Statistical mechanics model for the transit free energy of monatomic liquids

TL;DR

This paper develops a statistical mechanics model for the transit free energy in monatomic liquids, calibrated with experimental data, improving the accuracy of thermodynamic property predictions within Vibration-Transit theory.

Contribution

The paper introduces a two-parameter statistical mechanics model for transit entropy, calibrated to experimental data, enhancing the predictive power of V-T theory for monatomic liquids.

Findings

Model accurately fits experimental entropy data across temperatures.

Model agrees with molecular dynamics for internal energy of Na.

Enables ab initio evaluation of thermodynamic properties.

Abstract

In applying Vibration-Transit (V-T) theory of liquid dynamics to the thermodynamic properties of monatomic liquids, the point has been reached where an improved model is needed for the small (approx. 10%) transit contribution. Toward this goal, an analysis of the available high-temperature experimental entropy data for elemental liquids was recently completed [D. C. Wallace, E. D. Chisolm, and N. Bock, Phys. Rev. B 79, 051201 (2009)]. This analysis yields a common curve of transit entropy vs. T/\theta_{tr}, where T is temperature and \theta_{tr} is a scaling temperature for each element. In the present paper, a statistical mechanics model is constructed for the transit partition function, and is calibrated to the experimental transit entropy curve. The model has two scalar parameters, and captures the temperature scaling of experiment. The calibrated model fits the experimental liquid entropy to high accuracy at all temperatures. With no additional parameters, the model also agrees with both experiment and molecular dynamics for the internal energy vs. T for Na. With the calibrated transit model, V-T theory provides equations subject to ab initio evaluation for thermodynamic properties of monatomic liquids. This will allow the range of applicability of the theory, and its overall accuracy, to be determined. More generally, the hypothesis of V-T theory, which divides the many-atom potential energy valleys into random and symmetric classes, can also be tested for its application beyond monatomic systems.