characterization of cure kinetics and physical...

CHARACTERIZATION OF CURE KINETICS AND PHYSICAL PROPERTIES OF A

HIGH PERFORMANCE, GLASS FIBER-REINFORCED EPOXY PREPREG AND

A NOVEL FLUORINE-MODIFIED, AMINE-CURED COMMERCIAL EPOXY

Bryan Bilyeu, B.S., M.S.

Dissertation Prepared for the Degree of

DOCTOR OF PHILOSOPHY

UNIVERSITY OF NORTH TEXAS

December 2003

APPROVED: Witold K. Brostow, Major Professor and Chair Kevin P. Menard, Co-Major Professor Michael R. Kozak, Committee Member

Bruce Gnade, Committee Member and Chair of the Department of Materials Science and Engineering

Oscar N. Garcia, Dean of the College of Engineering Sandra L. Terrell, Interim Dean of the Robert B. Toulouse

School of Graduate Studies

Bilyeu, Bryan, Characterization of cure kinetics and physical properties of a high

performance, glass fiber-reinforced epoxy prepreg and a novel fluorine-modified,

amine-cured commercial epoxy. Doctor of Philosophy (Materials Science), December,

2003, 251 pp., 1 table, 86 illustrations, references, 829 titles.

Kinetic equation parameters for the curing reaction of a commercial glass fiber

reinforced high performance epoxy prepreg composed of the tetrafunctional epoxy

tetraglycidyl 4,4-diaminodiphenyl methane (TGDDM), the tetrafunctional amine curing

agent 4,4’-diaminodiphenylsulfone (DDS) and an ionic initiator/accelerator, are

determined by various thermal analysis techniques and the results compared. The

reaction is monitored by heat generated determined by differential scanning calorimetry

(DSC) and by high speed DSC when the reaction rate is high. The changes in physical

properties indicating increasing conversion are followed by shifts in glass transition

temperature determined by DSC, temperature-modulated DSC (TMDSC), step scan DSC

and high speed DSC, thermomechanical (TMA) and dynamic mechanical (DMA) analysis

and thermally stimulated depolarization (TSD). Changes in viscosity, also indicative of

degree of conversion, are monitored by DMA. Thermal stability as a function of degree

of cure is monitored by thermogravimetric analysis (TGA). The parameters of the

general kinetic equations, including activation energy and rate constant, are explained

and used to compare results of various techniques. The utilities of the kinetic

descriptions are demonstrated in the construction of a useful time-temperature-

transformation (TTT) diagram and a continuous heating transformation (CHT) diagram

for rapid determination of processing parameters in the processing of prepregs.

Shrinkage due to both resin consolidation and fiber rearrangement is measured as the

linear expansion of the piston on a quartz dilatometry cell using TMA. The shrinkage of

prepregs was determined to depend on the curing temperature, pressure applied and

the fiber orientation. Chemical modification of an epoxy was done by mixing a

fluorinated aromatic amine (aniline) with a standard aliphatic amine as a curing agent

for a commercial Diglycidylether of Bisphenol-A (DGEBA) epoxy. The resulting cured

network was tested for wear resistance using tribological techniques. Of the six

anilines, 3-fluoroaniline and 4-fluoroaniline were determined to have lower wear than

the unmodified epoxy, while the others showed much higher wear rates.

ACKNOWLEDGEMENTS

There are many people I would like to thank for the inspiration, encouragement,

advice, assistance and support during the course of my graduate work at UNT. First

and foremost, I thank Professor Witold Brostow, my major advisor, for introducing me

to the field of polymers, steering me into challenging work, encouraging me to

constantly improve my work and my writing and giving me enough freedom to find

answers in my own unique way while providing enough guidance to keep me going in

the right direction. Professor Brostow also encouraged my international travels,

providing opportunities to combine laboratory research with cultural exploration through

his colleagues worldwide. I would like to thank Doctor Nandika Anne D’Souza for

friendship and assistance during my first few challenging years in the Laboratory of

Advanced Polymers and Optimized Materials (LAPOM) and of course, for the many

enlightening discussions we had about everything. I owe a special thank you to Doctor

Bhaskar Gopalanarayanan for encouraging me to always make sure my work is the best

it can possibly be and never settle for less no matter how much work it takes. I also

want to thank Bhaskar for all of our enlightening discussions outside the lab and for our

great coffee breaks after long hours in the lab. I owe great thanks to Doctor Kevin

Menard for open access to all of his lab equipment and all the support I needed for

Perkin Elmer, but more importantly for his technical assistance and encouragement.

Kevin encouraged me to develop unique applications for new techniques, resulting in

rewarding work and wonderful presentations and publications. Our discussions inside

and outside the lab were very important to me academically and personally. I would

ii

like to thank Artemio Palos for encouraging my involvement in the Society of Plastics

Engineers (SPE) and for being a supportive friend through the years. I would like to

thank Doctor Michael Kozak for encouraging me to take a practical view to my work and

always consider the industrial significance and for his support of my involvement in SPE.

Of course, I also thank him for serving on my defense committee. I would like to thank

Doctor Rick Reidy for the wonderful classes I had with him (a wonderful role model for

teaching) and for our inspiring discussions outside of class.

There have been several people outside of the Materials Science and Engineering

Department I would like to thank. In Physics, I was lucky to work with Doctor John

Prince, Instructor Kay Littler and Doctor Carlton Wendel, each of whom stimulated my

interest in teaching. I do want to thank Bell Helicopter Textron for providing funding

for a project which was a key part of this work.

The greatest appreciation must of course go to my family who supported and

encouraged me throughout my years in school. My parents always supported me in

whatever I did. My sister Robin and her husband Leonard were always supportive, but

more importantly were great listeners who always calmed my doubts and eased my

worries. I thank all of my family, each of whom contributed some part to the support

network I relied on during my studies.

iii

TABLE OF CONTENTS

Page

LIST OF TABLES .................................................................................................viii

LIST OF ILLUSTRATIONS ..................................................................................... ix

Chapter

1. EPOXIES: PROPERTIES, CHEMISTRY AND APPLICATIONS

1.1 Introduction..............................................................................1

1.2 History .....................................................................................2

1.3 Chemistry .................................................................................3

I.4 Chemical Modification – Fluorination...........................................6

1.5 Physical Properties.....................................................................6

1.6 Curing ......................................................................................7

1.7 Prepregs...................................................................................8

1.8 Shrinkage .................................................................................9

1.9 Specific Systems...................................................................... 10

1.10 Abbreviations and Acronyms.................................................... 12

1.11 References............................................................................. 12

2. EXPERIMENTAL TECHNIQUES

2.1 Thermal Analysis ..................................................................... 21

2.2 Heat of Reaction ..................................................................... 22

2.3 Molecular Weight, Segment Mobility and Crosslink Density.......... 29

2.3.1 Differential Scanning Calorimetry........................ 31

iv

2.3.2 Temperature-Modulated DSC ............................. 33

2.3.3 Step Scan DSC.................................................. 37

2.3.4 High Heating Rate DSC...................................... 39

2.3.5 Thermomechanical Analysis ............................... 43

2.3.6 Dynamic Mechanical Analysis ............................. 44

2.3.7 Thermally Stimulated Depolarization................... 48

2.4 Chemoviscosity ....................................................................... 50

2.5 Gelation.................................................................................. 54

2.6 Vitrification ............................................................................. 56

2.7 Thermal Stability ..................................................................... 59

2.8 Shrinkage ............................................................................... 61

2.9 Tribology ................................................................................ 64

2.10 Abbreviations and Acronyms................................................... 66

2.11 Symbols................................................................................ 67

2.12 References............................................................................. 69

3. KINETIC MODELS AND EQUATIONS

3.1 Introduction.......................................................................... 116

3.2 Kinetic Equations................................................................... 117

3.3 Kinetic Methods..................................................................... 122

3.3.1 Isothermal DSC ................................................... 122

3.3.2 Single Scan DSC .................................................. 123

3.3.3 Multiple Scan DSC................................................ 124

v

3.3.4 Time-Temperature Superposition .......................... 128

3.4 Physical Models ..................................................................... 130

3.4.1 Glass Transition Temperature Shift........................ 130

3.4.2 Viscoelastic Relaxation Time Shift.......................... 132

3.4.3 Gelation .............................................................. 134

3.4.4 Chemoviscosity.................................................... 134

3.5 Decomposition Kinetics .......................................................... 137

3.6 TTT and CHT Diagrams.......................................................... 139

3.7 Abbreviations and Acronyms .................................................. 142

3.8 Symbols ............................................................................... 142

3.9 References............................................................................ 144

4. EXPERIMENTAL CONDITIONS................................................................ 153

5. RESULTS

5.1 Heat of Reaction ................................................................... 158

5.2 Dynamic Differential Scanning Calorimetry............................... 162

5.3 Glass Transition Shift ............................................................. 166

5.4 Viscosity ............................................................................... 170

5.5 Thermal Stability ................................................................... 173

5.6 Comparison of Kinetic Results................................................. 174

5.7 Transformations .................................................................... 175

5.7.1 Gelation................................................................. 175

5.7.2 Vitrification ............................................................ 175

vi

5.7.3 TTT diagram.......................................................... 179

5.7.4 CHT diagram.......................................................... 181

5.8 Shrinkage ............................................................................. 182

5.9 Tribology .............................................................................. 185

5.10 Abbreviations and Acronyms................................................. 192

5.11 Symbols.............................................................................. 192

5.12 References........................................................................... 193

6. CONCLUSIONS

6.1 Summary............................................................................... 194

6.2 Recommendations .................................................................. 198

6.3 Suggestions for Future Work ................................................... 199

REFERENCES ................................................................................................. 201

vii

LIST OF TABLES

Table Page

5.1 Results of calculations of activation energy and preexpo. factors ................ 174

viii

LIST OF ILLUSTRATIONS

Figure Page

1.1 Epoxide functional group .............................................................................3

1.2 Diglycidylether of Bisphenol A ......................................................................4

1.3 Common amine curing agents......................................................................5

1.4 Mechanism of primary amine cure of epoxy ..................................................5

1.5 Chemical structure of TGDDM and DDS........................................................ 11

1.6 Chemical structure of the fluorinated amines in this work .............................. 12

2.1 Schematic of heat flux DSC........................................................................ 23

2.2 Schematic of power compensation DSC ...................................................... 23

2.3 Isothermal DSC heat flow chronogram........................................................ 25

2.4 Total heat of reaction DSC scan ................................................................. 25

2.5 DSC isotherm series .................................................................................. 26

2.6 DSC residual heat chronogram................................................................... 27

ix

2.7 DSC residual heat series ............................................................................ 27

2.8 DSC single rate scan ................................................................................. 28

2.9 DSC multiple rate scans............................................................................. 29

2.10 Glass transition temperature shift shown by DSC ......................................... 30

2.11 DSC scan with both glass transition and curing exotherm............................. 32

2.12 Sine wave temperature modulations........................................................... 34

2.13 Square wave temperature modulations....................................................... 34

2.14 Step Scan DSC program and heat flow........................................................ 37

2.15 Step Scan DSC heat flow and separated signals ........................................... 38

2.16 High heating rate DSC Tg series at different rates ........................................ 40

2.17 High heating rate DSC fast scan to shift cure ............................................... 40

2.18 High heating rate DSC very fast scan to eliminate cure................................. 41

2.19 High heating rate DSC heating program and signals ..................................... 42

2.20 High heating rate DSC Tg series at different times ....................................... 42

2.21 Glass transition by TMA ............................................................................. 43

x

2.22 Signal and response in DMA....................................................................... 44

2.23 DMA three point bending thermogram........................................................ 46

2.24 DMA flexural frequency scan ...................................................................... 47

2.25 Plot of frequency vs. temperature of peak tangent delta............................... 47

2.26 TSD temperature program......................................................................... 49

2.27 TSD plot of discharge current with temperature........................................... 50

2.28 Frequency dependence of viscosity measurements ...................................... 52

2.29 Viscosity change series from DMA three point bending................................. 53

2.30 Gelation peak in DMA three point bending isotherm..................................... 56

2.31 Vitrification in TMDSC isotherms................................................................. 57

2.32 Vitrification in DMA parallel plate isotherm .................................................. 58

2.33 Vitrification in DMA three point bending isotherm ........................................ 59

2.34 Series of TGA degradation scans ................................................................ 60

2.35 Dilatometer cell ........................................................................................ 63

2.36 TMA signals in dilatometry......................................................................... 65

xi

3.1 TTT diagram .......................................................................................... 140

3.2 CHT diagram .......................................................................................... 141

5.1 Series of DSC heat flow isotherms ............................................................ 159

5.2 Calculated conversion vs. time from DSC isotherms ................................... 159

5.3 Calculated conversion vs. temperature from DSC isotherms........................ 160

5.4 Calculated value of k as a function of temperature from DSC isos ............... 160

5.5 Calculated value of ln k vs. inverse temperature from DSC isos................... 161

5.6 Calculated value of ln k vs. ln conversion from DSC isotherms .................... 161

5.7 Calculated conversion as a function of time and temp. from DSC ................ 162

5.8 DSC single scan heat flow........................................................................ 163

5.9 Calculated conversion vs. time from DSC single scan ................................. 163

5.10 Calculated conversion vs. temperature from DSC single scan...................... 164

5.11 Calculated temperature dependent function k from DSC single scan............ 164

5.12 Calculated conversion as a function of time and temp. from DSC ................ 165

5.13 DSC multiple rate scan ............................................................................ 165

xii

5.14 Curve fit of DSC multiple rate data at different scanning rates .................... 166

5.15 Glass transition temperature shift in time from DSC scans .......................... 167

5.16 Glass transition temp. shift vs. logarithmic time from DSC scans ................. 167

5.17 Curve fit of glass transition temperature shift data..................................... 168

5.18 Series of Tg’s at different cure times by high heating rate DSC ................... 169

5.19 Viscosity change in time from isothermal DMA three point bending ............. 170

5.20 Area of viscosity curves used to determine shift factor ............................... 170

5.21 Curve fit of viscosity shift factor data........................................................ 171

5.22 Viscosity change during curing from isothermal DMA parallel plate.............. 172

5.23 Curve fit of time to viscosity minima as a function of curing temp. .............. 172

5.24 Series of TGA degradation scans .............................................................. 173

5.25 Gelation from DMA parallel plate isotherm ................................................ 176

5.26 Gelation from both parallel plate and three point bending DMA isos ............ 177

5.27 Vitrification by TMDSC isotherms.............................................................. 177

5.28 Vitrification by DMA three-point bending ................................................... 178

xiii

5.29 Vitrification by DMA three-point bending and parallel plate ......................... 178

5.30 TTT diagram for TGDDM/DDS.................................................................. 180

5.31 CHT diagram for TGDDM/DDS ................................................................. 181

5.32 Dilatometry – void and fiber movement .................................................... 183

5.33 Dilatometry – chemical shrinkage............................................................. 184

5.34 Tribology – wear measurement................................................................ 185

5.35 DMA frequency scan of unmodified epoxy................................................. 187

5.36 Activation energy plot from frequency scan............................................... 187

5.37 DMA frequency scan of 2-fluoroaniline-cured epoxy ................................... 188

5.38 Activation energy plot from frequency scan............................................... 188

5.39 DMA frequency scan of 3-fluoroaniline-cured epoxy ................................... 189

5.40 Activation energy from frequency scan ..................................................... 189

5.41 DMA frequency scan of 3,5 difluoroaniline-cured epoxy.............................. 190

5.42 Activation energy from frequency scan ..................................................... 190

xiv

CHAPTER I

EPOXIES : PROPERTIES, CHEMISTRY AND APPLICATIONS

I.1 Introduction

Epoxy resins represent an important class of polymers primarily due to their

versatility. High degree of crosslinking and the nature of the interchain bonds give

cured epoxies many desirable characteristics. These characteristics include excellent

adhesion to many substrates, high strength (tensile, compressive and flexural),

chemical resistance, fatigue resistance, corrosion resistance and electrical resistance.1

In addition, processing is simplified by the low shrinkage and lack of volatile by-

products. Properties of the uncured epoxy resins, such as viscosity, which are

important in processing,2 as well as final properties of cured epoxies such as mechanical

strength or electrical resistance can be optimized by appropriate selection of the epoxy

monomer and the curing agent or catalyst.3,4 Because of the ease of application5 and

desirable properties, epoxies are widely used for coatings,6,7 corrosion protectants,8

electronic encapsulants,9 fiber optic sheathing,10 flooring and adhesives. Given so many

everyday uses, every hardware store carries a wide selection of epoxy adhesives and

coatings.

The properties which result in successful adhesives and coatings also made

epoxies the obvious choice for matrices11 in fiber-reinforced composites.12 Man-made

fiber-reinforced composites predate written history, being seen in the earliest straw-

filled mud huts.13 Even glass fibers, which seem to be a modern technological

achievement, date back 3,000 years to the Phoenicians.14 Commercialization and

1

exploitation of composites began in the Nineteenth Century15 and has steadily grown16

in both scale and range. Today glass fiber-reinforced epoxies are commonly the major

components in boats,17 aircraft,18 automobiles,19 medical prostheses20 and sports

equipment. Indeed, many developments were only possible using this material,

including the Chevrolet Corvette21 and the Bell/Textron V-2222 tiltrotor aircraft. Epoxies

and fiber-reinforced epoxy composites have influenced sports equipment,23 especially

for common leisure sports such as tennis,24 golf and water sports,25 but perhaps more

importantly, in high visibility sports, including Olympic cycling.26

The market for epoxy resins has grown as new epoxies are developed and new

applications are found. The worldwide consumption of epoxy resins in 1991 was over

one half million tons, with the United States taking about one third.27 In 1998 the

United States consumed 320,000 tons of epoxy resins, representing an overall annual

increase of 3 % over the past 10 years.28

I.2 History

Epoxy compounds were first synthesized as early as 1891; however,

commercialization did not come about for the next 50 years.3 Two independent

researchers, developing separate applications, synthesized the first commercial epoxy

resins. Pierre Castan of de Trey Frères in Switzerland, while developing dental

restoration materials, discovered the reaction of diglycidylether of bisphenol-A (DGEBA)

with pthalic anhydride. The patents were assigned to Ciba AG of Basel, Switzerland

(now Ciba-Geigy) in 1942.29 At the same time, Sylvan Greenlee at DeVoe and Raynolds

(later Celanese Chemical Company, and subsequently Hoechst-Celanese) in America,

2

while developing surface coatings, discovered another DGEBA resin, which differed only

in molecular weight. Greenlee’s first of many patents was granted in 1948.30 These

DGEBA resins and subsequent derivatives have, and continue to be, the largest product

in the epoxy market, primarily in the surface coatings industry for which it was

developed. The characteristics which Greenlee and Castan sought and found in DGEBA,

including adhesion, hardness, inertness and thermal resistance, are responsible for its

popularity.

