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Multiscale Modeling of Coupled Drying and Nonideal Polymerization in Sol-Gel Silica Films

Xin Li and Stephen E. Rankin. Chemical and Materials Engineering, University of Kentucky, 177 Anderson Hall, Lexington, KY 40506

Modeling silica curing in drying films prepared by processes such as sol-gel dip coating is important for overcoming challenges in controlling the thickness, cracking and homogeneity of the films. These films are of growing interest as engineered materials for controlled adsorption, membrane separations, sensor concentrators, and electronic materials. The formation of sol-gel coatings involves multiple length and time scales ranging from molecular to macroscopic. Therefore, a good model should link macroscopic flow and drying (controlled by process parameters) to film microstructure (which dictates the properties of the films). Here, we will describe a multiscale model in which dynamic Monte Carlo (DMC) simulations are coupled to a continuum model of drying. The DMC approach is needed to simulate nonideal polymerization effects including first-shell substitution effects (FSSE) and cyclization. The simulation tracks the populations of site pairs and bond blocks to derive the rates of bimolecular reactions and cyclization reactions, respectively. Unlike statistical methods, DMC simulations track the entire molecular structure distribution to allow the calculation not only of molecular weight but also of topological indices related to molecular size and shape. These topological indices can be used for improved correlations of transport coefficients in polymers with different degrees of branching and cyclization. The entire DMC simulation (containing ~ 106 monomers) is treated as a particle of sol whose position and composition are tracked using a diffusion/evaporation finite difference calculation. By simulating a swarm of particles starting from different positions in the film and using variable parameters, we observe the effect of drying parameters on the gelation regime, predict different drying/gelation phenomena, and predict the occurrence of gradients of concentration, gelation, and structure in the films.