80 years of the Mayo Lewis equation. A comprehensive review on the numerical estimation techniques for the reactivity ratios in typical and emerging copolymerizations

Microstructure and copolymer composition are characteristics important for both commodity and tailor-made materials synthesized by Free Radical Copolymerization (FRCoP) and other polymerization chemistries. The Mayo-Lewis equation (MLE), published in 1944, revolutionized copolymerization practice and theory by providing a straightforward relationship between comonomer and copolymer composition in terms of two parameters, the reactivity ratios (RR). Since that time, various forms of this non-linear equation, all based upon the terminal model (TM) of copolymerization, have been developed to facilitate estimation of RR values through fitting of experimentally measured copolymer compositions as a function of comonomer composition and/or monomer conversion. Early transformations introduced to allow linear regression methodologies have been replaced by powerful nonlinear numerical methods that provide statistically valid estimations of the reactivity ratios. In this review, the fundamentals of the linear and nonlinear numerical methodologies are described, with an emphasis on the recommended non-linear strategies for the determination of the RR using copolymer/monomer composition data at both low and moderate/high conversions. The shape and calculation of the Joint Confidence Regions (JCRs) associated with the RR values is also reviewed, and the optimal design of experiments for the determination of RR values is described.

While remarkably robust, the MLE does not provide an adequate description of copolymer composition for some systems. An examination of the assumptions associated with the derivation provides context for these exceptions. Systematic extensions of the MLE to capture the influence of penultimate unit effects, depropagation, and system (e.g., solvent, concentration, pH) dependencies are outlined. Additionally, discrepancies reported in the copolymer composition between the free-radical copolymerization and reversible deactivation radical copolymerization are analyzed in terms of kinetic fundamentals. While deviations from classic behavior are the exception rather than the rule, they demonstrate the need to carefully investigate any new system to validate the applicability of the MLE.