Mathematical modeling of the graft reaction between polystyrene and polyethylene

Polystyrene (PS) and polyethylene (PE) are two major components of household plastic waste whose blends are immiscible. Recycling them together is an attractive option that requires a compatibilization process to improve the blend mechanical properties. If a PE/PS copolymer is added or formed in situ, it may act as compatibilizer. The structure and molecular properties of this copolymer are key factors to assure its effectivity as a compatibilizer. In this work, we study the graft copolymerization reaction between polystyrene and polyethylene using the catalytic system composed of AlCl₃ and styrene. We develop a model of this process which considers that PE/PS grafting and PS degradation occur simultaneously. We propose a kinetic mechanism for the whole process and apply the method of moments to solve the mass balance equations. The model is able to calculate average molecular weights as well as the amount of grafted PS. It accurately describes the available experimental data, constituting a valuable tool for simulation and optimization purposes.