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English Pages 641 [644] Year 1987
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