Molecular Modeling of Inhomogeneous Fluids Using Computational Cluster-Integral Methods

The structure and thermodynamic properties of inhomogeneous fluids are fundamental importance to various industrial processes, such as membrane separation, batteries and lubricant systems. Due to the need for molecular understanding of the interfacial or confined systems, many theoretical approaches have been used to obtain equations in order to characterize the systems.;Virial treatments for fluids, in which properties are given as a series expansion in density, have a long history. They are gaining new attention resulting from the development of Mayer sampling methods for computation of the series coefficients. Most of the focus of these treatments has been on the bulk, homogenous phase, but there also have been formulations applicable to inhomogeneous phases, such as found in fluids under confinement. The effectiveness of virial methods for these systems has received little attention. In this work a virial approach work is extended to determine density distribution and other thermodynamic properties for the systems. We apply Mayer Sampling Monte Carlo method to calculate the coefficients of a series expansion of inhomogeneous systems. It is shown that our approach is entirely satisfactory and that application to system of various shapes is possible. We evaluate and examine the cluster integrals that contribute up to seventh order for the hard sphere system near a hard wall. We use the results to calculate the thermodynamic properties of inhomogeneous fluids and compare with the results of grand canonical transition-matrix Monte Carlo simulations. The results from the present work can demonstrate how fluid concentration, particle size and shape, particle-particle and particle- wall interactions, as well as the geometric character of the pore space contribute to the structural and thermodynamic properties of the fluid. The cluster integrals for an inhomogeneous fluid system to be calculated in this work can be converted to the virial expansion of the surface excess fluid adsorbed onto the pore walls, and also to the corresponding expansions of the component of the stress tensor and of the surface tension.;Furthermore we extend a cluster theory to fluid confined by surround surfaces. Despite the need for molecular understanding of confined systems, the statistical mechanical studies of confined fluids have been only developed for even simple cases. The most important reason for this situation is originated from the effects of the confinement and the effects of their interplay with other molecular interactions. We focus on the classical statistical derivation of thermodynamic properties of a confined system from its pair potential through the calculation of virial-type coefficients and also develop a useful method for modeling systems. In this work we extend the virial treatment to confined systems while retaining its suitability for general external fields and answer the question how one can calculate quantities of interest from the virial expansion. We also present critical properties; temperature, density of confined square-well fluid in various slit widths estimated using the truncated virial series and compared with literature values. In this work we chose chemical potential to determine the location of the critical point of the pore fluid. In this way the same equation can describe the phase behavior from the homogeneous state to inhomogeneous state. Also it is clear to define chemical potential for both states not like pressure which is not well-defined formula for the inhomogeneous fluid. We also present the effects of slit width and extra diagrams on the inhomogeneous virial coefficients and thorough them, the thermodynamics of confined system.;Finally we extend a virial expansion method to study selective adsorption. Multicomponent adsorption data over a wide range of state conditions are required to design the equipment for separating mixtures, and it is of considerable practical importance to have a reliable method for predicting mixed-gas adsorption isotherm. Reliable prediction of the properties of mixtures in the presence of adsorbents is a key factor for the design of adsorption processes. In this work, by formulating virial expansions for inhomogeneous fluids, we are able to predict mixture selectivity isotherms. We present virial expansion results for model methane-ethane mixtures in graphitic slit pores at near ambient temperatures. In addition, we perform grand-canonical transition matrix Monte Carlo simulation to make a self-consistent test of the ability of the virial approach.;In summary, virial expansion methods are used to understand the structure and thermodynamics properties of fluids near a surface and under confinement. The cluster-series treatment is a severely underutilized approach for understanding surface behavior and inhomogeneous systems in general. While most applications have been to hard-sphere systems in simple geometries, the advent of the Mayer-sampling methods demonstrated here opens the door to application to more realistic molecular models, and more complex surfaces and adsorption media. (Abstract shortened by UMI.).