Title: Efficient Statistical Methods for Modeling the Polymerization and Microstructure of Degradable Copolymers

Abstract: Synthetic polymers are central to modern materials, but their persistence in landfills and the environment has motivated growing interest in degradable alternatives. One promising strategy is copolymerization with a cleavable comonomer, such as a cyclic disulfide, that installs labile bonds along an otherwise robust C–C backbone. The resulting degradation behavior depends not only on how much cleavable monomer is incorporated but on how those units are distributed along each chain. Many cleavable comonomers also undergo significant depropagation, adding a layer of reversibility that conventional irreversible copolymerization models cannot capture. This dissertation develops a suite of efficient statistical and computational tools to model copolymerization kinetics, resolve copolymer microstructure, and connect both to material properties such as degradability.

First, we developed a deterministic kinetic model for reversible copolymerization formulated as a pure system of ordinary differential equations. By directly integrating the population balances rather than enforcing them as steady-state algebraic constraints, the model captures reversible copolymerization kinetics efficiently and predicts copolymer composition, chain-length, and sequence-length statistics. Second, we addressed the computational cost of conventional stochastic simulation for uncontrolled free radical polymerization by developing a trivially parallelizable hybrid Monte Carlo algorithm. We extended the deterministic balances governing the bulk kinetics to seed a stochastic simulation that grows individual discrete copolymer chains in parallel on a consumer-grade graphics processing unit (GPU). The method accurately recovers molecular weight, composition-chain length, and sequence-length distributions in close agreement conventional stochastic simulations while being orders of magnitude faster.

Finally, we combined these tools to predict the degradability of lipoate copolymers. A Bayesian inference workflow was developed to estimate and quantify uncertainty in reactivity parameters from experimental copolymerization data of n-butyl acrylate and ethyl lipoate. The uncertainty was propagated through GPU-accelerated hybrid simulations of copolymerization and degradation. This workflow demonstrates accurate predictions of degraded molecular weight distributions across temperature, concentration, and feed composition, while honestly reflecting the underlying parameter uncertainty. The workflow and code is open-source and provides a foundation for uncertainty-aware design of degradable copolymers.