| The first six chapters of this work present new analytical models taking into account nonrandom behavior for mixtures of monomers. The models allow one to better understand how molecular geometry and system dimensionality affect local ordering and phase transitions in fluids. All results presented are based on a lattice theory originally proposed by Ono and Kondo and recently generalized by our group. Note that Ono-Kondo theory is a lattice version of density functional theory, i.e., it has a rigorous basis in statistical mechanics and therefore takes into account system characteristics on a microscopic level. However, it is simple and flexible enough to be applicable to a large number of different problems of practical importance.; In Chapter 7, the method of projections onto convex sets (POCS) is used to calculate adsorption-energy distributions of heterogeneous surfaces. The POCS method, originally developed in the 1960s, has been successfully applied for many years to estimation problems, mainly in the fields of image processing, signal recovery, and optics. It allows one to incorporate into an iteration scheme available information about the experimental data and the measurement error as well as a priori constraints (such as nonnegativity) based on physical reasoning. To our best knowledge, this work provides the first application of the POCS method to inverse problems in adsorption. |
