Fast and reliable meta-data model for the mechanistic analysis of NR vulcanized with sulphur

A fast and reliable meta-model for NR vulcanized with sulphur in standard rheometer chambers is presented. The model requires only very little input information at a fixed vulcanization temperature, as for instance scorch time, t(90) and percentage reversion. It provides kinetic constants of the single reactions occurring during the curing process as output, within the assumptions of a suitable mechanistic model. The meta-model is subdivided into two phases, the first characterized by construction of experimental meta-data from limited rheometer information, and the second by the determination of partial reaction kinetic constants characterizing the vulcanization process, assuming those obtained in the previous phase with the meta-model as experimental data to fit. Meta-data are obtained using a very straightforward C-2 natural cubic spline interpolation of the rheometer curve, which is shown to fit the experimental data well. Both the presence and absence of reversion are discussed and how they are reflected in the model calculations. In step two, a simple new closed form equation representing the degree of vulcanization of NR cured with sulphur is deduced, where kinetic parameters are numerically determined through non-linear least squares fitting of meta-data determined previously. The closed form solution is derived from a set of first order differential equations representing the partial reactions occurring during curing. To assess the results obtained with the model proposed, several examples of the same blend in the presence of different accelerators, for which minimal experimental information was available from the literature, are analysed. In some cases, moderate to strong reversion was present. The procedure proved to be very fast and reliable and has the advantage of providing, for the single cases analysed, partial reaction kinetic constants.