Nonlinear Method for Determining Reactivity Ratios of Ring-Opening Copolymerizations

Abstract

A nonlinear errors-in-variables-model (EVM) regression method was used to determine reactivity ratios for enzyme-catalyzed ring-opening copolymerizations of ε-caprolactone (ε-CL) and δ-valerolactone (δ-VL). The cumulative copolymer composition model accurately described the experimental data, indicating that conventional models can be used to describe enzyme-catalyzed copolymerizations. Reactivity ratios were calculated from Raman spectroscopic data collected in situ and the model of monomer feed drift over the course of copolymerization. The analysis was combined for multiple experiments to improve the estimate. For the lipase-catalyzed copolymerization, the calculated reactivity ratios were rε-CL = 0.27 and rδ-VL = 0.39. Compared to conventional linearization techniques, the EVM method reduced the experimental work required and reduced the measurement error, as indicated by the 95% joint confidence region. In addition, the EVM method is influenced less by the apparent induction period of δ-VL. The conventional methods rely on low conversion data where the induction period is significant. The EVM method presented here determines reactivity ratios rapidly, saving both time and material waste.