Crosslinked Epoxies: Proceedings of the 9th Discussion Conference Prague, Czechoslovakia, July 14–17, 1986 9783110867381, 9783110108248

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Crosslinked Epoxies

Crosslinked Epoxies Proceedings of the 9th Discussion Conference Prague, Czechoslovakia, July 14 -17,1986 Editors Blahoslav Sedläcek • Jaroslav Kahovec

W G DE

Walter de Gruyter • Berlin • New York 1987

Editors

Blahoslav Sedld5ek, PhD.,DSc. Jaroslav Kahovec, PhD. Institute of Macromolecular Chemistry Czechoslovak Academy of Sciences Heyrovsky sq. 2 CS-162 06 Prague 616 Czechoslovakia

Library of Congress Cataloging in Publication Data Crosslinked epoxies. Bibliography: p. Includes indexes. 1. Epoxy resins-Congresses. I. SedlàCek, B. (Blahoslav) TP1180.E6C76 1987 668.4'226 87-8838 ISBN 0-89925-401-2 (U.S.)

CIP-Kurztitelaufnahme der Deutschen Bibliothek Crosslinked epoxies : Prague, Czechoslovakia, July 14-17,1986 / ed. Blahoslav Sedlàòek. - Berlin ; New York : de Gruyter, 1987. (Proceedings of the ... discussion conference / Institute of Macromolecular Chemistry ; 9) ISBN 3-11-010824-0 NE: Sedlàcek, Blahoslav [Hrsg.]; Ùstav Makromolekulàrni Chemie : Proceedings of the . . .

Copyright © 1987 by Walter de Gruyter & Co., Berlin 30. All rights reserved, including those of translation into foreign languages. No part of this book may be reproduced in any form - by photoprint, microfilm or any other means nor transmitted nor translated into a machine language without written permission from the publisher. Printing: Gerike GmbH, Berlin. Binding: Dieter Mikolai, Berlin. - Printed in Germany.

DEDICATED TO PROFESSOR MANFRED GORDON ON THE OCCASION OF HIS 70TH BIRTHDAY

PREFACE

Crosslinked epoxies are modern epoxy materials (resins and composites) , highly suitable for a variety of applications, which are frequently used in extreme conditions. This is a short, insufficient characterization of the materials and processes discussed at the 9th Discussion Conference as part of the 1986 Prague Meetings on Macromolecules. The Conference was organized by the Institute of Macromolecular Chemistry, Prague (V. Kubanek, Director, and P. Cefelin, PMM Chairman) under the sponsorship of IUPAC, the Czechoslovak Academy of Sciences and the Czechoslovak Chemical Society. The scientific programme of the Conference was prepared by K. Du§ek (Chairman) and the following members: E.M. Pierce, I. Havlifiek, J. Hrouz, M. Ilavsk£, J. Kolafik, L. MatSjka, and M. Raab. This volume consists of 55 papers based on special lectures and selected posters presented at the Conference. Its scope was delimited by 11 Conference topics, including nearly all the modern aspects of the synthesis, mechanism and kinetics of curing, network formation, chemical and physical properties and their changes, characterization of processes (diffusion, curing, ageing, mobility in resins, etc.), and application of epoxy resins and composites. All the accepted papers have been divided up into five chapters, the titles of which characterize the scope of each chapter: 1. New Epoxy Resins and Curing Systems; 2. Mechanism and Kinetics of Curing Reactions; 3. Network Build-up in Curing; 4. Structure and Properties of Resins - Curing, Ageing and Phase Separation; 5. Material Properties and Applications of Cured Resins and Composites. The individual papers vary in conception and aim: Some of them are theoretical, others experimental or applied; there are original papers and survey articles; there are also evaluations of scientific methods, instrumentation and economic aspects in some papers. In spite of the complex character of numerous papers, the division into chapters, used together with the Contents, Author Index and Subject Index, should allow the reader to find easily a required paper.

VIII I would like to express my warm thanks to all the authors who contributed to this volume for their efficient cooperation, permament effort and mutual understanding. When working together with the de Gruyter Publishers I always appreciate very much their careful and precise work. My sincere thanks. Prague, January 1987

Blahoslav Sedldfiek PMM Editor

CONTENTS

NEW EPOXY RESINS AND CURING SYSTEMS Epoxy/Episulfide Resins

3

J.P. Bell and W.H. Ku Photoinitiated Cationic Polymerization; a Study to the Polymerization and Molecular Mobility of Polyepoxide Networks Using Phosphorescence Spectroscopy

27

E.W. Meijer and R.J.M. Zwiers Interaction of Oligocarbodiimides with Oligoepoxides and Chemical Structure of the Resulting Crosslinked Polymers

41

V.A. Pankratov, Ts.M. Frenkel, A.M. Fainleib and V.V. Korshak Telechelic Prepolymers of DGEBA and Primary Monoamines

....

47

....

55

J. Klee, H.-H. HOrhold and W. Tanzer Investigation on Dithiol/DGEBA Addition Polymerization E. Klemm, H.-J. Flammersheim and H.-H. Horhold Transport Properties of Epoxide Prepolymers

61

J.V. Alemán, J.L. García-Fierro, R. Legross and J.P. Lesbats Preparation and Reactivity of Thiiranes

73

M. Vecera and V. Spacek Quality and Properties of N,N,N;n'-Tetraglycidyl-4,4'Diaminodiphenylmethane I. Dobás, S. Luñák, S. Podzimek, M. Mach and V. Spacek

81

X MECHANISM AND KINETICS OF CURING REACTIONS Kinetics of Photoinitiated Cationic Epoxide Polymerizations by Differential Calorimetry (1)

93

A.R. Shultz and L.D. Stang Kinetics and Mechanism of the Anhydride Curing of a 117

Diglycidyl Ester B. Steinmann Reactivity and Reaction Kinetics of 0- and N-Epoxy Groups towards Aromatic Amines in the Molten State

131

M.F. Grenier-Loustalot and P. Grenier Mechanism of Reaction and Processing Properties Relationships for Dicyandiamide Cured Epoxy Resins

14 7

Y.G. Lin, J. Galy, H. Sautereau and J.P. Pascault The Effect of the Prepolymer Structure on the Cure Kinetics of Epoxy-Amine Networks

169

J. Galy, J.P. Pascault and M.F. GrenierLoustalot Curing of Epoxy Resins with Piperidine

179

T.R. Cuadrado, A. Almaraz and R.J.J. Williams Characterization of Partially Cured Epoxy Resins by Thermomechanical Analysis

189

I. Antal A NMR Study of the Kinetics of Epoxy/Amine Reactions

203

J. Borbely and T. Kelen Quantitative Structural Investigation of an Epoxy Network by FT/IR and

13

C Solid State NMR Spectroscopy

213

J. Ancelle, A.J. Attias, B. Bloch, C. Cavalli, B. Jasse, F. Laupretre and L. Monnerie Curing Mechanism of Epoxides with Imidazoles, Studied by DSC, LC and NMR H.J.L. Bressers and L. Goumans

223

XI

Network Formation in the Curing of Epoxy Resins: A Comparison of the Curing of Bisphenol A Diglycidyl Ether and Polyepoxides Based on N,N-Diglycidylaniline

231

L. Matejka and K. Dusek Mechanism and Kinetics of the Reaction between Diglycidylaniline and Aromatic Amines

241

L. MatSjka, S. Pokorny and K. Dusek

NETWORK BUILD-UP IN CURING Structural and Rheological Changes During Epoxy-Amine Crosslinking

253

S.A. Bidstrup and C.W. Macosko Formation and Structure of Networks from Poly(oxypropylene) Polyamines and Diglycidyl Ether of Bisphenol A. I. Theory

269

K. Dusek, M. Ilavsky and S. Lunik, Jr. Formation and Structure of Networks from Poly(oxypropylene) Polyamines and Diglycidyl Ether of Bisphenol A. II. Reactivity of Amino Groups, Gelation, Sol Fraction and Equilibrium Modulus

279

K. Dusek, M. Ilavsk^, 5. Stokrovi, M. Matejka and S. Lunik Kinetics and Statistics of the Formation of EpoxyAmine Networks with Simultaneous Etherification

291

C.C. Riccardi and R.J.J. Williams Dynamics of Cure and Phase Separation in Chain Extended Epoxy Systems

311

H.N. Nae Theory of Elastic Properties of Heterogeneous Compressible Networks S.A. Patlazhan

325

XII

Properties and Structure of Networks Based on Epoxy 339

Resins M.A. Markevich, V.I. Irzhak and E.V. Prut The Structure and Properties of Networks Prepared from Tetraepoxide and Carboxyl-Terminated Polybutadienes

34 7

M. Ilarsky, J. Hrouz, K. Dusek, J. Nedbal and P. Vanëk

STRUCTURE

AND

AND P H A S E

SEPARATION

PROPERTIES

OF

RESINS

-

CURING,

AGEING

Relaxation Features of Crosslinked Epoxy Polymers

359

V.I. Irzhak, V.M. Lantsov and B.A. Rozenberg Mechanical and Physical Properties of Epoxy Matrices as a Function of the Degree of Cure

373

A. Noordam, J.J.M.H. Wintraecken and G. Walton The Water Absorption of Model Epoxy Resin Networks Cured with Aromatic Amines

391

K.A. Hodd, C.H. Lau and W.W. Wright Deformation and Fracture of Highly Crosslinked Epoxy-Aromatic Amine Networks

407

0.P. Erina, L.K. Pakhomova and A.A. Berlin Kinetics of Curing Reaction of Epoxy-Amine Systems in the Glass Transition Region. A Theoretical Approach

417

1. Havlicek and K. Dusek Vertical Shift in the Time-Temperature Superposition Observed in the Viscoelastic Behaviour of Epoxy-Amine Networks

425

M. Ilavsky, J. Hrouz and I. Havlicek The Viscoelastic Behaviour of Diepoxide-Diamine and Diepoxide-Triamine Networks M. Ilavsk^, A. Havranek, J. Hrouz, S. Lundk Jr. and K. Dusek

433

XIII

Influence of Phase Structure on the Mechanical Properties of Rubber-Modified Epoxies

443

A.I. Krasheninnikov, A.M. Ternovykh, M.O. Slobodchikov and V.S. Karetnikov Curing Degree Effect on the Ageing of Epoxy Polymer Adhesion Joints

451

Yu.A. Gorbatkina, N.K. Shaidurova and V.G. Ivanova-Mumzhieva Effect of Hydrothermal Aging on the Mechanical Properties of Epoxy Composites

459

R.J.A. Shalash and E.A. Sarah Rheological Behaviour of the TGMDA-DDS System During Isothermal Curing - Influence of Temperature

471

D. Serrano and D. Harran Chemorheological Method for the Characterization of Epoxy Resins

479

V. Liska Influence of Water on Some Properties of Epoxy Composites: Compressive Strength and Hardness of Matrix

487 A. Rudnicki

Influence od Dibutyl Phthalate upon Some Properties of an Epoxy-Novolak Block Copolymer

49 3

T.S. Gancheva, L.T. Bizheva and S.I. Lambov

MATERIALS PROPERTIES AND APPLICATIONS OF CURED RESINS AND COMPOSITES Epoxy/Aramid-Fibre-Based High-Grade Composites

501

H. Hacker, K.-R. Hauschildt and D. Wilhelm Epoxy-Rolivsan Compositions - Thermally Stable Binders for Reinforced Plastics B.A. Zaitsev, R.F. Kiseleva and S.L. Garkavi

517

XIV

The Effect of Polymer Binder Properties on the Strength of Fibre Reinforced Plastics N.A. Snigireva, S.M. Bazhenov, A.M. Kuperman and E.S. Zelenskii

525

Some Physical Properties of Epoxy Resin/Phenolic Microsphere Composites D. Zuchowska and W. Szczubiala

533

Dielectric Properties of ATBN/Epoxy Blends G. Levita, C. Domenici and A. Marchetti

541

Mechanical Properties of the Electronic Epoxy Moulding Compounds

549

L.K. Kostanski, A. Drotlew, W. Krôlikowski and E. Fabrycy Determination of the Stability of Epoxy Systems for Encapsulation of Microelectronic Packages

557

J. Birtovà, K. Bily and P. Marek Polyester Powder Coatings Crosslinked with Epoxies

563

B.J.R. Scholtens, R. van der Linde and E.G. Belder Temperature Dependence of the Adhesion Strength of Compositions of Metals with Rubber-Modified Epoxies

569

M.O. Slobodchikov, R.A. Bychkov, A.M. Ternovykh and S.S. Trushakov Mechanical Properties of Epoxy/Quartz Composites

577

J. Kolarik, V. Jelinek and F. Lednicky Mechanical Behaviour of Plasticized Epoxy Polymers

585

A.G. Farrakhov and V.G. Khozin Petroleum Components as Inhibitors for Crosslinked Polymers G.F. Bolshakov, A.A. Sidorenko, V.V. Uglev and T.V. Vasilchenko

591

XV

Use of Surfactants to Improve Stress-Strain Properties of Epoxy Polymers and Compatibility of Petroleum Stabilizers G.F. Bolshakov and Yu.P. Belousov

599

AUTHOR

607

SUBJECT

INDEX INDEX

609

ABBREVIATIONS

625

NEW EPOXY RESINS AND CURING SYSTEMS

EPOXY/EPISULFIDE

J.

