LIBRARY
Michigan State
Unlverslty

 

 

 

PLACE IN RETURN BOX to romavo this checkout from your record.
TO AVOID FINES Mum on or baton ddo duo.

DATE DUE DATE DUE DATE DUE
JAN 3573399

---
LJ-LJ
I ll

I 1| II I

MSU lo An Affirmative ActIoNEquol Oppottmlty Institution
chG—ot

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MICROWAVE PROCESSING OF VINYL ESTERS AND
VINYL ESTER/ GLASS FIBER COMPOSITES

by

Ramakrishna Dhulipala

Adviser: Dr. Martin C. Hawley

A THESIS

submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Chemical Engineering

1993

MI (

ll
studied a
research
Vinyl tolL
Tl
model, b;
rt‘lerttsent
the mjm‘m
Prediction
microwave
using the 5
Possible ex
through the
Uni<
Processed i
techquC ar

thermally cu

ABSTRACT

MICROWAVE PROCESSING OF VINYL ESTERS AND VINYL
ESTER/GLASS FIBER COMPOSITES

By
Ramakrishna Dhulipala

Microwave Processing of polymers and polymer matrix composites has been
studied as an alternative to conventional thermal processing. In further pursuance of this
research area, different aspects related to the microwave processing of vinyl esters (with
vinyl toluene as comonomer) and vinyl ester/ glass fiber composites have been studied.

The kinetics of polymerization during thermal curing was investigated and a
model, based on considering equal reactivities for vinyl groups, was formulated to
represent the kinetics. The different parameters for the model were estimated based on
the minimization of the square of the error between the experimental values and model
predictions of the extent of cure. The same model was used for the representation of the
microwave cure kinetics. The different parameters for the microwave data were found
using the same procedure, but the fit was not as good as the fit for the thermal data. A
possible explanation is the enhancement of the reactivity of vinyl group from vinyl ester
through the interaction with microwaves.

Unidirectional 12—ply vinyl ester/ glass fiber laminates were prepared and
processed in a thermal oven, and in a microwave cavity using a mode-switching
technique and the same cure cycle. The mechanical properties of the microwave and

thermally cured laminates in flexure were compared and were found to be the same.

Dedicate

less in s.

Dedicated to my Parents who, half the world away, have sacrificed no

less in seeing me through to this important milestone of my life.

iii

 

I Wt
direction. E
difficult ph.
under his It

A v
completed i
Susannah I
different St,

The
Michael Ri
mates inclr
the other t
exDress In}

All
exterrded U
he‘P While
int-01V-ed_

[as

mom] Chet

ACKNOWLEDGEMENTS

I would like to thank Dr. Martin C. Hawley for his constant guidance and
direction. His steadfast support provided me the confidence and strength to tide over the
difficult phases of my research. I will be indebted to him for all things I have learnt
under his leadership.

A work of this nature with all the associated experimental work cannot be
completed in such a time frame without a lot of assistance and for this I wish to thank
Susannah Travis, Gretchen Kreig and Richard F. Falk for their steady efforts during the
different stages of the work.

The excellent infrastructural support and the unfettered cooperation provided by
Michael Rich, Dan Hook and Brian Rook have proved invaluable to me. All my group-
mates including Jianghua Wei, Valerie Adegbite, and Larry Fellows have at one time or
the other been instrumental in seeing me through the taxing segments of my work. I
express my gratitude to all of them.

All the people I have had a chance to interact with in the course of this work have
extended their fullest possible cooperation with alacrity. I gratefully acknowledge their
help while regretting my inability to credit them individually because of the numbers
involved.

Last but not the least I am thankful to my family members and friends whose

moral encouragement and emotional support can never be overestimated.

iv

 

 

 

LIST OF
LIST OF
NOMEM

l. INTRO
1.1

1.2."

1.3 T

”HR.“

2.1 Ba
2.2 Th

TABLE OF CONTENTS

LIST OF TABLES ..................................... viii
LIST OF FIGURES ..................................... ix
NOMENCLATURE ..................................... xi
1. INTRODUCTION ..................................... 1
l. 1 Background 1

1.1.1 Microwave processing concept 1

1.1.2 Microwave system 2

1.1.3 Advantages of microwave processing 4

1.2 Materials 4

1.2.1 Highlights of vinyl esters 4

1.2.2 Vinyl ester chemistry 4

1.3 Thesis objective 7

1.3.1 Materials used in the studies 7

1.3.2 Neat resin study 8

1.3.3 Studies on composite laminates 8

2. Fl‘IR ANALYSIS ..................................... 9
2. 1 Background 9

2.2 Theory 10

2.2.] Development of the method 10

2.2.2 Quantitative analysis 12

 

 

3. THE

4- MIC]

AAA

5- THE]

3. THERMAL KINETICS OF POLYMERIZATION

2.2.3 Application to kinetic study
2.3 Spectra recording
2.4 Experimental
2.5 Results

2.6 Limitations and sources of error

2.7 Summary

3. 1 Background
3.2 Theoretical development of the model

3.3 Materials and methods
3.3.1 Sample preparation and curing
3.2.2 Analytical technique
3. 3. 3 Data processing

3.4 Results and discussion

3.5 Summary

4. MICROWAVE KINETICS OF POLYMERIZATION ..........

4. 1 Background
4.2 Experimental
4.3 Results and discussion

4.4 Summary

5. THERMAL PROCESSING OF LAMINATES ...............

5.1 Introduction

5.2 Development of the method

5.3 Experimental
5.3.1 Preparation of the laminates and laminate molds
5.3.2 I’m-consolidation cycle

vi

000000000000

13
13
14
15
20
21

22
22
23
28
28
29
32
34
39

3888

48

49
49
50
51
51
53

 

 

5.4 I
5.5 I

6. MICRO‘
6.1 I
6.2 I
6.3 l
6.4 S

7. GLASS '
7.1 l
7.2 I

8. CONCLi
8.1 I
8.2 1

5.3.3 Ihennal curing 53

5. 3. 4 Mechanical testing of cured laminates 54

5. 3.5 Void fraction analysis of the laminates 54

5. 3. 6 Fiber volume fiaction analysis 54

5.4 Results and discussion 55

5.5 Summary 56

6. MICROWAVE PROCESSING OF LAMINATES ................ 57
6.1 Introduction 57

6.2 Experimental 58

6.3 Results and discussion 60

6.4 Summary 66

7. GLASS TRANSITION TEMPERATURE DATA ................ 67
7. 1 Experimental method 67

7.2 Results 67

8. CONCLUSIONS ..................................... 70
8.1 Summary of results 70

8.2 Scope for future work 73
APPENDICES ........................................ 75
Appendix A: Derivation of kinetic equations 75
Appendix B: OBEY programs 86
Appendix C: MATLAB script files 97

LIST OF REFERENCES ................................. 114

vii

 

Table 2.1

Table 3.1

 

‘ Table 3.2
1

Table 4.1

 

Table 5.1
Table 6.1

Table 7.1

 

Table 2.1

Table 3.1

Table 3.2

Table 4. 1

Table 5.1

Table 6. 1

Table 7. 1

LIST OF TABLES

Absorbencies of vinyl toluene at different wave numbers

The baselines and the limits for the areas under the different
peaks

Kinetic parameters for vinyl ester/vinyl toluene polymerization
Comparison of kinetic parameters for thermal and microwave
curing

Properties of thermally cured laminates

Properties of microwave and thermally cured laminates

Tg of thermal and microwave cured samples

viii

17

31

35

43

55

68

 

 

 

Figure 1.
Figure 1.1
Figure 1.:
Figure 1,.

Figure 2.2

Figure 1.1
Figure 1.2
Figure 1.3
Figure 1.4
Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Figure 3.1
Figure 3.2
Figure 3.3
Figure 3.4
Figure 3.5
Figure 3.6
Figure 3.7
Figure 4.1

LIST OF FIGURES

Cross section of tunable cylindrical microwave cavity

Microwave diagnostic and processing system circuit

Chemical structures

Reaction mechanism of vinyl ester resins

Spectra of the chemical systems

Absorbance at 1632 cm‘1 vs. absorbencies in 550—590 cm" region
Absorbance at 1632 cm'1 vs. absorbencies in 1155-1189 cm'1 region
Absorbance at 1632 cm’1 vs. absorbencies in 1220-1250 cm'1 region
Absorbance at 1632 cm'1 vs. absorbencies in 645-660 cm'1 region
Area used for determining concentration of analyte

Model predictions and experimental data of extent of cure at 80°C
Model predictions and experimental data of extent of cure at 90°C
Model predictions and experimental data of extent of cure at 100°C
Model predictions and experimental data of extent of cure at 110°C
Error windows based on error in temperature measurement

Model predictions of rate of reaction vs. extent of cure at 90°C

Temperature profile of microwave curing of a neat resin sample

16

18

18

19

19

31

36

36

37

37

38

38

42

Figure
Figure
Figure

 

Figure

Figure .
Figure 1
Figure 5
Figure 6
Figure 6.

Figure 6.

 

Figure 6.4

Nature 6.5

“gun: 6.6

Flgul'e 6.7

Figure 6.8

Flglue 7.1

Figure 4.2
Figure 4.3
Figure 4.4
Figure 4.5
Figure 4.6
Figure 5.1
Figure 5.2
Figure 6.1
Figure 6.2
Figure 6.3

Figure 6.4

Figure 6.5

Figure 6.6

Figure 6.7

Figure 6.8

Figure 7-1

Temperature profile during microwave curing (close up)

Model predictions and experimental data during microwave curing
Model predictions and experimental data during microwave curing
Model predictions and experimental data during microwave curing
Model predictions with microwave and thermal parameters at 80°C
Laminate coupon

Laminate coupon in the teflon mold

Position of temperature probes on the sample

Position of the sample in the cavity

Single mode heating pattern of sample RP1244 in one orientation
Single mode heating pattern of sample RP1244 in different
orientation

Single mode heating pattern of sample MwB7

Single mode heating pattern of sample MwB8

Comparison of flexural strength of Autoclave, Oven and Microwave
cured laminates

Comparison of tangent modulus of Autoclave, Oven and Microwave
cured laminates

Tg vs Extent of cure of thermal and microwave cured samples

42

46

46

47

47

52

52

59

59

61

61

62

62

65

65

69

AM

Ca, Cb

pa, pb

68M, 6b)“

x, x.

NOMENCLATURE

Absorbance of the mixture at wavelength A,.

Concentrations of the components in moles or grams per total volume of
the mixture.

Path length of the sample.
Either of the two chemical species present.
Moles or grams per unit volume of the respective pure components.

Molar or mass absorptivities of the components ’a’ and ’b’ at the
wavelength hi.

wavelength in any region of the spectrum.

xi

 

 

 

1.1 Bacl

C
chemical.
mechanis
electroma
of curing j
have an ef;
similar prc
effect wou
systems. it

[1.2].

I-1.I Micro

M icrc
Of Visible Iigp
pr OP'Srties. II

in eqlliitioi) 1,

  
  

distribution a,

l . INTRODUCTION

1. 1 Background

Conventional processing of polymer matrix composites involves the heating of the
chemically reactive precursors through convective and conductive heat transfer
mechanisms. Microwave processing involves the transfer of energy to the materials by
electromagnetic radiation which offers a much faster and more easily controllable method
of curing polymers and polymer matrix composites. In addition microwave radiation can
have an effect on the chemical reaction mechanism which can enhance curing rates under
similar processing conditions and reduce processing times. An implication of such an
effect would be a possible enhancement of the mechanical properties of the cured
systems. Work done on epoxies and graphite/epoxy composites has given such results

[1,2].

1.1. 1 Microwave processing concept

Microwaves are electromagnetic waves of a frequency far less than the frequency
of visible light. These are absorbed by materials depending on the materials’ dielectric
properties. The relations that govern the absorption of microwaves by materials are given
in equation 1.1. In materials composed of components of different dielectric properties,
the microwaves are absorbed non-uniformly. This results in a non-uniform power

distribution across the volume of the material exposed to microwave radiation.

 

 

1.1.2 .llicra

A or
Composites :
cFlindrica] c
is “56d that .
a fT'thtIOn 01

Supplied to

description c

 

P=—%eoe"w|Elz
e " = e” + o
d so to

P = power dissipated as heat (1'1)
8 " = loss factor
2",, = dipolar contribution
a = conductivity
at = frequency
so = permittivity of vacuum

I E | = electric field strength

1. 1.2 Micmwave system

A cross section of the cylindrical cavity used for the curing of polymers and
composites is shown in Figure 1.1. The microwave processing circuit that contains the
cylindrical cavity is shown in Figure 1.2. A single frequency microwave power source
is used that emits microwaves at 2.45 Ghz frequency. The directional couplers redirect
a fraction of the power to the power meters to enable the measurement of the power
supplied to the cavity and the power reflected back from the cavity. A complete

description of the system is available elsewhere [3].

 

 

 

Figure 1.1

Microwave 8.

 

Ifigure 1,2

 

 

 

 

 

 

 

 

“\Top plate

Composite .
E__‘___]~ qfi Eff? -_-

 

: Teflon 01610 Bottom plate
f
g L rI/

1

 

 

 

 

 

 

Figure 1.1 Cross section of tunable cylindrical microwave cavity

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fluoroptic Ternperatm'c Sensing System
Power Meter
PI
Microwave Source
Directional Coupler
X Y
X-Y Oscilloscope Pb diagnostic
[robe
Power Meta
, Pr
Power Meter

Figure 1.2 Microwave diagnostic and processing system circuit

 

 

1.1.3 Adv
Mi
results in
involves I]
to the slox
results in
thermoset
there is a p-
to which er

also be ma;

1.2 Materh
1.2.1 Highi
Vin)
They have
unsimitation
the Secondar-

acid and hid

4

1. 1.3 Advantages of microwave processing

Microwave processing involves direct transfer of energy to materials and this
results in a greater controllability compared to thermal heating. Microwave processing
involves the volumetric heating of materials and this results in rapid heating compared
to the slow heat transfer controlled thermal heating. The much faster response times
results in the ability to control the exothermic excursion during the processing of
thermoset polymers. Temperature gradients are not necessary for heat transfer and so
there is a possibility of maintaining very good temperature uniformity across the material
to which energy is being transferred using microwave radiation. Preferred gradients can

also be maintained to reduce voids during condensation polymerization.

1.2 Materials
1.2.1 Highlights of vinyl esters

Vinyl ester resins are noted for their high chemical resistance and toughness.
They have excellent reactivity during polymerization due to the terminal vinyl
unsaturations. They have very good wetting and bonding to glass reinforcements due to
the secondary hydroxyls on the vinyl ester resin molecule. These materials have superior

acid and hydrolysis resistance [4].

1.2.2 Vinyl ester chemistry
Vinyl ester resins are formed by reacting epoxy resins with ethylenically

unsaturated carboxylic acids. The most commonly used epoxy resin is DGEBA based and

i; g
.t
rt; :1 S's-.1: -
‘ n.- -— - - ‘ur ._'rl ‘

 

the commOn

cleavage of dc
by a free radiC
therefore uns.‘
polymerizatior
the unsaturatet
chemical struc

The fre
in parallel. F ig
Strip involves t
radicals that im
Chains reacting
lengths, The te:
dead chain,

The tern
form of termina
a molecular
disPrOPOnionan

thereby becomi

 

 

5

the common carboxylic acid used is methacrylic acid. Crosslinking occurs due to the
cleavage of double bonds and the formation of single bonds. The polymerization proceeds
by a free radical mechanism. Vinyl ester resins typically homopolymerize sluggishly and
therefore unsaturated low molecular weight monomers are added to increase their
polymerization rates and also to reduce the working viscosity of the resins. Examples of
the unsaturated monomers used include styrene and vinyl toluene. Figure 1.3 shows the
chemical structures of a vinyl ester resin and vinyl toluene.

The free radical polymerization of vinyl esters consists of three steps occurring
in parallel. Figure 1.4 illustrates the different steps of the polymerization. The initiation
step involves the decomposition of the initiator and results in the production of free
radicals that initiate the chain formation. The propagation reaction involves the growing
chains reacting with the unreacted unsaturations and results in the increase in chain
lengths. The termination reaction involves the interaction of two free radicals to form a
dead chain.

The termination reaction can proceed in two different ways. In the combination
form of termination the two free radical ends combine together to form a chain that has
a molecular mass equal to the sum of their individual molecular masses. In
disproportionation, one of the free radicals transfers a proton to the other free radical

thereby becoming unsaturated while the other free radical becomes a dead chain [5].

 

' hi .5
figure 1.3

In

P

R

R

F

F

'l

I

I

Figure 1.4

raw—Lo—cuz-CH—crgrt—cuxrtrt—cn—crt-o—b—c—crt,

vinyl ester

=CH2

CH3
viriyl toluene

Figure 1.3 Chemical structures

Initiation

» 2R°

 

Propagation
R10 + M1 —-—> R1.
R10 + M2 ——> R2-
R20 + M1 _K’_‘) R1-
R20 + M2 ____> R20
Termination

Rn'+ Rm‘—'+Rn+m
Rno+ Rm. ___’Rn+Rm

Figure 1.4 Reaction mechanism of vinyl ester resins

 

1.3 Thesis obi

The ovc
polymer matri
properties simi
a comprehensi
study of differ
important asp
interaction of
understand the
These relative
mCChanism of

11111135131 reqt

1.3.1 Materia

The m
Supplied by T
Diglycidyr ct
toluene as the
flash POint [112
Only BPO WE

”moon... Ian

1.3 Thesis objective

The overall goal of the research group is to use microwave technology to process
polymer matrix composites in a microwave cavity and to produce composites with
properties similar to or better than autoclave processed composites. To achieve this goal
a comprehensive understanding of the fundamentals must be attained. This involves the
study of different aspects of the processing with different materials. For this work two
important aspects have been identified: (1) Neat resin studies to understand the
interaction of microwaves with polymers and (2) Studies on composite laminates to
understand the macro-level aspects related to the microwave processability of composites.
These relatively fundamental studies are expected to give a better insight into the
mechanism of microwave curing and are hoped to assist in scaling up of the process to

industrial requirements.

1.3.1 Materials used in the studies

The material used in the studies is an experimental vinyl ester resin XU-71973.00
supplied by The Dow Chemical Company, USA. The resin is a methacrylic ester of
Diglycidyl ether of Bisphenol-A based epoxy and contains 45 % by weight of vinyl
toluene as the cross linking monomer. Vinyl toluene was used because it has a higher
flash point than styrene and is easier to handle in a laboratory from a safety perspective.
Only BPO was used to catalyze the reaction. Glass fiber was used in the studies with

composite laminates.

