure characteristics vary gave insight

as to which type of adhesions occurred.

2. Interphase Reactions

In this section, the reaction schemes of both glass-
reinforced and carbon-reinforced epoxy resins were
considered. The chemical reactions in the glass-reinforced
epoxy interphase have been well documented [73-75]. An
understanding of how a glass fiber and an uncured epoxy
resin reacted may give insight into how a carbon fiber and

an uncured epoxy resin reacted.

a. Glass-Epoxy

The adhesion of glass fillers to epoxy resin were due
to many of the mechanisms previously described. Analogous
to carbon-reinforced epoxy resins, the strength of the

bonding between glass fillers and epoxy.resins was enhanced

51
by a surface treatment, specifically a silane treatment.
Silane-coated glass-filled surface contains R groups, as
shown in Figure 11.16(a). These R groups were any groups
which can react with the epoxy monomers. Figure 11.16(b)
shows that during the cure, some of these R groups reacted
with the epoxy monomers to form covalent bonds to the

crosslinked palymer network.

I i I
O—Si—O—Si—O—-Si—O

 

i‘f'?

             

   

   

/

All . .‘
1.5/1.2], ’v’
/ //

p// "I/ fly pr" I // . i
v, . ,, , C'- /’,/ 5.1/ ,.1/, ' 3",‘54 "’ «/. ,z/C.’, I, ,/ /

I, [I ~/ / I, /‘l/, . I an I _’ ,/ 11.“, I, ,: 3 17,]: '. V, 0).: 7' c, //.
/ x , I, -/ a . ///'-'/.r/"~" ' ’I’ x '/ ' ’// / 77”:

           

Figure 11.16. Illustration of a: (a) glass-silane
coupling-agent: and (b) the R groups covalently bonding
with the epoxy resin [2].

Evidence of chemical bonding between a silane-coupling
agent on the glass filler and epoxy resin has been obtained

from both XPS and FTIR spectrometry [2,75]. Plueddeman

[75] has postulated the following bonding mechanism: The

52
outermost layer of the glass filler consisted of physisorbed
epoxy groups. The next layer consisted of physisorbed
epoxy groups and a few chemical bonds between the glass
fillers and epoxy. In the layer adjacent to the glass
surface, interconnecting crosslinks and a three-dimensional

network existed.

b. Carbon-Epoxy

Researchers have proposed that covalent bonds occur
between the carbon-fiber surface groups and epoxy resin
[1,2,18,65,71,74]. In Section II.A, it was shown that the
most prevalent carbon-fiber surface groups were carbonyls
and carboxyls. Proposed interphase reactions between a

carbonyl and carboxyl with an epoxy monomer were [2]

- O-Hgo‘c'um

and

In both of these reactions, heat was required to
initiate the bimolecular reaction between the acidic
carbon-fiber surface groups and epoxy monomer.

17, the hydroxyl end of the carboxyl reacted with the

OH

\
Pxo

0- CHZ- CH —/V\

OH

(17)

(13)

In Equation

oxygen of an epoxy monomer and bonded preferentially with

the least steric-hindered carbon of the epoxy monomer.

Equation 18, an identical reaction occurred between the

hydroxyl end of the carboxyl of an epoxy monomer.

In

54

Fitzer [5] has proposed the following reaction,

8th 1: Fiber-Hardener Coupling

0
//
fl
C\ . ,
O-H reer
/ \

Step 2: Hardcncr-Epoxy Coupling

/OWH‘ Rrfi: -----u>
Row/N- CHZ

/' (19)
(Ken-flv\
o H
// //O T
CK , j' C\ “f“f'CH‘/Vm
0‘v4PNx IFR-
Cflz- lCH -/V\ CH2- CH -/V\
I
OH OH

between an epoxy-hardener complex and a carbon-fiber
surface group. In step 1, a hydrogen bond formed between
the oxygen atom of the carboxylic group and the hydrogen
atom of the amine group. Step 2 represented the bonding of

the epoxy monomer to a nitrogen atom of the hardener.

3. Cure Characteristics

Important reinforced epoxy-resin parameters, such as

the ultimate reaction exotherm, extent of cure, glass

transition temperature, and cure kinetics were determined

55
in the experimental study. These reinforced epoxy-resin
parameters have been studied by three teams of
experimenters, Dutta et al. [43], Mijovic et al. [44], and
Wang et al. [74]. Dutta et al. have studied the effects of
both carbon and glass fillers on the epoxy-resin cures:
Mijovic et al. have studied the effect of glass fillers on
epoxy-resin cures: and Wang et al. have studied the effect
of carbon-filler surface functionality on the epoxy-resin

cures .

Due to the lack of data on long-fiber carbon-
reinforced composites, only composite systems in which
fillers are used as the reinforcement were considered.

Both glass and carbon filler cure data were considered.

The reader should keep in mind that the physical and
morphological structure of fillers are not accurate models

of the fiber surface.
a. Reaction Exotherm

Dutta et al. [43] have investigated two important
parameters, the ultimate reaction exotherm, Hultl and the
total reaction exotherm, MT. The But, is the maximum
obtainable exotherm and occurred when all the epoxy
monomers reacted: and the HT is the reaction exotherm

necessary to fully cure the epoxy resin. They have used

 

56
DSC to cure and analyze their reinforced epoxy resins.
Their H,[, was experimentally determined from DSC analyses:
whereas their H, was experimentally determined from

isothermal-DSC analyses.

Dutta et al. [43] have studied reinforced resins which
contained one-, two-, four-, and six-percent filler
concentrations, c. Their results showed a 12-percent
increase in the nut: for glass-filled epoxy-resin cures
relative to the But, for neat epoxy-resin cures: and
the But, for the carbon-filled epoxy-resin cures showed no
significant change relative to the Butt for the neat epoxy-
resin cures. The H, for glass-reinforced epoxy-resin cures
was thirteen percent higher than the H, for neat epoxy-
resin cures: and the H, for carbon-filled epoxy resin cures

was unchanged from the HT for neat epoxy-resin cures.

b. Glass Transition Temperature

Experimenters have long been aware of the mechanical
changes that were induced in a polymer by the introduction
of a filler. Studies where fillers were added to epoxy
resins showed that the amount of filler strongly influenced

the glass transition temperature, T [17,32,74].

Experimenters have felt that these changes in the T, were

indicative of the degree of fiber-matrix interaction and

57
the fiber-matrix interactions were contingent on the

filler-surface properties.

Ko [17] has studied high-strength and high-modulus
untreated and surface—oxidized carbon-fiber reinforced-
epoxy resins. His experimental results have shown the T,
for surface-oxidized carbon-reinforced epoxy resins was as
much as 25°C higher that the T, of neat epoxy resins. His
data showed that the T, was not significantly affected by
fiber-surface treatments, but the T, was affected by the
fiber type, high-strength or high-modulus, incorporated in
the epoxy resin. He believed morphological changes in the
epoxy resin were, presumably, induced by the graphitic
basal planes at carbon-fiber surfaces. Epoxy resins were
preferentially adsorbed on the graphitic basal planes,
which created an epoxy-amine gradient near the fiber-matrix
interphase. He credited the epoxy excess in the fiber-
matrix interphase with the tighter network and increased
'r,.

Ko [17] has shown the T, increased with increasing
carbon-fiber concentration, degree of fiber graphitization,
and mobility of the epoxy chains at elevated temperatures.
His results suggested that the chemical bonding between the
fiber and epoxy resin generated by carbon-fiber surface
treatments was outweighed by surface-energy effects of the

carbon-fiber surface. Therefore, he believed physical

58
bonding was responsible for adhesion between the carbon

fiber and epoxy resin.

Wang et al. [74] have considered the effect of carbon-
fiber surface functionality on difunctional and
tetrafunctional epoxy-resin cures. Their results showed a
decreased T, for difunctional carbon-reinforced epoxy
resins and a similar T, for tetrafunctional carbon-
reinforced epoxy resins relative to neat epoxy resins.
Increased functionality of the tetrafunctional epoxy resins
allowed an increase in the number of cure reactions and the
'r,.

These results have shown that the T, of a carbon-
reinforced epoxy-resin relative to the neat epoxy resin may
increase, decrease, or remain unchanged. In summary, the
epoxy or hardener functionality takes precedence over the

carbon-filler effect on the T,.

c. Cure-Kinetic Models

In this section, previous work on the effect of
fillers on epoxy-resin cure kinetics was discussed. Two
different approaches to modeling the carbon-reinforced

epoxy-resin cure has been undertaken.

59
In the first approach, Dutta et al. [43] have studied
glass- and carbon-reinforced epoxy-resin cures. They
modeled the epoxy-resin cure with the autocatalytic cure-

kinetic model given in Equation 6.

Dutta et al. have claimed that the carbon fillers have
a more significant effect than the glass filler on the
epoxy-resin cure. They assumed that the reaction rate
constants, k, and kg, were functions of filler content,
f1(c) and f2(c), and expressed mathematically as
k, = k1'f1(c) and (20)
k2 = R2 'fz (C)? (21)
where c a filler content.
They have represented f((c) and f2(c) by fitting a third-

order polynomials to their rate-constant data:

f1(c) = 1 - 0.22s + 7.82 x 10'2c2 - 6.49 x 10’3c3 (23)
and

f2(c) = 1 - 0.14c + 5.10 x 10%2 - 4.35 x 10'3c3. (24)

(Dutta et al. have found that their cure-kinetic model
fit the experimental epoxy-resin data well. Figures
II.17(a) and (b) show that the carbon-reinforced epoxy-
resin rate constant, k1, decreased to a maximum of 16
percent and k2 decreased to a maximum of 13 percent.

Figure II.17(c) and (d) show that the glass-filled epoxy-

60
resin rate constant, k1, decreased to a maximum of 13

percent and k2 decreased to a maximum of ten percent.

 

 

 

 

 

 

 

 

—-—.-—_—.——-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

'10 u n u u u
truth-enthr-

 

Figure 11.17. Experimental results reproduced from Dutta
et al. [43]: (a) k, for a carbon-black filled epoxy resin:
(b) k, for a carbon-black filled epoxy resin: (c) k, for a
glass-filled epoxy resin: and (d) k2 for a glass-filled
epoxy resin.

1n the Dutta et al. [43] study, differences between
neat and reinforced epoxy-resin rate constants were
considered. At six-percent c, k, and k2 increased and
leveled off to a constant value which was not significantly
different than the k, and k2 values for the neat epoxy

resin. Since typical commercial composites were between

40- and 70-percent filler concentration, they concluded

61
that filler did not significantly affect the epoxy-resin

rate constants.

In the second approach, Mijovic et al. [44] have used
DSC to cure a neat and 40-percent glass-reinforced epoxy
resin and modeled the cure kinetics with Equation 6. Their
experimental data showed a decrease in the HT for glass-
reinforced epoxy-resin cures relative to the H, for neat
epoxy-resin cures. They explained that this lower value of
H, was caused by glass fillers restricting the molecular

mobility of unreacted epoxies.

Mijovic et al. [44] cure-kinetic model for neat and
glass-reinforced epoxy resins is presented in Table 11.6.
Instead of adding a multiplication factor to the rate
constants, a modified Arrhenius expression for the rate
constants, k, and kg, was used. They have found similar
values for k, and a maximum of ten-percent lower values of
k2 for glass-reinforced epoxy resin cures when compared to
neat epoxy-resin cures. Their cure kinetic model showed a
98- to 99- percent decrease in frequency factors and a 34-
3l-percent decrease in activation energies for glass-
reinforced epoxy resins relative to neat epoxy resins. An
explanation for the decreased frequency factor and
activation energy was offered in terms of restrictions to

molecular mobility imposed by the glass filler.

62

Table 11.6. Mijovic et al. [44] cure-kinetic model for a
neat and 40% glass-reinforced epoxy resin.

 

 

Kinetic equation:

QR ' ( k1 + k2 a" I ( 1 ’ a )"3
dt
where k, = A1e‘EA/RI),
m 0.5 - 0.7, and
n 1.3-1.5.

Kinetic parameters:

 

 

 

 

 

 

 

 

 

 

k1 k2
A E, A a,
neat resin 2.22 -21.8 1.21 -15.7
x 108 x 106
reinforced 1.34 -15.0 2.41 -12.3
x 10‘5 x 104

 

 

 

d. Mechanical Properties

In an attempt to determine the effect of surface
oxidation of a carbon fiber in promoting fiber-matrix
adhesion, many researchers have studied the interfacial
shear strength and tensile strength of carbon-reinforced
epoxy composites [2,3,4,17,23,31,77,78]. These studies
have shown that interfacial static mechanical properties
nor the fracture properties were greatly affected by the

fiber-matrix interphase [3].

63

.Drzal et al. [7] have compared untreated and surface-
oxidized carbon-reinforced epoxy resins. Their data showed
that the interfacial shear strength for the surface-
oxidized carbon-reinforced resins is over three times that
of the untreated carbon-reinforced epoxy resins. Table
11.4 shows that the oxygen content in the surface-oxidized
carbon fibers is double that of the untreated carbon
fibers. They have attributed the interfacial shear
strength increase to the increased interactions between the
acidic carbon-fiber surface groups on the surface-oxidized

fibers and the polar-epoxy monomers.

Many experimenters [2,3,77] have studied the
interfacial shear strength of a carbon-reinforced epoxy
composite. Herrick [3] has shown that increasing the
chemical functionality by oxidation improves the
interfacial shear strengths of carbon-reinforced epoxy
composites. Ko [17] has reported that the interfacial
shear strengths of composites containing surface-oxidized
carbon fibers are 1.6 times higher than those from
untreated carbon fibers. Scola et a1. [2] have shown a 90-
to 120-percent improvement in the shear strengths of
surface-oxidized carbon-reinforced epoxy resins relative to
the neat epoxy resins. Using single fiber studies, Drzal

et a1. [4] have found a maximum of loo-percent increase in

64
the interfacial shear strength for surface-oxidized carbon-
reinforced composites relative to untreated carbon-

reinforced composites.

Surface-oxidized carbon-reinforced epoxy-resin
experiments implied that better fiber-matrix adhesion
occurred relative to the untreated carbon-reinforced epoxy
composites. Results from Riggs et al. [78] showed that
surface-oxidized carbon-reinforced epoxy composites'
exhibited increased shear strength relative to untreated
carbon-reinforced epoxy composites. The data also showed
that the surface-oxidized carbon-reinforced epoxy resins
decreased in the tensile strength relative to untreated
carbon-reinforced epoxy resins. Rand et al. [2] have found
a tensile strength decreases were accompanied by increases
in the Young's Modulus for surface-oxidized carbon—
reinforced epoxy resins relative to untreated carbon-

reinforced epoxy resins.

Wang et al. [74] have studied the effect of carbon-
fiber surface functionality on epoxy-resin cure reactions.
They have considered four different carbon-fiber surface
treatments on an epoxy resin prepared from a difunctional
epoxy monomer and difunctional hardener. Their results
indicated a reduction in the H, for reinforced epoxy-resin

cures relative to the neat epoxy-resin results. They

65
concluded that the carbon-fiber surface functionality had

little effect on the epoxy-resin cure.

Next, Wang et al. [74] have cured an epoxy resin
prepared from a tetrafunctional epoxy monomer and
tetrafunctional hardener. They concluded that similar H,
is found for the neat and carbon-reinforced epoxy-resin
cures. They have attributed the difference in the H,
between the difunctional and tetrafunctional epoxy-resin
cures on the greater importance of the crosslinking
reactions during the tetrafunctional epoxy-resin cures.
The increase functionality in the tetrafunctional epoxy
resins allowed extra intramolecular reaction, which
provided a means for the epoxy resin to bypass the

inhibition caused by the filler and achieve complete cure.

66

D. The Role of Cure Kinetics in Composite Manufacturing

In order to manufacture quality carbon-reinforced
epoxy composites, the cure was critically important. Cure
conditions were determined by the cure kinetics. As
previous sections have shown the cure kinetics of epoxy
resins have been well studied: but, few investigations have
existed on the cure kinetics of carbon-reinforced epoxy

composites.

Manufacturers have improved the adhesion of the carbon
fibers to epoxy resin by oxidizing the carbon-fiber
surface. Section 11.A.2 showed that the most common
functionalities added to the carbon-fiber surface are
carbonyls and carboxyls. Many researchers [1,2,5,20,21]
have hypothesized that improved adhesion was the result of
chemical reactions occur between the carbon fiber and epoxy
resin. Presently, the carbon-fiber effect on the epoxy-
resin cure kinetics is of concern to composite

manufacturers.

1. Composite Cure

Composites were processed in a variety of different

methods. Table 11.7 lists the most common manufacturing

processes.

67

Table 11.7. Composite manufacturing processes [2].

 

Manufacturing Outline of Fabrication

Route

and Processing Methods

 

Open Mold Processes:

1.

3.

4.

5.

Hand Lay-up

Chopped-strand mats, woven roving, and other
fabrics made from the fibers are placed on the
mold and impregnated with resin by painting and
rolling. Layers are built up until design
thickness is achieved. Molding cures with or
without heat or pressure.

Spray-up

Chopped rovings and resin are sprayed
simultaneously into a prepared mold and rolled
before the resin cures.

Vacuum Bag, Pressure Bag, Autoclave

Layers of fibers, usually unidirectional sheets,
are preimpregnated with resin and partially cured
to form a prepreg. The prepreg sheets are
stacked on the mold surfaces in pre-determined
orientations, covered with a flexible bag in an
autoclave at the required curing temperature.

Filament Winding

Continuous rovings or strands of fibers are
guided over rollers and guided through a bath of
resin and then wound, using a program controlled
machine, onto a mandrel at predetermined angles.
The resin is partially or completely cured before
removing the component, usually a tube, from the
mandrel.

Centrifugal Casting

Mixtures of the fibers and resin are introduced
into a rotating mold and allowed to cure in situ.

 

68

Table 11.7. (Continued)

Manufacturing Outline of Fabrication
Route and Processing Methods

 

Close Mold Processes:

1.

Hot Press Molding, Compression Molding
Heated matched dies or molds are loaded with raw
material (sheet molding compound, dough molding
compound, cloth or unidirectional prepreg)
pressed to the shape of the cavity and cured.