P. B e l l

RESINS

and W. H. Ku

Chemical Engineering Department U - 1 3 9 , U n i v e r s i t y of C o n n e c t i c u t ,

and Polymer Science S t o r r s , CT 0 6 2 6 8 , USA

Program,

Abstract Mixtures

of

provide

epoxy

stable

polyamide minutes

curing at

evolved.

and

episulfide

liquids

at

agent,

room

room

these

two g l a s s

analysis,

lower

water

The m e c h a n i s m of

episulfide,

epoxide

kinetics

the

of

determined.

epoxy-amine data

and

2)

predict

experimental

two

absorption, amine

groups

primary

formulated

When

mixed

gel

rapidly,

low

amount

regions, and

attack

by

of

epoxide

structures,

in

by

heat

dynamic

attractive a series

and

1)

the

a

2-10

of

compounds.

examined,

proceeds

and

via

to

with of

other

model

also

reaction

been

was s t u d i e d

were

anionic

o"n e p i s u l f i d e

very

transition

reaction

steps The

reaction,

ion

a

secondary

various

have

mixtures

with

has

properties.

sulfide

resin

temperature,

The p r o d u c t

mechanical

constants

resins

temperature.

The

the

the

rate normal

rather

stable

The

kinetic

groups. consistent

with

the

observations.

I n t r o d u c t i on Episulfide resins,

resins

such

with

the

the

epoxy

as

of

1) at

the

properties

comparable resins

have

to

atoms

to the

to

DGEBA

curing

resin these

those

of

no o d o r ,

structure

ether

of

replaced has

reaction is

their

epoxy

and p h y s i c a l l y

it

standard

a

was

of

amines

(1),

2)

appear

analogs

proceeds the

(3,4).

than

Crosslinked Epoxies © 1987 Walter de Gruyter & Co. • Berlin • New York - Printed in Germany

the

(2,3),

3)

than

or

better The

much

tendency

higher

a p p e a r much l i k e

of

important

synthesized

resins

but

The c h a n g e

number

with

epoxy

A(DGEBA),

sulfur.

significantly

from w h i c h episulfide

to

bisphenol

with

low t e m p e r a t u r e

crystallize

of

in

sulfur

relatively

episulfide

corresponding

similar

diglycidyl

oxygen

oxygens

rapidly

the

the

oxirane

consequences: more

appear

episulfide

their

DGEBA

4

cousins

except

for

some

improved

properties

which

we

shall

discuss

the

1960's,

below. Although

reported

episulfides may

be

few

and

have

at

purifying a

are

the

has

Recently

Ku

molecular

and

weight

can

be

improvements (4) w i t h i n is

for

data

are

the

(1)

the

at 92

inexpensive This

and

have

C, and y e t in

This in

cures

in

synthesizing epoxide

synthesis

related

described

were

route

synthesis

mixture

the

mixed

with

formulation

has

The

for

the

of

via

routes

effect be

curing of the

curing,

a

liquid Further

by

Fernandez

present

which

epoxies.

usual

inhibiting

as

agent.

purpose of

than

of

used

described

normal

formulating

wider

been

mechanism

as

of

may

liquid

have

few m o n t h s . the

a

a method blend

This

that

discuss

time.

difficulties

4-11).

episulfide/epoxy

episulfides

that

the

corresponding

such the

in

Difficulties

distribution.

last

to

from

since

to

which melts

simple,

(2,

an

readily in

the

primarily

same

a

patents

part,

temperature.

but

Bell

and

attention

in

episulfide

into

crystallization, which

solid

elsewhere

episulfide

little least

demonstrated.

been

described

the

at

room

deterrent,

thiourea

literature

received

a crystalline

minutes

also

both

attributed,

handling a

in

is

Some

report not

the

property

given.

Experimental Materi als The

following

curing

materials

reaction

kinetics

below

available

Epon

were

epoxy-episul fide are

828

A

of

used

system

this

new

for

and

the

for

system.

from m a n u f a c t u r e r s

(conventional

DGEBA

resin

development the The

in t h e

from

Shell

T3 CH 3 n = 0.2;

gram

N

equivalent

a

reagents

of

Chemical

Co.).

A

CH3 weight

=

rapid the

described

U.S.A.

T3 IH

of

measurement

189

5 Versamid Chemi cal

140 ( p o l y a m i d e Co.).

curing

agent

from

Miller

Stephenson

0 (CK^CNHCHp-^HR CH 0 /\ , . CH CH(CH^CNHCHp^HR CH^CHCH^CHiC^CHj (ÔVJPH,

Epon

836

resin

(viscous

has

the

same

gram

equivalent

Epon

1001

material gram

equivalent

is

DGEBA

the

resin

structure

weight

(solid has

DGEBA

as

Epon

from

structure

weight

Shell

Chemical

828

but

Co.).

with

n=

This

0.4,

and

the

312.

resin

same

from

is

Shell as

Chemical

Epon

828

Co.).

with

Thi s

n=0.6,

and

the

500.

N-methylbenzothiazol-2-thione

(99%

purity

from

Aldrich

Chemical

Co.)

CH, I

Pi e t h y l e n e t r i a m i n e

(technical

3

grade,

from J. T. Baker

Chemical

Co.) . 2,3-Epoxypropyl

p-methoxyphenyl

ether

(99%, from

Aldrich

Chemical

Co.) 0 CH3-0-@-0-CH2-CH-CH2

Dibutylamine

(99%, from

Aldrich

Synthesis

of d i e p i s u l f i d e

The

data

in

828

(a

Although

DGEBA

this

paper

resin),

the m o r e

from

was

with

recent

Chemical

Epon

Co.)

828

obtained

by

reaction

of

Shell's

N-methylbenzothiazol-2-thione

synthesis

route

from

Epon

828

Epon

(NMBTT). and

6 thiourea

is m o r e

comparable spectra,

in

and

economical,

terms

in

a 250 100

separatory

of

CH^Cl ^

containing carried

out

minutes. flask of

and

with

liquid The

was

viscous

(MeOHiH^O washing, then the

but

was

washed

with was

the

crystallize tweezers, Scanning

easily, and

by

form it

the

Calorimetry.

was

sample The

approximately

same

procedures

for the

The

g.

are NMR

(22 C)

trif1uoroacetate a very

form

was

thirty

into

The

the

to

for

added

828

flask

reaction

CF^COOH

of

Epon

bottom

o

then

by m e a n s

50 ml

the

addition

appearance

in

formation

of

formed

a Buchner

during

funnel.

viscous,

of m i x e d

a

Buchner

The

yellowish

it,

crystals. stirred was

with

product

was

The

the then

of

by

dried

was

purity

of

down

to

it

sample

tips

retested

during

solid

The

cooling the

mixture

formed

times.

then When

then

solvent

which

funnel.

several

of 2 , 3 - E p i t h i o p r o p y 1

the

the

mixture

Synthesis

followed

14.5

for 3 h o u r s .

melting

was

Almost

was

precipitate,

with

The y i e l d

were

spectra,

round

initiated

with

white

solvent

to

routes

purification.

out

checked

temperature

also

washed

filtered

stirred

vacuum

The

g)

neutralized

out

a

CH CI . 2 2 temperature

(20

sodium

for

was

40:1).

product

room

ready

liquid

=

The

filtered

of

to

ml

room

was

mixture,

was

100

at

system

under

two

infrared

solution

slowly

carbonate only

dried

which

and

not

was

a

added

stirring sodium

product.

neutralization

funnel,

was

the e n t i r e

episulfide

curve,

the

DEPPE

NMBTT

carbonate

reaction

filtrate

g

Ground

sodium

the

13.6

from

behavior.

NMBTT

ml

ml

products

melting

chromatographic

Epon 828 From

of

the

did a

pair

not of

Differential under

vacuum.

74%.

p-Methoxyphenyl

as t h o s e

synthesis

described

of E T M E .

Ether in the

To a 600 ml

(ETME) above round

section

7 bottom

flask

(EOME) ,

5.1

CH^Cl^ After

which

contained

grams

15 m i n u t e s

of

(anhydrous

powder) first

was

dried

in

a

methanol :water collected ETME a r e

was

compounds

have

similar

resin,

and

model

peak

overlap

as

tried

for

the

showed The

appeared

900

at

any

for

sodium

carbonate

solution.

was

washed The

The

completely with

1:1

product

was

NMR s p e c t r a

polymers

are

very

are

gels

to

of

EOME and

Owing

to

model

peak

the

in

I.R.

any for

a very

short

828,

the

chosen

the

in

of

this

was

ide

study. N.M.R.

peaks

the

none

for

absorption

of

ring,

measurements,

wiir.h

and

the

identification

epoxide

ether,

episul

characteristic

complexity

the

time.

dibutylamine

compounds,

for of

in

especially

p-methoxyphenyl and Epon

the

System

soluble

spectroscopy

resolve

three

in

were

Infrared

to

not

difficult,

ether,

polarity

promise 1

ml

stirring.

Epoxy-Episulfide

respectively,

specific cm

250

while

then

times. and

2,3-epoxypropy1

and

compound.

components.

IR

system which

spectroscopy,

each

methods

Kinetics

Versamid-140,

s p e c t r o s c o p y ""were

sample

four

The

p-methoxyphenyl

structure

UV/Visible

and

and

ether

(1-3).

resin

such

the

or

30%.

analyses

epoxy-episulfide

neutralize evaporation

dried

thermosetting

instrumental

2,3-epi thi opropyl

to

three of

added

room t e m p e r a t u r e ,

The

Reaction

crosslinked

at

slowly

vacuum

oven.

shown e l s e w h e r e

solvent, Model

by

a yield

of

was

added

dried

solution

with

Determination Because

acid

reaction

vacuum

p-methoxyphenyl

N-methy1 b e n z o t h i a z o l - 2 - t h i o n e

trifluoroacetic

sample

the

of

2,3-epoxypropyl

above

of

which also

the

usually

not

very

clear. The then

near

Infrared

region

investigated

mixtures

of

solvents

such

chloride,

toluene,

base

lines.

base

line

that

limiting

reading

the

determine

model

as All

is

to

over

wavelength,

a

2,500nm

three

be

the

a very

The f o l l o w i n g

for

range

unstable Table

of

the

the

for

Several methylene

stability

except

CC1 ^ ,

wavelength.

vibration

shows

was

peaks

chloroform,

wavelength

entire

l,100nm)

resolved.

were e x a m i n e d

limiting

to

particular

could

tetrachloride,

and m e t h a n o l showed

from

if

compounds

carbon

stable

occurred.

(wavelength

and

limiting

of

whose Above

off-scale

8 wavelength

for

the

solvents

which

Solvent

were

Limiting good

over

examined:

Wavelength

(nm)

the

range

entire

2,350 2,200 Toluene

2,100

ch3OH

2,000

Although

CC1 ^

measurements, CCl^ we

forced

did

us

ring, and

limiting

The

following

(1)

Sample

for

respectively.

CCl^.

(Sample

for

g ml

of

Sample

2,3-epoxypropyl

of

of

0.337

ml

were

of

ring,

2,238nm,

located

under

(2,350nm). A,B,C),

were

prepared

for

the

p-methoxyphenyl

ether

dibutylamine

of

2,3-epithiopropyl

of

of

Sample

p-methoxyphenyl

ether

dibutylamine

chloroform C:

0.364

g of

2 ,3-epoxypropy 1 p-methoxyphenyl

0.394

g

2,3-epithiopropyl

0.337

ml

l,450nm,

episulfide

peaks

in

Fortunately,

B: g

scanning

I.R.

chloroform

0.394

Cary

near compounds

wavelengths

These

chloroform

samples

of

peaks at

amine

the

model

instead

characteristic

of

for the

A:

0.337

2.65 The

three

chloroform

secondary

wavelength

0.364

3 ml (3)

three and

solvent

problem

measurements:

3 ml (2)

excellent

choose

l,543nm,

the

kinetic

an

solubility

to

observe

epoxide 2,206nm

is the

of of

ml

of

17D

was

ether

dibutylamine chloroform

Spectrophotometer

from

ether

p-methoxyphenyl

wavelength used

(Varian

2,300nm

measuring

2,100nm

to

record

secondary

amine.

Two

1

pathlength,

epoxide

and

Beckman

instruments),

and

the

sample

the

Cary

17D.

were The

the

to

cm

in

placed

in

experiment

the was

absorption

sample once

from

peak

rectangular

run

Instrument

and

of

quartz

containing and

10-30

to

episulfide, cells the

reference

every

Co.),

l,600nm

(from solvent

holder

minutes

of at

9 the

beginning

reaction

went

absorption A

duPont

of

Other The

then

The

determined

resolver

was After

concentration

every

base

from

6-12

lines

to

CHCl^,

of

each

species

each

the

the

it w a s

until

the

of

reacted

separate

calibrating in

hours

for

completely

used

of the m o n o m e r s

the

samples.

epoxy

and

spectrophotometer possible as

a

to

obtain

function

of

mixture

to

time.

Procedures procedures

yield and

and

completion.

absorptions. the

reaction

reaction,

were

curve

solutions

plots

in

to

peaks

episulfide with

of the

a

for

liquid,

procedures another

formulating

gel

for

of t h e

time

the

epoxy-episulfide

measurements,

mixing

the

authors'

resins

rheovibron

with

publications

curing

measurements,

agent

are

given

(1).

Results Characteristics curing

agent

equivalent

of

(Versamid

curing

given

in

the

Experimental

DGEBA-type

several

hours,

applications time.

curing

have Bell

are

(1),

Typical

almost

gelation

times

minutes.

used,

the

gelation 0.8

to

(no

rate of

to

a 1:1 Fig.

the

time

first

set

are

If time 2.0

equal

in

for

gelation

of d a t a , a

pure

later

decreases

as

e q . of c u r i n g

of

DEPPE more agent

of 22

in

days.

cure.

For

of

epoxy/DEPPE C.

of

DEPPE

Two

by

Fernandez

(4).

minutes.

