From simulation to distribution: A novel approach to depolymerization kinetics using PHB hydrolysis as a case study

• Development of a probability mass function for depolymerization, similar to the Flory-Schulz distribution • Combination of random scission of linear polymers (using PHB as example) with pseudo second order kinetics in melt hydrolysis • Assumption, that oligomers up to six repeating units are water-soluble • Validated via experimental data, including gas phase side reaction • Profound and versatile tool for prediction of polymer degradation processes The Flory–Schulz distribution has long been used to describe the probability mass function of polymerization processes, enabling the calculation of polymerization kinetics. However, an equivalent distribution function for depolymerization processes remains elusive. In this study, we present a novel simulation-assisted kinetics model to investigate the depolymerization dynamics of polyhydroxybutyrate (PHB). Our simulation replicates the random scission of a linear polymer chain and is calibrated against experimental data, yielding a conversion parameter that quantifies the extent of bond cleavage within the polymer. This conversion was then incorporated into the established pseudo second-order reaction kinetics for PHB to describe the temporal evolution of the depolymerization process. A key assumption in the model is that oligomers with six or fewer repeating units are water-soluble and constitute the measurable depolymerization yield. The simulation provides the proportion of these small oligomers, which were fitted as a function of conversion. This relationship was integrated into the kinetics model, resulting in a predictive expression for the water-soluble yield over time. To further simplify the application of the simulation results, we derived an analytical distribution function that approximates the fragment length distribution resulting from random chain scission. This distribution reproduces the simulation outcomes with high accuracy and enables easier application in analytical and modeling contexts. We additionally compare this distribution and a second, binomial-coefficient-based formulation to the simulation data to evaluate their respective accuracies. Together, the kinetics model and distribution function offer a comprehensive and practical framework for understanding and predicting polymer degradation behavior.