Injection Molding, Resin Transfer Molding
Molten or plasticized polymer mixed with short
fibers is injected, usually at high pressure into
the cavity of a split mold and allowed to
solidify or cure.

Pultrusion
A continuous feed of fibers, in pre-selected
orientations, is impregnated with resin and
pulled through a heated die to give the shape of
the final section (e.g. tubes or I-beams).
Partial or complete cure occurs during passage
through the die.

Cold Press Molding
A low pressure, low temperature process in which
fibers are impregnated with resin and then
pressed between matched dies. Heat is generated
during the cure.

Resin Injection ‘
Fibers in cloth form are placed in the tool which
is then closed. The resin is injected at low
pressure into the cavity and flow through the
fibers to fill the mold space.

Reinforced Reaction Injection Molding
A rapid curing resin system involving two
components which are mixed immediately before
injection is used. Fibers are either placed in
the closed mold before resin is injected or added
as short chopped fibers to one of the resin
components to form a slurry before injection.

69

Aerospace and automotive carbon-reinforced epoxy-
composite parts and structures were commonly produced by
laminate-autoclave curing. In laminate-autoclave curing,
the laminate or sheets of undirectional carbon-reinforced
epoxy-resin were formed into the desired shape and exposed
to elevated temperatures and pressures in an autoclave for
a predetermined length of time. The elevated temperature
applied during cure provided the heat required for
initiating and maintaining the cure reactions. The applied
pressure squeezed out trapped vapor bubbles and excess
epoxy resin of the composite. The magnitudes and durations
of the temperatures and pressures, or the cure schedule,

determined the properties of the finished composite [79].
2. Laminate-Autoclave Curing

Common commercial carbon-reinforced epoxy composites
have been made from laminates and cured-in an autoclave. A
laminate consisted of preferentially-oriented carbon-
reinforced prepregs. A carbon-reinforced prepreg was a
sheet of long unidirectional carbon fibers impregnated with

epoxy resin.

Carbon-reinforced prepregs were fabricated with a
prepregger. Prepregging was a process in which continuous
fibers were pulled through a vat of liquid resin [61].

Then, these resin-impregnated fibers were wound on a

70
circular mandrel as a second mechanism guided the carbon
fibers longitudinally across its surface with a prescribed
tension and motion. The finished prepreg was removed from
the mandrel and cut into sheets or prepregs. These
prepregs were stacked using a predetermined-orientation to

form a laminate.

Typical thermal processing began by placing the
stacked laminate into a vacuum bag. A schematic of the
laminate-fabrication sequence is shown in Figure 11.18.
The mold was necessary to form the composite and the

bleeders were necessary to adsorb the excess epoxy resin.

 

1. base plate 6. release fabric 11. air bleeder
2. mold 7. resin bleeders 12. vacuum bag

3. release film 8. release film 13. high-

4. release fabric 9. top plate temperature
5. laminate 10. tape sealant

Figure 11.18. A schematic of a laminate-fabrication
sequence [61].

71
During autoclave curing, a vacuum was drawn on the
laminate bag. The purpose of the vacuum was to consolidate
the laminate and removed the excess air and moisture
entrapped in the epoxy resin. Air or moisture entrapped in
the composite caused voids or holes, which reduced the

composite's properties.

Autoclave curing was suitable for individually cured
composite structures made of thin, uniform laminates: but,
autoclave curing was less appropriate for composite
structures, with thick or uneven dimensions. In these
cases, unavoidable temperature gradients due to the highly-
exothermic reaction prevented uniformly- and completely-cured
structures. Figure 11.19 shows how a thick autoclave-cured
specimen can be completely cured on the outside and remain

uncured on the inside.

72

 

1.0

0.6<

0.43

Extent oi cure, a

0.2~

 

 

\J

oofih'rflifomrcfia'to

Normalized Rodius. r/ R

 

Figure 11.19. Nonuniformity in conventionally-cured epoxy
composite.

Upon cooling thermal stresses occurred, due to the
thermal expansion differences between the outer and inner
layers of the composite. This differential cooling caused
more problems when curing thick composite materials
relative to the thin composite materials by forming cracks

or voids in the composite material.

73

E. Instrumentation Overview

In order to begin to understand the problems in
composite manufacturing, experimenters have analyzed
carbon-reinforced epoxy resins with analytical instruments,
such as the differential scanning calorimeter, DSC; and
Fourier transform infrared, FTIR, spectrometer. DSC and
FTIR elucidated changes in the reaction exotherm and
chemical structure, respectively, which accompanied the
epoxy-resin cure. In this section, the theory and analysis

techniques of differential scanning calorimetry and FTIR

spectroscopy were discussed.

1. Differential Scanning Calorimeter, DSC

The technique of differential scanning calorimetry was
introduced in the form of commerical instruments during the
early 19603. The differential scanning calorimeter, DSC,
provided a convenient and useful method of monitoring the
course of exothermic reactions including those occurring
during epoxy-resin cures. The Nomenclature Committee of
the International Confederation for Thermal Analysis, ICTA,
have defined the DSC as an instrument in which the
differential heat flow was measured as a function of
temperature while the sample and reference were subjected

to a controlled-temperature program.

74
A DSC was used to obtain both thermal and kinetic
information on neat and carbon-reinforced epoxy resins.
The techniques of differential scanning calorimetry applied
to polymerization studies of epoxy resins have been
investigated by many experimenters [40,54,80,81]. The DSC

theory and analysis techniques were presented here.

a . Theory

A DSC works on a "null-balance" principal, whereby the
heat-flow difference between the sample and a reference was
translated in terms of energy per time. Parameters
obtainable from DSC analyses of epoxy resins included:
reaction exotherm, degree of cure, cure kinetics, and glass

transition temperature [54].

The heating rate was fixed, so that there is a linear
relationship between time and temperature. If m moles
reacted with a constant heat of reaction per mole, then it
was assumed that heat flow relative to the instrumental
baseline was proportional to the reaction rate:

g3 = - C ° um: (25)

dt dt

where fin - differential heat flow,

gt 2 proportionality constant, and

fin = differential change in moles.
dt

75
Integration of Equation 25 at m equal to mo and Butt equal
to zero gave C equal to H,,,/m,, where m, equalled the
initial number of epoxies. Integration of

IQHLQSI a izfimlfitl (25)
Hut: “5

showed that at any time, t, H/H,,t equalled m/m,.

The reaction exotherm, H, was defined as the heat flow

up to time, t,

t
H a I fin dt. (27)
J0 dt
Most researchers have found it more convenient to work in
terms of extent of cure, a, where a = H/H,,t. Dividing
Equation 27 by H,,,, became

S19. 3 1.911819. (23)
dt Hult

Data acquisition was performed by data analyzers
connected to differential scanning calorimeters.
Instantaneous data reduction allowed the experimenter to
generate real-time plots. Various software packages

allowed experimenter to manipulate the cure kinetic data.

76

b. Analysis Techniques

The main advantages of the DSC were the relative ease
of operation and the requirement of small sample sizes
[54]. This techniques was very useful as a means of
following the overall course of the cure reactions through
changes in heat evolution, or changes in glass transition

temperature, T,.

Two DSC techniques used to study epoxy-resins, were
dynamic and isothermal curing. Many researchers [32,80]
have attempted to obtain from one dynamic-DSC experiment
all the cure-kinetic information available in a series of
isothermal-DSC experiments. Although dynamic-DSC
experiments were easy and quick in execution, Barton [34]
advised experimenters to obtain isothermal-DSC data at
several different cure temperatures. Prime [37] stated
that dynamic-DSC experiments gave activation energies
higher than isothermal-DSC experiments. Other researchers
[32,53,56] have shown that dynamic-DSC data, if modeled
with the Arrhenius-temperature law, yielded kinetic
parameters which were grossly in error. Based on these
findings, isothermal-DSC experiments were usually conducted

to obtain the epoxy-resin cure kinetics.

77

2. Fourier Transform Infrared, FTIR, Spectrometer

1n the past, infrared spectroscopy has been proven to
be time-consuming, expensive, and a very difficult task due
to limited computer facilities. However, with the
development of the fast Fourier transform algorithm and
advancement in computer technology, this difficulty has
been overcome. Today, real-time spectra could be obtained
within seconds. Many experimenters feel no other
analytical technique can yield so much information on the
molecular contituency of organic materials as conveniently
as FTIR spectroscopy [83,84]. In this section, the FTIR-
spectroscopy theory and techniques applied to epoxy-resin

cures were presented.
a. Theory

Detailed explanations of FTIR-spectroscopy theory were
found elsewhere [83,85], only an elementary discussion was
given here. A simplistic model of a FTIR spectrometer, the
Michelson Interferometer, is illustrated in Figure 11.20.
In general, an interferometer consists of stationary and

moveable perpendicular mirrors.

78

 

 

 

 

 

UNMODULATBD
INCIDENT BEAM
a .
M0 L8
MIRROR SOURG
U V BEAM
MODULATED SPLITTER
EX" BEAM
m

 

 

 

figure II.20. Illustration of the Michelson Interferometer
Once the experimenter activated the laser beam, half
of its incident radiation was reflected to the fixed mirror
and half of its incident radiation was reflected to the
moving mirror. Assuming monochromatic light and equal
pathlengths, either the two light beams returned to the
beam splitter in phase and constructively interfered
producing a maximum detection response, or returned out of

phase and destructively interfered.

Each frequency was treated independently and the
output was the sum of all the cosine oscillations caused by
the optical frequencies of the source. This result was

expressed mathematically as [83]:

79

+m
I(x) a [ B(v)cos(2xv) dv: (29)
J-m
where I(x) - interferogram intensity,
x a mirror displacement,
B(v) - source intensity, and
v a frequency.

The experimenter was usually interested in obtaining a
spectra in the frequency domain. Therefore, the spectrum,
B(v), was transformed by the following equation, which
represented one-half of the cosine Fourier transform pair
[83]:

+00
B(v) - [ I(x)cos(2xv) dx; (30)
4

Equations 29 and 30 related the interferogram intensity
I(x) and the spectrum B(v). A personal computer was often
programmed to perform the transformation and quickly
produced the resultant infrared spectrum for the

experimenter.
b. Analysis Techniques

An instrumental advantage of FTIR spectroscopy was
that it allows the experimenter to use a variety of
sampling techniques. The techniques commonly used to
characterize the epoxy resins include transmission,

internal reflectance, and diffuse reflectance spectroscopy.

80
With FTIR spectroscopy, the most desirable sample was
one producing the highest signal-to-noise ratio rather than
the high signal. If transmission FTIR-spectroscopy
measurements were coupled with signal averaging, very high
signal-to-noise ratios were obtained. Figure II.21(a)
illustrates the transmission-FTIR spectroscopy mode of

analysis [83].

a.

SAMPLE
mowem TRANSMITTED
l

b' INCIDENT 0,] REFLECTED
0‘ CRYSTAL
,SAMPLE ,

c- mcnoem oussuse

WPONENT
l

L , f...
I ." ./

/ \ -.'
/,. ,

‘A

b MI’LE

 

.—

Figure 11.21. FTIR-spectroscopy analysis techniques: a)
transmission; b) single internal reflection, IRS; and c)
diffuse-reflectance, DRIFT [83]. (Note: 8 = contact
angle)

81
One problem with transmission-FTIR spectroscopy was
maintaining a straight baseline. To maintain a straight
baseline, it was necessary to keep the absorbance in the

linear range of the Beer-Lambert law [85],

I = e‘"Y; (31)
where I 8 internal transmittance,
w - absorption coefficient of the material, and
y - uniform sample thickness.
To achieve linearity, experimenters kept the concentration
of epoxy resin in the transmission FTIR-spectroscopy
specimen at sufficiently low levels so the absorbance
reading was between 0 and 80 percent. This reduced the
spectral artifacts generated during the data processing
steps [83]. Of course, a linear optical signal required
that the infrared sample had no residual orientation, such
as voids or holes, and an uniform distribution of material.
Thus, careful sample preparation was necessary to obtain

reproducible transmission-FTIR spectra [85].

In FTIR internal reflection spectroscopy, IRS, the
incident beam passes through the prism onto the sample, as
illustrated in Figure II.21(b). Good optical contact
between the crystal and sample was essential. The degree
of contact between the crystal and sample was difficult to
reproduce and restricted the comparative and quantitative
aspects of the technique. Presently, the spectra obtained

with FTIR-IRS is not as accurate as spectra observed with

82
transmission-FTIR spectroscopy [85]. The long wavelength
side of the absorption bands in FTIR-IRS spectra distorted

and lengthened relative to transmission-FTIR spectra.

Diffuse-reflectance, DRIFT, FTIR spectroscopy appeared
to be the best suited for carbon-reinforced epoxy resins
[29,83,85]. Mertzil et. al. [85] mentioned that the DRIFT-
FTIR spectroscopy was superior for examining composite
materials since minimal sample preparation was required.
Young et. al. [83] stated that DRIFT-FTIR spectroscopy can
be used successfully for the study of surfaces and of bulk
samples which are finely ground. Cole et al. [29] reported
that an advantage of DRIFT-FTIR over IRS was that no

physical contact with the sample surface was required.

DRIFT-FTIR spectroscopy has been used in the visible
and ultraviolet frequency region for a long time, but was
only recently utilized in the mid-infrared region. As
illustrated in Figure II.Zl(c), diffuse reflectance arose
from radiation penetrating into the interior of an opaque
sample and re-emerged after being scattered numerous times.
DRIFT-FTIR spectroscopy relied on the measurement of the
reflected light from a powdered sample radiated with light.
Off-axis ellipsoidal mirrors collimated the reflected
radiation. The measurement required sufficient scattering

for isotropically reflected light. This was possible if

83
the powdered samples were finely ground and combined at

three to five percent with a nonabsorbing powder.

In the DRIFT-FTIR spectroscopy measurements, the
analog to Beer's law for transmittance-FTIR spectroscopy,

was the Kubelka-Munk equation.
NR.) = 1.1_:_B.l2 = a..: (32)
2 R. s

where R. - the sample diffuse reflectance, assumed to
be infinitely thick,
a, - molar absorption coefficient, and
s a scattering coefficient.
The Kulbelka-Munk equation was derived for infinitely thick,

weakly absorbing and highly scattering samples.

The scattering coefficient, s, was often assumed to be
constant at any wave number in the spectrum, but 5 was
affected by such variables as particle size, particle size
distribution, packing density, and moisture content [86].
Fuller [28] stated that for dilute samples in low absorbing

matrices,

a, = 2.303 5 cm; (33)

where e a molar absorptivity, and
ch a molar concentration.

Substitution of Equation 33 into Equation 32 demonstrates
how the Kubelka-Munk function was directly affected by the

sample concentration.

84

A linear relationship between the Kubelka-Munk
function, F(R.), and sample concentration occurred when s
was isotropic [86]. Under this condition, the Kubelka-Munk
theory related the sample concentration and scattered
radiation intensity much in the same manner as the Beer-
Lambert law of transmission-FTIR spectroscopy given in
Equation 31. Manufacturers have utilized these two
equations in software applications which provided
experimenters with comparable transmission-FTIR and DRIFT-

FTIR spectra.

In light of these findings, the uncured epoxy resins
are usually analyzed with transmission-FTIR spectroscopy
and the cured epoxy resins are analyzed with DRIFT-FTIR
spectroscopy. Irregardless of either FTIR-spectroscopy
technique used, the extent of cure, a, for the fully-cured

DGEBA epoxy resin was calculated by [87,88]

1 - Ai21§l_Aoill§&lJ I (34)

a:
A(1184) A°(916)
where A(916) = absorbance at 916 cm'1 of fully-cured

epoxy resin,

A°(1184) = absorbance at 1184 cm'1 of unreacted
epoxy resin,

A(1184) = absorbance at 1184 cm'1 of fully-
cured epoxy resin, and

A°(916) = absorbance at 916 cm'1 of unreacted

epoxy resin.

To help eliminate sample path-length variations, the epoxy-
intensity peak area was normalized by dividing by the

reference peak area at 1184 cm“. The intensity peak at

85
1184 cm'1 was caused from the C-C bond stretching of the
bridge carbon atom between the two p-phenylene groups [85].
Some experimenters have used the aromatic intensity peaks
at 1501 or 1607 cm’1 for the reference [87]. In this
study, the intensity peak at 1184 cm" peak was selected
over the aromatic intensity peaks at 1501 and 1607 cm“1 due
to the interference with the changing primary- and

secondary-amine bands at 1508 cm'1 and 1625 cm'1 [88].

CHAPTER III

EXPERIMENTAL STUDY

An experimental study was conducted to determine the
effect of carbon fibers on the cure characteristics of an
epoxy resin. Any cure differences found between neat and
carbon-reinforced epoxy-resin cures were attributed to
interactions in the fiber-matrix interphase. Two
analytical instruments, a differential scanning
calorimeter, DSC, and Fourier transform infrared, FTIR,
spectrometer, were used to analyze cured epoxy resins.
Extent of cure and glass transition temperature data were
generated for both neat and carbon-reinforced epoxy resins.
Then, cure-kinetic parameters for neat and carbon-
reinforced epoxy resins were modeled with the proposed
autocatalytic cure-kinetic model and Arrhenius-temperature
law. These cure characteristics were compared to gain
insight into interactions between carbon fibers and epoxy

resin.

A. Sample Preparation

All of the following materials were stored at room

temperature under dark, dry conditions until needed to

86

87
prevent degradation. The materials were used as supplied
without further purification or any other treatment. The
epoxy DER 332, is a commerical diglycidyl ether of
bisphenol A, manufactured by the Dow Chemical Company [89].
This epoxy was chosen because of its high purity and low
viscosity. These epoxy properties facilitated the
impregnation of the carbon fibers during sample
preparation. The hardener was diaminodiphenyl sulfone,
DDS, manufactured by the Aldrich Chemical Company [90].
Molecular structures of both the epoxy and hardener are
shown in Figure 111.1. This epoxy and hardener combination
has been used by other experimenters, such as Chan [41],
Sourour [40], and Dutta [43], allowing a direct comparison

of this study's experimental results.

a. _' —
0 CH2 OH T“: 0
/ | n / \
.2. _\..._.o.@|s@.cu,mcm_-o@s@-wc_m,
l
L CH2 CH2

 

 

b. o

H H H
H>”Hfi”<fl

Figure 111.1. The molecular structure of: (a) DER 332
[89]; and (b) DDS [90]. one equivalent of liquid epoxy and

88

To prepare a well-mixed, stoichiometric epoxy resin,
powdered hardener were weighed. One mole of epoxy,
molecular weight equal to 342.5 g/mol, equals two
equivalents of epoxy groups and one mole of hardener,
molecular weight equal to 168.0 g/gmol, equals four
equivalents of amine groups. The epoxy was agitated and
heated at 5'C/min. At 100°C, the hardener was added to the
epoxy forming a milky-white suspension. At 130’C, this
epoxy resin abruptly turned into a clear, homogeneous,
amber-yellow liquid. When the last hardener crystal
dissolved, the epoxy resin was removed from the heat source
and quenched to room temperature. Then, the epoxy resin
was degassed in a vacuum oven at 80°C and 30 inches of
mercury for three hours. This epoxy resin was either used
immediately or stored in a desiccator at 4°C for no more

than 30 days.

