Statistical mechanics approach to inhomogeneous van der Waals fluids

Abstract

A general methodology is proposed to formulate density functional approximation (DFA) for inhomogeneous van der Waals fluids. The present methodology needs as input only a hard sphere DFA, second order direct correlation function (DCF) and pressure of coexistence bulk fluid, and therefore can be applicable to both supercitical and subcritical temperature regions. As illustrating example, the present report combines a recently proposed hard sphere “Formally exact truncated non-uniform excess Helmholtz free energy density functional approximation” with the present methodology, and applies the resultant DFA to calculate density profile of the inhomogeneous Lennard-Jones (LJ) fluid in coexistence with a bulk LJ fluid being situated at “dangerous” regions, i.e. the coexistence bulk state is near the critical temperature or the gas-liquid coexistence line. The theoretical predictions are in very good agreement with the recent simulation results, it is concluded that the present DFA is a globally excellent one. A discussion is given why the present methodology can lead to so excellent DFA.

Keywords:

• Density functional approximation
• Potential of mean force
• Density functional perturbation approximation
• Integral equation theory

Acknowledgements

The author would like to thank the reviewers for helpful comments. This project is supported by the National Natural Science Foundation of China (20673150).