Chemorheological and dielectric study of epoxy-amine for processing control
Transcript of Chemorheological and dielectric study of epoxy-amine for processing control
Chemorheological and dielectric study ofepoxy-amine for processing controlS Pichaud,1 X Duteurtre,1 A Fit,1 F Stephan,2* A Maazouz2 and JP Pascault21Renault, Direction de l’Ingenierie Vehicule, Laboratoire des Proprietes Physiques des Polymeres, 92508 Rueil-Malmaison Cedex, France2Laboratoire des Materiaux Macromoleculaires, UMR CNRS 5627, Institut National des Sciences Appliquees de Lyon, 20 Boulevard A.Einstein, 69621 Villeurbanne, France
Abstract: The curing of an epoxy prepolymer based on diglycidyl ether of bisphenol A (DGEBA) with
isophorone diamine (IPD) as a hardener was analysed using differential scanning calorimetry,
rheological measurements, microdielectrometry, and insolubles in THF for gel point detection. The
effects of the initial hydroxyl concentration of the DGEBA prepolymer, the molecular features of which
are different, were determined on the cure kinetics of epoxy networks Chemical reaction kinetics of this
DGEBA/IPD system during isothermal conditions was studied in the 60±120°C temperature range and
a kinetic model relation based on assumption of an autocatalytic mechanism has been proposed.
Gelation and vitri®cation phenomena of this reactive mixture were studied and allowed us to establish
the TTT diagram. Furthermore, dielectric data and viscosity measurements have been interpreted
with respect to kinetics. Indeed, it was shown that the modi®ed percolation law equation suggested by
Macosko et al can be used to describe the chemoviscosity as a function of temperature and extent of
reaction by using a temperature- and conversion-dependent critical exponent. In other respects,
dielectric properties such as ionic conductivity were related on one hand to viscosity through a Stokes-
based equation in the 0 to 0.5 conversion range, and on the other hand to conversion through an
experimental equation.
# 1999 Society of Chemical Industry
Keywords: epoxy-amine; chemorheology; dielectric; processing control
INTRODUCTIONThe most important aspect in thermoset processing is
the chemorheological behaviour of the reactive bath
during the cure cycle. If injection moulding is an
attractive production technology for saving time and
costs, such a curing process of thermoset composite is
quite complex due in part to the high exothermicity of
the reaction but also to the low thermal conductivity of
the material under cure, leading to high temperature
gradients through the moulded part. Thus, emphasis is
placed on optimizing the cure process with the intent
of improving a part of the performance but also
improving productivity. As a consequence, in the last
decades, better understanding of the cure process has
become of foremost importance for thermoset manu-
facturers to optimize cure cycles. At present there is no
technique to carry out in-situ thermoset cure monitor-
ing. Microdielectrometry, which has been developed
for about 15 years, seems to be a promising technique
to obtain on-line real-time data and to interpret
properties such as the cure extent of a reinforced
composite. The dielectric behaviour of thermosets
during reaction has been reviewed by Senturia and
Sheppard1,2 and epoxy polycondensation, in particu-
lar, was studied. However, interpretation of dielectric
data with chemorheology is still subject to a great deal
of scienti®c discussion.3±10
Manufacturing processes such as compression
moulding, reaction injection moulding (RIM), resin
transfer moulding (RTM), etc3,4,10,11 are concerned
with this type of mould instrumentation. Nevertheless,
before including microdielectrometry as an expert
closed-loop process-control system in a production
line, preliminary laboratory study has to be carried out.
This report deals with the kinetic, rheological and
dielectric investigation of an epoxy-amine system
formulated for RTM processing. The main focus of
this issue is to establish relationships between time,
temperature, extent of reaction, glass transition
temperature, viscosity and ionic conductivity. For
this, the reaction of diglycidyl ether of bisphenol A,
DGEBA, and diamine, IPD, mixture was investigated
by means of calorimetry, microdielectrometry and
viscoelasticimetry, in the temperature range corre-
sponding to the process window. Isothermal poly-
condensations at 60, 80, 100 and 120°C were
examined. The experimental results for the reaction
kinetics and the effect of the initial hydroxyl concen-
tration of DGEBA reacted with a cycloaliphatic
diamine are presented. Results are compared with
Polymer International Polym Int 48:1205±1218 (1999)
* Correspondence to: F Stephan, Laboratoire des Materiaux Macromoleculaires, UMR CNRS 5627, Institut National des Sciences Appliqueesde Lyon, 20 Boulevard A. Einstein, 69621 Villeurbanne, France(Received 4 March 1998; revised version received 4 June 1998; accepted 7 July 1999)
# 1999 Society of Chemical Industry. Polym Int 0959±8103/99/$17.50 1205
theoretical and empirical models in terms of conver-
sion, viscosity and dielectric properties.
EXPERIMENTALMaterialsThis study was carried outusing a reactive system which
contains mainly an epoxy diglycidyl ether of bisphenol
A, (DGEBA) and a hardener comonomer isophorone
diamine, (IPD). The chemical formulae of the reactants
are shown in Fig 1. The present work investigates the
reaction kinetics of a liquid epoxy prepolymer DGEBA
with IPD that was catalyzed for RTM applications. The
kinetic, rheological and dielectric behaviour of this
catalyzed formulationwascompared to thatof a reactive
system also based on DGEBA and IPD mixtures, but
without any catalyst. Table 1 lists the different reactive
systems used. The components were stored separately
untilneededandthereactantswereusedasreceivedwith
a stoichiometric ratio of amino hydrogen to epoxy of 1;
the formulation is 100g DGEBA for 25g IPD. Because
of the high reactivity of systems based on DGEBA and
IPD, the reactive mixtures were prepared in a condi-
tioned room at 19°C just before being used in order to
prevent reaction starting during this procedure.
Differential Scanning CalorimetryA Mettler Thermoanalyser TA 4000 DSC, operating
in the ÿ100°C to 300°C temperature range and
equipped with a liquid nitrogen cooling system, was
used to determine the enthalpy of reaction, Tg
(detected at the onset of the de¯ection heat capacity
change), and variation of the heat capacity DCp
through the Tg of the samples.
