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

1206 Polym Int 48:1205±1218 (1999)

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

1210 Polym Int 48:1205±1218 (1999)

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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