 

1.3.2 New ’8
The l
polymfirizatio
to repress?“t
parameters ‘1‘”
conduCled 10‘

microwa"es a

1.3.3 Studies

Th6 fc
matrix compo
thermally CU“
examined for

The EC
laminates usin
(2) compare It
in the thetma
evaluate the \
investigation It
equivalent to t

the aSpects rel ;

 

 

1.3.2 Neat resin study

The focus of this study was to investigate the kinetics of the vinyl ester resin
polymerization during thermal and microwave curing. The goal was to evolve a model
to represent the kinetics of vinyl ester polymerization and estimate the different
parameters during thermal curing and during microwave curing. This investigation was
conducted to broaden the understanding of some of the fundamental interactions between

microwaves and polymers and explain any differences in the curing rates.

1. 3.3 Studies on composite laminates

The focus of this study was to process glass fiber reinforced vinyl ester resin
matrix composites in the microwave cavity, with equivalent mechanical properties to
thermally cured composites. Twelve ply unidirectional laminates were selected to be
examined for these composite processing studies.

The goals for this study were set as follows: (1) process vinyl ester/glass fiber
laminates using similar cure cycles, in a thermal oven and a microwave cavity
(2) compare the mechanical properties of the samples cured in the microwave cavity and
in the thermal oven with the mechanical properties of autoclave cured samples (3)
evaluate the void fractions of the laminates produced (4) use the feedback of this
investigation to reproducibly produce laminates in the microwave cavity with properties
equivalent to those of the autoclave cured samples and (5) make a preliminary study of

the aspects related to the industrial applicability of the microwave processing technology.

2. FTIR ANALYSIS

2.1 Background

Infrared spectroscopy is a well established technique for qualitative as well as
quantitative studies [6,7,8]. This is a valuable tool for the analysis of polymer mixtures
because of the highly specific nature of interaction between IR radiation and matter,
which depends greatly on the molecular structure and environment of a substance. This
technique has other advantages of being reproducible and nondestructive in its
application. Fourier Transform Infrared Spectroscopy (FTIR) has many advantages for
the present system because the morphological changes accompanying the crosslinking
reaction make the application of other techniques, like chromatography and NMR, very
difficult.

Generally, in the copolymerization of two different monomers, the fraction of
molecules entering the polymer chain at any instant (i.e the rate of polymerization of the
individual monomers) is dependent on the relative reactivities of the monomers and the
fraction of each component in the unreacted form [5]. The aim was to evolve a method
which would give the fraction reacted, of each component (vinyl toluene and vinyl ester),
at any stage of the reaction.

The work was undertaken from this perspective, but the investigation has resulted
in a technique which can be applied in general to the IR analysis of binary polymer
mixtures and which could give the required information in specific instances. A method

has been reported for use with UV spectroscopy [9] for binary mixtures where the sum

9

 

 

b.- __-_.,

of the concent
mixtures only
same. The pr:
mixture and 0.
therefore appl:

molar and ma:

2.2 Theory
The fol

method. This :

2.2.1 DeveIOp

Consid
balance Consi.
following BQL

10

of the concentrations of the two components is a constant. Such a condition will hold for
mixtures only if the mass or molar densities of the individual pure components are the
same. The present technique does not place that restriction on the constituents of the
mixture and can be applied to mixtures with components of different densities. This is
therefore applicable to resin systems where typically one of the components has a lower

molar and mass density relative to the other component.

2.2 Theory
The following is a presentation of the theoretical basis for the application of the

method. This analysis is based on material balance on the system and Beer’s law.

2.2.1 Development of the method

Consider two components ’a’ and ’b’ existing as a mixture. From a material
balance consideration (assuming no volume change in mixing), we can write the
following equation (2.1), where each term represents the volume fraction of the

respective components.

_._=1 on

Let A, represent any wavelength in a region of the spectrum. We can write Beer’s

Law at that wavelength as:

A)" = ez’lca + eg‘lcb (2'2)

 

SirT

 

W'e
Cb. If we
compositior

components

The

absorbance ;
abSOFbance

Same Path ler

For m

 

11

Similarly, at any other wavelength (say N), we can write the same equation as

Al1 = ez‘lca + czllcb (2-3)

We can use equations (2.1), (2.2) and (2.3) to eliminate the concentrations C,I and
Ch. If we assume that the path length l is the same for all the samples of different
compositions and use D,"i and D1,"i to represent the absorbencies of the respective pure

components at the particular wavelengths N, we get the following equation:

 

A A A A A A
Dl--D1 D‘Di-DID‘
All ___ Al,( bA a") +( a I; l; a) (2.4)
Dbi - Dal phi—Doi
where D: ' =ei'l p x (2'5)

The equation (2.4) shows that, for mixtures of different compositions, the
absorbance at one wavelength will yield a straight line when plotted against the
absorbance at any other wavelength. This is contingent on all the samples having the

same path length.

For mixtures with different compositions, we can plot the absorbencies at a
particular wavelength A, against the absorbencies at different wavelengths x,. If A, is in
a region where component ’a’ has no absorbance, we can substitute D,"i = 0 in equation
(2.4) to get equation (2.6).

This equation shows that all of the above-mentioned plots will yield straight lines

with a common intercept on the AM axis that is independent of the wavelength it, It also

 

 

 

it...

shows that

the compon

Simi
region A, w;
with a comr

pure compor

2.2.2 Qua)“;

Once
“Sing the abc

any mixture,

Component ”p

”Mutation

D —D
A11 = Al. (#4) + 1))Ll (2.6)

shows that the intercept will equal the pure component absorbance at wavelength )q, of

the component which does not absorb in the region it, of the spectrum.

Similarly, plotting the absorbance of the mixture at wavelength A, against another
region N where component ’b’ does not absorb will yield another set of straight lines
with a common intercept on the AM axis. This intercept will be the absorbance of the

pure component ’b’ at the wavelength is].

2.2.2 Quantitative analysis

Once the absorbencies of the pure components at the wavelength A, are found
using the above method, these values can then be used to calculate the composition of

any mixture, given its absorbance A“, by using the following relation.

0, = Ab-Dj' (2 7)
_ "T_T '
pb Dbl-D0.

This is obtained from equations (2. 1) and (2.3) and represents the volume fraction of the
component ’b’ in the mixture. If we know the densities, we can find the actual

concentration of each component in the mixture.

 

 

 

2.2.3 April.

Diff
of systems.
method ma,

Con
contribution
If it is poss
wavelengths
molecules, tl
due to these
reSpective n
Concentration
abSorbencies
described abc
Ca and C, are

diffel-em lime

 

13
2. 2.3 Application to kinetic study

Different kinds of situations are encountered when working with different kinds
of systems. The following paragraph identifies one such case and indicates how the above
method may be applied to find the extent of reaction of each component of the system.

Consider the absorbencies at two wavelengths, where the total absorbance has
contributions from both the reactive and nonreactive groups of both molecular species.
If it is possible to draw a baseline to yield the absorbance of the mixture at those
wavelengths, which includes only the contributions of the reactive groups in both
molecules, then we can still apply the above method because the absorbance contributions
due to these reactive groups will still be representative of the bulk concentration of the
respective molecules and equation (2. 1) holds if C, and Cb are considered the
concentrations of the respective reactive groups. It is then possible to estimate the
absorbencies of the individual reactive groups in the pure state by using the method
described above. When the reaction is in progress, equation (2.1) is no longer valid if
C, and Ch are considered the concentrations of the respective reactive groups, but at two
different times, equation (2.2) can be written for the two different wavelengths to give
four linear equations. These linear equations can then be solved to give an estimate of

the extent of each component reacted.

2.3 Spectra recording
The spectra were collected on a Perkin—Elmer Model 1800 Fourier Transform

Infrared Spectrophotometer with the following parameters: mode-double beam, range -

 

 

 

4000t04

detecror .

2.4 Expt
T.
DGEBA
toluene. l
syringe, 1
spectra of
Spectra in
bring the
concentratit
toluene allo
Sam]
polishing an

from 18 to 2.

be more accr

 

14

4000 to 450 cm", resolution - 2 cm“, jacquinot stop - 85 percent, apodization-medium,

detector - DTGS, number of cycles - 4, scans per cycle - 4 sample and 2 reference scans.

2.4 Experimental

The manufacturer supplied resin mixture with 55 % (w/w) methacrylic ester of
DGEBA and 45 % (w/w) vinyl toluene was diluted with different amounts of vinyl
toluene. Four microliter samples of these mixtures were transferred using a micro-
syringe, placed between two KBr disks, and scanned in the spectrophotometer. The
spectra of the plain KBr disks scanned prior to this were then subtracted from the sample
spectra in the absorbance mode. The resulting spectra were then shifted vertically to
bring the point of least absorbance to zero value. To extend the range to higher
concentrations of the vinyl ester, the resin mixture was placed on KBr disks and the vinyl
toluene allowed to evaporate for different amounts of time before scanning.

Sample thicknesses were measured by mounting the KBr disks in acrylic holders,
polishing and viewing them under an optical microscope. The sample thickness varied
from 18 to 24 microns. The sample thicknesses showed a lot of variation and could not
be more accurately reproduced even after using a micro-syringe to measure out the
quantity of vinyl ester. It was observed that polishing removes the KBr in macroscopic
crystals larger than the mesh size of the polisher, thereby leaving the interface very
jagged, non-uniform and sometimes indiscernible. This suggests that the measurement

of the sample thicknesses using this method is not very accurate.

 

 

 

 

Four regior
absorbance
axis) agains
have been f
Within whic
average rang
of the mid \

absorbance :

15
2.5 Results

Fig. 2.1 shows the spectra of vinyl toluene, vinyl ester and a mixture of these.
Four regions of the spectra have been identified where vinyl toluene exhibits very little
absorbance. The absorbencies of a few of the peaks of the mixture have been plotted (y-
axis) against the absorbencies at wavelengths in these regions (x-axis). The data points
have been fitted using a linear regression. Table 2.1 shows the midpoint and the range
within which the y-intercepts were obtained for each set of plots. Based on this, the
average range of the intercepts was calculated to be 0.005 absorbance units on either side
of the mid value. This can be considered the mean error in the calculated value of the

absorbance at any wavelength.

L

.emua..~.__

..___..__ Ht

«L

 

 

 

411.11.31.11

l6

 

100
80

0)

8

3 60

E

(I)

C

9 40

f—

N
20
100
80

G)

C

g 60

E

(f)

C

9 4o

'—

N
20
100
0.)

O

C

.9

'E

(D

C

O

,:

N

vinyl toluene spectrum

 

I r J 1
vinyl ester spectrum
«4720

1155—1190 550—590

1 632

 

 

 

Figure 2.1

Spectrum of mixture

1 . 1 x

 

 

O n A l I
1800 1530 1260 990 720
Wave number cm-l

Spectra of the chemical systems

450

 

 

Since I
common inter
respective wa‘
of pure vinyl
absorbance ur

method.

Table 2.1

l §

Regions
y axis

 

 

 

 

differem Mini

l
I

Verified by tll

Strong abSorb

 

17
Since the regions correspond only to absorption by vinyl ester (Figure 2.1), the

common intercepts on the y—axis represent the absorbencies of pure vinyl toluene at the
respective wavelengths. All sets of plots showed consistency in reporting the absorbance
of pure vinyl toluene at the corresponding wavelengths with an accuracy of 0.005
absorbance units (each row in Table 2.1). This is proof of the applicability of this

method.

Table 2. l Absorbencies of vinyl toluene at different wave numbers (Column 1)

Reg“? " 1700 - 1730 1220 - 1260 1155 - 1190
y ax1s - - ‘

cml cm1 cm1

0.183 :t 0.003 0.179 :1: 0.009 0.183 :l: 0.00

 

0.233 i 0.001 0.226 :1: 0.008 0.228 :1: 0.004

 

0.346 :1: 0.004 0.335 :t 0.015 0.341 :I: 0.005 .‘

 

 

0.359 :1: 0.004 0.359 :1: 0.002 0.363 :1: 0.002 ‘

 

 

 

More sets of plots were generated between the 1632 peak and a few more regions
where both components have significant absorption. They resulted in lines with widely
different y-intercepts. A few sets of plots are illustrated in Figures 2.2 - 2.5. It was also
verified by this method that there were no regions of the spectra that correspond to

strong absorbance by vinyl toluene and small absorbance by vinyl ester.

 

 

__ _‘

'llli'olil

.-
N

—. ‘
x
.

.. A

‘\.
N

‘h— ...

N _

‘.
s

.. ‘
x
-‘
C

s

~ .
s
.«

 

 

 

 

 

 

 

1.0
t /
0.9 7 /
// / t”/
.— 08 h / / / /’ / ’
l c C// / 4 ’ I I
E o 7 ~ /./' / ir‘ ’
U ' / / ,4 /
(\l i /, I” I
'0 0.6 * x l 13‘ ' +//’Ei /"/
LO » / /V j/
'— 130 / / / I
6 05 r g/g/ /’
l" 2:1; :1 | _+_ Q
8 0 4 ~ aka/ta
' /~ 1+5) '

g x 6:0 I 550 cmrl solid
{30.3 T Xl—t-A‘D 0 560 CTN—l dot dOSh
8 ’ A 57Ocm—1 tiny dosh
£0.12 " + 580 cm-l long dosh

01 _ '1 590 cm—l dosh dot dot

0‘0 1 1 1 l 1 1 4 1 1 1 1 1 1 1

 

 

 

0.00 0.15 0.30 0.45 0.60 0.75 0.90
Absorbance at 550. 560, 570, 580 8c 590 cm-1

1.05 1.20 1.35 1.50

Figure 2.2 Absorbance at 1632 cm" vs. absorbencies in 550-590 cm‘1 region

 

 

+l>O—

5cm‘l solid

0 cm-l dot dosh
l cm—l long dosh
9 cm-l tiny dosh

 

 

 

0.1 —
0.0 1 l l 1 l 1 l l 1 l 1 1 4 1
0.00 0.15 0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50

Absorbance ot1155,1170,1181 8c 1189 cm-1

Figure 2.3 Absorbance at 1632 cm" vs. absorbencies in 1155-1189 cm‘1 region

 

 

Ifigure 2.4

.11;’

 

 

l9

 

1.0
0.9 r l 1220 solid
’ o 1230 dot dosh
T 08 ’ A l240long dosh
E 0 7 _ + 1250 dot dotddsh

 

0.1 r

 

 

OO 1 l 1 I 1 l 1 l 1 l 1 l 1% I 1 1 1 1 1
0.00 0.15 0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50
Absorbonce ot1220,1230,1240 &1250 cm—1

 

Figure 2.4 Absorbance at 1632 cm'1 vs. absorbencies in 1220-1250 cm'1 region

 

 

 

0.70 ' ’
0 63 i ////
. _ /
- ~ .. zrg/
._ 0.50 ~ ,7 /
('E _ l + 0A
0 0.49 ~ - /
('31 42 F— // i/m
:9 O' . fl o/a
l ’J/‘L Coo/A
+6 0.35 r / " + £79
cu /
Q 0.28 ” I+ 013/
g / / /
9 0.21 ~ /
O ./ . // l 645 cm—1 solid
8 0.14 “ // O 650 cm—1 dots
<1 ' A 655 cm” long dosh
0.07 ”_ / + 660 cm—1 dot dosh
0.00 / ' L ‘ ‘ 1 ‘ l ‘ I 1 l I 1 1 l 1 I

 

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
Absorbance at 645. 650,655 8c 660 cm-l

Figure 2.5 Absorbance at 1632 cm'1 vs. absorbencies in 645-660 cm" region

 

 

 

2.6 Limit

Th
componen
the baselir
mixture. b.
results in

absorbs in

equation (2

 

20

2.6 Limitations and sources of error

The intercepts on the A"1 axis will also coincide if the spectra of both the
components are similar in the region considered [9]. Another limitation is the choice of
the baseline considered. If the baseline used does not yield the net absorbance of the
mixture, but instead yields the absorbance of the mixture offset by a value k‘, then this
results in lines with different intercepts on the AM axis even if only one component
absorbs in the region N. This can be verified by substituting the following relation in

equation (2.4).

A“,,,,,,,,, = Rm + k” (2.8)

It can however be observed that if ki is small then the deviations in the intercepts
on the AM axis will be small. The sample thickness for all the samples scanned should
be the same. This is very difficult to maintain with thin films on KBr disks. The effect
of this can be a scatter in the data as shown in the plots. The plots however, indicate
that regression lines through the data points can accommodate these variations and still
yield satisfactory results if a sufficiently large concentration range is taken for the two
components. Error can also result if the components do not form an ideal mixture, in
which case equation (2.1) does not apply. Some other sources of error that apply to this

method have been mentioned in literature [6,10,11,12].

 

 

 

 

2.7 Summit
A me
component
different de
spectra of a
for the quan‘
of each corr
of error hav
The 1
strong vinyl
the vinyl est:
It Was theref
the total vim
r55111 that has

he used as a

 

21
2.7 Summary

A method has been developed which can be used to identify the regions of single
component absorption in an IR spectra of a mixture of two chemical species with
different densities. The applicability of the method has been demonstrated with the
spectra of a mixture of a vinyl ester and vinyl toluene. The application of this method
for the quantitative analysis of mixture compositions and for finding the extent of reaction
of each component has been delineated. The limitations of the method and the sources
of error have been discussed.

The above method was used to verify that there are no regions of the spectra with
strong vinyl toluene absorbance and insignificant vinyl ester absorbance. This is because
the vinyl ester molecule has all the fundamental chemical bonds present in vinyl toluene.
It was therefore inferred that it is possible to extract information only on the fraction of
the total vinyl groups that have reacted but not the fraction of each component of the
resin that has reacted at any time. The fraction of total vinyl groups that have reacted can

be used as a measure of the extent of reaction.

 

 

 

3.1 Backg
The
to manufac
a resin mal
resin. The
characterist
These cons
experiments
Polymerizati
microwave c
The 1
POll'merizatit
microwave Cl

0f thermal cu

been CalCtllate

 

 

3. THERMAL KINETICS OF POLYMERIZATION

3. 1 Background

The study of polymerization kinetics offers a substantial incentive in the endeavor
to manufacture polymer matrix composites at high speeds. The study of the kinetics of
a resin makes it possible to specify the processing cycles for composites made with that
resin. The study enables one to optimize the curing cycle based on the specific curing
characteristics of the resin and also makes it possible to simulate the curing process.
These considerations, coupled with the faster kinetics observed during previous
experiments with different resin [13] provided the motivation to study the kinetics of
polymerization of the vinyl ester resin and the differences between thermal and
microwave curing.