The

curing

DEPPE

curing

and

agent

of

Ku

sets

work

2-10

(3).

occurs

a

the

and

of

with

several

amounts

at

set

range

equivalents

used

equivalents

mix

small from

gram amino

low.

of

equivalent

the

for

number

and

free

temperature

Even

polyamide

gelation least

1.

to

When

undesirably

the

in

time

is

at

room

a

contains

episulfide), requires

with

structure

which section.

complete

identical

gelation

two

range

upon The

about in t h e

shown

effect

are

extrapolated

added

is

shown:

curing effect

(DEPPE)

a large

of d a t a

this

agent,

cure

prevents

The

agent

resin

complete

solidification

diepisulfide and

epoxy

and

cured

approximate

the

typical

Gelation

The

of

are

many

140).

systems

weight

groups,

Often

Epoxy/Episulfide

agent epoxy is

and

is are

added,

10 50.

40.

vz

30

UJ z 20 UJ (J

10 -A Q_ —

!

2

5

4

is

EPISULFIDE/EPOXIDE EQ. RATIO Figure 1 . Time for gelation as a function of the equivalents o f eplsulflde added. O Ku and B e l l , 0 Fernandez

Water

absorption.

decrease

water

properties

of

interfacial agent

One

the

dry

regions

used

in

objective

absorption,

the

in

system

from

water

present

work

optimum f o r

low water

absorption

the

agent

a

curing

examine

the

This

is

shown

with

sulfur

at

effect in

Fig.

reduces

Transi ti ons.

The

DEPPE/DGEBA/curing The

lower

found

in

structure

of

dynamic agent

absence

created

and

of

strong

the

to

is

the

protect The

rather

systems. number

research

substrates polyamide

However, by

maintaining

of

equivalents, upon of

water the

epoxy-amine

epoxy base).

is

is

the

same

under

an can

atoms

mixtures Fig.

(very these

temperature

of 3-5.

temperature

attributable

reaction

expected

The upper

for

transitions,

at

one

oxygen

data

two d i s t i n c t

not

absorption.

mechanical

it

and

curing

and

significantly.

occurs

to

hydrophilic

replacement

i.e.,

is

mechanical

absorption

DEPPE, the

conditions

retain

concentration

transition

homopolymerization without

show

of

by

epoxy

to

Partial

the water

temperature the

2.

much

diffusion.

constant DEPPE

of order

to

the

little reaction

11 o o

Figure 2. Equ1l1br1un water absorption as a function o f dleplsulfide content. transition, is the

increased

and may be due to

DEPPE-amine

mechanism

reaction.

area

temperature tan

to

can

absorb

the

be

taken

range

over

areas

under

the

given

in

approximately value

Table 30%.

methods near

temperature

the

for

energy,

showing

range,

will

as the DEPPE

content

of the D E P P E ,

be d i s c u s s e d

further

which tan The

Since

onset

as

as of

epoxy

is

and e x t e n d s

over

a

alone.

measure

this

occurs

curves area

the g l a s s

for is

lower

near which the modulus

The

of

toughness. is

the The

or

in

the

that

the

very

under

ability

by

as

the

of

the

of

the

desirable. amounts

increased

Data

of

DEPPE

much

as

occurs

over

measurements

will

give

this

is

transition, first

area

a wider

broadening

various

transition

thermomechanical the

which o v e r l a p ,

greater

the

i.e.,

1.

such

is

peaks

than

temperature are

size

homopolymerization

These

of the two t r a n s i t i o n s ,

under

range

curves

sample

in

section.

One c o n s e q u e n c e combined

o 130 C, i n c r e a s e s

at about

drops.

since

Dynamic

a broad a

the

12

20.00 Figure 3.

mechanical above and

the

70.00 12a.00 Temperature (°C)

Dynamic Mechanical Data Epoxy/Episulfide/Curing Agent equivalents: 1/0.5/1

analysis

gives

transitions

calculations

170.00

show

also a

a more

meaningful

increases

picture.

regularly

progressively

with

The

DEPPE

more

tightly

The

Damping

modulus content,

crosslinked

network. Table 1. The Epoxy-Episulfide

Relative Systems

Areas

Episul fide/Epoxide/Curing Equivalents Ratio 0 / 1 / 1 0 . 5 / 1 / 1 0.75 / 1 / 1 1 . 0 / 1 / 1 1 . 5 / 1 / 1

Under Agent

Curves

Relative (cm^)

Area

15.0 19.9 20.8 20.2 19.2

for

13

O s* a tan S

O V-, J— o o

c>> k4

0Beô4*â*à o oo o

o O o

A o

A

«

20.00

Figure 4.

Heat

Evolution.

DEPPE 155 the

The

attributes

for

that

the

expect for

would

to t h e

containing

DEPPE

associated to

leads

be l e s s to

during final

Mechanical flexural

is

far

lower cure.

mechanical

properties

modulus,

and

are e q u i v a l e n t

20

methyl

opening

for

an

internal Both

of

epoxy stress

of

these

properties. such

as

compressive to or

at

reaction,

of

with than

about

less,

DGEBA-amine

polymerization

The e n e r g y

shrinkage

observations

evolved

a typical

be e x p e c t e d

lower

and

heat the

beneficial

Properties.

remarkable

for

evolution

tensile

samples

most

heat

and are

Mechanical

is even

ring

lower

development

strength,

or

the

136 m c a l / m g .

episulfide

ring.

of

one w o u l d

methacrylate,

170.00

Dynamic Mechanical Data Epoxy/Eplsulflde/Curlng Agent equivalents: 1/1/1 One

mcal/mg,

o_ A °OOOgOOO

70.00 120.00 Temperature (°C)

polymerization

mcal/mg, than

o. E ITJ a

better

tensile strength than

the

14

ft o

N O

30.00 Figure 5. corresponding These

data

manuscript

Mechanism Model

epoxy

materials.

be

currently

found in

and K i n e t i c s

were

by

180.00

reference

of

1/1.5/1

strength

is

and

(4),

improved. in

another

preparation.

of

Polymerization

i.e., used

near

for

2,3-epoxypropyl

Sample

A was

control

which a s i m p l e

p-methoxyphenyl

the

I.R.

prepared: in

tan S

Impact

in

2,3-epithiopropy1

dibutylamine, use

A

80.00 130.00 Temperature (°C)

compounds,

the

E-

Dynamic Mechanical Data Epoxy/Eplsul fide/Curing Agent equivalents:

can

ether(EOME),

C

measurement

ring

of

spectroscopy.

a mixture

of

opening

EOME

p-methoxyphenyl ether

Three and

reaction

(ETME),

reaction

samples

dibutylamine, of

amine

and

kinetics

with

were as

a

15 epoxide

would

dibutylamine, with

to

and

ring

occurred important

A

anionic

for the

Epoxy-Amine

a

well

the

The

equal,

be

equation

rates as

a

weakly

polar

in c h l o r o f o r m

The

solvent

be lower

+

R'-NH-R'

2

Solvents too,

(see

the

The

rate

than

those

I R'

R

=

CH3-O-^O)-O-CH2-

R1

=

CH3-CH2-CH2-CH2-

of

in

attacks

which the

disappearance observed

in

the

amine

group

is

ring

to

of

and

dibutylamine

Fig.

EOME 6.

An

form

a

epoxide

approximate

an rate

is: d(A)

-

= k 1 x ( E ) x ( A)

dt

a rate c o n s t a n t , concentration

of EOME, mol I

A

=

concentration

of d i b u t y l a m i n e , mol a

t

=

reaction t i m e ,

found

samples.

R-CH-CH,-N-R'

=

k^ was

very

constants

=

1

are

solvent.

should

the which

A).

reaction

is

dt

E

upon

Chloroform

polymerization.

and

d(E)

where, k

and

I

for this system

-

ETME

reactions

kinetic

2

known

should

the

EOME,

attack

the

OH

reagent

alcohol.

of

amine of

to the kinetic data of these

0

is

of

ion

to

Temperature

affect

(Sample

\ /

nucleophilic

reaction

and

solvent.

R-CH-CH,

This

ETME

a combination

addition

B.

is

system

polar

System

opening

pair

homopolymerization

episulfide

in

polarities

for

in a strongly

the

the

study was kept at room t e m p e r a t u r e .

experimental . section) constants

C was

related

in this

especially

Sample

and

was

ring ionic

which

parameters

different

the

B

the

observed

samples

The reaction with

in

was

in

Sample

al so

c o m p o u n d ; and

dibutylamine

epoxide

found;

investigate

episulfide

episulfide and

be

I mol

-1

; ;

hours.

to be 0.042 (tmol

the kinetic data shown

*h

in Fig. 6.

*h

1

from

a logarithmic

plot

of

16

o

IO

/. Epoxide O Amine

o

E

o u

/

!•

R-CH-CH.-N-R I |

2

I ft'

ch2-ch-r

The

equilibrium

consideration

of

constant, the

K

a dissociation

dissociation constants of CH SH .5 3 1.7x10 (13), respectively. The as

,

can

constants

3

where, K w = I . O x l O " 1 4

1

estimated of

and K

fol 1ows: K - * " /

be

- 7 » f 5. 3x10

21

RSH

(CH„)„N are 3 3 v a l u e can t h e n

-l/lrfO"2

and

by R N. 3

5.3x10 be

-8

the The and

calculated

19

This

value

ionic

indicates

form.

If

reaction

most

is

the

equations

and

the

a

formed

relation

that

ammonium in

the

negligible,

concentration

and

ion

of

mercaptan

considered

concentration rate

the

is

episulfide

that

of

amine

of

system the

consumed

between are

sulfide by

the

in

reverse

episulfide

ion

dibutylamine.

The

the

listed

remains

concentration

of

below:

d(A) .

= k2x(A)x(S) dt

d ( S) .

= k2x(A)x(S)

+ k3x(SIP)x(S)

dt (SIP) where,

k^ = r a t e (A

The

value

(4)

the

lists

= (A0)

)

o

=

-

(A)

constant, initial

concentration

of

k„ i s t h e n 2 k^ v a l u e s h o u l d

the

k^ v a l u e s

mol

calculated change

with

of

to

linearly

different

dibutylamine,

be

mol

i

0.54.

According to Eq. -1/2 (SIP) . Table 2

with

reaction

time

and

(SIP).

1/2 A

plot

which that

of

with

a curve the

derived Eq.

k^

was

basic by

(3)

higher

Szwarc , is

than

existence

solvent

do

not

mixtures

ion ion

rate rate

and

fit to

The

of

with a

constant constant

(k1), (k

1

")

during

of

equation.

triple may

dimethoxyethane the

(3). of ion

was

kinetic A

pair

rate

rate

derived.

means

is

that

living

end

and

ion

(14)

and/or why

that

(k)

(k"),

for

ion with

and

an the

binary

system

triple

constant

constant

much

benzene

of of

is

studied

and

formation

apparent

This

explain

data

in

episul fide-amine

reaction

Ise

8,

reason

with

the

the

associations

found

Eq.

relation

In

Fig.

polymerization,

The

system

M.

in

line.

anionic

data.

formation

Szwarc's

and

for

the

0.001

shown

a straight

these

increased

follow

consistent

suggested

not

M.

of

is

equation

intermolecular

p o l y s t y r y l 1 i t h i um, not

instead

than

is

0.001

of

1 / (SIP)

applicable

smaller (SIP)

to

rate

does

only

the

kinetics

obtained

kinetic

concentration system,

respect

was was free

triple

20 Table t

2.

k 3 Values

(h)

for

Epi s u ! f i d e - A m i ne

(Sample

(SIP)"1/* (mol/1)"1/2

(SIP)-(AQ)-(A) (mol/I)

0.1 0.5 1.0 1.2 3.0 4.0 6.0 11.0 16.0 28.0

System

0.032 0.120 0.150 0.202 0.287 0.324 0.356 0.402 0.413 0.438

5.590 2.887 2.582 2.225 1.867 1.757 1.676 1.577 1.556 1.511

o o

IpltulfUi-talM Syatw (•upi> a) Epoxy-Eplxilfldt-Aaln« SyatM (aupla c)

E o

1op o

O

.50

o 1.90

2.30

(SIP)~* Figure 8.

e

2.70

(1/mol)^

Apparent rate constant, k 3 >

versus (SIP)

for samples B anc C.

B) .

k 3 ( i/mol 4.890 2.541 1.620 0.586 0.163 0.180 0.099 0.081 0.077 0.071

h)

21

k = k1

1/2 ' (1 + (LE) /K

+ k"K

+ k,,,PK where,

(LE) K

Equation

= living

(1

q

ends

rate

constants,

numerical

Eq.

is

k',

methods.

did

The

are

mechanism

and

for

mechanical

ion.

ends

relationship

this

precise

K

and

constants

explanation of

by

q

the

the

means for

values

obtained

of

the

K

and

Therefore,

calculation

P

for

concentration

calculated

do

properties

(5)

equation.

be

can

rate

the

(LE)"1/2

kinetics

living

not

apparent

satisfactory

_1

q

mole/1.

Szwarc's

because

-1/2 '

of t r i p l e

k1"

We

yet

)"1/2K

low

and

system

(LE)

general

becomes

k"

episulfide-amine available.

a

At

(5)

q

constant

polymerization.

Kq value,

(LE)?K

-1/2

concentration,

actually,

large

work

+

= dissociation

(5),

anionic

1/2

p

)

of the

are

from

curing

not this

reaction

epoxy-episulfide

resin

system. Epoxy-Episulfide-Amine sample

C

are

given

concentration 40

hours

still

are

reaction,

shown

at

in w h i c h

included

in

decreased

continued

reaction, be

of

System Fig. very

9.

whereas

that

the

time.

reaction

and

The

kinetic

observes almost

consumption

This ion

C).

