We review the current state of knowledge of phase separation and phase equilibria in porous materials. Our emphasis is on fundamental studies of simple fluids (composed of small, neutral molecules) and well-characterized materials. While theoretical and molecular simulation studies are stressed, we also survey experimental investigations that are fundamental in nature. Following a brief survey of the most useful theoretical and simulation methods, we describe the nature of gas-liquid (capillary condensation), layering, liquid-liquid and freezing/melting transitions. In each case studies for simple pore geometries, and also more complex ones where available, are discussed. While a reasonably good understanding is available for phase equilibria of pure adsorbates in simple pore geometries, there is a need to extend the models to more complex pore geometries that include effects of chemical and geometrical heterogeneity and connectivity. In addition, with the exception of liquid-liquid equilibria, little work has been done so far on phase separation for mixtures in porous media.

We present a review of experimental, theoretical, and molecular simulation studies of confinement effects on freezing and melting. We consider both simple and more complex adsorbates that are confined in various environments (slit or cylindrical pores and also disordered porous materials). The most commonly used molecular simulation, theoretical and experimental methods are first presented. We also provide a brief description of the most widely used porous materials. The current state of knowledge on the effects of confinement on structure and freezing temperature, and the appearance of new surface-driven and confinement-driven phases are then discussed. We also address how confinement affects the glass transition.

Effect of the fluid-wall interaction on freezing of confined fluids: Toward the development of a global phase diagramUsing molecular simulations and free energy calculations based on Landau theory, we show that freezing/melting behavior of fluids of small molecules in pores of simple geometry can be understood in terms of two main parameters: the pore width H* ͑expressed as a multiple of the diameter of the fluid molecule͒ and a parameter ␣ that measures the ratio of the fluid-wall to the fluid-fluid attractive interaction. The value of the ␣ parameter determines the qualitative nature of the freezing behavior, for example, the direction of change in the freezing temperature and the presence or absence of new phases. For slit-shaped pores, larger ␣ values lead to an increase in the freezing temperature of the confined fluid, and to the presence of a hexatic phase. For pores that accommodate three or more layers of adsorbate molecules several kinds of contact layer phase ͑inhomogeneous phases in which the contact layer has a different structure than the inner layers͒ are observed. Smaller ␣ values lead to a decrease in the freezing temperature. The parameter H* determines the magnitude of shift in the freezing temperature, and can also affect the presence of some of the new phases. Results are presented as plots of transition temperature vs ␣ for a particular pore width. Experimental results are also presented for a variety of adsorbates in activated carbon fibers ͑ACF͒ covering a wide range of ␣ values; the ACF have slit-shaped pores with average pore width 1.2 nm. The experimental and simulation results show qualitative agreement.