A one-dimensional analysis of sol-gel film-coating drying: Pore evolution, network shrinkage and stress development

Highly porous sol-gel films have potential applications as electrical and thermal insulators, catalyst supports, sensors, and membranes for gas separations. Pore dimensions in these sol-gel films are usually small e.g., on the order of tens of nanometers or less. Their successful fabrications, however, greatly depend on the fundamental understanding of mechanisms that underlie the phenomena of pore evolution, network shrinkage, and stress development since the final microstructure of a solid gel film is strongly affected by composition of its starting sol and its processing conditions. This report documents a simplified one-dimensional analysis of drying a solidifying sol-gel thin film coating supported by an impermeable solid substrate. Portions of this work were presented at the 1994 Annual Joint Meeting of the New Mexico Section of the American Ceramic Society and Materials Research Society in Albuquerque. The authors considered the solid/liquid two phase coexistent regime during the drying solidifying process in which solvent is removed continuously via evaporation, the solid phase grows significantly in mechanical strength, and pore space shrinks appreciably. From overall and differential mass balances and a force balance at equilibrium, coupled with empirical correlations of solid phase modulus and permeability to strain or deformation, the authors followed the evolution of pore space, solid phase elastic stress, and liquid phase hydrodynamic pressure; they also determined their respective values at equilibrium. By assuming microscopic pore shape models, they estimated and compared the predicted mean pore radii. Their simplified one-dimensional analysis shows that the final mean pore radius is controlled by four parameters: pore-liquid surface tension, solid phase modulus, mean pore radius, and porosity at the initial stress-free state. The one-dimensional model can be employed to guide process design and optimization in sol-gel film fabrications