On the Increase of Viscoelastic Modulus With Advancement of Reaction of an Epoxy Resin

D. SERRANO and D. HARRAN

Institut Universitaire de Recherche Scientifique Laboratoire de Physique des Materiaux Industriels

Universite de PAU et des P a y s de I'Adour 64000 PAU, France

Log G* =f(X) isothermal variation curves were determined at various temper- atures for two epoxy-aromatic amine systems widely used in industry. G* = G' + jG" is the viscoelastic modulus, determined by sinusoidal shearing at constant frequency between parallel plates: X represents the degree of reaction, determined by calorimetry. These curves clearly show the phenomena of gelation and glass transition. In the temperature range studied, the value of X at the gel point varies between 0.7 and 0.9 for the DGEBA-DDS system, and from 0.3 to 0.8 for the TGDDM-DDS system. These variations reflect a major modification of the reaction mechanism, particularly before the gel point.

INTRODUCTION

hermosetting reactions considerably modify the T mechanical properties of a resin. Generally, the material changes from the liquid state to a glassy solid state, and consequently the viscoelastic modu- lus increases by some 10 decades. The extent of this variation has made it impossible to carry out rheolog- ical studies over the whole range of kinetics. An early analysis of this change in rheology has been provided by the torsion pendulum, based on use of an inert support on which the resin is placed (1). The presence of this support enables a reduction of the range of variation of the viscoelastic modulus measured by the apparatus. However, it has the disadvantage of providing a response which is dependent on the sup- port. Two advanced methods are now possible to study resin hardening over the full range of kinetics, both by sinusoidal shearing between parallel plates. The range of variation of torque measured by the apparatus can be reduced either by reducing defor- mation with time, or by decreasing sample size. In the second method, several kinetics measurements must be made, with decreasing plate size values. This method has already been used for rheological studies of the hardening of several DGEBA (diglycidyl ether of bisphenol A)-based epoxy resins (2, 3), while both methods have been used with the TGDDM-DDS (tetraglycidyl diaminodiphenylmethane-diaminodi- phenylsulfone) system (4). These experimental log G* = f( t) curves show the two macroscopic transitions of gelation and vitrification. The change of kinetics with temperature can thus be observed by determin- ing the laws governing the variations of gelation and glass transition times with the parameter T. The reaction mechanism of the epoxy resins studied here, DGEBA-DDS and TGDDM-DDS, were also sub-

jected to thorough investigation using NMR, FTIR, and chromatography (5.6). The kinetics of the degree of the chemical reactions were determined by the calorimetric method (7, 8). In this way the value X of the degree of reaction can be identified at any mo- ment and at any temperature. This article reports the results obtained by these two techniques, showing the variations of the visco- elastic modulus G* as a function of the degree of reaction X . These log G* =f(X) curves show partic- ularly clearly the determining influence of the cure temperature.

EXPERIMENTAL PROCEDURE

Resin Formulations

The diepoxy prepolymer DGEBA (diglycidyl ether of bisphenol A) was purified by fractioned crystalli- zation using the industrial resin DER 332. Only the n = O(Tf = 42°C) compound is retained. This prepo- lymer was mixed in stoichiometric quantity (one amine function for one epoxy function) with the ar- omatic diamine DDS (diaminodiphenylsuifone). The log G* = f(t) rheological curves studied for this DGEBA-DDS system have been reported in an earlier publication (3).

The tetraepoxy prepolymer TGDDM (tetraglycidyl diaminodiphenylmethane) used is LOPOX B 3302 manufactured by Charbonnage de France (CdF Chimie). This product is not pure, and its composition has been studied elsewhere (9). It was mixed with the same aromatic diamine DDS at the standard concen- tration used in industry, i.e. l O O g TGDDM for 30g DDS.

We have grouped the different predicted chemical reactions for these two systems in Figs. 1 and 2 (5,

POLYMER ENGINEERING AND SCIENCE, APRIL 1989, Yo/. 29, No. 8 531

D. Serrano a n d D. H a r r a n

I epoxy ~ p r i r n a r y Ornine react ion

2 -Epoxy - secondary amine react ion

0 0 H H O H / \ I I I R - C H 2 - C H - C H 2 + R - C H 2 - C H - C H 2 - N - R ' - [ P - C H z - C H - C H z ~ N -R'

2

3 - E p o x y - hyd ro ry l react ion

a) R - CH, - C H - C H,O H I 0 H

I OH H R - CH,- C H - CH,-N - R' A I I

R-CH,-CH-CH,*R-CH,-CH-CH,-N-R'-

\ Y H b) R-CH,-CH-CH,

I 0 H I I

R-CH,- CH-CH,-N-R'

Fig. 1 . Mechanism of cure of DGEBA-DDS R = 1 s y s t e m (5).