The goal of this study was to develop a cure kinetics model for vinyl ester
polymerization and estimate the parameters for the model during thermal as well as
microwave curing of neat resin samples. This chapter reports the results of the modelling
of thermal curing of the vinyl ester resin. The parameters for the proposed model have
been calculated based on the conversion-vs-time data generated at various temperatures
and benzoyl peroxide (initiator) concentrations. Isothermal curing runs were conducted
on different samples for different time intervals to generate the conversion-vs-time data.
The concentration of the initiator and the temperature of the run were the experimental

parameters that were varied between runs. The conversion was calculated based on the

22

 

 

disappeatan

determined

3.2 Theore
The
divided int.
therefore ti
the gel effe
to the incre
other. There
Phase III, tl
active chain
even though
the reaction 1
limited and t
The f(
the curing ref
Vinyl monom
reaction is m.
The c

monomem m.

23

disappearance of the total vinyl unsaturations. The extent of cure of the resin mixture was

determined using Fourier Transform Infrared Spectroscopy (FTIR).

3.2 Theoretical development of the model

The polymerization of a mono-vinyl monomer and a di-vinyl monomer can be
divided into four distinct phases. Phase I is characterized by low resin viscosity and
therefore the polymerization follows conventional kinetics. Phase H is characterized by
the gel effect during which the termination rate constant becomes diffusion limited due
to the increasing difficulty of the growing free radicals to come in contact with each
other. Therefore the termination rate constant falls and the reaction rate increases. During
phase HI, the termination rate constant stops falling and remains constant because the
active chain ends still possess a certain degree of mobility due to the propagation reaction
even though their translational motion is severely restricted due to their size. Therefore
the reaction rate falls. During Phase IV, the propagation reaction also becomes diffusion
limited and therefore the polymer vitrifies.

The following form the basis for the development of the cure kinetics model: (1)
the curing reaction is isothermal (2) the vinyl groups of the mono-vinyl monomer, di-
vinyl monomer and the intermediate oligomers have the same reactivity. (3) inhibition
reaction is not considered and (4) a single initiator is used.

The cure kinetics for a reaction mixture containing mono-vinyl and di-vinyl

monomers may be described by equations (3.1), (3.2) and (3.3) [14].

24

 

 

g); = 2f ’9: [1] _ (3.1)
d. W k. (1 X)
_ [110 _

[I] - dm CXP( kd t) (3.2)

l - — sX

( .,

s = (i) - 1 (3.3)
d"!

where X is the fractional conversion of the vinyl groups; 1‘ is the time of reaction; f is
the initiator efficiency; k4 is the rate constant of initiator decomposition; k, is the
propagation rate constant and k, is the termination rate constant. [I]0 and [I] are the
initiator concentrations at time 0 and t respectively; sis the volume shrinkage factor; (119
is the density of the thermoset polymer formed; and d, is the density of the monomer
mixture. Polymerization of methyl methacrylate/ethylene glycol dimethacrylate system
has been modelled using these equations with good predictions [14].

As the reaction proceeds and increasingly larger free radicals are formed, their
translational diffusional motion becomes increasingly restricted and results in a decrease
of the termination rate constant with increasing conversion. Even when the translational
motion of the free radicals is severely restricted, the termination rate does not approach

zero because the active chain ends still possess a degree of mobility due to the

25

propagation reaction [14]. So the termination rate constant was modelled as decreasing
continuously with cure until a limiting value and then remaining constant. Based on this

analysis the termination rate constant can be written as equation (3 .4)

k =k +k (3-4)

where km is the translational diffusion-controlled termination rate constant and ktp is the
residual termination rate constant dependent on the propagation reaction. The rate
constant k1,: can be correlated with conversion through free volume parameters as in

equation (3.5) [14].

 

f 1 1
k“ = kw exp B{— — — ] (3-5)
\ V10 Vf

kw is the rate constant at zero conversion, B, is an adjustable parameter and V1,, and V,
are the free volumes of the reaction mixture at zero conversion and conversion X
respectively. The rate constant kg, was correlated to be directly proportional to the
propagation rate constant with the proportionality constant B” being an adjustable

parameter as:

k :3 k (3.6)

‘P ‘:P P

 

The

 

conversion

where T is tl
the monomer
fOI‘med.

The 1:
increasing reg
Of It! With C0
When the fre
calculated usi
t0 zero We”
mOdelled to

be COmblned

26

The following correlation (equations 3.7-3.10 ) between free volume and

conversion was used [15]:

V}, = (0.025 + 0.001*(T-Tgm) ) (3.7)

V, = Vfl, + [4.8e-4*(T—Tgp) - 0.001*(T-Tgm)]*d>p (3.8)
e = (am/(1p) - 1 (3.9)

= M 3.10

(DP 1 + EX ( )

where T is the temperature of cure; T”, and T”, are the glass transition temperatures of
the monomer and polymer respectively; 4’, is the volume fraction of the polymer being
formed.

The propagation constant decreases with increasing conversion because of the
increasing resistance to the diffusion of free radicals towards each other. The behavior
of k, with conversion is close to a step function with the value of k, dropping to zero
when the free volume of the polymer is zero [14]. The free volume of the polymer was
calculated using equations (3.7-3. 10) and it was found that the free volume does not go
to zero even at complete conversion. Therefore, the propagation rate constant was
modelled to be independent of conversion. Equations (3.1), (3.4), (3.5), and (3.6) can

be combined to give equation (3.11).

 

 

 

 

 

The
1:, = (kpx/f/
Therefore eq
parameter Bl

constant and

temperature

SUbstitutmg e
(3.2) and (3.

flier-Vinyl t0

 

27

dX k, ff «219111

 

 

__ = 1-
dt ( X) (3.11)
f 1 1 B"
«km exp 3, —V—-—V- + T kp
K 10 f 1.10

 

 

 

The conversion-time data are sufficient to give only the value of the ratio
k, = (kpx/ f A/ kw). Molecular weight data are required to resolve the individual values.
Therefore equation (3.6) can now be rewritten using k, instead of k, and a new adjustable
parameter B“ replacing B” as shown below in equation (3.12). k, is the effective rate
constant and B, , B“ are the model parameters.The expression for k, as a function of

temperature will still be in an Arrhenius form.

kpfl and B = B"

e ('30 m t5 kw

(3.12)

 

 

Substituting equation (3.12) in (3.11) gives equation (3.13), which along with equations
(3 .2) and (3.3) forms the set of equations that describe the extent of reaction of the vinyl

ester-vinyl toluene resin system.

 

 

_ = 1-
dt \l r 1 1 ( X) (3J3)
eel-d1”: ,
. V10 Vf ’k

 

 

 

 

The model

experiment.

3.3 Materi:
A m
resin with 4

was used as

3.3.1 Sampl
A thi
P013'merizatil
bem’cen two
‘0 SUppon m.
the disks Was
from Water.
The 5
thermal Oven
Oven. The ter
probe ClOse
aPPIOpn‘ate

experifllénts

 

28

The model therefore contains two parameters B, , B“ to be evaluated based on the

experimental data, together with the Arrhenius expressions for the rate constants k, and

k,

3.3 Materials and methods
A methacrylic ester of Diglycidyl Ether of Bisphenol-A (DGEBA) vinyl ester
resin with 45% (w/w) vinyl toluene as the monomer was used. Benzoyl peroxide (BPO)

was used as the initiator.

3. 3.1 Sample preparation and curing

A thin film technique based on IR spectroscopy was used to study the kinetics of
polymerization of the resin. Samples were prepared by enclosing a thin film of the resin
between two KBr disks 13 mm in diameter and 1 mm in thickness. KBr disks were used
to support the resin because KBr is transparent to IR radiation. The KBr used to make
the disks was stored in a desiccator to keep it dry and avoid interfering IR absorbance
from water.

The samples were cured for different time intervals in a temperature controlled
thermal oven. A set of samples constituting a run were loaded simultaneously into the
oven. The temperature of the samples was measured by placing a fluoroptic temperature
probe close to the samples. Individual samples were removed from the oven at
appropriate time intervals and quenched in dry ice to freeze the reaction. The

experiments were run at five different temperatures of 80°C, 90°C, 100°C, 110°C and

 

 

 

 

 

120‘C. Rur

were made

3.2.2 Anal)

FT 1]
a range of 1
frequency is
frequency 0
matter allovt
This discrirr.

to estimate [

Thef

 

29
120°C. Runs with 1%, 2%, 3%, 4% and 5% (w/w) benzoyl peroxide concentrations

were made at each of these temperatures.

3. 2.2 Analytical technique

FTIR analysis involves irradiation of samples with electromagnetic radiation of
a range of frequencies in the infrared region. The fraction of light transmitted at each
frequency is recorded and the output can be obtained as a plot of the transmittance vs the
frequency of radiation. The specific nature of the interaction of the IR radiation with
matter allows particular chemical groups to absorb strongly at only a few frequencies.
This discrimination in absorption by different groups in a chemical system can be used
to estimate the concentrations of the different chemical species in a given system.

The fundamental basis for quantitative FTIR analysis is Beer-Lambert’s law:

—log(7) = A = abc (3-14)

where T is the transmittance, A is the absorbance or integrated absorbance, a is the
molar absorptivity or the integrated molar absorptivity of the absorbing species, b is the
path length and c is the molar concentration of the absorbing species.

The spectra of the samples were scanned using a PERKIN-ELMER model 1800
FTIR spectrophotometer. The spectra of the plain KBr disks, the resin samples (held
between the KBr disks) before cure and the resin samples after cure were taken. The
spectra of the plain KBr disks were subtracted in the absorbance mode from the spectra

of the sample (held between KBr disks) to correct for the absorbance of KBr. The

 

 

 

 

resulting SF
zero. This 1
To 1
spectra, a
background
draun betwc
baseline and
represent the
should be in
is illustrated
Wave numhe;
area, The sh.
The ‘
identification
that the calcu
A conseunn
limits and [h
Entities that tl
Obtained in ti
3 “action pe
also selected

Vllly] “man”

30

resulting spectra were then shifted vertically to bring the point of least absorbance to
zero. This procedure was applied to the sample spectra before and after cure.

To eliminate the local background absorbance in the region of interest in a
spectra, a baseline is usually drawn that closely matches the absorbance of this
background in that region of the spectra. This usually is of the form of a straight line
drawn between two appropriately chosen points on the spectra. The area enclosed by the
baseline and the spectra between the wavelength limits imposed by the analyst is used to
represent the integrated absorbance of the analyte as used in equation (3.14). The spectra
should be in the absorbance mode for the area calculation. The calculation of the areas
is illustrated in Figure 3.1 . The wave numbers b1 and b2 are the baseline limits and the
wave numbers WI and w2 are the limits on the wave numbers for the calculations of the
area. The shaded region represents the area calculated.

The baseline limits and the area limits selected should be based on the
identification of the peaks, the interference from neighboring peaks, and the requirement
that the calculated area represent the concentration of the analyte as closely as possible.
A consequence of this requirement is that the areas obtained from the selected baseline
limits and the area limits should follow certain relations that are followed by the physical
entities that they represent. These are delineated in the next section. Based on the spectra
obtained in the initial runs and the criteria mentioned, a reference peak, a BPO peak and
a reaction peak were chosen. The baseline limits and the area limits for the same were
also selected. They are listed below in Table 3.1. The reaction peak measures the total

vinyl unsaturation.

 

 

 

 

Absorbance

Flgun: 3.1

Table 3.1

 

 

 

31

 

Absorbance

 

 

 

 

 

bl wl W2

 

b2

 

 

Wave number

Figure 3. 1 Area used for determining concentration of analyte

Table 3.1 The baselines and the limits for the areas under the different peaks

Baseline limits

Area Limits

 

1655-1560 cm'1

1612-1602 cm'1

 

1800-1662 cm"

1800-1765 cm'1

 

1655-1560 cm‘1

 

 

1645-1630 cm'1

 

 

 

 

The extent 0

3.3.3 Data
Erro
computatior
interference
by a straigh
distortion 01
during curin
errors distor
extent of cu;
Of these phg
different pea]
Was checked
themselves,
VerjfiCatiOn
“Perimmai
Should be 53
For 3

Peak

 

32

The extent of cure was calculated using equation (3.15)

[ Alix" lARef lqfier cure (3.15)

 

[ ARI" lARef lbefare cure

3.3.3 Data processing

Errors are introduced into some data points over the course of experimental and
computational procedures. Plain KBr disks that are very smooth and parallel result in
interference effects that result in the background being wavy. This cannot be eliminated
by a straight line baseline. Foreign matter that gets into certain samples results in the
distortion of the spectra and the quantitative data derived thereof. The application of heat
during curing causes some resin flow that changes the sample geometry. These and other
errors distort the quantitative information that is obtained from the spectra. Therefore the
extent of cure calculated for these data point will be unreliable. To minimize the effects
of these phenomena, different criteria were selected to verify that the areas under the
different peaks were coherent with respect to their physical interpretation. This coherency
was checked by verifying that the areas under the peaks satisfied relations, between
themselves, that should be satisfied by the physical quantities they represent. This
verification ensures that many of the errors induced into the data points through the
experimental and computational procedures are eliminated. Some of the relations that
should be satisfied by the values obtained from the spectra are listed below:
1. For any set of spectra of samples of the same composition, the area under any

peak should be directly proportional to the thickness of the sample. Therefore, if

 

 

These cr

failed to

is the tin
in a shit
eliIIlinate
fitted Wit

Subtractet

33
the area under any peak (of the different samples), is divided by the area under

the same peak of a reference sample, then these normalized areas represent the

relative thickness of the samples with respect to the reference sample. These

values should be the same if the reference peak, the BPO peak and the reaction
peak are used.

2. For each sample, the ratio of the reaction peak area to the area of the reference
peak (both before cure) is directly proportional to the concentration of the
unreacted double bonds of the resin system. Since the concentration of the
unreacted double bonds is the same in all the samples (before cure), the ratio of
the reaction peak area to the reference peak area should be the same for all the
samples. The same argument holds for the ratio, before cure, of the BPO peak
area to the reference peak area for samples with the same BPO concentration.

These criteria were used to evaluate the data points obtained and eliminate those that

failed to satisfy these criteria.

There is a latency associated with the heating of samples in a thermal oven. This
is the time for the samples to heat up to the oven temperature. This heating time results
in a shift in the conversion-time data along the time axis towards higher times. To
eliminate this error in the conversion-time data, the data points at low times of cure were
fitted with a straight line using linear regression and the intercept on the time axis was

subtracted from all the data points of that run.

 

 

3.4 Resul
TI
expressior
of the Bf
mentione:
Tl
Scanning
evaluated
found usi
eviperimei
obtained i
"ll
illustratec'
The accul
Of Other
b6cause t
“imperatu
the [Cmpe
oven {em}

34
3.4 Results and discussion

The initiation reaction was modelled separately as a first order reaction. The
expression for k, as a function of temperature was found using a least squares regression
of the BPO reaction data. The reaction was monitored by the benzoyl peroxide peak
mentioned earlier.

The glass transition temperature of the polymer was found using Differential
Scanning Calorimetry (DSC) and the glass transition temperature of the monomer was
evaluated using the equation by Soh [16]. The adjustable parameters of the model were
found using a Simplex algorithm for minimizing the square of the error between the
experimental data points and the model predictions. The values of the parameters
obtained for this model are given in Table 3.2.

The predictions of the model and the experimental data at those conditions are
illustrated for four different temperatures in Figures 3.2, 3.3, 3.4 and 3.5 respectively.
The accuracy of the predictions is very good. The quality of the fit is comparable to that
of other literature [14, 16]. The least error in the temperature measurement is 1°C,
because this is the error in the measurement of the temperature using the fluoroptic
temperature probe placed near the samples. The actual error would be more because of
the temperature differences in the oven and also the fluctuations during the control of the
oven temperature. The model predictions at 89°C and 91°C have been evaluated for
different BPO concentrations and are illustrated in Figure 3 .6, along with the model
predictions and experimental values at 90°C. This gives a window of possible errors in

the experimental values based on the estimated error in temperature alone. Most of the

 

 

data points '
experimental
the window. '
by the mode

completion at

polymerizatio
as the initiato
Table 3.2
d” 1
dp 1
Tgm .]
Tip 8‘

 

 

35
data points fall within this window indicating that the fit is very good. Other

experimental errors exist and these cause some of the data points to fall slightly outside
the window. The rate of reaction as a function of the extent of cure at 90°C, as predicted
by the model has been illustrated in Figure 3 .7. The reaction does not proceed to
completion at low temperatures or low BPO concentrations. This is because of dead end
polymerization whereby the short half-life of the initiator causes the reaction rate to fall

as the initiator is consumed [17].

Table 3.2 Kinetic parameters for vinyl ester/vinyl toluene polymerization

2.9885

0.5068

8.02e7 exp (-8795'4) s"l

T+273

-6760.4) [ L %

2.051e6 exp (

T+273 mole -s

Note: T is the temperature in 0C

 

 

| ;‘ gj
. . ' I'm-v I U’

 

11"

'Hi l‘i'

ii!

figure 3.2

Figure 3.3

 

 

36

 

 

 

 

1 O T 2 8e FC
3 v t7ZBPO i
0'9 L a :7 0P0 ° ,
0.8 o 4:: BPO 0 j
0 4
q) 07 *- O C] _
506 » U a D D ~
0 .
3 05 ~ c ~
C
+2 0.4 ~ 0 U -
LLi V
0.3 . 0 El .7 -
0.2 i O , v a
0.1 ~ .
OO 1 1 l 1 4L 1 1 l l
o 1000 2000 3000 4000 5000

time (secs)

Figure 3.2 Model predictions and experimental data of extent of cure at 80°C

 

 

 

 

 

 

 

 

:0 0
1,0 . .T “Q C . ,
. 1
0.9 — A A ° - A Q
08 ~ ‘ <> 0 .
0.7 » <> - 5 -
‘8
306 ~ a o D i
20.5 b A O D C] d
a) U ‘7
50.4: A I V n
O 3 ~ . . v v V r
t at.
- 9 . ~
‘ ‘ v 1:7.BPO
- A V V ‘
O 2 2, ‘ a 27: BPO .
0.1 — . V <2 37. BPO -
x/zr‘ V a 57: BPO -
OO , 1 l L l L L L L A.
o 800 1 600 2400 3200 4000

time (secs)

Figure 3.3 Model predictions and experimental data of extent of cure at 90°C

 

 

Figure 3.4

P1sure 3.5

 

37

 

 

 

 

 

 

 

: 0“
10 ' l ' IT 1'00 L T
0.9 '- O "‘
0.8 - O o D
0.7 e O D _
g .
E06 e 0 i3 \7 Z
O ,_ O V V
_E()5 F "CD. a
-%(14 r C3 .vvv ‘
UJ * 4
0.3 . D ‘7 -
. v 4
0.2 ~ 0 v v 17. 8P0 .
. “ I'v D 2ZBPO a
0.1 - a ' o 4:: BPO —
0.0 ' r 1 . l a n . l 1
0 600 i 200 1800 2400 3000

time (secs)

Figure 3.4 Model predictions and experimental data of extent of cure at 100°C

 

 

 

 

 

 

 

 

T = 110 OC
1.0 l f r T O I T
v 17. BPO ‘
O 37. BPO i
o 47: BPO -
OO 1 l n 1 L l 1 l A
0 400 800 1200 1600 2000

time (secs)

Figure 3.5 Model predictions and experimental data of extent of cure at 110°C

.Z: . To 2:17.