Many other monomers and polymers have been subsequently epoxidized31 to

increase the desirable properties of DGEBA and to develop special properties such as

high electrical resistance and thermal stability.32

I.3 Chemistry

Epoxies are characterized by the presence of one or more epoxide functional

groups (shown in Figure 1.1) on or in the polymer chain. The epoxide group is planar,

with a three-membered ring composed of one oxygen and two carbon atoms.33 Due to

the high ring strain, similar to that in cyclopropane, the group is very reactive.34

C CH2

O

HR1

Figure 1.1: The epoxide functional group, where R1

represents the functionalized molecule.

Although DGEBA (Figure 1.2) and its derivative resins are still the most common

epoxies, especially in the field of coatings, they had limited applications in the structural

composites field due to their limited strength and relatively low thermal degradation

3

temperature. The demands of the structural composites field spurred development of

high performance epoxies.35 These requirements were met by increasing the

functionality (number of epoxide groups per molecule), modifying curing agents, and

replacing the thermally weak aliphatic linkages in glycidyl groups with rigid bonds.36

OCH2OC

CH3

CH3OCH2

O CCH3

CH3

O CH2C

OH

CH2O n

Figure 1.2: Diglycidylether of Bisphenol-A (DGEBA).

The ring-opening polymerization and crosslinking in epoxy resins can be of two general

types, catalyzed homopolymerization or bridging reactions which incorporate a

coreactive crosslinking agent into the network. Homopolymerization, or reactions

between epoxy chains, involve elimination reactions on the oxygen atom of the

epoxide group using acid or base catalysts,37 often activated by radiation. The

incorporation, or bridging reaction, involves nucleophilic attack on one of the epoxide

carbons by an amine or an anhydride compound. A selection of common amine curing

agents are shown in Figure 1.3. Reviews of curing reactions are available in the

literature38,39 and terminology40 has been standardized by the International Union of

Pure and Applied Chemistry (IUPAC). An obvious and important difference in the result

of the two different curing methods is that in homopolymerization the network is only

composed of the cross-linked epoxy monomers, whereas in the bridging reaction the

network is composed of a copolymer of both epoxy monomers and a curing agent, as

shown in Figure 1.4. Therefore in a bridging reaction the network properties are a

4

a. c.

NH2 CH2

NH2n

NH2 CH2

NHn C

H2n

NH2n

NH2

SO

ONH2 NH2

d. b.

Figure 1.3: Common aliphatic (a,b) and aromatic (c,d) amines, including

Polymethylene diamine (a), a polyamine (b), aniline or phenylamine (c)

and 4,4’-diaminodiphenylsulfone or DDS (d)

R1 NH2O

R2+ R1 N CH2CHOH

R2

R1 N CH2CHOH

R2H

+O

R2 R1 NCH2CH

OH

R2

CH2CHOH

R2

a)

b)

c) R1 N CH2CHOH

R2H O

R2+R1 N CH2CH

OR2

HCH2CH

OH

R2

Figure 1.4: Mechanism of primary amine cure of an epoxy resin, with the epoxide

group under nucleophilic attack by a) a primary amine, b) a secondary amine

and c) a hydroxyl group generated from reactions a and b.

5

function of two components, which allows modifications to be incorporated in either

component. Thus, a rigid epoxy with high strength can be used with an impact

resistant hardener to yield a desirable network.41

In addition, in amine-cured epoxy reactions a side reaction between the products

and reactants occurs, as shown in Figure 1.4c. Epoxy monomers may be attacked by

the hydroxyl group of the product of the primary amine opened epoxy,42 if either the

secondary amine is less reactive than the hydroxyl group, or by the hydroxyl group of

the final product, in the case of epoxy rich systems or low functionality amines.43

I.4 Chemical Modification – Fluorination

Epoxies and curing agents have been chemically modified for a variety of special

purposes, with recent attention given to the addition of fluorine functional groups to

increase electrical resistance and dielectric constant as well as for improved tribological

properties, namely reduction of friction and wear. While significant work has been done

in fluorinating epoxy resins or epoxidizing fluoropolymers,44,45 the costs are typically

prohibitively high. Researchers are working to develop an economically viable epoxy

with the friction-reducing fluoro groups bonded into a wear-resistant epoxy network.

The novel approach I utilized for this work was to use a commercially available

fluorinated amine curing agent.

I.5 Physical Properties

The physical properties of uncured epoxy resins vary widely. As with any

polymer, the viscosity of the monomers or prepolymers depend on both the molecular

weight and the molecular structure. A simple example is DGEBA, already shown in

6

Figure 1.2. Higher linear molecular weight monomers, i.e. those with higher values of

n, exhibit higher viscosities.46 In addition, molecular structure and types of bonds will

greatly affect the viscosity of the resin.47 Since epoxies are almost always used with

catalysts, crosslinking agents, accelerators and various other additives, viscosity effects

like plasticization must be considered.48 Many highly crosslinked epoxies exhibit low

fracture toughness, so a dispersed phase49 of an elastic component, typically an

elastomer or a tough thermoplastic,50-52 can be introduced into the matrix.

I.6 Curing

Epoxy curing involves two phenomena, polymerization and crosslinking.

Although each phenomenon is complicated and the two are in competition during the

overall curing process, generalizations and simplified models can be made. During the

initial stage of curing, polymerization is favored53 because in the case of catalyzed

homopolymerization, terminal epoxides are the most reactive, and in the case of

coreactive agents, primary reactions are more reactive than secondary ones. Also, the

terminal epoxide reactivity already mentioned plays a role. In most cases the

polymerization is an addition reaction,54 and thus follows a rate equation for addition

polymerization described below in Chapter 3. The molecular weight of the growing

polymer increases until the molecular weight approaches infinity, so that all monomers

are connected by at least one bond and a network is formed.55 At this point, called the

gel point,56 the polymer possesses high molecular weight and few crosslinks, and thus

behaves much like a very high molecular weight thermoplastic.57 From the gel point,

crosslinking becomes the dominant phenomenon due to the lack of free monomers.

7

Crosslinking involves interchain bonding of intrachain reactive sites, either intrachain

epoxides or secondary sites on coreactive agents.58

Although crosslinking is a different phenomenon, the rate of chemical conversion

of the epoxide groups is unaffected in most epoxy systems.59 The crosslinking

reactions produce a growing network60 and reduce the mobility of the chain segments.

The growth of the network results in mechanical and thermal stabilization of the

structure, resulting in increasing modulus61 and glass transition and degradation

temperatures.62 At a certain high degree of crosslinking, the increasing molecular

weight of the structure exceeds the molecular weight which is thermodynamically stable

as a rubber, and the material transforms into a glass, a process called vitrification.63 In

a glassy state, the mobility of reactants is severely restricted, reducing the rate of the

reaction to a diffusion-controlled reaction, which is much slower.64 Further conversion

is still possible; however, the rate is much slower since the process relies on diffusion

rather than mobility to bring the reactants together. When the crosslinking reaction

exhausts all the reactive sites available, the resulting structure is hard (high modulus)

and insoluble due to a high degree of interchain bonding.

I.7 Prepregs

Since epoxy resins must be mixed with various curing agents, catalysts, modifiers

and additives, as well as any reinforcements, many epoxy suppliers provide premixed

molding compounds (MCs) and preimpregnated fibers (prepregs). MCs and prepregs

have many advantages to manufacturers since all of the careful mixing is done by and

ensured by the supplier in large batches.65 The manufacturer is thus only concerned

8

with the actual processing of the compound. MCs are very popular in high volume

industries like automotive and consumer products, whereas prepregs are very common

in hand and machine layup of high fiber content laminates66 in aerospace and specialty

markets.67 Prepregs are typically cured via a multiple step autoclave vacuum bag

process68,69 or compression molding, depending on the part geometry and application.

I.8 Shrinkage

Shrinkage is the change in volume during processing associated with both

molecular rearrangement due to curing and thermal contraction due to cooling from the

processing temperature to ambient conditions. Epoxies are favored due to their low

shrinkage of a few volume percent. However, in some processes, specifically closed

molding, this 4 or 5 percent change can affect a products properties and integrity. In

addition, when processing highly filled resins, the effect of fiber or particulate

movement can affect the volume changes. Typically, as with thermoplastics, excess

material is injected into the mold under high pressure to compensate for shrinkage.

However, determining how much excess material is necessary and how much pressure

is required is important for molders. The thermal contraction is relatively easy to

determine, since on cooling, the material should be in a solid state, either cured or

gelled. Thermal contraction is determined by measuring the volumetric change

associated with the temperature change and is expressed as the Bulk Modulus. The

changes due to chemical rearrangement during cure must be determined by dilatometry

measurements, where the resin and curing agent are placed in a closed mold with a

small piston, which measures the change in volume. The procedure has been done

9

with pistons of oil and of quartz, depending on the viscosity of the material being

measured. In the case of a highly filled prepreg, the rearrangement of the

reinforcement and the chemical shrinkage can be determined in a similar manner under

processing pressures using either mercury or quartz as the piston.70 The results of

these measurements are very important in applications where critical dimensional

tolerances are required, as well as situations where internal stresses on encapsulated

components and internal stresses in the epoxy itself are a concern.

I.9 Specific Systems

The two materials used in this study were a high temperature epoxy molding compound

and a commercial epoxy system. The high temperature molding compound is a

premixed compound of epoxy resin and amine curing agent, designated 8552 by its

manufacturer Hexcel. The material consists of the tetrafunctional epoxy tetraglycidyl

4,4-diaminodiphenyl methane (TGDDM) and the tetrafunctional amine curing agent

4,4’-diaminodiphenylsulfone (DDS), along with an ionic initiator/accelerator and a

thermoplastic modifier, shown in Figure 1.5.71,72 This material is common in the

aerospace industry73,74 and has been the subject of many studies;75 - 101 however a

comprehensive study of the material using different techniques is not available.

Several manufacturers produce similar prepregs with glass or carbon fiber

reinforcement.102 Commercial TGDDM/DDS prepregs are prepared with an epoxy-rich

stoichiometry.103 Samples were acquired in the form of both unreinforced premixed

resin and 66 weight % glass fiber-reinforced prepreg tapes.

10

TGDDM

CH2 NNCH2

CH2

CH2

CH2

CH

CH

CH

CH

CH2

CH2 CH2

CH2

O O

OO

SO

ONH2 NH2

DDS

Figure 1.5: Chemical structure of TGDDM epoxy and DDS amine curing agent

The other system consists of a DGEBA epoxy, as shown in Figure 1.2, which is

mixed with an aliphatic amine curing agent, as shown in Figure 1.3a. This system is

similar to many of the common commercial epoxy-based adhesives in which the epoxy

resin is mixed with an amine curing agent by volume. This system was characterized

after mixing the two components per the manufacturer’s recommendations, but was

also used in a fluorination modification experiment. Specific amounts of a fluorinated

amine curing agent were substituted for part of the aliphatic amine. The chemical

structures of the fluorinated amines used are provided in Figure 1.6. The fluorination

study was intended to find an economically feasible method of reducing the friction on

the cured epoxy surface. Most previous attempts have focused on synthetically

fluorinating the epoxy chain, which is costly and complicated on industrial scale.

11

Figure 1.6: Chemical structures of the eight fluorinated amines used

with the aliphatic amine to cure the DGEBA epoxy.

I.10 Abbreviations and Acronyms

DDS 4,4’-diaminodiphenylsulfone

DGEBA diglycidylether of bisphenol-A

IUPAC International Union of Pure and Applied Chemistry

MC molding compound

TGDDM tetraglycidyl 4,4-diaminodiphenyl methane

I.11 References

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8 R.A. Dickie, Applied Polymer Science, Eds. R. Tess and G. Poehlein, Chap. 32,


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Chem. & Eng. News, 77 (1999) 32.

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29 P. Caston, European Patents CH 211116 (1938), DRP 749512 (1938), GB 518057

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33 D. Peters, Chemistry of the Ether Linkage, Ed. S. Patai, Wiley, New York (1967).

34 J.A. Gannon, High Per ormance Polymers, Ed. R.B. Seymour and G.S. Kirshenbaum,

Elsevier, New York (1986).

35 R. Seymour and C. Carraher, Structure – Property Relationships in Polymers, Plenum,

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37 V. Percec, Applied Polymer Science, Eds. R. Tess and G. Poehlein, Chap. 5, American


38 R.S. Bauer, Applied Polymer Science, Eds. R. Tess and G. Poehlein, Chap. 39,


39 T. Kamon and H. Furukawa, Advances in Polymer Science, Vol. 80, Ed. K. Dusek,

Springer Verlag, Berlin (1986).

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41 W.F.A. Su, K.C. Chen and S.Y. Tseng, J. Appl. Polymer Sci., 78 (2000) 446.

15

42 S.C. Lin, B.J. Bulkin and E.M. Pearce, J. Polymer Sci., Chem., 17 (1979) 3121.

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44 J.R. Griffith and J.B. Romans, J. Fluorine Chem., 34 (1987) 361.

45 S. Matuszczak and W.J. Feast, J. Fluorine Chem., 102 (2000) 269.

46 A.T. DiBenedetto, The Structure and Properties of Materials, McGraw-Hill, New York

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48 F. Rodriguez, Principles of Polymer Systems, McGraw Hill, New York (1982).

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42 (2001) 7971.

50 P. Punchaipetch, Ph.D. Dissertation, University of North Texas (2000).

51 P. Punchaipetch, V. Ambrogi, M. Giamberini, W. Brostow, C. Carfagna and N.A.

D’Souza, Polymer, 43 (2002) 839.

52 J. Lopez, I. Lopez-Bueno, P. Nogueira, C. Ramirez, M.J. Abad, L. Barral and J. Cano,

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53 S. Zhu and A.E. Hamielec, Macromol., 25 (1992) 5457.

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55 R.B. Prime, Thermal Characterization of Polymeric Materials (Second Edition), Ed. E.

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16

56 J.K. Gillham, Developments in Polymer Characterization 3, Ed. J.V. Dawkins, Applied

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57 C.E. Carraher, Jr. and R.B. Seymour, Applied Polymer Science, Eds. R. Tess and G.

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59 G. Wisanrakkit and J.K. Gillham, Polymer Characterization, Eds. C. Craver and T.


60 R.F.T. Stepto, Cross-Linked Polymers, Eds. R.A. Dickie, S.S. Labana, R.S. Bauer,


61 D.E. Kranbuehl, M.S. Hoff, T.C. Hamilton, W.T. Clark and W.T. Freeman, Polymer

Characterization, Eds. C. Craver and T. Provder, Chap. 14, American Chemical Society,

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62 H.T. Lee and D.W. Levi, J. Appl. Polymer Sci., 13 (1969) 1703.

63 J.D. LeMay and F.N. Kelley, Advances in Polymer Science 78, Ed. K. Dušek, Springer

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64 J.K. Gillham and C.A. Glandt, Chemsitry and Properties of Crosslinked Polymers, Ed.

S.S. Labana, Academic Press, New York (1977).

65 H.R. Reffe, Handbook of Fiberglass and Advanced Plastics Composites, Ed. G. Lubin,


66 F. Elkink and J.H.M. Quaijtaal, Integration of Fundamental Polymer Science and

Technology, Vol. 3, Eds. P.J. Lemstra and L.A. Kleintjens, Elsevier, London (1989).

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68 J.H. Oh and D.G. Lee, J. Compos. Mater., 36 (2002) 19.

69 J.M. Kenny, A. Trivisano, M.E. Frigione and L. Nicolais, Thermoch. Acta, 199 (1992)

213.

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71 M. Opalicki, J.M. Kenny and L. Nicolais, J. Appl. Polymer Sci., 61 (1996) 1025.

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73 C. A. May, Applied Polymer Science, Eds. R. Tess and G. Poehlein, Chap. 24,


74 J.A. Harvey, Processing, Fabrica ion and Applications of Advanced Composites, Ed. K.

Upadhya, ASM International, Materials Park, Ohio (1993) 199.

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78 S.H. Dillman and J.C. Seferis, J. Macromol. Sci., 26 (1989) 227.

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80 J. Mijović and K.F. Lin, Adv. Chem., 206 (1984) 323.

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92 T. Jianmao, Int. SAMPE Symp., 39 (1994) 311.

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19

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20

CHAPTER II

EXPERIMENTAL TECHNIQUES

II.1 Thermal Analysis

In the most basic sense, thermal analysis is the study of the state or changes of

state of a material in terms of thermal energy. A qualitative understanding of changes

of properties of materials with temperature has existed since the first pottery and bricks

were fired and the first bread was baked, with evidence depicted graphically in

numerous carvings and drawings, including well preserved Egyptian excavations1

depicting a balance and fire. In 1789 Josiah Wedgewood of pottery fame studied the

effect of heat on the shrinkage of clays.2 However, quantitative thermal analysis

required measurable quantities. The first and most important of these being

thermometry which was introduced in 17th century Florence.3 With temperature,

properties like heat capacity could shed light onto the intrinsic properties of materials.

Differential thermal analysis was introduced in the late 1800’s by Le Chatelier.4 Nernst5

introduced the thermobalance in 1903, and other techniques, as well as improvements

in existing techniques followed quickly.6 Extensive reviews of the history of thermal

analysis are available in the literature.7-9

The International Confederation for Thermal Analysis and Calorimetry (ICTAC)

defined thermal analysis as “a group of techniques in which a property of the sample is

monitored against time or temperature while the temperature of the sample, in a

specified atmosphere, is programmed.”10 This definition was adopted by the

International Union of Pure and Applied Chemistry (IUPAC) and the American Society

21

for Testing and Materials (ASTM).11 Although thermal analysis of polymers is a

relatively young field, compared for instance to metallurgy and analytical chemistry, the

great variety and number of reviews of techniques,12-27 instrumentation,28-31

properties32-57 and terminology58-60 demonstrates the importance of the subject. It is

clear that thermal analysis of polymers is a field which is multidisciplinary, incorporating

chemistry, physics, biology, engineering and other diverse disciplines.61

II.2 Heat of Reaction

Due to the high potential energy of the ring-strained epoxide groups in the

uncured resin, there is a large Gibbs function difference associated with the ring-

opening reaction. Since the Gibbs function change (∆G) is expressed in the form of

both enthalpic (∆H) and entropic (∆S) changes, the reaction is called exergenic.62

Although structural changes will result in a significant entropy change, the enthalpy

change is the dominant product. The change in enthalpy results in the evolution of

thermal energy or heat, making this an exothermic reaction. Since the opening of the

epoxide rings have much higher energy (and enthalpy) differences than the other

reactions, the amount of heat evolved and the rate of evolution will correspond to the

number of epoxide groups reacting and the rate of the reaction.

Reactions which generate heat are studied by calorimetry. Many types of

calorimeters exist, although only a few are appropriate for polymerization reactions.

