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The grafting of PE onto PS through a Friedel‐Crafts reaction, which results in a mixture of PE‐g‐PS copolymer, unmodified PE, and modified PS, is investigated. The copolymer may be suitable for compatibilization of immiscible mixtures in the household plastic waste stream, where PE and PS are majority components. Since the compatibilization effect depends on the composition and block lengths in the copolymer, a model is presented for predicting the complete molecular weight distribution of the homopolymers and the chemical composition distribution of the graft copolymer. The model has potential for application in an optimization tool for the compatibilization process, as it is able to account for the opposing effects of competing reactions that characterize the graft reaction.