Probabilistic models of porous materials

Hosts of natural processes and technologies depend on phenomena taking place inside nanometer-sized pores. Heterogeneous catalysis, adsorption separation processes, the weathering of porous rocks are but a few examples. The effect of pore size on confined phenomena has been described for a long time by famous laws such as the Gibbs-Thomson and Kelvin equations. However, the underlying analyses assume geometrically perfect pores having the shape of cylinders or spheres, which is never encountered in practice. The role played by geometrical disorder in confined phenomena remains relatively unexplored. The aim of this presentation is twofold. First, we illustrate with the case of nitrogen adsorption how geometrical disorder modifies the stability of confined liquids. Second, we show that disorder per se does not rule out quantitative experimental data analysis, which we illustrate with in situ SAXS of confined liquid-liquid phase separation. In both cases the discussion is based on probabilistic models of porous materials, which is the natural mathematical tool to capture the role of geometrical disorder.