Early studies of epoxy polymerization used differential thermal analysis (DTA), which

monitors temperature differences between the sample and a reference, and adiabatic

calorimetry, which monitors the temperature of a thermally isolated system.63

22

However, these techniques have low sensitivities and many limitations.64 The current

standard technique for quantitative evaluation is the measurement of the change in

enthalpy using Differential Scanning Calorimetry (DSC), since the heat flow during a

constant pressure reaction is defined65 as the change in enthalpy of the system.66

Two types of DSCs are available, a heat-flux DSC (based on the Boersma67 DTA

design68) and a power-compensation DSC. The heat-flux DSC,69 shown in Figure 2.1,

measures the difference in temperature between a sample and reference heated at a

programmed rate in a common oven using thermocouples attached to the bottom of

the sample holders. The power-compensation DSC,70,71 shown in Figure 2.2, employs

separate heating elements and thermocouples for sample and reference, applying

separate currents to the heaters to maintain a null difference in the temperature.

Figure 2.1: Schematic of a heat-flux DSC.

2

Figure 2.2: Schematic of a power-compensation DSC.

3

Both types of DSC instruments generate plots of heat flow as a function of the

programmed temperature. However, due to the difference in measurement techniques,

the heat flow ordinate value is calculated differently. Since the heat-flux DSC measures

the temperature difference between the sample and reference cells, calculation of the

heat flow requires an accurate temperature and sample dependent thermal resistance

value of the system as a proportionality factor.72,73 The power-compensation DSC also

requires a thermal resistance value; however, that value represents the heating

elements, not the entire system, and is constant74 over a wide operating temperature

range.75-77 The power-compensation DSC maintains the programmed temperature

ramp in both sample and reference, ensuring greater temperature control in the

sample.78-80 This is important in temperature sensitive reactions, including thermoset

curing. The sensitivity and limits of detection,81,82 as well as the linearity of the

signals83,84 of both types of DSC have been evaluated. Schawe and Höhne have

thoroughly described the linearity,85 signal86 and influence of materials properties87,88 of

power-compensation DSC measurements. The influence of changes of heat capacity of

a sample during a measurement has been established89 and evaluation techniques90

have been proposed to account for it. To determine the extent of a curing reaction or

the degree of cure, α, the change in enthalpy is compared to the total change in

enthalpy of the complete reaction, as represented by Equation 2.1 and illustrated in

Figure 2.3. This technique is common in research.91-111

α = ∆H/∆Htotal (2.1)

24

Figure 2.3: An example of a DSC thermogram showing the portion of the total

reaction, as measured by the enthalpic exotherm, reacted at time t.

Figure 2.4: An example of a DSC thermogram showing the

total ∆H from a slow temperature scan.

25

Alternatively, the difference between the total and any residual enthalpy

changes can be compared to the total, where ∆H in Formula 2.1 would be replaced by

(∆Htotal -∆Hresid).112-114 Generally the total change in enthalpy is determined using a slow

temperature ramp from a low temperature to a temperature just below the onset of

thermal degradation, as shown in Figure 2.4. The reaction enthalpic changes are

measured during isothermal measurements, as shown in Figure 2.5. Or, if residual

enthalpies are used, then an isotherm is followed by a similar ramp as the total

enthalpy measurement, as shown in the chronogram in Figure 2.6 and the thermogram

in Figure 2.7. Although the value is reported as the degree of cure, it should be

understood that the actual degree of cure is not necessarily equal to this value since an

assumption has been made that the total enthalpy represents complete or 100 %

conversion.115-117

Figure 2.5: An example of a DSC thermogram, showing a series of

isothermal measurements at 120°C, 140°C and 160°C.

26

Figure 2.6: Temperature program and measured heat flow for a

residual enthalphy measurement using DSC.

Figure 2.7: A series of residual enthalphy measurements for different curing times. The reaction rate, dα/dt, is related to the heat flow, dH/dt, by the

27

relationship

dα = 1 dH (2.2) dt ∆Htotal dt .

The rate of the curing reaction can be determined from the isothermal data used to

determine the degree of cure. Since the enthalpy change is plotted as a function of

time, the rate of change in time, dH/dt will represent the rate of the reaction.118,119

Nonisothermal methods,120-122 utilizing a single temperature scan run to monitor

reaction enthalpic change,123-125 as in Figure 2.8, or using a series of scans with

different rates,126-137 as shown in Figure 2.9 are advantageous due to the shorter time

to run the experiments and avoidance of estimation of the lost area at the beginning of

the isotherms. However, nonisothermal experiments are generally less accurate than

isothermal ones.138,139

Figure 2.8: An example of a DSC thermogram of a ∆H scan (at 5 K/min) from

which the rate of the reaction can be calculated using a single scan model.

28

Figure 2.9: A Series of DSC thermograms at different scanning rates (5, 10

and 20 K/min), from which a time dependant rate can be calculated.

II.3 Molecular Weight, Segment Mobility and Crosslink Density

Epoxy curing involves an increase in both linear molecular weight and crosslink

density, both of which result in reduced chain segment mobility. Increasing the linear

molecular weight or crosslink density of a polymer chain increases the position of the

glass transition temperature, Tg, as shown in Figure 2.10. Many thermosetting polymer

systems exhibit a relationship between the Tg and the degree of chemical

conversion.140-158 Most epoxy-amine systems exhibit a linear relationship, which implies

that the change in molecular structure with conversion is independent of the cure

temperature.159-166 Such a Tg shift, in many circumstances, gives better resolution of

cure state than enthalpy changes,167 especially at high and low degrees of cure.

Descriptions of the shift as a function of chemical structure,168-172 as well as

29

extensive theoretical models based on either free volume173-180 or time-dependent

relaxation181-191 are abundant in the literature, including a review.192 Evidence for free

volume models comes primarily from the pressure dependence of Tg in both

Thermomechanical Analysis (TMA)193-199 and DSC200-208 measurements, whereas

relaxation effects can be seen in the frequency dependence of Dynamc Mechanical

Analysis (DMA) measurements,209-218 as well as the effect of scanning rate in most

thermal analysis techniques.219-227 The Tg can be measured by a variety of techniques,

each with certain advantages and disadvantages depending on the material and

conditions. Comparisons of techniques show that while sensitivity to transitions

vary,228-231 the value of the Tg is similar given appropriate conditions.232

Figure 2.10: A DSC thermogram showing a series of Tg measurements of

samples cured for different times at specific temperatures.

30

II.3.1 Differential Scanning Calorimetry

The most convenient, and generally most accurate, method for determining the

Tg of polymers is Differential Scanning Calorimetry (DSC).233,234 The Tg is taken as the

temperature at the inflection point (peak of derivative curve)235,236 of the baseline shift

in heat flow, or as the temperature at the half height shift in baseline heat flow. In

situations where the Tg is distorted or masked by other events, like curing exotherms or

enthalpic relaxations, the Tg may be determined by the onset, but results should be

noted as onset values to avoid confusion. For consistency in reporting, an ASTM

standard has been established.237

The shift in baseline heat flow associated with the glass transition is a result of

the difference in heat capacity between the rubber and the glass.238-240 Since this shift

is an effect of the heat capacity change,241 resolution of the glass transition can be

increased by calculating and plotting the constant pressure heat capacity, Cp.242 The Cp

curve is calculated by comparing the heat flow (or differential power supplied), a

baseline, and a reference material,243-246 usually sapphire, as described in an ASTM

standard.247 A power-compensation DSC has a long term energy calibration stability,

hence the sapphire measurement is unnecessary if the curve is available in the software

or has been run before, provided that the DSC has been properly calibrated using a

high purity heat of fusion standard such as indium248,249 or a liquid crystalline polymer

standard250,251 reference material. The Cp curve can be used to calculate the constant

volume heat capacity Cv; 252-254 however, the validity of the conversion is not absolute

and the benefit is not clear. Wunderlich has compiled a database of Cp values for many

31

different polymers from the literature and compared them with molecular structures.255

The versatility of DSC to measure both exotherms and Tgs is also a limitation,

because when measuring an uncured or a partially cured thermoset, a residual

exotherm follows the Tg being measured, sometimes even overlapping it as shown in

Figure 2.11.

A

and the

only be

Figure 2.11: An example of a DSC thermogram with the curing exotherm

occuring right after the Tg , distorting both measurements.

ccurate Tg calculations require stable baselines before and after the transition,

curing exotherm interferes with the upper baseline. In these cases, the Tg can

determined as the onset.

32

II.3.2 Temperature-Modulated DSC

An alternative to the measurement of Cp is Temperature-Modulated DSC

(TMDSC). TMDSC utilizes a modulated temperature ramp, much like dynamic

mechanical analysis uses a dynamic force, and dielectric relaxation analysis uses an

alternating current. TMDSC is a derivative of an earlier technique, Alternating Current

(AC) Calorimetry.256-260 AC Calorimetry utilizes an oscillating heating ramp,

accomplished by the use of an auxiliary pulsed heat source (usually a chopped laser)

over the linear programmed heating ramp, to measure the Cp during the single run

experiment.261 Analogous to Dynamic Mechanical Analysis (DMA) and Dielectric

Analysis (DEA),262 TMDSC mathematically deconvolutes the response into two types of

signals, an in-phase and an out-of-phase response to the modulations, as well as

producing an average heat flow, which is analogous to the DSC signal using a linear

heating ramp.263 There are two primary methods of performing TMDSC, sinusoidal and

square wave modulation.

The first method, introduced and patented by Reading264-268 and developed by

Reading269-273 and Wunderlich274,275 utilizes a sinusoidal modulation superimposed over

the traditional linear heating ramp or isotherm, shown in Figure 2.12. The other

method, introduced, patented276 and developed277,278 by Schawe, utilizes square wave

modulations, shown in Figure 2.13. The two methods can be described by a single

temperature function

T(t) = T0 + β0t + (4/π)Ta[ (sin(ω0t)/12) - (sin(3ω0t)/32) + (sin(5ω0t)/52) - ….] (2.3)

33

where T0 is the initial temperature, β0 is the underlying heating rate, Ta is the amplitude

of the temperature modulation and ω0 is the angular frequency.279 In the special case

of sinusoidal modulation, the first harmonic would dominate the series.

Figure 2.12: Sine wave temperature Figure 2.13: Square wave temperature

modulations (Reading). modulations (Schawe).

Although the modulations are related and can be described by a single

function (Equation 2.3), the methods of evaluation of the signal developed by Reading

and Schawe are quite different. Both methods use a Fourier transform to produce an

average heating rate (qav), an average heat flow (hav), an amplitude of heating rate

(Aq), an amplitude of heat flow (Ah) and a phase angle between the heating rate and

heat flow (ϕ).280 However, Reading and Schawe use these values in different ways to

calculate the values of the components.

Reading’s technique281 produces three values. The total heat flow (HT = hav/qav)

is usually expressed as the total heat capacity (CpT) representing the response to the

34

overall average heating ramp, which is similar to what would be observed in linear DSC

heat capacity measurements. The “reversing” component (Cprev = Ah/Aq) represents the

ratio of the amplitude of the heat flow to the amplitude of the heating rate. These two

signals are subtracted to yield the “non-reversing” component (Cpnrv = Cp

T - Cprev). The

reversing component represents thermally reversible events, such as Tgs and meltings,

whereas the non-reversing component will represent thermally irreversible events,

including relaxations, crystallizations and curing exotherms.

Schawe’s technique282-284 uses a linear response approach, which includes a

dependence on the phase lag between the signal and response. His approach also

begins with the total heat capacity (CpT = hav/qav) and includes a Cp value calculated as

the ratio of the heat flow amplitude to the heating rate amplitude, however his value is

called the complex heat capacity (Cp* = Ah/Aq). The reason for the difference is that

from this value, he proposes a separation of the complex heat capacity (Cp* ) into two

components, real and imaginary :

Cp* = Cp’ + i Cp” (2.4)

with Cp’ representing the real, in-phase component, termed storage heat capacity, and

Cp” representing the imaginary, out-of-phase component, termed loss heat capacity.

The two values are calculated using the phase angle, ϕ, between the signal and

response :

35

Cp’ = Cp*cosϕ (2.5)

Cp” = Cp*sinϕ (2.6)

Hutchinson285 has evaluated the various types of modulations based on sine and

square waves and the methods of evaluation and constructed a single parameter model

to explain and predict the signals generated in TMDSC. Other models have also been

proposed and evaluated,286-289 although the basis for the modulation signals and

evaluation, including the phase lag, is derived290,291 from electrical signal modulation292

in the electronics and telecommuncations field. The frequency dependence of the

measurement is a parameter which has drawn considerable attention.293-298 Corrections

to the phase angle to compensate for various sample and instrument effects have been

proposed.299-306

As in DMA and DEA measurements, the storage signal will include the elastic, or

in-phase response of the material, which in this case will be the molecular level

responses, including glass transitions and meltings. The loss signal represents viscous,

or out-of-phase events, which are the kinetic effects, such as stress relaxations,

crystallizations and curing. The total heat capacity is the non-separated average signal,

which is equivalent to the heat capacity signal produced by traditional DSC.

TMDSC has been used for separation of Tgs from crystallizations, 307-312 enthalpic

relaxations313-317 and curing exotherms.318-332 It also has the advantage of measuring

heat capacities in one scan,333-341 as opposed to the two or more scans required in

traditional DSC, giving insight into the thermodynamic properties of the polymer.342-348

36

TMDSC is also well-suited to measure thermal conductivity of polymers and

composites,349-352 which gives valuable insight into the molecular structures. It has also

been used to evaluate physical aging in both thermoplastics and thermosets353 as well

as materials354,355 in other industries. Phase separation can also be monitored during

the cure of a thermoset system.356-361

II.3.3 Step Scan DSC

Step Scan DSC362, 363 is a calorimetric technique involving applying a short

heating step followed by an isotherm, which can separate quick intrinsic transitions like

glass transitions from time dependent kinetic processes. A representation of a typical

Step Scan DSC heating program is shown in Figure 2.14. Similar to AC Calorimetry,

Step Scan separates events which occur during a quick change in temperature from

Figure 2.14: Step Scan DSC temperature program and resulting heat flow signal.

37

those which occur after the temperature change, during the isotherm.364 Events which

occur during the heating portions are plotted in the Thermodynamic Cp line, while those

occurring during the isotherms are plotted in the Iso K line, as shown in Figure 2.15.

For the thermodynamic events to be separated from the kinetic ones, the rate

and duration of the temperature jumps, as well as the length of the isotherms are

important – if the ramp is too slow or the jump to great, some kinetic events may occur

during the ramp. The parameters for the temperature step, heating rate and

isothermal time depend on the material and the events to be separated. Typically for

Figure 2.15: The heat flow generated by the Step Scan heating program is separated

into a Thermodynamic Cp signal including events occurring during the heating

and an Iso K signal for events which happen during the isotherm.

38

polymers, a temperature jump of 1 to 5 °C with a heating rate between 2 and 20

°C/min provides the time necessary for the thermodynamic molecular rearrangements,

while happening faster than the kinetic effects. Kinetic effects typically occur within

about 30 to 60 seconds of the temperature jump. Typically, a small temperature jump

of a few degrees over the course of 10 to 30 seconds, followed by a 30 to 60 second

isotherm allows separation of events in many polymers.365

II.3.4 High Heating Rate DSC

A recent method to separate thermodynamic events from kinetically controlled

ones is high heating rate DSC, commercialized by Perkin Elmer as Hyper DSC. The high

heating rate DSC technique exploits the time dependence of kinetic events to push

them to higher than usual temperatures. Intrinsic thermodynamic events are rate

independent, so the event will occur at the same temperature, regardless of what rate

is used, 366 as shown in Figure 2.16. Somewhat analogous to the temperature jump

method367 of measuring kinetic reaction rates, high heating rate DSC allows the

measurement of glass transitions so fast that the kinetic reaction doesn’t have time to

begin before the material is quenched, thus glass transitions of a reacting system can

be measured without the typical simultaneous reaction. This technique is only possible

due to recent advances in instrument design, which allow controlled heating and

cooling rates up to 500 °C/min. To separate an overlapping epoxy cure from the glass

transition, rates on the order of 100 °C/min are usually sufficient, as shown in Figure

2.17. However, to complete the Tg scan without affecting the cure state requires rates

of 200 to 500 °C/min, as shown in Figure 2.18.368

39

Figure 2.16: Verification that the Tg and onset are rate independent

for rates from 5 to 200 °C/min.

Figure 2.17: Six consecutive scans on one sample at 100 °C/min with

the curing exotherm shifted away from the Tg, but not eliminated.

40

Figure 2.18: Six consecutive scans on one sample at 200 °C/min with the curing

exotherm pushed beyond the range of the scans as shown by the constant Tg.

One very practical application to come from high heating rate DSC is the

measurement of Tg as a function of time with a single sample. Typically each time the

Tg of a thermoset is measured for a given time and temperature, a new sample must be

used. With high heating rate DSC, one sample can be cured for a certain amount of

time at a specified temperature, then the Tg can be determined at such a high rate that

the sample’s cure state is not affected, then the same sample is quenched, ramped to

the cure temperature for another certain amount of time and the process repeated until

the reaction is complete at that temperature, as shown in Figure 2.19. A series of Tg

values are produced for curing times at a specific temperature, as shown in Figure 2.20.

41

Figure 2.19: The heating program in high heating rate DSC which cures a sample for a

specific amount of time at a certain temperature, then scans for the Tg

without affecting the cure state, so the process can be repeated.

Figure 2.20: Series of Tg values generated by a single sample using high heating rate

DSC. Cure temperature is 140 °C and the times are given in minutes.

42

II.3.5 Thermomechanical Analysis

The Tg can also be measured accurately using thermomechanical analysis (TMA).

TMA is the measurement of changes in linear or volumetric dimension as a function of

temperature or time.369,370 The Tg appears as an abrupt increase in slope in the linear

thermal expansion curve, shown in Figure 2.21, with the Tg indicated as the calculated

onset of the change in slope, as described in an ASTM standard.371 In addition to the

sensitivity of the technique to the Tg,372 the linear or volumetric change in dimension

with temperature gives insight into molecular structure.373-375 The slope of the

dimensional change as a function of temperature is the thermal expansivity or the

ASTM376,377 defined “linear coefficient of thermal expansion” (LCTE).378

Figure 2.21: An example of a TMA thermogram showing the change in slope of

the expansion, or linear displacement with temperature, with the onset of

change in slope representing the Tg.

43

Modern TMA instruments employ a low voltage differential transducer (LVDT) to

measure dimensional changes against the probe tip, producing resolution of linear

changes in micro- to nanometer scale. A TMA instrument must be calibrated for both

height, using dimensionally precise quartz standards, and temperature from the melting

(collapse) of a high purity standard like indium, as described by ASTM 1363.379

II.3.6 Dynamic Mechanical Analysis

Epoxies undergo changes in mechanical behavior as a function of cure.380-388 In

addition to the shift in Tg, there are changes in the viscoelastic behavior389,390 due to

both polymerization391 and crosslinking.392,393 Dynamic Mechanical Analysis (DMA)

instruments394-397 allow the application of a dynamic force in addition to the static force

of TMA, just as TMDSC allows a modulated temperature signal over the linear

temperature ramp of DSC. As shown in Figure 2.22, the phase lag between the applied

dynamic force and the response yields a complex modulus, which can be

mathematically separated into storage or in-phase, elastic response and loss or out-of-

phase, viscous response, as shown in Equation 2.7.

