Stochastic and Deterministic Analysis of Reactivity Ratios in the Partially Reversible Copolymerization of Lactide and Glycolide
Louise Kuehster, Young Kuk Jhon, Yan Wang, William C. Smith, Xiaoming Xu, Bin Qin, Feng Zhang, Nathaniel A. Lynd
Abstract
Poly(lactide-co-glycolide) (PLGA) is an important component in many pharmaceutical applications. A detailed understanding of repeat unit ordering in PLGA is complicated by a prohibitively large number of equations that would be required for a conventional deterministic mathematical description of the reversible lactide/glycolide copolymerization. Established copolymerization models apply only to irreversible polymerization chemistry. Here, we proposed a numerical copolymerization model that includes forward reactivity ratios (rG, rL) and a third parameter to account for lactide reversibility (r–L/L). We combined a simplified deterministic model and full stochastic model to extract reactivity ratios from experimental time-evolution data taken at several initial feed compositions. We fit the kinetic data at four initial glycolide compositions (fG0 = 0.10, 0.15, 0.20, and 0.25) to the simplified deterministic model to determine the full set of reactivity ratios: rG = kGG/kGL = 4.5 ± 0.3, rL = kLL/kLG = 0.32 ± 0.01, and the reversibility parameter for lactide: r–L/L = kL–L/kLL = 0.15 ± 0.02 mol/L. Glycolide was consumed early in the copolymerization and did not exhibit reversibility. The stochastic model was used to verify that the reactivity ratios provided an accurate description of the partially reversible copolymerization by comparison of the fully parameterized model against experimental data.