Modeling the gelation of silicon alkoxides

This paper reviews the experimental evidence which suggests that the gelation of alkoxides can be modeled using analyses developed for organic condensation polymerizations, and presents a model which can be used to predict the gelation of acid catalyzed silicon alkoxides. Parameters that characterize the polymerization products, such as weight averaged molecular weight, are calculated from the extent of the molecular reactions using a recursive solution technique applied to the random branching theory of polymerization. The extent of the hydrolysis and condensation reactions as functions of time are calculated from the kinetic schemes of Assink and Kay [J. Non-Cryst. Solids 99 (1988) 359; 104 (1988) 112] and Pouxveil and Boilot [J. Non-Cryst. Solids 94 (1987) 347]. Results of this modeling give molecular weight versus conversion and molecular weight versus time. The predictions of gel times and conversion using this recursive technique combined with the kinetic models of Assink and Kay for TMOS are in reasonable agreement with the experimental data of Kelts and Armstrong [J. Mater. Res. 4 (1989) 423] if the effects of cyclization are considered. For the gelation of TEOS, using the kinetic scheme of Pouxveil and Boilot, the agreement is not as good due to the larger extent of cyclization.