Shrinkage during drying of silica gel

A model is provided for predicting gel shrinkage during drying by combining the empirical observations that: (1) the bulk modulus of a gel increases with density, ρ, according to K_p = K₀ ( ρ ρ_y)^m (2.5 ≤ m ≤ 4); and (2) the variation in pore radius, r, is approximately proportional to pore volume (contrary to the dependence, r α ρ ^{-1 3}, conventionally assumed). No allowance is made for viscoelastic relaxation, so the model applies only for drying from an inert solvent. The model may be used to guide processing efforts to yield either aerogel-like materials with high porosity or xerogels with high density and small pore size for adsorbents, membranes, etc. The extent of shrinkage is governed by two dimensionless parameters, P and m. The quantity P = A_s γ cos(θ)mρ_y K₀ (where A_s is specific surface area, γ is surface tension, and θ is the contact angle) represents the relative magnitudes of capillary pressure and gel stiffness, and m describes the variation of stiffness with density. For P values less than 1, the shrinkage upon drying is less than 10%, and is reversible. For shrinkages greater than {reversed tilde equals} 50%, the density increase is irreversible, and is proportional to P1/(m - 1). Predicted shrinkage is compared with experimental results for silica gels dried from different surface tension pore fluids (2 < γ < 68 dyn/cm), initial wet gel density (0.06 < ρ₀ < 0.15 g/cm³), and gel stiffness (0.3 < K₀ < 1 MPa).