The heating rate was 10°C minÿ1 in a nitrogen
atmosphere. The Tg0and the isobaric heat capacity of
the initial unreacted mixture DCp0were determined
during a ®rst scan, whereas the fully cured material
glass transition temperature Tg?and its corresponding
heat capacity change DCp?were obtained during a
temperature scan of a sample isothermally cured at
170°C during a time that ensures complete reaction.
The reported values of the total enthalpy of the
reaction DHT, the initial properties of the reactive
mixture and the properties of the ®nal network are the
average of at least ®ve DSC scans.
Isothermal cures were examined in this study.
Microdielectrometry analysis and DSC pan sample
preparation were carried out using the same heating
press device developed in our laboratory.3 DSC pans,
sealed in air and containing approximatively 10mg of
monomers, were cut off during the thermal treatment
at various reaction times. Then, for the conversion
analysis, the heat ¯ow evolved during completion of
curing was measured. This residual heat of reaction
DHR was noted. The conversion, x, can be deduced
from DSC scans and calculated from the following
equation:
x � 1ÿ DHR
DHT
�1�
For the kinetic study, the reported conversion data are
the average of two DSC scans.
ViscoelasticimetryA Rheometrics Analyser (RDA II) was used to
measure the complex viscosity. Parallel plate geometry
was used with a diameter of 40mm and a gap size of
around 1.5mm. Measurements were carried out
during isothermal cures in the 50±90°C temperature
range over a frequency range from 1rad sÿ1 to 100rad
sÿ1 in three or ®ve steps depending on the cure
temperature. An initial strain amplitude of 50% at the
edge of plates was reduced during reaction down to
1% to ensure a linear viscoelastic response. The
evolution of the storage (G') and loss (G@) moduli
was recorded as a function of both the reaction time
and the frequency. Consequently, the complex vis-
cosity magnitude was derived from the frequency
dependence of the complex modulus, through the
complex relation Z* =G* /jo.
Figure 1. Molecular structure of the epoxy prepolymer and diamine used for the synthesis of eopxy networks.
Table 1. Systems studied
System
no DGEBA IPD
1 RTM formulation RTM formulation
2 DER332 (Dow) Merck
3 DER330 (Dow) Merck
4 DGEBA 0164 (Bakelite) Merck
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S Pichaud et al
Insolubles methodThe gelation reference timeswere determined by curing
samples at different temperatures in an isothermal bath
at various curing times. Gelation is considered to be the
timeatwhich thepresence of an insoluble fraction is®rst
detected in tetrahydrofuran (THF).
MicrodielectrometryDielectric measurements were performed using a
Micromet Eumetric System III apparatus. The elec-
trode con®guration was an interdigitated comb pattern
and a small amount of the reactive mixture was layered
over the electrode area. The Tool Mount Sensor
(TMS) allows dielectric measurements to be made
throughout the entire thermal cycle. This Micromet
Eumetric System III generates sinusoidal signals
between 5�10ÿ3Hz and 105Hz and transmits them
to the sensor electrodes. The reported dielectric
measurements were performed at a frequency range
of 1Hz to 100kHz. The evolution of permittivity (e'),loss factor (e@), and ionic conductivity (s) was
recorded as a function of both the reaction time and
the frequency. Ionic conductivity data were extracted
from dielectric measurements performed at a fre-
quency range of 1Hz to 100kHz. e@e0o is frequency
independent when conduction effects dominate, and
all curves of e@e0o as a function of curing time with
frequency as a parameter lie on each other and ensure
an accurate ionic conductivity measurement.
RESULTS AND DISCUSSIONEffect of DGEBA prepolymer structure on reactivityThe characteristics of the initial reactive mixtures and
of the ®nal networks were determined by DSC as
described in the experimental section. Thermograms
obtained from dynamic DSC scans are plotted in Fig 2
for the various DGEBA/IPD systems studied. Except
for the RTM formulation which contains an unknown
catalyst, all the other reactive mixtures differ from one
another in molecular characteristics of the DGEBA
prepolymer through the initial concentration of
hydroxyl groups which depends on the polymerization
degree n. Those values of n for each DGEBA
prepolymer are reported in Table 2. Table 2 lists the
experimentally obtained values of Tg0, Tg?
, DCp0,
DCp?, DHT and l (de®ned as the ratio of DCp?
and
DCp0) for each DGEBA/IPD formulation studied. The
values found (DHT=106kJ/epoxy equivalent) are of
the same order of magnitude as reported by Galy etal.12 Furthermore, the overall reaction heat values are
determined for each mixture and the results are
consistent with the values reported in the literature.
When considering the overall shape of the thermo-
gram, assumption of the non-equireactivity of primary
and secondary amino hydrogen groups can be stated.
Moreover, some authors13 showed that the main peak
characterizes mainly the reaction between the oxirane
function and the primary amino hydrogens. The
second peak at higher temperature that superimposes
on the ®rst one, resulting in a shoulder, is due to the
reaction of the secondary amino hydrogens. In fact the
particular case of IPD is really more complex because
primary and secondary aliphatic and cycloaliphatic
amino groups are involved in the cure process. It
should also be noted that the thermograms obtained
are somewhat different as a function of DGEBA
structure. As a matter of fact, higher reactivity is
exhibited with an initial hydroxyl concentration
increase. Moreover, the cure characteristics such as
the temperature at which curing started Ti, peaked Tp,
and completed Tf of the selected dynamic scans
Figure 2. DSC thermograms obtained at 10°C minÿ1 for the variousDGEBA/IPD based systems (no1: RTM formulation; no2: DER 332/IPD;no3: DER330/IPD; no4: DGEBA 0164/IPD).
Table 2. Experimental values of DSCcharacterization for the variousDGEBA/IPD resins considered
DGEBA/IPD
reactive system
Tg0
(°C)
DCp0
(J gÿ1 Kÿ1)
Tg?
(°C)
DCp?
(Jgÿ1 Kÿ1) lDHT
(Jgÿ1)
RTM formulation ÿ37 0.58 156 0.20 0.35 485
DER330, n=0.15 ÿ42 0.59 158 0.18 0.31 486
DGEBA 0164, n=0.15 ÿ39 0.62 154 0.21 0.34 469
DER332, n=0.03 ÿ43 0.58 153 0.21 0.36 481
Average* ÿ41 0.59 155 0.20 0.350 475
Standard deviation* 2 0.016 3 0.015 0.036 9
* Calculated from all experiments.
