Dynamic Monte Carlo simulation of gelation with extensive cyclization

Recent investigations have implicated cagelike precursors in the unusually high gelation conversion (approximately 82%) of acid-catalyzed tetraethoxysilane. However, the statistical models used so far cannot capture kinetic or composition-dependent features of alkoxysilane polycondensation. Here we take a first step toward unified modeling of the kinetics and structure of silica gelation. Dynamic Monte Carlo simulations are developed which permit competition between extensive cyclization and growth. The model includes well-established kinetic trends (hydrolysis preequilibrium and first-shell substitution effects). As a first approximation, unimolecular-like terms for cyclization reactivity follow the experimental pattern of bimolecular rate coefficients. The present simulations allow unlimited formation of three-site rings, giving rise to many structures that are not those of real silicates (where four-site rings dominate). However, the level of cyclization (both cycles per molecule and per site) is consistent with that of real silicates and is enough to delay gelation to 82% conversion or higher. These simulations also display a broader range of gelation behavior than prior kinetic models. At high to moderate monomer concentrations, competition between cyclization and growth causes the expected delay of gelation. Upon further dilution, we discover a third regime, absent from prior kinetic gelation models but important for siloxanes: formation of a distribution of polycyclic precursors that still retain enough functionality to gel.