Perturbation Theory Of Liquids Research Articles

The mean distance of closest approach in the theory of liquids

Abstract The mean distance of closest approach, for two colliding particles, is defined as an average over their relative kinetic energies. It is shown that the mean distance of closest approach thus defined, is formally identical to the effective hard-sphere diameter in the Barker and Henderson perturbation theory of liquids.

Equation of state of liquid rubidium

Abstract An ultrasonic dilatometer has been used to measure the volume of a specimen of liquid rubidium as a function of temperature (up to 200°C) and pressure (up to 1·38 kbar). The results may be fitted by a polynomial with nine terms. A curve of pressure versus temperature at constant volume may be deduced from the polynomial, and it is shown that this curve is in good agreement with predictions based upon the Weeks–Chandler–Andersen formulation of the perturbation theory of liquids, using an effective ion–ion potential for rubidium derived from Ashcroft's empty-core pseudopotential and Shaw's approximation for electron exchange and correlation.

A note on the forms for the integrals of the Percus–Yevick expression for g(R) for hard spheres

A new method is presented for evaluating the integrals of the Lennard-Jones potential and the Percus–Yevick (PY) radial distribution function which occur in the Barker–Henderson perturbation theory of liquids. It is shown that the PY g(R) has a simple dependence on R which allows it to be separated into a number of terms of which the integrals with the LJ potential may then be evaluated “computationally” exactly using simple formulae. Some results for pure substances are presented. The method is generally applicable to obtaining the integral of the product of any inverse Laplace transform, obtained by the method of residues, with an inverse power of the argument. The formulae presented here allow the evaluation of residues of up to 4th order poles.

Speed of Sound in Liquid Metals and Alloys

The speed of sound c in liquid metals and alloys is calculated using the perturbation theory of liquids and the pseudopotential theory of metals. An effective hard-sphere diameter, as defined by the Gibbs-Bogoliubov inequality, and its density dependence are determined for each metal from thermodynamic data. The structure independent contribution to c is calculated from the expression for cohesive energy given by Heine and Weaire [Solid State Phys. 24 (1970)]. The results, including the temperature and pressure dependence of c, are in quantitative agreement with experimental data.

Percus-Yevick theory and the Chandler-Weeks-Andersen reference fluid

Chandler, Weeks and Andersen have recently developed a successful perturbation theory of liquids. In their theory, the radial distribution function of the reference fluid is calculated from that of the hard-sphere fluid. In their published work, the Percus-Yevick theory is used to calculate the hard-sphere radial distribution function. In this paper, the Percus-Yevick theory is used to calculate directly the thermodynamic properties and radial distribution function of the reference fluid. If the Carnahan and Starling averaging procedure is used, the Percus-Yevick thermodynamic properties are excellent. However, the radial distribution function shows the same discrepancies as that of Chandler, Weeks and Andersen. Finally, recent calculations of Chandler, Weeks and Andersen, using the Monte Carlo estimates of the hardsphere radial distribution function are shown to give good results for the reference fluid distribution function. This indicates that the Percus-Yevick theory, rather than fundamental errors in...

On the relation between perturbation theory and distribution function theories of liquids

Perturbation theory of liquids and distribution function theories of liquids (as typified by the Percus–Yevick theory) are examined. It is shown that the energy equation, relating the pair distribution function to the internal energy, may be integrated to yield an expression for the free energy which is similar to that obtained from perturbation theory. The equation of state resulting from this approach, based on the energy equation, is shown to be better than that obtained from the pressure or compressibility equations. Finally, the similarity between perturbation theory and distribution function theories is exploited to provide simple improvements to either approach.