Polym Int 48:1205±1218 (1999) 1207
Chemorheological and dielectric study of epoxy-amine
presented in Fig 2, reveal that the variation in the
DGEBA structure affects the mixture reactivity. The
reactivity trend for the DGEBA/IPD systems can be
stated as DGEBA DER 330>DGEBA
0164>DGEBA DER 332; but the highest reactivity
is obtained for the catalyzed RTM formulation.
Evolution of the extent of reaction and glasstransition temperature versus cure time for variousisothermal curing temperaturesIn the ®rst stage of investigation, the RTM formulation
(DGEBA/IPD no 1) was examined at different iso-
thermal curing temperatures. Results from DSC
measurements during the reaction of this system at
60° 80, 100 and 120°C are presented. The increase in
theextentofreactionwasmonitoredasafunctionoftime
and the curves are plotted in Fig 3. In the early stage of
polymerization, namely at times shorter than vitri®ca-
tion time, no particular dif®culty occurs to determine
Tg. Nevertheless, when the sample Tg reaches the
temperature range at which residual polymerization
occurs, superposition of de¯ection heat capacity varia-
tion, related to glass transition and exothermic variation
duetotheresidual reaction,makes theTgdetermination
dif®cult. Accuracy of Tg determination is altered even
more,when, close tovitri®cation,physical ageing14,15 of
quenched specimens can be observed just before the
residual reaction isotherm.
Figure. 4 shows the extent of reaction vs time results
at Ti=80°C and for DGEBA/IPD (system no 1),
DER332/IPD (system no 2) and DGEBA 0164/IPD
(system no 4). Increase in the reaction rates was
observed when using DGEBA 0164 prepolymer
compared to DER332. This enhancement of the
polycondensation rate by replacing the DGEBA
prepolymer could be explained by the hydroxyl group
concentration contained in the prepolymer chains, as
previously expected from DSC thermograms com-
parison. In fact reactions are all the more catalyzed
that the hydroxyl concentration initially present in
DGEBA prepolymer is high. Moreover RTM formu-
lation remains the most reactive mixture and the
reactivity order previously stated was con®rmed.
Kinetic model of the curing reactionTwo main forms for the thermal cure kinetics have
essentially been proposed in the literature:16±26 these
are empirical and mechanistic models. Taking into
account the autocatalytic feature of epoxy-amine
systems, Kamal and Sourour16 suggested the following
semi empirical expression:
dx
dt� �k1 � k2xm��1ÿ x�n �2�
where n and m exponents represent the order of
reaction. The reaction rate constants k1 and k2 depend
on the temperature according to an Arrhenius
Figure 3. Extent of reaction versus time at different isothermal curingtemperatures (^) 60°C, (~) 80°C, (*) 100°C and (&) 120°C for DGEBA/IPD RTM formulation. Comparison between experimental data and kineticmodel prediction ( gelation; vitrification).
Figure 4. Comparison of the extent of reaction dependence on curing timesfor (*) DGEBA/IPD RTM formulation (^) DER 332/IPD and (~) DGEBA0164/IPD at 80°C (- fit).
Figure 5. Variations of the rate constants with temperature ln (^) K0, (~)K1=f(1/T) calculated from the second-order autocatalytic model.
1208 Polym Int 48:1205±1218 (1999)
S Pichaud et al
behaviour. Although the introduction of exponent
parameters allows an accurate adjustment of such
kinetic models from the experimental data to describe
satisfactorily the reaction advancement as a function of
both time and temperature, the main drawback of
these empirical equations comes from the fact that no
mechanistic information is contained in the kinetic
expression. Nevertheless, from an industrial point of
view, this ®rst form of kinetic model is very useful
because of its practical and relatively easy evaluation.
The second form of kinetic model is based on
mechanistic considerations and has been reviewed by
several investigators. Accordingly, including on one
hand reactions of the epoxide groups with primary and
secondary amino groups, and on the other hand other
possible reactions, namely etheri®cation and homo-
polymerization of the epoxy groups, very complex
kinetic expressions have been proposed to model the
different reactions involved during curing. Moreover,
Horie et al17 demonstrated that catalytic and non-
catalytic mechanisms have to be considered. Thus,
assuming equireactivity of primary and secondary
amines, they have proposed the following kinetic
model:
dx
dt� �k1 � k2x��1ÿ x��r ÿ x� �3�
in which k1 and k2 represent the reaction rate
constants of the autoaccelerated reactions of epoxide
with primary and secondary amines respectively, and rcorresponds to the stoichiometric ratio. Cole et al 18
have completed this kinetic model by taking into
account various etheri®cation mechanisms catalyzed
by tertiary amino groups, but different reactivities of
the primary and secondary amino groups have not
been explicitly considered.
By representing the complex curing reactions, as
developed by several authors, and in particular by
Riccardi et al19,20 the cure kinetics can be successfully
described. Owing to the temperature range concerned
(low temperatures) and to stoichiometric aliphatic
mixtures, etheri®cation and homopolymerization re-
actions can be neglected. The reactions can be
schematised as follows:
E� A1ÿ!k1A2 � �OH� �4�
E� A2ÿ!k2A3 � �OH� �5�
E� A1 � �OH�ÿ!k01
A2 � 2�OH� �6�
E� A2 � �OH�ÿ!k02
A3 � 2�OH� �7�
E� A1 � �HX�ÿ!k001
A2 � �OH� � �HX� �8�
E� A2 � �HX�ÿ!k002
A3 � �OH� � �HX� �9�
in which ki, k'i, k@i represent the rate constants of the
non-catalyzed reactions, those of the autocatalytic
reactions and those of the reactions catalyzed by
proton donor impurities, respectively. E, A1, A2, A3,
OH and HX correspond respectively to the epoxy,
primary amino, secondary amino, tertiary amino,
hydroxy and proton donor groups.
