Equilibrium theory of liquids : an exponential perturbation theory



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In this work, the equilibrium theory of liquids, molecular correlation functions, radial distribution function, and perturbation theories are reviewed and discussed. A new exponential perturbation theory was developed to calculate the radial distribution function and the thermodynamic properties of liquids. A function called the potential difference function is defined as the difference of the molecular interaction potential and the potential of average force, and expanded into a Taylor series of the reciprocal of the temperature. By a topological reduction method, an integral equation is obtained for the function. The integral equation provides a generalization of the perturbation, and the various possibilities of approximation were analyzed. With certain assumptions, the integral equation can be solved by knowing the interaction potential and the hard sphere radial distribution function. A simple procedure was proposed to correlate the hard sphere diameter as a function of temperature and density. The theory was tested against the computer simulation results of Verlet for a Lennard-Jones (6,12) fluid. The agreement was excellent, the radial distribution function and the annodynamic properties are reproduced with high accuracy. The computation time is reasonable. Calculations were also extended to argon, and it was confirmed that the Lennard-Jones (6,12) fluid is a good approximation for argon. With suitable choice of potential parameters, the pressure-volume- temperature relations of liquid argon can be reproduced successfully. [...]