Dynamic Mechanical Analysis

Applied Force Response

Phase Lag Figure 2.22: Signal – Response for DMA measurements

44

E* = E’ + i E” = σ* /ε*. (2.7)

tan δ = E”/E’ (2.8)

The Tg can be measured accurately using dynamic mechanical analysis (DMA),

which can in the case of highly filled398-403 or highly crosslinked polymers404-407 give

better resolution and more information than DSC,408-415 and better reproducibility416

than older techniques, such as Vicat softening417 and deflection418 temperature

standards.419 The Tg in DMA measurement is generally taken as the peak in tan δ.420-422

ASTM423-425 recommends the peak in the loss modulus.426,427 Other methods include the

inflection point or the half height value of the drop in storage modulus (M’), the onset

of the drop in storage modulus, the onset of increase in loss modulus and the onset of

the increase in tan δ. A DMA thermogram is shown in Figure 2.23 with storage and loss

moduli and tan δ shown. There is also a frequency dependence to the DMA signals, as

shown in Figure 2.24. This frequency dependence is due to the viscoelastic nature of

the polymer and can be used to determine the activation energy of the transition,

namely how much energy is required to make the transition. A plot of the tan δ values

as a function of frequency, from which the activation energy is calculated, is shown in

Figure 2.25.

DMA (and TMA) measure dimensional changes and force responses using a

variety of fixtures, each with specific applications and benefits.428 Applications include

tensile, compression or expansion (linear and volumetric), flexural and shear.429,430

Specialized techniques for shear measurements include torsional pendulum,431-435

torsional braid analysis (TBA)436 and torsional impregnated cloth analysis (TICA).437-439

45

A DMA instrument must be calibrated for temperature, height and force. The

temperature calibration is described by ASTM440 using the melting temperature of a

high purity standard. Height is done using a quartz height standard. Force motor

calibration is performed by balancing standard weights.

Figure 2.23: A DMA thermogram using 3 point bending fixtures,

showing all the signals used to calculate the Tg.

46

Temp Cel120.0100.080.060.040.0

E' Pa

1.0E+04

8.0E+08

tanD

500.00

400.00

300.00

200.00

100.00

0.00

E" Pa

1.0E+04

8.0E+08

Figure 2.24: A series of DMA scans through the glass transition

of a fluorinated epoxy at various frequencies.

t .

Figure 2.25: The frequencies plotted as a function of temperature of peak

angent delta, from which the activation energy of the transition is calculated

47

II.3.7 Thermally Stimulated Depolarization

Another method to measure the change in Tg and chain segment mobility during

the curing process is thermally stimulated currents (TSC).441 TSC is basically a very low

frequency (10-2 to 10-4 Hz) dielectric relaxation study.442-448 TSC can be performed in

either polarization (TSP)449-451 or depolarization (TSD)452-460 mode. TSC involves the

polarization of electrets,461-470 or polar chemical bonds within the polymer chain,

making it very sensitive, even in copolymers,471-484 highly crosslinked thermosets and

filled composites.485,486 The sensitivity of TSC, specifically TSD, to molecular

motion487-490 and chain segment mobility yields well resolved Tg measurements,491-504 in

many cases, better resolved than DSC.505-518 Also, TSC experiments are not affected by

mechanical effects like gelation as in DMA. TSC, especially TSD, measurements exhibit

a time dependence, which can be measured as the characteristic Debye519 relaxation

time, which is analogous to the DMA retardation or phase lag time.520-527 A series of

relaxation times528,529 can be used to calculate the compensation point,530-533 which is

the convergence of the frequency dependent relaxation times, much like extrapolation

to zero heating rate in DSC or zero shear in DMA. TSP measures the polarization or

absorption of charge, reflected in a change in the current supplied to maintain the

electric field, by the polymer as a function of time or temperature, whereas TSD studies

the current induced by depolarization or release of stored charge in a polarized sample.

TSD is more useful in curing studies than TSP, so emphasis is on TSD.534 Shifts in Tg as

a function of conversion are performed in a similar fashion as shifts by DSC; samples

are cured at a certain temperature for a certain time, then quenched and the Tg

48

determined during a controlled heating ramp, with Tg values plotted as a function of

curing conditions (time and temperature).535-551

In TSD a sample is quickly heated to a poling temperature where an electric field

of predetermined strength is applied through parallel plates for a specific time.

Alternatively, the sample can be polarized by corona552-556 or electron beam557-561

charging.562 For thermosets, the poling temperature will be at the curing temperature

and the poling time will be a part of the curing time. After poling, the sample is

quenched to a relatively low temperature maintaining the electric field. At the selected

low temperature, the electric field is discontinued and the circuit is shorted to dissipate

any residual static charges on the surface or in voids caused by the electric field. The

sample is heated from this low temperature to a temperature higher than the poling

temperature at a slow, controlled rate and any current discharged is measured using a

sensitive picoammeter (sensitive to 10-15 Amperes or 107 electrons per second), and

plotted against temperature. The TSD temperature program is depicted graphically in

Figure 2.26. A typical TSD current thermogram is shown in Figure 2.27.

Figure 2.26: Temperature program in TSD, with applied electric field shaded.

49

Figure 2.27: TSD plot of discharge current as a function of temperature.

II.4 Chemoviscosity

The conversion induced change in viscosity, known as chemoviscosity, can

be used to monitor conversion (analogous to Tg shift) and the change of physical

state.563-570 Since viscosity describes a material’s resistance to flow, it is defined as the

ratio of shear stress to shear strain,

η = __τ__ (2.9) (dγ/dt) .

where η is the viscosity, τ is the stress and dγ/dt is the rate of strain. Viscosity

50

measurements are performed routinely on liquids using a variety of methods, including

capillary, concentric cylinder, cone and plate and many other viscometers.571 These

techniques are well suited to measurements of liquids from low viscosity fluids, such as

water (10-3 Pascal seconds) to higher viscosity ones, such as syrup (102 Ps), and even

some polymer melts (102 to 107 Ps). However, measurment of very high viscosity

materials from heavy pitch (109 Ps) to window glass (1021 Ps) is beyond the range of

most shear measurements. These high viscosity materials can be measured using

DMA. However, DMA measures mechanical or Young’s modulus (E), rather than the

shear modulus required for viscosity computation. Young’s modulus (E) is related to

shear modulus (Gs) by either the Poisson ratio (ν)572 or the bulk modulus (KB),573 given

by

E = 2Gs(1 + ν) = 3KB (1 - 2ν) (2.10)

The Poisson ratio, also called the lateral strain contraction ratio, relates the change in

lateral strain to the longitudinal strain. DMA measurements record the complex

modulus, E*, which is the ratio of complex stress, σ*, to complex strain, ε*, and

deconvolute that signal into a storage (E’) and a loss (E”) signal and a phase

dependent tan δ:

E* = σ*/ε* = E’ + i E” (2.11)

tan δ = E”/E’ (2.12)

From the moduli and the frequency (ω) of the measurements, the complex viscosity,

51

η*, can be calculated, which can be separated into storage and loss components.

η* = η’ - iη” = E*/iω = [ (E’)2 + (E”)2 ]1/2 (2.13) ω η’ = E”/ω (2.14) η” = E’/ω (2.15) The frequency of the dynamic signal has a large effect on the response, as depicted in

Figure 2.28.

Figure 2.28: Two 3-point bending DMA thermograms taken at different frequencies (1

and 2 Hz), showing the response as a function of frequency.

A single frequency series of isothermal DMA measurements of complex viscosity

as a function of time, shown in Figure 2.29, exhibits the characteristic changes

happening during a curing cycle.574-576 The epoxy prepreg is heated quickly to the

52

isothermal

minimum v

that no sign

the time sc

be determin

effect of th

other isothe

calculations

molecular w

to the rise i

weight, and

Figure 2.29: A series of isothermal 3-point bending DMA plots

of the change in complex viscosity as a function of time.

temperature resulting in a temperature-dependent drop in viscosity. The

iscosity will generally be a function of the isothermal temperature, provided

ificant reaction has occurred, provided that the heating rate is faster than

ale of the reaction onset. Of course, the value of the minimum viscosity will

ed by the molecular structure of the components of the prepreg and the

e overall mixture.577 However, usually the relative viscosities (relative to

rms) are used, so that the absolute value is not important in kinetics

. After the minimum viscosity, the reaction will proceed, increasing the

eight and the relative viscosity.578,579 This increase in viscosity, analogous

n Tg used in previous models, is proportional to the increase in molecular

thus the kinetics of the reaction.580-588

53

II.5 Gelation

Gelation refers to the point during the curing reaction where the molecular

weight approaches the maximum, usually assumed to be infinite, meaning that all

monomers are connected to the network by at least one chemical bond. While gelation

is a microscopic effect, it produces macroscopic effects. Microscopic gelation refers to

the definition of the gelation phenomenon, i.e. all monomers connected by at least one

bond to the network. Since it occurs at a defined point in polymerization, it will occur at

a specific degree of conversion.

Microscopic gelation is difficult to measure since the measurable properties

would be solubility589 and molecular weight. However, the consequence of exceeding

the microscopic gel point, is macroscopic gelation, which is much easier to measure.

The macroscopic gel point is a mechanical property and can be identified by common

thermal analysis techniques,590 including in-situ testing. Beyond gelation, there is no

increase in molecular weight,591 only an increase in crosslink density and a decrease in

free chain segment length.592,593

Gelation does not significantly affect the chemical conversion or curing reaction,

so it does not appear in DSC measurements.594,595 However, it does have a large

influence on the mechanical properties of the polymer. Gelation affects the stiffness

(modulus), adhesion and general processability of thermosets and composite

prepregs,596 so it is important from an industrial processing standpoint.597 Gelation

appears in the complex modulus, tan δ and complex viscosity of DMA measurements;

however, as with many thermal events, there is no unequivocal definition at which point

54

the gelation occurs. Gillham,598-602 who first plotted gelation curves as part of overall

time-temperature-transformation (TTT) diagrams603 developed with Enns,604-606 defines

it as the a peak in the tan δ of a DMA isotherm, which was also adopted as an ASTM

standard.607 This definition is common in scientific literature.608-614 Others define it as

the peak in loss modulus.615 Some define it by the onset or inflection point of the

increase in the storage modulus, whereas others define it as the onset of the plateau of

the maximum of the storage modulus. A common method has been to use the

crossover point,616-620 which is where the storage and loss moduli cross, or are equal,

and the tan δ is equal to unity,621 however it has been shown to be inaccurate in many

cases622-624 and can only be used as a quantitative measure or as a reference

conversion value for one particular system. This discrepancy lies primarily in the

application for which the data is being used, i.e. someone concerned with laminate

adhesion would identify a different point than someone concerned with ensuring

dimensional stability, and different than a researcher interested in characterizing the

physical state of the material. The DMA isothermal plot in Figure 2.30, identifies the gel

point using Gillham’s terminology, i.e. the peak in tan δ.

As described earlier, DMA transitions exhibit a frequency dependance. However,

since gelation is an isoconversion event, it is frequency independent. The gel point is

defined as the point where the tan δ becomes frequency independant.625-628 However,

this method requires many measurements at different frequencies. The gel point can

be defined in terms of viscosity since it represents the maximum viscosity.629-631

55

Figure 2.30: A DMA isothermal 3 point bending plot showing tan δ,

from which gel point can be defined.

II.6 Vitrification

Vitrification is defined as the point at which the molecular weight or cross-link

density of the curing polymer exceeds that which is thermodynamically stable as a

rubber, and the material undergoes a transition from a rubber to a glass at which point

the reaction dramatically slows due to the reduced mobility of the reactants. The

vitrification point can be measured using DSC, TMDSC and DMA.

56

Although vitrification is a thermal transition from a rubber to a glass and does

appear in DSC measurements,632 the determination of the point and quantification of

the shift in baseline heat flow or Cp usually occurs around the end of the curing (since it

is a decrease in the reaction rate) and as such is usually masked by the curing reaction

exotherm. This is one of the clearest applications of TMDSC, since the curing exotherm

appears in the loss Cp and the vitrification appears in the storage Cp.633-641 A series of

isothermal TMDSC plots identifying the vitrification point are shown in Figure 2.31.642

DMA has been used extensively to investigate the vitrification point, and

continues to be the most common method. The first epoxy TTT diagram, proposed by

Gillham and Enns,643 was constructed primarily from torsional braid analysis (TBA),644 a

specialized torsional DMA measurement. Gillham defines the vitrification in TBA and

Figure 2.31: TMDSC isotherms showing vitrification as half height drop in storage Cp.

57

DMA measurements as the highest tan δ peak below the melt, which usually

corresponds to the maximum value of the storage modulus during an isothermal

experiment. Measurement of vitrification in isothermal DMA and TBA studies are

common.645-647 DMA isotherms showing vitrification points from parallel plate and 3-

point bending modes are shown in Figures 2.32 and 2.33. Vitrification generally occurs

when the increasing Tg equals the cure temperature.648 Although the reaction

dramatically slows, it is still significant until the Tg exceeds the cure temperature by 20

to 40 °C.649,650

Figure 2.32: A parallel plate DMA isotherm (160 °C), with vitrification

defined by the second peak in tangent delta in time.

58

Figure 2.33: A 3-point bending DMA isotherm (160 °C), with vitrification

defined by the second peak in tan δ in time.

II.7 Thermal Stability

Thermogravimetric Analysis (TGA) is the measurement of weight loss as a

function of temperature or time. A TGA instrument consists of a sensitive (typically

+0.1 µg) microbalance monitoring the weight of a sample enclosed in a programmable

oven. Many reviews of TGA instrumentation are available in the literature.651-654 TGA is

used extensively to study decomposition,655 especially of multicomponent systems,

including polymer blends, polymers with additives and reinforced and filled polymer

composites.656 The offgassing of absorbed moisture657 or residual solvent658 can

indicate the viscosity and gas permitivity of a sample in an indirect manner. Thermal

stability,659 or resistance to thermal degradation, is related to the degree of cure, since

the bond energies of aliphatic linkages tend to be higher than those of unsatured

structures.660,661 This relationship can be used to relate the kinetics of thermal

59

decomposition to the curing reaction.662-670 TGA can be used to study the kinetics of

either decomposition671-675 or chemical reactions involving the release of volatile by-

products, i.e. condensation reactions.676 Kinetics can be evaluated using isoconversion

data plots, activation energy calculated from the slope of initial reaction,677 varied

heating rate678,679 analysis or a “model-free” method680,681 and comparisons of

techniques have been evaluated.682,683 A modulated TGA technique exists and some

separation of weight losses have been described;684 however, since most weight losses

are non-revesible events, only weight losses with different time dependancies may be

separated. TGA experiments can be performed in either oxidizing (O2 or air) or non-

oxidizing (N2 or Ar) environments, depending on the reaction or decomposition being

examined. A series of TGA decomposition thermograms are shown in Figure 2.34.

Figure 2.34: A series of TGA decomposition thermograms at different scanning rates.

60

TGA instruments must be calibrated for both temperature and weight. Weight

calbrations are performed with standards which have been weighed to the desired

accuracy (usually + 0.1 µg) and will not react with moisture or oxygen in the air, as

such platinum is a common standard. Temperature can be calibrated by two methods –

fusable link or magnetic Curie temperature. The fusable link technique uses a small

weight attached to the balance by a link made of a high purity standard which will

result in a sudden weight loss at the melting point of the standard.685,686 The magnetic

Curie temperature method uses the well known temperture-dependant magnetic

properties of some metals and alloys. These materials exhibit a change in magnetism

at a specific temperature, called the Curie point.687 The calibration is performed by

placing a magnet above or below the standard in the TGA sample pan, where it will

display an exceptionally high or low weight due to the magnetic field, until the

temperature is raised to the Curie temperature.688 Materials and procedures have been

recommended by the National Institute of Standards and Technology (NIST).689

II.8 Shrinkage

Shrinkage during processing of epoxies is due to the chemical rearrangement of

the molecular components, the rearrangement of any fibers or fillers in reinforced

materials, and the thermal contraction in epoxies cured above ambient temperatures.

The thermal contraction is the easiest component to measure, since the dimensional

change in the solid state will correspond to the Bulk Modulus times the difference in

temperature between processing and ambient conditions. The shrinkage due to

chemical rearrangement during the cure is also straightforward, except when pressure

61

is applied. Since the most important measurements are for injection and compression

molders, pressure usually is a very important factor. The rearrangement of fibers and

fillers depend on many factors including the nature of the reinforcement, temperature

and viscosity of resin and the cure state of the matrix, as well as what pressure is

applied. Measurement of volume changes is called dilatometry. Dilatometry allows the

measurement of volumetric changes associated with thermal contraction and expansion

in amorphous690, 691 and semicrystalline692 thermoplastics, rubbers,693-695 epoxies696 and

even inorganic crystals,697-699 as well as a means to describe bulk, aging700 and

composite701-703 and pressure704 effects on phase transitions.

Thermal shrinkage due to the difference in temperature between processing and

ambient conditions depends solely on the Bulk Modulus705-707 of the material, which is

simplified due to the fact that the product will be in the solid state and it usually does

not undergo a phase change during the cooling process. For isotropic materials, the

Bulk Modulus can be estimated from the Linear Coefficient of Thermal Expansion (LCTE)

determined from linear TMA measurements. However, the preferred method is to

confine the sample in a closed cell with a confining fluid to measure the dimensional

change of the fluid. Unlike the linear TMA measurements, the sample can be any shape

and homogeneity and isotropism is not required. The confining fluid which surrounds

the sample may be any inert liquid which does not undergo a phase change over the

temperature interval, including silicone oils,708, 709 mercury710-712 and even powdered

alumina. The closed cell can be of any material, but low expansivity materials like

quartz or invar are preferred. Obviously, the thermal volume change due to the cell

62

and the fluid must be subtracted from the results. Typically minimal pressure is used,

since during the cooling stage after a part is ejected from the mold, the part is not

under pressure. A sample dilatometry cell is shown in Figure 2.35.

Figure 2.35: A quartz dilatometry cell using alumina powder as the confining

fluid which measures volumetric changes via linear measurement.

During the curing reaction, there will be a small amount of shrinkage due to the

chemical rearrangement of the molecules themselves. This is typically between a

fraction of one and a few volume percent. This measurement is done in a dilatometer

like the one used for thermal shrinkage for nonpressured processing like casting or

potting. However, in many applications like injection and compression molding,

pressure is an important factor. Measurements should be made under similar pressures

63

as those used in the processing, since pressure will affect713-715 the molecular

rearrangement. For this reason, the dilatometer must employ a piston, the cell must

maintain structural integrity at that pressure, and the fluid must not undergo any

pressure-induced changes.

