Mechanism and Kinetics of Epoxy-Amine Cure Studied by Differential Scanning Calorimetry Sergey Vyazovkin* ,† Department of Chemistry, The University of Toledo, Toledo, Ohio 43606-3390 Nicolas Sbirrazzuoli Laboratory of Experimental Thermodynamics, UMR-CNRS-139, University of Nice-Sophia Antipolis, 06108 Nice 2, France Received August 8, 1995; Revised Manuscript Received October 11, 1995 X ABSTRACT: The isoconversional kinetic analysis has been applied to nonisothermal DSC data on the cure of an epoxynovolac resin. The process reveals a dependence of the activation energy (ER) on conversion (R). The shape of the dependence has been interpreted in the terms of the reaction mechanisms. It has been found that the model dR/dt ) (k1 +R m k2)(1 -R) n used for the kinetically controlled cure gives rise to the dependence of ER on R similar to the experimentally found one. To completely describe the diffusion- controlled cure, the effect of both T and R on the change in diffusivity has been taken into account. The equation for the specific rate constant of diffusion, kD(T,R) ) Do exp(-ED/RT + KR), has been induced. Its use allows us to obtain a model dependence of ER on R closely matching the experimental one. A technique of predicting isothermal cure from the sole dependence of ER on R has been considered. Introduction Differential scanning calorimetry (DSC) which mea- sures the heat flow from the reacting system is a very convenient tool to study the overall epoxy-amine cure. 1-16 It is especially useful when a detailed mech- anism has been established by other methods such as FTIR, 2,4,10,16-21 HPLC, 4,16-18,22,23 and NMR. 5,6,16,18 In such a case, the kinetic analysis of DSC data helps to determine those steps which most profoundly contribute to the overall process. This allows for the reduction of intricate mechanisms to an effective kinetic scheme. Another practical problem which requires the knowl- edge of the overall kinetics is predicting the progress of cure at different temperatures. Both problems can be solved if an adequate method of kinetic analysis is used. Obviously, DSC data do not allow the measured heat flow to be separated into contributions from single reactions. This, in no way, means that the actual complexity of curing can be ignored in kinetic calcula- tions. A method of kinetic analysis should allow for a possible change of the rate-limiting step (and associated Arrhenius parameters) of the process. Nevertheless, the kinetics of thermal transformations are usually de- scribed 1 by eq 1 of a single-step reaction: where f(R) is the reaction model, R is the extent of conversion, k(T) is the Arrhenius rate constant, T is the temperature, and t is the time. For nonisothermal conditions, when the temperature varies with time with a constant heating rate,  ) dT/dt, eq 1 is represented as follows: where A is the pre-exponential factor, E is the activation energy, and R is the gas constant. The straightforward application of eqs 1 and 2 yields a single kinetic triplet (A, E, and the reaction model) for the overall process. This type of analysis does not allow for a possible change in the rate-limiting step. Isoconversional kinetic analysis offers a viable alter- native in this situation. The basic idea of this type of analysis is that the reaction rate at a constant conver- sion depends only on the temperature. In other words, where E R is the effective activation energy at a given conversion. For a single-step process, E R is independent of R and may have the meaning of the intrinsic activa- tion energy. Multistep processes reveal the dependence of E R on R, the analysis of which helps not only to disclose the complexity of a process but also to identify its kinetic scheme. 24 In this study the isoconversional analysis has been applied to nonisothermal DSC data on the epoxy-amine cure. An emphasis is made on the interpretation of the dependence of E R on R in the terms of the reaction mechanisms as well as on its use to predict the cure kinetics under isothermal conditions. The experimental dependence of E R on R has been interpreted in the frameworks of models generally accepted to describe the cure. These models have been used solely to derive corresponding model dependencies of E R on R. The pure numerical problem of fitting these models to the experi- mental data of dR/dt has been deliberately left aside because of two reasons. Firstly, it has been solved many times. 3,7-13 Secondly, as it follows from the present results, neither explicit model nor its parameters are necessary to predict the cure progress at a given temperature. What we really need to determine is the dependence of E R on R alone. Experimental Section The epoxy resin was an epoxynovolac containing 1,4- butanediol diglycidic ether (Ciba-Geigy; araldite LY 5052) with an epoxy equivalent of 146 g/equiv and viscosity of 900-1600 mPa at 25 °C. A hardener of isophorone diamine (mixture of two stereoisomer forms of 3-(aminomethyl)-3,5,5-trimethylcy- clohexylamine) with diaminodimethyldicyclohexylmethane (Ci- ba-Geigy; araldite HY 5052) was used to cure the resin. The † Present address: Department of Chemistry, The University of Utah, Salt Lake City, UT 84112. X Abstract published in Advance ACS Abstracts, February 1, 1996. d ln(dR/dt) R /dT -1 )-E R /R (3) dR/dt ) k(T) f(R) (1) dR/dT ) (A/) exp(-E/RT) f(R) (2) 1867 Macromolecules 1996, 29, 1867-1873 0024-9297/96/2229-1867$12.00/0 © 1996 American Chemical Society