Simple kinetic numerical model based on rheometer data for Ethylene–Propylene–Diene Monomer accelerated sulfur crosslinking

A simple numerical model for the interpretation of the reaction kinetics in ethylene–propylene–diene monomer (EPDM) vulcanized with accelerated sulfur is presented. The model is based on the assumption that during vulcanization, a number of partial reactions occurs, both in series and in parallel, which determine the formation of intermediate compounds, including activated and matured polymers. Once written a standard first-order differential equation (DIFF-EQ) for each partial reaction, an ordinary DIFF-EQ system (ODEs), was obtained and solved through Runge–Kutta algorithms. Alternatively and more efficiently, a single second-order nonhomogenous DIFF-EQ with constant coefficients was deduced, for which a closed-form solution was derived, provided that the nonhomogenous term was approximated with an exponential function. Kinetic constants were evaluated through experimental data fitting on standard rheometer tests. To assess model predictions, an experimental campaign at different temperatures on two EPDM compounds was performed. They exhibited moderate reversion at intermediate and high curing temperatures. A nonlinear least-squares fitting was performed to evaluate unknown constants entering into the DIFF-EQ model proposed. Scaled rheometer curves fit rather well, also in the presence of reversion. In addition, partial reaction kinetic constants were provided: this gave an interesting insight into the different reticulation processes occurring during vulcanization.