Accurate Determination of Reactivity Ratios for Copolymerization Reactions with Reversible Propagation Mechanisms

Abstract

An understanding of monomer sequence is required to predict and engineer the properties of copolymers. In stochastic polymerizations involving more than one monomer, monomer sequence is typically inferred or determined from reactivity ratios, which are measured through copolymerization experiments. The accurate determination of reactivity ratios from copolymerizations where one or both monomers undergo reversible propagation, however, has been complicated by the difficulty in solving the underlying population balance equations, the presence of myriad copolymer equations in the literature derived under varying assumptions and simplifications, and lack of an easy-to-fit integrated model. Here, we rectify and assert the consistency between previously reported copolymer equations of disparate forms, introduce a new method to explicitly solve the underlying population balance equations, and perform stochastic copolymerization simulations to evaluate the ability of these three methods to produce consistent comonomer consumption predictions and fits to simulated copolymerization data. We find that all methods produce consistent predictions given the same input parameters, which implies both accuracy and precision when modeling copolymerization, fitting experimental data, and making predictions of comonomer sequence. Considering this consistency, we make a recommendation to use numerical integration of the appropriate copolymer equation to fit real copolymerization data due to its ease of implementation. We further identify the minimum number of parameters required for accurate data fitting and suggest ways to measure other information ex situ from copolymerization to expedite accurate fitting. Finally, the practical utility of the methods developed herein is demonstrated through fitting seven distinct copolymerization data sets, which span a wide range of copolymerization reactivities.