Combining ternary phase diagrams and multiphase coupled matrix-based Monte Carlo to model phase dependent compositional and molar mass variations in high impact polystyrene synthesis

Abstract

High impact polystyrene (HIPS) production starts from a homogeneous grafting of styrene (St) on polybutadiene (PB). However, already at low St conversion, the reaction mixture becomes heterogeneous due to the incompatibility between polystyrene (PS) and PB. First a PS-rich phase appears, dispersed in a PB-rich phase, and then the situation reverses. At even higher St conversions, the PB-rich phase also includes PS occlusions (defined as a third phase). In the present work, a multiphase coupled matrix-based Monte Carlo (CMMC) model is presented, tracking the molecular variations of individual molecules for the first time per phase. This is done accounting for (i) phase equilibria as inputted based on a literature-based ternary phase diagram for St-PB-PS mixtures, and (ii) diffusional limitations by means of apparent rate coefficients, demonstrating a preference for the composite kt model for the representation of the gel-effect. The simplified single phase model output is acceptable up to St conversions of 30 %, justifying the previous efforts on tuning modeling parameters also including model validation for high yield general purpose PS synthesis. However, at higher St conversions (up to 60 %), a single phase model predicts too high St amounts in the graft copolymer, and too low PS average chain lengths and dispersities. Furthermore, post-processing at a given St conversion reveals the contributions to the total PS log-molar mass distribution (log-MMD) from the PS-rich phase, the PB-rich phase, and PS occlusions. Moreover, the multimodality of the observed (total) log-MMD is uniquely explained based on these contributions, with specifically a more pronounced second peak due to blocked mass transfer of PS to the PS-rich phase at higher St conversions.