6.
3
We

 

DU

 

RN
T, ommv .e\xu cozooom

r:
0.
m0 macm

   

r}.

Pu.

 

Flgllre 3. 7

II

38

 

 

 

 

 

 

 

3.0 I l T I
i' _
09 .- | IIIIII ‘_-_n --__‘“j*_““_—“— — -<
0.8 ~ D . . . r
0.7 — ' ’ "—0 -
“2
30-6: 1
30.5 e .
E, r .......... . ----------- -
3:04P """" ,ii’flr'T-“
LLJ r v a
0.3 r v i’ZBPOa
. :1 27.1390
0 37.8130
0 2f a szapo
890C
0.1 - —— 900C
’ — — 9100
00' 1 1 a J l l l l A
0 800 1600 2400 3200 4000

time (secs)

Figure 3.6 Error windows based on error in temperature measurement

Xioe—3

 

N
o

in

.0
tn

Rate of Reaction dX/di (sec '1)
o

 

 

 

l

0.0 0.2 0.4 0.6 0.8 1 .0
Extent of Cure

 

.0
0

Figure 3.7 Model predictions of rate of reaction vs. extent of cure at 90°C

 

 

__ ._.__

3.5 Summary

The p<
modelled. Th
expression. T
initiator with
of this data. T
of reaction. T
until a limitir
propagation r
algorithm to n
and the expe:
predictions an

cOncentrations

 

 

39

3.5 Summary

The polymerization reaction of a vinyl ester resin during thermal curing was
modelled. The initiation reaction was modelled separately using a first order rate
expression. The BPO reaction peak was monitored to obtain the conversion of the
initiator with time and the initiation rate constant It, was obtained based on a regression
of this data. The propagation rate constant was modelled to be independent of the extent
of reaction. The termination rate constant was considered to fall with the extent of cure
until a limiting value is reached. The limiting value is directly proportional to the
propagation rate constant. The model parameters were evaluated using a simplex
algorithm to minimize the sum of the squares of the error between the model predictions
and the experimental values. A good agreement was observed between the model
predictions and the experimental data generated at different temperatures and initiator

concentrations.

4. MICROWAVE KINETICS OF POLYMERIZATION

4.1 Backgron
To better understand the effect of microwaves on the cure kinetics process,
different materials have to be studied. This chapter reports the results of the study of

microwave cure kinetics of a vinyl ester resin.

4.2 Experimental

A thin film technique similar to the one used in the thermal curing experiments
was used to cure the microwave samples. The same materials used for the thermal
kinetics study were used. In the preparation of the thin film samples, about 4 mg of the
resin was evenly distributed on KBr disks 13 mm in diameter and 1 mm in thickness.
The resin was covered with another disk with a fine hole in the center for placing the
temperature probe.

Microwave curing experiments were conducted at temperatures of 80°C, 90°C,
and 100°C respectively. At each of these temperatures runs were made with 1%, 2% ,
3 %, 4% and 5% BPO. Higher temperatures were not used because the reaction rate at
those temperatures is very fast compared to the time for loading the sample in the cavity
and removing them to quench the reaction. The runs were made in a cylindrical, single
mode microwave tunable cavity at 2.45 Ghz, as described in Chapter 1. The samples

were held horizontally in a cylindrical teflon holder with a hole in the center,

40

 

 

..
rig...

“ 'P'Ll '1‘-

I

correspondin
different [lint
The t
probe placed
temperature 1
illustrate the
sample temp:
bring the ca
microwave c:
The s;
‘0 Yield the e
were used for
The resin san
Spectra of the
Wmmmm'
comm fro
to find the ex
The d
Previous Cha
for the heat-
item the [em

temperamfc

 

41
corresponding to the hole in the top KBr disk. The samples were individually cured for

different time intervals at constant temperatures.

The temperature of the sample was monitored using a fluoroptic temperature
probe placed in contact with the sample through the hole in the top KBr disk. A typical
temperature profile during the curing process is shown in Figures 4.1 and 4.2. These
illustrate the heat-up time as well as the steadiness of the sample temperature. The
sample temperature was controlled by appropriately tuning and detuning the cavity to
bring the cavity into or out of resonance. The samples were removed from the
microwave cavity at appropriate times and quenched in dry ice.

The spectra were obtained using an FTIR spectrophotometer and were processed
to yield the extent of cure of each sample. The same scan parameters and procedures
were used for the microwave cured samples as the thermal samples (refer Chapter 3).
The resin samples were scanned to obtain the before—cure and after—cure spectra. The
spectra of the plain KBr disks (with one disk having the hole in the center) was taken
prior to placing the resin between them so that the absorbance of the KBr disks can be
corrected from the sample spectra before and after cure. The corrected spectra were used
to find the extent of reaction of the samples at different times.

The data points were checked to eliminate erroneous values as detailed in the
previous chapter. The times of cure of the sample as recorded, were modified to correct
for the heat-up time for the samples. The heat-up time for each sample was calculated
from the temperature profile data of the curing run as the time taken to reach the reaction

temperature.

 

 

'rliljriylililllt‘”

l

‘(ilitlftf‘

in“), i.

I (

ii)

VV
'.-

 

A
h —.
‘ ,_
x.
t.
».
A
>4
\.
n
' 7-
HI

 

 

 

 

42

 

100 a T . . . . . ,
90 ~ «

d
i H A—flzn‘w A W Pvammmfiv" ~W*‘bzm‘fm — _ — —-
_.

80

L

70
60
50

 
 

40
30
20 ~

Tenaperoture<X3

10 e

 

 

O 1 l n I 1 l 4 I

0 500 1000 1500 2000 2500
Thue<3fcure<secsl

 

Figure 4. 1 Temperature profile of microwave curing of a neat resin sample

WOO 1‘ j v r v j I i 1—

 

:— -1
90 ’- d
>— -4

Tenoperoture‘N:

 

 

l
I
l
l
I
i
l
i
10+ H —

 

 

 

Heot—upthne l
O 1 A 1 l n l 1 l 1
0 20 40 60 80 100

Thneiofcure(secs)

Figure 4.2 Temperature profile during microwave curing (close up)

 

 

4.3 Rosa]

Tl
same mo
separately
evaluated
this k, w
Therefore

Tl
calculated
extent of
cure. The
thermal cr
Table 4.1

illustrated

Table 4.1

 

43
4.3 Results and discussion

The extent of reaction vs. time data was used to model the reaction using the
same model as that used for the thermal curing. The BPO reaction was modelled
separately and it was found that the initiation rate constant k, was close to the value
evaluated for thermal curing. The progression of the BPO dissociation as predicted with
this It, was close to the values predicted using the k, evaluated for thermal curing.
Therefore the k, evaluated for thermal curing was used as the k, for microwave curing.

The different model parameters including the effective rate constant k,, were
calculated using a Simplex procedure to minimize the square of the error between the
extent of cure predicted by the model and the experimental value at the same time of
cure. The initial guess for the procedure was taken to be the parameters estimated for the
thermal curing. The model parameters for thermal and microwave curing are given in
Table 4.1. The model predictions and the experimental data at three temperatures are

illustrated in Figures 4.3, 4.4 and 4.5.

Table 4. 1 Comparison of kinetic parameters for thermal and microwave curing

     
 
  
  
 
  
 

Parameters Thermal Microwave

 

B, 2.9885 4.367

 

 

 

0.5068

 

0.9440

 

    
  
 

  
 

2.051e6 *
exp[-6760.4/(T+273)]

3.336e7 *
exp[-7818.6/(T+273)]

 

 

 

 

 

The r
where the 5211
other experit
run. Therefo
data. The me
At high extei
model has li.
(possibly, aft

One 1
reactivities of
same. This n
the experime
microwaves c
group of vin)
being greater
increase in its
of the Vinyl 1
mode], A cot
each m0n0m(
ass“mptions
considerau'on

n10Homer.

 

44

The microwave samples were cured individually, in contrast to thermal curing
where the samples were cured as a set. Therefore their temperature profiles, along with
other experimental factors like heat-up time etc. , vary from sample to sample in the same
run. Therefore the microwave data are more scattered, than the corresponding thermal
data. The model predictions match well with the experimental data at low extent of cure.
At high extent of cure, the model under-predicts the conversion. This suggests that the
model has limitations when used to predict microwave curing at high extent of cure
(possibly, after gelation).

One of the assumptions used in the development of the model is that the
reactivities of the vinyl groups in the mono-vinyl monomer and di-vinyl monomer are the
same. This might not be valid, resulting in the predicted extent of cure being less than
the experimental values. The reason could be that, during microwave curing, the
microwaves can preferentially couple with the dipole carbonyl group close to the vinyl
group of vinyl ester, resulting in the kinetic energy of the vinyl group in vinyl ester
being greater than that of the vinyl group from vinyl toluene. This could also lead to an
increase in its reactivity over the corresponding thermal curing values. The reactivities
of the vinyl toluene and vinyl ester can be considered to be different to improve the
model. A complete quantitative analysis would require further data on the fraction of
each monomer reacted at different times, but a qualitative analysis under simplifying
assumptions is given in part IV of Appendix-A. The simplifying assumptions are the
consideration of the radical reactivity to be independent of the radical chain end-

monomer.

 

 

The r
can be done
conSIant fror
available in I
the propagat
However, of
Special techr
could also be
This would 1
temperatures

The c
microwave a
extent of cut
Therefore th.

conversions ;

 

 

45

The model can also be refined by introducing more parameters in the model. This
can be done by obtaining molecular weight data and separating the propagation rate
constant from the effective rate constant as used in this model. More detail on this is
available in literature [15, 16, 17]. An adjustable parameter can then be introduced into
the propagation reaction based on the expected interaction of microwaves with the resin.
However, obtaining molecular weight data could be a problem after gelation takes place.
Special techniques have to be investigated for this purpose. The experimental procedure
could also be improved by taking the IR spectra while the sample is curing in the cavity.
This would eliminate a lot of scatter and also make it possible to collect data at higher
temperatures because there would be no quenching of the reaction.

The comparisons of the model predictions using parameters estimated from the
microwave and thermal data are shown in Figure 4.6. The model predictions at low
extent of cure are almost the same, when predicted using either of these parameters.
Therefore the parameters estimated for the thermal curing can be used to predict the

conversions at low extent of cure.

 

 

Figure 4.3

 

Microwave Curing 0t 80 0C

 

 

 

 

TO ' T T I F T I
v izBPo *
()9: a zzepo O “
0.8 _ O 47, BPO O -1
. o .
0.7 ~ a
s — o 1
3 0.6 F i
S 0.5 " O s D “
@114 ~ 0 ' :
L1_l ’ I ‘1
0.3 ~
L O D ‘.' <
0.2 r ' v ~
1. O I -
O.l " O - V V v V T
. /' ‘ 1
0.0 1 1 1 1 1 L 1 1 1
0 1000 2000 3.000 4000 5000

time (secs)

anue1L3 INnxkdluedhnhuuiwndruquuhnenudthuathnmngrnkuowmwe«numng

Microwave curing of 90 0C

 

 

 

 

 

 

 

 

1.0 I l T fir r I
0.9 - AA s
o o e C]
08 ~ A D D v -
0.7 r [:1 ' r
8 i .
80.6: 1 v \7 ‘
3(15- 0 V ~
E114 : CD :
L1_l A v a
ogs- A .
’ 1:] v v 17.8130 1
02 T, F a 2ZBPO .
01 - V o 4ZBP0..
’ a SZBPO .
OO 1 l 1 l 1 A; 1 1 1
0 1000 2000 3000 4000 5000

time (secs)

IFunueut4» Zthkdjuedhnhnuiandtuquuhnemmdthuathudngrnkuowmweinudng

47

hMcrowovei:unng<3tiCK)OC

 

 

 

 

 

 

 

 

 

1.0 T T T l l f T T
’ A
119 ~ 0 AA .
>~ __\/
1.] LJ
C18- A o -
’ v v
057» V ~
9 1 O 57
3116 — O -
3115 ~ V j
C a
3114 — 0 ~
)4
“J ” 1
()3 — .
V v 1ZBP0 .
O2 - a 27BPO .
o azapo -
01 r o 4ZBPO .
a SZBPO 1
OO 1 l 1 1 1 m 1 1m 1
0 1000 2000 3000 4000 5000

trne(secs)

Ifigure‘LSF hdodel[uedhmfionssunlcuqxuinuuuad(unaidurhmgrnhuxuwavetuning

 

 

 

 

80 0C
l .O r m . ‘ l f l r
. —- i 7. BPO, Mw predictions
0 9 _ -— 272 8P0, Mw predictions ________ _
‘ —— 471 BPO. Mw predictions ’ , , """ q
- - - 17: 8P0, Th predictions , I ’
0-8 T - - - 27. 890, Th predictions I ’ ‘
t — - - 47. 890, Th predictions/ I ‘
0f7~ / e
(l) - / ’ ._ .. - -:
L / ’ ‘ ’
306” I I,”
s.- “ / , ’
3115 — ’ -
C / 4
2 O4 ’- I / "‘
X /
L1_J ” / x
0.3 - ’ I ’ _ __ _ ._
02- g, .
I , v ’ ’ ’
01 . ,j/j,"’ —
O O 1 I 1 l 1 1 4m 1 1
0 1000 2000 5000 4000 5000

tkne<secs)

Figure 4.6 Model predictions with microwave and thermal parameters at 80°C

48
4.4 Summary

The polymerization reaction of a vinyl ester resin during microwave curing was
modelled. A thin film technique based on FTIR analysis was used to obtain the extent
of cure data. The initiation reaction was modelled separately to obtain the initiation rate
constant. It was found that the initiator decomposition rate is the same during both
thermal and microwave curing. The propagation rate constant was modelled to be
independent of the extent of reaction. The termination rate constant was modelled to fall
with reaction until a limiting value is reached. The model parameters for microwave
curing were evaluated using a simplex procedure to minimize the error between the
experimental and predicted values.

A good agreement between model predictions and experimental data was found
at low extent of cure. The model under-predicts the conversion at higher extent of cure.
This indicates that the model needs to be refined based on the expected interaction of
microwaves and the resin. This could be done by obtaining the propagation constant
separately using molecular weight data, and then introducing a parameter based on the
effect of microwaves on the propagation reaction. The model predictions at low
conversions are close to the model predictions calculated using the parameters estimated
with thermal cure kinetics data. Therefore the microwave cure kinetics at low extent of
reaction can be modelled using the same parameters and improvements are required to

make good predictions at higher extent of cure.

5. THERMAL PROCESSING OF LAMINATES

5.1 Introduction

Consolidation is a very important step in the manufacture of polymer matrix
composites. Usually, consolidation is accomplished by the application of mechanical
pressure on the composite boundary, accompanied by the application of vacuum and
suitably high temperatures. While curing thermosetting matrix composites, pressure and
vacuum are maintained at least as long as the gelation time for the resin. This process
squeezes air and other sources of voids (including volatiles) out of the composite and also
increases the fiber volume fraction.

The present setup of the microwave cavity does not allow the application of
pressure during the curing process and this results in large volume fractions of voids in
the laminates cured in the microwave cavity. The effect of voids on the mechanical
properties of the laminates is more of a statistical nature rather than a deterministic
nature. To make a proper comparison of the microwave and thermal curing processes,
the void fractions must be very low so that the inherent differences, if any, are not
masked by the statistical noise in the mechanical properties of high void fraction
composites.

This chapter presents the development of a pre-consolidation technique which can
be used to produce low void fraction laminates without the application of pressure during
curing. This study was conducted to produce good laminates in a thermal oven under

conditions similar to those that can be applied, at present, in the microwave cavity. The

49

50

technique was demonstrated by reproducibly producing laminates in the thermal oven
with very low void fractions and mechanical properties comparable to autoclave cured
laminates. This study also forms a part of the effort to demonstrate that laminates can
be manufactured in a microwave cavity with properties equivalent to thermally cured

laminates.

5.2 Development of the method

Recent studies have characterized the behavior of laminates during the consolidation
process [18-22]. Gutowski [19-22] has shown that the fibers act as elastic springs during
the consolidation process, and also that the load carried by the fibers increases with
increasing fiber volume fraction.

It was initially attempted to reduce the void content by just subjecting the laminates
to mechanical pressure and vacuum prior to the application of temperature for curing the
laminate. This method was unsuccessful in reducing the void content of the laminates.
This is attributed to the following. The initial application of pressure squeezes out the
voids and some resin. The removal of pressure results in the relaxation of fibers to their
original state with the surrounding air occupying the volume thus formed. This
phenomenon is analogous to the deconsolidation of thermoplastic composites on heating
above their melt temperature [19].

Based on the above mentioned aspects, a pre-consolidation technique has been
developed, that can be used to produce low void fraction composites. In this method the

uncured laminate is enclosed in a resin-rich environment. The enclosure is suitably

51

prepared to control the flow of resin during pre—consolidation, while allowing the
evacuated air (voids) to leave the surroundings of the laminate. Pressure and vacuum are
simultaneously applied for specific times during the pre-consolidation. The resin-rich
environment ensures that the resin takes most of the load during the initial stage of the
pre-consolidation. The accompanying high hydrostatic pressure aids in forcing the voids
out of the laminate. The enclosure ensures that during the fiber relaxation process
accompanying the release of pressure after pre-consolidation, the resin surrounding the
laminate occupies the volume between the fibers. This results in an overall decrease in

the void volume fraction.

5.3 Experimental
5.3.1 Preparation of the laminates and laminate molds

Prepreg was made in-house from glass fiber and a vinyl ester resin (containing
45% vinyl toluene by wt. and 1% benzoyl peroxide). It was cut to 3" X 3" pieces and
stacked to make twelve-ply, unidirectional laminates. Individual laminates were then
placed on nonporous teflon sheets cut to about 9" X 9" in size. Fifteen milliliters of the
vinyl ester resin containing 1% benzoyl peroxide as the catalyst was then spread on the
laminate to make it resin-rich for pre-consolidation. The nonporous teflon sheet was then
folded closely over the laminate and was held in place by tape near the edges of the
laminate and running around the laminate. The laminate coupon in this stage of the pre-

consolidation is shown in Figure 5.1.

52

 

te coupon

amina

L

Figure 5.1

 

te coupon in the teflon mold.