Long, high-strength, untreated carbon fibers, AU4, and
surface-oxidized carbon fibers, A84, manufactured by
Hercules Incorporated, were used as reinforcements.
Considerable care was warranted to develop a suitable
laboratory technique for the preparation of carbon-
reinforced epoxy composites. The technique that evolved
met the criteria of minimum void space, good wetting of the
carbon-fiber surface, and a random distribution of fibers.
Carbon-reinforced epoxy-composite specimens were prepared

from a prepreg, a film of epoxy-resin impregnated

89
unidirectional carbon fibers. In this study, carbon-
reinforced epoxy prepregs were prepared with a prepregger
machine manufactured by the Research Tool Company, shown in

Figure III.2.

 

Figure III.2. Photograph of a prepregger machine
manufactured by the Research Tool Company.

Figure III.2 illustrates how a carbon-fiber tow, a
bundle of 12,000 fibers, was spooled on the back of the
prepregger (a). Then, the carbon-fiber tow was threaded
through a heater (b) in which the fibers were preheated to
180'C to allow the desorption of volatiles. Finally, the
carbon-fiber tow was pulled through the prepregger-resin
vat (c) and spun onto a polycarbonate-covered l4-inch
diameter mandrel (d). Polycarbonate was used to prevent

the prepreg from adhering to the mandrel.

90

Caution was taken to avoid overheating the epoxy resin
in the prepregger-resin vat to minimize the possibility of
reaction. Prior to impregnation, the gelation glass
transition temperature, Tg'gel, was determined with a
Brookfield viscometer. The Tg'gel is defined as the
temperature where the epoxy resin undergoes a change from
an ungelled glass to a viscous liquid. As the viscometer
temperature increased, a dramatic drop in viscosity
occurred at T,,,,l. The Tg'gel for DER 332-DDS epoxy resin
was found to be 80’C. Thus, the prepregger-resin vat was
maintained at a 80'C throughout the impregnation process.
This insured that a proper resin viscosity was maintained,
which allowed the epoxy resin to flow and wet the carbon

fibers.

The mandrel was rotated at a speed of 20 r.p.m.,
therefore, approximately two hours were needed to cover the
mandrel with epoxy-impregnated fibers. A 14- by 84- inch
polycarbonate film was cut and placed over the epoxy-
impregnated fibers. This reinforced epoxy resin sandwiched

in polycarbonate is called a prepreg.

ASTM D 792, method A1 [91], was used to find the
density of the prepreg by the displacement of water. The
prepreg density, dp, was found by immersing a specimen in

water and performing the following calculation:

91

dp=d.°(m/B): (35)
where d" - water density,
m a specimen weight in water, and
B - buoyancy force of the water.
Next the fiber-weight fraction, w,, of the uncured
prepreg was determined by refluxing the specimen in acetone
at 25'C for 90 hours. After drying at 100°C, the carbon

fibers were weighed to give an average w, of 0.60. The

fiber-volume fraction, vf, was calculated by

vfgwf ° (dp/df): (35)

where d, a fiber density.

The average v, for the uncured prepreg was 0.51. To ensure
good matrix wetting of carbon fibers, the void fraction,
v0, of the prepreg was found. The V0 between 0.03 to 0.06

was obtained by

 

Vo=1-Vf-[_Qp-Vf°df_], (37)
d...
where d, = epoxy-resin density.

A photograph of a test specimen with w, equal to 0.60, v,
equal to 0.51, and v0 equal to 0.05 is shown in Figure

III.3.

92

 

Figure 111.3. A 500x photograph of a carbon-reinforced
epoxy composite with a fiber-weight fraction, w,, of 0.60.

The confidence limits on measured values of d,, dm,
dc, and the calculated v, had an accumulated error of 1.5
percent [17]. However, similar consideration showed that
the error transferred to V0 was 6.5 percent. Since vo lies
in the range of 0.03 to 0.06, this calculation was only

helpful in eliminating grossly-flawed specimens.

Neat and reinforced epoxy resins with carbon fiber-
weight fractions of 0.01, 0.10, and 0.60 were examined. To
make composites with fiber-weight fractions of 0.01 and
0.10, partially-cured epoxy resin from the prepregger-resin
vat was added to premeasured amounts of carbon-reinforced

epoxy prepregs. This mixture was agitated at 80°C until

93
the carbon fibers were well-distributed throughout the

epoxy resin.

Next, DSC and FTIR-spectrometer test specimens were
prepared. DSC test specimens were made by placing material
which contained five to fifteen milligrams of resin in a 4
mm-diameter DSC-sample pan and sealed with a DSC-sample pan

cover 0

Uncured and cured FTIR-spectroscopy test specimens were
prepared differently. Uncured-FTIR epoxy-resin samples
were analyzed with transmission-FTIR spectroscopy. These
transmission-FTIR test specimens were prepared by combining
stoichiometric amounts of acetone-dissolved epoxy and
hardener. Two to three drops of this mixture were placed
on a KBr pellet and allowed to dry before analysis. A
pellet was formed by pressing 300 milligrams of the KBr
powder at 10,000 psi approximately five minutes or until

the center of the disk was transparent.

Cured-FTIR epoxy-resin samples were analyzed with
DRIFT-FTIR spectroscopy. These DRIFT-FTIR spectroscopy
test specimens were prepared by placing the neat and
carbon-reinforced epoxy resins in 0.5 cm X 0.5 cm X 2.5 on
silicon molds. Then, specimens were fully-cured in a
convectional oven and filed into small particles which were

further ground into a powder with a mortar and pestle.

94
Approximately fifteen milligrams of this specimen powder
was homogeneously mixed with 240 milligrams of KBr powder.
Then 150 milligrams of this mixture was placed on a 1-cm
diameter DRIFT-FTIR spectrometer sample holder, levelled

without using a spatula, and analyzed.

B. Experimental Instrumentation

In this study, the DuPont 9900 DSC and Perkin-Elmer
1800 FTIR spectrometer were used to investigate the neat
and carbon-reinforced epoxy-resin cures. The DSC and FTIR
spectrometer were selected because of their speed, ease of
operation, availability, and low operational costs. DSC
monitored the total conversion with time; whereas, FTIR
spectrometer monitored the formation and disappearance of
specified functionalities. Detailed discussions of both

the DSC and FTIR spectrometer were given in Section II.E.

1. DSC

The DuPont 9900 DSC cell consists of a silver block
chamber which contains a thermoelectric disc with raised
platforms for sample and reference containers. A cross-
section of the DSC cell is shown in Figure III.4.
Temperature differentials between the sample and reference
were monitored by thermocouples beneath the sample and

reference platforms. Output from thermocouples was

95
controlled and amplified by DuPont's thermal analyzer, TA,
as shown in Figure 111.5. The TA transmits heater voltages
and thermocouple signals between the programmer and the DSC
cell and provides a linear-calorimetric response over a
wide-temperature range, assuming the DSC is accurately

calibrated [92].

I‘LL
JAR

   
 

sauna '

1/ '5“ “VII me
“(AIM

" ”It“:

   

 

 

 

 

 

 

 

 

 

 

\H‘
EK‘ "' 'I». /
mm not:
cm ‘ 08: cm cums-acne!
nu

Figure III.4. Cross-section of the DuPont 9900 DSC cell
[92].

96

 

Figure III.5. Photograph of the DuPont thermal analyzer,
TA, and 9900 DSC.

The thermocouples were calibrated weekly using an
indium standard supplied the Aldrich Chemical Company.
Calibration involved exposing ten milligrams of indium to
5°C/min temperature ramp from 140°C to 170°C. The
transition area and melting point were found and compared
to the known heat of fusion, 28.4 J/g, and melting point,
156.6'C. The cell-coefficient constant and temperature

calibration were adjusted accordingly.

Precision of the DSC was checked by subjecting two
empty DSC-sample pans to a preprogrammed isothermal
temperature profile. A straight baseline was achieved by

adjusting the baseline-slope control on the DSC-cell base.

97
When balanced, the DSC monitored the differential rate of
heat evolution between the specimen and reference or empty
pan with a maximum nominal sensitivity of 0.6 mW/cm. This

gave a experimental precision of 2.5 percent.

2. FTIR Spectrometer

Infrared spectra experiments were performed on a
Perkin-Elmer 1800 FTIR spectrometer, shown in Figure III.6.
Uncured epoxy resins were analyzed with transmission-FTIR
spectroscopy; whereas, cured epoxy resins were analyzed

with DRIFT-FTIR spectroscopy.

 

Figure III.6. Photograph of the Perkin-Elmer 1800 FTIR
spectrometer.

98
Transmission-FTIR spectra were obtained by
transmitting light through a sample on a KBr pellet.
Signal-to-noise ratios were increased by averaging ten

signals to obtain one-transmission spectrum.

Diffuse-reflectance, DRIFT, FTIR measurements were
obtained with a Perkin-Elmer diffuse-reflectance, PEDR,
accessory shown in Figure III.7 [93]. Incident radiation
was reflected off of several mirrors before reaching the
sample. Then the M4 reflector collimated the diffuse
component, which was sent through another series of mirrors
on its way to the detector. Poor signal-to-noise ratios
were improved by averaging one-hundred signals to obtain

one DRIFT-FTIR spectrum.

 

 

 

 

:ZJ“

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure III.7. Illustration of the Perkin-Elmer diffuse-
reflectance, PEDR, accessory [93].

99

C. Experimental Procedure

Introductory experiments were performed with carbon
fibers and either epoxy or hardener. Next, the epoxy and
hardener were combined to form a stoichiometric epoxy
resin. Finally, various amounts of long, high-strength,
untreated and surface-oxidized carbon fibers were added to
the epoxy resin.» These neat and carbon-reinforced epoxy
resins were either DSC-cured and DSC-analyzed or
convectionally oven-cured and FTIR-analyzed. The

experimental procedure for both analyses were given below.

1. DSC-Cured and DSC-Analyzed

Isothermal DSC analyses were employed to study changes
in the reaction exotherm resulting from variations in
either fiber content or fiber-surface treatment. DSC data
collection was microprocessor-controlled,-which allowed the
operator to set various parameters for data processing.

Experimental parameters used in this study were:

Specimen: 5 to 15 mg of epoxy resin, housed in
hermetically-sealed sample pans

Program: Dynamic or Isothermal

Atmosphere: Nitrogen at 50 cm3/min

Data Sampling: 0.2 sec/data point to 5.0 sec/data
point '

Three to five scans were obtained for each DSC data point,

in an effort to reduce sampling errors and inherent

100
variations of the fiber content within samples. All
experimental data were normalized with respect to epoxy-
resin content [32,34,40]. Numerical integration of the
rate of heat generation, dH/dt, as a function of time, t

was performed by the DuPont TA.

DSC experiments of uncured epoxy resins were performed
to obtain an estimate for the ultimate reaction exotherm,
Halt. The Halt was defined as the maximum reaction
exotherm obtainable when all epoxy monomers have reacted.
DSC experiments were started by placing both sample and
reference pans on the specimen holders in the DSC cell.
Next, the preprogramed method was initiated. Figure
III.8(a) shows that analysis was performed by drawning a
sigmoidal baseline from cure initiation to cure cessation.
Integration of the area under this heat generation versus

time curve gave the Hult°

Next, uncured DSC specimens were isothermally cured to
obtain a measure of the total reaction exotherm, HT. The
H, is defined as the reaction exotherm necessary to fully
cure a specimen. A reference pan was placed on the
reference platform in the DSC cell as shown in Figure
III.4. Then, the DSC cell was preheated to the desired
_cure temperature, Tc. After the DSC cell had equilibrated,
the data acquisition was initiated and the specimen was

placed on the sample platform. Thermal equilibrium of the

101
specimen as measured by the thermocouple was achieved in
less than one minute. Figure III.8(b) shows a typical
isothermal cure curve in which a straight baseline is drawn
from cure initiation to cure cessation. The time when the
reaction is considered complete or full-cure time, t,,
occurs when the baseline becomes horizontal. Integration
of the area under the heat generation versus time curve

determines the HT.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

'Figure III.8. Experimental DSC curves of (a) the ultimate
reaction exotherm, Hut: for an uncured epoxy resin; (b)
the total reaction exotherm, H, for an uncured epoxy resin;
and (c) the glass transition temperature, T9, for a fully-
cured epoxy resin.

102
Following each isothermal-DSC cure, the specimen was
quenched to 25°C with cold tap water and the glass
transition temperature, T,, was determined. These post-
cure glass transition temperatures were obtained from DSC

analyses from 140°C to 240°C at a heating rate of 10°C/min.

Since the transition region embraced a temperature
range of about 30°C, it was necessary to define a T9. The
T, was taken at the intersection of the extrapolated
baseline at the low temperature end and a line tangent to
the inflection point. For example, the T9 in Figure

III.8(c) is 220.52'C.

2. Convectionally-Cured and FTIR-Analyzed

The FTIR-spectroscopy scanning chamber was maintained
at 25°C. All FTIR-spectroscopy analyses were performed in
an atmosphere which was continuously purged with nitrogen.

Infrared spectra were collected from 400 to 4000 cm".

The resultant spectra for either the transmission- or
DRIFT-FTIR spectroscopy specimens were the difference
between a specimen and background spectrum. The background
spectrum for transmission-FTIR analyses was a spectrum of
the nitrogen-purged spectrometer cell. The background
spectrum for the DRIFT-FTIR analyses contained non-

absorbing KBr powder with a carbon-fiber concentration

103
identical to the carbon-fiber concentration in the specimen
spectrum. The background was subtracted from the sample
spectrum by automatically scaling a band common to both

spectra.

Once the transmission- and DRIFT-FTIR spectra were
obtained, extents of cure were calculated. Equation 34
shows that the extent of cure, a, is related to the ratio
of the epoxy-intensity peak area at 916 cm‘1 and the

initial epoxy-intensity peak area at 916 cm".

Spectra of an uncured and a fully-cured epoxy resin
are given in Figure III.9. During cure, epoxy molecules
reacted with primary amines to form secondary amines.

These secondary amines contained hydroxyl groups.
Consequently, two differences between the uncured and
fully-cured spectra were found. First, a decrease in the
concentration of epoxy groups corresponded to a decrease in
epoxy-intensity at 916 cm". Secondly, an increase in
hydroxyl concentration caused an increase in the intensity

of the broad O-H stretch between 3000 - 3500 cm".

104

      

11.111111111111113... 11111111111111.1111.1111111111....
1.11.11.11.11...

1i
;
- I

          

          

 

 

     

1
1..
1155511.. _1_1_=_1_11_=_===.

1111111111111111111.1111111111111111111
11111111111111.111111.111118111111111.
11111111111 .111mm1w1ue111
11111111111111.388111111111 1
11111111111111

.11_11_1=mm...1111
ag=111§1111111

   

           

    

 

    
     

 

”nun-muu-nm-
n .._ -- -

FTIR-spectrometer absorbance spectra of:

(a) an uncured epoxy resin; and (b) a cured epoxy resin.

Figure III.9.

105

D. Experimental Results and Discussion

In a carbon-reinforced epoxy resin, two different
materials have been united to form a composite with
physical properties different from either component.
Carbon-fiber experiments were conducted prior to adding
fibers to the epoxy resin. Next, epoxy resins containing
various amounts of high-strength, untreated and surface-
oxidized carbon fibers were thermally cured. These
experiments were conducted to determine the carbon-fiber
effect on the epoxy-resin cure parameters or

characteristics, listed in Table III.1.

Related terminology in the previous table include the
following. The ultimate reaction exotherm, Halt, and glass
transition temperature, T,, of epoxy resins were found from
DSC measurements. Isothermal-DSC curing determined the
total reaction exotherm, 8,, which was used to estimate the
extent of cure, a, and cure kinetics. FTIR-spectra of the
cured epoxy resins were also used to calculate the extents
of cure. These FTIR-spectroscopy a results were compared
with the DSC-a results. Finally, a comparison between neat
and carbon-reinforced epoxy-resin cure characteristics was
performed to determine if carbon fibers affected the epoxy-

resin cure characteristics.

Table III.1.

 

106

Cure Characteristics.

 

 

 

Symbol Description
a Extent of Cure
P w
5916_ Ratio of uncured epoxy intensity at 916
L A1184 cm‘1 to a reference intensity at 1184 cm'1
-o
5916_ Ratio of epoxy intensity at 916cm“1 to a
A1184 reference intensity at 1184 cm'1
. 1
H,(Tc) Total reaction exotherm
Hut. Ultimate reaction exotherm
t, Full-cure time
T, Glass transition temperature
Tg'gel Glass transition temperature of the gelled
epoxy-resin
Tgo Glass transition temperature of the uncured
epoxy-resin
Tg,ul: Ultimate glass transition temperature

 

 

 

-

l. Carbon-Fiber Experiments

A literature review on the carbon-fiber surface was

presented in Section II.A. Generally, carbon-fiber

surfaces consist of inert graphitic basal planes with

primarily carbonyl and carboxyl functionalities. Several

experimenters [2,5,18,65], have proposed that chemical

reactions occur between these surface groups and epoxy

molecules

107

Cook [2] has shown two covalent-bonded reactions
between carbon fiber and epoxy resin. Such bonds were
formed between an epoxy molecule and carbonyl or carboxyl
on carbon-fiber surfaces to form either ether or ester
bonds, respectively. Fitzer et al. [5] stated that "...the
diamine hardener acts as a coupling agent between the fiber
surface and the (epoxy) monomer to form strong chemical
bonds between the fiber surface and the matrix." A
discussion of these proposed chemical reactions between
carbon-fiber surface groups and epoxy resin given in

Section II.C.

