Kinetic Models\nfor Polymer Upcycling by Tag-and-Cut\nStrategies

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