L

Figure 5.2

53

A mold was prepared by covering a circular teflon block (12.6 cm in diameter)
with release film. A cork dam was prepared on this to the exact dimensions of the
laminate coupon. The cork dam was prepared such that the height of the dam was greater
than the height of the laminate coupon. The cork dam was then sealed on the outside
with tacky tape (a vacuum bag sealant). The laminate coupon was then placed in this
mold as shown in Figure 5.2. The whole assembly was then covered with three layers
of bleeder cloth and sealed hermetically in a vacuum bag, with a tube attached for

connection to a vacuum pump.

5.3.2 I’m-consolidation cycle

The laminate mold prepared as mentioned above was placed in a Carver press and
subjected to a force equivalent to approximately 250 psi. Vacuum was simultaneously
applied. At the end of the pre-consolidation period of 10 minutes, the vacuum was

released slowly, followed by the release of the force.

5.3.3 Thermal curing

The laminate coupon, pre-consolidated as described above, was cured in a thermal
oven at 90°C for 1 hour and post-cured at 125°C for 2 hours. This curing cycle was
chosen because there is no exotherm under these conditions and therefore it is easier to
control the cure conditions and more importantly study the microwave and thermal curing

under similar conditions.

 

 

54
5.3.4 Mechanical testing of cured laminates

The thermal and microwave cured laminates were conditioned at the standard lab
conditions of 23°C and 50% relative humidity for over 48 hours. The laminates were cut
parallel to the fiber direction into approximately 3 " X 0.4" specimens. These specimens
were polished to make the top and bottom surfaces flat and parallel and were subjected
to a three point bending test in accordance with the ASTM standard D790M. The test
data were used to evaluate the flexural strength and the tangent modulus of elasticity in

bending of each sample [23].

5.3.5 Void fraction analysis of the laminates

10 x 10 mm sections were cut from each laminate. These were set in acrylic
mounts and polished to 0.05 micron grit. These finely polished surfaces were viewed
under an optical microscope at a linear magnification of 50. The images observed were
digitized and stored into a computer. An image processing program was used to evaluate
the fractions of the different degrees of gray scales present in the image [24]. The void

volume fraction was calculated based on the degree of gray scales constituting the voids.

5. 3. 6 Fiber volume fraction analysis

The polished surfaces of the acrylic mounts were treated with a mixture of
chromic acid and sulfuric acid to etch the matrix material of the laminate. The surfaces
were viewed under an optical microscope at a linear magnification of 400. The unetched

glass fibers appear as bright circles in a dark background of the acid-etched matrix of the

55

laminate. The fiber volume fraction of the laminate was found as before, based on the

degree of white scales constituting the glass fibers.

5.4 Results and discussion

Table 5.1 lists the properties of the thermally cured laminates. The pre-
consolidation technique developed here has been very successful in reducing the void
fractions of the laminates to very low values. The mechanical properties of the thermal
cured laminates are comparable to the autoclave cured laminate which further prove the

success of the pre-consolidation technique in eliminating most of the voids.

Table 5. 1 Properties of thermally cured laminates

r_.——— ________—.———-—___——_—__

 

 

 

 

 

S (Flex. Eb (Flex. Void fraction Fiber fraction
Sample # Strength, MPa) modulus, GPa) (%) (%)
Th #1 1066 47.0 0.96 67.6
Th #2 1150 65.9 1.14 63.4
Th #3 1135 68.9 1.88 57.0
Th #4 1036 85.0 5.90 66.6
Th #5 1110 93.5 1.34 53.0

 

 

 

 

 

= e tren , = fit]: Tangent filfilflus 1n finfimg

56

There are certain drawbacks of this method. This method results in laminates that
have very poor surface appearance. The laminates made using this method also have
higher resin content than the laminates made with the application of pressure during
curing. This method however, is useful in giving a common basis for the comparison of

the thermal and microwave curing processes.

5.5 Summary

A pre-consolidation method was developed to make very low void fraction
laminates without the application of pressure during curing. This method was used to
process twelve-ply unidirectional laminates made from glass fiber and vinyl ester/vinyl
toluene resin mixture in a thermal oven. The mechanical properties of the thermally
cured laminates were evaluated and it was found that the properties were comparable to

the properties of autoclave cured sample.

6. NHCROWAVE PROCESSING OF LAMINATES

6.1 Introduction

Microwave processing has been investigated as an alternative to the conventional
processing of polymers and polymer matrix composites. Different studies have
demonstrated its viability and advantages [1, 2, 25-27], but various aspects related to its
industrial applicability are still being investigated.

Different resonant modes of the microwave cavity have been found to transfer
energy non-uniformly across the volume of the composite. Processing of composites in
single modes therefore results in large temperature gradients in the material. Different
modes have different energy distribution patterns. Temperature probes can be placed at
different positions on the sample to measure the temperatures as the material is heated
in different single modes. From a knowledge of such single mode heating patterns, it is
possible to switch between appropriate modes to reduce the temperature gradients and
obtain relatively uniform temperature profiles in the material being processed.
Automation of such processing using knowledge based control systems is presently being
investigated [28].

In this chapter, the results of the study of two aspects related to the industrial
applicability of this process are presented. A qualitative evaluation was done to determine
the reproducibility of heating patterns of these laminates in different resonant modes of

a cylindrical microwave cavity under the following conditions: (1) the same sample is

57

58

heated in slightly different orientations in the cavity and (2) different samples prepared
to similar physical and chemical specifications are heated in the cavity.

Another evaluation was done to compare the mechanical properties of microwave
and thermally cured laminates subjected to flexural load. The samples were processed
using similar cure cycles. The microwave samples were cured using a mode-switching
technique and the thermal samples were cured in a temperature controlled oven. A pre-
consolidation technique was used, that allows the production of very low void fraction
composites in the cavity without the application of pressure during the curing process.
These studies are necessary to determine the arnenability of microwave processing to

automation and its suitability for industrial production of composites.

6.2 Experimental

The laminates were prepared and pre-consolidated as described in the previous
chapter. The pre-consolidated laminate, along with the mold, was placed in a 7"
microwave cavity. The microwave processing circuit has been described elsewhere [3].
The position of the temperature probes on the laminate and the position of the sample in
the cavity are shown in Figures 6.1 and 6.2. The different resonant modes available were
found using a sweep oscillator. The heating patterns for each mode were determined by
heating the laminate to about 65°C at 60 Watts of microwave power input to the cavity.
A mode-switching technique was used to heat the laminate as uniformly as possible

during curing [29]. The curing cycle was the same as that of the thermal cured samples.

59

 

Fiber Direction

0T3 1'20

 

 

 

 

Coupling Probe

Figure 6. 1 Position of temperature probes on the sample

 

i

Adjustable Length

i

 

 

FlborDir

 

 

[ Sample I

 

 

 

Coupling Probe ‘ q

 

 

Figure 6.2 Position of the sample in the cavity

60

The cured laminates were conditioned and tested for their mechanical properties
as described in the previous chapter. The void fractions and the fiber volume fractions

were also evaluated as described in the previous chapter.

6.3 Results and discussion

Figures 6.3 and 6.4 illustrate the heating patterns of the same sample in two
slightly different orientations (fiber orientations within 5° of the coupling probe) in the
same resonant mode. The heating patterns are very similar, indicating that the cavity is
not very sensitive to small variations in the orientation of the sample in the cavity.
Figures 6.5 and 6.6 show the heating patterns in the same mode of two different samples.
The heating patterns obtained were very different from each other, as illustrated by these
plots. This is attributed to the manual lay-up of the molds which results in significant
differences in the amount and shape of the accompanying material used for each mold.
These differences give rise to very different heating patterns. Further experiments are
needed to establish the sensitivity of the cavity to small differences in the physical
specifications of the material being processed in the cavity. Finding the heating patterns
of the laminates without any mold lay-up would be a good beginning.

Table 6.1 lists the properties of the microwave cured laminates and compares
them to thermally cured laminates. The low void fractions achieved using the pre-
consolidation technique demonstrate the success of the method. The mechanical

properties of both the thermal and microwave cured laminates are equivalent, which

61

 

 

 

 

70
l
66 e 0 T1
- A T2
I‘fl‘l\.‘\ \’A‘\‘/‘/‘
62 r [:1 T 3 ea“) “nee/An... . , anew/immense. ..
e . is “Li/J» “AAA AA;
58 —+ T4 AA “
/-\. v *- {:1 8| I b
L) _ a DUB DUDE mflmaggflaoénnoooo‘
0 AA D qug”)OOOUT dB DODGE
izf54 i A DD 00moohi‘do“
L. i- 51 i EDD AO ‘
3 A [3 21V)
nIRQ ~ A D o”
O V \ A DD (.JL’) T
(Ll-J " AL; D (“OT A
A 4 6 — EDGE - O n++++++++++++++
) f. ['51:], U .1. ++ + ‘i‘
[E 4 2 T " LEE] p.013 +++ +
_ 4D -0” .+
A (“111+ ++T
.0” +
38 ” éi afir++
34 §§¢@¢+m5mU
30 i’ 1 l 1 l 1 l 1 l g L 1 4 1 l 1 l 1 1 1
0 1 2 3 4 5 5 7 8 9 1 0

Thn€>0munutes)

Figure 6.3 Single mode heating pattern of sample RP1244 in one orientation

 

70
66 e 0 T1
L n
A T/ AAA
2 A QAAA
l— A ‘ ’A l A A
62 D T3 ”AAA AAAAAAAA AAAA AAA
" + T4 AA A
A
O " AA ODD OOflOOOOO-OU
V _ A a 00 V
3 AA DD 000
+1 5 O b ,, A d3 00
E - ATDD 00
m A O OO + +
CL 4 6 T AA 1:] O +H+ ‘i’ M
E _ AGED 00 ++ +++++++
e afio oO +++++++ +
,_ 42 _ .~o Oo ++
. ++++
1 1 1 1 1 n J 1 1 l

 

 

 

 

4 5 6 7 8 9 '10
Tuneinmnutes)

Figure 6.4 Single mode heating pattern of sample RP1244 in different orientation

Temperature (0C)

31.6 r
28.4

62

 

 

Figure 6.5

66

)
UT 07
b- [\3

who;
00m

Temperature (0C

Figure 6.6 Single mode heating pattern of sample MwBS

UT
(I)

U
070

.11..
L232.
7 O.

000 0.2

T1

T3
T4

+C11>O

54

Single mode heating pattern of sample MwB7

C]
O
A
1

0.81

D
O

A

1

O

is A

l 1 l

.08 1.35

1

Time (minutes)

1.62

D
D»

 

2.43 2.70

 

 

4.8

l 1 l

6.0

Time (minutes)

7.2

l

8.4

 

l

9.6

1

10.8 12.

 

63

demonstrates conclusively that microwave curing can be used to produce laminates with
properties equivalent to a thermally cured laminate. Modification of the microwave cavity
to apply pressure during curing is however necessary because the lack of pressure during
curing results in a poor finish. The pre-consolidation technique has however, helped
establish that microwave processing is inherently capable of producing laminates with
very good mechanical properties. The greater variation in the flexural modulus values
is possibly due to the differences in the curing between samples and also the differences
in the fiber and void volume fractions. Figures 6.7 and 6.8 illustrate the comparison of
the average mechanical properties of microwave and thermally cured laminates with the

mechanical properties of the autoclave sample.

Table 6.1 Properties of microwave and thermally cured laminates

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sample # "l S (Flex. Eb (Flex. Void fraction Fiber fraction 6
Strength, MPa) modulus, GPa) (%) (%)
Th #1 1066 47.0 0.96 67.6
Th #2 1150 65.9 1.14 63.4
Th #3 1135 68.9 1.88 57.0
Th #4 1036 85.0 5.90 66.6
L; Th #5 1110 93.5 1.34 53.0
Mw #1 1060 52.2 0.9 65.8
Mw #2 1082 70.9 2.81 54.0
Mw #3 1158 84.0 0.46 58.9
Mw #4 1255 94.3 0.11 59.3

MW #5 1170 107.2 0.41 63.9 I

L,

 

S = Flexural Strength,

E" = Initial Tangent Modulus in Bending

 

 

65

 

 

 

 

     

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

e
V
m
< _ a _ H m — 1 d H
w
.m
you H -2 s: m ._._,_,.:_,.,..C M .c: 36,... _, m new H d: ELL
t .JV 7.4” 4&6 w . x x \ A
\\\ \_\\.\, . _ ,1 m \\ \\\\ \ \\
C\ Cy, _\\\\ W .. \._.\_.\ \l
\ .\ \x .. 9 fl _ _ . \
\t. __ \_\\ . t e .\ \
vflhlii\r\. . \\\ . \hr\l__ll .IH “ _\\\ \x \. >lxki .,
r. .w .f .% Tins»...
t
m u
it b; W .C J 8,01) A .17 ‘1 f 1,
till 1141A} ill? “N f 1741* LN
x a , // ,r /
7,, m. - x/ g -
v til: V/iIVrI?[ [TV/i. T n V: /,l
m Q L r 5..»
i A n 1
.L f a I n
L... 0 w.
n I
m .I.
m.d
e
r _ _ _ , _ _ a m
0 O 0 AU fly 0 O c _ a . _ . _
O O O .1 O O 1,. J, .r
2 O 8 E 4 2 mu W cm 5 O

0&2 £3,187, 65$; 0 0 @239: Emmi:

Figure 6.7

" W ‘3 V "‘

Au i, «Q C it; v e

 

Figure 6.8 Comparison of Tangent modulus of Autoclave, Oven and Microwave
cured laminates

66
6.4 Summary

Twelve-ply unidirectional laminates were made from glass fiber and vinyl
ester/ vinyl toluene resin mixture. The heating patterns for these laminates in individual
resonant modes were evaluated. It was found that the microwave cavity is not very
sensitive to small variations in the orientation of the same sample in the cavity. The
heating patterns in the different individual modes were also evaluated for different
samples prepared as similarly as possible in their physical and chemical specification.
Large differences were found in the heating patterns between these samples. This is due
to the manual lay-up of the mold, which introduces significant differences in the amount
of material used for the mold and the physical specifications of the mold. Further
experiments are necessary to evaluate the sensitivity of the cavity to small and controlled
changes in the physical specifications of the sample and the mold. A pre-consolidation
method, to make very low void fraction laminates without the application of pressure
during curing, was used to process laminates in a microwave cavity using mode-
switching. The mechanical properties of the microwave cured laminates were compared
with those of the thermal cured laminates. It was shown that vinyl ester/ glass fiber
laminates can be cured in a microwave cavity with properties equivalent to those of

thermally cured laminates.

7. GLASS TRANSITION TENIPERATURE DATA

7. 1 Experimental method

The Glass Transition Temperatures (Tg) were determined using TMA for different
samples cured in the thermal oven and microwave cavity for different extents of cure .
A small section of the sample used to study the cure kinetics was used to measure the Tg
at different extents of cure. The section was obtained by cutting the sample used for
kinetic study into four parts. A load of 1 gram was placed on the specimens and a
heating rate of 10°C per minute was used. At low extents of cure, liquid nitrogen was
used to cool the specimens to below -125°C before the heating was started. This method
was followed because at low extent of cure the Tg is close to zero and therefore there
needs to be sufficient time for the system to stabilize to a constant heating rate of 10°C
per minute. The Tg was measured as the point of slope change in the graph of dimension
change vs. temperature. If the slope change was gradual instead of being sharp, then the

Tg value was taken to be the intersecting point of the linear portions of the graph.

7.2 Results

The Tg values for the microwave and thermal cured samples are given in Table

7.1 and are illustrated in Figure 7.1.

67

Table 7. 1

  
  
  

|
i
i

              

 

 

   

 

   

     
    
   
   
      

Thermal Sampels

       
   

68

Microwave samples

L Extent of cure Tg (°C) ;

Tg of thermal and microwave cured samples

 

 

 

 

 

0.20

-12

0.20

      

 

0.26

       

I Extent of cure Tg (°C) I
L-. - - .7 - 7, 7k. _ -1 ,- - _ 7_ _ _ _._ n%_ -1
0.00 7 0.00 7 l

0.02 6 0.08 22

0.10 -13 0.13 25 J

l

l

l

l

17

 

   

0.23

 

0.36

45

   

       

0.36

 

0.41

  

38

     

0.37

 

0.48

   

37

         

0.42

 

 

0.60

  

58

       

0.58

 

0.72

  

0.83

 

0.81

  

0.90

 

0.90

 

0.93

 

 

1.00

 

69

 

200 T I Y I I I r I I I T I 1 I r W I I T
A Thermol
,1 r: O O M i C r‘ C“: W O 6:
v) 1—
O A
A A ‘

WOO . O
/\
L)
O
G A
’— 50 . ‘0 O

A ‘ O
O O
P o o
W O A
A
O a
‘ A

mSO l 1 1 l 1 l 1 l 1 1 4 l 1 1 4 1 1 l

 

 

 

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Extent Of Cure

Figure 7-1 Tg vs Extent of cure of thermal and microwave cured samples

8. CONCLUSIONS

8. 1 Summary of results

Studies have been conducted to enhance the understanding of the interaction of
microwaves with polymer resins. A vinyl ester resin with vinyl toluene as the
crosslinking monomer was used to study the differences between thermal and microwave
polymerization. Benzoyl peroxide was used as the initiator for the polymerization
reaction. Composite processing studies were also conducted to demonstrate the
applicability of microwave curing to the industrial production of polymer matrix
composites.

A method has been developed which can be used to identify the regions of single
component absorption in an IR spectra of a mixture of two chemical species with
different densities. The applicability of the method has been demonstrated with the
spectra of a mixture of a vinyl ester resin and vinyl toluene. Based on this method, an
experimental protocol was developed for the kinetic analysis of the vinyl ester resin.

The polymerization reaction of a vinyl ester resin during thermal curing and
microwave curing was modelled. The initiation reaction was modelled separately using
a first order rate expression. The Benzoyl peroxide reaction peak was monitored to obtain
the conversion of the initiator with time. The initiation rate constant It, was obtained on
a regression of this data. The initiation rate constant was evaluated for both microwave
and thermal curing and was found to be the same. The Benzoyl peroxide decomposition

rate constants for different solutions are reported in literature [30]. The decomposition

70

71

rate constants at the same temperature vary a lot between solutions. There are also
different values reported by different sources, for the same solutions at the same
temperature. The decomposition rate constants for the current mixture were evaluated for
different temperatures and were found to be comparable to the range of values found in
literature [30].

The propagation rate constant was modelled to be independent of the extent of
reaction. The termination rate constant was considered to fall with the extent of cure until
a limiting value is reached. The limiting value is directly proportional to the propagation
rate constant. The model parameters were evaluated, for both the thermal and microwave
curing, using a simplex algorithm to minimize the sum of the squares of the error
between the model predictions and the experimental values. A good agreement was
observed between the model predictions and the experimental data generated at different
temperatures and initiator concentrations during thermal curing. During microwave
curing, the model predictions were accurate at low extent of cure but under-predict the
conversion at high extent of cure. The difference could be the coupling of microwaves
to one of the vinyl groups, thereby increasing its reactivity over the corresponding
thermal case. The increase would result in a corresponding increase in the total extent
of cure as measured here. This is shown in part IV of Appendix-A.

