Population Balance Kinetic Model for Interaction of 2-Bisbenzothiazole-2-2'Disulfide (MBTS) with Sulfur

Abstract

Abstract The first step in accelerated vulcanization is the formation of the active sulfurating species via the incorporation of sulfur by an accelerator like benzothiazole. Several mechanisms for the pick-up of sulfur by the accelerator have been proposed, including lumped pick-up of the full S8 species, sequential pick-up of individual sulfur atoms in S8 and numerous proposals where the stoichiometry is not clearly specified. For the reaction of MBTS with S8 Gradwell, et al. observed that benzothiazole terminated sulfurating species with lower sulfur rank form in greater concentrations than the sulfurating species with higher sulfur rank, where a sequential sulfur pick-up mechanism was then postulated. A detailed kinetic model will be developed to describe the Gradwell, et al. data. Density functional theory (DFT) simulations were used to provide information on the thermochemistry of the various reaction intermediates. The DFT simulations indicated that both sequential and lumped S8 pick-up are thermodynamically feasible. Population balance models have been developed that explicitly account for all polysulfidic species that are present in the MBTS+S8 reaction system. The chemically consistent population balance model includes the following reactions: (i) dissociation of polysulfides, including the opening of S8 rings, to form radical pairs, (ii) combination of a pair of persulfenyl radicals, (iii) reaction of a persulfenyl radical with a polysulfide. The effect of chain length on the kinetic constants for these reactions was determined from the DFT simulations, where the bonds that are close to the benzothiazole groups have significantly different rates of reaction. It is shown that (i) lumped sulfur pick-up alone is not thermodynamically consistent, and (ii) sequential sulfur pickup alone can not adequately describe the experimental data of Gradwell, et al.; however, a chemically consistent model with both sequential and lumped sulfur pick-up can explain the data. The identification of the above mechanism and the associated distribution of sulfurating species of different sulfur rank provide the starting point for a quantitative kinetic description of the accelerated vulcanization.