The statistical mechanics of argon

Abstract

Liquid and dense gaseous argon has been simulated (using the Barker-Bobetic potential) by means of molecular dynamics techniques similar to those developed by Rahman. The equilibrium properties have been calculated using 108 particles interacting through a truncated potential, together with perturbation theory to correct for the finite size of the systems well as quantum and three-body effects. Good agreement with the experimental values of the pressure and internal energy has been obtained using these techniques. In addition excellent agreement with values calculated by Barker using Monte Carlo methods has resulted from this work, showing that there are no systematic differences between the two methods. Partly as a result of this work the Barker-Bobetic potential has been modified to give even better agreement with experimental liquid pressures. The transport properties of argon have also been investigated using the results of this work. The diffusion coefficient has been calculated and the results are in reasonable agreement with experimental values and with the Lennard-Jones results of Levesque and Verlet. It has not proved possible to correct these results so as to represent argon exactly since the perturbation theories developed to date are not suitable. In addition the coefficients of shear and bulk viscosity and thermal conductivity have been studied using the Kubo approach to transport. It has not proved possible to obtain accurate results from this work, or to check the validity of this theory of transport. Research related to this thesis has shown that the assumptions underlying the friction coefficient approach to transport are not valid for argon. The properties of solid argon at temperatures between 40 and 80°K have been calculated using Monte Carlo methods and the new Barker potential just mentioned. The calculated pressures and internal energies are in excellent agreement with experimental values. The elastic constants are found to be closer to the Lennard-Jones results than to the experimental values, but the agreement has been quite pleasing here as well. Related properties of solid argon have also been studied in this work. The radial distribution function for the Barker-Bobetic potential has been calculated and tabulated values have been included in an appendix for use by other workers. Some investigations of the time dependent distributions have also been undertaken and the results discussed. Good agreement has been obtained between the values of the energy and pressure calculated directly and using the radial distribution function. Both solid and liquid argon have been successfully simulated and the results have established that the present Barker potential combined with the Axilrod-Teller triple-dipole interaction is an excellent model of interactions in argon in two areas of great theoretical interest.