Thermodynamics of confined nano-phases

We consider a phase of nano-scale dimensions (the adsorbate) confined within a porous material, and in thermal, chemical and mechanical equilibrium with a bulk phase of fixed temperature, pressure and composition. From a corresponding states analysis of the partition function for pores of simple geometry (e.g., slit- or cylinder-shaped) we show that the principal system variables for most cases are the pore shape and width (expressed in terms of molecular diameters), H∗, and a microscopic wetting parameter, αw, that is a measure of the relative strength of the adsorbate-wall and adsorbate-adsorbate interactions. We illustrate the utility of this model by considering experimental, theoretical and molecular simulation results for adsorption, (vapor + liquid) condensation for pure fluids and mixtures, freezing, and pressures for these confined nano-phases. The wetting parameter is shown to be of central importance, determining both the magnitude of the effects of confinement and also the qualitative behavior, for example, whether the freezing temperature is raised or lowered upon confinement. These confinement effects become larger as the pore width is reduced; reducing the pore width can also result in qualitative changes, such as phase changes. For pores of slit- or cylinder-shape there are two independent pressures within the pores, one acting normal to the pore walls and one (the tangential pressure) acting parallel to the walls. Molecular simulation results show that these two pressures, which are of the order thousands or tens of thousands of bars for small pores in equilibrium with a bulk phase at ambient pressure, differ greatly in magnitude and in their response to changes in the system and state variables.