Prior to experimentation, carbon fibers were stored at
25°C. Thermal analyses were performed on bare surface-
oxidized carbon fibers to determine if carbon-fiber surface
changes occurred during thermal heating. These fibers were
analyzed with a DSC to determine if reactions can be
detected between carbon-fiber surface groups. Thermal
gravimetric analyzer, TGA, analyses were used to measure

the amount of volatiles on carbon-fiber surfaces.

It was assumed that if chemical reactions occurred
between carbon-fiber surface groups, the resultant exotherm
would be too small to be detected by DSC. This assumption
was verified by exposing surface-oxidized carbon fibers to
DSC analyses from 25°C to 250°C at 2°C/min. No exotherm

could be detected from these DSC analyses.

108

TGA analyses from 25°C to 500°C at 5°C/min were
conducted on surface-oxidized carbon fibers. TGA recorded
the weight difference as carbon fibers were heated. The
0.2-percent weight change observed was below the
experimental-error detection limit of five percent.
Therefore, this weight change was considered insignificant.
Neither the reaction exotherm nor desorption of volatiles

could be detected from thermal analyses of carbon fibers.

Next, DSC and FTIR-spectrometer experiments were
conducted on mixtures of carbon fibers, carbon fibers and
hardener, and carbon fibers and epoxy. Table III.2 lists
these test materials and gives their composition. DSC-
exothermic measurements should show an increased heat flow
if epoxy molecules reacted with carbon-fiber surface
groups. FTIR-spectroscopy epoxy-intensity ratio
measurements should show a decrease in the epoxy intensity
at 916 cm'1 if epoxy molecules reacted with carbon-fiber

surface groups.

109

Table III.2. Specimens for carbon-fiber experiments.

 

 

 

 

Experiment wt % fiber* wt % epoxy wt % hardener
carbon fiber 80 20 0

BPOXY

carbon fiber 80 0 20
hardener

 

 

 

 

* - surface-oxidized carbon fibers

 

a. Carbon Fiber and Hardener Experiments

Experiments were carried out to determine if hardener
reacts with carbon-fiber surface groups. Hardener and
surface-oxidized carbon-fiber mixtures were prepared
according to Table III.2. They were analyzed with DSC
analyses from 25°C to 350°C at 2°C/min. The only observed
baseline deviation was the hardener phase'transition from a
powder to a liquid at 178°C. No reaction exotherm was

detected.

b. Carbon Fiber and Epoxy EXperiments

Experiments were conducted to determine if epoxy
molecules react with carbon-fiber surface groups. First,
carbon fiber and epoxy resin mixtures were prepared

according to Table 111.2 and exposed to DSC analyses from

110
25°C to 350°C at 2°C/min. Again, no reaction exotherm was

found.

This result was verified by a calculation on a 0.60
fiber-weight fraction, w,, surface-oxidized carbon-
reinforced epoxy composite, given in Appendix A. This
calculation showed that if all functional carbon-fiber
surface groups reacted with an epoxy molecule, the
resultant exothermic increase would be less than one
percent. Since the precision of the DSC is approximately
2.5 percent, detecting any reaction at the one-percent

level was not possible.

The FTIR spectrometer was also used to analyze these
surface-oxidized carbon fiber and epoxy mixtures. These
test materials were placed in sterile beakers and
isothermally heated in a convectional oven at 220°C for 170
minutes. Remaining uncured epoxy molecules dissolved in
acetone; whereas, cured epoxy molecules did not. To ensure
that all unreacted epoxy molecules were removed, surface-
oxidized carbon fibers were refluxed with acetone for 90

hours.

Transmission-FTIR spectra of unused and acetone-washed
surface-oxidized carbon fibers were obtained. Because
carbon fibers tended to absorb infrared radiation across

the entire range, a difference of the two spectra was

111
obtained to eliminate the carbon-fiber effect. Epoxy-
intensity peak decreases or hydroxide-intensity peak
increases would indicate that epoxy molecules reacted with
carbon-fiber surface groups. Unfortunately, resultant
differences were less than eight percent or less than the
minimum resolution of transmission-FTIR spectroscopy
analyses. Therefore, this result was not conclusive to
support reaction between carbon-fiber surface groups and

epoxy resin.

These carbon fibers were weighed on an analytical
balance before isothermal heating and after acetone
washing. No weight change could be measured beyond the

instrumental error of the analytical balance.

Above experiments were inconclusive to confirm any
chemical reaction between carbon-fiber surface groups and
epoxy molecules. Either more precise techniques or more
sensitive instrumentation were required. Recommendations
for "interphase-specific" and "non-destructive"

experimental techniques are given in Section V.

112

2. Neat and Carbon-Reinforced Epoxy-Resin Experiments

Experiments were performed to determine carbon-fiber
effects on epoxy-resin cures. Neat, untreated carbon-
reinforced, and surface-oxidized carbon-reinforced epoxy
resins were cured to determine the cure characteristics
listed in Table III.1. The ultimate reaction exotherm,
Hult, initial FTIR-spectroscopy epoxy-intensity ratio,

( A9,6 c_-1 / A1184 ¢.-1 )0, and full-cure time, t,, were
found and used to determine the full-cure extent of cure,
a. Next, these fully-cured extents of cure were integrated
over time to obtain cure-kinetic rate constants k1, kg, and
k3. Finally, the glass transition temperature, T9, of

fully-cured specimens were analyzed.
a. Ultimate DSC Reaction Exotherm, Hut.

The ultimate reaction exotherm, Hult, for a
stoichiometric epoxy resin was defined as the total heat
liberated when all epoxy molecules reacted [40]. The Hult

was experimentally determined with a DSC.

DSC analyses were selected over isothermal analyses to
find the Halt. During DSC analyses, unreacted epoxy
molecules gained energy with increasing temperature. This
increased temperature enabled epoxy and hardener molecules

to move faster and farther in the resin.matrix. Unlike

113
isothermal cures, DSC analyses allowed more epoxy molecules
to react before becoming trapped in the matrix network

[41].

A typical DSC analysis for an epoxy resin cure is
shown in Figure III.8(b). In this study, reaction
exotherms were obtained using DSC-heating rates from
0.5'C/min to 20°C/min as shown in Figure III.10. Maximum
reaction exotherms occurred at 2°C/min. “At heating rates
slower than 2°C/min, the margin of error was large relative

to the error at 2°C/min.

 

0

total Reaction (Indium. H, J/g

f,

 

 

 

Figure III.10. Total reaction exotherm, HT, versus DSC-
heating rate for epoxy resin.

114

At heating rates faster than 2°C/min, the cure
temperature, Tc, exceeded the Tg,ul. before all epoxy
molecules reacted. Lower reaction exotherms were found due
to revitrification and devitrification of the epoxy resin.
Revitrification corresponded to a second rubber-to-glass
transformation and led to char formation. Devitrification
marked the glass-to-rubber transition led to thermal

degradation [36,41].

Ultimate reaction exotherms for epoxy-resin were
determined by integrating a DSC heat flow versus time curve
from 25°C to 322°C. Experimental Hut. for a stoichiometric
epoxy resin was found to be 24.6 i 0.75 kcal/gmol and
compared well with the literature values given in Table

II.5.

. Ultimate reaction exotherms for carbon-reinforced
epoxy resins with 0.01, 0.10, and 0.60 fiber weight
fractions, w,, are given in Table III.3. Average ultimate
reaction exotherms for untreated carbon-reinforced and
carbon-reinforced epoxy resins were 25.0 i 1.1 cal/gmol and
surface-oxidized 24.9 i 1.3 cal/gmol, respectively. This
standard deviation difference among the ultimate reaction

exotherms was not significant.

115

Table III.3. Ultimate reaction exotherm, Hult, versus
fiber weight fraction, wf.

 

w, untreated surface-oxidized
0.01 24.5 24.1
0.10 24.6 25.0
0.60 26.1 25.6

 

 

 

 

As Table III.4 shows, the chemical functionality of

the carbon fiber did not affect the Butt. This result was
inconsistent with Wang et al [74] findings. Wang et al. cured
difunctional and tetrafunctional carbon-reinforced epoxy

with difunctional hardener. They found reduced ultimate
reaction exotherms by adding carbon fibers to the

difunctional epoxy resin and ultimate reaction exotherms

were by adding carbon fibers to the tetrafunctional epoxy
resin. Wang et al. also found that the Hut. could be
increased by 26 percent depending on the carbon-fiber

surface functionality.

The Hult results, shown in Table III.4, were
consistent with Dutta et al. [43] finding. Dutta et al.
cured glass-and carbon-filled epoxy resins. Their results
showed an increased Hal. for glass-filled epoxy resins
relative to neat epoxy resins and similar Hut. for carbon-

filled epoxy resins relative to neat epoxy resins.

116

b. Initial FTIR-Spectroscopy Epoxy-Intensity Ratio,

(A916 cm" / A1134 cm°1)o

Extents of cure were calculated from FTIR-spectra as a
function of the fractional change in the epoxy-intensity
ratio, (A916 c.-1/A113‘ c.-1). The epoxy-intensity ratio
is defined as the epoxy-intensity peak at 916 cm'1 divided
by the reference-intensity peak at 1184 cm‘1 [88].
Intensity peaks at 916 cm" and 1184 cm" were proportional
to concentrations of epoxy molecules and aromatic-hydrogen
bonds, respectively. The epoxy-intensity ratio decreased
as the amount of unreacted epoxy molecules decreased. The
reference-intensity ratio at 1184 cm'1 remained constant
because aromatic hydrogens are not affected by the

polymerization or crosslinking reactions.

The maximum amount of epoxy molecules available for
reaction was estimated from transmission-FTIR spectra of an
uncured epoxy-resin mixture. The epoxy-resin film was
placed on a KBr pellet and infrared spectra from 400 to
4000 cm‘1 were collected. The data were obtained at one-
minute intervals and averaged over ten scans which gave a
spectral resolution of four cm". A spectrum of an uncured
epoxy resin is shown in Figure 111.6 (a). The average
initial epoxy-intensity ratio equalled 0.4 and was used to

calculate the FTIR-spectroscopy a, as shown in Equation 34.

117

c. Full-Cure Time, t.(Tc)

Prior to fully curing the epoxy resins, the full-cure
time, t,, was determined. Neat epoxy-resin samples were
isothermally DSC-cured at temperatures between 120°C to
250°C. A typical isotherm for the DER 332-DDS epoxy resin
is shown in Figure III.8(b). The total reaction exotherm,
H,, is dependent on the full-cure time, t.. The full-cure
time was defined as the time between cure initiation and
cure cessation. Cure initiation was chosen at the time'
approximately one minute after a specimen was exposed to
the cure temperature, Tc. Cure cessation occurred when.

the incremental heat flow became constant.

Rapid increases in heat generation prior to the
exotherm peak in Figure III.8(b) are characteristic of the
highly-exothermic, epoxy-polymerization reactions. The
decreased reaction rate after the exothermic peak was due
to the onset of the diffusion-controlled crosslinking
reactions. Leveling of the reaction rate to the original
isothermal baseline indicated cessation of the cure
reactions and the onset of vitrification [41]. The H, was
found by integrating the area under this heat flow versus
time curve with a straight baseline from cure initiation to

cure cessation.

118
The total reaction exotherm versus Tc for the fully-
cured DER 332-DDS epoxy resin is given in Figure III.11(a).
At lower cure temperatures, premature vitrification caused
reduced total reaction exotherms. As the Te increased, the
H, increased. The maximum H, of 23.4 cal/gmol for the DER
332-DDS epoxy resin occurred at 220°C. Samples cured above
220°C were darkly discolored and gave smaller total

reaction exotherms because of revitrification and

 

 

 

 

 

 

 

devitrification.
a. b. 2%
4004 §‘”. .
o 9 1
9 3 . 9
1 o o , o . .0.
o o .
g :9 93220-1 ’:
{JN‘ ' T
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209 vvvvvv 1 x . -
100 120130 160 150 200 mire zoo ‘00

 

* T' I ' I ' I ''''' fir T
100 120 I40 '60 '80 200 220 240 260

Cure YMm. T,, Q: Cure Temperature. 1". 'C

Figure III.11. DSC analyses of the: (a) total reaction
exotherm, HT, versus cure temperature, Tc; and (b) the
glass transition temperature, T9, versus Tc.

Following the isothermal-DSC cures, the specimens were
dynamically scanned to determine the glass transition
reCommended

temperature, T9. DuPont, the DSC manufacturer,

119
using a heating rate of lO'C/min for glass transition
determinations because the T, is independent of the DSC-
heating rate. Glass transition temperatures for fully-
cured DER 332-DDS epoxy resin are plotted in Figure
III.11(b). A comparison between Figures 11(a) and 11(b)
shows the T, data followed the same trends as the HT data.
This was expected since the T, is a function of the number
of molecules between crosslinks and the HT is a measure of
the number of cure reactions. Table III.4 lists the H,,

T and t. data at various cure temperatures.

”I

Table III.4. Total reaction exotherm, HT, glass transition
temperature, T,, and full-cure time, t,, versus cure
cl

 

temperatures, for neat epoxy-resin cures between 120°C

and 250°C.

W?
T, HT T, t.
120 271 141 650
130 326 154 500
140 347 167 450
150 359 177 420
160 371 187 360
170 378 198‘ ' 330
180 375 205 240
190 382 217 210
200 394 222 190
210 395 225 180
220 404 230 170
230 400 228 160
240 393 223 120
250 391 221 120

 

 

 

 

120

The T, increased with increasing T, up to the maximum
or ultimate glass transition temperature, T,,,l,. For
isothermal cures above 230°C, the T, decreased with
increasing T, because of thermal degradation and charring.
Chan et al. [41] used DSC analyses and determined the
T,,,,, for DER 332-DDS epoxy resin to be 229°C. This 1°C
difference was well within the five-percent experimental
error. Experimental precision of the DSC data is shown by

standard deviation error bars in Figure III.11.

The relationship between H, and T, formed the basis of
a theoretical model for the time-temperature-
transformation, TTT, diagram. The TTT diagram, presented
in Figure II.11 of Section 11.8.1, is a model of an
isothermally-cured thermosetting material. Appendix B
outlines the procedure for estimating the full-cure line

for the DER 332-DDS epoxy resin.

The full-cure line was determined as follows. The
total reaction exotherms given in Figure III.11(a) are
integrated at various cure times [41,94]. Next, a
logarithmic relationship between H, and T, was assumed, as
shown in Figure III.12(a). From these results, the T, can

be estimated at various cure times.

121

 

 

 

 

 

 

 

 

 

a. b.
‘60 0.0
o T. - LJO‘C

4404

420* -.2~
\o 1
'9 4001
1' . 0.
8‘ mi 3
a - -.4-1
5 + °
° -
.1: 350< I 5?
5 . . a:
'3’ 340« §
.. n -.o-
a: ‘ 7‘
_ . .
3 320~ ‘1 '
.2

300‘ —,8-1 .

‘ o
280‘
200 - , - 1
-1.0 e
4.9 . - -
5 5 1.5. 5.35 0 20: 21’: 2:25
'09 610:: Transabon Temp. log T', 'C Class Transition Temperature. T. 'C

Figure III.12. Illustration of the: (a) total reaction
exotherm, Hr, versus the log1o(glass transition
temperature, T,); and (b) log1(residual extent of cure,

a,,, = 1 - a), versus the T,.

Next a linear relationship was assumed to exist

between T, and T, at each cure time,

T,=A+BT,; (37)
where A = intercept and
B = slope.
After solving for A and B, Equation 37 enabled the
experimenter to estimate the T, any T,. According to Peng

et al. [94], full cure occurs when the T, equals T,,,[,

with:

T. = a + b (log tf)! for T, < T,,ult; (38)

where T, = isothermal full-cure temperature,
a,b = fitted constants, and
t, = full cure time.

122
to correlate isothermal cure data and obtain an estimation

()1? ‘:t1€3 12f 0

An estimation of t. was performed by replacing t. and
T, in Equation 38 with T,. The constants, a and b, for DER

332-DDS resin were 232 and -5.32, respectively.

 

250<

T

 

Cate Temperature,

 

3.5 7 4'0 .:

ch time. t. mir

Figure III.13. Illustration of the full-cure line. Cure
temperature, T, versus log time, t.

From Equation 38, the calculated isothermal full-cure
temperature, T,, equalled the T,,,l, of 230°C after eight
minutes. An experiment was performed to test this full-
cure condition. A neat epoxy resin was isothermally cured
at 230°C for only eight minutes. Then the DSC exotherm was
integrated which gave the extent of cure equal to 0.45. A

post-cure T, determination gave an T, ,t, at 225°C.

123
Section III.2.g.(4) showed that the epoxy resin was pre-
cured between ten and thirteen percent prior to DSC-curing.
This explains why the extent of cure was not 0.58, the
theoretical a, and maximum T, in Figure III.11(b) was only

225'C.

Full-cure times were calculated from Equation 38, by
letting T. equal 230°C. For isothermal cures at 220, 200,
and 170°C, the full-cure times are 170 minutes, 1.04 x 105
minutes or 72 days, and 4.51 x 1011 minutes or 86034 years,
respectively. Fava [80] stated, "...(that the isothermal-
DSC cure method) is suitable for cure times on the order of
hours. If a cure proceeds for longer than about six hours,
the exotherm is generally too slight to be detected
accurately ...". Equation 38 verified that full cure was
not practical for isothermal cure temperatures much lower

than 230°C [35].

Full cure could not be achieved for T, above 230°C
because endothermic reactions, such as thermal degradation
and charring, occurred before polymerization and
crosslinking reactions were completed [32]. This was shown

by the decreases in Figure III.12 above 230°C.

The gelation and vitrification lines for the DER 332-
DDS epoxy-resin TTT diagram were also formulated in

Appendix B. The gelation line represents the temperatures

124
where the extent of cure, a, equalled 0.58 and is given by
T, - 281 - 93.2 log t. The vitrification line equals the
time where the T, equalled the T, and is given by T, = 478

- 155 log t.

