Local mean-field study of capillary condensation in silica aerogels

Abstract

We apply local mean-field (i.e. density functional) theory to a lattice model of a fluid in contact with a dilute, disordered gel network. The gel structure is described by a diffusion-limited cluster aggregation model. We focus on the influence of porosity on both the hysteretic and the equilibrium behavior of the fluid as one varies the chemical potential at low temperature. We show that the shape of the hysteresis loop changes from smooth to rectangular as the porosity increases and that this change is associated to disorder-induced out-of-equilibrium phase transitions that differ on adsorption and on desorption. Our results provide insight in the behavior of $^4$He in silica aerogels.