So, on the basis of this reaction scheme, and
assuming that:
(i) the reactivities of the epoxide groups are
independent,
(ii) the asymmetry of the aliphatic and cycloalipha-
tic amino groups of the diamine does not imply
different reactivities,
(iii) the ratio of rate constants k2/k1 (=n) does not
depend on conversion,
(iv) the single value of the ratio k2/k1, k'2/k'1 and
k@2/k@1 is respected,
(v) no etheri®cation occurs,
a series of differential equations as described by
Riccardi et al19,20 may be written in the particular
case of a stoichiometric epoxy/amine mixture, and
leads to the following expression, generally called the
second-order autocatalytic model:
dx
dt� 1ÿ x
2ÿ n�K0 �K1x��2��1ÿ n� � n�n=2� (10)
x � 1
2ÿ n�2ÿ �ÿ n� n�ÿ �n=2� �11�
8><>:with � � �A1�=�E0� �12�
K0 � k1 � k01�OH�0 � k001�HX�0�E�0 �13�K1 � k1�E�20 �14�
in which [E]0, [OH]0 and [HX]0 correspond to the
epoxy, hydroxy and proton donors initial concentra-
tions, respectively.
Details of the complete mathematical description
are reported elsewhere.21 This kinetic analysis has
been applied to obtain an expression for the extent of
reaction as a function of time and temperature of the
DGEBA/IPD system. According to values reported in
the literature concerning the ratio of secondary to
primary amino hydrogens' rate constants,22±25 k2/k1,
to the special dif®culty introduced by IPD for which
the two initial primary amines are different (aliphatic
and cycloaliphatic) and to the extent of cure value
reached at the critical gelation point (we shall refer to
this again elsewhere), this ratio was estimated to be
Table 3. Parameters of the second-order autocata-lytic model for DGEBA/IPD (RTM formulation)kinetics
Temperature
(°C)
K0
(minÿ1)
K1
(minÿ1)
60 0.023 0.056
80 0.049 0.285
100 0.234 0.524
120 0.473 1.634
Polym Int 48:1205±1218 (1999) 1209
Chemorheological and dielectric study of epoxy-amine
0.4. According to these considerations, the kinetic
parameters can be determined by ®tting the isothermal
cure experimental data to the previously described
autocatalytic function by a numerical Runge±Kutta
integration method. The calculations have provided
acceptable accuracy for the particular DGEBA/IPD no
1 system concerned as illustrated in Fig 3. Table 3
summarizes the K0 and K1 values calculated. The
experimental values were found to obey an Arrhenius
law (Fig 5). The rate constants K0 and K1 are thus
de®ned by the following relations:
K0 � 2:41 107 expÿ58:103
RT
� �minÿ1 �15�
K1 � 1:25 108 expÿ59:103
RT
� �minÿ1 �16�
If the activation energy of the autocatalytic reaction
rate constant K1 was found to be of the same order of
magnitude as those reported by other authors,20,26 the
evaluated activation energy associated to the rate
constant K0 was greater than expected.
Whilst the adjustment between experimental and
calculated results is satisfactory in the pre-vitri®cation
stages, discrepancy is clearly shown in the model after
vitri®cation. In fact, after vitri®cation, the reactions
become diffusion-controlled and the ®tting of the
previous kinetic model to the experimental results
fails. In order to describe the reaction throughout the
whole range of the cure, the effect of diffusion control
should be taken into account as proposed by some
authors.27,28
Relationship glass transition temperature versusextent of reactionIt is well known that in the case of epoxy/amine
reactive mixtures, the only relationship between Tg
and conversion that complies with data before and
after gelation is that which is also independent of the
cure temperature.29 Figure 6 presents the Tg vs extent
of reaction results for the different DGEBA/IPD
systems. The data points are experimental (experi-
mental errors derived from DSC measurement are also
shown on the data points), and the continuous line is
the model prediction based on DiBenedetto's ap-
proach:
Tg ÿTg0
Tg1 ÿTg0
� lx
1ÿ �1ÿ l�x �17�
From an extension of the Couchman equation,
Pascault and Williams29 showed that the adjustable
parameter l is equal to the ratio DCp?/DCp0
, where
DCp0and DCp?
are respectively the heat capacities of
the initial mixture and of the fully cured network. The
independence on one hand of the cure temperature
and on the other hand of the DGEBA/IPD system, as
veri®ed in Fig 6, indicates that a similar molecular
structure of the network is obtained, whatever the cure
temperature and the DGEBA molecular structure,
and the presence or not of an unknown catalyst.
Another explanation can be that the measured glass
transition temperatures are not suf®ciently sensitive to
detect small structural differences. The best DiBene-
detto compliance equation that was used to success-
fully describe the experimental Tg versus extent of
reaction data for the systems under study leads to a
value of l parameter of 0.35. Indeed, this adjustable lparameter was compared with the calculated DCp?
/
DCp0values. Results are reported in Table 2. Taking
into account the standard deviations induced by
experimental errors, the minimal and maximal limit
values of l can be estimated. The DiBenedetto model
predictions based on these latest values are illustrated
in Fig 6 by broken lines. As can be seen in this ®gure, it
should be of interest to note that such data processing
enables all the experimental values to be included
independently of the DGEBA/IPD system considered.
In other words, it means that the weak scattering
Figure 6. Dependence of Tg on degree of conversion for: DGEBA/IPD RTMformulation ([^] 60°C; [~] 80°C; [*] 100°C; [&] 120°C), DGEBADER332/IPD ([&] 80°C), DGEBA 0164/IPD ([*] 80°C) and DiBenedetto’smodel prediction (— l, ----- lmin and lmax).
Table 4. Gel time (tgel) for the differentDGEBA/IPD systems studied
tgel (min)
DGEBA/IPD system 60°C 70°C 80°C 90°C 100°C
no1 RTM formulation 51 26.5 14.5 8 4.5
no2 DER332 68 38 22 13.5 8
no3 DER330 ± ± 17.5 ± ±
no4 DGEBA 0164 65 34.5 18.5 10.5 6
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S Pichaud et al
observed in such representation could be attributed to
experimental dif®culties and not to possible differ-
ences in reactive system compositions; namely that a
single l value is able to describe all DGEBA/IPD
behaviour.