One

rapidly

episulfide

in the

(Sample

means

attacks

system.

The

the

amine after

epoxide

another

epoxide

basic

groups possible

ring,

reaction

should

mechanisms

below:

R-CH-CH Z

+

R'-NH-R'

>

R-CH-CH 2 -N-R'

0

OH

(6)

R' H

R-CH-CHo V

+

R'-NH-R'

2

h -¿->

l+

R-CH-CH.-N-R" 2 i 1 S_ R'(Free ion, Ion pair and/or Triple ion)

S

Ion pair

K

P

of

disappeared of

that

the

that

data

Free ion

equations continued on next page

22

Triple ion H 1+ R-CH-CH,-N-R' 2 I I R'

Ion pair

K, —'-->
p o 2 o

(21)

where y Q is the value of da/(l-a)dt at t = t .

Eq. (19) was applied to the data in Tables 3 and 4 using H^ equal to the heat of reaction during the light on/light off run plus the heat of reaction in a subsequent continuous irradiation.

The three longest time y values in each

data set were discarded due to their sensitivity to the H used. To the right 2 hand side of Eq. (19) an arbitrary X • (t-t ) term was added. By iteration o the value of B was determined which rendered X = 0 upon solution of the modified (second degree in t-t ) Eq. (16) by least squares linear regression for each of the t data sets. At 50°C the t = 60, 120, 180, and 240 sec sets o o yielded B values 0.0000204, (-0.000000), 0.000276, and 0.000875 s. From these B values and the slopes of the ln[(B/y)+l) vs t-t 20.5 (t

0

= 60 s ) ,

2.6 (t

0

= 180 s ) ,

lated.

Assuming B=0, the data for t

gave k

/k

and 3.7 (t

o

functions k„. /k = tr p o = 240 s ) were calcu-

= 120 sec were treated by Eq. (20) which

The least squares straight line for B vs. t (excluding 2 - 1 - 1 the t = 60 s run) gave K.k = 0.31 * 10 1 mol s from the slope and ° -5 -I P [Z] = 3.2 • 10 K. mol 1 from the intercept/slope ratio. Accepting k /k 0

= 3.6.

2

2

= 3.6, K j k t r = 1.1 • 10

-1

1 mol

t r

-1

s

.

P

We note that the rate constants calcu-

lated from the initital rate data are approximately five times the rate constants calculated from these dark reaction rate decay data within the Case I framework.

This is unacceptable.

At 60°C treatment of the dark reaction kinetic data (Table 4) as just described yields k. /k

= 16.8, 4.3, 2.3, and 3.7 for t = 60, 120, 180, and 2 -1 - 1 ° -5 K„k = 1.1 • 10 1 mol s and [Z] = 2.7 • 10 K, 2 P o 2 (dependent on Case I assumption). The data fits were less good than tr

240 s, mol 1

P

respectively.

those for the 50°C data.

The relative k,. /k values obtained in the dark tr p

reactions at 50°C and 60°C are not consistent with those indicated by the Arrhenius treatment of the initial rate data. The foregoing analyses of the reaction kinetic data within the framework of the Case I assumptions indicate that Case I is not acceptable.

106

Figure 7 1 1 1 1 r t TBPHGE K b .00922 g»/g« 500 Light on for X nil), then off for 30-X «in,

6

8

.01 *

10

t

12

14

16

18

1 — — i

1

1

(sec)

20

Figure 8 1

1

0,45

0 m i

1

1 —

i

TBPHGE I-Sb .00922 g«/g« 60C

Light on for X Min, then off for 30-X «in.

0,40

A i m n

0,35 0,30

* A 0,25 * I H 0,20 \

0,15

#

0,10

1

9 9 H

0,05

1V ^ 1

0,00,

1

ti

\ 2 «in

2

"—x i i * —i 6 8 10 12 14 16 .01 * t (sec)

IT f 1 |

4

1

i

i

18

20

107

Case II.

Very slight dissociation of the acid

If the photolytically-generated acid is only slightly dissociated, i.e., if 4xt/K^ >> 1 for all times of practical interest in the reaction, [H + ]=(K l X t ) 1 / 2

(22)

d[H+]/dt=(K1i)1/V1/2/2

(23)

d[P]/dt=K 2 (K 1 x) 1/2 t" 1/2 /2-k tr [P][Z]

(24)

To examine the approximate form of the rate and conversion expressions in terms of the Case II assumptions we will first look at the prediction for no terminating transfer ( i ^ = 0).

Defining W=k K „ K Î / 2 x 1 / 2 p 2 1

(25)

[P]=k X W t 1 / 2 P

(26)

y/t 1 / 2 =W

(27)

leads to the relations

Figure 9 presents the 50°C TBPMGE data (Table 1) as y/t conversion range a = 0.0 to 0.7.

vs. a over the

In the absence of terminating transfer a

horizontal straight line plot is predicted at each initiator concentration 1/2 (Eq. (27)).

It is seen that there is deviation from such constancy for y/t

particularly in the region of a > 0.5.

However, we should recognize the sen-

sitivity and discrimination of our data presented in this 1/2 manner. each initiator concentration the average value for y/t

Taking at

of the seven points

(a=.20,.25,.30,.35,.40,.45,.50) we obtain the following c ( g/g ), 10 4 y / t 1 / 2 = 10 4 W ( s ~ 3 / 2 ), W / x 1 / 2 (mol" 1/2 1 1 / 2 s " 1 ): 0.00922, 1.89, 0.391; 0.00796, 1.69, 0.377; 0.00 535, 1.33 , 0.3 62 ; 0.00411, 1.19, 0.370; 0.00247, 0.88, 0.353; 0.000823, 0.315, 0.219.

The values of V just listed have been substituted

into the following Case II (no terminating transfer) conversion rate and conversion relations, and the results are plotted as broken line curves in Figures 1 and 3.

108

Figure 9 — —

0 m 01

0,20

TBPMGE I-ik c I-ft c ft . 8 0 9 2 2 D , 8 0 4 1 1 B ,80796 E ,80247 C .00535 F .( -4+ r~ - V V ¥ Ì X X A X 1 X c — + -

0,15

A

i

A

D-- o - - o -

4» 0,10 \ 31

7

V

"

T

-V

t\

50C

+

T

X

X

x

A

A D

A

-0-

n

T

'

0

0,05

0 0 8 H

0

0

« —

0,1

0,2 0,3 0,4 C O N V E R S I O N ,

0,5 a

0,7

0,6

Figore 10 1,8 1,6

co 0 0 VI

1,4 1.2

+ x a D '

I 1(0 80 70 60 50 40

i TBPMGE

I i I I - S k ,00922 (JM/jm) Continuous irradiation , •

+

+

+

I

+

u J

+

1,0

4* \ 7i

9 8 S H

0,8

x

L

A

A.

A.

-0

D

0

-X — X — X — x — X

0,6

0,4 0,2

"2

I—D0,1

A

à~ - A

-0

A—A 0-

0,2 0,3 0,4 C O N V E R S I O N ,

0,5 a

o-

0 0,6

D

! 0,7

109

da/dt=Wt1^2exp(-2Wt3/2/3)

(28)

a=l-exp(-2Wt3/2/3)

(29)

E q u a t i o n s (28) and (29) are f a i r l y good r e p r e s e n t a t i o n s of the observed r a t e and c o n v e r s i o n data f o r TBPMGE at 50°C during continuous i r r a d i a t i o n i n

spite

of t h e i r f a i l u r e t o take i n t o account the t e r m i n a t i n g t r a n s f e r which i s

occur-

r i n g . An experimental

study which involved only the d e t e r m i n a t i o n of

conver-

s i o n as a f u n c t i o n of time would l i k e l y not d e t e c t d e v i a t i o n from the form of Eq. ( 2 9 ) e x c e p t i n the f i n a l

s t a g e s of r e a c t i o n .

(The r e a c t i o n r a t e data f o r

the c = .000823 system are anomalously low r e g a r d l e s s of the method of theoretical analysis.) There i s a s l i g h t downward t r e n d in the c a l c u l a t e d 1/2 which may be the r e s u l t of not taking k i n e t i c t e r m i n a t i o n i n t o a c c o u n t .

W/x

The d e t e r m i n a t i o n of k

tr

/k

p

from r a t e decay in the dark on the assumption of

t r a n s f e r t e r m i n a t i o n by an (unknown) agent should be the same f o r Case I I as f o r Case I .

The parameter B (see above) in Case I I f o r m u l a t i o n

is

B=k [Z] - W t 1 / 2 p o o F i t t i n g the B v a l u e s found f o r the t runs t o a f i r s t degree polynomial in t 0.395, 10

i

from the s l o p e , s"

1

and [Z]

.

o

= 5.4

(30)

= 1 2 0 , 1 8 0 , and 240 s

dark r e a c t i o n

y i e l d s 1 0 4 W = 1 . 9 0 and W / x 1 ^ 2 = • 10~ 3 K . K ^ 2 . Z 1

k,. [Z] = 7 . 7 • tr o

The temperature s e r i e s data t r e a t e d as above f o r Case I I in the of k t r = 0

g i v e s the W vs a p l o t s shown in F i g u r e 10 over the

range a = 0 . 0 t o 0 . 7 .

approximation conversion

As temperature i s i n c r e a s e d the approximation of a con-

s t a n t W becomes l e s s and l e s s s a t i s f a c t o r y .

I t appears t h a t the r e a s o n a b l y

good approximation of the TBPMGE 50°C r a t e and c o n v e r s i o n data by Eqs. and (29) may be f o r t u i t o u s .

When an average V i s t a k e n in the a = 0 . 2 t o 0 . 5

range f o r each of the temperature s e r i e s data s e t s we o b t a i n the T ( 4 C ) , 1 0 4 W:

(28)

40, 0.83; 50, 1 . 8 9 ; 60, 3 . 7 5 ; 70, 7 . 3 ;

c o n v e r s i o n as f u n c t i o n s of t computed by Eqs.

80, 1 1 . 9 .

following The r a t e and

( 2 8 ) and ( 2 9 ) using t h e s e

age W v a l u e s a r e d i s p l a y e d as broken l i n e curves i n F i g u r e s 4 and 6 .

aver-

One can

only c h a r a c t e r i z e the e x t e n t of agreement of the computed curves with the e x p e r i m e n t a l curves as m a r g i n a l . The Case I I assumption of propagating s p e c i e s f o r m a t i o n r a t e p r o p o r t i o n a l

to

110

the proton formation rate for a very slightly dissociated acid is more satisfactory than the Case I assumption involving a highly dissociated acid.

Nei-

ther the Case I nor Case II framework gives a truly satisfactory fit to the y vs t data.

The observed acceleration in propagating species production during

later stages of continuous irradiation has been here postulated to derive from exhaustion of a terminating species in the system.

The decrease in y during

the dark reaction is a definite indication that there is a kinetic chain termination process.

However, the source of the acceleration in propagating

species production may lie in initiation and termination mechanisms not consistent with the assumptions used in the approximate theoretical evaluations here presented.

Evaluation of BPADGE Polymerization Parameters

The polymerization kinetic data of BPADGE are rendered more complex than those of TBPMGE by the added complication of network formation.

The y=da/ (1-

a)dt values rise with increasing continuous irradiation time (Figures 11 and 13) in a manner similar to that of TBPMGE (Figures 2 and 5) until a = 0.4 0.5, then they decrease.

Thus, increases in [P] with increasing irradiation,

which must certainly occur, are overbalanced by decreased accessibility of network-bound oxirane rings and cations. cause

Increasing local viscosity may

further reduction of the reaction rate.

The initial polymerization

rate at 50°C for the c =0.00983 mixture was comparable to that of the TBPMGE for c =0.00922.

However, the initial rates for BPADGE decrease more rapidly

with decreasing initiator concentration than do the initial rates for TBPMGE.

The average H^ for 10 of 11 polymerizations of TBPMGE (cf. Tables 1 and 2) was -88.2 ± 0.7 cal g

or -18.2 kcal m o l - 1 of oxirane ring.

On the rea-

sonable assumption that the same heat evolution per oxirane ring occurs for BPADGE its H^ is -1.82 • 10 4 /188 = -96.8 cal g

Observed H after 22 min

of continuous irradiation of the c = .00983 system were -46.6 (30°C), -62.7 (40°C), -72.0 (50°C), -73.9 (60°C), -80.5 (70°C), and -85.5 (80°C) cal g

.

Although these are not H^ values they indicate asymptotic fractional conversions, a, less than unity which decrease with decreasing temperature (cf. Figure 14).

In the initiator conc. series reactions at 50°C the c =0.00955 sys-

tem gave H = -78.4 cal g shown.

The conc.

somewhat higher than the -72.0 cal g

series 22 min

1

just

continuous irradiation heats were -78.4

(.00955), -75.7 (.00808), -74.6 (.00601), -67.6 (.00406), -51.8 (.00201), and

111

Table 5.

BPADGB P o l y e r l r a t l o n at 30C.

I n i t i a t o r Concentration S e r i e * .

BPADGE: I-Sb Conc. S e r i e » . l^SOC. a - f r a c t . conv., cal/g I--Sb g/g a 0 .041 0 .081 0 .121 0 .162 0 .202 0 .243 0 .283 0 .324 0 .364 0 .405 0 .445 0 .486 0 .526 0 .567 0 .607 0 .648 0 .688 0 .729 0 .769

t

(-96.8) .00955 100 z da/dt

49 72 93 114 134 154 173 193 214 236 259 285 315 351 397 * 460 558 717 974

Table 6.