1 Reaction I epoxy-primory omine

\ I t c*,- c *

I no . epoxy-recondory omine =w

Ild : epoxy - hydroxyl Ub ; epoxy-hydraxyl

C", c"l

F ig . 2. Mechanism of cure of TGDDM-DDS s y s t e m (6).

6). For the DGEBA-DDS system we know that only intermolecular reactions take place in the 100°C- 180°C temperature range (epoxy-amine and etherifi- cation reactions). However, for the TGDDM-DDS sys- tem, there is evidence to suggest that there is a re- action mechanism involving inter- and intramolecu- lar reactions, given the proximity of the epoxy groups. Moreover, homopolymerization and epoxy/hydroxyl reactions are favored by the fact that the mixture is

532

not stoichiometric: there are fewer amine functions than epoxy functions.

Rheological Kinetics

The rheological kinetics were determined using an Instron 3250 rheometer, by sinusoidal shearing be- tween parallel plates, at constant frequency (w = 30 rad/s). The angular deformation was maintained constant (a , = 0.533"), but the size of the plates (and of the sample) was reduced during the study, with increasing rigidity of the medium. Three plate diam- eters were used successively: 4 = 4cm for the begin- ning of cure, then 4 = 2cm and finally d~ = 0.5cm. The log G I =f(t) rheological curves are thus deter- mined in three stages. They coincide correctly if the measurements are perfectly isothermal (hence the need to control the reactions' exotherm to limit the effects of the sample size) and if the sample prepa- ration procedure is perfectly stable.

The curves obtained are quite comparable to those determined with a Rheometrics RDA 700 rheometer. In this case, the diameter of the plates remains con- stant (4 = lcm) but the deformation decreases during the hardening of the resin.

Chemical Kinetics

The polycondensation kinetics were studied using isothermal calorimetry (7, 8), in a temperature range of 100°C to 180°C. and with a high-temperature model Calvet microcalorimeter. The mass of the sam- ples was of the order of 2 to 3 grams. Calibration was carried out electrically. In order to calculate the de- gree of reaction, the total heat of the reaction was determined by DSC (Differential Scanning Calorime- try) on various epoxy-aromatic amine prepolymer systems.

Since the polycondensation reaction is auto-cata- lyzed, the kinetic law used is the following:

d X / d t = K ( 1 - X ) 2 + K l X ( 1 - XI2

where the first term is the initiation term, the second represents the autocatalysis term, and X is the con- centration of consumed epoxy functions.

The parameters K and K 1 vary with temperature according to Arrhenius laws. For each of the two systems, the laws of variation are as follows:

DGEBA-DDS R = 1 L, K = 10.66 - 5300/T L, K 1 = 28.40 - 11400/T

TGDDM-DDS 100-30 L, K = 14.13 - 6930/T

L, K 1 = 25.93 - 10600/T

K and K1 are thus expressed in (hours)-', Tin Kelvin. Figure 3 shows some X = f ( t ) curves obtained at

several temperatures with the TGDDM-DDS (1 00-30) system.

INTERPRETATION OF THE RHEOLOGICAL KINETICS

Figures 4-7 show a few examples of log G* =f ( t ) curves that can be obtained at various temperatures.

POLYMER ENGINEERING AND SCIENCE, APRIL 1989, Vol. 29, No. 8

Viscoelastic Modulus wi th Reaction of a n Epoxy Resin

8 -

7 -

6 -

5 -

4 -

3 -

Fig. 3. Extent of reaction x us time for several curing temperatures for TGDDM-DDS 100-30 system.

I ; 10:' t 3 i

Fig. 6. Example of experimental curves (Rheometric RDA 700). TGDDM-DDS 100-30 system.

T = 170% w = 30 rods-' i : .

1- 2 3 . 0 I-

* , f i i A u L i u l v u l L u - & - t ( h )

Fig. 4 . Example of experimental curves {lnstron 3250). DGEBA-DDS R = 1 system.

