Processive Depolymerization Catalysts: A Population Balance Model for Chemistry's "while" Loop

A processive catalyst associates with a substrate and performs multiple reactions before dissociation, a mechanism used by enzymes to increase efficiency. Recent work [Tennakoon et al. Nature Catalysis 2020, 3, 893-901] reported a synthetic processive catalyst for polyethylene upcycling. In this paper, we embed a microkinetic model for processive depolymerization within coupled population balance models for the bulk and adsorbed polymer molecular weight distributions. Nondimensionalization reveals a small parameter that enables a reduction to one bulk population balance equation coupled to a pseudo-steady-state distribution for the distribution of adsorbed chains. We develop solutions to the model, with varying degrees of processivity, and starting from experimental molecular weight distributions taken from recent publications. The model predicts identifiable signatures of processivity in the evolving molecular weight distribution. The model also provides a framework for analysis of experimental data to obtain the underlying catalytic rate parameters.