Physical parameters in the TTT diagram for the DER
332-DDS epoxy resin, T,,, T,',,l, and T,.,l, were
determined. From Figure III.11(b), the T,.,l, was found to
be 230°C. The unreacted glass transition temperature, T,,,
was found by extrapolating the residual extent of cure,'
a,,, = 1 - a, versus the log1o(T,) curve given in Figure
III.12(b) to an uni, equal to one [40]. The T,o for a DER
332-DDS epoxy resin was 1°C. The gelation glass transition
temperature, T,',,l, was found by placing uncured epoxy
resin in a Brookfield viscometer and increasing the
temperature at a rate of 5°C/min. A sudden decrease in
viscosity at 80°C marked the transition from a gelled glass
to a viscous liquid where T,,,,l occurred; These data are
in agreement with Chan et al. [41] results. They reported

a T for DER 332-DDS epoxy resin of approximately 80°C.

9.0el

The DER 332-DDS TTT diagram is illustrated in Figure

III.14.

125

 

 

 
    
   

GELLED III-.‘\~'ITRIF mm
RUBBER CHAR
'r l . 229°C
30 l ‘
.1 5.x
5 vmmcanon um: M
\_ . , 762.45,“. nan-nun WWW

LIQUID GELLED GLASS

 

_. UNGELLED GLASS

 

 

 

time

Figure III.14. Time-temperature-transition, TTT, diagram
for a stoichiometric DER 332-DDS epoxy resin.

This exercise demonstrated how a TTT diagram can be
formulated. The physical parameters, T,,, T,',,l, and
T,.,l,, was in excellent agreement with literature values
[36,41,94]. This TTT diagram was used to predict the full-

cure times.

d. Full-cure Extent of Cure, 0 (T,)

Isothermal experiments were performed and analyzed
with both DSC and FTIR spectrometer to determine the full-
cure extent of cure, a. Isothermal-DSC full-cure a equals
the quotient of total reaction exotherm, H1, divided by the
ultimate reaction exotherm, Hul,. FTIR-spectroscopy full-
cure a is a function of the epoxy-intensity ratio as shown

in Equation 34.

126

Neat, untreated carbon-reinforced, and surface-
oxidized carbon-reinforced epoxy resins were fully cured at
temperatures of 170, 190, 200, 210, 220, 230, and 250°C at
times equal to 300, 240, 190, 180, 170, 150, and 120
minutes, respectively. Table III.5 shows an analysis of
variance, ANOVA, of isothermal-DSC total reaction exotherms
for neat and surface-oxidized carbon-reinforced epoxy-resin
cures. A high F-ratio, the ratio of the variation standard
deviation divided by the residual standard deviation, in
the ANOVA implied that isothermal-DSC H, data were greatly
dependent on the cure temperature, T,. A low F-ratio
implied that isothermal-DSC H?T? data are independent of
the amount of surface-oxidized carbon fiber weight
fraction, wf.
Table III.5. Analysis of variance, ANOVA, of the total
reaction exotherm, H,, for the following sources of

variation: (a) cure temperature, T,: and (b) fiber weight
fraction, wf.

 

 

 

m =_ ' - =
Variation Sum of Degree of Standard F-
Squares Freedom Deviation Ratio
T, 2800 6 470 8.6
w,‘ 14 3 4.5 0.09

 

 

 

 

 

* - fiber-weight fraction of surface-oxidized carbon
fibers.

 

 

127

These difunctional epoxy-resin H, results were
consistent with the findings reported by Dutta et al. [43]
and inconsistent with the findings of Wang et al. [74].
Dutta et al. cured glass- and carbon-filled difunctional
epoxy resin. They found no statistical significant
difference between total reaction exotherms for filled
epoxy-resin cures and neat epoxy-resin cures. Wang et al.
[74] cured a difunctional and tetrafunctional epoxy resin.
Then they added carbon fillers to determine the effect of
epoxy functionality on carbon-reinforced epoxy resin cures.
They found that difunctional epoxy-resin cures gave reduced
H, relative to neat epoxy-resin cures and tetrafunctional
epoxy-resin cures gave similar H, relative to neat epoxy-

resin cures.

Full-cure a versus T, curves for untreated carbon-
reinforced, and surface-oxidized carbon-reinforced epoxy
resins are shown in Figure III.15(a) and (b), respectively.
Isothermal-DSC full-cure 0 results reached a maximum
between 210°C and 230°C. Isothermal curing below 230°C
resulted in an undercured epoxy resin and isothermal curing
above 230°C resulted in a thermal-degraded or charred epoxy
resin. Inspection of fully-cured epoxy resins showed full-
cure a versus T, data were well within the five-percent
experimental error. No significant differences between

neat and carbon-reinforced epoxy resins were observed.

Extent 0! Cure. a

128

 

 

 

 

 

 

 

 

 

 

 

a . b . C .
1.00 1.00 1.00
H Moot Rum
H Surface—om ' ad (u, - 0.01)
095‘ . H SMoco-Oidizd (I, I 0.10)
. 0.95.4 0.95« 0-0 Swine-Odom (I, - 0.60)
0.904 0.901 0.90-
8
0' a
035-: 3 055- 2' 0.05-4
o 6
‘5 3
0.801 ‘5 0.30.. E 0.80-4
3 3:
‘3 U
0.75- 0.75‘ 0.75-
0.704 H Nut nit 0'70‘ o-o that win 0'70"
HW“"°" awn-.01)
‘JHW(I,I.:) Hm(u,-.TO)
0.33 W ”I.“ ouh'm. 0‘5 ": MW, (":4 f f
100 100 200 220 240 200 no 150 250 220 230 200 0”100' ' 350* ' '200' ' 220 ' 3250' 200.
MTmm.T,'C CunTW.T,'C Mum...“ 1 nc
° 0’

Figure III.15. Full-cure extent of cure, 0, versus cure
temperature, T,, for the: (a) DSC-cured and DSC-analyzed

untreated carbon-reinforced epoxy resin; (b) DSC-cured and
DSC-analyzed surface-oxidized carbon-reinforced epoxy
resin; and (c) convectionally-cured and FTIR-analyzed
surface-oxidized carbon-reinforced epoxy resin.

Surface-oxidized carbon-reinforced resins were also
analyzed with diffuse-reflectance, DRIFT, FTIR
spectroscopy. Before DRIFT-FTIR spectroscopy analyses,
samples were fully-cured in a conventional oven at cure
temperatures and times identical to the DSC-cured
specimens. A typical DRIFT-FTIR spectrum for a fully-cured

DER 332-DDS epoxy resin was shown in Figure III.9(b).

A comparison of the uncured and fully-cured FTIR
spectra presented in Figure III.9 showed a smaller epoxy-

intensity peak at 916 cm'1 for the fully-cured specimen.

129
This decrease was due to epoxy molecules reacting with
amines and forming secondary amines, which contained
hydroxyl groups. An increase in hydroxyl groups was
represented by the broad intensity strength from 3000 to

3500 cm".

FTIR-spectroscopy full-cure a results for neat and
surface-oxidized carbon-reinforced resins is shown in
Figure III.15(c). Two-percent higher FTIR-a results
relative to the DSC-a results for the 0.60 carbon-
reinforced specimens was believed to be due to nonuniform
sample sizes and high infrared absorbance of the carbon
fibers. In DRIFT-FTIR spectroscopy, the infrared beam
penetrated the epoxy-resin specimen completely and part of
the beam was reflected back to a detector [29]. This
reflected light was scattered by the specimen to produce
the infrared spectrum. Unfortunately, the infrared beam
was absorbed by carbon fibers across the total spectral

range [29,86].

An investigation on the FTIR-spectroscopy errors will
be addressed in Section III.D.2.g.(4). The errors due to
the high infrared absorbance of the carbon fibers can be
explained by high scattering coefficient, 5, values in the
Kubelka-Munk equation, Equation 32 [28]. High values of 5

caused increased absorbance across the entire FTIR

130
spectrum, reduced sample intensity separation, and poor

spectral resolution»

The maximum FTIR-spectroscopy full-cure a occurred at
250°C. Figure III.15(a) shows the maximum isothermal-DSC
full-cure a occurred at 220°C. The FTIR-spectroscopy full-
cure a implied that more epoxy molecules react as the T,
increased. Since more epoxy molecules should react at a

higher cure temperatures, T,, the lower DSC full-cure a at

 

250°C was believed to be caused from endothermic reactions,

such as thermal degradation and charring.

These extent of cure results showed that full-cure a
for carbon-reinforced epoxy-resin cures were not
statistically different from fullbcure a for neat epoxy-
resin cures. A comparison of DSC-cured and DSC-analyzed
specimens versus convectional-oven cured and FTIR-
spectroscopy analyzed specimens showed n0'significant

difference between full-cure extents of cure.

 

 

131

E. Cure Kinetics

Physical, mechanical, and electrical properties of an
epoxy resin depend to a large extent on the extent of cure,
a, [7]. Qualitative analyses showed no significant
difference between full-cure extents of cure for neat and
carbon-reinforced epoxy resins. A cure-kinetic analysis

quantified these a results.

Criterion for selecting the cure type for kinetic
analysis is the ability to accurately describe the a at any
given temperature. Dynamic curing was appealing because
much information can be obtained from a single-temperature
programmed experiment. Unfortunately, dynamic cures are
not reliable for depicting the course of a reaction over a
wide time-temperature range [54]. For this reason,
isothermal cures were used to experimentally determine the

a and, ultimately, the cure kinetics.

DSC-analyzed full-cure a data from Section III.2.D
were integrated at various times, t. These a versus t data
were fit to a cure-kinetic model to attain a better

understanding of the carbon-reinforced epoxy-resin cures.

A comparison between neat and carbon-reinforced epoxy-
resin cure kinetics would demonstrate whether carbon fibers

affect the reaction rate. A comparison.between untreated

132
and surface-oxidized carbon-reinforced epoxy-resin cure
kinetics would give insight into what interphase mechanisms

are occurring.

In Section II.B.3., it was determined that nth-order
kinetics can not predict the sigmoidal shape of an
isothermal reaction exotherm. Furthermore, nth-order cure-
kinetic equations cannot realistically describe
polymerization and crosslinking reactions which occur

during an epoxy-resin cure [80].

Polymerization reactions are catalyzed by hydrogen-
bond donor and hydroxyl groups [34]. If it is assumed that
amine-hydrogen atoms have equal reactivity [32], then epoxy~
molecules are consumed in two simultaneous reactions. The
first reaction was catalyzed by hydrogen-bond donor groups,
and the second reaction autocatalyzed by hydroxyl groups in
the reaction products. The rate equation'which described
these polymerization reactions was:

3% = (k, + k2 a) (1 - a); for a S a,,l (13)

where a = extent of cure,

k1 = A1 exp ('En/RT):

k2 = A2 exp (“EAz/RT),

A, = frequency factor for k,,

A2 a frequency factor for k2,

E,, = activation energy for k,,

E,2 a frequency factors for k2, and

0.48.

133

Gelation marked the change from the rate-controlled
polymerization reactions to diffusion-controlled
crosslinking reactions. The theoretical extent of cure at
gelation, a,,,, for a tetrafunctional epoxy and
difunctional amine is calculated from Equation 1 to equal
0.58. Section III.E.2.g.(3) showed the epoxy resin is
between ten- and thirteen-percent cured prior to DSC-

curing. Therefore a,,, was assumed to equal only 0.48.

The rate equation which described the diffusion-

controlled crosslinking reactions was [42,57]:

fig = k, e‘M/RT (1 - a); for a > a,,, (14)
dt 1
where D a fitted diffusion-limited constant,

k3 = A3 exp (‘EAs/RT):

A3 - frequency factor for k3, and

EA; = activation energy for k3.

The polymerization rate equation, shown in Equation 13, has
been used by numerous experimenters [34,40,43,44,55]. The

crosslinking rate equation, represented by Equation 14, has
been developed by Loos et al. [57] and used by Finzel [42]

to model the crosslinking reaction mechanism which other

experimenters neglect.

Cure-kinetic analyses were conducted as follows:
Full-cure a data for neat, untreated carbon-reinforced, and
surface-oxidized carbon-reinforced epoxy resins at cure

temperatures equal to 170, 200, and 220°C were integrated

134
over time, t. These 0 versus t data are shown in Figure
111.16 and tabulated in Table C.1. The most pronounced

decrease in the reaction rate, da/dt, occurred near

 

 

 

 

 

 

 

 

 

 

gelation.
a. b.
1.0 10
4 n-22m
/' — : ~
08- .
/ 1,
///T.-200'c
o a ' '
. . 4;/
g 3 0.6-‘ '
3 3 , >
o o / IA
‘5 3 4 //'
u a ,z'
5 5 04"
u a ' I, /
x x .
m m ,
] 7,-170'C
I.
0.2 '
NootRuin
mmmwoyum
. . . , . . , . . , , f
0 30 80 90 1120
' tinie.t.min

 

Figure III.16. Extent of cure, 0, versus time, t, for a:
(a) DSC-cured and DSC-analyzed untreated carbon-reinforced

epoxy resin; and (b) DSC-cured and DSC-analyzed surface-
oxidized carbon-reinforced epoxy resin.

A comparison between the gelation time, tact, for
untreated and surface-oxidized carbon-reinforced epoxy-
resin cures is given in Table III.6. The maximum

t,,, difference between neat epoxy resin and carbon-

reinforced epoxy resins was ten percent. These t,,l

135
differences are significant and consistent findings
reported by Mijovic [44]. He found that the time to the
exothermic peak was lengthened adding fillers to an epoxy

resin.

At gelation, an increased local viscosity and steric
hindrance of the reactants caused the diffusion-limited
crosslinking reactions. In a carbon-reinforced epoxy
resin, the epoxy molecules in the vicinity of the'
reinforcement were "shielded" by the carbon fibers and,‘
hence, were less likely to encounter reactive species than

epoxy molecules in the bulk epoxy matrix.

Table III.6. Gelation time, t,,,, versus cure
temperature, T,, and fiber weight fraction, w,, for: (a)
untreated carbon-reinforced epoxy resin; and (b) surface-
oxidized carbon-reinforced epoxy resin.

 

 

 

a.

TC Wf ‘ tQQ, l t
('0 (mm)
220 0.0 4.63

0.01 4.97
0.10 ' 5.25
0.60 5.40
200 0,0 13.2
0.01 13.1
0.10 13.8
0.60 14.2
170 0.0 64.5
0.01 65.2
0.10 67.08
0.60 70.15

 

 

Table III.6 (continued)

136

 

 

 

Tc Wf tag l *
(°C) (mm)
mm
220 0.0 4.63
0.01 5.23
0.10 5.79
0.60 5.86
200 0.0 13.2
0.01 12.9
0.10 13.3
0.60 14.9
170 ,0.0 64.5
0.01 62.0
0.10 69.7
0.60 69.7

 

 

 

 

Note *: The gelation extent of cure, a,,,, is based on the
assumption that the resin is already ten-percent cured prior
to DSC-curing, as shown in Section III.2.g.(5); therefore,
a,,, equaled 0.48.

     

 

Table III.6 shows that the t,,, is not a function of
carbon-fiber surface functionality. Instead, the t,,,
varies as a function of average distance between
reinforcement. At gelation, local viscosity and steric
hinderance of reactants increased. Carbon fibers further
resitricted the movement of epoxy molecules and lengthened

the epoxy-resin cure.

Next, Equation 13 was rearranged by dividing the
reaction rate by the product, (1 - a)(B - a). This

quantity is defined as the reduced polymerization reaction

 

rate, a,,,,,

137

a,,,, = da/dt a k, + k2 a, where a s a,,l. (39)
(1'0!) (B-a)

The a,,,, versus a for the neat epoxy resin is given in
Figure III.17(a). The a,,,, increased with a during the
initial stages of cure as predicted by equation 39. At 0
approximately equal to 0.3, a sharp increase in a,,,1
values was caused by the increasing importance of

diffusion-controlled crosslinking reactions.

 

 

0.5 0
e—e 220 'c , e 220 'c

HZOO'C e ZOO'C
-1~ a 17cc

-J-‘ A

, e
-4-4

1

Reduced Polymerization Reaction Rate.
a... '
Reduced Croeefinking Reaction Rate.
a“. mun“
I
U!
1

 

 

 

 

 

 

 

vrv'vvv

' ' 1 l ' w—r ' ' T ' T ' f a 1 . y
0.0 0.2 0.4 0.6 0.8 1.0 0.5 0.5 0. 7 0.8 0.9 1.0
Extent 0! Cote. d Extent of Cure. a

Figure III.17. Reduced: (a) polymerization reaction rate,
a,,,,, versus extent of cure, a, for the neat epoxy resin;
and (b) crosslinking reaction rate, aR,,2, versus a for the
neat epoxy resin.

A least-squares linear regression of Equation 39 was
performed between an a equal to 0.05 and 0.3. Rate

constants, k, and k2, were modeled with Arrhenius kinetics

and shown in Figure III.18. Lines drawn in Figure III.18

Rate Constant. lg. s"

138

was fitted to the neat epoxy-resin rate constants.

Correlation coefficients for neat and reinforced resin rate

constants, k,

and k2, were between 0.969 and 0.999.

No significant difference was found between the neat and

reinforced epoxy resins.

 

-IO.-(

 

-11.

 

O...

Neat Refin

Surface-Oxidized (w, - 0.01)
Surface-Oxidized (w, I 0.10)
S'urfooo-Oxidized (w, - 0.60)

 

 

2.0

Figure III.18.

I I
2.1 2.2

Cure Temperature. 1000/T .. 'K"

2.3

Rate Conetont. lg. e"

 

 

 

 

b.
-3.
-4..-
.4 In k,
15.-
15.1 In k,
-7.-
In k,
-8.-‘
-9.-
-10.- e Neat Resin
e Untreated (w, - 0.01)
‘ e Untreated (w, - 0.10)
0 Untreated JV, = 0.60)
-1 1. I r v T
2.0 2.1 2.2 2.3

Cure Temperature. [GOO/T,. 'K-'

Logarithm of the rate constants, k,, kg,

and k3 versus inverse absolute cure temperature, T,, for:
(a) untreated carbon-reinforced epoxy resin; and (b)
surface-oxidized carbon-reinforced epoxy resins.

Values for neat and carbon-reinforced epoxy-resin

reaction-rate constants, k, and k2, are given in Table

III.7.