In processing fiber-reinforced compression molded prepregs, fiber wound

injection molded epoxy or highly filled parts, the movement of the reinforcement under

pressure can change the volume of the parts. The shape and orientation of the

reinforcement, as well as the nature of the material (glass or carbon), will affect this

change, but the temperature, viscosity and degree of cure of the matrix and the

pressure applied will have a large influence on how much the reinforcement can move.

This measurement must be done in situ, in that processing conditions must be

simulated in the instrument. The dilatometer must be brought to the processing

temperature and pressure applied as quickly as possible, since curing will be occurring

simultaneously and will drastically affect any movement of the reinforcement, as shown

in Figure 2.36.716

II.9 Tribology

Tribology, the study of frictional properties, is typically studied using materials in

contact moved in a shear direction. Obviously, static friction would be force without

motion and dynamic friction would be force producing motion. Tribological instruments

typically consist of a monitored surface in the form of a skid or plate in contact with a

stationary surface or object. Depending on the application, a skid in contact with a

surface or a pin in contact with a movable disk may be used. A skid of the same or

64

Figure 2.36: The TMA measurement of a dilatometry cell showing both void elimination

and fiber rearrangement and shrinkage due to curing.

65

different material as the stationary surface may be pulled, and either the force

necessary to produce initial movement or the force necessary to maintain motion is

recorded. A pin on disk study typically uses a disk of the investigated material subject

to rotational force while in contact with a pin of a certain geometry and material, which

yields data on both friction and also wear or abrasion. Both skid and plate717 and pin on

disk are common in tribological studies.

Wear, another tribological property, is measured by depth of penetration caused

by abrasion of a material by a standard material. One system718 uses a diamond

indenter to measure the scratch depth as a function of force applied.

II.10 Abbreviations and Acronyms

AC Alternating Current

ASTM American Society for Testing and Materials

CHT Continuous Heating Transformation

DEA Dielectric (Relaxation) Analysis

DMA Dynamic Mechanical Analysis

DSC Differential Scanning Calorimetry

DTA Differential Thermal Analysis

ICTAC International Confederation for Thermal Analysis and Calorimetry

IUPAC International Union of Pure and Applied Chemistry

LCTE Linear Coefficient of Thermal Expansion

LVDT Low Voltage Differential Transducer

NIST National Institute of Standards and Technology

66

TBA Torsional Braid Analysis

TGA Thermogravimetric Analysis

TICA Torsional Impregnated Cloth Analysis

TMA Thermomechanical Analysis

TMDSC Temperature-Modulated Differential Scanning Calorimetry

TSC Thermally Stimulated Currents

TSD Thermally Stimulated Depolarization

TSP Thermally Stimulated Polarization

TTT Time-Temperature-Transformation

VCTE Volumetric Coefficient of Thermal Expansion

II.11 Symbols

A Amplitude

Cp Specific Heat Capacity at Constant Pressure

Cp * Complex Specific Heat Capacity at Constant Pressure

Cp ‘ Storage Specific Heat Capacity at Constant Pressure (Elastic Component)

Cp “ Loss Specific Heat Capacity at Constant Pressure (Viscous Component)

Cv Specific Heat Capacity at Constant Volume

E Young’s (Mechanical) Modulus

E* Complex Young’s Modulus

E’ Storage Young’s Modulus (Elastic Component)

E” Loss Young’s Modulus (Viscous Component)

g gram

67

G Gibb’s Function

Gs Shear Modulus

H Enthalpy

dH/dt Rate of Change of Enthalpy in Time

Hz Hertz (cycles per second)

Ks Bulk Modulus

P Pascal (pressure unit)

q Heat Quantity

s Second (time unit)

S Entropy

T Temperature

Tg Glass Transition Temperature

α Degree of Conversion

δ phase angle (usually given as tan δ)

ε Mechanical Strain

γ Shear Strain

η Viscosity

η* Complex Viscosity

η’ Storage Viscosity (Elastic Component)

η” Loss Viscosity (Viscous Component)

ν Poisson’s Ratio

ϕ Phase Angle

68

σ Mechanical Stress

τ Shear Stress

ω Angular Frequency

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115

CHAPTER III

KINETIC MODELS AND EQUATIONS

III.1 Introduction

Chemical kinetics is the description of conversion of reactants to products. In

the case of cure kinetics of an epoxy+amine system, the rate of conversion will be

described by the consumption of epoxide and amine functional groups and the

production of aliphatic bonds, as described in Chapter 1. The traditional chemical

method for kinetic rate determination is mechanistic - the concentrations of products or

reactants are monitored throughout the reaction and the rates of change in

concentrations are fitted to an equation. Once the mechanism is determined and

modeled, then the reaction can be described by reactant or product concentrations in

time as a function of a temperature-dependant rate constant.1

However, many curing reactions are quite complex, involving multiple competing

reactions with several kinetic equations superimposed at different degrees during the

overall reaction, producing very complicated models.2-5 In addition, in many instances

the exact chemistry or concentrations of reactants may not be known, especially in

industrial applications where premixed compounds or prepreg composites are supplied

by an outside source. For these situations, phenomenological models are attractive and

have demonstrated value and validity.6-8

Phenomenological models use properties which are related to the reaction, for

example the change in viscosity or shift in glass transition temperature of a growing

polymer. These models describe the degree of conversion or per cent of cure from

116

uncured to fully cured as a function of time and temperature. Phenomenological

models are advantageous because they do not require knowledge of the reaction

mechanism, only the changes in properties.

Due to the complexity of the 4,4’-diaminodiphenylsulfone (DDS) cured

tetraglycidyl 4,4-diaminodiphenyl methane (TGDDM) system and the application of

curing commercial prepregs in this work, emphasis is on phenomenological modeling,

with references to mechanistic models where applicable.

III.2 Kinetic Equations

As any chemical reaction, the curing reaction will be described by a rate

equation, which will relate the rate of the reaction to the rate constant and the

consumption of reactants or production of products. In the case of thermoset curing, a

generalized rate function utilizing the degree of cure, α, which is the disappearance of

epoxide functional groups or appearance of chemical bonds, with (1 - α) representing

the epoxide group concentration.

dα/dt = k (1 - α)n (3.1)

This equation describes an nth order equation, so that the reaction rate is

dependant only on the concentration of epoxide (and curing agent). However, many

thermosetting materials are autocatalytic, so that the product of the reaction serves as

an additional catalyst in the reaction, as in the catalyzation of the epoxy+amine system

by generated hydroxyl groups.

117

Kinetic modeling of autocatalytic reactions requires an additional term to account

for this effect, namely

dα/dt = k αm (1 - α)n (3.2)

where αm represents the catalytic effect of the products of the reaction with an order of

m. It is also apparent, that an nth order reaction is a special case of the autocatalytic

reaction where m = 0.

Most epoxies exhibit either nth order or autocatalytic curing reactions, although it

is not always apparent which type an epoxy will follow. However, the two types are

readily differentiated by experimental data. As can be easily predicted from Equation

3.1, an nth order reaction will exhibit its maximum rate at the beginning of the reaction,

whereas the autocatalytic reaction, predicted from Equation 3.2, will exhibit its

maximum rate at some later time during the reaction, typically 20 to 40 % of the

reaction.9 The order is generally determined by plotting the degree of conversion as a

function of time and fitting the curve. This is usually accomplished using a log-log plot

and fitting using the Least Squares10 method. In addition to the time dependence of

the rate of conversion, the rate constant, k, is temperature dependent, usually assumed

to follow an Arrhenius relation of the form :

k = Ae-Ea/RT (3.3)

118

where k is the reaction rate constant, A is the pre-exponential function, and Ea is the

activation energy. Thus, Equations 3.1 and 3.2 can be written as

dα/dt = (Ae-Ea/RT ) (1 - α)n (3.4)

dα/dt = (Ae-Ea/RT )αm (1 - α)n (3.5)

with the incorporation of the Arrhenius temperature dependence. The initial rate of an

autocatalytic reaction is not necessarily zero since the reaction can proceed via

alternative paths, especially in the presence of impurities like water and catalyzing ions.

Taking this into account, the autocatalytic equation is given as

dα/dt = (k1 + k2αm)(1 - α)n (3.6)

where k1 is the reaction rate constant at zero time and k2 is the rate constant of the

reaction by traditional pathways. The initial rate constant, k1, is easily calculated from

the experimental data since it equals the rate at zero conversion.

The activation energy, represented by Ea in the Arrhenius temperature

dependence of the rate constant k, can be calculated for both mechanistic and

phenomenological models, and as such allows a comparison between the results. As

with other chemical reactions, the activation energy can be conceptually thought of as

the energy, in this case thermal energy, necessary for the reaction to proceed.

In mechanistic models, the activation energy is the slope of the ln k vs. 1/T (or

119

1000/T) curve since ln k = ln A – Ea(1/RT). The natural logarithm of the pre-

exponential factor, A, is the y (or ln k) intercept. The activation energies of

phenomenological models are usually calculated from a time-temperature relationship

computed with a shift factor, or via the temperature dependence of the time to reach a

certain conversion.

A mechanistic model has been developed for autocatalytic, amine-cured epoxies.

To fully account for the autocatalysis by hydroxyl groups generated, the multifunctional

nature of the amine curing agent, and the presence of ionic catalysts, including

impurities like water and other hydroxyl containing species, Horie11 has proposed a rate

equation which considers all reactions possible including

A1 + E + (HX)E -k1--> A2 + (HX)E (3.7)

A1 + E + (HX)0 -k1’--> A2 + (HX)0 (3.8)

A2 + E + (HX)E -k2--> A3 + (HX)E (3.9)

A2 + E + (HX)0 -k2’--> A2 + (HX)0 (3.10)

where A1, A2 and A3 are primary, secondary and tertiary amines, E is epoxide, (HX)0 are

hydroxyl groups and catalysts present in the system initially, and (HX)E are hydroxyl

groups generated by epoxy reactions. These reactions can be assembled into the

overall kinetic equation12

dx/dt = k1a1e0x + k1’a1e0c0 + k2a2e0x + k2a2e0c0 (3.11)

120

where x is the epoxide consumed, c0 and e0 are the initial concentrations of (HX)0 and

epoxide, a1 and a2 are the concentrations of primary and secondary amines. When the

primary and secondary amines are approximately equal in reactivity, the reaction rate

may be simplified to

dx/dt = (k1x + k1’c0)(e0 – x)(α0 – x/2) (3.12)

Converting the concentration of epoxide loss, x, to fractional conversion, α, transforms

Equation 3.12 to:

dα/dt = (k1α + k1’)(1 - α)(B - α) (3.13)

where k1 = k1(e0)2 / 2, k1’ = k1’e0c0 / 2 and B = 2a0 / e0. B, the stoichiometric ratio

of amine hydrogen equivalents to epoxide equivalents, is unity in balanced mixtures.

This model has been used successfully for some systems following the required

assumptions.13-17 However, commercial TGDDM/DDS systems can not be adequately

modelled with this equation.18,19 In addition, extensive knowledge of the chemistry and

stoichiometry of the mixture is essential. In the specific case where B = 1, Equation

3.13 reduces to Equation 3.6 with m = 1 and n = 2, as expected.

Epoxy curing reactions are further complicated by the diffusion controlled20

reaction occuring at the onset of vitrification when the kinetic reaction ends. The

overall reaction is actually

121

1 1 1 (3.14) ka(α,T) kT(T) kd(α,T)

where ka is the overall reaction rate constant, kT is the Arrhenius rate constant for the

kinetically controlled reaction and kd is the diffusion rate constant.

III.3 Kinetic Methods

III.3.1 Isothermal Differential Scanning Calorimetry

Fitting isothermal DSC data to the autocatalytic phenomenological Equation 3.6 is

difficult due to the number of variables, including two different exponents. Several

numerical methods, including rate analysis and linear regression,21 have been used.

However, many methods rely on a combined order which limits the generality. A

differential method has been proposed which does not rely on a combined order.

Several methods assume a combined, or overall, reaction order where the sum

of exponents m and n is assumed to be constant. In the simplest method, the overall

reaction order assumption allows the calculation of the rate constant, k2, which can be

substituted back into Equation 3.6 and the values of m and n calculated. This method

is based on several assumptions - the primary and secondary amines are of similar

reactivities and the hydroxyl groups function only as catalysts for the amine reactions,

i.e. reaction 1.3c is insignificant. This has been verified for some amine catalyzed

epoxy systems,22-24 especially in amine-rich systems. However, Dušek25,26 found that

the assumption of equal reactivities of amines is only true for aliphatic amines, not for

aromatic amines. The combined reaction order has been shown to be invalid for

multifunctional aromatic amines27-31 and epoxy-rich systems,32,33 specifically for the

122

epoxy-rich commercial TGDDM/DDS systems.34-38

A method, proposed by Ryan and Dutta,39 uses the time at maximum rate. It

was successfully used to model an epoxy-amine system. However, this model also

relies on the combined order assumption, limiting its applications. A nonlinear

regression analysis method was used by Moroni et al.40 for an epoxy; however, this

method also relies on the combined order assumption, limiting its use.

One method which does not rely on a combined order was proposed by Kenny.41

The method involves taking the natural logarithm of both sides of Equation (3.6), which

yields

ln(dα/dt) = ln(k1 + k2αm) + n ln(1 - α) (3.15)

A plot of ln(dα/dt) as a function of ln(1 - α) generates a line with slope n. Rearranging

Equation 3.6 in a different form yields

ln{[(dα/dt)/(1 - α)n] – k1} = ln k2 + m lnα (3.16)

Substituting n and k1, m can be calculated by the slope and k2 from the intercept.

III.3.2 Single Scan Differential Scanning Calorimetry

Although isothermal DSC evaluation produces accurate quantitative results, it is

very time-consuming, stimulating a desire for a fast method to characterize cure

kinetics, even at the cost of accuracy. The desire for a method to quickly characterize a

123

curing reaction in a single DSC scan led to several methods.

The first single scan DSC method was proposed by Borchardt and Daniels.42 The

method is similar to the isothermal method in that the degree of conversion throughout

the scan is a function of the fractional enthalpy change in time. The same equation is

ln [(dα/dt) / (1 - α)n] = ln k = ln A – E/RT (3.17)

with the temperature T, as a function of time. Using Equation 3.17, the variables ln A,

E and n can be calculated from a single DSC scan. Such an nth order equation, as well

as the autocatalytic equation are generally written as

kn = (dα/dt) / (1 - α)n (3.18)

ka = (dα/dt) / α(1 - α)(B - α) (3.19)

For the nth order equation, Barrett43 proposed plotting ln [(dα/dt) / (1 - α)n] as a

function of T-1 gives ln A and E from the slope and intercept provided that n is chosen

to produce a linear plot. Alternative evaluation techniques have proposed using the

incremental form44 and second derivative45 of Equation 3.15. While this technique has

given adequate approximations for some nth order reactions,46-49 it generally gives

much higher activation energy values,50-54 in some cases completely invalid results.55-57

III.3.3 Multiple Scanning Rate DSC

Multiple heating rate dynamic DSC scans are isoconversion measurements,

124

meaning that the time-dependant temperature to reach a certain degree of conversion

as a function of heating rate is measured. Several models have been proposed to

relate the isoconversion temperatures to scanning rate. Most models use the peak in

the curing exotherm in the scan as an isoconversion point.

One of the first successful models to relate the temperature of the exotherm

peak to the scanning rate was proposed by Kissinger.58,59 His model, based on

Differential Thermal Analysis (DTA) studies, provides

d[ln(ϕ/Tp2)] - E (3.20)

d[1/Tp] R

where ϕ = dT/dt is the heating rate and Tp is the peak temperature. Equation 3.20

may also be written as

ϕEexp[E/RTp] ϕEexp[E/RTp] (3.21) RTp

2[n(1 - αp)n-1] RTp2

A

where αp is the conversion at the peak and the approximation is based on Kissinger’s

assumption that [n(1 - αp)n-1] = 1. This is the model for an nth order reaction.

However, an autocatalytic equation based on this relationship has been developed,60 as

follows:

ϕE exp[E/RT] (3.22) RTp

2[2αp + 2Bαp - 3αp2 – B]

A

125

The most common method is based on work by Ozawa61,62 and Flynn and

Wall.63,64 Integration of the general rate equation and rearrangement produces

αi dα AE p(E/RTi) (3.23) 0 dt ϕR

where αi is a specified conversion and Ti is the temperature to reach that conversion, ϕ

is the scanning rate and p(E/RT) is an approximate solution to the exponential integral.

Using values tabulated by Doyle,65 the exponential can be approximated as

log p(E/RTi) ≅ - 2.315 - 0.4567 E/RTi (3.24)

Using this value, the equation can be rewritten as:

- R ∆(log ϕ) - R ∆(ln ϕ) (3.25) 0.4567 ∆(1/Ti) 1.052 ∆(1/Ti)

E

A similar model proposed by Fava,66 employs a rigorous approach based on

Ozawa’s model. Values for (dα/dt)p at various scanning rates are plotted against 1/Tp

and parameters calculated.

Barton67 used a model relating conversion and conversion rate to activation

energy:

126

ln (dα/dt)i - E ln A (3.26) (1 - αi)n RTi

where i = 1, 2, representing the two different scanning rate values. Setting α1 = α2

for the isoconversion peak temperatures, T1 and T2, and combining the equations yields

(dα/dt)1 - E 1 - 1 (3.27) (dα/dt)2 R T2 T1

This model allows calculation of the activation energy from two different rate scans,

independent of rates. However, this equation gives no indication of reaction order or

pre-exponential factor (A). Hernández-Sánchez and Vera-Graziano68 set (dα/dt)1 =

(dα/dt)2, yielding

ln 1 - α1 - E 1 - 1 (3.28) 1 - α2 nR T2 T1

Equation 3.25 can also be solved for a nonisoconversion situation where T1 = T2,

ln (dα/dt)1 n ln 1 - α1 (3.29) (dα/dt)2 1 - α2 .

ln

These equations, particularly Ozawa’s and Barton’s, have been used successfully for

both simple69-72 and complex73-75 thermosetting systems, including the TGDDM/DDS76

system, which was not able to be modeled by the single rate method. In addition, in

127

situations where multiple curing reactions77-80 can be resolved separately, e.g. primary

and secondary amine reactions, the parameters can be calculated for each reaction.81

III.3.4 Time-Temperature Superposition

The viscoelastic nature of polymers is the basis for the principle of time-

temperature superposition82 - the time of an event is related to the temperature at

which it takes place. This is apparent in polymers which have large viscous and elastic

characteristics, although it can be detected in viscous liquids and elastic solids also.