.1563 .1838 .1952 .2004 .2041 .2049 .2030 .1986 .1918 .1812 .1675 .1476 .1243 .1010 .0761 .0521 .0333 .0197 .0126

BPADGE

(-96.8) .00808 a

t

66 0 .039 0 .078 97 0 .117 126 0 .156 153 0 .195 179 0 .235 205 0 .274 231 0 .313 257 0 .352 284 0 .391 312 0 .430 343 0 .469 376 0 .508 413 0 .547 456 0 .586 508 0 .625 575 0 .665 667 0 .704 802 0 .743 1012

cal/g ( -96.8) T = 40C íoo; da/dt t a

0..032 0..065 0,,097 0,.130 0,.162 0,.194 0..227 0 .259 0 .291 0 .324 0 .356 0 .389 0 .421 0 .453 0 .4 86 0 .518 0 .551 0 .583 0 .615

99 149 194 236 277 317 356 396 435 475 516 558 604 654 710 776 857 963 1108

.0591 .0694 .0747 .0781 .0805 .0816 .0822 .0825 .0818 .0805 .0780 .0741 .0680 .0617 .0536 .0446 .0355 .0269 .0188

.1116 .1312 .1409 .1474 .1507 .1517 .1500 .1468 .1415 .1340 .1248 .1118 .0986 .0833 .0683 .0501 .0357 .0231 .0152

Polymrization.

BPADGE :^I-Sb Conc.-.00983 g/g . H

106 k da/dt

t

a

0.,038 0,.076 0..115 0,.153 0,.191 0 .229 0 .267 0 .305 0 .344 0 .382 0 .420 0 .458 0 .496 0 .534 0 .573 0 .611 0 .649 0 .687 0 .725

45 64 80 96 112 127 142 157 173 188 203 220 237 257 281 312 358 441 630

t

0 .039 82 0 .077 123 0 .116 159 0 .154 193 0 .193 225 0 .231 257 0 .270 288 0 .308 319 0 .347 350 0 .385 382 0 .424 415 0 .463 450 0 .501 488 0 .540 532 0 .578 585 0 .617 651 0 .655 741 0 .694 870 0 .732 1059

(-96.8) .00406 100 z da/dt .0855 .1028 .1110 .1166 .1207 .1226 .1244 .1249 .1233 .1198 .1132 .1052 .0945 .0813 .0664 .0507 .0363 .0248 .0170

Tempe r » tare S e r i e » . a=fract. conv., (-96.8) 70C

100 z da/dt

rate da/dt( s _ 1 )

(-96.8) .00601

(-96.8) 60C a

t(s),

a

.1814 0..042 .2197 0..083 .2343 0.,125 .2426 0.,166 .2471 0,,208 .2506 0,,250 .2529 0.,291 .2537 0,.333 .2529 0..374 .2487 0,.416 .2402 0 .458 .2259 0 .499 .2051 0 .541 .1769 0 .582 .1432 0 .624 .1028 0 .666 .0658 0 .707 .0334 0 .749 .0129 0 .790

t 37 50 62 73 83 93 103 113 122 132 143 154 166 180 199 225 271 364 579

t(s),

100 z da/dt

a

t

0 .035 113 0 .070 166 0 .105 212 0 .140 255 0 .175 296 0 .210 336 0 .244 375 0 .279 415 0 .314 454 0 .349 493 0 .384 534 0 .419 576 0 .454 622 0 .489 671 0 .524 727 0 .559 792 0 .594 872 0 .628 976 0 .663 1119

100 z da/dt .0585 .0774 .0794 .0839 .0864 .0880 .0889 .0893 .0892 .0872 .0842 .0802 .0741 .0670 .0579 .0491 .0387 .0291 .0210

Continuos» L i g h t . rate da/dt( s " 1 )

a

(-96.8) 80C "100 z t da/dt

.2756 0..044 .3390 0,.088 .3715 0.,132 .3888 0,,177 .4050 0 .221 .4163 0 .265 .4236 0 .309 .4274 0 .353 .4246 0 .397 .4131 0 .442 .3926 0 .486 .3611 0 .530 .3193 0 .574 .2620 0 .618 .1897 0 .662 .1245 0 .706 .0668 0 .751 .0318 0 .795 .0123 0 .839

27 37 46 54 62 69 76 83 91 98 106 115 125 137 153 177 219 302 488

.3943 .4933 .5351 .5650 .5 837 .5998 .6099 .6073 .5921 .5607 .5313 .4720 .4019 .3289 .2361 .1429 .0790 .0367 .0145

112 Figure 11 0,50 ' 0,45 0 01 w Jj '5

«

0,40 0,35

\

0,15

H

x it

H ^ : (-96.8 cal/jH)

D .80486 ? .88201 .88184

Continuous irradiation

0,25

0,20

s

BPADGE S 8 C

0,30

I H

J 8

I-Sb (gw/gm)

0,10 0,05 0,00

3 4 8 . 0 1 *

5 t

6 7 ( s e c )

Figure 12

3 4 0 . 0 1 *

5 t

6 7 ( s e c )

113

Figure 13

2 0.01

*

3 t

4 (sec)

Figure 14 —i 1(C) + 80 x 78 u 7

r BPADGE I-Sb .68983 (gn/gM) H : (-96.8 oal/gn)

3» 40 / {

Jir

^

.....

0-

S

3 0.01

4

*

5 t

6

7 (sec)

9

10

114 - 4 2 . 3 (.00104) cal

g" 1

( c f . Figure 1 2 ) .

Considering the l e s s than s a t i s f a c t o r y r e s u l t s obtained i n the approximate treatment of the IBPMGE p o l y m e r i z a t i o n r a t e s , the even more divergent r e s u l t s f o r the BPADGE p o l y m e r i z a t i o n rate a n a l y s e s w i l l not be d i s c u s s e d .

Conclusions Observation of the r e a c t i o n exotherm rate during p h o t o i n i t i a t e d

cationic

epoxide polymerization provides k i n e t i c data s u i t a b l e f o r examining p o s t u l a t e s of r e a c t i o n mechanisms.

The rate data f o r p - t e r t - b u t y l p h e n y l

e t h e r c a t i o n i c p o l y m e r i z a t i o n i n i t i a t e d by the p h o t o l y s i s of

mono-glycidyl di-(p-tert-

butylphenyl) iodonium hexafluoroantimonate suggest that the HSbF p h o t o l y s i s i s only s l i g h t l y d i s s o c i a t e d .

produced by

The e x i s t e n c e of k i n e t i c chain t e r -

mination i s shown by the decrease with time of d a / ( l - a ) d t

(a = f r a c t i o n of

t o t a l heat evolved) during the dark r e a c t i o n a f t e r periods of continuous diation.

P o s t u l a t i o n of a propagating c a t i o n formation rate proportional

irrato

the proton formation rate due t o p h o t o l y s i s and i t s disappearance rate proport i o n a l to the product of i t s c o n c e n t r a t i o n and that of a terminating t r a n s f e r agent l e a d s t o n o n l i n e a r , f i r s t order d i f f e r e n t i a l equations which have not been solved«

A marginal f i t of the rate and conversion data i s achieved by

assuming very s l i g h t d i s s o c i a t i o n of the Bronsted a c i d and no k i n e t i c chain termination. Early s t a g e s of the p h o t o i n i t i a t e d p o l y m e r i z a t i o n of the d i - g l y c i d y l ether of bisphenol-A are k i n e t i c a l l y s i m i l a r to those of TBPMGE.

However, network f o r -

mation and the approach t o a g l a s s y c o n d i t i o n cause rapid decreases i n r e a c t i o n r a t e s beyond conversions a = 0 . 4 to 0 . 5 .

The conversions appear to be

approaching l i m i t i n g v a l u e s which decrease with decreasing r e a c t i o n temperature.

115 References

1.

The r e s e a r c h here d e s c r i b e d has been r e p o r t e d in major p a r t a t the Seventh Northeast Regional Meeting, Am. Chem. S o c . , Albany, NY, S e p t . 1976, and i n a Polymer Science I n s t i t u t e Seminar, U n i v e r s i t y of Akron, Akron, OH, Oct. 13, 1977. J . V . C r i v e l l o and J.H.W. Lam,

3.

J . V . C r i v e l l o and J.H.W. Lam, J . P o l y m . S c i . , Polyn.Chem.Ed. 17 (1979), 977999, 1047-1057, 1059-1065,

4. 5.

Macromolecoles, 1 0 ( 1 9 7 7 ) ,

1307.

2.

(1979).

Y.Kawakami, A. Ogawa, and T. Yamashita, i b i d . , ( 1 9 7 9 ) , S. Penczek, P. Kubisa, and K. M a t y j a s z e v s k i ,

3785.

Advances in Polymer S c i -

ence, 37_> " C a t i o n i c Ring-opening P o l y m e r i z a t i o n of H e t e r o c y c l i c Monom e r s " , S p r i n g e r - V e r l a g , Berlin/Heidelberg/New York 6.

J . V . C r i v e l l o , Ann. Rev. Mater. S c i . 13 ( 1 9 8 3 ) ,

7.

J . Robins and C. Yonng,

(1980).

173-190.

ACS Symp. S e r . , No. 286, 2 6 3 - 2 7 4 , ( J . E .

McGrath,

ed.). Am. Chem. S o c . , Washington, DC, ( 1 9 8 5 ) . 8.

J . E . Moore, S.H. S c h r o e t e r , A.R. S h n l t z , and L.D. Stang,

in: U l t r a v i o l e t

L i g h t Indnced R e a c t i o n s in Polymers, ACS Symposium S e r i e s , No. 2 5 , ( S . S . Labana, ed.), Am. Chem. S o c . , Washington, DC, (1976), 90-106. 9.

G.R. Tryson and A.R. S h u l t z , Fox Memorial I s s u e ) 17 ( 1 9 7 9 ) ,

10.

A. Ledwith,

J . P o l y m . S c i . , Polym.Phys.Ed.

(Thomas G.

2059.

P r e p r i n t s , 22nd F a l l Symp., Soc. Photogr. S c i . E n g . , A r l i n g -

ton, VA, (1982), 4 4 - 4 5 . 11.

S. P. Pappas,

"New Trends in the Photochemistry of Polymers" ( N . S . A l l e n

and J . F . Rabek, Eds.), E l s e v i e r Appi. S c i . P u b l i s h e r s , (1985), 99-111.

London

New York ,

KINETICS AND MECHANISM OF THE ANHYDRIDE CURING OF A DIGLYCIDYL ESTER

B . S teinmann P&A Division, Ciba-Geigy Ltd, 1701 Fribourg, Switzerland

Introduction The curing of epoxy resins with anhydrides

was

the

subject

of

many publications during the last 30 years. From the studies of curing of bisphenol A epoxy resins with phthalic .anhydride, Fisch and Hofmann suggested the following reaction mechanism (1, 2): 0 ROH + L O I _ p

-

^¿A.COOH

formation of monoester

II 0 ^COOR

C°X V^-COOH

+

cl£>CH-R'

^-COOR

- (oT COO-CH.-CH-R 2

formation of dies ter

1

I OH

The polymerization is started by OH groups which are present in the reaction mixture and proceeds by the formation of a monoester intermediate. The epoxy groups react then with the carboxylic acid groups. A significant side reaction can be ether formation of OH groups with epoxy groups (1, 2): 0H n R'-CH-CH 2 + ROH — R'-CH-CH 2 -0R This mechanism was confirmed by Stevens (3, 4), who could detect the monoester intermediate by carrying out FT-IR

measurements.

There is less agreement about the amine-catalyzed

anhydride

curing. The reaction could be initiated by complex formation of the amine with the anhydride and continue by an anionic mechanism (5) , or it might be started by a complex of amine and a proton donor

(6, 7). Tanaka and Kakiuchi as well as Luston and Manasek

suggested that the active site for the polymerization could be a ternary complex of amine, epoxide and anhydride (8, 9, 10).

Crosslinked Epoxies © 1987 Walter de Gruyter & Co. • Berlin • New York - Printed in Germany

118

Matejka et al found by studying a model reaction that a quaternary ammonium ion was formed from the amine and an epoxy group which reacted immediately with the anhydride to form an ester and a carboxylate ion (11):

R-CH_-CH-CH_ + N R , t z J

® R-CH„-CH-CH„-NR,

—

la

0 0 II II R'-C-O-C-R' •

® 2

2

\Q

I

C-R

3

+

R1 COO

1

II O

R'COO® + R-CH.-CH-CH» 2 \>' 2

—

R -C H —C H -C H _ OCOR' etc.

This mechanism was confirmed by Dusek et al, who carried out a statistical treatment of network formation

(12). Their

prediction

of critical conversion at the gel point as function of the amine concentration agreed with the experimental results found for the anhydride curing of bisphenol A epoxy

resins.

All these investigations were done with bisphenol A diglycidyl ether or model substances such as phenyl glycidyl ether, but very little is known about the anhydride curing of diglycidyl

esters,

which are important compounds for the fabrication of electro insulators. We therefore studied the reaction of hexahydrophthalic anhydride with hexahydrophthalic diglycidyl ester, with and without catalyst,by DSC, FT-IR

and chemical analysis of functional

groups. 0

o

II

^~VX-0-CH2-CH-CH

2

r, r-u C-U-LH„-LH-CH„ 2 II No' 2 0

a

hexahydrophthalic diglycidyl ester

o II

•

c

\

/

o

hexahydrophthalic anhydride

(HHPA)

(HHDGE)

119

Experimental HHDGE

was

a Ciba-Geigy

and a hydroxyl during HHPA

and filtered

Benzyldimethylamine Geigy)

were

combined

at ca. At

40°C this

mixture was

rature

(BDMfl)

used without

anhydride).

measurements were IR

Nicolet FT—IR windows

two small oven.

thick

prepared. The (1738

-

cm l)

to

reaction

of of

could pass

the g e l p o i n t ,

3 samples

to

were

content was determined

1858 band

samples

flasks, removed

calorimeter.

time of

thin into

intervals the

cm-l)

epoxy

of

closed

the

cm l.

during

the

the r e a c t i o n At

and carboxylic and Hofmann

in

mixan

certain

and cooled quickly

as d e s c r i b e d b y F i s c h

ester -

and placed

temperature.