Gelation, vitrification and TTT isothermal cure dia-gramIn terms of industrial processing, the major event of
critical importance is the phenomenon of the viscosity
increase up to gelation. The occurrence of gelation
corresponds to the time at which an in®nite network
begins to form. The insoluble method in THF was
chosen to detect gelation and Table 4 reports the
experimental tgel values determined in the 50°C±
100°C temperature range. From these results, it was
found that gelation takes place at a conversion xgel
close to 0.61. From a theoritical point of view, for the
particular case of diepoxide-diamine polymerization
and according to the Flory±Stockmayer theory, gela-
tion occurs at xgel=0.577 for a reactivity ratio n =k2/
k1=1, and increases to 0.618 when k1�k2.22 Indeed,
it was shown experimentally and theoretically that gel
conversion depends on the magnitude of the substitu-
tion effect. When the primary amine hydrogens are
much more reactive than the secondary amine hydro-
gens, gelation occurs of course at a conversion degree
higher than that expected when equal reactivity of all
amine hydrogens is assumed. Consequently, the
established 0.61 conversion value at gel point agrees
with the theoretical prediction for the case when
k1�k2 and con®rms the assumptions expressed in
kinetics modelling. The gelation phenomenon was
found to obey an Arrhenius law, according to the
following relation:
tgel � 1:3110ÿ8 exp61:103
RT
� �;min : �18�
The gel point can also be determined using
rheological experiments. In fact, Winter30 showed
that the gel point can be directly measured by
following the loss tangent, tan d (o), versus cure time,
with the frequency as a parameter. These curves
intersect at the gel point. It was also found that G'(o)
and G@(o) are linear and parallel over the entire
frequency range measured at gel point and G@(o)�oD.
The theoretical critical exponent was evaluated at
0.72. Experimental results are shown in Table 5 and a
good agreement can be observed between the different
methods for determining the gel time. Moreover, the
established values of the percolation critical exponent
D show that the behaviour of this reactive model can be
satisfactorily described by the percolation theory.
Vitri®cation occurs when the glass transition tem-
perature of the reactive mixture reaches the isothermal
curing temperature Tcure. As described in the litera-
ture,31 when the Tg of the growing network is lower
than the cure temperature, the reaction occurs in the
liquid state and is controlled by the chemical reactivity
of the functional groups. Therefore, for isothermal
cures carried out at temperatures below Tg?(156°C),
the reaction may be affected by vitri®cation phenom-
ena. In fact when Tcure<Tg?, curing occurs in two
main stages: the ®rst one controlled by the chemical
reactivity of the groups, and the second one by
molecular diffusion when the growing network's Tg
reaches the cure temperature. As a consequence, the
vitri®cation process may hinder the reaction between
60°C and 120°C. In Fig 3, dotted arrows indicate the
vitri®cation times for the various isothermal cure
conditions studied.
The time-temperature-transformation (TTT) dia-
gram32±35 is commonly used to display gelation and
vitri®cation curves and helps interpret the curing
process. The TTT isothermal cure diagram for the
DGEBA/IPD system formulated for RTM applica-
Figure 7. TTT isothermal cure diagram for DGEBA/IPD RTM formulation[(*) gelation; (*) vitrification], DER 332/IPD [(&) gelation; (&) vitrification]and DGEBA 0164/IPD [(~) gelation; (~) vitrification].
Table 5. Critical times as a function ofgel criterion and critical exponent of thepower law G'(o)�G@(o)�oD for theDGEBA/IPD system no1 cured atvarious isothermal temperatures
T(°C) 50 60 70 80 90 100
tgel (insoluble) (min) 102 51 27 14 8.5 5
ttan d (min) ± ± ± 15 10 ±
t G' / G@ / oD (min) ± ± 26 14 9 6
D ± ± 0.719 0.721 0.729 ±
Polym Int 48:1205±1218 (1999) 1211
Chemorheological and dielectric study of epoxy-amine
tions is given in Fig 7. Gelation curves related to
DGEBA/IPD mixtures no 3 and 4 are also plotted.
The critical temperature gelTg, at which vitri®cation
and gelation occur simultaneously, can be deduced
from such a diagram and was estimated at around
32°C.
Rheological measurements and modellingFigure 8 shows the evolution of the magnitude of the
complex viscosity, Z* , as a function of time for various
isothermal conditions using neat and fresh RTM
formulation (system no 1). Using the dynamic analysis
described in the experimental part, we assume that the
complex viscosity gives a good estimation of the
viscosity during the curing reaction up to the gel
point. Viscosity pro®les indicate that molecular
modi®cations due to reaction effects provide signi®-
cant variations in rheological behaviour. In fact, as a
consequence of the increase in molar mass of the initial
prepolymer and subsequent branching and further
crosslinking progress, viscosity rapidly begins to
increase, all the more that the DGEBA/IPD system
reactivity is very high.
The effects of temperature and time on the
chemorheological behaviour can also be described in
terms of conversion from the knowledge of both the
kinetics of the reaction and the temperature. Thus, by
combining the effect of reaction as described in the
®rst part, a model of the chemorheology Z=f(T, x) can
be established.
The chemorheology of thermosets during cure and
especially for epoxy polycondensation has been
reviewed by Roller36 and recently by Halley and
MacKay.37 Several chemoviscosity models, which
have been developed for about 20 years, appeared in
the literature to forecast isothermal and non-isother-
mal cure data of thermosets. In the particular case of
reactive mixtures based on epoxy, it seems that two
predominent chemorheological models are used to
predict the viscosity behaviour from the extent of the
cure, expressed as epoxy conversion, x, or glass
transition temperature, Tg(x), and temperature data.
The ®rst kind of empirical expression was derived from
the modi®ed WLF equations38,39 based on the free
volume theory and was formulated as:
ln��T,t���Tg�x�� �
C1�x��TÿTg�x��C2�x� �TÿTg�x�
�19�
where x is the extent of reaction, Z (Tg) is the viscosity
at Tg, C1(x) and C2(x) are both material- and
conversion-dependent parameters.
