Coupled matrix kinetic Monte Carlo simulations applied for advanced understanding of polymer grafting kinetics

Abstract

One of the challenges for modelling of polymerization kinetics is the detailed description of the molecular build-up of both linear and non-linear chains, specifically those with many grafts and crosslinks. Such grafted/crosslinked (co)polymers are relevant as emulsifiers, surface-modifying agents, coating materials, and compatibilizers. In the present work, we put forward a coupled matrix-based Monte Carlo (CMMC) concept to be successful in this respect, avoiding computational stiffness. The CMMC concept is illustrated for single phase grafting of polybutadiene (PB) with styrene (St) at 343 K by limiting the St conversion to 30%. Considering literature kinetic parameters, a benchmark for average characteristics as obtainable by deterministic method of moments simulations is first presented to then gradually extend the level of modelling output addressing (i) conventional grafting performance indicators (e.g. the grafting yield and mass ratio); (ii) univariate chain length distributions for all macrospecies types (polystyrene, PB, PB with only T grafts, PB with at least one H graft, etc.); (iii) bivariate St–butadiene distributions showing a compositional drift, due to the kinetic tendency to attack longer chains if they are sufficiently present and the competition between grafting and crosslinking; (iv) the explicit molecular build-up of individual molecules predicting the positioning of the St–Bd and St–St connectivity points and the chain formation history. It is demonstrated that the CMMC tool allows the simulation of the contribution and structure of molecules that are hard to access purely experimentally, so that in the long run, novel structure–property relationships are within reach. It is also showcased that consideration of elementary reactions is highly recommended and that even at 343 K, thermal self-initiation with St and related chain transfer reactions matter for a full appreciation of molecular variations. The current work also opens the pathway to identifying pragmatic equations for the experimentalist and online control benefiting from a detailed CMMC solution under any desired conditions.