A pre-consolidation method was developed to make very low void fraction
laminates without the application of pressure during curing. This method was used to
process twelve-ply unidirectional laminates, made from glass fiber and vinyl ester/vinyl

toluene resin mixture, in a thermal oven. The mechanical properties of the thermally

72

cured laminates were evaluated and it was found that the properties were comparable to
the properties of the autoclave cured sample. The autoclave cured sample was processed
under similar temperature cycles but with the simultaneous application of pressure and
vacuum during the curing process.

Twelve-ply unidirectional laminates were prepared from glass fiber and vinyl
ester/vinyl toluene resin mixture. The heating patterns for these laminates in individual
resonant modes were evaluated. It was found that the microwave cavity is not very
sensitive to small variations in the orientation of the same sample in the cavity. The
heating patterns in the different individual modes were also evaluated for different
samples prepared as similarly as possible in their physical and chemical specification.
Large differences were found in the heating patterns between these samples. This is due
to the manual lay-up of the mold, which introduces significant differences in the amount
of material used for the mold and the physical specifications of the mold.

A pre-consolidation method, to make very low void fraction laminates without the
application of pressure during curing, was used to process laminates in a microwave
cavity using mode-switching. The mechanical properties of the microwave cured
laminates were compared with those of the thermally cured laminates. Laminates were
reproducibly produced in the microwave cavity with mechanical properties equivalent to
the thermal and autoclave cured samples. Coupled with the advantages of faster and more
controllable heating, this demonstrates that microwave processing is a viable and
attractive alternative to the conventional thermal processing of polymer matrix

composites.

73
8.2 Scope for future work

Various possibilities exist for further studies in the area of microwave processing.
A broad range of issues have to be studied to obtain a comprehensive knowledge of the
microwave processing aspects before the application can be used on a large scale in the
industry. Some of the important issues are listed below.

The model can be refined by obtaining the molecular weight data and separating
the propagation rate constant from the effective rate constant. A parameter can then be
added to the propagation rate constant to reflect the possible interaction between the resin
and microwaves. Molecular weight distribution is difficult to determine and special
techniques have to be utilized for this purpose. The experimental procedure for
microwave curing can be modified to obtain spectra while the sample is curing in the
cavity. This would greatly reduce the experimental error involved in the measurement
of the time of cure and therefore improve the results. Fiber optics may be used to
optically connect the sample to the spectrophotometer.

The model can be also improved by considering the vinyl ester and vinyl toluene
to have different reactivities [5]. This would require the ability to obtain the change in
concentrations of each component in the reacting system. NMR can be used for this
purpose. An analysis of such a consideration is given in Part IV of Appendix-A.
Different model monovinyl compounds (such as styrene) and their homopolymerization
rate constants obtained from literature can be used instead of vinyl toluene. The transient
reaction can also be monitored which can give the ratio of k, to 11:, using the rotating

sector method.

74

Studying the mechanical properties of laminates of non-planar shapes will give an
insight into the amenability of microwave processing of products of industrial value. Such
a study is also likely to generate a database of information on the heating patterns during
the curing of different shaped materials. This database can later be used to model the
behavior of complex shaped materials in the cavity.

Application of pressure and vacuum are vital in the processing of polymer matrix
composites, to eliminate a lot of voids and give a proper finish to the products. Presently
the microwave curing processes suffer from the inability to apply pressure during the
curing process. This could mean the loss of otherwise easily achievable and desirable
properties. Future work can be directed towards achieving this goal in a systematic and
phased manner.

Automation using computers will greatly enhance the quality of the product
obtained through microwave processing. Algorithms can be developed that utilize a
database and appropriately control the cavity to produce composites efficiently and also

incorporate versatility, to cure different kinds of materials, into the system.

APPENDICES

Appendix A: Derivation of kinetic equations

 

Part I Derivation of equation considering equal reactivity for the vinyl groups
The derivation of equation (3.1) from fust principles is presented below. Some of the
nomenclature is in common with chapter 3.

Chain polymerization occurs in three stages. During the initiation stage an
" active" center is formed that initiates the chain polymerization. Propagation is the
addition of more monomer to the growing chain end. Termination is the disappearance
of "active" centers. The schematic notation for these stages is given in Figure 1.4. The

kinetic model based on this mechanism assumes the following.

1. The reactivity of all the intermediate free radicals is the same. Therefore all the
free radicals formed can be considered as one chemical constituent for kinetics
purpose. They can be represented by [R.].

2. The reaction proceeds slowly enough that a steady state is reached, where the

radical population does not change rapidly with time. Therefore we have

$5.1 = 0 (A4)
dt

Hence, a material balance on the components gives the following equation:

d {[11]}
(it

= 0 (A-Z)

 

2nm-nmr=

75

76
Therefore from equation (A-2) we get

 

[R1 = 2 m1] (A4”
\ k:

The reaction is considered to be based on the disappearance of the monomer

 

 

molecules. The propagation reaction occurs so much more often than the others
that it is effectively the only consumer of the monomer. The rate of

polymerization therefore becomes:

Rate of polymerization = RP = kp[R.] [M] (A4)

The design equation for the variable volume reactor is

p i d {V-[M] (A-S)
V dt

Combining equations (A-4) and (A-5), we get
- J—“ 3”} = km (V . 1M1) (A45)

The conversion of the monomer is defined as

X = V0.[M]o - V.[M] (A-7)

V0 . [M]0

 

from which we get

V. [M] = V0.[M]o (1 - X) (A-8)

 

10.

77
Substituting equation (A-8) in equation (A-6), we get

 

- V.[M], d i “d“ X’} = k,[R1{V,.IM1, (1 — )0}
Therefore

dX
E = k,[R.1(1-X)

Substituting equation (A-3) in (A-10) we get

2 k, [1]
dt P k,

 

(l-X)

(A-9)

(A-10)

(A-ll)

If only a certain fraction ’f’ of the initiator fragments can successfully react then

the concentration of the initiator should be multiplied by ’f’.

 

ngazgn (1-x,

t

(A-12)

 

78
Part II Decomposition of Benzoyl peroxide

The derivation of Equation (3.2) from first principles is presented below.

[110

 

 

[I] = e (-k t)
a," ‘p d (3.2)
l - — sX
dP
1 . The design equation for the conversion of the initiator is
R: = _ .1. 0' V-Ul} (A-l3)
V dt
2. The first order rate expression for the decomposition of the initiator is
R, = kd . [1] (A-l4)
3. Combining equations (A-13) and (A-14) and integrating, we get
{Vollll t
d V.[Il} = f - k, . dt (A-IS)
{Volloll {VJ} 0
Therefore
V.[I] = V0110] exp(-kd t) (A46)
4. The total volume ’ V’ of the polymerizing mixture is the sum of the volume of the

unreacted monomer and the volume of the polymer formed

79
V = V," + VP (A-l7)

The total number of moles of monomer left in the polymerizing mixture after a

conversion ’21” is

V0.[M0] (1 — X) (A-l8)
where [M,] is the monomer concentration and V, is the volume, both at zero

conversion.

Therefore the volume of the monomer in the polymerizing mixture is given by

 

V," = V0. (1 — X) (A-l9)

The weight of polymer formed is equal to the weight of monomer reacted

(moi. of monomer reacted)(mol. wt. of monomer) = Me V0.X .Mw (13-20)

where M, is the monomer molecular weight.

Volume of polymer formed is then given by

 

M .M
VP = V0.X.( 0 w] (A-zl)
d?

where d, is the polymer density.

Substituting equations (A—19) and (A-21) in equation (A-l7) gives

80

 

(A-22)
d

M0.Mw
V = Vo(l -X) + V0.X
P

(A-23)

where (Mon) is the monomer density and s is given by equation (3.3).
Substituting equation (A-23) in (A—16), we get

( a,” ”w" ') (A-24)
l - — sX

 

81
Part III Comparison with Poehlein’s model

The following section gives the differences between the model used by Poehlein
[14] and the model used in this work. These simplifications were used because, in their
case the propagation rate constant was available a priori and also because it was felt that
the error involved in the experiments was high enough that the fine differences in the
predictions as made by their model are masked anyway. The rate constant k”, in their

case was correlated to jump length and jump frequency as follows:

r

 

 

 

( 150 )3”
. 2 2,3
kg; = {fl Jc 03 NAV kp (I: llsm[d])} In [R*]AV

where j, is the average number of monomer units in a dangling chain, a is the average
root-mean—square end-to-end distance per square root of the number of monomer units
in the dangling chain, N .w is the Avogadro’s constant, [111] is the concentration of the
monovinyl monomer, [d] is the concentration of unreacted vinyl group in the divinyl
monomer, and [R‘] is the concentration of the free radicals.

The propagation rate constant was considered to vary as follows
. __1_

i
"po kw

i
k?

 

82

where k” is chemical reaction controlled propagation rate constant and k” is the

translational diffusion controlled propagation rate constant. It", was described by the

 

 

 

following equation.
N [m] [d]
k = AV] 4 0 + 0 l ' 2 D R
N (moo “{(tm],+ldlo) (lmlo+ldlo)( )0} ‘3 AB

where [m], and [(110 are the vinyl group concentrations of the monovinyl and divinyl
monomers at zero conversion, respectively. DA, is the mutual diffusivity and RA, is the
collision radius for the encounter between spheres A and B.

The propagation reaction involves the reaction between a macroradical and
monomer molecule. Since the mobility of a macroradical is much smaller than that of a
monovinyl or divinyl monomer molecule, DA, was represented as the average diffusion
coefficient for the monovinyl and divinyl monomers. The free volume concept was used

to correlate change in DA, with conversion as given below.

]

where D”, is the mutual diffusivity at zero conversion and B, is an adjustable parameter.

(
DAB = m expkBp

l 1

Vin Vf

 

 

 

V, and V, are the fractional free volumes of the reaction mixture at zero conversion and

conversion X, respectively.

 

83
Part IV Consideration of unequal reactivities for the vinyl groups

The following section considers the analysis based on considering the reactivities
of vinyl ester and vinyl toluene as different. This analysis is provided to show that the
consideration of different reactivities for the vinyl groups from both the vinyl ester and
vinyl toluene could possibly explain the higher extents of cure observed in the microwave
case compared to the model predictions. The analysis in this case involves more kinetic
constants than the case where the reactivities are assumed to be same. Therefore proper
quantitative analysis would require the information on the fraction of each component
reacted at different times. Therefore some simplifying assumptions have been made to
illustrate the possibility that this form of analysis could better explain the data. The
equations have been derived based on the mechanism shown in Figure 1.4. The

assumptions still remain the same as those used in part I.

The net change in concentrations of the vinyl groups is measured by the disappearance

of the monomers M1 and M2.

 

11021] = k11 [M1][R1.] + k21 [MlllRZ-l

(A-25)

18:21 = k1, [M2][R1.] + k22 [M2][R2-]

 

 

 

84
We can assume that the reactivity for a free radical is independent of the end group in

the radical, but is dependant only on the monomer with which it reacts. Therefore we

have the following relations

(A46)

Since we are assuming that the radical reactivity is independent of the end group, we can
substitute [R.] in place of [R1.] and [R2.]. Substituting this and equation (A-26) in

equation (A-25) we get the following

M1
”4717] = 2 k1 (mum
(A-27)

-%2_] = 2 k, [mun]

Since the total radical concentration is assumed constant, equation (A-3) can be used to
substitute for [R.]. If we include the effect of the volume change, the equations become
very difficult to integrate because of the dependance of [l] on the volume change. If we

neglect the volume change, the concentration of [I] is given as follows:

[I] = [’10 exp( 7kg 0 (A-28)

 

85
Substituting equations (A-3) and (A-28) in (A-27) we get the following equation for

monomer Ml:

 

2 k —k
_flgfl = 2 k1 [M1] \J " [11° kem " t) (A-29)

t

This canbe rearranged as:

2 k -k t
———‘:[AZI]] = 2 k1\J 4km" exp( 2" )da (A—30)

 

 

 

We will have a similar equation for [M2]. The equations can now be integrated to give
the change in the individual concentrations with time. The addition of the integrated
equations gives the change in the total vinyl concentration with time which can be related
to the extent of reaction data that has been acquired here. Now if one of the rate
constants is higher than the corresponding value in the thermal case because of the
interaction of the microwaves with that vinyl compound, then the net rate of reaction as
measured in this work would be higher and this could therefore explain the microwave

data where the current model under-predicts the conversion.

 

Appendix B: OBEY programs

 

Given below are the OBEY Programs written for the idris operating system running on
the PERKIN-ELMER model 1800 Fourier Transform Infrared Spectrophotometer. The
programs can be used for similar future work without any modifications. The lines that
begin with a "*" are the comment statements for the programs and do not affect the

running of the programs.

eteeeeeeeeeeeeeeeeeeetee:teeeeeeeeeeteeeeeeeeteteeteeteeeeeeeeeeeeeeeee

* RamKBrl.oy "'
****#****#*********¥***##4##!*****#**************#************#********
gclear

do sclear

* This obey program was used to scan the spectra of the plain KBr disks

4:

* Enter a file name to save into ( File will be saved into drive f0: )

&enter a1

scan x 4 4000 450 1.00

do display off

&def a2 = clk
&def a3 = date
&def a5 = "1992"
ident x &a3

&def a4 = ident x l 7

ident x Plain KBr disks for correction. &a4&a5, &32 (24 hr clock)
do display on

save x /usr/user/Dhulipal/Spectra/&a1

save x f0:&a1

86

87

*****##************#***********fiitltitlltttttttttfi*******#***#*****#**#

* Rachurel .oy *
****#*‘##¥#**$**#*¢*****##****##1##***##*********#*********************
gclear

do sclear

"' Enter a file name to save into ( File will be saved in drive f0: )
i

11

&def a1 = ""

&enter a1

scan x 4 4000 450 1.00
do display off

&def a2 = ""
&def a3 = ""
&def a4 = ""
&def a5 = ""
&def a2 = clk
&def a3 = date
&def a5 = "1992"
ident x &a3
&def a4 = ident x l 7
ident x &al

&def a8 = ""

&def a8 = ident x 1 2

ident x &a8 samples before cure &a4&a5, &a2 (24 hr clock)
do display on

save x /usr/user/Dhulipal/Spectra/&al

save x f0:&a1

eeeeeeeeeeeeeeeeeeeeeteeeteeeeeeeeeeeeeeteteeeeeeeeeeeeeeeteeeeeeeeeeee

* RamAcure1.oy "'
##fitttttt#****####¢###********tttt***#*******¢**#*#**#**********#**#***
gclear

do sclear

* This FTIR obey program was used to scan the spectra of samples after cure

*

* Enter a file name to save into. (File will be saved in drive f0:)

&def a1 = ""

&enter a1

*

*Enter the time of cure in mins. If seconds exist enter afier decimal point.

* e.g : 10 min and 45 secs should be entered as 10.45

*If no secs exist enter .0 after the time in mins

"' e.g : 10 mins as 10.0

 

88

#
t

&def a9 = ""

&enter a9
t

‘Enter the BPO concentration in wt% used
&def a10 = ""

&enter a1 0
up

"' Enter the Temperature of curing in deg C

 

&def all = ""
&enter all

scan x 4 4000 450 1.00
do display off

&def a2 = ""

&def a3 = ""

&def a4 = ""

&def a5 = ""

&def a2 = clk

&def a3 = date

&def a5 = "1992"
ident x &a3

&def a4 = ident x 1 7
ident x &al

&def a8 = ""

&def a8 = ident x 1 2

ident x T=&a1 lC,BPO=&a10%,&a9 min &a8 cure(num afi pt is sec)&a4&a5,@ &a2
do display on

save x lusr/user/Dhulipal/Spectra/&al

do display on

save x f0:&a1

##1##****#$***##*****#******#*****#$*#**********************************

* Proc2.oy *
******#*******#***#**#t**#***********#****t**#***********************#**
gclear

do sclear

"' THIS PROGRAM WAS WRITTEN BY DHULIPALA RAMAKRISHNA ON 10 July
1992

“ WHILE DOING HIS MASTERS PROGRAM IN CHEMICAL ENGINEERING

e:
e

* This program takes a series of spectra and then subtracts these from a series
* of other spectra ; The subtraction being done in the absorbance mode

89

"' Then it shifis the resultant spectra to bring the least absorbance value to
"' zero value. It then converts the spectra into transmittance mode and saves
* it as another series. This can be used to subtract the spectra of plain

* KBr disks from the fresh and cured sample spectra.

t

"' The series is assumed to be of the form BB(A1-A2)CC

"' Where BB is the string in the name before the numeric series
* CC is the string in the name after the numeric series

* Al is the beginning number of the series and

* A2 is the ending number of the series.

*

" You can stop the program anytime by pressing the break key.

"' THIS PROGRAM TAKES ONLY THE RANGE 4000 - 450 WAVE NUMBER OF
THE SPECTRA

* Press enter when ready

&enter a1

do sclear

* The input spectra files are to be placed in the directory

"' lusr/user/Dhulipal/ Spectra

a
a:

* NOTE CAREFULLY
* WARNING! WARNING! WARNING! WARNING! WARNING! WARNING!

