Effective closed form mathematical approach to determine kinetic constants of NR vulcanized with sulphur and accelerators at different concentrations

Abstract

The basic reaction scheme due to Han and co-workers for NR vulcanized with sulphur is adopted and modified taking into account the single contributions of the different accelerators, focusing in particular on some experimental data ad hoc obtained at Pirelli’s laboratories, where NR was vulcanized at different temperatures (from 150 to 180 °C) and concentrations of sulphur, using TBBS and DPG in the mixture as co-agents. Typically, the chain reactions are initiated by the formation of macro-compounds that are responsible of the formation of the unmatured crosslinked polymer. This first reaction depends on the reciprocal concentrations of all components and their chemical nature. In presence of two accelerators, it was considered that the reactions between each single accelerator and the NR raw material occur in parallel, making the reasonable assumption that there are no mutual reactions between the two accelerators. From the kinetic scheme adopted, a closed form solution was found for the crosslink density, with the only limitation that the induction period is excluded from computations. Even kinetic constants are evaluated in closed form, avoiding a numerically demanding least-squares best fitting on rheometer experimental data. Two series of experiments available, relying into rheometer curves at different temperatures and different concentrations of sulphur and accelerator, are utilized to evaluate the fitting capabilities of the mathematical model. Very good agreement between numerical output and experimental data is experienced in all cases analysed.