Efficient Deterministic Modeling of Reversible Copolymerizations

Mathematical modeling of copolymerizations with depropagation remains significantly more challenging than those with only irreversible propagation. Current models require solving a system of nonlinear equations to calculate chain-end dyads at every integration step, which is inefficient and prone to numerical instability. This paper formulates the core species balances as a pure system of ordinary differential equations by directly integrating these chain-end dyad balances, increasing the computational efficiency by roughly an order of magnitude and improving the numerical stability. Two model systems of controlled polymerization with a single depropagating monomer and uncontrolled polymerization where both monomers undergo depropagation were studied and validated with stochastic simulation and experimental data, respectively. A model system approximating the controlled copolymerization of ethyl lipoate and n-butyl acrylate was analyzed by systematically varying accessible experimental conditions. The developed model was used to quantify the variation in average monomer sequence length along the polymer backbone. As temperature increases or concentration decreases, the resulting copolymer transitions from a highly gradient microstructure to an even monomer distribution, revealing accessible design handles that chemists can use to manipulate sequence. For uncontrolled polymerization, the high-temperature bulk copolymerization of α-methylstyrene and methyl methacrylate was simulated and accurately reproduces experimental conversion and composition profiles. The validation of time-resolved predictions of composition and sequence length under highly reversible conditions enables applications in process monitoring and optimization. In summary, this model demonstrates sophisticated predictions of sequence statistics while retaining both efficiency and stability even under conditions with significant reversibility or compositional asymmetry.