*ittttttttttittt##*******it##ttt#*#*****#******t*tt********t**t*#**t****
*

* THESE INPUT FILES WILL AUTOMATICALLY BE DELETED AFTER
" THE PROCESSING IF YOU WISH TO, PRESS y if you want this to happen

a
as
t

* Enter (y/n)

&enter a7

do sclear

&def a3 = ""

&def a12= ""

&def a14= ""

&def a16= ""

"' do you want the numeric series (1-9) to be of the form (01-09) enter (y/n)
&enter a2

&if a2 = "n" then L90 *
&def a3 ="0"

do display off

&L90 do display on

*

 

9O

"' Enter the beginning value of the numeric series
&enter a5
a

"' Enter the end value of the numeric series

&enter a6

"‘ calc v1 = &a5
* calc v2 = &a6
do sclear

"‘ For the Spectra to be subtracted

* Enter the general name of the files before the numeric series
&enter all

a

* Enter the general name of the files after the numeric series
&enter a12

do sclear

"' For the spectra from which to subtract

"' Enter the general name of the files before the numeric series
&enter a13

*

"' Enter the general name of the files after the numeric series
&enter al4

do sclear

* For the resulting spectra to be stored

* Enter the general name of the files before the numeric series
&enter a15

a

"' Enter the general name of the files afier the numeric series
&enter a16

do sclear

&for v3 = a5,a6,1

&if v3 > 9 then L110 *

do display off

retrieve x lusr/user/Dhulipal/Spectra/&a1l&a3&v3&a12
&error L150

retrieve y /usr/user/Dhu1ipal/Spectra/&a13&a3&v3&al4
&error L150

copy x x 4000 450

copy y y 4000 450

mfiyxz

abex z z 1

taat z z

ident z &al3&a3&v3&al4 corrected using &al l&a3&v3&a12
&L100 *

save 2 f0:&a15&a3&v3&a16

 

91

&error L200

&if a7 <> "y" then L105 *
idris rm /usr/user/Dhulipal/Spectra/&al l&a3&v3&a12.sp
idris rm lusr/user/Dhulipal/Spectra/&al3&a3&v3&al4.sp
&L105 do display on

* &al 1&33&v3&a12 and &a13&a3&v3&a14 processed and stored in F0:
&al 5&a3&v3&a16

&goto L120

&L1 10 do display off

retrieve x /usr/user/Dhulipal/Spectra/&al l&v3&alZ
&error L150

retrieve y /usr/user/Dhulipal/Spectra/&al3&v3&al4
&error L150

copy x x 4000 450

copy y y 4000 450

mfiyxz

abex z z 1

taat z z

ident z &a13&v3&a14 corrected using &al l&v3&a12
&L115 *

save 2 f0:&al 5&v3&a16

&error L210

&if a7 <> "y" then L117 "'

idris rm /usr/user/Dhulipa.l/Spectra/&al l&v3&a12.sp
idris rm /usr/userthulipal/Spectra/&a13&v3&a14.sp
&L1 17 do display on

* &al l&v3&a12 and &a13&v3&a14 processed and stored in F0: &a15&v3&a16
&L120 do display off

&next v3

&goto L800

&L150 do display on

* File Not Found (This is at line 150)

&goto L120

&L200 do display on

&gosub L250

&goto L100

&L210 do display on

&gosub L250

&goto L115

&L250 do display on

t

"‘ The floppy in F0 seems to be full.

* Either replace it and press return or press return to re-try to save
"' in the same floppy

 

92

a

&enter a1

do display off
&return

A

&L800 do display on
" end of program

*ifititfifitittfittfitttttt****¥**********¢t***************#****************

* RamAreaRxnl .oy *
*fittttttttttitttt*******ifit#*****it*1ttttt*#t****tt*****#t****#********
gclear

do sclear

do display on

"' This is for finding the areas under different peaks in the spectrum.

"' This program finds the areas under four different peaks using a user

* defined baseline. The areas under the zero base line and user defined

* base line are output for all the four peaks. The screen is printed to the

"‘ plotter at the end of the program. This limits the number of files to

* 15 if all the areas are to be printed on the plotter. If the series has more

"' than 15 files then it has to be done by running this program more than once

11
e

" For each peak the area under the zero baseline is reported first followed by
"' a comma and the area under the user defined baseline. Each line contains the
* areas pertaining to each spectra.

* Press enter when ready
&enter a1
do display off
* The variables all to a26 are used to store the peaks under which the areas
* are to be found out.
"' Each set of four variables (a1 1-a14), (a15-a18), determine a peak and
"‘ in each set the first two values determine the baseline higher and lower
’ wave number and the next two values determine the limits within which the
* area has to be found out. If no user baseline is required just give
" the same values for the baseline definition as are given to the limits of
"’ integration. Then just ignore the minus baseline areas.
*
" e.g :- a15 has the higher wavenumber of the user defined baseline and the
value al 6 has the lower wavenumber of the user defined baseline
a17 has the higher wavenumber of the limits of integration
and a1 8 has the lower wavenumber of the limits of integration

9

t
a
a

93

fiitfitttlttfittttttttttttttttt

&def all = "3150"
&def 312 = "2650"
*

 

&def a13 = "2972"

&def al4 = "2965"
eeeeeeeeeeeeeeeeeeeeeteasees
&def 815 = "1655"

&def 816 = "1560"

e

 

&def a17 = "1612"

&def 318 = "1602"
eeeeeeeeeeeeeeeeeeeeestates:
&def al9 = "1800"

&def a20 = "1662"

e

 

&def a21 = "1800"
&def a22 = "1765"
****¥*#*****#*¥**ttt*#****##t
&def a23 = "1655"
&def a24 = "1560"
is
&def a25 = "1645"
&def a26 = "1630"

it*fittttitttittitttfit*t**¢***
*

 

do sclear

do display on

" THIS PROGRAM WAS WRITTEN BY DHULIPALA RAMAKRISHNA ON 15 July
1992

* WHILE DOING HIS MASTERS PROGRAM IN CHEMICAL ENGINEERING.

a
t

" This program takes a series of spectra and then finds the areas under certain
* peaks of the spectra with a user defined baseline. It will do that for four

"‘ peaks and output the results to the plotter. Make sure it is switched on and
"‘ is working properly. The areas under the zero baseline as well as the area

" under the user defined baseline will be output.

A

"‘ The spectra are taken from the directory lusr/user/Dhulipall Spectra

* Make sure that the spectra are in that directory

t

* The series is assumed to be of the form BB(Al-A2)CC

94

* Where BB is the string in the name before the numeric series
"' CC is the string in the name after the numeric series

"' Al is the beginning number of the series and

as

A2 is the ending number of the series.

1|

* You can stop the program anytime by pressing the break key.
"' Press enter when ready

&enter a1

do sclear

&def a3 = ""

&def a1 = "y"

"' do you want the numeric series (1-9) to be of the form (01-09) enter (y/n)
&enter a1

&if a1 = "n" then L90 "‘

&def a3 ="0"

&L90 do display on

t

* Enter the beginning value of the numeric series
&enter a5
4:

"' Enter the end value of the numeric series

&enter a6

do sclear

"’ For the series of spectra for which the areas are to be calculated
"‘ Enter the general name of the files before the numeric series
&enter a4

*

* Enter the general name of the files after the numeric series
&enter 37

do sclear

do display on

 

*Base line limits->&all-&a12! &alS - &al6 ! &al9 - &a20 ! &323 - &a24 !
I"Area limits -> &al3 - &a14 ! &a17 - &a18 ! &a21 - &a22 ! &a25 - &a26 !

&for v3 = a5,a6,1

&if v3 <10 then L95 *

&def a3 = ""

&L95 do display ofi‘
&defa2=a4+a3+v3+a7

do display off

retrieve x /usr/user/Dhulipal/Spectra/&a2
&error L150

"' This is where the area have to be found out and output
area x &all &al3 &a14 &a12

calc VI] = v58

95

calc v12 = v57

area x &a15 &al7 &al8 &al6
calc v13 = v58

calc v14 = v57

area x &al9 &a21 &a22 &a20
calc v15 = v58

calc v16 = v57

area x &a23 &a25 &a26 &a24
calc v17 = v58

calc v18 = v57

do display on
*&a2->&vl1.4,&v12.4<>&v13.4,&v14.4<>&vl5.4,&v16.4<>&v17.4,&v18.4#
&L120 do display off

&next v3

&goto L800

&L150 do display on

’&a2 File NOT found
&goto L120

&L800 do display on

rprint

* End of program

ititfiiittifiitttfitttt*ttttttit**¢*#****¢****t*#it********#*****#****#***

"' RamTrans2.oy *
titttttittfifittttttttttitttitt********#*#***tttt##************t*****t***
do sclear

* THIS PROGRAM WAS WRITTEN BY DHULIPALA RAMAKRISHNA ON 29th
OCT

* 1991 WHILE DOING HIS MASTERS PROGRAM IN CHElvflCAL ENGINEERING.

t

'5'}!-

‘ THIS PROGRAM CALCULATES THE ABSORBANCE AT ANY POINT IN A
"' SEQUENCE OF FILES AND OUTPUTS THE VALUES ON TO THE SCREEN.

*

**§

1

"' You can stop the program anytime by pressing the break key.
‘ Press enter when you are ready

&enter a4

&L 100 *

96

do sclear

"' Enter the general name of the files before the start of the numeric sequence
" i.e The file names are assumed to be namel(l-number of files)name2
* So enter the name before the number sequence

&enter 36

do sclear

" Enter the total number of files.

&enter a7

&L105 *

do sclear

* Enter the wave number where you want to calculate the absorbance values.
&enter a4

do sclear

* Place the floppy containing all these files in the drive 0 (left drive)
* Press enter afier you are ready.

&enter a25

do sclear

* Filename Wave number Absorbance

&for v1 = 1,a7,l

do display off

retrieve x f0:&a6&vl

calc le=absr(x(&a4))

do display on

* &a6&vl &a4 &le

do display off

&next v1

do display on

&goto L800

&L500

do display on

* &a6&vl&a15 File not found

&if a1 = "n" then L115

&goto L107

&L800 "'

* Do you want to calculate for another wave length (y/n)

&enter a22

&if a22 = "y" then L105

"' End of program

 

Appendix C: MATLAB script files

 

Given below are the script files used in MATLAB. Some of the files were used to
perform the Simplex minimization of the total error between the experimental and n
predicted values of the extent of cure. Other files were used to plot the predicted extent

of cure data along with the experimental values. The lines that begin with a " % " are the

 

comment statements for the files and do not affect the running of these script files. The L1

three lines identifying the file names must however be deleted before execution.

eeeeeeeeeeeeeeeeeeeeeeeeeasserteeeeeeeeeeeeeeeeeeteeseseeeeeeeeteeeeeee

"' Total_Reg3.m *
$¢¢¢¢¢¢¥tt$i¥¥t¢tit****tt*****#*¥#*#*#******¥******##*********¢**t$#***
% This is a matlab script file.

% This program starts the simplex procedure and stores the results in the

% file Total_Reg_Data3. The lines that start with a % are comment lines.

%

diary Total_Reg_Data3;

diary on;

options(18) = 0;

options(l) = l;

options(2) = 1e-4;

options(3) = le-4;

options(l4) = 500;

fmins(’Total_Error3_New’,[6437 18.2420 2.7446 0.5787], options)

diary off;

quit;

****#*¢***#***##¢****#********#***#****#************#********#*********

‘ Total_Error3_New.m *
itittfitittfitfittitfiit***#*#*fi***##*#*******tiit****¢**¥*************fi**t

function f = Total_Error3_New(X_In)

97

98

Kpm = X_In(1);

Kpc = X_In(2);

Btc = X_In(3);
Ktp_Factor = X_In(4);
Btrn = 0;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% REMEMBER To CHANGE THE RHS OF THE FIRST LINE TO THIS FILE

% NAME IF THE NAME OF THIS FILE IS CHANGED
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Error = 0;
T = 080;

%%%%° o%° o%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The files tc080b11.m etc. contain the extent of cure vs time

% data for the corresponding temperatures and BPO concentrations.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

tc080b1 1;
tc080b21 ;
tc080b31;
tc080b41;

%° o° o° 0° o%° o%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% For each of the temperatures and each BPO concentrations the following lines

% find the sum of the square of the error between the predicted and experimental

% values of the extent of cure and then add this to the total error. That value

% is then returned to the matlab function ’fmins’ that does a simplex

% minimization of the error.

%° o%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear t_Actual;

clear X_Actual;

wt_Percent_I = 1;

Size_of_Exp_Data = size(TC080Bl 1,1);

for Junk = 1:1:Size_of_Exp_Data
t_Actual(Junk) = TC080B11(Junk,2);
X_Actual(Junk) = TC080B11(Junk,1);

end;

Max_Time = t_Actual(Size_of_Exp_Data);

Total_EFinder_New;

%

 

 

%

%

%

99

clear t_Actual;

clear X_Actual;

wt_Percent_I = 2;

Size_of_Exp_Data = size(TC080B2 1 , 1);

for Junk = 1:1 :Size_of_Exp_Data
t_Actual(Junk) = TC080B21(Junk,2);
X_Actual(Junk) = TC080B21(Junk,l);

end;

Max_Time = t_Actual(Size_of_Exp_Data);

Total_EFinder_New;

 

%clear t_Actual;

%clear X_Actual;

%wt_Percent_I = 3;

%Size_of_Exp_Data = size(TC080331,1);
%for Junk = l:1:Size_of_Exp_Data

% t_Actual(Junk) = TC080B31(Junk,2);
% X_Actual(Junk) = TC080B31(Junk,l);
%end;

%Max_Time = t_Actual(Size_of_Exp_Data);
%Total_EFinder_New;

 

 

clear t_Actual;

clear X_Actual;

wt_Percent_I = 4;

Size_of_Exp_Data = size(TC080B4l ,1);

for Junk = 1:1 :Size_of_Exp_Data
t_Actual(Junk) = TC08OB41(Junk,2);
X_Actual(Junk) = TC080B41(Junk,l);

end;

Max_Time = t_Actual(Size_of_Exp_Data);

Total_EFinder_New;

 

%clear t_Actual;

%clear X_Actual;

%wt_Percent_I = 5;

%Size_of_Exp_Data = size(TC080B51,l);
%for Junk = l:1:Size_of_Exp_Data

% t_Actual(Junk) = TC080B51(Junk,2);
% X_Actual(Junk) = TC080B51(Junk,l);
%end;

100

%Max_Time = t_Actual(Size_of_Exp_Data);
%Total_EF inder_New;
%

 

(y0 eeeeeeeeununuu"tunusneuuunuunuuen”extenu-e
AAAMAMAAAAMAMAMMAAMAMAAAAMAMAAAAMMAAMMMMAAMAAM
%

T = 090;

tc090b1 l;
tc090b21;
tc090b3 l ;
tc090b41;
tc090b5 1 ;

clear t_Actual;

clear X_Actual;

wt_Percent_I = 1;

Size_of_Exp_Data = 10;

for Junk = l:1:Size_of_Exp_Data
t_Actual(Junk) = TC090B11(Junk,2);
X_Actual(Junk) = TC090B11(Junk,1);

end;

Max_Time = t_Actual(Size_of_Exp_Data);

Total_EFinder_New;

 

%

 

clear t_Actual;

clear X_Actual;

wt_Percent_I = 2;

Size_of_Exp_Data = 14;

for Junk = l:1:Size_of_Exp_Data
t_Actual(Junk) = TC09OBZI(Junk,2);
X_Actual(Junk) = TC090B21(Junk,1);

end;

Max_Time = t_Actual(Size_of_Exp_Data);

Total_EFinder_New;

%

 

clear t_Actual;

clear X_Actual;

wt_Percent_I = 3;

Size_of_Exp_Data = 14;

for Junk = l:1:Size_of_Exp_Data
t_Actual(Junk) = TC090B31(Junk,2);

%

%

%

101

X_Actual(Junk) = TC09OB3 1(Junk,1);
end;
Max_Time = t_Actual(Size_of_Exp_Data);
Total_EFinder_New;

 

%clear t_Actual;

%clear X_Actual;

%wt__Percent_I = 4;

%Size_of_Exp_Data = 11;

%for Junk = l:1:Size_of_Exp_Data

% t_Actual(Junk) = TC090B41(Junk,2);

% X_Actual(Junk) = TC090B41(Junk,l);
%end;

%Max_Time = t_Actual(Size_of_Exp_Data);
%Total_EFinder_New;

 

clear t_Actual;

clear X_Actual;

wt_Percent_I = 5;

Size_of_Exp_Data = 13;

for Junk = l:1:Size_of_Exp_Data
t_Actual(Junk) = TC090B51(Junk,2);
X_Actual(Junk) = TC090B51(Junk,1);

end;

Max_Time = t_Actual(Size_of_Exp_Data);

Total_EFinder_New;

 

% *tittltfittfifi4ltt*itfiifittt*#*¢*******titit!!!#¢***#***************

%

 

T = 100;

tc100bl 1;
tc100b21;
tc100b31;
tc100b41;
tc100b51;

clear t_Actual;

clear X_Actual;
wt_Percent_I = l;
Size_of_Exp_Data = 13;

 

 

 

%

%

102

for Junk = l:1:Size_of_Exp_Data
t_Actual(Junk) = TC100B11(Junk,2);
X_Actual(Junk) = TC100B11(Junk,1);

end;

Max_Time = t_Actual(Size_of_Exp_Data);

Total_EFinder_New;

 

clear t_Actual;

clear X_Actual;

wt_Percent_I = 2;

Size_of_Exp_Data = 11;

for Junk = 1:1 :Size_of_Exp_Data
t_Actual(Junk) = TC100B21(Junk,2);
X_Actual(Junk) = TC 1 0082 1 (Junk, 1 );

end;

Max_Time = t_Actual(Size_of_Exp_Data);

Total_EFinder_New;

 

 

%clear t_Actual;

%clear X_Actual;

%wt_Percent_I = 3;

%Size_of_Exp_Data = 14;

%for Junk = l:1:Size_of_Exp_Data

% t_Actual(Junk) = TC100B31(Junk,2);

% X_Actual(Junk) = TC100B31(Junk,l);
%end;

%Max_Time = t_Actual(Size_of_Exp_Data);
%Total_EFinder_New;

 

clear t_Actual;

clear X_Actual;

wt_Percent_I = 4;

Size_of_Exp_Data = 10;

for Junk = l:1:Size_of_Exp_Data
t_Actual(Junk) = TC100B41(Junk,2);
X_Actual(Junk) = TCIOOB41(Junk,1);

end;

Max_Time = t_Actual(Size_of_Exp_Data);

Total_EFinder_New;

 

103

%clear t_Actual;
%clear X_Actual;
%wt_Percent_I = 5;
%Size_of_Exp_Data = 10;
%for Junk = l:1:Size_of_Exp_Data
% t_Actual(Junk) = TC100B51(Junk,2);
% X_Actual(Junk) = TC100B51(Junk,l);
%end;
%Max_Time = t_Actual(Size_of_Exp_Data);
%Total_EFinder_New;
%

 

% *****#*#*****#*$*****#*****#itit*********#**********************

%AMAMMAMMAMAAAMAMAAAAMMAAMMAMAAAMAAMAMAMAAMAAM

T = 110;
tc110b11;
tcl 10b21;
tc110b31;
tc110b41;
tc110b51;

clear t_Actual;

clear X_Actual;

wt_Percent_I = 1;

Size_of_Exp_Data = 05;

for Junk = l:1:Size_of_Exp_Data
t_Actual(Junk) = TC110B11(Junk,2);
X_Actual(Junk) = TC110B11(Junk,1);

end;

Max_Time = t_Actual(Size_of_Exp_Data);

Total_EFinder_New;

 

%clear t_Actual;

%clear X_Actual;

%wt_Percent_I = 2;

%Size_of_Exp_Data = 10;

%for Junk = 1:1 :Size_of_Exp_Data

% t_Actual(Junk) = TC110B21(Junk,2);

% X_Actual(Junk) = TC110B21(Junk,l);
%end;