, anhydride

were

evaluating

at 4545

groups

a

two

as a

followed by

(1788,

the d e s i r e d

0°C. F o r e a c h p o i n t , the epoxy

tempe-

between glass plates

the epoxide

small

a

introduced

a measurement

of f u n c t i o n a l

in Erlenmeyer

were mol

room of

through

placed

taken in c e r t a i n

the mixture

the a r e a of

oven which was preheated time i n t e r v a l s ,

and

in the s a m p l e

the r e a c t i o n w e r e

determination

ture w e r e w e i g h e d

melted

a d d e d at room

mixture was

finished. For

(Ciba-

reactants

immediately.

the anhydride b a n d

or

the c h o m i c a l

reaction up

the anhydride

started

The

silicon plates which were

films

of

impurities.

(1 m o l e p o x y d e : 1 . 1

catalyst was

Spectra were

kinetics

the i n t e n s i t i e s

For

5 . 78 m o l / k g

reactions

carried out on a Mettler TA2000

the r e a c t i o n was 1 mm

1:1 w/w

i n s t r u m e n t . T h e XR b e a m

the p r e h e a t e d

band

of

and 1-methylimidazole

a small oven was placed

in the o v e n . T h e

film between

was

acid

purification.

temperature,

and the experiment

studies,

(Fluka)

further

obtained. The

DSC

group,

content

(caused by side

to r e m o v e

in a ratio

For

until

an epoxy

glycidylation).

was distilled

clear

product with

c o n t e n t of 0.57 m o l / k g

below acid (1,

2).

120

Results DSC

Studies

It h a s b e e n of e p o x y Initial

shown by

experiments

however,

that

questionable. extents

T

=

fte-

total

= HT

area

the c o m p u t a t i o n . order

investigations

the m o d i f i e d

kinetics

measurements. revealed, runs was

rate

flrrhenius

It w a s

the

impossible energy.

carried out, equation

parallels

quite

and on

and activation

were

the r e a c t i o n e x t e n t

the

which

(the

the

heat

14): =

heat

H

a

that

for

the h e a t i n g

of r e a c t i o n

DSC

In k + n I n H r +

= h e a t of

r

values

Ea/RT

H

E

depended on

k

Ht

riH In ip^ =

H

e v a l u a t i o n of d y n a m i c DSC

is m a d e

(13,

that

the s y s t e m H H D G E / H H P A / B D M A

results

evaluated by using

evolved)

(13 - 16)

can be studied by DSC

the k i n e t i c

isothermal

assumption

=

authors

The

reliable

Therefore,

1 "

' - C I : ] H Z D W r P O

1

j

O -

C " I h

• epoxide primary amine " secondary amine

0

Figure 2.

Reaction mechanisms of Afunctional system

It is known that this reaction is autocatalyzed by the formation of hydroxyl groups and that its initial rate is very low. This compound can then react : 1) with aniline (D) and 2) on the resin (R). Pathway 1 involves the same mechanism as above, i.e. opening an epoxy bridge by a primary amine, except that this bridge is more sterically hindered than the one reacting

previously

(compound B). At

this stage of

the reaction, all

the products formed contain only secondary amine protons. We have shown

(5) that

although not impossible, substitution by this type of proton is slow, decreasing with the increasing viscosity of the medium. It is thus consistent to predict that the polycondensation will preferentially continue by the reaction of A on the resin, leading to compound C. Once the product forms, the reaction can continue by the rapid attack of the hardening agent D on the two epoxy bridges of compound C, yielding products E and F. Examining the reaction pathways thus shows that periodically the progression of the polycondensation is slowed by the obligate reaction between an epoxy bridge and a secondary amine. This confers a nonnegligible importance on side reactions. These hypotheses were confirmed by following the initial steps of the reaction with HPLC the

and 13C NMR. In the case of O-epoxy (5a) compounds (systems 9, 10, 11),

resins synthesized

in the laboratory contained relatively

few impurities

(HPLC

purity greater than 98 %). The reaction mechanisms occurring within the first 3 hours complied with those shown in Figure 1. Figure 3 shows the example of the reaction between

1,3-diglycidyl benzene

(peak 2) and aniline (peak

1), followed with

HPLC.

Their condensation product A (peak 3) reacts with aniline to give product B (peak *f) (rapid step) and with the resin to give product C (peak 5). During this time, peak k remained larger than peak 5, since it was produced more rapidly and was consumed more slowly. The same reasoning can be applied to the other chemical species.

136

Figure 3. HPLC. Reaction between 1,3-digiycidylbenzene and aniline, i -100° Solvents m e t h a n o l / w a t e r . Flow 1 ml/min.

V CM; — C M

—CM.

\ 2a

\

2b

/

CHj — C H

\

CHj - NH

R

CM, — CM — CHj — N —

/

u C - C . - C H ,

C»-,

— CM —

CHj

\

/

Figure V; Reaction mechanisms of N(epoxy)2 group. (I) Primary epoxy reaction Epoxy-hydroxy and epoxy-secondary amine reactions (2a) intermolecular crosslinks ; (2b) intramolecular rings.

137 For the N-iepoxy^ resins (systems 12, 12', 13, 14 we were forced to study the mechanism by using "secondary" intramolecular reactions (Figure 4), given the proximity of epoxy groups. These reactions occur to a greater extent as the resin in more impure (non-distilled commercial products) (5b). As an example, Figure 5 shows the HPLC monitoring of the reactions of system 12' (the main impurity

is the toluidine monoepoxy, peak 2). During the first 2 hours,

the d i f f e r e n t reactions occurring here agree with the mechanism predicted in Figure 3 (peaks 4,5,6,7). Beyond

3 hours of reaction, however, we observe the formation of

new compounds, e.g. peak 8, c h a r a c t e r i s t i c of polar products which could result only from side reactions involving the epoxy prepolymer. These reactions a r e more important as the prepolymers contain impurities.

.Jul ^-M.

^A...

JJ

^CHjCM-CHj Y^-CH-CH, o DGor

iJL

(#. A -

Figure 5. HPLC. Reaction between N,N-diglycidyl-o-toluidine and aniline, T = 100°C Solvents m e t h a n o l / w a t e r . Flow 1 ml/min. The solid CP MAS 13C NMR study (Figure 6) of samples obtained at the end of polycondensation

for

systems

12 and 12' (Figure 6) show two distinct bands, between 0 and 70 ppm (envelope

confirm

the

different

mechanisms.

The spectra

obtained

corres-

ponding to the mobile part of the network) and between 100 and 160 ppm (the a r o m a t i c

138 in

— .

, — .

150

,

,

,

100

50

0

. —

ppm

Figure 6 .

13C NMR spectra of liquid and solid (CP MAS) state systems a) before gelation ; b) commercial resin ; c ) purified resin.

or rigid part of commercial envelope

the network). When we compare

prepolymers,

corresponding

a structural to

these

change

different

the spectra obtained with

in the

groups

12 and

flexible

shows

that

12'

purified

fragments is seen. The the

chemical

balance

d i f f e r s as a function of the prepolymer chosen. The chemical balance of the reactions can be performed only

by

deconvolution of these bands into elementary lines, because

of the 13C chemical shifts obtained with model compounds (6).

139

Study of t h e epoxy ( A f u n c t i o n a l ) /amine ( t e t r a f u n c t i o n a l ) s y s t e m (system 17) In this s y s t e m , t h e polycondensation

r e a c t i o n s can be followed p e r f e c t l y

by solid and

liquid 13C NMR of t h e epoxy ( C j ) , hydroxyl ( C 2 ' ) and e t h e r ( C 2 " ) groups (see F i g u r e 7) : spectrum recorded a t the gel point). The position of the secondary a m i n e can be f o l l o wed with t h e I and II signals.

160

i t0

120

100

80

60

ppn

1

OH

(1)

H

(E - CH - CH,-), N - A

(2)

1

H

Scheme 2 (epoxy homopolymerization or etherification) : initiation (3)

(3') . propagation : R'o® • (x+1)CH, - CH - E .2 0

->

R'0( -CH- - CH - 0 -) CH, - CH - 0® I * I E E

Scheme 3 : DDA acts as a latent cyanamide donor : . Formation of 2-aminooxazoline

E - CH - CH °N / 0

H N - C = N - CN ' 2

or iminooxazoline

->

NH

1

N

/ CH,

""

\ -

in

- CN

x

.... CH

"

£

^

CH

0

(5)

/

NH - C

/ CH 2

(1) and (2))

C

f* \

0

X

. Reaction of cyanamide :

H2NCN

+

2E - CH - CH 2

->

(E - CH - CH 2 -) 2 N - CN

(7)

152

Table 3. Analyses of Various Fractions; R =

Fractions

A

Products

/—\ \P/~

^O/-0-CH 2 -CH-CH 2 OH Type of reaction

^H-CN °-CH 2 -CH-CH,-NH-C

condensation (1) and etherification

I

OR

t

s N - c

/ I

NHR

,N - C = H „

, \

|

0 — CH

/

CH_ 2

CN reaction

'-0-CH-CH-CH 2 ~KH-C 0R

condensation (1)

o-

^

NH-CH2-CH-CH_,r

and etherification

OR

-o-• R^NH

OH

Ó®

E - CH - CH_ - NHA + E - CH - CH. le 0°

(31)

+ E - CH - C H 2 - NHA

2

\

/ 0

>- E - CH - CH- - NHA I 0

2

(4)

2

I

CH-CH20

e

However, the mono-substituted amine species are an intermediate product, their life-time and content are related to the reaction temperature and to the a/e ratio: - At a low curing temperature

(100°C) the life-time of the mono-

substituted amine species is long enough to develop the etherification process for a/e = 0 . 6

or a/e = 1.0.

- In the formulation with a/e = 1.0, at different curing temperature there are enough monosubstituted amine species to favour the etherification. The final production of ether linkages is rather limited by the initial amount of accelerator BDMA, and these cured epoxy networks have a similar value of

H

n20//H830

at

t

' le

en
r c the system does not gel any more. For an ideal case of the random reaction with equal and independent reactivities of functional groups and in the absence of cyclization we have (?

A>c («E»c =

(f

A"1)"1

(f

E-1»"1'

so that r

c = C =1 res

Pective

conversions and

functionalities

of amine and epoxide.

Network formation of the following epoxy resins and amines was studied: DGEBA, TGDDM, diglycidylaniline (DGA) and diaminodiphenylmethane (DDM), diaminodipheny1 sulfone (DDS), octamethylenediamine (OMDA), aniline.

Experimental N,N,N~,N -tetraglycidyl-4,4 -diaminodiphenylmethane (TGDDM) contained 9.16 mmol epoxy groups/g, M n =440(VPO). An approximate composition of the resin was estimated from GPC and liquid chromatography 91.7% TGDDM, 8% dimer of TGDDM and 0.3% chlorohydrin .

233 N,N-diglycidylaniline (DGA) and DGEBA contained 9.75 mmol epoxy groups/g and 5.62 mmol epoxy groups/g, respectively (theory 9.76 and 5.88 mmol epoxy groups/g). The synthesis of DGA and TGDDM was described elsewhere (1,2). 4,4'-Diaminodiphenylmethane (DDM) (99.5% gas chromatography) was recrystallized from toluene; aniline (100%) was redistilled. The purity of octamethylenediamine (OMDA) and 4,4 - diaminodiphenyl sulfone (DDS) was 99.3 and 100%, respectively. Triethylene glycol dimethyl ether (TEGDME) was used as received (98% - gas chromatography). The reaction of epoxides with excess amine proceeded in bulk or in the presence of the diluent TEGDME for 2-7 days at 130-150'C up to the full conversion of epoxy groups. A series of samples with various ratios of functional groups r was prepared. The samples were extracted with DMF at 80"C, then DMF was exchanged for CHC1 3 and the samples were dried to constant weight. The sol fraction was determined from the weight of a dry extracted sample, w^, and weight of reactants in the initial mixture, w Q : w g = 1 -w(J/wq. The critical molar ratio rc was determined as an interval between the last sample containing the gel and the first completely soluble sample. The equilibrium shear modulus, G g , of a sample in the rubbery state was determined from the stress relaxation using the instrument Rheometrics System Four (Rheometrics Inc., USA). The temperature of the experiment (120-140"C) was higher than T of the systems by at least 30 K. In the case of very lightly crosslinked networks the equilibrium was not achieved during the experiment. Therefore, the Thirion-Chasset extrapolation method (3) was used to obtain G g . The parallel-plates experimental arrangement (plate diameter 25 mm) with samples about 1 mm thick was used.