The second kind of empirical expression is based on
the percolation law40±42 applied to viscosity and was
developed by Macosko et al41,42 through the following
expression:
��T��0�T� �
xgel
xgel ÿ x
� �A�Bx
�20�
where
�0�T� � A� expE�
RT
� ��21�
in which Z0 is the initial viscosity of the unreacted
mixture, x is the conversion, xgel is the critical
conversion at the gelation point, A and B are
material-dependent parameters, AZ and EZ are the
parameters of the Arrhenius law concerning initial
viscosity. Referring to previous comments concerning
the ability of the percolation theory to describe the
behaviour of the reactive system at gelation, this
second approach was chosen and was found to be
able to describe the chemoviscosity behaviour of
DGEBA/IPD systems.
Assuming any extent of reaction, the initial viscosity
Figure 8. Viscosity of DGEBA/IPD system no1 as a function of time withcure temperature as a parameter: (&) 90°C; (*) 80°C; (~) 70°C; (&)60°C; (^) 50°C.
Figure 9. Arrhenius plot of the initial viscosity Z0 vs 1/T (K) for the DGEBA/IPD system.
1212 Polym Int 48:1205±1218 (1999)
S Pichaud et al
of the epoxy system was measured by a dynamic
rheometer as described previously at different fre-
quencies for various temperatures. The data agree
with an Arrhenius temperature-dependent viscosity
(see Fig 9). The viscosity function is as follows:
�0�T� � 1:15:10ÿ12 exp68:103
RT
� �; �Pa s� �22�
By combining the critical value xgel=0.61 and the
effect of cure expressed through the chemical kinetics
x =f(t, T) with rheological measurements performed
at various isothermal cure temperatures, log Z=f(x)
curves can be plotted as illustrated in Fig 10. The data
points are experimental values and the lines are the
model predictions based on eqn (19). Such a
representation shows a very good agreement between
the experimental curves up to x =0.50 and those
obtained by the modi®ed percolation law. Although
the percolation model was initially established to
describe properties near the gel point through a
constant critical exponent, the chemoviscosity calcula-
tion was able to follow the behaviour exhibited by the
experimental data from the beginning of the reaction
up to the gelation limit. It can be explained by the use
of a conversion-dependent critical exponent, leading
to a widening of the window of validity of application
of such a law. Correlation plots show also that some
deviations of the predictive law were observed when
conversion comes near to xgel. Moreover this model is
able to forecast cure data up to x =0.50. The
explanation of such deviation derives from the fact
that a frequency effect due to the viscoelastic feature of
the reactive system arises when approaching the gel
time that the previous model does not take into
account. Thus, for the studied isothermal cure
temperatures, the values of the percolation law par-
ameters were deduced by an adjustment method based
on error minimisation. Table 6 presents the results
obtained. In fact, very little is available in the literature
to compare the order of magnitude of these parameters
of various epoxy-amine systems. If this type of viscosity
modelling can satisfactorily be included in industrial
processing and more particularly in a process-simula-
tion program, the temperature dependence of such a
relation has also to be established. In fact, it seems that
this temperature dependence is included in the
Figure 10. Comparison of the variation of measured and predicted viscosity of DGEBA/IPD RTM formulation as a function of extent of reaction at differenttemperatures: (^) 50°C; (&) 60°C; (~) 70°C; (*) 80°C; (—) model prediction.
Table 6. Values of the parameters deduced byadjustment of Z /Z0=(1ÿx/xgel)
A�Bx law of theexperimental curves
Temperature
(°C) A B
50 2.49 11.72
60 2.34 10.19
70 1.62 8.32
80 1.43 8.47
Polym Int 48:1205±1218 (1999) 1213
Chemorheological and dielectric study of epoxy-amine
formalism of the modi®ed percolation law through the
critical exponent expression. Indeed, both of the
parameters of the critical exponent (A, B) can be
related to the temperature by linear relationships, such
as:
A � A1 � A2T � 14:8ÿ 0:04T �23�B � B1 � B2T � 50ÿ 0:12T �24�
These results are illustrated in Fig 11. One must also
note that, because of the temperature linear depen-
dence and of the empirical extension of the percolation
theory, no physical signi®cance should be of course
assigned to parameters of the predictive law.
Dielectric measurements and modellingThe cure process of DGEBA/IPD systems was
investigated by means of microdielectrometry. Using
microdielectrometry to monitor cure progress through
an industrial process, emphasis is placed on a better
understanding of the kinetic and rheological beha-
viours during the cycle, in order to be able to optimize
the cure process by in-mould control towards di-
electric information.1±11 In terms of real-time control
of RTM composite manufacturing applications, two
dielectric models have to be investigated. The relevant
one concerns the ®rst stage of the mould cycle, the
mould ®lling step which is governed by the viscosity of
the reactive system. The second one refers to the cure
phase and can be expressed through the relation of
conversion as a function of ionic conductivity.
At ®rst sight, isothermal polymerizations at 60, 70,
80, 90, 100, 110 and 120°C of the reactive systems
were examined (Fig 12). Each isothermal experiment
was performed twice and the data showed good
reproducibility. This plot presents the classical di-
electric behaviour of an epoxy/amine cure, with about
a ®ve decade decrease of ionic conductivity. The
dielectric response of the reactive system under cure
stems from its capacitive component (characterized by
its dielectric constant or relative permittivity e') and its
conductive component (characterized by its loss factor
e@). Two main phenomena contribute to this electrical
behaviour: (i) orientation and vibration of permanent
dipoles in the electric ®eld and (ii) ionic displacements
inside the dielectric due to impurities which can also
induce blocked charge phenomena at low frequen-
cies.1,2 e@e0o is independent of the frequency when
conduction effects predominate. Thus, if the charge
carrier's concentration is the same all over the cure
cycle, reduction of conductivity during curing re¯ects
the increasing viscosity of the resin, and when ionic
conductivity contribution is small enough, dipolar loss
peaks can be observed. Indeed, at the beginning of the
cure, when the Tg of the reactive mixture is substan-
tially lower than the cure temperature, ionic species
are highly mobile with the electric ®eld. When the
reaction proceeds, ionic movements are restricted and
this leads to a decrease in ionic conductivity. Dipolar
relaxation peaks can be observed when vitri®cation,
that corresponds to the transformation from a rubber
state to a gelled glass state, occurs. Indeed when the
glass transition temperature of the reacting mixture
reaches the isothermal curing temperature, vitri®ca-
tion restricts mobility through the medium and dipolar
contribution has to be taken into account.
