Multiscale modeling of solvent-cast sol-gel ceramic films

The sol-gel method is a liquid-phase chemical route to ceramics through the hydrolysis and polycondensation of alkoxysilane precursors. Coating of these films from a solution of a volatile solvent (ethanol) is a widely used technique to form thin, porous ceramic films. The process can be easily modified to permit the formation of structured organic-inorganic hybrids, but it is still challenging to create thick, uniform films. To better understand the process, we have developed a multiscale model of silica curing in drying films. Because silica polycondensation is a highly nonideal network polymerization, it is best modeled by a dynamic Monte Carlo simulation (similar to a population balance model). This model uses a small set of rate coefficients to predict how the molecular structure distribution evolves during polymerization up until the gelation point. Our model is better able to predict the silica gelation conversion and the concentration dependence of gelation times than any other kinetic model is able to. To model film formation, it is necessary to also incorporate the effects of drying. We will describe a model in which we couple the dynamic Monte Carlo simulations to a continuum model of drying. The coupling is accomplished by treating the entire Monte Carlo simulation (containing over 10⁵ monomers) as a particle of sol whose position and composition are tracked throughout the continuum calculation. To best understand the coupling between scales, we begin by using a 1D finite difference method to simulate drying with a concentration gradient. By performing several Monet Carlo simulations for sol packets that start from various positions throughout the film, we determine the evolution of the molecular weight distribution at each point in the film. Under fast drying conditions, these simulations allow us to predict the rapid onset of gelation near the film surface, and slower gelation of a sublayer of sol. A comparison will be made of the predicted molecular structure of silica gels formed at different drying rates and film thicknesses, and at different positions in films with concentration gradients.