%Max_Time = t_Actual(Size_of_Exp_Data);
%Total_EFinder_New;

 

%

%

%

%

104

 

clear t_Actual;

clear X_Actual;

wt_Percent_I = 3;

Size_of_Exp_Data = 12;

for Junk = l:1:Size_of_Exp_Data
t_Actual(Junk) = TCl 10B31(Junk,2);
X_Actual(Junk) = TC110B31(Junk,l);

end;

Max_Time = t_Actual(Size_of_Exp_Data);

Total_EFinder_New;

 

clear t_Actual;

clear X_Actual;

wt_Percent_I = 4;

Size_of_Exp_Data = 09;

for Junk = 1:1 :Size_of_Exp_Data
t_Actual(Junk) = TC110B41(Junk,2);
X_Actual(Junk) = TC110B41(Junk,l);

end;

Max_Time = t_Actual(Size_of_Exp_Data);

Total_EFinder_New;

 

%clear t_Actual;

%clear X_Actual;

%wt_Percent_I = 5;

%Size_of_Exp_Data = 09;

%for Junk = l:1:Size_of_Exp_Data

% t_Actual(Junk) = TC110B51(Junk,2);

°/o X_Actual(Junk) = TC110B51(Junk,l);
%end;

%Max_Time = t_Actual(Size_of_Exp_Data);
%Total_EFinder_New;

 

% eeeeeeeeeeeeeeeeeeeeeeeean:eeeeeeeeeue*eueeeuuneuneeeteeu
MAAMMAAMAAAMMMMMAAMAMAMMAMAMAMAAMAAMMMMAAM
%

T = 120;
tc120b11;
tc120b21;

 

105

tc120b31;
tc120b41;
tc120b51;

%

“/o

%

clear t_Actual;

clear X_Actual;

wt_Percent_I = l;

Size_of_Exp_Data = 07;

for Junk = l:1:Size_of_Exp_Data
t_Actual(Junk) = TC120B11(Junk,2);
X_Actual(Junk) = TC120B11(Junk,1);

end;

Max_Time = t_Actual(Size_of_Exp_Data);

Total_EFinder_New;

 

clear t_Actual;

clear X_Actual;

wt_Percent_I = 2;

Size_of_Exp_Data = 08;

for Junk = 1:1 :Size_of_Exp_Data
t_Actual(Junk) = TC120B21(Junk,2);
X_Actual(Junk) = TC120B21(Junk,l);

end;

Max_Time = t_Actual(Size_of_Exp_Data);

Total_EFinder_New;

 

 

%clear t_Actual;

%clear X_Actual;

%wt_Percent_I = 3;

%Size_of_Exp_Data = 11;

%for Junk = 1:1 :Size_of_Exp_Data

% t_Actual(Junk) = TC120B31(Junk,2);

% X_Actual(Junk) = TC120B31(Junk,1);
%end;

%Max_Time = t_Actual(Size_of_Exp_Data);
%Total_EFinder_New;

 

clear t_Actual;

clear X_Actual;
wt_Percent_I = 4;
Size_of_Exp_Data = 12;

106

for Junk = l:1:Size_of_Exp_Data
t_Actual(Junk) = TC120B41(Junk,2);
X_Actual(Junk) = TC12OB41(Junk,1);

end;

Max_Time = t_Actual(Size_of_Exp_Data);

Total_EFinder_New;

 

%
clear t_Actual;
clear X_Actual;
wt_Percent_I = 5;
Size_of_Exp_Data = 07; L
for Junk = l:1:Size_of_Exp_Data
t_Actual(Junk) = TC120351(Junk,2); '
X_Actual(Junk) = TC120B51(Junk,1); I
end; *'
Max_Time = t_Actual(Size_of_Exp_Data);
Total_EFinder_New;
%

 

96=¥$$¥ttitt$¢tttttt*tt************#****#*#*************#**********
AMAMAAMAAMMAAAAAAMMMAMAMMMAAAMAMAMMAAMMAMAAM
%

f = Error;

*************t*#¢***********t*tt*¢*#t#**¥¥*t*ttt#************#*******#*

* Total_EFinder_New.m *
eeeeeeeeeeeeteeeeeeeeeeeeeteeeeeeeeeeeeee*eeeeeeeeeeeeeeteeeeeeeeeeeeit
% This script file actually calculates the predicted values of extent of cure

% for each unit time at a particular cure temperature and benzoyl peroxide

% concentration. It then calculates the square of the error for each

% experimental data point and then adds that to the total error.

Step_Time = 1;

No_of_Steps = Max_Time/ Step_Time;
f = 1;

KttO = 1;

Tgrn = -160;

Tgp = 080;

VFO = (0.025 + 0.001 * (T-Tgm));

Kp = 1e-2 "' exp((-Kprn/(T+273)) + Kpc);
Bt = (Btm * T) + Btc;

Ktp = Ktp_F actor * Kp;

107

dm = 1.04;
CIO = (wt_Percent_I/242.2)/(0.1/dm);
s=00h

Kd = 8.02e7 "‘ exp(-8795.4/(T+273));

time = [0:Step_Time:Max_Time];
clear Extent;

Extent(l) = 0;

Kt_Array(2) = O;

for N = 2:1 :No_of_Steps+l
X = Extent(N-l);
= time(N);

PhyP = X / (1+s - s‘X);

Vf = VFO + PhyP "' (0.00048*(T-Tgp) - 0.001*(T-Tgm));
Ktt = KttO * exp(Bt*((1NFO) - (1ND));

Kt = Ktt + Ktp;

R = s / (s + 1);
CI = ( C10 * exp (-Kd * t) )/(1 - R‘X);
Dx_by_dt_Templ = Kp * sqrt(2*f"Kd*CI/Kt);
Dx_by_dt = Dx_by_dt_Temp1 * (1 -X);
X_New = X + ( Dx_by_dt * Step_Time) ;
if X_New > 1

X_New = 1;
end;

Extent(N) = X_New;
Kt_Array(N) = Kt;

end;

for jj = l:1:Size_of_Exp_Data

t_Data = t_Actual(jj);

X_Data = X_Actual(ij);

X_Calc = Extent(t_Data + 1);

Error = Error + ((X_Calc - X_Data)"2);
end;

eeseetsetseeeeeeeeesteeeeeeeeeeeeeeeeeeeeee*eeeeeeeeeeeeeeeeteeteeeeeee

* Total_Draw090.m *

##1##**********#**********##*****10*t*******##**************#************

% This program generates the predicted cure curves and plots it along with the

 

 

108

% cure data generated at 90 C and different BPO concentrations.
% The same script file with minor modifications can be used to plot

% similar curves for reaction at other temperatures.
%

clear;

!rm T090;
diary T090;
diary off;

% Uncomment the following if the plot of rate of reaction vs. extent of cure is also
required.

%subplot(2,1,l), hold off;

%subplot(2,1,2), hold off;

% DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
tc090b1 l;
tc090b21;
tc090b3 1 ;
tc090b41;
tc090b5 1 ;
% DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

% **¢********it!t****tit##it**¢*¥**$¢#tt*****tt*

T = 090;
Max_Time = 4000;

%

wt_Percent_I = 5;

subplot(l,1,1); plot(TC090B51(:,2),TC09OBS1(:,1),’b+’);

diary on;

TC090B5 1(:,2)

TC090B51(:,1)

diary off;

% The following script file generates the extent of cure data for the conditions above.
Total_Extent_New;

hold on;

plot(time,Extent,’b’);

% Uncomment the following if the plot of rate of reaction vs. extent of cure is also
required.

%subplot(2,1,2); plot(Extent,Dxdt_Array,’b’);

hold on;

diary on;

% The following lines output data to a file.

 

109

time’

Extent’

diary off;
%Dxdt_Array’ * 1000
diary off;

%MAAAMAAMAAAMMMAAMAAMAMAMAMMAMAAAMMAAAAAMAA

% The following sets of code are similar except that some of the lines are commented
because

% the corresponding plots are not needed.
%

wt_Percent_I = 4;

subplot(l,1,1);

%diary on;

%TC090B41(:,2)

%TC090B41(:, 1)

%diary off;

Total_Extent_New;

hold on;

%plot(time,Extent,’c’);

%subplot(2,1,2); plot(Extent,Dxdt_Array,’c’);
hold on;

diary on;

%time’

Extent’

diary off;

%%Dxdt_Array’ "‘ 1000

%diary off;

%AMAMAAMAMAMAAMAMMAAAMAMAMMMMMAMMAMAMAM

 

 

%

wt_Percent_I = 3;

subplot(l,1,1); plot(TC090B31(:,2),TC090B31(:,1),’gx’);
diary on;

TC090B3 1(:,2)

TC090B31(:,1)

diary off;

Total_Extent_New;

hold on;

plot(time,Extent,’ g’);

%subplot(2,1,2); plot(Extent,Dxdt_Anay,’g’);
hold on;

diary on;

%time’

 

110

Extent’

diary off;
%Dxdt_Array’ " 1000
diary off;

%AMMMMAMAMAMAAMAMAAMMMAAMAAMAAAAMAAMMMAM

%

wt_Percent_I = 2;

subplot(l,1,1); plot(TC090B21(:,2),TC090B21(:,1),’m*’);
diary on;

TC090B21(:,2)

TC090B21(:,1)

diary off;

Total_Extent_New;

hold on;

plot(time,Extent,’m’);

%subplot(2, l ,2); plot(Extent,Dxdt_Array,’m’);
hold on;

diary on;

%time’

Extent’

diary off;

%Dxdt_Array’ * 1000

diary off;

%MMMAMAAAMMAAAMAMMMMAAAMMMAAAMAAAAMAMAAMA

%

 

 

wt_Percent_I = 1;

subplot(l,1,1); plot(TC09OBl 1(:,2),TC090B11(:,1),’r+’);
diary on;

TC09OBl 1(:,2)

TC090B11(:,1)

diary off;

Total_Extent_New;

hold on;

plot(time,Extent,’r’);

%subplot(2, 1 ,2); plot(Extent,Dxdt_Array, ’ r’);
hold on;

diary on;

%time’

Extent’

diary off;

%Dxdt_Array’ "' 1000

diary off;

111

 

%

96ltfitttttilltt*****¢**#***##***#*****#*****#¢*******¢*

subplot(l,1,1); axis([0 Max_Time 0 1]);

ylabel(’Extent of cure ’);

xlabel(’time’);

title([’Extent of cure vs time at T = ’,num23tr(T),’ C’]);

text(200,-0.1,[’Kpm = ’,num23tr(Kpm),’ Kpc = ’,num28tr(Kpc),’ Bt = ’,num2str(Bt) ,’
Ktp_factor = ’ ,num28tr(Ktp_Factor)]);

print -append junk;

**********##*****##*titttttttttt*tii*********¢**¢***¢**#***************

* Total_Extent_New.m "‘
¢#**#¢**$*#*##tiltttttfi**##***##*#**#¢****tttt##ttfi##****##*¢**********

 

% Given a set of parameters this will automatically calculate the X vs

% t for the current set of conditions. The set of conditions are the

% Temperature T (C), Wt percent of BPO, and the Maximum time of the reaction

% This script file is called from different places in other files like Total_Draw090.m
% A finite difference approach is used here to calculate the rate of reaction and extent of
cure

% as a function of time.

Kpm = 6760.4;
Kpc = 19.1390;
Btrn = 0.0;

Btc = +2.9885;
Ktp_Factor = 0.50682;

04
% The actual Kp is calculated from the simulation parameters Kpm and Kpc.
Kp = le-2 "' exp((-Kpm/(T+273)) + Kpc);

Bt=(Btm*T)+Btc;

Ktp = Ktp_Factor * Kp;

qéeeeeeteeeeeeeeee*eeeeeeeeaeseetees:eeeeeeeeeeeeeeeeeeeeeeett

if T = 80
Max_Time = 5000;
Step_Time = 2;
end;
if T > 85
if T < 95

Max_Time = 4000;
Step_Time = 2;

 

112

end;
end;
if T = 100
Max_Time = 3000;
Step_Time = 2;
end;
if T = 110
Max_Time = 2000;
Step_Time = 1;
end;
if T = 120
Max_Time = 1000;
Step_Time = 1;
end;

No_of_Steps = Max_Time/ Step_Time;
f = 1;

KttO = 1;

Tgm = -160;

Tgp = 080;

VFO = (0.025 + 0.001 * (T-Tgm»;
dm = 1.04;

C10 = (wt_Percent_I/242.2)/(0.l/dm);
s=00h

Kd = 8.02e7 * exp(-8795.4/(T+273));

time = [0:Step_Time:Max_Tirne];

clear Kp_Array;
clear Vf_Array;
clear Phyp_Array;
clear Extent;
clear Dxdt_Array;
clear Ktp_Array;

Extent(l) = 0;
Kt_Array(2) = 0;

for N = 2:1 :No_of_Steps+1
X = Extent(N-l);
t = time(N);

PhyP = X / (1+s - s*X);

 

1 l3
Vf = VF 0 + PhyP * (0.00048*(T-Tgp) - 0.001*(T-Tgm));

Ktt = KttO * exp(Bt*((lNFO) - (le)));
Kt = Ktt + Ktp;
R = s/(s+1);
CI = (C10 "' exp (-Kd * t) / (1 - R‘X) );
Dx_by_dt_Templ = Kp "' sqrt(2"'f"'Kd*CI/Kt);
Dx_by_dt = Dx_by_dt_Temp1 * (l-X);
X_New = X + ( Dx_by_dt * Step_Time) ;
if X_New > 1

X_New = 1;
end;

Extent(N) = X_New;
Kp_Array(N) = Kp;
Kt_Array(N) = Kt;
Vf_Array(N) = Vf;
Phyp_ArrayCN) = PhyP;
Ktp_ArraflN) = Ktp;
Dxdt_Array(N) = Dx_by_dt;
end;

Kp_Array( 1) = Kp_Array(2);
Kt_Array( 1) = Kt_Array(2);
Vf_Array(l) = Vf_Array(2);
Dxdt_Array( 1) = Dxdt_Array(Z);
Ktp_ArraY( 1) = Ktp_AHaY(2);

 

LIST OF REFERENCES

LIST OF REFERENCES

 

[1]

[2]
[3]

[4]

[5]

[6]

[7]
[8]
[9]

[10]

[11]

[12]

[13]

Wei J. , Delong J. D. and Hawley M. C. , Proceedings of the American Society
for composites, 5th Tech. Conf., 239, June, (1990).

Agrawal R. and Drzal L. T., J. Adhesion, 29, 63, (1989).

Jow J ., Hawley M. C., Finzel M. and Kern T., Polymer Engineering and
Science, vol. 28, no. 22, Nov (1988).

Goodman S. H. , Handbook of Ihermoset Plastics, Noyes Publications, New
Jersey, (1986).

Rodriguez F. , Principles of Polymer systems, Chapter 4, Second edition,
McGraw Hill Book Company, New York, (1982)

Henniker J. C. , Infrared Spectrometry of Industrial Polymers, Academic Press,
London, New York, (1967).

Koenig J. L., Appl. Spectrosc., 29, 293 (1975).
Koenig J. L. and Antoon M. K., Appl. Opt., 17, 1374 (1978)

Bershtein 1. Ya. and Kaminskii Yu. L., Optics and Spectroscopy, 15, 381
(1963).

Hirschfield T. B., Anal. Chem, 48, 721 (1976).

Koenig J. L., D’Esposito L. and Antoon M. K., Appl. Spectrosc., 31, 292
(1977).

Ingle J. D. and Crouch S. R. , Spectrochemical Analysis, Prentice Hall, New
Jersey (1988).

Wei J. , DeLong J. D., DeMeuse M. and Hawley M. C. , "Comparison of

Microwave and Thermal Cure of Epoxy Resins" , Polym. Eng. & Sci. (in
press) (1992) .

114

 

 

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

[25]

[26]

[27]

115

Chorng-Shyan Chem and Poehlein G. W. , Polym. -Plast. Technol. Eng. ,
29(5&6), 577-591 (1990).

Ross R. T., Jr. and Lawrence R. L., AICIE Symp. Ser., 72(160), 74 (1976).

Soh S. K. and Sundberg D. C., J. Polym. Sci. Polym. Chem. Ed., 20, 1299,
1315, 1331, 1345 (1982).

Bamford C. H. and Tipper C. F. H. , Comprehensive Chemical Kinetics, Free—
Radical Polymerization, Vol. 14A, Elsevier Scientific Publishing Company,
New York (1976).

Kim Y. R., McCarthy 8. P. and Fanucci J. P., Proceedings of the Society of
Plastics Engineers 48th Annual Technical Conference, pp 1252 - 1255, (1990).

Gutowski T. G., SAMPE Quarterly, Volume 16, No. 4, pp 58-64, July, (1985).

Gutowski T. G. , Kingery J . and Boucher D. , Proceedings of the Society of
Plastics Engineers 44th Annual Technical Conference, pp 1316-1320, May,
(1986).

Gutowski T. G., Cai Z., Kingery J. and Wineman S. J., SAMPE Quarterly,
Volume 17, No. 4, , pp 54-58, July, (1986).

Gutowski T. G., Cai 2., Bauer 8., Boucher D., Kingery J. and Wineman S. J.,
Journal of Composite Materials, Vol 21(6), 650-669, (1987).

ASTM Standards and literature references for COMPOSITE MATERIALS, First
Edition, ASTM, p. 360, (1987).

Waterbury M. C. and Drzal L. T. , J. Reinforced Plastics and Composites, 8,
627-636, (1989).

Wei J ., Chang Y., Thomas B. and Hawley M. C., ICCM/VII Conf., Honolulu,
Hawaii, July, (1991).

Delong J. D., Jow J. and Hawley M. C., 2nd Topical Conf. on Emerg. Tech.
in Mat., Am. Inst. of Chem. Eng., San Francisco, CA, paper 220e, (1989)

Hottong U. , Wei J. , Dhulipala R. and Hawley M. C. , Microwaves: Theory and
Application in Materials processing. Ceramic Transactions, vol. 21, ACerS Inc.
p587 , (1991).

 

 

[28]

[29]

[30]

116

Adegbite V. , Hawley M. C. , Ahmed K. and Sticklen J. , Proceedings of the
Materials Research Society-Spring 1992, San Francisco, CA, (1992).

Fellows L. A. and Hawley M. C. Composites: Design, Manufacture and
Application, edited by S. Tsai and G. Springer, presentation 12-E, Eighth
International Conference on Composite Materials, Honolulu, Hawaii, July 15-19,
(1991).

Bradrup J. and Emmergut E. H. , Polymer Handbook, Second edition, John wiley
and sons, New York (1975).

 

HICHI

1131

 

GRN STRTE UNIV. LIBRARIES
Willlllllll111111111111IIIHIIWHIIWHIIHI
1293010555252