The principle is well accepted in the field of polymers, as demonstrated by predicted

ambient temperature lifetime studies conducted in short times at elevated

temperatures,83 and the velocity dependence of impact tests,84 which can lead to low

velocity predictions of ballistic impact property predictions conducted at low

temperatures. The relationship has been demonstrated for many characteristics by

Ferry85 and Goldman.86 While a qualitative understanding of the relationship between

time and temperature has been known for a long time, creating a quantitative formula

which would describe the behavior has proven difficult.

The most common relationship for polymers above the glass transition is the

Williams-Landel-Ferry87 (WLF) model given as

log aT = - [C1 (T – Tr)] / [C2 + (T – Tr)] (3.30)

where aT is defined as the shift factor, or the degree to which the property curve will be

shifted vertically or horizontally in relation to the reference curve by the temperature

128

difference, and C1 and C2 are constants. However, this model only works for

temperatures greater than the glass transition temperature. For temperatures below

the glass transition temperature, i.e. in the glassy state, the most common model is

based on an Arrhenius relationship given as,88

ln aT E 1 _ 1 (3.31) R T T0 .

A model based on free volume derived by Brostow,89,90 which works for all

temperatures is

ln aT = A + [B/(ν - 1)] (3.32)

where A and B are constants and ν is the reduced volume, defined as the ratio of

volume to incompressible or hard-core volume. The WLF equation is a special case of

Equation 3.29 which relies on linear proportionality of reduced volume and temperature,

which is only a good approximation from the Tg to around 50K above. However, the

simplicity of the formula and the lack of complex intrinsic material behavior combined

with the fact that most studies are performed within the limited range of reliability

provide the popularity of the equation.

These models have been applied to thermosets usually in the form of time to

reach a specific conversion as a function of temperature.91,92 Prime93 proposed an

isoconversion Arrhenius relationship between the times (t1 and t2) to reach a certain

129

conversion at two temperatures (T1 and T2),

ln aT E (T1 - T2) (3.33)

R T1 T2

Wisanrakkit and Gillham94,95 proposed a similar isoconversion relationship,

ln aT = ln (t2) - ln (t1) (3.34)

where t1 and t2 are the times to reach a specified conversion.

III.4 Physical Models

III.4.1 Glass Transition Temperature Shift

During the polymerization part of the reaction, before gelation and crosslinking,

the increase in Tg associated with the linear chain growth is proportional to the

concentration of monomers, using the decrease in concentration α in the form

1/Tg = 1/Tg0 + kα (3.35)

where Tg0 is the glass transition temperature at zero conversion, k is the rate constant

and α is the conversion, which is only valid for values up to gelation. This equation

assumes that no crosslinking takes place, which is a good approximation at low

conversion.

In the region between gelation and vitrification where crosslinking is the

dominant reaction, two primary models have been used. Fox and Loshaek96 proposed a

130

model which predicts a linear increase in Tg with crossslink density, whereas DiMarzio97

proposed a model which predicts linearity of 1/Tg with crosslink density. Later modeling

approaches combined both effects, polymerization and crosslinking, into one model.

The first of these, Tg as a function of conversion models was proposed by DiBenedetto.

DiBenedetto98 established a relationship to predict the shift in Tg based on

lattice energies and segmental mobilities of the cured and uncured materials,

Tg - Tg0 (ε∞/ ε0 - C∞/ C0) x (3.36) Tg0 1 - (1 - C∞/ C0) x

where x is the crosslink density or fraction of segments crosslinked, ε is the lattice

energy, and c is the segmental mobility. This equation has been used successfully for

many cross-linking systems,99-103 except in cases of very high cross-linking.104 This

equation was modified by Couchman105 to combine the lattice energy and segmental

mobility into the heat capacity value,

Tg - Tg0 _ λα _ _ (3.37) Tg∞ - Tg0 1 - (1 - λ) α

where λ is a structural dependent parameter defined as ∆Cp∞/∆Cp0 . This equation was

found to model some systems106 with λ values ranging from 0.43107,108 to between 0.46

and 0.58.109 However, the equation does not adequately model epoxy-rich systems,

due to the complexity of the reactions.110,111 Venditti and Gillham112 further modified

the equation to the following form:

131

ln (Tg) (1 - α) ln(Tg0) (∆Cp∞/∆Cp0) α ln(Tg∞) _ (3.38) (1 - α) + (∆Cp∞/∆Cp0) α .

This equation was found to model the epoxy-rich systems, which the previous models

could not, in addition to the systems which were modeled by the other equations.

The diffusion controlled part of the reaction after vitrification has been evaluated

by phenomenological models, and Wisanrakkit and Gillham proposed a separate

conversion-Tg model to cover this part of the overall reaction

ln [kd(T)] = ln [kd(Tg)] + 2.303 C1 (T - Tg) (3.39) C2 + T - Tg

where C1 and C2 are WLF parameters. Assuming kd(Tg) is constant and setting

r = 2.303C1, Equation 3.25 becomes

ln (kd) = ln (kd0) + r (T - Tg) (3.40) C2 + T - Tg

which may be used to calculate the activation energy and preexponential factor.

III.4.2 Viscoelastic Relaxation Time Shift

The glass transition temperature shift described above can also be described

using viscoelastic theory. The Tg shift is described as resulting from changes in the

frequency-dependent relaxation time, τ(ω), due to the change in mobility of the

growing chains and network.113

The relaxation time is taken to be a thermally activated process, so it can be

132

modeled by an Arrhenius relationship

τ (T, α) = τα exp (Ea/RT) = 1/ω (3.41)

where Ea is the activation energy of the glass transition, τ is the relaxation time, τα is

the relaxation time at the conversion at the transition and ω is the frequency of the

stimulus. The Tg can be defined as

Tg = - Ea / [R ln(ωτα)]. (3.42)

Substituting viscoelastic relationship equations, this can be written as

Tg Ea (3.43) R ln[C1 (1 - α)Φ + C2]

where C1 = exp(Ea/RTg0) – exp(Ea/RTg∞) (3.44) C2 = exp(Ea/RTg∞) (3.45)

and Φ is a parameter accounting for chain entanglement. The activation energy of the

transition may be determined by multiple frequency experiments using the

relationship114,115

Ea d(ln ω) (3.46) d(1/Tmax)

133

This viscoelastic relaxation model has been used to successfully model a

multifunctional epoxy through the complete curing reaction.116

III.4.3 Gelation

The degree of conversion at the microscopic gel point can be calculated if the

chemistry of the reactants is known. The first formula for calculating the microscopic

gel point, proposed by Flory117 in 1941, is

(α1α2)gel 1 _ (3.47) (f1 -1)(f 2 -1)

where α1 is the conversion of reactant 1, α2 is the conversion of reactant 2, f1 is the

functionality of reactant 1, f2 is the functionality of reactant 2, and

α2 = B α1 (3.48)

where B is the stoichiometric ratio. For an epoxy-amine reaction, where the amine is

reactant 1 and the epoxy is reactant 2, B is the ratio of amino hydrogens to epoxide

groups, so Equation 3.16 reduces to

α2gel B _ 1/2 (3.49) (f1 - 1)(f2 - 1)

III.4.4 Chemoviscosity

The molecular weight dependant viscosity change during the reaction has been

134

modeled using the semi-empirical model118-120

η(t) = η0 exp(kt) (3.50)

where η0 represents the minimum viscosity at very low conversion and k is the reaction

rate constant. An Arrhenius temperature dependence for both η0 and k was introduced

by Roller121,122 in the form

ln η(t) = ln η∞ + ∆Eη/RT + tk∞ exp (∆Ek/RT) (3.51)

where η∞ is the viscosity at infinite temperature or T∞, ∆Eη is the activation energy for

viscosity, k∞ is the rate constant at infinite temperature and ∆Ek is the activation energy

for the reaction kinetics. In the early stage of cure, the viscosity is assumed to be

Newtonian. Analogous to models using other techniques, this isothermal model can be

modified to a dynamic model by integration of the kinetic term123

ln η(t,T) = ln η∞ + Eη/RT + 0∫t k∞ exp (∆Ek/RT) dt (3.52)

The change in viscosity during the curing reaction has also been modeled124 using a

Williams-Landel-Ferry (WLF) equation of the form

log η(T) = log η(TS) + a(T - TS) (3.53) b + (T - TS)

135

where TS is a reference temperature which will depend on the degree of cure and a and

b are constants. The shift factor, aT, between the isothermal viscosity functions is

defined by

aT = η(T)/η(TS). (3.54)

Tajima and Crozier125 found TS to be a linear function of α2 and log η(TS) to be a linear

function of α by regression analysis of epoxy viscosity data. Lee and Han126 modified

Equation 3.35 to

log η(T,α) = (a1 + b1α) - a2(b2 + T - c2α) (3.55)

a3 + T - c2α

where a1, a2, a3, b1, b2 and c2 are parameters. A simple equation, which is used often,

was developed by Castro127 and Wang et al.128

η/η0 αg f(α,T) (3.56) α - αg

where αg is the conversion at the gel point and η0 is the initial viscosity at zero

conversion at the isothermal temperature, which is described by the Arrenhius equation

η0 = Aη exp (Eη/RT) (3.57)

where Aη and Eη are the viscosity dependent pre-exponential factor and activation

136

energy. This equation has been used successfully for fast curing resins.129

A similar relationship introduced by Stolin et al.130 relates η to degree of cure

with the equation

η = η∞ exp(Eη/RT) - Kα (3.58)

where η∞ is the viscosity at maximum cure, a constant, Eη is the activation energy of

the viscosity change, and K is a constant. Using this data, good estimations of η in

time have been found for a TGDDM/DDS system.131

III.5 Decomposition Kinetics

Thermal degradative stability has been related to the degree of cure.132

Activation energy of the degradation process increases with increasing cure

temperature, implying that increasing crosslink density, raises the amount of thermal

energy required to degrade the chemical structure. Prime133 has verified this for a

cross-linking magnetic tape coating. The degree of cure of many thermosets have been

investigated by TGA thermal stability.134-136

Degradation of cured epoxies is a multistep process, which includes chain

scission, char formation or carbonization, and char stabilization.137 Since both TGDDM

and DDS contain aromatic ring structures and the network contains cyclic structures,

degradation begins at these points.138-140

TGA degradation kinetics may be performed by either isothermal or by varied

heating rate methods. The derivation of the equations from differentiation and

137

integration of formulas relating the degree of cure to activation energy and temperature

are described elsewhere by Dickens and Flynn,141 Flynn and Wall,142,143 and in the ASTM

standard.144

Although a series of isotherms of different samples at different temperatures can

be performed, and the curves analyzed by classical curve fitting and the parameters

determined, the technique is very time consuming and tedious, and other techniques

give similar results. A technique called “factor-jump” simulates the series of isotherms

by using temperature jumps between isotherms with one sample. This is similar to the

temperature-jump and pressure-jump methods common in chemical rate

measurements.145 In the factor-jump method, the sample is subjected to a series of

isotherms, with rapid jumps between the isotherms, while the weight and temperature

are monitored. The activation energy is estimated from the relationship,146

Ea = RT1T2 ln r2 . (3.59) T2 – T1 r1

where r and T are the rates and temperatures of the two isotherms. These isotherms

are assumed to occur at the same degree of conversion, thus this is not a variable.147

A common method in TGA degradation stability is the use of multiple scanning

rates. The scanning rate and temperature of degradation are related by

ln β = 1.05(Ea/RT) (3.60)

138

where β is the scanning rate and Ea is the activation energy associated with the

degradation process occurring at temperature T.148-150 The activation energy can be

calculated by plotting ln β versus 1/T for a series of different heating rate scans.

III.6 TTT and CHT Diagrams

Adjusting parameters during thermoset curing was difficult in industry until the

introduction of the TTT diagram since a 10% decrease in temperature didn’t usually

correspond to a 10% increase in curing time. In fact, a 10% decrease in temperature

might produce uncured parts regardless of the time given. The TTT diagrams have

been used extensively to describe time and temperature dependent transformations in

metals151 for many years, especially in nonequilibrium states. The adaptation of the

TTT diagram to thermosetting polymers by Gillham and Enns152 gave a fast easy to read

understanding of the relationship between processing parameters and an understanding

of the physical state of the material in response to the conditions it had been exposed

to. The TTT diagram tells processors what temperature to store their materials to

ensure no precuring, how much they can precure material and still ensure adhesion

between components, how much they have to precure to ensure dimensional stability,

what the optimum processing conditions should be, the lowest temperature that

ensures full cure or a certain degree of cure and the maximum cure temperature to

avoid degradation. A TTT diagram is usually presented with Tg plotted as as a function

of the natural logarithm of curing time in isoconversion curves.153,154 The primary

curves shown are gelation and vitrification as a function of time and temperature.

139

do

pe

lik

ind

m

Tr

Figure 3.1: A typical Time-Temperature-Transformation (TTT) diagram, showing the

various physical states caused by time and temperature-dependent curing.

One limitation with a TTT diagram is that many isotherms and Tg scans must be

ne. While special DSC’s capable of high heating rates, described in Chapter 2, can

rform multiple scans on a single sample, traditional DSC and other Tg measurements

e DMA and TMA require many measurements on multiple samples to determine the

ividual points used to construct each line. One alternative to the many

easurements required for a TTT diagram is to construct a similar Continuous Heating

ansformation (CHT) diagram from a series of single scans at different rates,

140

dramatically reducing the number of experiments required.

The CHT diagram is constructed from single scans at different rates as shown in

Figure 3.2. Each scan is plotted on a temperature vs. natural log time graph with the

key transitions indicated by points. The points representing initial Tg, gelation (from

DMA scans) and vitrification from all of the scans can be connected to form a

transformation diagram which gives the same information as a TTT diagram.

Figure 3.2 A typical Continuous Heating Transformation (CHT) diagram, with the scans

represented by lines and the resulting transformations connected by a dashed line.

141

III.7 Abbreviations and Acronyms




DTA Differential Thermal Analysis




WLF Williams-Landel-Ferry

III.8 Symbols

a amine concentration.

aT shift factor in time-temperature superposition.

A preexponential term or frequency factor.

B stoichiometric ratio of amine hydrogen to epoxide equivalents.

c segment mobility

Cp specific heat capacity at constant pressure.

e epoxide concentration.

Ea activation energy of reaction or transformation.

f functionality of components, i.e. number of functional groups on reactant.

HX abbreviation for hydroxyl groups

k rate constant.

K constant

142

m order of catalytic term in autocatalytic reaction.

n order (power function) of non-autocatalytic or nth order reaction.

r rate

R gas constant.

t time.

ti,g,p time to reach specific point i, gel point or peak rate.

T temperature.

T0,i,g,p temperature at beginning of reaction, point i, gel point or peak rate.

α degree of conversion or cure representing the % aliphatic bonds formed.

αi,p,g degree of conversion at a specific value i, peak rate or gel point.

dα/dt rate of conversion in time.

β heating rate.

δ phase angle (usually expressed as tan delta or phase lag)

ε lattice energy

ϕ heating rate.

Φ chain entanglement factor.

η viscosity

η0,∞ viscosity at beginning of reaction or end of reaction.

λ structural parameter

τ relaxation time

ω angular frequency

143

III.9 References

t

t r.


2 C.C. Riccardi and R.J.J. Williams, J. Appl. Polymer Sci., 32 (1986) 3445.

3 M.R. Dusi, W.I. Lee, P.R. Ciriscioli and G.S. Springer, J. Compos. Ma er., 21 (1987)

243.

4 S.L. Simon and J.K. Gillham, J. Coat. Tech., 64 (1993) 57.


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152

CHAPTER IV

EXPERIMENTAL CONDITIONS

The two materials used in this study were a high temperature epoxy molding

compound and a commercial epoxy system. The high temperature molding compound

is a premixed compound of the tetrafunctional epoxy tetraglycidyl 4,4-diaminodiphenyl

methane (TGDDM) and the tetrafunctional amine curing agent 4,4’-diaminodipheny-

lsulfone (DDS), along with an ionic initiator/accelerator and a thermoplastic, designated

8552 by its manufacturer Hexcel. The compound was provided as neat resin and as 66

weight percent glass fiber reinforced prepregs, both as uniaxial and biaxial fibers.

The commercial epoxy system is a DGEBA epoxy resin and a separate aliphatic

amine, manufactured by System3. The System3 epoxy resin was mixed with the curing

agent and in the fluorination studies was also mixed with a mixture of aliphatic amine

and various fluorinated amines, including 2-fluoroaniline, 3-fluoroaniline, 4-fluoroaniline,

3,5-difluoroaniline, 3,4-difluoroaniline, 2,6-difluoroaniline, 3-aminobenzotrifluoride and

3,5-bis(trifluoromethyl)aniline obtained from Fluorochem USA (West Columbia, SC).

Differential Scanning Calorimetry (DSC) experiments were performed on a

Perkin-Elmer DSC-7 (power compensation type) operating on a UNIX platform using ice

coolant and nitrogen (30 ml/min) purge gas on resin and composite samples of 5 to 10

mg, weighed on an analytical balance to +.05 mg enclosed in crimped aluminum pans.

Isothermal measurements were performed at 10 K intervals between 100 and 180°C

scanning from ambient to the isothermal temperature at 40 K/min and holding at the

isotherm for an appropriate time (100 - 1000 minutes). Temperature scans for total

153

enthalpy changes and glass transition temperatures were performed using the same

conditions with a scanning rate of 5 K/min from ambient to 350°C. The DSC-7 was

burned out and calibrated for temperature with indium and zinc. It was also calibrated

for enthalpy using the heat of fusion of indium at the beginning of this project and on a

monthly basis during the project. The sensitivity of the DSC-7 is 35 µW with

calorimetric precision of 0.1 %. The temperature accuracy and precision is 0.1 °C.

TMDSC experiments were performed on a Perkin-Elmer Pyris-1 operating on a

Windows NT platform using liquid nitrogen as the coolant and helium (20 ml/min) as

the purge gas on resin and composite samples of 5 to 10 mg in crimped aluminum

pans. Isothermal measurements were performed at 10 K intervals between 120 and

180°C holding for an appropriate time (100 to 500 minutes). Temperature scans were

performed from subambient (-100°C) to 300°C at 10 K/min. The Pyris-1 was burned

out and calibrated for temperature with both indium and zinc standards and for

enthalpy with the heat of fusion of indium at the beginning and monthly during the

project. The sensitivity of the Pyris-1 is 35 µW with calorimetric precision of 0.1 %.

The temperature accuracy and precision is 0.1°C.

Step Scan experiments were performed on a Perkin-Elmer Pyris-1 operating on a

Windows NT platform using liquid nitrogen as the coolant and nitrogen (20 ml/min) as

the purge gas on resin and composite samples of 5 to 10 mg in crimped aluminum

pans. Temperature scans were performed from subambient (-100°C) to 300°C at 10

K/min. The Pyris-1 was burned out and calibrated for temperature with both indium

and zinc standards and for enthalpy with the heat of fusion of indium at the beginning

154

and monthly during the project. The sensitivity of the Pyris-1 is 35 µW with calorimetric

precision of 0.1 %. The temperature accuracy and precision is 0.1°C.

