EPDM accelerated sulfur vulcanization: a kinetic model based on a genetic algorithm

A simple closed form equation for the prediction of crosslinking of EPDM during accelerated sulfur vulcanization is presented. Such a closed form solution is derived from a second order non homogeneous differential equation, deduced from a kinetic model. The kinetic 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 polymer. Once written standard first order differential equations for each partial reaction, the differential equation system so obtained is rearranged and, after few considerations, a single second order non homogeneous differential equation with constant coefficients is derived, for which a solution may be found in closed form, provided that the non-homogeneous term is approximated with an exponential function. To estimate numerically the degree of crosslinking, kinetic model constants are evaluated through a simple data fitting, performed on experimental rheometer cure curves. The fitting procedure is a new one, and is achieved using an ad-hoc genetic algorithm, provided that a few points, strictly necessary to estimate model unknown constants with sufficient accuracy, are selected from the whole experimental cure curve. To assess the results obtained with the model proposed, a number of different compounds are analyzed, for which experimental or numerical data are available from the literature. The important cases of moderate and strong reversions are also considered, experiencing a convincing convergence of the analytical model proposed. For the single cases analyzed, partial reaction kinetic constants are also provided.