I1 1 3 5

G' i . 11, i - log G', G" ( P a l

log G' , G" (Po) 9

Fig. 5. Kinetics of hardening a t several temperatures (Instron 3250). DGEBA-DDS R = 1 system.

The TGDDM-DDS system exhibits rheological behav- ior closely similar to that of the DGEBA-DDS system, which has already been studied.

I t can be seen that the storage modulus G' and the

I l l f i TGDDMIDDS

Fig. 7 . Kinetics of hardening a t several temperatures (instron 3250). TGDDM-DDS 100-30 system.

loss modulus G" do not increase regularly. At high temperatures in particular, the curves exhibit two successive plateaus, though the first is only partially marked. The second plateau is naturally associated with vitrification, along with the maximum of the loss modulus G". We have verified elsewhere (2, 3) that the first plateau is connected with gelation of the system. Moreover, we have shown that the gel point can be determined, either by the beginning of the shoulder corresponding to the first log G" plateau, or, when this feature is no longer visible, by the point at which the slope begins to decrease between two linear portions.

The gel times measured in this way agree closely with a transition observed under reverse gas chro- matography (10) and attributed to gelation. The the- ory of percolation, applied to the curves of viscosity variation with the TGDDM-DDS system, also dem- onstrated that the critical threshold for percolation

POLYMER ENGINEERING AND SCIENCE, APRIL 1989, Vol. 29, No. 8 533

D. S e r r a n o and D. H a r r a n

gL

5 -

4-

2 -

and the rheological gel point as defined above are very close to each other.

Finally, the degree of reaction at the gel point de- termined on the rheological curves was determined for DGEBA-DDM (diaminodiphenyl-methane) (1 1). I t has been shown that the same reaction path is fol- lowed whatever the temperature in the range under study (12). I t is known also that for this system, only the normal primary and secondary epoxy/amine re- actions are involved, the reactivities of the amines being similar. Secondary epoxy/hydroxyl or inter- molecular epoxy/epoxy type reactions only occur to- wards the end of the cure cycle. Measurement of the degree of advancement of the reaction at the gel point, carried out by C13NMR and FTIR, gave the average value Xgel = (0.59 k 0.02). This is in excel- lent agreement with the value 0.58 predicted by the classical Flory-Stockmayer theory. This agreement clearly confirms that the point we defined on the rheological curves does represent the theoretical gel point, at which the molecular network becomes infi- nite.

Thus, in the temperature range studied (thermal degradation excludes going beyond the maximum glass transition temperature Tga for these systems), the rheological curves determined during resin hard- ening can be classified into three categories:

-at high temperatures, gelation causes the for- mation of a relatively pronounced shoulder of log G" (and log G') prior to the glass transition.

-at lower temperatures, this shoulder no longer appears: gelation is shown by decrease in the slope of log G" =f( t ) between two linear regions.

-for temperatures below a critical level Tcgel, there is no longer any change in slope (Tcgel = 1 10°C for the DGEBA-DDS system, T,gel = 80°C for TGDDM-DDS 100-30). Gelation, if it takes place, is no longer revealed by the experimental curves.

3 -

DISCUSSION

F i g u r e s 8 and 9 show a number of log G" = f(X) curves obtained at several temperatures for each of the two systems. By studying the appearance of these curves and their development as a function of tem- perature, we can draw a certain number of conclu- sions.

Shape of the log G* =f(X) Curves

For the two systems the general shape of log G* = f(X) curves is the same as for log G" = f ( t ) curves. This is due to the fact that the degree of reaction X varies regularly with time, as Fig. 3 shows (the gela- tion and glass transitions do not appear explicitly on these X =f( t ) curves). However, it can be observed that the first plateau of G' and G", associated with gelation, is more pronounced. This observation can be explained by the fact that the kinetics of X =f( t ) are relatively rapid up to the gelation region, and are then slowed considerably by the glass transition. At low temperature (1 20°C) with the TGDDM-DDS sys- tem, the first plateau of the modulus does not appear,

9 log G ' , log G" ( P o ) ,

/

OGEBA ( n = O l / D O S R = l

w=30rod .s - '

It X

0 ' l ' l " ' ' l " " ' ' ~ l i

Fig. 8. Viscoelastic modulus us extent of reaction at seu- era1 temperatures. DGEBA-DDS R = 1 system

10 log G', log G" (Pal

Y -

8 - TGDDM/DDS

. 100/30 W = 30 rad.s-'

6 -

5 -

4 -

T = l40 'C 3 -

2 -

y. I -

.; ,,< El "".'I"".:"".:'

..': i :

Fig. 9a. Viscoelastic modulus us extent of reaction at several temperatures. TGDDM-DDS 100-30 system.

but the change in both the log G" = f ( X ) slope and the log G' =f(X) slope is very pronounced.