Results Figure 1 shows the dependence of the sol fraction and equilibrium modulus on the molar ratio of functional groups r. For an ideal network without defects the sol fraction is zero (wg =0) at the stoichiometric ratio r = 1. With increasing r, the sol fraction increases and at the critical ratio the polymer is completely soluble, w g = 1. Similarly, the modulus decreases with increasing r

234

r

Figure 1. The dependence of the sol fraction w g and equilibrium modulus G e of the non-stoichiometrlc networks on the ratio of functionalities r = 2 [NH2]0/[epoxy]Q. 0 - theoretical curve for the ideal reaction DGEBA-DDM 1 DGEBA-OMDA, 2 DGEBA-DDM, 3 DGA-DDM, 4 DGA-DDS, 5 DGA-DDS (20% solvent), 6 TGDDM-aniline, 7 TGDDM-aniline (40% solvent). and at the critical ratio G„ e is zero. The theoretical curve was calculated by means of the theory of branching processes for a diepoxide-diamine system with molecular weights corresponding to DGEBA and DDM under the assumption of an ideal random reaction without cyclization and with an equal reactivity of the functional groups. From Fig. 1 it is obvious that the sol fraction in the studied systems for a given r is higher than in the ideal case. These deviations from ideality are caused by cyclization and/or different reactivity of functional groups. Figure 1 shows that the deviations increase in the series: DGEBA-OMDA Ea—A4J. + OH

E0+ A4 2-+ OH - X E a - A 4 j + OH E0+ A4 2.+ OH

> Ea— A4 3 + OH

E„+ A 4 , + O H — U E.—A,.

= 4[Eq] [ A4_Q][A1 + A4 [OH]] = [E(j] [ A4 i][2^I + + 2fc4[0H] +AJ[OH]] - 4[E0] [ +i:4 [OH]] = 2[E0] ([A4_J-][*2 + k5 [OH]]-[A 4 J U ^ *„[OH]]}

-d[A42,l jp-

= [E,,] [2[A42.]]«:1+t4lOH]]-[A41J[fc,+i:5[OH]]}

"d[A"-31

=

dt

d[A44]

+ OH

[E0]([A43][t2 + yOH]]-2[A42.][t1+t4[OH]] - 2[ A4 2-][A2 + [OH]] }

= -[E0][A43][t2 + yOH]]

Figure 4. Kinetic scheme for the DGEBA-DDS system.

257 The third reaction (etherification) is thought to occur by tertiary amine or base catalyzed mechanisms. Formation of polyether oligomer has not been observed in the DGEBA-DDS systems when the amine is present in excess or at stoichiometric concentrations/ 2 , 1 1 ' However, when epoxide is present in excess, the hydroxyl groups may become serious contenders with the amines for the consumption of epoxy groups/ 11,12 ' All three of the reactions which occur in epoxy-amine systems can be accelerated by the presence of alcohol, water or other hydrogen donors/ 2 ' Since a hydroxyl group is a product of the epoxide-amine addition, the course of reaction will be autocatalytic. Using this information concerning the cure mechanism, a kinetic model can be proposed for the formation of various types of units during the polymerization. The assumptions made in the kinetic scheme are listed below: 1) The reactivities of the epoxide groups are independent 2) The reactivities of the amino hydrogens are dependent 3) No etherification occurs 4) The presence of hydroxyl groups catalyzes the amine - epoxy reaction 5) The ratio of rate constants does not depend on conversion Suppose the reaction begins with A 4 moles of amine monomer and E 2 moles of DGEBA. Then the stoichiometric ratio is defined as r = 2 Ej/ 4 A 4

(1)

If at time t a fraction p A of the amino-hydrogens has reacted and a fraction p E of epoxide groups has reacted, then PA =

R

PE

(2)

Furthermore, assume at time t that there are A 4 0 moles of A 4 units with 0 reacted sites, A 4 j moles of amine units with 1 reacted s i t e , . . . , A 4 4 moles with 4 reacted sites. Thus, the proportion of amine units which have i reacted sites will be defined as follows: (3) Then the overall extent of reaction of the amino-hydrogen groups can be written:

258

PA= X(i/4)pA4 i=0

(4)

Using the above assumptions and notation, the cure of D G E B A with D D S can be described by a system of differential equations (Figure 4). If it is assumed that the ratio of uncatalyzed primary to secondary amine reaction is the same as the ratio of the catalyzed/ 4 ' the system of equations have an analytical solution:

PA.I

=2X

(PA.OY-PA,O)

PA,2* = * 2 ( - 2 P A y

+

(5)

PA,o+PA,o a/2 )

(6)

PA,2'

= -2XPA,0Y+AXPA,0+2PA,01/2

(7)

PA,2

= P A , 2 * + PA,2'

(8)

PA,3

= * 2 { ( « + 2 ) P A / " « PA.O" (2-A)p A , 0 1 / 2 -2 p A 0 ^ 2 + ( 2 - a ) p

PA,4

=

1

A

^4}

- P A ,0 - PA.1 - PA,2 - PA,3

where

a

= tyk j = k^/k^

x

=

y =

(9) (10)

l/(l-Ct/2) (1+ a/2)/2

Through the system of equations (5) - (10), the structural configuration of all the monomer units during the cure is known as a function of the fraction of amine monomelic units which are completely unreacted ( p A Q), the initial stoichiometric ratio of epoxide groups to amino-hydrogen groups (r), and the ratio of rate constants (a). The reaction vector [ p A j, . . . , p A 4 , p E ] is used in the probability model described in the next section for the prediction of structural parameters during polymerization.

Branching Theory A s an epoxy cures with an amine, complex branched molecules are formed.

The

development of these three dimensional structures determines processing properties, including viscosity, gel point, crosslinking and modulus. Following the structural build-up

259 of the network during polymerization is difficult. Before gelation, branched systems are characterized by a broad molecular weight distribution. Experimental determination of this distribution is difficult. After the gel point part of the reacting system is incorporated into an insoluble gel with an infinite weight average molecular weight. Very few methods exist which can characterize the gel structure. Clearly theoretical relations capable of predicting network structure from the starting materials and the extent of reaction would be valuable. Several statistical methods have been developed to calculate relations between the extent of reaction and molecular parameters. Flory and Stockmayer^14) established the basic theoretical concepts of a tree-like model to describe the branching of a polymer during curing. However, this technique computes the entire molecular weight distribution and therefore is quite difficult to apply to more complicated cure mechanisms (for example, copolymerization with substitution effects). Two other approaches have been developed to extend the basic concepts set forth by Flory and Stockmayer. The first approach by Gordon and co-workers (15 ' 16 ) uses the theory of stochastic branching processes and requires deriving probability generating functions. Macosko and Miller'17,18^ have developed an alternative approach for predicting network structure which is based directly on the recursive nature of the blanching process and elementary laws. Using the recursive approach and the assumptions listed in proceeding section concerning the reaction mechanism, an expression has been derived' 18 ) for the weight average molecular weight as a function of the reaction vector [p A j

p A 4 , p E ], and the

stoichiometric ratio of epoxy to amino-hydrogen groups (r). Figure 5 shows the predicted change of the weight average molecular weight with increasing conversion of epoxy groups for three different stoichiometric ratios. The reaction vector is dependent on the ratio of rate constants of the secondary amine to primary amine reaction, and in Figure 5 a is assumed to be 0.2. The gel point is defined as the conversion at which the weight average molecular weight diverges and an infinite network begins to form. As is illustrated in Figure 5, the molecular weight builds very slowly until near the gel point. The conversion at gelation is highly dependent on the initial ratio of epoxy groups to amino-hydrogen groups. An expression can be derived for the gel conversion of epoxy groups (Figure 6), by setting the molecular weight equal to infinity and solving for the conversion as a function of the stoichiometric ratio/ 18 ) There is a point at which the ratio of epoxide to amino-hydrogen groups is so small that the system will not gel. This is known as the critical stoichiometric ratio. Under the condition that a = 0.2, the critical stoichiometric ratio is predicted to be 0.42.

260

Figure 5. Recursive model predictions for molecular weight as a function of conversion at three different stoichiometric ratios. For the model predictions, the ratio of the secondary amine to primary amine (a ) is assumed to be .2.

STOICHIOMETRIC RATIO

Figure 6. Recursive model prediction for the gel conversion of epoxide groups as a function of the initial stoichiometric ratio of epoxide groups to aminohydrogens. For the model predictions, the ratio of the primary to secondary amine reaction (a) is assumed to be .2.

CONVERSION

Figure 7. Recursive model predictions for the weight fraction of soluble material versus the conversion of epoxide groups at three stoichiometric ratios.

261 The recursive approach can also be used to predict post-gel properties. Using the preceding assumptions concerning the epoxy-amine cure reaction, an expression has been derived for predicting the weight fraction of soluble material/ 18 ^ Figure 7 shows the predicted change of sol fraction as a function of epoxide group conversion, assuming a = 0.2. Another parameter which can be derived from the recursive theory is the weight average molecular weight of the longest chain which passes through a randomly chosen point on the molecule. This structural parameter reflects the hydrodynamic size of a branched polymer and thus has been found useful in correlating the viscosity rise during polymerization/19^ Miller et al/ 2 0 ' have derived the longest linear chain for a chemical system which has equal reactivity of functional groups of the same type, and where the monomeric molecular weight of the crosslinker is negligible compared to the weight of the other monomer.

This

derivation has been extended to include the substitution effect and the monomer weight of the amine crosslinker/ 21 ^ Figure 8 compares the rise of the weight average molecular weight with the molecular weight of the longest linear chain at balanced stoichiometry. Figures 5 - 8 assume that the ratio of rate constants for the secondary amine to primary amine reaction is 0.2. However, as discussed in the previous section, the magnitude of the substitution effect in the DDS system is controversial. The literature reports values ranging from 0.2 - 0.6. In systems with complicated cure chemistry, it is frequently difficult to ascertain specific values for the rate constant ratios of the various reactions which occur during polymerization. Hence, it is important to consider the sensitivity of the predictions for structural parameters to variations in rate constant ratios. Figure 9 examines the change in gel conversion with the magnitude of the substitution effect. At balanced stoichiometry, when a = 0.2 the predicted gel conversion is .61, while the gel conversion is .59 when a = 0.6. The gel conversion is most sensitive to variations in a in systems containing excess amine. Experimental The goal of this study is to develop relationships between rheological properties and the build up of network structure during polymerization. Therefore, it is first necessary to test the ability of the branching expressions to predict molecular parameters. Then these expressions can be combined with rheological and kinetic data to form structure-property models. As described in previous section, the recursive method is capable of predicting conversion at gelation as a function of the stoichiometric ratio of epoxide to amino-hydrogen

262

MOLECULAR WEIGHT

0.25 0.50 CONVERSION

0.75

Figure 8. Comparison of the weight average molecular weight and the molecular weight of the longest linear chain at gelation.

GEL CONVERSION

r = 1.0

0.6

r = 2.0

0.4 0.2

0.1

0.01

k2/K1

Figure 9. Conversion of epoxide groups at gelation versus the rate constant ratio of the secondary amine to the primary amine reaction for three different stoichiometrics.

l.o 0.8

GEL CONVERSION 0.6

0.5

1.0

1.5

STOICHIOMETRIC RATIO

Figure 10. Gel conversion of epoxide groups versus stoichiometric ratio. Predictions of the recursive theory are indicated by the solid line. Experimental gel conversion values ( • ) were obtained by DSC.

263

groups. To test this relationship, samples of given stoichiometric ratios were cured in narrow test tubes immersed in a 177°C oil bath. At various reaction times, the samples were removed from the oil bath and rapidly plunged into an ice bath to stop the reaction. The samples were then removed from the test tubes and extracted with tetrahydrofuran. The gel time was designated as the cure time at which the sample just cannot dissolve in the solvent. The conversion of epoxide groups at this time is determined by differential scanning calorimetry (DSC)/ 21 ' These results are plotted along with the predictions of the recursive theory (assuming a=0.2) in Figure 10. Good agreement is seen between the experimental points and the recursive theory. The critical stoichiometric ratio predicted by the branching theory can be verified by curing samples with different stoichiometric ratios and performing extraction experiments to determine gel content. Several DGEBA-DDS samples were prepared with the stoichiometric ratio of epoxide to amino-hydrogen groups ranging from 0.2 to 0.6. The samples were placed under nitrogen in a 177°C oven for approximately 24 hours, and then were post-cured at 230°C for 8 hours. The samples were then crushed, placed in cellulose thimbles, and extracted for a week in tetrahydrofuran. The critical stoichiometric ratio is the largest ratio of epoxide to amino-hydrogen groups where the polymer is still completely soluble. The critical stoichiometric ratio for DGEBA-DDS was determined to be 0.40 ± 0.01. Comparison between this value and the predicted value from the recursive theory is shown in Figure 10. The sol fractions of samples cured beyond the gel point were also measured for the DGEBA system. Samples were cured at various time in a 177°C oil bath. The reaction was stopped by quenching in an ice bath. Pre-weighed samples were crushed, placed in extraction thimbles, and extracted in tetrahydrofuran for several weeks, with the solvent exchanged periodically. Then the samples were dried under vacuum until no further weight loss could be detected. The final sample weight was obtained and the weight fraction of solubles was calculated. The conversion of epoxide groups at a given cure time was determined by DSC. Figure 11 shows excellent agreement between theoretical and experimental values obtained for DGEBA-DDS at balanced stoichiometry. Correlations between structure and rheological properties can be established by simultaneously measuring viscosity and conversion during cure. The steady shear viscosity rise for the DGEBA-DDS system has been monitored using the parallel plate geometry (50 mm diameter plates with ~ 1 mm gap) on a Rheometrics System Four Rheometer. The cure was conducted at 177°C under a nitrogen environment. At specific times during the cure, the reaction was stopped in the rheometer by quenching in liquid nitrogen. Sample was then

264

SOL FRACTION

0 6

0.4 0.6 CONVERSION Figure 11. Weight fraction of solubles versus conversion of epoxide groups with balanced stoichiometry. Predictions of the recursive theory are indicated by the solid line and experimental values by the symbol ( • ).

