The prediction of properties in complex materials is a problem of importance in many applications in chemical and materials engineering; by the term “complex material” we mean a heterogeneous substance, like a porous material containing a confined fluid. Such materials appear in many technological applications, including: (1) processes using supercritical fluids to dry porous aeorogels and thin films [1], (2) physical adsorption of trace components from gaseous effluents, (3) gas storage using microporous materials [2], and (4) chemical separation using inorganic membranes [3]. Inorganic membranes are often highly porous and randomly structured materials with large surface areas available for adsorption, a property that makes them useful in chemical separation and as catalyst supports. In addition to their heterogeneity, complex materials have another distinguishing characteristic that relates to the structure of the heterogeneity itself. Is it periodic, or is it dispersed throughout in some random fashion? These two situations are quite distinct and may, in each instance, show critical behavior for a confined fluid belonging to entirely different universality classes, an issue that to the present time is still unsettled in the literature. In this chapter, we investigate the critical properties of fluids confined in randomly structured host materials like that found in porous silicon. The main question we address is: how does confinement in a porous structure affect the critical point or phase behavior of a fluid mixture? Before investigating some of the more advanced ideas in this area, we look at the basic thermodynamics of interfaces, and the phenomenon of capillarity in a single idealized pore structure. This simple example provides the impetus for a more detailed study of confinement effects. Consider two phases in equilibrium separated by an interface. The total energy of the composite system is the sum of the energy of each phase plus the energy associated with the interface. In formulating the fundamental thermodynamic equation for energy in this system, we presume that the formation of an interface requires energy; therefore, the energy equation must reflect this fact.
Cylindrically and non-cylindrically symmetric expansion dynamics of tin microdroplets after ultrashort laser pulse impact