As part of the introduction of microdielectrometry
into a RTM production line,43 the key parameter is
obviously viscosity which governs a great deal of the
process. As a consequence, the relationship between
ionic conductivity and viscosity, mainly in the range of
the processing window, namely before gelation, con-
stitutes one of the main points of this work. Viscosity
diverges when the reacting system nears gela-
tion.30,44,45 In opposition to viscosity behaviour, ionic
conductivity preserves ®nite values through the gela-
tion progress. Nevertheless, even if it is established
that dielectric and rheological properties originate
from different phenomena, a correlation between s
Figure 11. Variation of percolation exponent parameters (A, B) vstemperature.
Figure 12. Log(ionic conductivity) for isothermal polymerizations at (*)60°C; (^) 70°C; (~) 80°C; (&) 90°C; (~) 100°C; (&) 110°C; (*) 120°C.
1214 Polym Int 48:1205±1218 (1999)
S Pichaud et al
and Z can be drawn through a limited conversion range
from 0 up to near xgel. Because of the drastic increase
of viscosity at gelation, accuracy of the correlation
equation would be all the lower as the curing system
nears this critical point. Nevertheless, considering
ionic motion in viscous surroundings, and far from the
gelation phenomenon, Stokes' law was found to be
able to relate ionic conductivity and viscosity, accord-
ing to the following equation:46
� � Eq2�n
6�r��25�
where E is the electric ®eld, q the charge magnitude on
the ion, r the ion density, r the radius of ion, n the
number of ions, and Z the medium viscosity.
In the particular case of reactive mixtures under
cure, some deviations of the law could be observed
which lead to a modi®ed Stokes-based equation, also
named Walden's rule (47):
��T����T��m � const �26�
in which s(T) is the ionic conductivity at temperature
T, Z(T) is the viscosity at T, m is the exponent that was
found to be lower than 1.
Considering such an equation, Koike48 suggested
that the exponent of Walden's rule could be consid-
ered to be a measure of the ratio of the segmental
mobility to the ionic mobility. Also Johari et al49±51
suggested that this exponent value could be attributed
to the fact that, through the cure progress the ionic
conductivity decrease is due in part to a viscosity
increase which hinders ion migrations and also in part
to a modi®ed ionic transport mechanism, associated to
amine group consumption. When ionic conductivity is
directly related to viscosity, the basic assumption is
made that ionic species types and concentrations do
not vary during cure. If the ionic content in the
medium changes, analysis of the conductivity variation
requires the knowledge, of both the concentration and
mobility of each kind of charge carrier. Friedrich et al7
investigated the determination of real-time ionic
mobility evolution in a course of resin curing by means
of electric DC measurements using the Time-Of-
Flight method. Using such a fundamental method,
dependence of ion mobility and segment mobility
would be interpreted and correlated exactly.
Nevertheless, considering the present RTM appli-
cation, and without undertaking such a fundamental
investigation, a simple dielectric model of chemovisc-
osity could be expected to empirically correlate
conductivity and viscosity in the range of the process
window. In fact, for RTM applications, the mould-
®lling stage of the cure cycle is more particularly
concerned with viscosity real-time control. Of course,
Figure 13. Determination of the prediction model of [ionic conductivity/viscosity] correlation for (a) DGEBA/IPD RTM formulation, (b) DGEBA0164/IPD and (c) DGEBA/DER332/IPD. (&) 50°C; (^) 60°C; (~) 70°C;(*) 80°C; (~) 90°C.
Figure 14. Log(s)/Log(si) ratio versus extent of reaction for DGEBA/IPDRTM formulation for isothermal polymerizations (^) 60°C; (~) 80°C; (*)100°C and (&) 120°C.
Polym Int 48:1205±1218 (1999) 1215
Chemorheological and dielectric study of epoxy-amine
with regard to all the above considerations, the aim of
this modelling investigation is not to state a general
expression of conductivity and viscosity dependence,
but only to develop a correlation for the particular
reactive system studied. Log-Log plots of viscosity vs
ionic conductivity for DGEBA/IPD system no 1
isothermal polycondensations are shown in Fig 13a.
Well before gelation, in the conversion range of 0 up to
0.5, it was found that ionic conductivity and viscosity
could be tightly correlated and unexpectedly, results
exhibited a temperature independence of the [Z/s]
relation and are consistent with Walden's rule which
can be expressed in the following form:
Log� � ÿ8:60ÿ 0:58Log� �27�Some authors5 found that the Walden exponent was
sometimes temperature-dependent. It can be inferred
that such behaviour can be observed when there is
temperature dependence of ionic transport mechan-
isms.
Furthermore, correlations between viscosity and
ionic conductivity for mixtures based on DGEBA
DER 332 and DGEBA 0164 seem to lead to one and
same exponent value ÿ0.68 (see Fig 13 b, c). It should
also be noted that the scattering of the experimental
data observed for these two mixtures makes it dif®cult
to compute accurately Walden's law exponent, but
temperature dependence could not be stated. So,
through these results, it could be assumed that the [Z/
s] correlation exponent does not seem to be strongly
dependent on DGEBA prepolymer structure, suggest-
ing that, for any reacting mixture, similar charge
carrier sizes are involved in the ionic transport.
Moreover, a similar exponent value suggests that
similar free volumes are concerned during ionic
motions. Considering these results, it should be also
stated that such a relation is highly dependent on
initial ionic conductivity, and consequently on initial
charge carrier concentration, and on initial viscosity.
So, it could be assumed that, even if the DGEBA
structure does not act directly on the exponent value,
this structure dependence is still contained in the
initial viscosity value.