1 0 •>

VISCOSITY (Pa-sec)

10 1

o

i

o •

*

a

r = .60 r - .80 r = 1.00 1 = 1.72 • 1 = 2.00

• • A 0

•

•

,

»

o 10-1 " "

•

• O A • A Ci

10-

0.0

0.2

0.4

0.6

0.8

1.0

CONVERSION

Figure 12. Viscosity rise versus conversion of epoxide groups at stoichiometric ratios ranging from .6 to 2.0.

265 removed from the rheometer and analyzed for conversion by DSC. Thus, the viscosity rise can be obtained as a function of conversion (Figure 12). Using the recursive theory, the molecular weight of the longest linear chain can be determined at any conversion. Thus in Figure 13 the viscosity is plotted as a function of molecular weight of the longest linear chain. As seen, the viscosity data for different stoichiometric ratios collapses onto a single curve. It has been shown that the viscosity for many undilute polymers with chain lengths less than 300 - 500 main chain atoms is dependent on the friction factor £ and molecular weight M: T) 2 "Ai

=

i21nAi

(7)

fAw

is the functionality average derived from the second moment of the functionality distribution ("weight" average). Gel point The critical conversion at the gel point is given by the equation

Det

1

-F*

1

fAe fEa

= 1

0 ,

(8)

where = (3Fa(ze)/3ze)

or, using Eqs. (3) - (7)

and k

f£ = O F e ( z a ) / 3 z a ) z

A

273

n

_

F

Ai(as+2at)2

a

+

EinA.(as+2at] F

t

aA

= aE

E

so that the ring-free gel point condition is given by [

VfAw"

2 )

+

VttA]aE

1

=

(9)

'

and the following relation exists between a,A. and a„ £J a

E

= r

AaA '

Where

r

A

=

2N

AO / N EO

and N„_ and are the initial numbers of moles of amino and AO EO epoxy groups, respectively. For an ideal case (all hydrogens are 2

of equal reactivity), a^ = a n d equation (f

Eq.(9) goes over to the well-known

- 1) c^Og = 1•

The critical mole ratio of amino hydrogens to epoxy groups, r A c , necessary for gelation, is obtained from Eq.(9), upon making the substitution a

A=1/rAc

and

a

E=1

One obtains the relation (f

Aw"2)/rAc

+ r

Ac a t = 1

'

which yields r

For an

Ac

1 + [1 - 4a(f - 2)] 1 / 2 T ^ 2a t

ideal case, Eq. (10) gives r„

= f. - 1.

Ac

The extinction probabilities

Aw

and v E are the key quantities for

the postgel stage. They are conditional probabilities saying that, given a bond exists, the sequence of bonds (subtree) is finite (2-4). They are given by the relations V

A = W

V

which, in this case, gives

E = F E ( v A'

'

274

= i

Vft

s_E a

V

E

=

1

"aE

+ a

t_E

(12)

f

A An

EvA

(13)

The roots 0 Sv < 1 are the values of

and v E looked for.

Sol fraction The sol fraction, w g , is composed of units having all bonds with finite continuation. The sol fraction w g is calculated from the pgf's F q a and after weighting the probability that a bond exists with the extinction probability. Thus, W

S = ^mAi(ap + asVE + atVE)l+raDE(1 "

^

W

2

(14)

'

where the Weight fractions m , are given by Ai N m

Ai

=

M m

N .M +N M Ai Ai DE DE

DE

=

1

" ? m A1 i

;

(15)

N,. and N-,, are numbers of moles of PA having i amino groups and of LJti

A 1

diepoxide, tespectively, and M ^ and Mpg are the respective molecular weights. Since N

PA=

r

A = f An N PA / 2 N DE

P Ai'

n

FA = N P A / ( N P A + N DE»'

N

Ai/(NPA

+I

V

= n PA n Ai

and

„ m

or

n

PA =

2r

A/(2rA

+ f

An> '

2n. . M . r_ Ai Ai A ¿r, En, .M, , + f-M_,_ A i Ai Ai A DE

Concentration of elastically active network chains (EANC) An elastically active network chain in the gel is defined as a sequence of units having two and only two bonds with infinite continuation terminated at both ends by units having at least three bonds with infinite continuation. The EANC's may have finite

275

side branches, so that the definition of the molecular weight between crosslinks depends on whether these side branches and parts of the end units are counted or not (8). The number of EANC's per unit is derived from the number of their end units (cf. e.g. Ref.2).. In the present case, only the PA units can contribute to the number of EANC's, because the DE units are bifunctional. The distribution of the PA units with respect to the number of bonds with infinite continuation is obtained by substitution of the variable z„ according to z. E whereupon only bonds with infinite continuation are counted. The pgf's for this distribution T (z) is thus

(17) For networks formed from small monomers it is the standard procedure to consider each unit having j (j 6 3) bonds with infinite continuation to contribute jt ./2 to the number of EANC's. Here, however, the PA units contain flexible chains which.themselves may contribute to the number of EANC's, if the definition of an EANC is fulfilled. Thus, in diamines the polyether chain and in higher polyamines the arms of the star can become EANC's. The particular result depends on the number of arms of the star PA. Considering here the case of the commercial triamine which may be composed of non-functional molecules, monoamine, diamine and triamine molecules, it is only the diamine and triamine molecule which can contribute to EANC's. An analysis of the possible contributions, considering also the role of the central branch point, shows that the number of EANC's N , can be expressed as e 6 N

e

=n

PA

(1/2)

I

6 (3

3 -6)tAj =

(3n

PA/2) i

(j

"2)t

Aj

(18)

276

The sums E jtB. and « j?3

£ t . can be obtained from. T R ( z ) by differenA j=3

tiation. Thus, ,^3jtAj and

6 I3TAj

=

=

T

1

A(1) "

T

k(0) ~

-TA(0)

_ T

A

T

A

(0)

(0)/2

Here, T^(X) = 3TR (z) / 3 z) z = x and T " (X) = (3 2 T A (z)/3z 2 )

z=x

The concentration of EANC's per unit volume in the whole system including sol v

e

and per unit volume of the gel, v

eg

, is

v Ve

fi

"

N d M eg eg = Mwg

(19)

,

where d and d g is the specific mass of the system and gel, respectively, w

= 1-w

is the gel fraction and M is the average

molecular weight of the system M = n_,, in„.M,. + n^M,.,, PA h Al Ai DE DE

.

Calculation of the coefficients of the generating

(20)

functions

To be able to calculate the gel point conversion, the extinction probabilities, and the postgel parameters, one needs a relation between a , a . a. and the conversion of amine functionalities a,. p s' t A It has been shown before

(2,9) that these relations include the

rate constants for the reaction of the amino groups with epoxy groups k

A

P

+ E

A E +E s

k

1 2

»•

A E s A. E_ t 2

Under the reservations discussed in Ref. 2, the relations are

a

s = 7 ^ - K " V

0. At this mix mix point phase separation occurs. This is shown in Figure 6 for all three

systems,

in

which

X A =X B =10

at

150 oc.

While

in

systems

containing DR and MY the rubery segments are still soluble in the epoxy matrix, phase separation occurs in the trifunctional system at rubber concentration 20% < X 0 C in a system containing DR. The elastomeric domains are continuously developed

322 during the isothermal cure. If the reaction is quenched before the reaction is completed, morphologies other than those of particles may be obtained. The final shape and size of the domains are determined by the temperature and time of cure.

Figure 8. Optical micrographs of a system containing DR/BER/DDS with 8% rubber cured at 80OC for: (a)14h, (b)15h, (tetra) > T g (di). The overall reaction order of the reaction and activation energies decrease with increased BER content in systems containing DR and XD but remain about the same in systems containing MY.

323 While systems containing BER are transparent, phase separation was observed in systems containing BER-CTBN diepoxide. Phase separation depends on the chemical nature of the reacting time and the rubber monomers, reaction temperature and concentration. Phase separation was followed dynamically and explained by thermodynamic considerations, taking into account the changes in entropy and in enthalpy of the system. Compatibility depends on the solubility parameters of the rubber and the epoxy system and was presented dynamically as a function of reaction time and temperature.

References

1. 2. 3.

L.E. Nielsen, J. Macromol. Sci., Revs., C3 (1969), 69-103. J.P. Bell, J. Polym. Sci., b-2, 8 (1970), 417-436. K. Dusek, M. Ilavsky and S. Lunak, J. Polym. Sci., Polym. Symp., 53 (1976), 29-44.

4.

K. Dusek, in: Rubber modified thermoset resins (C.K. Riew and J.K. Gillham, Eds.), Advances in Chemistry Series) 208 (1984), 3-14.

5. 6.

K. Dusek, Br. Polym. J. , 17 (1985), 185-189. C.W. Macosko and D.R. Miller, Macromolecules 199-206.

7.

C.K. Riew, E.H. Rowe and A.R. Siebert, in: Toughness and brittleness of plastics ( R.D. Deanin and A.M. Crugnola, Eds.), Advances in Chemistry Series, 154 (1976), 326-343. L.T. Manzione, J.K. Gillham and C.A. McPherson, J. Appl. Polym. Sci. 26_ (1981) 889-905, 907-919.

8. 9.

9 (1976),

Rubber Modified Thermoset Resins (J.K. Gillham and C.K. Riew, Eds.), Advances in Chemistry Series 208 (1984).

10. C.K. Bucknall and T. Yoshii, Br. Polym. J.

10

(1978),53-59.

11. W.A. Romanchick, J.E. Sohn and J.F. Geibel, in: Epoxy Resin Chemistry 2 (R.S. Bauer, Ed.), ACS Symposium Series 221 (1983), 85-118. 12. W.J. Gilwee and Z. Nir, Polym. Mater. Sci. Eng. Prep. 49(1983), 228-237.

324 13. T.G. Fox, Bull. Am. Phys. Soc. 1 (1956), 123. 14. L.C. Chan, H.N. Nae and J.K. Gillham, J. Appi. Polym. Sci. 29 (1984), 3307-3327. 15. T.G. Fox and S. Loshaek, J. Polym. Sci., 15, ( 1955), 371-390; ibid, 15 (1955),391-404. 16. K. Horie, H. Hiura, S. Sawada, I. Mita and H. Kambe, J. Polym. Sci., Al, 15 (1970), 1357-1372. 17. R. B. Prime, Polym. Eng. Sci. 13 (1973), 365-371. 18. H.N. Nae, J. Appi. Polym. Sci. (1986), in press. 19. H.N. Nae, J. Appi. Polym. Sci. 3J. (1986), 15-25. 20. A.J. Kinloch, S.J. Shaw, D.A. Tod and D.L. Hunston, Polymer 24 (1983), 1341-1354, 1355-1363. 21. S. Krause, J. Macromol. Sci. C7 (1972), 251-314.

THEORY OF ELASTIC PROPERTIES OF HETEROGENEOUS COMPRESSIBLE NETWORKS

S.A. Patlazhan Institute of Chemical Physics, Academy of Sciences of the USSR, 1424 32 Chernogolovka, Moscow region, USSR

Introduction The majority of works on high-elasticity properties of rubbers are based on the assumption that the specimen volume does not change in the deformation process, i.e., on the so-called incompressibility condition. This assumption is quite justified for the solution of some problems. At the same time, the volume of real polymer networks show small deformation changes (1,2). Neglecting of this fact may give rise to rough errors in some calculations. Thus, a small deviation of Poisson's ratio of a polymer binder from 0.5 in the calculation of the effective elastic constants for highfilled composites results in a substantial change of these characteristics (3) . Compressibility of polymers has been studied using homogeneous elastomers (1,2,4,5). An alternative approach consists in the consideration of the microstructure effect of crosslinked polymers on their properties within the framework of the statistical theory of elasticity. Indeed, crosslinked polymers are, as a rule, heterogeneous, which may be explained by, e.g., the phase stratification, presence of crystallites, spatial fluctuations in cross-link density, supramolecular formations, etc. In turn, heterogeneities may change the elastic behavior of the material as a whole, including the dependence of the compressibility on deformation. The study of high elasticity in heterogeneous systems is also of interest because of the possible application of the results to the calculations of the macroscopic properties of polymer composites. This paper is devoted to an investigation of the above mentioned problems . With this aim, the relationship between the mean stress and the

Crosslinked Epoxies © 1987 Walter de Gruyter & Co. • Berlin • New York - Printed in Germany

326 deformation has been derived, called the high-elasticity equation, for compressible Gaussian networks, taking into account random spatial fluctuations of the elastic moduli. This equation permits one to establish the dependence of the high-elasticity behavior of networks as a function of the measure of structure inhomogeneitv - dispersion of shear modulus fluctuations. The relative change in the volume has been studied as a function of the measure of structure inhomogeneity and the deformation of the specimen.

Theory High-Elasticity Equation for Compressible Heterogeneous Gaussian Networks Let us consider an amorphous elastically heterogeneous crosslinked polymer. ]ji order to calculate the high-elasticity behavior of such a material as a whole, one should know the dispersion of elasticity modulus fluctuations, conditions at the interface, and the shape of heterogeneities. Therefore, there is no need in specifying the nature of heterogeneity. The suggested theoretical analysis is valid for a description of the elastic properties of both networks with the random cross-linking distribution and filled polymer composites. We shall assume that heterogeneous regions are of an equiaxial shape and that the displacement vector of the phase is continuous everywhere. On a small scale, when the distances are comparable by an order of magnitude with the grain size of heterogeneities, the material may be considered as homogeneous with definite values of the elasticity moduli. The elastic properties of heterogeneous regions of compressible Gaussian networks obey the high-elasticity equation in the Flory form (4): a i k (?) =

3