The two phenomena of gelation and glass transi- tion appear clearly on log GI =f(X) curves. They seem more clearly separated, for medium and high temperatures, than on log G+ =f(t) curves. It can easily be observed that gelation causes a rubbery plateau with G" values of the order of lo4 or lo5 Pa (this value varies with temperature), whereas the storage modulus G ' is limited to approximately lo6 or lo7 Pa. The glass transition leads to a G" maxi-

POLYMER ENGINEERING AND SCIENCE, APRIL 1989, Vol. 29, No. 8 534

Viscoelastic Modulus with Reaction of a n Epoxy Resin

3 -

log G', log G" (Pa)

Fig. 9b. Viscoelastic modulus us extent of reaction a t several temperatures. TGDDM-DDS 100-30 system.

mum and then a final plateau at around 1 O7 Pa, while G' increases to around lo9 Pa.

Development of log G* =fo Curves with Temperature

The curves obtained at different temperatures can- not be superimposed. For example, at high tempera- tures, the gel point corresponds to a much more advanced degree of reaction. So for both systems, the conditions of the classical theory of gelation. which point to a value Xgel = C, are far from satisfied. The reaction mechanism changes considerably with tem- perature, and in particular before the gel point, con- trary to certain results reported in the literature.

For example, for the TGDDM-DDS resin, the G" modulus can only be measured with our apparatus (log G" = 2(Pa)) at values of X above 0.20 when T = 120°C. However the same value for the modulus at T = 180°C cannot be measured until X = 0.80. The same remark can be made for DGEBA-DDS. In terms of elasticity and viscosity, the reactions which occur at high temperatures are therefore less efficient. We know that reactions other than the usual epoxy- amine reactions take place, especially at high tem- peratures. For the DGEBA-DDS system, hydroxyl- epoxy reactions occur. For the TGDDM-DDS system, the mechanism is even more complex since there are intramolecular as well as intermolecular reactions. The former do not create crosslinking and therefore have little effect on the G' and G" moduli.

It was observed that, for an identical temperature

variation, the displacement of the log G* = f ( X ) curves is greater for the tetrafunctional resin than for the difunctional resin.

Examination of the log G* =f( t ) rheological curves reveals that, for the DGEBA-DDS system (3). the elastic modulus G ' is approximately constant at the gel point throughout the temperature range studied. For the TGDDM-DDS system this is true between 120°C and 180°C (normal temperature range) (4). So the materials possess equivalent elastic properties at the gel point. However, the log G* = f ( X ) curves for these two systems show quite clearly that the mate- rials are not equivalent, since the degree of reaction at the gel point is markedly different as a function of temperature. The reactions involved at high temper- atures are therefore different, not only after the gel point, but also before. It can thus be suggested that the products obtained at the end of the reaction cycle might have different mechanical properties.

Variation of the Degree of Reaction at the Gel Point as a Function of Temperature

In a previous study (1 1). we used C13NMR and FTIR to measure the degree of reaction for several samples in which hardening had been stopped at the gel point. The gel point was determined by the rheological method. For the samples of DGEBA-DDM, the value obtained is independent of the oven temperature (al- lowing for uncertainties). It agrees closely with the value 0.58 predicted by the classical Flory theory. On the other hand, the results obtained with the DGEBA- DDS system (with the same functionality) are higher, and seem to increase with the cure temperature. We were able to confirm this result by means of the log G* = f ( t ) and X =f(t) curves; a similar, but more pronounced deviation from the results predicted by the theory was observed with the TGDDM-DDS sys- tem.

Tables 1 and 2 and Figs. 10 and 1 1 show how the degree of reaction varies with cure temperature. Xgel was determined from the rheological gel time, which obeys the following Arrhenius laws, and from the kinetic laws X =f( t):

DGEBA-DDS R = 1

R T

Table 1. DGEBA-DDS R = 1 System.