Emphasis is also placed on the determination of
empirical correlations of the conversion (as deter-
mined by DSC) and ionic conductivity which would
be very useful in practical engineering RTM applica-
tions. It should be noted that, even if it is established
that dielectric measurements are a powerful method of
investigation for monitoring thermoset cure, at pre-
sent, no universal relation between ionic conductivity
and extent of reaction has been ascertained. Various
empirically established equations are reported in the
literature and have recently been reviewed by SteÂphan
et al3,4 and Eloundou et al.5 Also the approach of
connectivity and percolation theories applied to ionic
conductivity evolution through the epoxy-amine cure
process was examined by Johari et al.6
In the particular case of DGEBA/IPD systems, it
should ®rstly be noted that no singular dielectric event
can be associated with the critical gel point. The
dependence of the ionic conductivity on the extent of
reaction has been determined by converting experi-
mental data, so that the dielectric measurements are
represented as a function of the extent of reaction
instead of reaction time. Normalized ionic conductiv-
ity data with respect to initial ionic conductivity (si),
namely Log (s)/Log (si), combined with calorimetric
results in the case of DGEBA/IPD system no 1
isothermal cures, are presented in Fig 14. To correlate
these properties, the phenomenological model of
SteÂphan et al3 can be suggested. Seeking an empirical
correlation between degree of cure and ionic con-
ductivity, these authors suggested the following
empirical expression:
Log��x�Log�i�T� �
Log��x�K1=T�K 01
� K 001 �K 0001 x
1ÿ �1ÿK 00001 �x�28�
where K1;K01;K
001 ;K
0001 and K 00001 are material-dependent
parameters, si(T) is the initial ionic conductivity at
temperature T, s(x) is ionic conductivity and xrepresents the extent of reaction.
This model was veri®ed for various epoxy/amine
and epoxy/anhydride based systems.3,4,5 Temperature
dependence of the initial ionic conductivity was found
to obey an Arrhenius law, although other authors
found this relationship to conform to the Vogel±
Fulcher equation. Nevertheless, unexpectedly, ac-
cording to a graph of [Log (s)/Log (si)] ratio versus
extent of reaction (see Fig 14), some deviations from
predictive law were noted and the analysed relative
ionic conductivity parameter does not follow any
speci®c behaviour. A similar behaviour was also
observed by Eloundou et al5 for a DGEBA/MCDEA
(4,4'-methylenebis[3-chloro 2,6-diethylaniline]) sys-
tem. To identify the reason for such a discrepancy
between experimental and predictive values, one must
Figure 15. Determination of the prediction model of [ionic conductivity/extent of reaction] correlation for the DGEBA/IPD RTM formulationisothermal polymerizations for (^) 60°C; (~) 80°C; (*) 100°C and (&)120°C.
1216 Polym Int 48:1205±1218 (1999)
S Pichaud et al
consider the temperature range at which isothermal
cures were carried out, comparatively to ultimate glass
transition temperature, Tg?. In fact, poor adjustment
between experimental and predictive values seems to
be observed only at isothermal temperatures lower
than Tg?(i) at 80°C and 135°C for DGEBA/MCDEA
(Tg?=177°C),5 (ii) at 100°C for DGEBA/DDA
(dicyandiamide) (Tg?=139°C),3 (iii) at 60, 80, 100,
120°C for the DGEBA/IPD (Tg?=156°C). Conver-
sely, adjustment between experimental and calculated
results in the case of a DGEBD (diglycidyl ether of
1,4-butanediol)/4D (4,9-dioxa 1,12-dodecane dia-
mine) system5 studied in the 40°C to 60°C domain
(Tg?=ÿ12°C), is satisfactory. Such remarks suggest
that the phenomenological model of SteÂphan should
be revisited and the vitri®cation effect taken into
account. In fact in the temperature range concerned,
dielectric measurements are sensitive to vitri®cation
phenomena that show up in frequency-dependent
relaxation peaks. When the glass transition tempera-
ture of a reacting mixture reaches the isothermal
curing temperature, vitri®cation occurs and restricts
reactivity and mobility through the medium. In such a
case, a vitri®cation phenomenon governs dielectric
curves and in order to take it into account, it is
necessary to introduce an additional parameter, xvit, in
the predictive law. Evolution of the [Log (s)/Log (si)]
ratio versus [x/xvit] ratio was examined as plotted in Fig
15:
Log�
Log�i�T� �Log�
K2=T�K 02� K 002 �
K 0002x
xvit
1ÿ �1ÿK 00002 � xxvit
�29�in which xvit represents the extent of reaction at the
vitri®cation point and is of course temperature-
dependent, and K2;K02;K
002 ;K
0002 and K 0002 are material-
dependent parameters. Predicted and experimental
®ndings were observed to agree well, and it was shown
that the modi®ed expression of the mathematical
predictive model proposed by SteÂphan et al3,4 was able
to forecast isothermal data.
CONCLUSIONThe effects of the initial hydroxyl content of a DGEBA
prepolymer on the cure kinetics of DGEBA/IPD
networks were determined. The following order of
reactivity was found: DGEBA DER330>DGEBA
0164>DGEBA DER 332, but the highest reactivity is
obtained for catalyzed RTM formulations.
In view of simulating RTM applications and
predicting such important events as viscosity increase
up to gel time, demould-time, etc, an empirical
approach for modelling the behaviour of an epoxy-
amine formulation throughout the isothermal cure
process has been developed by considering relation-
ships between electrical conductivity and network
structure expressed in terms of both conversion and
viscosity. Kinetic and viscosity relations describing the
reactive system under cure are therefore required and
it was shown that, in the range of 60°C to 120°C, the
reaction proceeds mainly by a second-order autocata-
lytic mechanism. The lower reactivity of the secondary
amino groups compared to primary amino groups,
obtained by the ®tting of the kinetic model to
experimental DSC data, agrees well with values
reported in the literature. The Macosko and Castro
model, describing the viscosity as a function of
temperature and conversion, was found to be able to
predict the rheological behaviour of the DGEBA/IPD
reactive system over the temperature range explored.
Moreover, dielectric investigations on a curing
epoxy network have shown that dielectric data
combined with temperature information can yield
both the extent of reaction and viscosity evaluation. It
was shown that the mould-®lling stage should be
monitored using a Walden-based equation which
empirically correlates ionic conductivity and macro-
scopic viscosity in the conversion range of 0 to 0.5.
The single relation we found may be of great use in an
industrial production line to analyse the curing process
of an epoxy resin by on-line real-time dielectric
measurements, which allow the ionic conductivity
data to be collected and provide viscosity information
through this relation. Furthermore, it was suggested
that the curing step of the moulding cycle could be
monitored by using an empirical model to predict the
reaction advancement of the epoxy from dielectric
data, then by taking into account the vitri®cation
phenomenon.
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