Equation of state and integral equation theory for hard sphere and hard sphere chain fluids.

摘要

The development of an accurate equation of state based on molecular thermodynamics for simple and complex fluids is important to chemical process design. In this dissertation we study the thermodynamic and intermolecular structural properties of hard sphere and hard-sphere chain fluids. These are theoretically challenging problems, the solution of which are useful for perturbation theory of more realistic potential models.; We obtain a real expression for the radial distribution function of the hard sphere fluid up to the third shell by transforming Baxter's integral equation into a recursive differential equation. With this expression we develop a completely analytic perturbation equation of state for the square-well fluid to second order. This equation of state is used to predict the critical properties and vapor-liquid equilibria of square-well fluids of variable well width, and also to predict the thermodynamic behavior of real fluids, including neon, argon, and methane.; We next develop a modified version of the thermodynamic perturbation theory, referred to as TPT-dimer theory, for the hard-sphere chain fluid by incorporating intermolecular structural information for the diatomic fluid. To test this theory, we performed Monte Carlo simulations for a bulk hard-sphere chain fluid, and obtained the compressibility factor using Nezbeda's pressure equation. When compared with the simulation results obtained in this research, the TPT-dimer equations of state are found to be accurate both at low and high densities.; The correlation functions of homonuclear hard-sphere chain fluids are studied using the Wertheim integral equation theory for associating fluids and the Monte Carlo simulation method. In the Wertheim theory such a chain molecule is described by associating hard spheres with two independent attraction sites. The OZ-like equation for this system is analytically solved using the polymer-PY closure and the single bonding approximation, and we obtain accurate predictions for both the inter- and overall correlation functions for chains up to 16-mers. The TPT-dimer and Wertheim integral equation theories are generalized to mixtures of homonuclear hard-sphere chain fluids. From comparison with the computer simulation results for several mixtures, those theories are found to be very accurate tools to estimate the pressure and correlation functions of hard-sphere chain mixtures.