Phase transitions of binary mixtures in random media

Abstract

We consider a porous solid, or a gel, saturated by a two fluid system A + B, in the limit where the thickness ξ of the AB interface is smaller than the pore size D. The solid prefers to be in contact with one of the fluids (A). But, if we decrease the chemical potential of B, the B fluid enters the structure. We discuss the reversible penetration process, and find two distinct modes : a) « Capillary invasion » with clusters of B regions growing progressively. b) « Flip process » where all pores are abruptly invaded by B (except possibly for a thin sheath of thickness ξ near the walls). The « fields » H (= chemical potential changes) required to perform capillary invasion (Hc ) or flip (Hf) are in ratio : Hf/ Hc ≅ (ξ/D)2-df where df is the fractal dimension of the pore surface. Gels made with rod-like molecules have df = 1, while flexible chains in good solvents have df = 5/3. For all gels the flip process should dominate, and we expect a sharp transition. On the other hand, porous solids (d f = 2) require a special discussion. Modeling the pores as interconnected capillaries of random diameter D, we find that capillary invasion dominates in this case, and we expect no sharp transition