Avrami 이론에 의한 에폭시 수지계의 경화 속도론 연구

여만경, 심미자．, 김상욱

서울시립대학교 화학공학과, ．서울시립대학교 생명과학과

A Kinetic Study on Curing of Epoxy Resin Systems by Avrami Theory

M. G. Lu, M. J. Shim． and S. W. Kim

Dept. of Chem. Eng., The Univ. of Seoul, ．Dept. of Life Sci., The Univ. of Seoul

Introduction

Even though many experimental techniques and studies ralating to epoxy cure reactions have been reported in the literature with emphasis on the chemical, physical, and mechanical property changes with time, there are often conflicts in the kinetic parameters. These problems arise primarily from the assumptions used in the calculations and the negligence of the physical phenomena likely to take place in the system. Therefore, it is necessary to understand the fundamental  principles that govern the process.

In generally, kinetic expressions may be phenomenological or mechanistic.       Phenomenological models relate to the main features of the reaction kinetics and do not take into account individual reactions, whereas mechanistic models are obtained from balances of species involved in the reaction. In our opinion, the phenomenological approach prefer in this  study because the cure process is so complex that it is very difficult to identify each and every reaction, especially, the mechanistic model will not be valid for the later stages of cure where the reaction mechanism is diffusion-controlled.

In our laboratory, the cure kinetic behavior of epoxy systems and their composites has been conducted systematically. We now focus on the phenomenological model and the fundamental kinetic results and analysis will be given as the preliminary experiments using differential scanning calorimetry. In this research, isothermal experiments were performed for  DGEBA-MDA and DGEBA-CTBN-MDA systems. The cure kinetic parameters and a suggested mechanism based on Avrami theory have been given.

Analysis of Data

In the standard isothermal method, the DSC curves were constructed by integrating the area under the exothermic peak according to the following equation:

[eqn: { alpha }_{ t} = { TRIANGLE H}_{t } over { TRIANGLE H}_{0 }]                                 (1)

where △Ht is the heat generated up to time t; △H0 is the total heat of complete cure.

The isotherms obtained were analyzed by means of the simple Avrami equation:

(1-□t) = exp (-ktn)                            (2)

where the rate constant k and Avrami exponent n were calculated either from a plot according the relation

log [-ln(1-□)] = log k + n logt                   (3)

Experimental

The epoxy resin systems used in this study consist of a commercial diglycidylether of bisphenol A (DGEBA) (Shell Chemicals, Epon 828), 4, 4′-methylene dianiline MDA (Fluka Chemie Co.) and a low molecular weight carboxyl-terminated butadiene-acrylonitrile (26%) copolymer (CTBN) (Kukdo Chemical Co.). These materials were used as supplied without further purification. The epoxide equivalent weight of the resin was taken as 184 and the concentration of CTBN is 10%.

The resin was cured employing stoichiometric quantities of diamine. The epoxy resin was mixed with CTBN and melted MDA under good stirring about 80℃, then cooled rapidly to room temperature. The resulted material was kept in a freezer at -20℃ and under desiccation prior to use.

Samples consisting of 3-6 mg mixture are placed in aluminum DSC pans and run on a SEIKO Ⅰ- 5000 series. In the isothermal scans, the test samples are heated to the test temperature at 100℃/min at five temperatures between 80-120℃. The carrier gas is nitrogen at a flow rate of 50ml/min.

Results and Discussion

The degree of cure as a function of curing time was plotted in Fig. 1 at 90℃ for two systems. From this figure, we can find that there is a higher extent of cure at the given cure temperature and time for DGEBA-CTBN-MDA system. This kind of behavior has been observed by other workers. However, a perfect interpretation can not be given using the general analytical methods, in which the initial acceleration of cure rate was attributed to the initial hydroxy concentration and the addition catalysts such as the impurities, although little hydroxy group was comprised in the CTBN. According to the Avrami theory, it  is clear from eq. 2, that in the case of large value of k and small value of n for DGEBA-CTBN-MDA system, the fraction of cure at the early stage of cure will be larger than in the case of smaller k and large n for DGEBA-MDA system. This result can be attributed to the accelerating influence of CTBN which was related to the faster heterogeneous nucleation due to the incompatibility between epoxy and CTBN oligomer.

The kinetic parameters are obtained by plotting the data according to eq. (3). A plot of ln[-ln(1-□)] vs. lnt yields a straight line; the slope is equal to n and the intercept is equal to lnk. Typical Avrami plots for two systems are given in Figs. 2  and 3, respectively.

An Arrhenius plot (Fig. 4) shows a good linear correlation. The kinetic rate constant, k, in eq. (2) determines the rates of the nucleation and growth process which control the cure. The values are consistent with the results obtained from other analytical methods. It can be expressed as:

for epoxy-MDA system

k = 3.15×104 exp (-64.4/RT)                    (4)

for epoxy-CTBN-MDA system

k = 3.02×105 exp (-66.8/RT)                (5)

Activation energy based on the slope of Fig. 4 was obtained. Ea values are between 46 KJ/mol for the autocatalyzed rate constant k1 and 84 KJ/mol for [eqn: { k}`_{1 } ^{ prime }] (catalyzed rate constant) and show that a balanced result is obtained from this phenomenological model. Both the activation energy Ea and the pre-exponential factor increase with the addition of CTBN. Normally, the pre-exponential factor might decrease if the added CTBN acts as a diluent. However, it was observed that the reaction was accelerated with its addition. Therefore, a diluent effect of CTBN on the

cure kinetics of the epoxy resin cannot explain the above phenomenon. The reason of accelerating effect has been described above.

The Avrami exponent provides qualitative information on the nature of nucleation and the growth processes. Figs. 2 and 3 show the n values do not vary significantly with temperature. It suggests that the same cure mechanism occurs in the whole course of cure for DGEBA-MDA and DGEBA-CTBN-MDA systems. The nonintegral values of n cannot be explained in terms of the physical assumptions made in arriving at the Avrami equation. Fractional values of n may be expected mathematically, if certain constraints are imposed such as diffusion controlled growth. The observed deviations could also be attributed to the factors such as time-dependent nucleation, variant growth rate constants, combination of homogeneous and heterogeneous nucleation. Meanwhile, it also implies a catalytic mechanism to some degree.

The reaction degree can be calculated from the constants obtained using eq. (2). It is accurately consistent between theoretical and experimental data. These results showed that the cure behavior of epoxy systems can be described by Avrami expression in the entire temperature range.

Since the values of Avrami exponent n for both epoxy systems lie between 1∼2, in summary, the cure process may involve either homogeneous nucleation or heterogeneous nucleation with one directional growth and two directional diffusion controlled growth (n→2). In the case of CTBN toughening epoxy resin, heterogeneous nucleation will predominantly occur on the interface forming between CTBN and resin. Homogeneous nucleation may also take place simultaneously in the prepolymer bulk. Such nonuniform nucleation could lead to complicate cure kinetics and mechanisms, and the experimental kinetic results may present a combined effect.

Conclusions

In this work, the isothermal cure behavior has been investigated for DGEBA-MDA and DGEBA-CTBN-MDA systems. The results lead to the following conclusions.

The cure process for the two resin systems may involve either homogeneous or heterogeneous nucleation, and CTBN composition can induce the faster heterogeneous nucleation as a nucleating agent.

Avrami phase change theory can be used to describe the cure process of epoxy resins and can give the even more satisfactory explanation to some experimental phenomena. The kinetic parameters obtained are consistent with that from other thermal analytical methods. The kinetic results from Avrami theory may present a combined effect of all factors.

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