Research On Analytic Equation Of State Of Simple Fluids And Solids Over Wide Range Of Pressure And Temperature

Researches on analytic equation of state of simple fluids and solids have been made in this dissertation. Several analytic equations of state of simple fluids and solids are presented with further intention to study simple fluids and solids, such as N₂, H₂, He, He-H₂ binary fluid mixture and protein-salt solution based on Ross varational perturbation theory and analytic radial distribution function by use of various potential model. An analytic equation of state of fcc argon has been derived based on the free volume theory (FVT) and the analytic mean field approach (AMFP) theory with exp-6 potential.In charpter 1, research background and significance of the analytic equation of state are reviewed. Then main concept and theory on the subject are briefly introduced such as interaction between molecules, the radial distribution function (RDF) and perturbation theory. Ross theory, the free volume theory and the analytic mean field approach (AMFP) theory as the theoretic foundation of this dissertation has been introduced.In charpter 2, analytic expressions for the equation of state and thermo-physical quantities of exponential-6 (exp-6) fluid are derived based on the Ross variational perturbation theory. The developed formalism is applied to the N₂ fluid. Comparisons of the theoretical results and simulations for the exp-6 potential fluid are presented. The agreement of numerical results of pressure and internal energy with Monte Carlo (MC) simulations show that the theoretical model is impressive. The expression has been applied to fluid nitrogen and the fitting to experimental data of fluid N₂ is surprisedly good. The predictions of pressure in the range of high temperature and high density are satisfactory. It has also been found that the analytic equation of state for exp-6 potential fluid based on RDF proposed by Sun et al is better in a wide range of pressure and temperature than that derived from PY expression. Comparisons show that a potential dependent on temperature and density (or volume) may be necessary to understand interaction between N₂ molecules. The equation of state can also be extended to application of important real gases such as H₂,O₂, CH₄, CO and CO₂.In charpter 3, an analytical expression for the equation of state (EOS) of Exp-6 fluid mixture is derived based on the Ross variational perturbation theory with the quantum effect taken into account. The derived formalism is applied to the He-H₂ mixture in better agreement with Monte Carlo results than the analytical equation of state devoloped by Ali. et al. The calculated results of excess Gibbs free energy and entropy are partly different from those of Ali's. Additionally, a simpler law of fluid mixture for effective mass has been tested with almost the same accuracy as the one from literature. The new EOS is believed to be extended to other binary simple fluid mixtures.In charpter 4, analytic expressions for the equation of state and thermodynamic properties have been derived for a generalized Lennard-Jones fluid and generalized Morse fluids based on the Ross variational perturbation theory and the analytic Percus-Yevick (PY) expression for the RDF of hard spheres. It is shown that the variational procedure is absolutely convergent and the calculations are convenient and fast. The numerical calculations have been made within wide temperature and density ranges. The results show that the precision is equivalent to the non-analytic mWCA and complete analytic MSA theories as compared with computer simulation results. It is concluded that the analytic theory can be applied to research practical fluids within wide temperature and density ranges.In charpter 5, a simple analytic equation of state for the three-Yukawa potential is derived based on the Ross varational perturbation theory. The model is used to describe the non-idealities of the aqueous protein-salt solutions. The results of correlation and prediction of osmotic pressure are better than those from previous model developed by others, and a soft-core Yukawa repulsion is introduced to replace the hard-core in view of the softness of the protein molecules. Analyses have been made with conclusion that the the three-Yukawa potential model is reasonable and the soft-core modification is important especially for the protein solutions with heavier molecular weight.In charpter 6, the AMFP is applied to the exp-6 potential model solid. The analytic expressions for the Helmholtz free energy, internal energy and equation of state have been derived and applied to fcc argon solid. The results are satisfactory except in the case of the volume expensivity. Two sets of potential parameters have been obtained by fitting pressure and bulk modulus, respectively. The analyses to results predicted by two set of parameters suggest that the present model is incomplete over a wide temperature range and density-dependent or a temperature-dependent potential model may be desirable.In charpter 7, the research of this dissertation is summarized and the next work is predicted.