THEORIES OF INHOMOGENEOUS MEDIA: FAR-INFRARED ABSORPTION IN COMPOSITES AND A DENSITY FUNCTIONAL THEORY OF FREEZING

This thesis first addresses the long-standing problem of the orders of magnitude "enhancement" of measured Far-Infrared (FIR) absorption coefficients in small-metal-particle/insulator composites compared with theoretical predictions. Three new models for the FIR absorption, all assuming the metal particles to be clustered into large, compact clusters, are presented. Their predictions are in agreement with experiment. The models span the full range of internal cluster structures by assuming (i) the clusters to be highly metallic, leading to large absorption from the decay of induced eddy currents, (ii) the clusters to range from insulating to metallic, with large FIR absorption due to the low frequency electric dipole resonances in the tenuous metallic structures which exist in those clusters near the insulating to metallic (percolation) transition region, or (iii) the metal particles in a cluster to be coupled to each other by tunnel junctions which results in large electric dipole absorption.; The thesis next addresses the density functional theory of inhomogeneous liquids, and its application to the freezing transition of a homogeneous liquid to a crystalline solid. An approximation for the Helmholtz free energy is presented which depends on a weighted average of the physical density yet retains the nonlocality of the exact functional. The weighting function is so chosen that in the limit of weak density variations the exact functional is regained. This weighted density approximation (WDA) is actually a summation of all orders of a perturbation expansion in density of the free energy about that of a homogeneous liquid in which some terms are retained exactly. The WDA is then used to study the crystalline solid, an application in which the non-local nature of the WDA is crucial. Results for the hard sphere (hs) FCC solid equation of state and the hs liquid-FCC solid coexistence conditions are in good agreement with simulation data. Thermodynamic perturbation theory about a hs reference system is used to extend the WDA to other systems and the calculated phase diagram of the Lennard-Jones system agrees well with simulation studies.