Statistical kinetic modeling procedure for cationic polymerization and its application to polyisobutylene

Abstract

A statistical modeling procedure is established for carbocation polymerization with the characteristics of living with chain transfer. A single state model is suggested for cases of narrow molecular weight distribution, whereas a multi-state model is claimed for cases of broad distribution. In the multi-state case, it is demonstrated how the overall kinetics can be derived using the expectations and variances of the kinetic parameters rather than those of individual states, thereby simplifying the modeling step. 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. The proposed statistical method minimizes the number of parameters to identify and therefore is expected to help establish a model with fewer experiments. The whole procedure is demonstrated through an experimental study of isobutylene polymerization.

Statistical Kinetic Modeling Procedure to Predict Exo-Olefin Content in Cationic Polymerization and Its Application to Polyisobutylene

“…The molecular weights and olefin content, including the exo form, obtained from the batch experiment are summarized in Table . From the results of this experiment, it can be seen that the number-average molecular weight decreases with polymerization time, the chain transfer to proton was determined to be dominant, and the TRP model was used as the model of the molecular weights according to the preceding study . In addition, it was confirmed that most are high-reactive PIBs with an exo-olefin content of 80% or higher.…”

“…In eq , constraints (i)–(iii) represent the assumptions A1–A3 used to apply the Arrhenius equation . The estimated objective function value “ fval ” for varying choices of “ m ” is shown in Figures and .…”

“…In the molecular weight model, , which is not a weighted value, requires only the expectation of the states’ kinetic parameters. However, , a weighted value, requires the variances as well as the expectations . Since the exo-olefin content in this model is not a weighted value like , each kinetic parameter is replaced by only its expectation over the ‘ m + 1’ states.…”

“…The above exo-olefin content model of multistate cation polymerization can be integrated with the molecular weight model proposed by Shim et al The parameters of the multistate molecular weight model in the integrated model can be adjusted according to the following eqs –. The list of the overall kinetic parameters is shown in Table . …”

“…For example, looking at a molecular particle at P 0 , the probability of the particle moving to the next position, R 0 + at time t is modeled as an exponential distribution, as shown in eq 7. 1 RT Pd 0 represents the average residence time in state P 0 .…”