Modeling diffusion-control in the cure kinetics of epoxy-amine thermoset resins: An approach based on configurational entropy

Abstract

In this study we propose a new equation to describe the effect of diffusional limitations on the cure kinetics of epoxy-amine resins, based on (i) modeling the average diffusion coefficient D via a power–law relationship with the structural relaxation time τ (i.e. Dτξ = const, with ξ a fractional exponent) and (ii) describing the increase of τ with the advancement of reaction in terms of configurational entropy reduction driven by covalent bond formation. The approach proposed reconciles the description of the diffusion-controlled kinetics with the configurational entropy-based description of the structural dynamics near vitrification, already applied successfully to epoxy-amine polymerization. The model equation is built on a modified version of the Kamal equation where the initial ratio of amino hydrogens to epoxy groups appears explicitly, in addition to the exponents m and n giving the effective order of reaction. Replacing each chemical rate constant with an overall diffusion-corrected one, allows us to describe the full polymerization process. A comparison with experimental data indicates that, contrary to what assumed in the literature, the effect of diffusional limitations cannot be properly described by assuming the diffusion coefficient to be inversely proportional to the relaxation time (ξ = 1). Rather, we find that for many systems the fractional exponent ξ takes values very close to the parameter β that measures the stretching of the relaxation function. Concerning the chemically intrinsic parameters, it is found that the rate constants kc1 and kc2 for all the systems scale onto a master-curve corresponding to thermally activated behavior with, surprisingly, the same activation energy for the non-catalytic and autocatalytic process. Moreover, m and n assume approximately constant values, independent of the temperature and molar ratio of the mixture, with m ≈ 1 and n in the range between 1 and 2. Although these results contradict other reported findings and the widespread belief that the autocatalytic process has a lower activation energy, they are consistent with the expectation that a similar mechanism underlies the general reaction between epoxy group and amino hydrogen, and that m and n are related to the intrinsic reaction mechanism. The new modeling also removes some evident discrepancies among results from different studies.