Hyper DSC (high heating rate) experiments were performed on a Perkin-Elmer

Diamond DSC operating on a Windows 2000 platform using liquid nitrogen as the

coolant and helium (20 ml/min) as the purge gas on resin samples of 5 to 10 mg in

crimped aluminum pans. Temperature scans were performed from subambient (-

100°C) to 300°C at rates up to 500 K/min. The Diamond DSC was burned out and

calibrated for temperature with both indium and zinc standards and for enthalpy with

the heat of fusion of indium at the beginning and monthly during the project. The

sensitivity of the Diamond DSC is 35 µW with calorimetric precision of 0.1 %. The

temperature accuracy and precision is 0.1°C.

Thermomechanical Analysis (TMA) experiments were performed on a Perkin-

Elmer TMA-7 operating on a UNIX platform using ice coolant without a purge gas on

composite prepregs cubes of 5 mm per side. A quartz linear expansion probe was used

on both the surface of the cube and on the movable piston of a quartz dilatometry cup.

Temperature scans were performed from ambient to 300°C at 10 K/min, using a probe

force of 5 mN except in the pressure dependence studies where the force was varied

from 5 to 20 mN. The temperature was calibrated using indium under the compression

probe tip. The linear sensivity of the TMA-7 is 0.4 mm. The temperature accuracy is +

2°C.

Dynamic Mechanical Analysis (DMA) experiments were performed on a Perkin-

Elmer DMA-7e operating on a Windows NT platform using either ice or liquid nitrogen

155

coolants depending on the experiment and nitrogen (30 ml/min) purge gas on

composite prepreg tape (2 mm X 10 mm X 10 mm). Temperature scans were

performed from either ambient or subambient (-100°C) to 300°C. Isotherms were

performed from ambient to the isotherm at 20 K/min and held for an appropriate time

with isothermal temperatures at 10 K increments between 120 and 180°C. DMA

experiments were performed using steel three point bending and parallel plate fixtures.

The DMA instrument was calibrated for temperature with indium and for force with a

500 mg weight, as well as for position, deflection and furnace control. The linear

sensitivity of the DMA-7e is 0.4 mm. The temperature accuracy is + 5°C.

Dynamic Mechanical Analysis (DMA) frequency scans were performed on a

Perkin-Elmer Diamond DMA operating on a Windows 2000 platform using liquid

nitrogen coolant and nitrogen (30 ml/min) purge gas on cured resin samples (2 mm X

10 mm X 10 mm). Temperature scans were performed from ambient to 300°C. These

experiments were performed using steel flexural fixtures. The linear sensitivity of the

Diamond DMA is 0.4 mm. The temperature accuracy is + 5°C.

Thermally Stimulated Depolarization (TSD) experiments were performed on a

Thermold TSC/RMA using liquid nitrogen coolant and ultra-high purity helium as the

purge gas and chamber atmosphere. Steel screw-down 5 mm diameter disc fixtures

were used on tape prepregs. The poling temperature was the same as the isothermal

curing temperature - between 120 and 180°C. The poling time was 5 minutes with a

500 V/m electric field. The total curing time was the sum of the poling time and

prepoling time at the curing temperature. The cooling ramp was 5 K/min, and the

156

depolarization heating ramp was 2 K/min. The current sensitivity of the Thermold

TSC/RMA is 1 femtoampere. The temperature accuracy is + 5°C.

Thermogravimetric Analysis (TGA) experiments were performed on a Perkin-

Elmer TGA-7 operating on a UNIX platform using air cooling and dry air (30 ml/min) as

the purge gas and as the pneumatic control source on prepreg tape samples of about

50 mg. Temperature scans were performed from ambient to 500°C at rates of 5, 10,

20 and 40 K/min. The TGA was calibrated for temperature with a two standard

calibration using the magnetic Curie temperatures (Tc) of Perkalloy (Tc = 596°C) and

Alumel (Tc = 163°C). The microbalance was calibrated for weight with a 100 mg

standard. The weight sensitivity of the TGA-7 is 0.1 µg, with accuracy of 0.1 % and

precision of 10 ppm. Temperature accuracy is + 5°C.

Tribological scratch testing was performed on a CSEM microscratch tester using

CSEM software version 2.3. The indenter was a 200 micron radius diamond tipped

Rockwell indenter.

157

CHAPTER V

RESULTS

V.1 Heat of Reaction

Isothermal Differential Scanning Calorimetry (DSC) scans were performed to

characterize the time and temperature-dependent rates and degrees of conversion.

The isothermal scans are presented in Figure 5.1. The results of integration and fitting

the data to the autocatalytic model, given in Chapter 3 as Equations 3.2 and 3.5, are :

the activation energy is 54.9 + 7.0 kJ/mol, the natural logarithm of the preexponential

term is 8.38 + 0.02 s-1 and the combined reaction order equal to one with n = 0.7 and

m = 0.3. The total enthalpy change is 557 + 1 J/g obtained from a separate DSC

temperature scan. The plot using DSC results of degree of conversion as a function of

time for the isothermal temperatures studied is presented in Figure 5.2. Figures 5.3

presents the calculated isochronal time curves on a conversion vs. curing temperature

plot. Figure 5.4 illustrates the temperature dependence of the combined rate constant,

k = k1 + k2, in a plot of natural logarithm of k vs. inverse temperature (1000/T) from

which the activation energy is calculated. Figure 5.6 is a plot of natural logarithm of

rate (ln dα/dt) as a function of natural logarithm of conversion (ln αn{1-α}m). Figure

5.7 depicts the calculated isoconversion curves demonstrating the relationship between

time and temperature.

158

Figure 5.1: Series of isothermal DSC heat flow measurements showing the

changes in enthalpy in time for three temperatures :120, 140 and 160 °C,

which are proportional to the number of constituents reacting in time.

Figure 5.2: Calculated conversion vs. time for curing temperatures given in °C using

data from isothermal autocatalytic measurements.

159

Figure 5.3: Calculated conversion vs. curing temperature for several isochronal times,

given in minutes from isothermal autocatalytic DSC results.

Figure 5.4: Calculated temperature dependent function k from

isothermal autocatalytic DSC results.

160

85% 95%

75% 65%

55%

45%

Figure 5.5: Calculated natural logarithm of k as an inverse function of temperature

for each isothermal temperature with isoconversion lines.

140 °C 160 °C

120 °C

Figure 5.6: Calculated natural logarithm k as a function of natural logarithm

conversion, given by the order parameters m and n with isothermal

lines drawn from isothermal autocatalytic DSC results.

161

90%

80%

70% 60%

50% 40%

Figure 5.7: Calculated conversion as a function of time and temperature, shown

are isoconversion curves from isothermal autocatalytic results.

V.2 Dynamic Differential Scanning Calorimetry

Dynamic kinetics were determined with both single scan and with varied

scanning rate methods. These were done to compare with the isothermal results and

determine the reliability of scanning kinetics .

The single scan method, shown in figure 5.8, was applied with the scanning rate

of 5 K/min. The results of integration of this curve are that the activation energy is

81.9 + 3.1 kJ/mol and the natural logarithm of the preexponential factor is 15.3 + 0.9

s-1 with the reaction order estimated as one. Figures 5.9 and 5.10 are plots of the

calculated degree of conversion as a function of time and temperature. Figure 5.11 is a

plot of natural logarithm of the rate constant as a function of inverse temperature

(1000/T). Figure 5.12 is a plot of calculated isoconversion curves as a function of time

and temperature. An additional single scan experiment was performed with the rate of

162

10 K/min providing similar results : the activation energy is 81.0 + 1.5 kJ/mol and the

natural logarithm of the preexponential factor is 14.7 + 0.4 s-1.

Peak 217.6 °C Area -4001 mJ ∆H -546.7 J/g

Figure 5.8: DSC single scan at 5 K/min for use in kinetic calculations.

Figure 5.9: Results of calculated conversion vs. time at specified curing

temperatures given in °C, from single scan kinetic equation.

163

Figure 5.10: Results of calculated conversion vs. temperature at specified curing times

given in minutes, calculated from single scan kinetic equation. Note: curves

shift to shorter times at higher temperatures.

Figure 5.11: Calculated temperature dependent function k

from single scan kinetics.

164

90%

80%

70% 60% 50%

40%

Figure 5.12: Calculated conversion as a function of time and temperature, shown are

isoconversion curves. Note: shape of curves demonstrates Arrhenius relationship

and high conversion curves have higher time and temperature values.

Scanning DSC measurements were also done using the multiple scanning rate

method. The scanning rates were 5, 10 and 20 K/min, as shown in Figure 5.13. The

values of peak conversion and scanning rates were fitted to Equation 3.25, shown in

Figure 5.14. The resulting activation energy is 61.8 + 4.3 kJ/mol.

Figure 5.13: DSC scanning exotherms for three scanning rates, 5, 10 and 20 K/min

with peak conversion rates identified and total integrated change in enthalpy given.

165

Figure 5.14: Curve fit of the natural logarithm of scanning rates as a function of

inverse temperature from which activation energy and preexponential factor can be

calculated. High value of coefficient (R) indicates precision of equation fit to data.

V.3 Glass Transition Temperature Shift

The glass transition temperature shift as a function of time and temperature was

performed by DSC and Thermally Stimulated Depolarization (TSD). The DSC studies

were performed by curing at a certain time and temperature in isothermal mode,

quenching and performing a temperature scan. The Tg was calculated as the onset of

the shift in baseline heat flow since the half difference in heat flow shift could not be

accurately determined due to the residual exotherm overlap with the later part of the Tg

shift. The Tg values of various time and temperature values are displayed graphically in

Figure 5.15. Plotting the Tg shift as a function of time on a logarithmic time scale,

shown in Figure 5.16, allows calculation of the shift factor by Equations 3.33 and 3.34,

shown in Figure 5.17. Since the slopes are approximately equal, the shift factor is

166

Figure 5.15: Tg shift as a function of time at curing temperatures as measured from

DSC with the ultimate Tg for each temperature shown as a line from TSD.

Figure 5.16: Tg shift as a function of time at various curing temperatures,

plotted on logarithmic scale so shift factor can be calculated.

167

Figure 5.17: Natural logarithm of the shift factors as a function of inverse temperature,

from which activation energy and preexponential factor are calculated.

determined by the difference in time-intercepts (x-intercept) from curve fitting. The

activation energy is calculated as the slope of the plot of shift factors as a function of

inverse temperature. The activation energy by this method is 65.9 + 1.2 kJ/mol.

The TSD measurements of chain mobility and Tg were performed similarly by curing at

an isothermal temperature for a certain time (including the poling time), quenching,

and subsequently scanning as a function of temperature. The Tg (increase in mobility)

is taken as the peak in discharge current. The Tg’s of the maximum isothermally cured

samples were well resolved using TSD; however, the partially cured samples showing

the Tg shift with curing time were unreliable. The TSD apparatus manufacturer

recommends and the controlling software requires a slow quench rate (5 to 20 K/min)

which is not fast enough to quench the reaction in the partially cured state. For

comparison, the other techniques for quenching the reaction use a 50 to 200 K/minute

168

cooling ramp. The quality of the fully cured Tgs justifies further work with TSD which

was not possible in this study.

A series of Tg’s for the DGEBA epoxy taken at different times during an

isothermal experiment is shown in Figure 5.18. Note that unlike the previous series,

this series was done with one sample on one program using high speed DSC which

drastically reduced the time necessary to generate the series of points.

Figure 5.18: A series of Tg’s for DGEBA at 140 °C at various times generated with a

single sample on a single high speed DSC program.

169

V.4 Viscosity

The viscosity as a function of time during a series of isothermal Dynamic

Mechanical Analysis (DMA) 3-point bending experiments is presented in Figure 5.19.

The area of interest on log scale is shown in Figure 5.20.

Figure 5.19: Plots of viscosity as a function of time during a series of

isothermal DMA 3-point bending measurements.

Figure 5.20: Area of viscosity as a function of time curve from

which the shift factors are determined.

170

Fitting the shift factors shown in Figure 5.20 to a linear relationship between the

natural logarithm of shift factor and inverse temperature yields the line shown in Figure

5.21. The Equation of this line was used to calculate the activation energy to be 33.8 +

1.8 kJ/mol and the preexponential factor to be 1.5 + 0.5 s-1.

7.4

7.6

7.8

8

8.2

8.4

8.6

8.8

9

2.2 2.3 2.4 2.5

Viscosity Shift Factorsy = -1.4783 + 4.0689x R= 0.99734

1000/T (K)

��

y = m1 + m 2 * M0��ErrorValue

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0.49896-1.4783m 1

��

0.210174.0689m 2 ��

NA0.0055822Chisq��

NA0.99734R

��

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��

��

Figure 5.21: Curve fit of shift factors from superposition of viscosity curves from

which activation energy and preexponential factor can be calculated.

The viscosity change during curing at various isothermal temperatures is shown

in Figure 5.22. The curves are DMA parallel plate measurements providing better

resolution at low viscosity values. The values of the minimum viscosities are plotted as

a function of inverse temperature in Figure 5.23. Substituting the slope and intercept

into the Arrhenius equation, Equation 3.57, the viscosity activation energy is calculated

to be 17.5 + 2.5 kJ/mol and the logarithm of the preexponential factor is 10.7 + 0.7 s-1.

171

Figure 5.22: A series of isothermal parallel plate viscosity plots in time.

Figure 5.23: Curve fit of time to minimum complex viscosity for various isothermal

temperatures plotted as natural logarithm vs. inverse time.

172

V.5 Thermal Stability

The rate of thermal decomposition was determined by variable scanning rate

TGA studies. The kinetic rate was calculated using Equation 3.60 with linear regression.

The activation energy of decomposition is 131.9 + 12.0 kJ/mol and the natural

logarithm of the preexponential factor is 15.1 + 2.0 s-1 with a first order decomposition

reaction. Similar work in the literature1 found a much lower value, around 50 – 80

kJ/mol. The series from which this calculation was performed is presented in Figure

5.24.

Figure 5.24: The series of different scanning rate thermal decomposition curves,

plotted as weight loss as a function of temperature, from which the

activation energy and preexponential factor are calculated.

173

V.6 Comparison of Kinetic Results

A compilation of the results of activation energy and natural logarithm of

the preexponential factor calculations of the techniques used is presented in Table 5.1.

Method Ea(kJ/mol) lnA (s-1) DSC Isothermal 54.9 + 7.0 8.38 + 0.02 DSC Single scan 81.9 + 3.1 15.3 + 0.9

DSC Multiple scan 61.8 + 4.3 14.2 + 1.1 DSC Tg Shift Factor 65.9 + 1.2 11.0 + 0.4

DMA Viscosity Shift Factor 33.8 + 1.8 1.5 + 0.5 DMA Viscosity Minima 17.5 + 2.5 10.7 + 0.7

TGA degradation 131.9 + 12.0 15.1 + 2.0

Table 5.1: Results of calculation of activation energy and preexponential factor.

Values for activation energy in the literature for similar prepregs are 50,2 71,3,

734 and 705 kJ/mol. From these results, an average literature value of 66.0 kJ/mol can

be used for comparison. One study in the literature on a similar prepreg using single

scan DSC determined the activation energy to be 1096 kJ/mol which is expectedly

higher than for other techniques.

The results given in Table 5.1 cover a large range of activation energy values;

however, three of the seven techniques are in the range reported in the literature. The

three results which agree with literary values are from isothermal, multiscan and Tg

shift by DSC. The Tg shift result is the closest to the average reported in the literature.

The single scan DSC is somewhat higher in activation energy value, likely due to the

effect observed and explained in literature comparisons of isothermal and single scan

DSC studies.7-11 The viscosity shift factor result is less than the literary average by

about 50 %, which implies that it is useful but within limitations. The viscosity minima

calculations produce a very low value of activation energy; however, this is the viscosity

174

activation energy not the kinetic activation energy produced in the other methods. The

result from TGA degradation is higher than the rest of the techniques, as well as higher

than the literature values. This implies that this value does not follow the same model

as the rest. This is reasonable since thermal stability, while related to degree of cure, is

not necessarily a simple one-to-one linear relationship.

V.7 Transformations

V.7.1 Gelation

The gel point was identified as the lower of the two peaks in the tan δ of parallel

plate DMA isotherms, shown in Figure 5.25. This feature is also evident in three-point

bending DMA isotherms as a small peak or shoulder, shown with the corresponding

parallel plate isotherm in Figure 5.26. Gelation occurs on at a certain degree of

conversion, so it appears as an isoconversion line on the TTT diagram.

V.7.2 Vitrification

Vitrification was determined by TMDSC and DMA isotherms and Step Scan DSC ramps.

TMDSC isotherms showing the characteristic downward shift in baseline storage Cp are

shown in Figure 5.27. Vitrification appears in DMA measurements as the higher of two

peaks in the tan δ, as shown in Figure 5.28. Vitrification also appears in parallel plate

DMA isotherms, shown in Figure 5.25. Due to the extremely high modulus of the glass

fiber reinforced prepreg, the vitrification point is not well resolved in parallel plate

measurements.

Vitrification points during scanning experiments were performed using Step Scan

DSC at various rates. The curing exotherm was separated from the rubber to glass

175

transition and the time of half height change was recorded. The curing exotherm was

used to determine the time/temperature of full cure or the point of flat baseline.

Figure 5.25: DMA parallel plate isotherm (160°C) showing the gel point as the lower

temperature peak of two in tan δ and the vitrification point as the higher

temperature transition. Note that gelation is evident in tan δ

and storage and loss moduli. Also, vitrification is poorly resolved.

176

Figure 5.26: A plot of tan δs from both parallel plate and three-point bending DMA

isotherms (120°C), with gelation visible in both as the lower temperature peak.

Figure 5.27: TMDSC isotherms showing vitrification as the half height drop in Cp’.

Note: vitrification occurs at higher times for lower curing temperatures.

177

Figure 5.28: A tan δ plot in time from a DMA three-point bending isotherm (at 120°C)

with the gelation and vitrification points identified. Note: vitrification is well resolved

while gelation appears as a shoulder.

Figure 5.29: Plots of tan δs from both parallel plate and three-point bending

DMA isotherms (at 160°C) showing difference in sensitivity to vitrification.

178

V.7.3 Time-Temperature-Transformation Diagram

A time-temperature-transformation (TTT) diagram, Figure 5.30, was constructed from

the best resolved gelation and vitrification data. The initial Tg was determined by both

TMDSC and DMA three-point bending, with TMDSC having greater temperature

accuracy. The final Tg was measured by TMDSC, TMA and DMA three-point bending

with DMA being the best resolved. The increase in Tg with time at various temperatures

was measured by DSC, gelation was measured by DMA parallel plate and vitrification

was measured by TMDSC and DMA three-point bending. The regions and transitions

identified follow conventions proposed by Gillham. Notable curing temperature effects

can be seen in the TTT diagram. At temperatures below the Tg0 (6°C) there is no

reaction, so this is the safe storage temperature. Between Tg0 and Tg-gel (6 to 86°C) the

material will react, albeit very slowly, and will eventually vitrify before it gels. Between

Tg-gel and Tg-vit (86 to 248°C) the material will first gel, then vitrify. Above Tg-vit (248°C)

the material will gel, but will not vitrify. This diagram provides an easy to read

description of the transformations taking place in processing of composite prepregs,

and allows manipulation of processing conditions to modify physical properties. This

TTT diagram is consistent with a similar diagram12 for DDS cured TGDDM found in the

literature.

