Kinetic Models for Polymer Upcycling by Tag-and-Cut Strategies

Population balances are natural frameworks for modeling chemical recycling processes for plastics. In this paper, we develop coupled species and population balance equations to model a process that randomly cleaves polymers in two steps. A “tagging” reaction installs functional groups (e.g., double bonds) at random locations along the chains. The tagged segments become susceptible locations for a subsequent chain cutting reaction. We provide equations and analytical solutions for systems where the tag and cut steps occur concurrently and systems where they occur in two stages. We apply the model to a dehydrogenation/olefin-metathesis system using gel permeation chromatography data [Arroyave et al. J. Am. Chem. Soc. 144, 23280–85 (2022)]. We then compare the depolymerization rates of a concurrent tag and cut system to those of a sequential/two-stage system. Assuming identical rate parameters regardless of the process design, the concurrent system theoretically outperforms all two-stage tag-and-cut processes. However, the two-stage process avoids potential complications with catalyst compatibility and allows residence times and process conditions (which influence the rate parameters) to be separately optimized for the two stages.