Variation with Curing Temperature of the Extent of Reaction at the Gelation Point.

T°C 130 140 150 160 170 180 Xgel 0.67 0.73 0.785 0.83 0.87 0.905

Table 2. TGDDM-DDS 100 - 30 System.

Variation with Curing Temperature of the Extent of Reaction at the Gelation Point.

TOC 120 130 140 150 160 170 180 Xgel 0.32 0.39 0.475 0.56 0.655 0.725 0.79

POLYMER ENGlNEERlNG AND SCIENCE, APRlL 1989, Vol. 29, No. 8 535

D. Serrano and D. Harran

0 90-

o ao-

0 7 0 -

0 6 0 -

050-

040-

0 3 0 -

lXgei- I

X gel

I I l l I I I 1 I I T'C 110 120 130 140 150 160 170 iao 190 200

O 6 O I 0 50

O 4 O I 0 30

D G E B A I D D S R = l

I I I I I I I 1 1 I I T'C 110 I20 130 140 150 160 170 180 190 200

Fig. 10. Extent of reaction at gelation us curing temper- aturefor DGEBA-DDS R = 1 system. + Xgel calculated from log G" =f(t) and X =frt., curues. 0. Xgel measured b y NMR and FTIR (1 41.

TGDDM-DDS 100-30

RT (the activation energies are expressed

in Joules)

Figure 1 0 shows that approximate agreement is obtained between the two methods in the case of the difunctional resin. There is, however, a major dis- crepancy with respect to the classical theory, which becomes more marked as the temperature increases. This discrepancy can be explained by the remarks above: the reaction mechanism varies greatly with temperature even before the gel point; secondary type reactions have activation energies different from those of the main reactions, and are favored at high temperatures.

With the TGDDM-DDS system, the range of varia- tion of Xgel is even greater since i t extends from 0.3 to 0.8. An approximate theoretical value can be cal-

culated using Flory's theory. Supposing the DDS to be difunctional (the secondary amines react very lit- tle, in particular before the gel point), and with a stoichiometric ratio calculated from the average real epoxy equivalent, 130.5g, we obtain Xgel (theoretic) = 0.32. So the higher experimental values express a major change in the reaction mechanism.

Variation of the Degree of Reaction in the Middle of the Glass Transition as a Function of Temperature

Figures 8 and 9 also show that the G" maximum, associated with glass transition of the medium, ap- pears for values of X which decrease with tempera- ture. Thus, not only is hardening slower at low tem- peratures, but also the glass transition appears ear- lier on this curve. It is generally accepted that the glass transition causes marked slowing of chemical reactions. It is, therefore, very difficult to reach the complete reaction stage at low temperatures.

At high temperatures, however, the glass transition appears almost at the end of the reaction. This means that it is possible to reach rapidly a high degree of reaction ( X = 1) at the end of the cure cycle. But we saw above that the material obtained is very different because the reaction mechanism is different. From these findings it is easy to understand the usefulness of cycles with two temperatures: the first relatively low to construct a homogeneous network until the gel point, followed by a second high temperature to complete the chemical reactions and thus reach a stable state.

However it should be noted that the glass transition observed on the log G+ = f ( t ) or log G* = f ( X ) curves is related to the shearing frequency w = 30rad/s, and does not directly determine the rate of chemical re- actions. Nonetheless it is reasonable to suggest that the cure temperature affects the speed of chemical reactions in the same way as it affects the glass transition. An advanced degree of reaction at the end of the cure cycle is thus more easily achieved at high temperatures.

CONCLUSION

The log G* =f(X) curves obtained through the com- plementary rheological and calorimetric techniques clearly show the two phenomena of gelation and glass transition. For the two systems under study, these curves are very different depending on the cure tem- perature, and this reflects a highly significant change in the reaction mechanism, particularly before the gel point. There is therefore no simple relationship between the degree of reaction and the viscoelastic modulus. Moreover, the final properties of the prod- ucts obtained at the completion of the reaction de- pend to a large extent on the cure temperature.

ACKNOWLEDGMENT We are indebted to the SocietC Nationale Elf-Aqui-

taine (P) for their financial support.

536 POLYMER ENGINEERING AND SCIENCE, APRIL 1989, Vol. 29, No. 8

Viscoelastic Modulus with Reaction of an Epoxy Resin

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