179

Figure 5.30: Time temperature transformation diagram for the TGDDM/ DDS system in

this study with gelation and vitrification curves identified. The initial Tg used for the

curve was determined by DSC; however, the value from DMA three-point bending is

included as points for comparison. The gelation points were determined by DMA

parallel plate measurements. The points used to construct the vitrification curve were

determined by TMDSC; however, values from DMA three-point bending were included

as experimental points for comparison. The final Tg values were determined by DMA

three-point bending, TMDSC and TMA, with DMA three-point bending values used to

construct the curve since it was the highest, ensuring that this is the maximum.

180

V.7.4 Continuous Heating Transformation (CHT) Diagram

The glass to rubber and rubber to glass transitions determined from Step Scan

DSC temperature scans were used to construct the CHT diagram shown in Figure 5.31.

Three lines connecting the glass to rubber transition points, the rubber to glass

transition points (vitrification points) and the points of final cure at the end of

exotherms, indicate the physical states of the reacting epoxy.

Figure 5.31: The CHT diagram constructed from Step Scan DSC scanning

measurements. Average heating rates, including both heating and isotherm, are

plotted on a temperature vs. Log time. The initial Tg and vitrification points are

indicated on each scan line. The points are connected to indicate a transformation.

181

V.8 Shrinkage

The results of prepreg shrinkage during the curing process in the mold from

dilatometry for different pressures and fiber orientations after separating the void

elimination and fiber rearrangement from the resin shrinkage are presented in Figures

5.32 and 5.33.

The shrinkage due to fiber rearrangement shows a strong dependence on the

cure temperature, the pressure applied and the fiber orientation. Higher pressure (10

psi vs. 5 psi) results in larger shrinkage. Higher cure temperatures (160°C vs. 120 and

100°C) typically result in lower shrinkage, due to the faster reaction rate which means

less time for rearrangement before gelation and the faster increase in viscosity. At the

lowest cure temperature (100°C), when there is sufficient time for rearrangement,

biaxially oriented fibers exhibit higher bulk shrinkage than uniaxial ones, likely due to

the higher void content between the layers. At higher cure temperatures (120 and

160°C), the orientation has less effect.

As expected, the resin shrinkage is a constant 0.5 % regardless of orientation,

cure temperature or pressure. Since the resin shrinkage is due to chemical bonding

and network structure, it should be a constant value, and epoxies in general have very

low values of shrinkage. In addition to providing the shrinkage value, the consistency

verifies that the separation of chemical and macroscopic changes are correct.

182

Figure 5.32: The change in volume due to void elimination and fiber rearrangement

measured by dilatometry at cure temperatures of 100, 120 and 160 °C and pressures of

5 and 10 psi for both uniaxial and biaxial fibers.

183

Figure 5.33: The change in volume due to resin shrinkage during cure measured by

dilatometry at cure temperatures of 100, 120 and 160 °C and pressures of 5 and 10 psi

for both uniaxial and biaxial fibers. The scaling chosen is appropriate for the precision

of the measurement.

184

V.9 Fluorinated Amine Curing Agents

The eight fluoroanilines described in Chapter 1 were used in conjunction with the

aliphatic amine to cure the DGEBA epoxy and were evaluated for wear resistance and

physical properties, as well as verification of cure state. The results of wear testing,

shown in Figure 5.34, imply that the formulations with 2- and 3-fluoroamine and 3,5

difluoroaniline reduce the wear rate of the epoxy, namely the depth of the probe as a

function of the number of passes was less than that of the unmodified epoxy.

0

50

100

150

200

250

300

350

0 100 200 300 400 500 600 700 800 900 1000

Distance and Number of Passes (mm)

Prob

e D

epth

(nm

)

2,6 difluoro

3,5 trifloromethyl

4 fluoro

3,4 difluoro

2 fluoro

3 fluoro3,5 difluoro

Base Epoxy

Figure 5.34: Results of tribological wear testing for various fluorinated amines. The

probe depth as a function of distance across the 100 mm test area (0 – 100 mm is first

pass, 101 – 200 is second pass on same area) is shown for each compound.

185

Since physical properties unrelated to the presence of fluorine groups, such as

degree of cure and hardness, may also affect the wear properties, the storage moduli

and frequency dependence of the tan δs of the formulations were measured and

activation energies calculated to compare to the unmodified cured epoxy. The storage

modulus of the unmodified epoxy at 1 Hz is 4.7E7 Pa, with the peak in tan δ occurring

at 52°C, as shown in Figure 5.35. The corresponding frequency dependent activation

energy is 317.8 kJ/mol, as shown in Figure 5.36.

The storage modulus of the 2-fluoroaniline-cured epoxy at 1 Hz is 8.0E7 Pa, with

the peak in tan δ occurring at 38°C, as shown in Figure 5.37. The corresponding

frequency dependent activation energy is 224.2 kJ/mol, as shown in Figure 5.38.

The storage modulus of the 3-fluoroaniline-cured epoxy at 1 Hz is 5.0E8 Pa, with

the peak in tan δ occurring at 46°C, as shown in Figure 5.39. The corresponding


The storage modulus of the 3,5 difluoroaniline-cured epoxy at 1 Hz is 6.0E8 Pa,

with the peak in tan δ occurring at 48°C, as shown in Figure 5.41. The corresponding


In the three formulations, the storage moduli increased, the Tgs indicated by

peak in tan δ decreased and the activation energies of the transitions changed. The

storage modulus for the 2-fluoroaniline formulation increased by a small amount, while

the other two increased by an order of magnitude. This is expected, since the

incorporation of aromatic rings will make the network more rigid. The decrease in Tgs

186

and lower activation energies are likely due to the lower amine functionality, resulting in

lower degree of crosslinking.

Tem p Cel807060504030

E' Pa

1.0E+04

8.0E+08

tanD

600

500

400

300

200

100

0

E" Pa

1.0E+04

8.0E+09

Storage Modulus

Loss Modulus

tan Delta

0

Figure 5.35: DMA frequency scan of unmodified epoxy showing storage and loss

moduli for various frequencies, as well as the corresponding tan δs.

Figure 5.36: Activation energy of unmodified epoxy

calculated from frequency dependence of tan δ.

187

Temp Cel100.080.060.040.0

E' Pa

1.0E+04

8.0E+08

tanD

500.00

400.00

300.00

200.00

100.00

E" Pa

1.0E+01

8.0E+08

Storage Modulus

Loss Modulus

Tan Delta

Figure 5.37: DMA frequency scan of 2-fluoroaniline-cured epoxy showing storage

and loss moduli for various frequencies, as well as the corresponding tan δs.

Figure 5.38: Activation energy of 2-fluoroaniline-cured epoxy


188

Temp Cel80.0070.0060.0050.0040.0030.00

E' Pa

1.0E+04

8.0E+08

tanD

600.00

500.00

400.00

300.00

200.00

100.00

0.00

E" Pa

1.0E+04

8.0E+08Storage Modulus

Loss Modulus

Tan Delta

Figure 5.39: DMA frequency scan of 3-fluoroaniline-cured epoxy showing storage


Figure 5.40: Activation energy of 3-fluoroaniline-cured epoxy


189

Temp Cel100.080.060.040.0

E' Pa

1.0E+04

8.0E+08

tanD

600.00

500.00

400.00

300.00

200.00

100.00

E" Pa

1.0E+04

8.0E+08Storage Modulus

Loss Modulus

tan Delta

Figure 5.41: DMA frequency scan of 3,5 difluoroaniline-cured epoxy showing storage


Figure 5.42: Activation energy of 3,5 difluoroaniline-cured epoxy


190

Fluorinated compounds tend to phase separate in mixtures, many times

migrating to the surface of the mixture due to Gibbs function considerations. This can

be advantageous in the case of self-stratifying coatings, i.e. a small amount of

fluorinated compound migrates to the surface of the bulk compound to form a coating.

However, it can be a disadvantage if the goal of fluorination is to modify bulk

properties, as in attempts to increase bulk electrical resistance or dielectric strength.

The fluorinated aniline-cured epoxy systems were all tested by infrared scans across a

cross sectional sample to test for phase separation. The distribution of fluorine groups

was determined to be equivalent across the entire cross section, which means that

there was no phase separation or migration of the fluorine functional groups. The most

likely explanation for the lack of phase separation is that the viscosity increases and the

network forms faster than the fluorinated anilines can migrate. Also, since the

fluoroanilines are aromatic amines, with a highly electronegative fluorine group, the

amine group will be much more reactive than the nonfluorinated aliphatic amine. The

fluoroaniline should react quickly with the epoxy monomers, thus rapidly increase in

molecular weight and quickly bond to the growing network through crosslinking.

191

V.10 Abbreviations and Acronyms



DMA Dynamic Mechanical Analysis




TMDSC Temperature-Modulated Differential Scanning Calorimetry

TSD Thermally Stimulated Depolarization


V.11 Symbols

C Celsius (degrees Celsius)

Cp Specific Heat Capacity

g grams

J Joules

k rate constant

K Kelvin

min minutes

mm milimeters

mol mole (6.02 X 1023 molecules)

nm nanometers

t time

192

T temperature

Tg glass transition temperature

α degree of conversion

V.12 References

1 H.K. Soni, V.S. Patel and R.G. Patel, Thermoch. Acta, 196 (1992) 327.

2 M.E. Ryan and A. Dutta, Polymer, 20 (1979) 203.


4 M. Opalicki, J.M. Kenny and L. Nicolais, J. Appl. Polymer Sci., 61 (1996) 1025.

5 F.E. Arnold and S. Thomas, Inter. SAMPE Tech. Conf., 28 (1996).


Soc., 22 (1981) 224.


8 F. Severini, R. Gallo and R. Marullo, J. Thermal Anal., 25 (1982) 515.

9 T.H. Grentzer, R.M. Holsworth, T. Provder and S. Kline, Polymer Prepr. Am. Chem.

Soc., 22 (1981) 318.

10 L.J. Taylor and S.W. Watson, Anal. Chem., 42 (1970) 297.

11 O.R. Abolafia, Proc. Ann. Tech. Conf. Soc. Plast. Engrs., 15 (1969) 610.


193

CHAPTER VI

CONCLUSIONS

VI.1 Summary

Mechanistic models are not applicable to most industrial prepregs, especially

complex systems like the ion-initiated 4,4’-diaminodiphenylsulfone (DDS)-cured

tetraglycidyl 4,4-diaminodiphenyl methane (TGDDM) studied here. These models

require knowledge of the initial concentrations of all components including impurities

and of all steps in the reaction. The simplified mechanistic model for TGDDM/DDS

proposed by Horie considers four reaction steps, which have four different rate

constants and eight variables. Obviously, fitting an experimental curve to a four term,

eight variable equation is meaningless unless each step can be modeled separately.

Phenomenological models monitor property changes during the overall curing

reaction and have the advantage of not requiring detailed knowledge of concentrations

or reaction mechanisms. The property changes as a function of curing studied were the

heat of reaction, shift in glass transition temperature (Tg), viscosity and thermal

stability. These changes were related to the rate and degree of the curing reaction.

The heat of reaction was studied as the change in enthalpy using differential

scanning calorimetry (DSC) in both isothermal and dynamic measurements. Both

isothermal and multiscan measurements produce similar values of activation energy

consistent with values reported in the literature. Single scan experiments produced

higher values of activation energy; however, this result is expected and is consistent

with both theory of the technique and with similar studies in the literature. While

194

isothermal and multiscan DSC results are both consistent, the multiscan technique is

more attractive for industrial applications due to the much shorter time to complete the

series of experiments.

The Tg change during the reaction was studied by DSC with the final Tg of each

curing temperature determined by thermally stimulated depolarization (TSD) due to

limited resolution of DSC at very high crosslink densities. The ultimate Tg at full or

maximum cure was determined by thermomechanical analysis (TMA) and dynamic

mechanical analysis (DMA). DSC is advantageous due to the small sample size and

temperature accuracy; however, it has low sensitivity at high degrees of crosslinking

and high filler levels due to heat capacity effects. Although they have lower

temperature accuracy due to the furnace size, TSD, TMA and DMA are more sensitive to

the Tg at high degrees of crosslinking. In addition, the pressure dependence of TMA

and frequency dependence of DMA must be considered. Standard values for pressure

in TMA and DMA, frequency in DMA and scanning rate in DSC have been established by

organizations like the American Society of Testing and Materials (ASTM) to ensure

consistency in reported values. The Tg shift was modeled using the shift factor based

on the time-temperature superposition principle. The value of activation energy was

slightly higher than the heat of reaction values, but within the range of values in the

literature. This could be due to the use of Tg by onset rather than the standard half

height shift in baseline heat flow. The use of high heating rate DSC solves these

problems by allowing the half height shift Tg to be calculated without the usual

195

interference from the overlapping curing exotherm, in addition to offering much faster

Tg series measurements from a single sample on a single program.

The cure-dependent viscosity, chemoviscosity, was monitored by DMA. Two

methods were used – shift factor and time to minimum viscosity. The shift factor was

determined by comparing a series of isothermal 3-point bending experiments. The

calculated activation energy was lower than expected, possibly due to the limitations of

using a bulk phenomenological property to monitor molecular changes. The time to

minimum viscosity was determined for a series of temperatures using isothermal

parallel plate experiments. This comparison produces a viscosity activation energy

which is related to but not equal to the kinetic activation energy - the value calculated

in the other techniques. Although this value is representative of the changes occurring

during curing, it can not be easily compared to the results of other methods. The result

of the minimum viscosity measurements is also limited by the resolution of low

viscosities in DMA.

Thermal stability of the prepreg was determined by thermogravimetric analysis

(TGA) using the variable scanning rate technique. The calculated value of activation

energy is much higher than obtained by other techniques and than the literature values,

implying that the thermal stability is not directly proportional to the degree of cure.

Cure kinetics is described accurately using isothermal and multiscan heat of

reaction by DSC and glass transition shift by DSC. Chemoviscosity shift factor produces

acceptable results while single scan DSC should only be used as an estimation

technique with expected high results. Thermal stability results are exceptionally high

196

and should not be used with this epoxy system, unless an appropriate relationship can

be established. Likewise, the minimum viscosity results require an appropriate

relationship to curing to be useful in models.

While the cure kinetics are important, other effects not described by the models

are important in processing, namely gelation and vitrification. These effects, along with

cure kinetic information are effectively presented in a time-temperature-transformation

(TTT) diagram or a continuous heating transformation (CHT) diagram. Gelation is

determined by DMA with parallel plate exhibiting greater sensitivity than 3-point

bending. Vitrification is both a thermodynamic transition and a mechanical effect and

appears in temperature-modulated DSC (TMDSC) and Step Scan DSC as well as DMA

3-point bending isotherms.

In a processing environment, shrinkage is also an important consideration. The

shrinkage due to curing as well as that due to pressure induced void elimination and

fiber rearrangement was characterized. While curing causes some shrinkage, the

largest dimensional change is due to voids and fiber rearrangement. The void

elimination, and especially the fiber rearrangement was dependent on the curing

temperature and the pressure applied, while the shrinkage due to curing was not. The

quartz dilatometer cell with alumina as a confining fluid produced consistent and

reliable data.

Attempts to produce an economical wear-resistant coating material from

commercial DGEBA and fluorinated amines produced promising results. Wear

resistance was increased in three of the seven formulations, while the goal of

197

commercially available, economical additives was maintained – each fluoroaniline was

added to the epoxy as a curing agent, just like any other amine, so no added

complications in processing. The three promising formulations were 2-fluoroaniline, 3-

fluoroaniline and 3,5 difluoroaniline.

VI.2 Recommendations

• Multiscan DSC is attractive in industrial settings due to the accuracy of results and

the short time to complete the series of experiments.

• Isothermal DSC and Tg shift methods provide accurate results; however, both are

time consuming and the isothermal method is limited to low curing temperatures

due to lost data during the heating step. These limitations can be compensated for

by recent advances. Isothermal DSC should be performed using high heating rate

DSC (500 °C/min) to avoid reactions during the ramp to isothermal temperature.

The Tg shift measurements should be done with high heating rate DSC, so that one

sample can be rapidly scanned for Tg, then quenched before any curing takes place,

then ramped to the isotherm, cured for a predetermined amount of time, quenched,

then rescanned for Tg, and so on. This way, one sample and one program series

determines all the points for one isothermal curing line.

• DSC is an efficient method for determining the Tg values during the multiple

experiments required for the shift model due to the small sample size (5 – 10 mg)

and accuracy (+0.01 °C); however, resolution decreases with increasing crosslink

density. High heating rate DSC increases efficiency of data generation.

198

• Ultimate Tg is well resolved using TSD and DMA, extending the range from DSC

alone.

• The viscosity shift factor models the reaction; however, the minimum viscosity

model is limited by the simplicity of the model (and assumptions) and the limitations

of measuring low viscosities using parallel plate DMA.

• Gelation and vitrification are well resolved in DMA with a strong fixture dependence:

parallel plate is more sensitive to gelation with three-point bending sensitive to

vitrification.

• The time-temperature-transformation (TTT) and continuous heating transformation

(CHT) diagrams provide useful processing information in a graphical format making

it well-suited in industrial applications.

• Shrinkage due to chemical curing as well as that due to pressure dependent void

elimination and fiber rearrangement can be easily determined from a quartz

dilatometer measured with a TMA.

• Wear resistance of an epoxy can be economically increased by using a fluorinated

aniline curing agent.

VI.3 Suggestions for Future Work

• Residual enthalpy DSC or high heating rate DSC measurements would eliminate the

error in the lost area approximation in isothermal measurements and provide Tg

values in the same scan, thus allowing construction of both enthalpy and Tg models

in the same experiment.

199

• TMDSC and Step Scan DSC would also allow measurement of both residual enthalpy

and Tg simultaneously with the added benefit of separation of the signals for

improved resolution.

• Minimum viscosity measurements could be improved through the use of a technique

sensitive to low viscosity like shear rheometry.

• Shrinkage measurements could be improved by using a higher force TMA and a

steel or invar dilatometer cell to simulate pressures closer to those used in

compression molding.

• The preliminary attempts to fluorinate a commercial DGEBA epoxy resin with

fluorinated amine curing agents should be explored further – the cure state,

modulus and tribological properties should all be coordinated to ensure that the

effects seen in tribological experiments are actually due to the fluorination and not

the physical state.

200

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characterization of cure kinetics and physical...

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