Population Balance Models for Catalytic Depolymerization: From Elementary Steps to Multiphase Reactors
Here, the ongoing accumulation of plastic waste in landfills and in the environment is driving research on chemical processes and catalysts to recycle polymers. Traditional modeling strategies are not applicable to these processes because they involve too many reactants and intermediates, one for each molecular weight and each functionalization. To model the kinetics, we have developed population balance models (PBMs) that account for macromolecular reactants in the bulk and macromolecular catalytic intermediates. These PBMs couple to each other through polymer adsorption and desorption models and to traditional rate equations for small molecule products and co-reactants (like hydrogen or ethylene). The models, in combination with experimental data, are being used in many ways: (i) to test mechanistic hypotheses, (ii) to extract rate parameters, (iii) to quantitatively compare catalyst activities, (iv) to account for mass transfer and vapor–liquid partitioning in two-phase reactors, and (v) to design novel support architectures and catalysts that mimic the processive action of natural depolymerization enzymes. Some key theoretical advances allow PBMs to be constructed from elementary rates and mechanisms, as opposed to traditional formulations with pseudoelementary rate parameters invoked as fitting parameters. We discuss ways to build these models “bottom-up” from first-principles calculations and ways to extract model parameters from “top down” analyses of rate data. The combination provides a quantitative bridge between first-principles calculations and the kinetics of complex macromolecular transformations for polymer upcycling and beyond.