Differences between neat and carbon-reinforced

139
epoxy-resin reaction-rate constants, k, and k2, showed no

significant trends.

Table III.7. Reaction-rate constants, k,, kg, and
k3, versus cure temperature, T,, and fiber-weight fraction,
w,, for: (a) untreated carbon-reinforced epoxy resin; and
(b) surface-oxidized carbon-reinforced epoxy resin.

 

 

170 0.00036 0.00029 0.00177 0.00193 0.00038 0.00040

 

200 0.00119 0.00108 0.00508 0.00513 0.00107 0.00102
220 0.00237 0.00235 0.00958 0.00918 0.00199 0.00187
m m
T, k, k2 k

3
('C) (8.1) (8-1) (8.1)

170 0.00062 0.00049 0.00173 0.00176 0.00039 0.00035
200 0.00111 0.00117 0.00458 0.00495 0.00101 0.00097

220 0.00215 0.00253 0.00928 0.00872 0.00186 0.00177

 

 

 

(5C) (5-1) (5-1) (5-1)

Wf =3 0 Wf = 0.01 Wf = 0 Wf = 0.01 Wf = 0 Wf = 0.01
170 0.00036 0.00031 0.00177 0.00183 0.00038 0.00041
200 0.00117 0.00128 0.00508 0.00527 0.00107 0.00145

220 0.00237 0.00242 0.00958 0.00968 0.00199 0.00194

140

Table III.7 (continued)

 

'1'. 1:, 1:; k;
('C) (3-1) (5-1) (5- 1)

Wf . 0.1 Wf - 0.6 Wf = 0.1 Wf = 0.6 Wf = 0.1 Wf = 0.6
170 0.00035 0.00035 0.00175 0.00162 0.00043 0.00035
200 0.00119 0.00125 0.00507 0.00483 0.00104 0.00095

220 0.00225 0.00232 0.00918 0.00941 0.00183 0.00177

 

 

Cure-kinetic parameters for the crosslinking region,
R; and D, were found by taking the logarithm of the
crosslinking rate equation shown in Equation 14. Logarithm
of the reaction rate multiplied by the quantity (1 - a) was
defined as reduced crosslinking reaction rate, 09.82-

08.82 =ln[s%_(l - a)]- 1n k3_+ Da, where a 2 09,1.(40)

The “3.02 versus a curve for neat epoxy resin is shown
Figure III.17(b). Higher aRedZ values were observed at
lower cure temperatures; this is due to decreasing reaction
rates after gelation. The slope, D, at Tc of 170, 200, and
220'C appeared to be similar. A least-squares linear
regression analysis was performed on Equation 40. The rate
constant, k3, correlated with temperature according to the
Arrhenius equation and is shown in Figure III.18. The a
data fit the cure-kinetic model well, which was verified by

obtaining correlation coefficients between 0.980 and 0.999.

 

141
Table III.7 shows that k; for carbon-reinforced epoxy
resins was significantly lower than k; for neat epoxy
resin. This is consistent with findings presented in
Table III.6, which showed that carbon-fiber effects were
physical. The reaction rate constant k; decreased with

increasing wf.

At low w,, carbon-reinforced epoxy-resin rate
constants were generally higher than neat epoxy-resin rate
constants. This result was consistent with Dutta et al.
[43] findings, shown in Figure II.13. They have claimed
that carbon fibers helped promote or catalyze the

crosslinking reactions.

The exponential kinetic parameter, D, decreased by a
factor of four whenever carbon fibers are present in the
epoxy resin. The change in D was due to the physical
carbon-fiber effect. Initally, epoxy molecules and local
viscosity were small. Polymerization reactions were not
significantly affected. As the cure progresses, the
network characteristic dimensions approach those of the
carbon fibers and the local viscosity increased. Carbon
fiber were added "barriers" to the already limited epoxy-

molecule movement during the crosslinking reactions.

The frequency factor, A, and activation energy, BA,

for the neat and carbon-reinforced epoxy-resin rate

142
constants, k1, k2, and R3, are given in Table III.8. As
the fiber weight fraction, wf, increased, frequency factors
and activation energies decrease. Frequency factor and
activation energy decreases were probably due to chemical

effects of the carbon fibers on the epoxy-resin cure.

Table III.8. Cure-kinetic parameters for the neat and: (a)
untreated carbon-reinforced epoxy resin: and (b) surface-
oxidized carbon-reinforced epoxy resin.

Neat I rate equation =

fig = (k, + k; a) (1 - a); for a S anal

 

 

dt
gg = k; e'°°/RT (1 - a): for a > agel
dt
where k, = A1 exp (-E1/RT),
k2 = A2 exp (“Ez/RT),
k3 ' 33 exp (-E3/RT),
A1 a frequency factors for R1,
A2 a frequency factors for k2,
A3 a frequency factors for R3,
E1 = activation energy for R1,
E2 = frequency factors for k2,
E3 = activation energy for R3, and
a'.l = 0.5.
A1 = 26500 E,1 = 15.9 kcal/g
A2 = 31500 EAZ = 14.7 kcal/g I - D = ‘2.0
A3 = 25500 E” = 15.9 kcal/g (

 

 

143

Table III.8 (continued)

 

 

IL

mm

w, A EA (kcal/g)
Wg==
# 1 2 3 1 2 3

 

 

0.01 16600 24400 5700 16.1 14.6 11.8

 

 

 

 

0.10 16100 8820 567 15.5 14.7 10.2

13.5 10.3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

D3 = -7 o 9
w, A EA (kcal/g)
# 1 2 3 1 2 3
_mmm l

0.01 17100 29400 5380 16.2 14.3 11.1
0.10 15500 13600 499 15.3 13.7 9.6
13.2 9.3

D; = -8.2

 

 

Frequency factor decreases were caused by a more-
ordered or less-entropy system. Ten-precent decreases in
entropies were caused by acidic carbon-fiber surface groups
attracting epoxy molecules. This attraction restricted the
movement of the epoxy molecules and created a more-ordered

system. Table III.9 shows entropy differences were

144
polymerization reactions and significant during

crosslinking reaction.

Table III.9. Calculation of the entropy for: (a) untreated
carbon-reinforced epoxy resin: and (b) surface-oxidized
carbon-reinforced epoxy resin.

 

 

Arrhenius temperature law: k = A eEA/RT;

 

From the transition theory [95],
k = 3.1 essln- e-an/Rr

 

 

 

 

 

 

 

 

 

 

 

 

 

Therefore,
h
where k' = Boltzmann constant,
T = absolute temperature,
h = Planck constant, and
R = universal gas
constant.
m
a.
m '
w, A 68(kcal/gmol'K)
#—
# 1 2 3 1 2 3
“m =
0.0 26500 31500 26500 -57 ‘ -57 -57
fl== é
0.01 16600 24400 5700 -58 -58 -60
0.10 16100 8820 567 -58 -58' -65
0.60 15500 3650 418 -58 -58 -65

 

 

 

 

145

Table III.9 (continued)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b.
m =
Wf A
=-- J
# 1 2 3 1 2 3
0.0 26500 31500 26500 '57 '57 '57
0.01 17100 29400 5380 '58 ‘57 '60
m E
0.10 15500 13600 499 ‘58 ‘58 '65
m __
0.60 14500 7620 290 ‘58 '58 ‘66
===I=I===== ==£=====

 

Activation energy decreases were believed to be caused
from hydrogen-donor groups present on carbon-fiber surfaces)
catalyzing cure reactions. Such fiber-matrix bonding has
been suggested by other experimenters [5,55,65]. Moroni et
al. [55] have used FTIR spectroscopy to determine hydrogen-
bonding occurred between carbon-fiber surface groups and
epoxy molecules. Both Horie and Fitzer [5] have studied
carbon-reinforced epoxy resins and also proposed hydrogen
bonds exist between carbon-fiber surface groups and epoxy
molecules. Garton et al. [65] have used FTIR spectroscopy
and reported polymerization reactions were influenced by

carbon-fiber surface groups.

 

146
Table III.10 shows that good agreement between this
study's activation energies and literature values.
Average-reported activation energiers for catalyzed
polymerization reactions, 8,1, for stoichiometric epoxy
resins were 17.0 t 3.8. Average reported activation
energies for autocatalyzed polymerization reactions, EAZI

for stoichiometric epoxy resins were 13.9 i 1.8.

Table III. 10. Comparison of activation energy, BA, for
epoxy resins modeled with the autocatalytic cure-kinetic
equation given in Equation 13. -n

 

Resin System EA

Experimenter(s)

 

 

 

 

 

 

 

(kcal/gmol)
Kamal et al. [55] DGEBA-DDS l4.8,l4.5
Horie et al. [55] " 13.9,13.4
Sourour et al. [40] " 20.0,11.0
Monori et al. [55] " 13.5,12.0
Mijovic [44] " ‘ 22.0,16.0
Smith et al. [55] DGEBA-amine' 14-16
Kil et 81. [55] " 14.2,14.4
Prime [32] " 11-14
Average EA, 17.0 i 3.8
Average 8,; '13.9 t 1.8
m

 

 

a - amine other than DDS

 

 

Table III.10 shows activation energies found by
Sourour et al. [40] and Mijovic [44] were high when

compared to other activation-energy values. Inspection of

 

their data suggested that Sourour et a1. and Mijovic et al.

used a data greater than a to model k, and k2. These a

get

data were influenced by crosslinking reactions. Since

crosslinking reaction rates are slower than polymerization

147
reaction rates, Sourour et al. and Mijovic et al. obtained
rate constants with higher frequency factors and activation

energies.

Frequency factors and activation energies found in
this study for carbon-reinforced epoxy resins were compared
with cure-kinetic parameters reported by Mijovic [44] for a
40-percent glass-reinforced epoxy resin. Table II.5 showed
Mijovic found a 98- to 99-percent frequency-factor decrease
and a 23- to 35-percent activatin-energy decrease for
glass-reinforced epoxy-resin cures relative to neat epoxy-
resin cures. Their kinetic parameters followed trends
identical to trends found in this study. His reinforced
rate constants have decreased frequency factors and
activation energies relative to neat epoxy-resin cure-
kinetic parameters. Mijovic attributed these decreases in
A and EA to glass fillers restricting the mobility of

unreacted epoxy molecules.

Dutta et al. [43] findings were compared with this
study's results. They DSC-cured a neat, glass-filled and
carbon-filled epoxy resins. Their reinforced epoxy-resin
formulation contained one-, two-, four- and six-percent
filler concentration. They modelled reaction rates with a
single autocatalytic equation and rate constants as third-
and fourth-order functions of filler content as shown in

Section II.C.3.c. The glass-reinforced epoxy resins showed

 

 

148
a maximum reduction in E, for R, from 15.4 to 14.4 kcal/mol
[32]. The E, reduction they reported was consistent with

results of this study.

Figure II.12 showed Dutta et al. [43] carbon- and
glass-reinforced epoxy-resin rate constants, k, and k2,
decreased to a minimum value at two-percent filler
concentration relative to neat epoxy-resin rate constants.
Above this filler concentration rate constants increased
and leveled off to a constant value, which was not
significantly different than neat epoxy-resin rate
constants. These results were inconsistent with findings

of this study.

Two major conclusions drawn from this cure-kinetic
study were summarized as follows. First, carbon fibers
have a physical effect on epoxy-resin cure kinetics. As
more carbon-fibers were added to epoxy resins, gelation
times increased and reaction rate constants k3 decreased.
These results implied carbon fibers "hindered" epoxy
molecules and slowed crosslinking reactions. Secondly, the
carbon-fiber surface treatment have a small effect on
epoxy-resin cure kinetics. Frequency factors and
activation energies for carbon-reinforced epoxy resins
decreased relative to neat epoxy-resin values. These
results implied that carbon-fiber surface groups attracted

epoxy molecules catalyzed cure reactions.

 

 

149

f. Glass Transition Temperature, T,(a)

After isothermally curing neat and carbon-reinforced
epoxy resins, glass transition temperatures were found. A
comparison between neat and carbon-reinforced resins was
conducted to determine whether the epoxy-resin bulk matrix

changed.

In the liquid state, molecular structure is disordered
and atoms do not behave with the regularity exhibited in
the glassy state. In the glassy state, however, molecules
are ordered and atoms move around equilibrium positions.

In glassy state, large-scale molecular motion does not
occur, but atoms or small groups of atoms move against
local restraints of secondary bond forces. The glass

transition temperature, T , corresponds to the transition

9
from liquid-like movement which is characteristic of the
liquid state to limited movement which is-characteristic of

the glassy state.

Neat and carbon-reinforced epoxy-resin samples were
isothermally cured at temperatures ranging from 170°C to
250'C. Initially, liquid epoxy resins polymerized and the
Tg increased with increasing extent of cure, a [80]. When
the Tg equaled the cure temperature, Tc, vitrification
occurred. During vitrification the epoxy resin became

glass-like and diffusion-controlled crosslinking reactions

 

 

 

150
began. Further curing beyond vitrification caused
increased glass transition temperatures above the T,. When
no further reaction exotherm was detectable with DSC,
isothermal cures were terminated. Following cure, samples

were scanned at 10'C/min to observe the T,.

The ultimate glass transition temperature, T,.ult is
defined as the maximum T, when all epoxy molecules have
reacted. At cure temperatures below the-T,,lt, epoxy-resin
samples were undercured and formed loose-network
structures. DSC analyses performed on these undercured
specimens showed an "overshoot" in the heat flow versus
temperature diagram. This "overshoot" was explained by a
free-volume changes as the temperature increases. Liquid-
like motion of atoms in the rubbery state requires more
free volume than short-range excursions of atoms in the

glassy state.

Since the fully-extended chain is the conformation of
minimum energy, it occurred more frequently during

isothermal cures below T,,lt. The free volume was defined

as [33]
f = f, + ( T - T,,l, ) Ga, for T 2 T901: or
(41)
f = f, for T < T,“t ,

where 6a, = change in volume expansion coefficient and
f, - free volume at temperatures below T,,lt.

 

151
The volume expansion coefficient, a,, is a measure of the
amplitude of molecular vibrations with temperature. As
cure temperatures increased, cured epoxy resins have more
crosslinked chains. When samples were heated beyond the
T9011: epoxy molecules became more energetic and increased
in volume. This rapid increase in energy manifested itself
as an "overshoot" on DSC heat flow versus temperature
diagram as shown in Figure III.19(a). As temperatures
increased, cured epoxy resins remained in a crosslinked-
chain conformation and little or no "overshoot" was seen as

shown Figure III.19(g).

A difference of 20'C was found between T, and Te for
samples isothermally cured below T,,lt. This trend has
been reported for similar epoxy resins [32,40]. During low
temperature cures, epoxy resins vitrified prior to
completion of polymerization reactions. At low cure
temperatures, reduced molecular energy slowed diffusion of
reactive species in the glassy matrix and decreased the

amount of cure reactions.

Glass transition temperature versus Tc data for neat,
untreated carbon-reinforced, and surface-oxidized carbon-
reinforced epoxy resins are shown in Figure III.20. A
comparison of Figure III.11 and III.20 show that precuring
epoxy resins, during fiber impregnation, prior to cure

decreased the final T, from 230’C to 225'C.

 

 

 

152

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

was utfl.flw- "fl ”I‘m-.0.-

 

 

 

 

 

 

Figure III.18. DSC analyses of fully-cured epoxy resin at:
(a) 170°C; (b) 190°C; (c) 200°C; (d) 210'c; (e) 220‘c; (f)
230'c; and (g) 250°C. '

153

 

 

   
  
          

a 0 210 b . 240
230- I
n S) /
b. .J' l fix
g 22°“ 5 zzoj * \\
.4 3 ,/ \‘v
E E I r
g g i f/ \\i
gzw- E 4
§ 8 I
4; 3‘3 ‘
g E l
» 200~ : 2004
= V,
2 8
o G
190-
" Noe! Ruin o—o Neat Rosin
H Swine-0505206 (I, - .01) H Unnamed ’
._ ,-0m
: mace-0mm“ (v, - .10) H unmouu E: - 0.10;
1804 oct—Ofldll“ I - .60 15 ‘ H Untreaxoc (w -
H O 180 200 220 240 200 160 160 200 220 240 260

 

 

Cure Temperature. T., 'C Cure Temperature. T, 'C

Figure III.20. Glass transition temperature, T,, versus
cure temperature, T,, for: (a) untreated carbon-reinforced
epoxy resin; and (b) surface-oxidized carbon-reinforced
epoxy resin. '

Figure III.11(b) shows that the highest T, of 225°C
occurred at a Tc equal to 210°C. Epoxy resins cured above
210°C show a decreased T,. Note that Tg equal to T,ult of
230°C was not attained. This can be explained by
rearrangement of crosslinked epoxy-resin networks and

degradation of samples prior to completion of cure

reactions.

Glass transition temperatures given in this study were
inconsistent with findings reported by Ko [17]. He found a

25°C increase in the T9 for untreated carbon-reinforced

 

154
epoxy resins and 45'C increase in T, for surface-oxidized
carbon-reinforced epoxy resins relative to the T, for neat
epoxy resins. He believed epoxy molecules adsorbed on
graphitic basal planes of carbon-fiber surface and created

an epoxy-amine gradient in the fiber-matrix interphase.

These difunctional epoxy-resin T, results were also
indifferent with Wang et al. [74]. They found carbon-fiber
effects on tetrafunctional epoxy-resin cures did not change
the epoxy-resin glass transition temperatures; but, carbon- 1:
fiber effects on difunctional epoxy-resin cures reduced
glass transition temperatures by 25‘C. They have concluded
epoxy-resin functionality plays a large role in the matrix

network formation.

This study showed no significant differences existed

 

between glass transition temperatures of neat and carbon-
reinforced epoxy resins. Therefore, regardless of the
carbon-fiber type or content added to epoxy resins,

identical crosslinked matrices resulted.

155

g. Reproducibility and Accuracy

Sample preparation was the major cause of variability
in the reproducibility and accuracy of this study. The
following sample-preparation techniques were investigated:
1. hardener addition, 2. fiber impregnation, 3. prevention
of environmental contamination, and 4. transmission- and

DRIFT-FTIR spectroscopy.

