Modeling of First Shell Substitution Effects and Preferred Cyclization in Sol−Gel Polymerization

Abstract

We compare two approaches in modeling first shell substitution effects (FSSE) coupled with cyclization in acid-catalyzed sol-gel polymerization. First, an approximate, statistically based, kinetic- recursive model (KR) is developed that is computationally inexpensive for investigating trends in the polymerization. Second, an exact Monte-Carlo model (MC) that tracks a finite pool of growing polymer clusters is constructed for comparison to the KR model. The two models agree well prior to gelation when using rate constants typical of sol-gel polymerization. However, near the gel point, discrepancies between the two models arise because of the KR model's inability to account for correlations in the growing structure beyond the site distribution. We show that both FSSE and cyclization cause the polymer's structure distribution to be history dependent. We also show that the inclusion of both FSSE and cyclization in the model is capable of increasing gel conversions above the 0.50 limit of previous exclusive FSSE models. We show that FSSE aids cyclization by increasing the concentrations of oligomers that are candidates for intramolecular reaction and that a strong FSSE with cyclization causes a local maximum to occur in the polydispersity index as a function of conversion. Both models fall short of predicting experimentally observed gel conversions; indicating that, in addition to the small cycles allowed in the present work, cage formation may also be significant.