The Radial Distribution Function and the Thermodynamic Properties of Monatomic Liquids. A Statistical Mechanical Theory of the Coefficient of Thermal Conductivity of Monatomic Liquids

Abstract

A fluid consisting of molecules interacting with the Lennard-Jones intermolecular potential but with rigid cores is treated by the Kirkwood and the Born-Green statistical­ mechanical formulations. The integral equation for the radial distribution function of this fluid is solved numeri­cally by a series expansion of all temperature dependent quantities in the reciprocal of the temperature. The first three terms of this series for the radial distribution func­tion have been evaluated over a wide range of densities for the Born-Green integral equation. The distribution functions so obtained have been used to calculate the equation of state, the excess internal energy, and the excess entropy of this fluid. The two phase region of this equation of state is determined. For reason­able values of the parameters in the potential, these calcu­lated quantities agree within 10% to 20% with experimental data available for argon. At one density a comparison between the Kirkwood and the Born-Green theories shows that the two formulations agree closely. A molecular theory of the coefficient of heat conduc­tivity of monatomic liquids is developed on the basis of the general theory of transport processes presented by Kirkwood in 1946. The coefficient is expressed in terms of the inter­molecular force and the equilibrium radial distribution func­tion. Substituting for these, respectively, the Lennard-Jones potential and a reasonable analytic approximation to the experimental radial distribution function, the product of the thermal conductivity and the friction constant has been eval­uated, for liquid argon at 89°K. With a preliminary estimate of the friction constant, the value of the coefficient of thermal conductivity is then given.