(1) Hardener Addition

The powdered hardener was dissolved in the epoxy resin
prior to curing. The purpose of these experiments was to
determine: (1) How the cure characteristics of a non-
stoichiometric epoxy-resin compares to the cure
characteristics of a stoichiometric epoxy resin: and (2) if
the epoxy resin partically cures prior to DSC-curing or

convectional-oven curing.

(a) Stoichiometric Variations

A stoichiometric epoxy resin consisted of 35.8 grams of
DDS 100 grams of DER 332 epoxy monomer. The precision of
the analytical balance used to measure the reactants was i
0.5 mg. Assuming error occurred during mixing or
measuring, slight non-stoichiometric mixtures with epoxy-

amine equivalent ratios of 1:1.01 and 1:0.99 were prepared.

 

 

156
Then, these unstoichiometric samples were isothermally DSC-
cured and DSC-analyzed to obtain the extent of cure and

glass transition temperature, T,.

The extent of cure, a, and T, for each
nonstoichiometric specimens were compared with the a and T,
for a stoichiometric epoxy resin. No significant
difference in a or T, was observed between the

stoichiometric and either non-stoichiometric epoxy resin.

 

(b) Extent of Cure, 0

The purpose of this experiment was to determine if the
epoxy resin partially cures prior to DSC-curing or
convectional-oven curing. In order to combine the liquid
epoxy monomer and powdered hardener, the hardener was
dissolved in the epoxy monomer by heating the epoxy resin

from 100°C to 130°C over a period to approximately five

 

minutes. A DSC analysis which simulated heating during the
mixing process was performed. The average DSC-analyzed

extent of cure, a, after hardener addition equalled 0.05.

The extent of cure, a, after hardener addition was
also analyzed with FTIR spectrometer. Totally unreacted
epoxy resins were prepared by measuring stoichiometric
amounts of epoxy monomer and hardener, then dissolved each

in acetone. Next, these stoichiometric-acetone-diSsolved

157
epoxy monomer and hardener mixtures were combined. Several
drops of this uncured mixture were placed and allowed to

dry on a KBr plate.

FTIR-transmission spectra of this uncured mixture and
neat epoxy resin were performed. Equation 27 was used to
calculate FTIR-spectroscopy epoxy-intensity ratios. The
average FTIR-spectroscopy a after hardener addition

equalled 0.11.

These results showed that the epoxy resin was precured
between five and eleven percent after hardener addition.
Why the FTIR data differs from the DSC data will be

considered in Section III.D.g.(4).
(2) Fiber Impregnation

Commerical fiber composites were often made from
laminates. A laminate is defined as several layers of
prepregs or sheets of fibers impregnated with epoxy resin.
In this study, a prepreg was created by pulling a carbon
fiber bundle through a prepregger-resin vat of liquid epoxy
resin and winding the impregnated fiber bundle on a

mandrel.

The extent of cure, a, for the prepreg was determined

from the residual exotherms of several 80°C oven-aged

 

 

158
epoxy-resin samples. The term "residual exotherm" refers
to the magnitude of the remaining exotherm as measured by
DSC after the epoxy resin is partially cured. DSC analyses
of the residual exotherms for a stoichiometric epoxy resin
cured at 80°C gave the 0 versus time, t, data shown in
Figure III.21. Since the average residence time in the
prepregger—resin vat was estimated at two hours, the curve

was integrated after two hours to give an 0 equal to ten

percent.

 

 

1.0
0.8-4

0.6-1 X

/

 

Extent 0! Can, a
\

0.2~ '/

 

 

 

0.0 ''''''' r r l ' I ' v ' T
0 20 40 60 80100120140160!!!)
time. t. hours

Figure III.21. Extent of cure, 0, versus time, t, for a
neat epoxy resin cured at 80°C.

The extent of cure after fiber impregnation was also
analyzed with the FTIR-spectrometer. A thin film of the
epoxy resin from the prepregger-resin vat was cast on a KBr

plate and analyzed with the FTIR spectrometer. The

159
difference between this epoxy resin and the stoichiometric
acetone-dissolved uncured epoxy mixture described in
Section III.2.g.(3) as measured from the transmission-FTIR

analysis was 13 percent.

The a data after hardener addition and fiber
impregnation as measured by DSC and FTIR spectroscopy is
summarized in Table III.11. The difference between the DSC
and FTIR-spectroscopy data was considered insignificant
since Section III.E.e.g(4) shows that the experimental
error of the transmission-FTIR spectroscopy data was eight
percent.

Table III.11. Extent of cure, a, after hardener addition
and fiber impregnation.

 

 

 

 

DSC FTIR-Spectrometer
After Hardener 0.05 0.11
Addition
After Fiber 0.10 0.13
Impregnation
m;

 

 

 

 

 

(3) Preventation of Environmental Contamination

Protecting samples from environmental contamination
was imperative. A five-percent decrease in total reaction

exotherm, H,, was seen when the epoxy resin was not

 

160
contained in a desiccator. Reduced HT due to adsorbed
volatiles from the environment have been reported by other

investigators [25,32].

Initially, neat and carbon-reinforced samples were
stored in dry ice at -40°C to facilitate handling and
prevent premature curing. Stored samples were assumed to
absorb water or volatiles from the dry ice. Drzal et al.
[25] reported that the major epoxy-resin absorbate is water
and minor absorbates are carbon dioxide and carbon
monoxide. They implied that the absorbates diffuse into
the free volume present in the epoxy resin and associate
with hydroxyl groups present in the network. Absorbed
volatiles were believed to interfere with the hydroxyls
causing a reduction in the number of cure reactions and

forming a looser matrix network.

Isothermal-DSC analyses showed a two5percent decrease
in the total reaction exotherm, H,, for a carbon-reinforced
sample with a 0.10 fiber weight fraction, wf, when compared
with non-contaminated samples [96]; whereas, the HT for a
carbon-reinforced sample with a 0.60 w, was reduced by ten
percent relative to a non-contaminated samples.
Corresponding glass transition temperatures for
contaminated samples with a 0.10 w, showed a 5°C decrease

relative to non-contaminated samples; whereas, the T, for

 

 

 

 

161
carbon-reinforced samples with a 0.60 w, was reduced by

10°C relative to non-contaminated sample.

This decrease in T, was consistent with the results of
Brant [32]. He found a 10°C decrease in T, for epoxy
resins which were exposed to water. Drzal et al. [25] and
Peyser et al. [81] also reported a decrease in T, for

water-absorbed epoxy resins.

Reduced total reaction exotherms and glass transition
temperatures for the contaminated reinforced resin cures
suggested that absorbed volatiles interfere with the
polymerization and crosslinking reactions. The greater
reduction in the total reaction exotherms and glass
transition temperatures for 0.60 w, carbon-reinforced
samples suggest that volatiles adsorb more readily on the
carbon-fiber surface than in the epoxy resin. After dry
ice was found to contain volatiles which reduce the H, and
T,, the dry ice was not used for sample preparation.

Instead, a desiccator was used to store the epoxy resin

sample prior to DSC-cured convectional curing.
(4) Transmission- and DRIFT-FTIR Spectroscopy
In this study, stoichiometric epoxy resins were DSC-

cured and compared with literature values. Excellent

agreement was found; therefore, the DSC.experimentation and

 

 

162
methodology appeared to accurately characterize the thermal
and kinetic cure parameters. As Figure III.15 shows, the
FTIR-spectroscopy 0 results differed from the DSC-a
results. Uncured epoxy-resin data from transmission-FTIR
spectroscopy analyses and cured epoxy resin data from
diffuse-reflectance, DRIFT, FTIR spectroscopy analyses wre

not as accurate.

Hamadeh et al. [86] found that obtaining accurate
FTIR-spectroscopy measurements were difficult due to
numerous variables that affect the reproducibility of
sample preparation. As Table C.2 shows, poor
reproducibility existed among the FTIR-spectroscopy data.
This lack of accuracy in FTIR-spectroscopy data was assumed
to be due to the sample make-up and poor sample preparation

[97].

Hertzel [85] and Cole [29] stated that the variability
of film thicknesses on the KBr plates is the major cause of
variation among transmission-FTIR spectra. Young et al.
[83] also reported that transmission-FTIR spectroscopy was
subjected to substantial error caused from non-uniform film
thickness. Differences between the reference-intensity
ratio, 1146 cm°‘/1184 cm", between two identical

transmission-FTIR sample spectra were acceptable at four

 

 

163
percent. Table III.12 shows that the error for the epoxy-
intensity ratio, 916 cm'1/1184 cm", was unacceptable at

thirteen percent.

Table III.12. FTIR-spectroscopy sample-preparation errors.

 

 

Relative Standard Deviation Between FTIR-
Spectroscopy Intensity-Peak Heasurements‘

 

 

 

 

 

 

 

Epoxy - Reference
Peak‘ Peak°
Sources of Error (%) (%)
Transmission:
Uniform Film Thickness 13 4
DRIFT:
Particle Size 24 4
Particle-Size Distribution 17 2
Packing Density 15 1
Day-to-Day Reproducibility 28 3
Sample Concentration - 45 2
Using a Broader Baseline 17 1
No Liquid N2 Purge of
FTIR-Spectroscopy Chamber 11 1

 

 

 

& - experimental data for these results-can be found in
Table C.2.

* - epoxy-intensity ratio = (916cm'1/1184cm")

+ - reference-intensity ratio = (1146cm'1/1184cm")

 

According to Mertzel [85], DRIFT-FTIR spectroscopy has
been successfully used for the study of surfaces and bulk
materials. Hertzel et al. also emphasized that careful

control of the sample preparation must be practiced to

 

 

164
achieve reproducible measurements in the infrared

examination.

DRIFT-FTIR spectra gave acceptible differences among
reference-intensity ratios between one to four percent.
Unfortunately, as Table III.11 shows, the small but
important cured epoxy-intensity ratios gave large

experimental errors.

 

Two consecutive spectra of the same sample gave epoxy-
intensity ratios which differed by fifteen percent. This
difference in epoxy-intensity ratios are believed to be
caused from the dissimilar packing of the sample powder in

the sample holder.

FTIR spectra of a specimen with large-particle sizes
gave inaccurate spectral intensities. Larger peaks, such
as the reference-intensity peak at 1184 cm", gave reduced

intensities relative to smaller peaks. These findings were

 

consistent with Fuller et al. [28]. Their results also
showed that FTIR-spectra bandwidths and relative

intensities change considerably with particle size.

Next, studies were conducted to determine sources of
variation. Obtaining FTIR-spectra of fine and coarse
specimen particles showed a maximum epoxy-intensity ratio

difference of 24 percent. FTIR-spectroscopy analySes of a

165
sample containing a wide particle distribution (ie. fine
and coarse specimen particles) tended to give spectral

intensities which varied by seventeen percent.

Environmental contamination was considered. Samples
were analyzed before and after a 24-hour exposure to 25°C
and 50 percent relative humidity environment. A 28-percent
decrease in the FTIR-spectroscopy epoxy-intensity ratio was

found.

In conclusion, the maximum difference in the epoxy-
intensity ratio among the different particle sizes,
paricle-size distributions, packing density, and moisture
absorption were 24, 17, 15 and 28 percent, respectively.
Variables such as particle size, particle-size
distribution, packing density, and moisture content
affected the scattering coefficient, s, in the Kubelka-Munk
equation shown in Equation II.32. Presumably, dry small, evenly-
distributed particles loaded into a sample cup as a loose
powder were more closely packed yielded a smaller 3. A
smaller s would decrease the absorbance signal, and

therefore, produces a better spectra.

Other experimenters [27,83,86,97] have experienced
similar problems. Sellitti et al. [27] used FTIR
spectroscopy to study carbon-reinforced epoxy composites

and claimed that analyses were difficult due to severe

 

166
scattering and high carbon-fiber absorptivity. Painter et
al. [97] also found that obtaining reproducible FTIR-
spectroscopy data was greatly effected by sample
preparation procedures. Hammadeh et al. [86] could not
obtain reproducable DRIFT-FTIR spectroscopy data and
recommended using a Wig-L-Bug to obtain suitable DRIFT-FTIR
spectroscopy samples with uniform particle size and

particle-size distribution.

Cole et al. [29] claimed that the DRIFT-FTIR spectra
of carbon-reinforced epoxy composites are not accurately
characterized because of complications arising from the
reflective effects of the carbon fibers. They found poor
data reproducibility and reported a relative standard
deviation between the epoxy-intensity peaks as high as 15

percent.

In summary, neither transmission- nor DRIFT-FTIR
spectroscopy were perfected. These FTIR analyses were too
variable to obtain quantitive thermal or kinetic data due
to errors caused by sample preparation and carbon-fiber
absorbance. Therefore, the FTIR-spectroscopy data was only

used to qualitatively verify DSC extent of cure data.

 

 

CHAPTER IV

CONCLUSIONS

Effects of carbon fibers on the epoxy-resin cure were
determined and results were compared with published data.
Long, high-strength, untreated and surface-oxidized carbon
fibers were added to an epoxy resin in concentrations equal
to 0.01, 0.10, and 0.60. DSC and FTIR-spectroscopy
analyses were conducted to obtain extents of cure, glass
transition temperatures, and cure kinetics. It was
determined that the addition of carbon fibers to an epoxy
resins: (1) did not cause more or less epoxy molecules to
react; (2) did not significantly affect thermal cure
characteristics; and 3) did significantly affect kinetic-

cure parameters.

Major conclusions of the literature review were

summarized as follows:

1. Carbonyls and carboxyls are the most prevalent carbon-
fiber surface functionalities [6-8,18,21,24,27]. Surface-
oxidized carbon fibers contained twice as many functional

groups as untreated carbon fibers. Many experimenters have

167

 

 

168
reported that physical and chemical interactions between

carbon fibers and epoxy resin exist [2,5,25,55,65].

2. This region, where physical and chemical interactions
existed, is called the fiber-matrix interphase. The fiber-
matrix interphase has been described as the three-
dimensional region between the bulk epoxy matrix and a

carbon fiber, which included the two-dimensional interface

[4].

3. Cure kinetics for an epoxy-resin cure were modeled with

the following two equations [52,57-60]:

gg = (k, + k2 a) (l - a); for a S a,,l (13)
dt

gg = k; e'°¢/R' (1 - a); for a > 02,,l (14)
dt

where ki A, exp (-Ei/RT),

A, frequency factors for ki,
B, activation energy for ki,
a,“ = 0.48.
Initially, the reaction rate was modelled with

Equation 13, which represented the rate-controlled
autocatalytic-polymerization reactions. At a particular
extent of cure, gelation occurred and increased local
viscosity and steric hinderance of the reactants was found
[32-34,40,44]. Following gelation, the diffusion-limited
crosslinking reactions dominated and reaction rates were

modelled with Equation 14.

169
4. Neat versus reinforced epoxy-resin cures have been
discussed in the literature. Results from such studies
were summaried as follows: (1) Dutta et al. [43] had found
that glass-reinforced epoxy-resin cures gave 12-precent
higher extents of cure relative to neat epoxy-resin cures;
but carbon-reinforced epoxy-resin cures gave extents of
cure which were not significantly different than neat
epoxy-resin cures; (2) Wang et al. [74] cured neat and
carbon-reinforced difunctional and tetrafunctional epoxy
resins and found that reinforced difunctional epoxy resins
a maximum of 25°C reduction in glass transition
temperature, T,, relative to neat epoxy resins, and
reinforced tetrafunctional epoxy-resin glass transition
temperatures were not significantly different than neat
epoxy resins; (3) Ko [17] had used various carbon fibers
for reinforcements to find that glass transition
temperatures for high-strength carbon-reinforced epoxy
composites 25°C higher than glass transition temperatures
for neat epoxy resins and concluded that the T, was
affected by fiber type; and (4) Mijovic [44] have studied a
glass-reinforced epoxy resin and found a 98- to 99-percent
frequency-factor decrease and a 23- to 31-percent

activation-energy decrease relative to neat epoxy resins.

Major conclusions of the experimental study were

summarized as follows:

170
1. Experimental DSC full-cure extent of cure data showed
no significant difference between the neat and carbon-
reinforced epoxy resins. FTIR-spectroscopy full-cure
extent of cure data were also inconclusive in detecting any
difference between neat and carbon-reinforced epoxy resins.
These findings were consistent with carbon-reinforced
epoxy-resin results of Dutta et al. [43]. Small changes in
reaction exotherm and chemical structure due to fiber-
matrix interactions can not be measured by DSC and FTIR, a

more "interphase-specific" instrument was needed.

2. No significant difference was found between glass
transition temperatures for neat, untreated carbon-
reinforced, and surface-oxidized carbon-reinforced epoxy
resins. Similar glass transition temperatures suggested
that similar network formation occurred in the bulk-epoxy
matrix. The glass transition temperature, T,, results
presented in study were different than results given by
Wang et al. [74] and Ko [17]. Wang et al. [74] cured neat
and reinforced difunctional epoxy resins and found a 25°C
T, reduction for the reinforced formulations. Ko [17]
found a 45°C T, increase for high-modulus carbon-reinforced
epoxy resins and a 25°C T, increase for high-strength
carbon-reinforced epoxy resins relative to neat epoxy
resins. Ko concluded the fiber type, not the fiber

surface, affected glass transition temperatures.

 

171
3. Fully-reacted extents of cure for neat and carbon-
reinforced epoxy resins were integrated over time.
Gelation times increased to a maximum of ten percent when
the fiber-weight fraction increased to 0.60. At gelation,
the movement of unreacted epoxy molecules was restricted by
concurrent local increases in viscosity and steric
hindrance of reactacts. This physical carbon-fiber effect
created another "barrier" the epoxy molecules must

encounter and lengthened the epoxy-resin cure.

 

4. The diffusion-controlled crosslinking reaction rate
constant k3 decreased with increasing fiber-weight
fraction. The maximum decrease relative to the neat epoxy
resins occurred at ten percent when the fiber-weight
fraction equalled to 0.60. This result also showed carbon
fibers affected the epoxy molecules' mobility in an epoxy-

resin cure.

