Generalized kinetic modeling procedure based on statistics for parameter estimation of cationic polymerization and its application to polyisobutylene

Abstract

Literature on cationic polymerization suggests different mechanisms that can be followed from case to case and show reaction rate constants that significantly differ depending on the electrical strength and stability according to the choices of catalyst and solvent. Therefore, to end this problem, a general procedure for building a mathematical model suitable for a given cationic polymerization system and finding its parameters in this study. First, in the model for number-average and weight-average molecular weights, a single state model is suggested for cases of narrow molecular weight distribution, whereas it is argued that a multi-state model is needed for cases of broad distribution. In the multi-state case, it is demonstrated how the overall kinetics can be derived by using the expectations and variances rather than the individual states’ kinetic parameters. In the multi-state model, although the expectation and variance do not follow the relationship of the Arrhenius equation, a procedure is given for how to account for temperature dependence. Second, the exo-olefin content model focuses on the molecular particle behavior in the isomerization reaction from a microscopic view and derives macroscopic results through statistics. Therefore, it is expressed as difference equations, and the result is consistent with mass balance-based differential equations but has a computational advantage. The multi-state exo-olefin content model is integrated with the molecular weights model and is extensible to temperature-dependent systems through the Arrhenius equation. Finally, we demonstrate the overall procedure for estimating parameters using data from experiments of PIB. The first application shows the parameters estimating for the molecular weights model through the experiments of conventional PIB. Next, the second application explains the estimating of the isomerization reaction parameters along with parameters for the molecular weights through experiments of high-reactive PIB, including exo-olefin content.