Using Fundamental Measure Theory to Treat the Correlation Function of the Inhomogeneous Hard-Sphere Fluid

TL;DR

This paper uses Fundamental Measure Theory to accurately predict the contact value of the correlation function in inhomogeneous hard-sphere fluids, which is crucial for improving classical density functionals in fluid modeling.

Contribution

It introduces two averaged contact correlation functions derived from Fundamental Measure Theory and validates one against Monte Carlo simulations, demonstrating high accuracy.

Findings

Excellent agreement between one averaged correlation function and Monte Carlo data.

Derived formulas improve the prediction of correlation functions at contact.

Validation supports use in classical density functional theories.

Abstract

We investigate the value of the correlation function of an inhomogeneous hard-sphere fluid at contact. This quantity plays a critical role in Statistical Associating Fluid Theory (SAFT), which is the basis of a number of recently developed classical density functionals. We define two averaged values for the correlation function at contact, and derive formulas for each of them from the White Bear version of the Fundamental Measure Theory functional, using an assumption of thermodynamic consistency. We test these formulas, as well as two existing formulas against Monte Carlo simulations, and find excellent agreement between the Monte Carlo data and one of our averaged correlation functions.