5. An Arrhenius-temperature model of these reaction rate

constants showed frequency factors decreased by 99 percent

 

and activation energies decrease by 35 percent with
increased fiber-weight fractions. Decreased frequency
factors and activation energies were attributed to a
chemical effect of carbon-fiber surface groups on epoxy-
resin cure reactions. Decreased frequency factors were
likely caused from polar carbon-fiber surface groups

attracting polar groups in the epoxy resin. Decreased

172
activation energies were caused from carbon-fiber surface
groups catalyzing epoxy-resin cure reactions. Such fiber-
matrix bonding has been investigated by other experimenters
[5,55,65]. Reduced frequency factors and activation
energies were consistent with Mijovic [44]. He has shown
that carbon-reinforced resins have 99-percent frequency
factor decreases and 21-35 percent activation-energy
decreases relative to frequency factors and activation
energy decreases for neat epoxy resins. Surface-oxidized
carbon-reinforced epoxy resins showed that frequency
factors and activation-energies were decreased by
approximately ten percent relative to untreated carbon-
reinforced epoxy resins. These decreases were expected
since surface-oxidized carbon fibers contained twice as

many polar surface groups as untreated carbon fibers.

6. This study did not confirm whether chemical reactions
occurred in the fiber-matrix interphase. This study did
show that using DSC and FTIR spectroscopy to analyze cured
epoxy composites can not give quantitative fiber-matrix
interphase cure characteristics. "Interphase-specific"
instrumentation must be used, such as an X-ray

Photoelectron Spectroscopy, XPS.

7. Recently, XPS study performed by Hooke [89] showed a

small, but siginificant change subsequent to reaction with

173
a thermally-heated epoxy. There was an approximate three-
to five-percent increase in the carbonyl concentration at
the carbon-fiber surface. This increase indicated a
chemical interaction between carbon fiber and epoxy
molecule. The XPS result further supported this study's

finding that a chemical carbon-fiber effect existed.

The amount of carbon fibers and the carbon-fiber
surface treatment had a small, but significant effect on
the epoxy—resin cure kinetics. Kinetic differences between
neat and carbon-reinforced epoxy-resin cures were explained
by carbon fibers possibly restricting the molecular
mobility of reactants and forming chemical interactions
with epoxy molecules. These carbon-fiber effects were
considered significant because a composite material's
performance is highly dependent on interactions in the

fiber-matrix interphase.

 

 

CHAPTER V

RECOMMENDATIONS

A major problem encountered in this experimental
study was the inability of the DSC and FTIR spectrometer
to give quantative "interphase-specific" data. This
problem will be addressed and accompanied with suggestions.
Then recommendations for alternative curing methods will be

presented based on insight obtained from this study.
A. Problems and Suggestions

A major difficulty found in this study was that
experimental techniques used were not "interphase-
specific". Differential scanning calorimetry analyses were
not sensitive enough to detect the small variations in the
reaction exotherm; FTIR-spectroscopy methods were not
precise enough to accurately detect the variations in the

chemical structure of the fiber-matrix interphase.

Two high-vacuum techniques, not accessible at the
start of this research project, now available in the
Composite Materials and Structures Center Laboratory at

Michigan State University, are the electron spectrOscopy

174

 

 

175
for chemical analysis, ESCA, and Auger spectroscopy. Both

instruments are "interphase-specific".

ESCA- and Auger-spectroscopy techniques irradiate the
specimen with an incident beam set at a grazing angle to
the sample surface. ESCA bombards the sample surface with
monoenergetic x-rays and ejects inner, ls, 25, and 2p,
electrons from various atomic levels. Auger spectroscopy
bombards the surface with high-energy electrons and an
inner electrons are ejected. The vacancy is filled by an
outer electron and energy is released which causes an Auger
electron to be ejected. The energy of the ejected
electrons is determined by means of an electron
spectrometer which quantifies the chemical structure of the
sample surface. Unfortunately, neither the ESCA nor Auger
spectroscopy are "non-destructive". They require the

interphase to be fractured to expose the sample surfaces.

According to Sellitti et al. [27], an analytical
technique which can satisfactorily characterize the carbon-
epoxy interphase must be "interphase-specific" and "non-
destructive”. Both Sellitti et al. [27] and Garton et al.
[65] claimed that FTIR internal reflection spectroscopy,

IRS, was both "interphase-specific" and "non-destructive".

Other FTIR-spectroscopy techniques that show promise

are using microscope and heating attachments with ’

 

 

176
transmission-FTIR spectroscopy. These attachments would
allow the epoxy-resin to be cured while focusing on a
region as small as 10 A in diameter [87]. These two FTIR-
spectroscopy techniques would enable the experimenter to
obtain a spectra of the fiber-matrix interphase at various

cure times and use these data to model the cure kinetics.

Today, a complete understanding of the carbon-epoxy
interphase falls short of being fully adequate to control
and optimize the composite interphase. The critical gaps
in knowledge are primarily related to the detailed
structure of the interphase and its implication with
respect to chemical and mechanical behavior. The delicacy
and dimensional scale of the fiber-matrix interphase make

them very difficult to address experimentally.

One of the more promising experimental approaches to
these problems is through the use of scanning tunneling
microscopy, STM. In the past, STM has been applied to
atomic imaging of carbon fibers [5]. Commerical STM
instruments are available which are capable of producing
images ranging from atomic resolution up to areas of square
micrometers. Sophisticated tools, such as the STM, could
make it possible to obtain the information about the carbon
surface-defect structure and epoxy-resin chemistry required
to formulate valid quantitative theories of the fiber-

matrix interphase.

 

 

177
This study and recommendations should helpfuture
experimenters gain insight on how to better study composite
interphases. In the next section, several suggestions will
be given which may also assist in further composite

research and experimentation.

B. Further Research

The major problem facing epoxy manufacturers is
achieving a fast, efficient, and uniform epoxy-resin cure.
Today, conventional curing is limited to only thin epoxy
resins, because large thermal gradients which are generated
during epoxy-resin cures. Typically, epoxy resins are
cured under heat and pressure in autoclaves. As Figure
II.19 shows the heating mechanism for a convectionally-
cured specimen is through its boundaries. Upon cooling,
these epoxy resins develop residual stresses in the matrix
due to differences in the thermal expansion and, then,

fracture.

Microwave and laser curing provides sufficient energy
to initiate the polymerization reactions in the epoxy
matrix [95,99]. With electromagnetic or laser curing,
manufacturers may achieve a more efficient, uniform,
complete, and economical cure than convectional-oven curing
regardless of the composite's geometry. Microwave curing

enables specimens to be cured from its interior to its

 

 

178
boundaries. Laser curing enables the beam to be focused at

any point on a specimen.

Experimenters [57-60,99,101-103], have cured epoxy
resins using microwave energy. Microwave energy is the
energy associated with electromagnetic radiation within the
microwave frequency range. Energy density stored in the
electric field is always equal to the energy density stored
in the magnetic field for electromagnetic radiation [101].
From electrostatics, the dielectric media includes both~
polar and non-polar molecular structures. Polar molecules
align themselves with the oscillating electric field. Non-
polar molecules take on an induced dipole, then orient
themselves in the electric field. These molecules also
adsorb rotational and vibrational energy from
electromagnetic radiation of the appropriate frequency.
When a dielectric material is placed in this field, epoxy
molecules attempt to move and align themselves with it.
However, since the field is oscillating, epoxy molecules
are continually redirected. The increased movement of
epoxy molecules creates an increase in the thermal energy

of the system [102,103].

Since carbon fibers are much more lossy than the epoxy
resin, the carbon fibers will increase in temperature
faster than the epoxy resin. Whether the increase in

carbon-fiber temperature will advantageously or adversely

 

 

179
affect the ultimate structure and properties of the
composite material is not known. It may be possible that
the conductive carbon fibers will distrubute the heat more
efficiently and uniformly; or the carbon fibers may excite
polar carbon-fiber surface groups, such as carboxyls and

carbonyls, and cause more epoxy monomers to react.

One disadvantage of microwave curing is that the
experimenter has little control over the-direction of the
radiation. Laser curing of resins can offer more
flexibility by directing the beam to only certain areas of
a composite material. Unfortunately, the laser curing of
composites has been less studied than the microwave curing

of resins.

New research indicates that laser can be directed such
that one part of a material may be cured while an adjacent
part is left unaffected. Studies have been conducted where
a carbon-dioxide infrared laser is used to cure an epoxy
resin [104]. After a simulated production cure, the shear
strength of the epoxy-resin samples are tested. The shear
strength of the laser-cured samples are found to be equal
to those obtained with the conventionally-cured samples.
Newbould et al. [104] has reported that the failure modes
are cohesive rather than adhesive. They also believed that

laser curing has much potential once stable power

 

 

180
deliveries are obtained and laser beam equipment capable of

scanning complex surfaces is available.

As a direct benefit, this study can be used as an aid
in the designing and processing of composites. Comparative
studies of conventionally-cured versus microwave- or laser-
cured composites should be performed to gain insight on
whether other types of curing are superior to conventional [I

curing.

1‘ '

Due to the lack of understanding of the fiber-matrix
interphase, currently marketed commercial composites are
optimized with respect to information available. In order
to aid in future "a priori" selection of composite
components, other fiber composites such as glass or Kevlar
should be cured, modeled, and compared with this study.
Gaining an understanding of the structure and composition
of different fiber-matrix interphases should enable a
future "a priori" selection of composites based on the

needs of composite-material users.

 

181

Appendix A

MAXIMUM EXOTHERM BETWEEN CARBON FIBERS AND EPOXY MATRIX

The difference in the atomic percentage of oxygen on
the surface-oxidized and untreated fiber surface was 0.09
and 0.05, respectively. The actual surface of the fiber
which was available for reaction with an epoxy molecule
remained very small. Using bond lengths and geometry, the
maximum number of sites containing functional, oxidinated,
the number groups on the surface of the surface-oxidized-
carbon fiber, is 4.99 * 101s sites/cm2 or 4.88 * 10'8
9'°‘/°'2- This value is multiplied by the reaction
exotherm and the surface area of the reinforced
formulations, to determine the maximum change in the
reaction exotherm. The calculated maximum increase in the
reaction exotherm for the surface-oxidiZed carbon-
reinforced composite is 5.40 cal/g; and the maximum
increase in the reaction exotherm due to physisorption is
0.022 cal/g. ”

Adhesion at the Fiber-matrix Interface:

The carbon fiber consists of layers of basal planes
[8] with an interplanar distance of 3.35 A and a planar
distance of 7.7 A. The distance between a C-C bond is 1.42
A. All angles in a perfect hexagon are 120°, and an equil-
lateral triangle can be drawn between the center of the
hexagon and two neighboring perimeter points of the
hexagon.

Suppose the graphitic basal plane of a carbon fiber
surface can be illustrated as follows:

C atoms

chemical bonds in
outer basal layer
chemical bonds in
inner basal layer

0

 

Figure A.1. Chemical reaction of a carbon fiber and an
epoxy resin.

 

 

-4 x.

182
3( 1.42 A ) - 2 - ( 0.94 A ) = 8.01 A
4 (1/4) + 2 (1/2) + 2 = 4 atoms

°_A_12 - 9122_x_19‘5_999m§_ef_9
( 8.01 A ) ( 1 cm@ ) cmz

Assume: 1. The surface area, S, per gram of epoxy equals
4500 cmF. This surface area was observed with
by using a krypton adsorption technique or BET
analysis [7]

2. Equilmolar reaction between an epoxy and a
carbon-fiber surface group. The reaction
exotherm for this reaction equals 24.6~

kcal/g,,,xy.

Therefore, the maximum change in the ultimate reaction
exotherm, 5301:: due to chemical reaction between the
epoxies and the carbon-fiber surface groups is

5301. = [2919.3991 ][ 1999991 ][ 4999.9m2_] .
gmol kcal gepoxy

9129_x_19‘5.5199§_nes§1919 _______gmel______
cm@ 1.023 x 1023 atoms

or 6H“t = 5.40 cal/g or 22.6 J/g. This value is only
1.26% of the ultimate reaction exotherm, Hult. Since the
precision of the DSC is i 2. 5%, sample error, detecting
such a small change in reaction exotherm is unobtainable
with the DSC.

Let's consider the 6H,,t due to physisorption, from
Adamson the physisorption reaction exotherm equals 0.1
kcal/g,,,xy. Therefore the

6H... = [ 0-1_k931][ 1999991 ][ 1599.9m1_] .
gmol kcal g,,,xy
A122.x.19LL_§ite§_29§§ihle gmol -
[ cm2 ][ 1.023 x 1023 atoms J

or 6H,], = 0. 022 kcal/g or 0.092 J/g. Obviously, this
value can not be determined from DSC analyses either.

 

 

183

Appendix B

TTT DIAGRAM TRANSITIONS

DEIEBMINIE§_IHE_EQLL_QHBE_LIHE

The full cure line on a TTT diagram represents the
time where the all cure reactions cease. This method is
similar to a procedure outlined by Peng et al.

1. Assume a linear relationship exists between T, and
Hult, for isothermal cures below the ultimate glass
transition temperature.

 

 

1,13) T 13) H._. l , (lzgmol)

170 98 330

190 215 358

200 222 374

210 V 225 386

220 227 394
The following equation fit the data: = 33. 2 + 0.503
H,,,_ The correlation coefficient equailed 0.9902.

2. Next the glass transition temperature at different
times during the isothermal cures at 170, 200, and 220°C
are calculated using the previous equation.

 

 

t H T H T, H T,
' 7 t 00.t1 (200.t) I t O t
30 241 157 348 188 361 215
40 276 172 354 211 376 220
50 289 179 358 213 378 223
70 295 182 364 216 380 224
100 314 191 371 220 381 225
3. A linear relationship exists between T, and T,. The
previous data was fit to the equation, t, = A + B T,
t(min) data A B r*
30 _T, 170 200 220 -52.9 1.21 0.9988
T, 154 208 215
40 _1', 170 200 220 6.92 . 0.987 - 0.9734

 

172 211 220

 

 

184

t(min) data A B ’ r*

50 _J; 129 299 229 28.0 0.900 0.9820
T, 179 213 223

70 _];__119__ZQQ__22Q 37.6 0.863 0.9741
T, 182 216 224

100 _j; 129 299 229 73.8 0.702 0.9632

T, 191 220 225
* = correlation coefficient

4. Determine the isothermal cure temperature needed to
achieve full cure at the times of 30, 40, 50, 70, and 100
minutes.

gimin) 30 4o 50 79__199
T,(°C) 224 223 222 222 221

The data fit the following equation:
T, - 232 - 5.32 log t.
The correlation coefficient is 0.9557.

DEIEBMINIH§_IHE_§§LAIIQH_LIEE

The gelation line represents the line in a TTT diagram.
in which the extent of cure, a, equals the extent of cure
at gelation,a a,,[

1. Assume a linear relationship between gelation
temperature, T,,l, and the log1o of the gelation time, log
t or

eel.

Tgel = a + b 109 tool;

where a, b = fitted constants.
The theoretical a,,l for a stoichiometric difunctional
epoxy is 0.58, and the resin is found to be five to ten

percent precured; therefore, the a,,l is assumed to be
0.50.

 

 

 

___JkILQl $9.11minlf* 1°910£gel
170 16.60 1.2
200 7.10 0.85
220 4.70 0.67

** = Data from Table III.7.
2. This data is fit to:

Tf = 232 - 5.32 log t.

185

DEIEBMIHIH§_IHE_¥IIBIEIQAIIQH_LIHE

The vitrification line in a TTT diagram represents the
line when the T, equals the T,.

l. The experimental T, versus H, data has been extrapolated
to determine the vitrification time, tvit, or the time
when T, equals T,.

 

___I.(°C) tannin;
170 100
200 57
220 50

2. A linear regression is performed on the previous table.
The resultant equation is:

T, = 478 - 155 log t.

186

Appendix C
DSC AND FTIR-SPECTROSCOPY EXPERIMENTAL DATA

Table C.1. The DSC extent of cure, 0, versus time, t, and
fiber weight fraction, w,, for the neat, surface-oxidized
carbon-reinforced and untreated carbon-reinforced
isothermally-cured at: (a) 170°C; (b) 200°C; (c) 220°C.

(a)

 

 

0.60

2 0.02

3 0.03

4 0.04

5 0.06

6 0.08 0.07 0.08 0.08

7 0.10 0.09 0.10 0.17

8 0.12 0.12 0.11 0.12

9 0.14 0.14 0.13 0.13

19 0.27 0.26 0.26 0.25

29 0.38 0.38 0.37 0.36

39 0.43 0.42 0.41 0.43

49 0.48 0.48 0.48 0.47

59 0.50 0.49 0.49 0.48

89 0.54 0.53 0.53 0.52

119 0.54 0.54 0.53 0.52

149 0.55 0.54 0.54 0.53

179 0.56 0.55 0.55 0.54

329 0.56 0.56 0.55 0.55
m

 

 

 

 

 

 

Table C.1 (continued)

 

 

 

 

2 0.24 0.25
3 0.37 0.38
4 0.46 0.44
5 0.52 0.52
6 0.56 0.56
7 0.59 0.59
8 0.63 0.63
9 0.66 0.65
19 0.78 0.77
29 0.83 0.82
39 0.84 0.83
49 0.85 0.84
59 0.85 0.84
89 0.86 0.85
119 0.86 0.85
149 0.86 0.86
179 0.86 0.86
329 0.86 0.86

187

 

 

 

 

 

 

 

0.23
0.37
0.44
0.51
0.55
0.58
0.61
0.62
0.76
0.82
0.82
0.82
0.83
0.84
0.85
0.85
0.85
0.86

 

Table C.2.

188

FTIR epoxy intensity peaks data.

Epoxy intensity peak
peak‘

 

Transmission:

0.05476
0.05154
0.05348
0.05125

 
   

Source/
Relative Error (%)

 
 

Particle size

13

 

DRIFT-FTIR:

 

 

    

 

  

Particle size

 

 

distribution
0.09878
0.08465 24
0.05274
0.05016
w
Packing Density
0.09332 -
0.07811 17
0.06615
0.08125
m=
Day 1 Day2
Day-to-Day
Reproducibility
0.05696 0.04274
0.06189 0.04016 28
0.06655 0.04494
0.05016 0.04222

0.05050
0.1028

0.09682
0.05125

 

Sample Concentration

45

 

 

Table C.2. (continued)

 

W
Broader Baseline

0.1694
0.1761 17
0.2048
0.1502

No N2 Purge

 

0.06154
0.05860 11
0.06690

0.06257
w

 

10.

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