A novel model describes copolymerization of isobutylene and inimer (initiator‐monomer) via living carbocationic polymerization. Six different propagation rate constants and two types of equilibrium reactions are considered. Simplifying assumptions are made to enable implementation in PREDICI, so that the molecular weight distribution (MWD) could be predicted for molecules with different branching levels. Four apparent rate constants were estimated from experimental data with <5 branches per molecule. Model predictions provide a good fit to data, and simulation results show that polymers with high‐branching levels and ≥15 inimer units contribute significantly to the MWD, even though their concentrations are very low. magnified image

A Monte Carlo (MC) model is developed to predict molecular weight distribution and branching during the production of arborescent polyisobutylene. The model describes self‐condensing vinyl copolymerization (SCVCP) of isobutylene and inimer via living carbocationic polymerization. Six different propagation rate constants are required to account for two types of vinyl groups and three types of carbocations in the system. MC model predictions are better than predictions from a previous PREDICI material balance model because fewer simplifying assumptions are required. The MC model predictions reveal that reactions that were previously neglected have an important influence on polymer properties.

An advanced Monte Carlo (MC) model is developed to predict the molecular weight distribution and branching level for arborescent polyisobutylene produced in a batch reactor via carbocationic copolymerization of isobutylene and an inimer. This new MC model uses differential equations and random numbers to determine the detailed structure of dendritic polymer molecules. Results agree with those from a traditional MC model for the same system, but the proposed model requires considerably less computational effort. The proposed MC model is also used to obtain information about polymer segments between branch points and dangling polymer segments.

A mathematical model is developed for estimating kinetic parameters that influence the production of arborescent polyisobutylene via carbocationic copolymerization of inimer (IM) and isobutylene. Six different propagation rate constants arise due to the two types of vinyl groups and three types of carbocations. These six parameters are estimated using parallel simulation systems in PREDICI that track (1) functional groups, (2) internal and dangling segments in the polymer, and (3) concentrations of IM and polymer molecules. Parameter estimates obtained using the proposed model result in a better fit to literature data than was obtained using a previous model that neglected two types of propagations reactions. Predictions from the proposed model are consistent with Monte Carlo simulations for molecular weight distribution of the internal and dangling segments.

A mathematical model is developed for the arborescent poly­isobutylene system in a batch reactor, using multidimensional method of moments, to predict the concentrations of monomer and inimer as well as number and weight average molecular weight. This model is significantly efficient in computation, making parameter estimation practical. Simulation results agree with results obtained by Monte Carlo simulations. Parameter estimation results show that using the weight average molecular weight data provide better overall fit than leaving them out in the previous model.