A fundamental-measure density functional for mixtures of parallel hard cylinders

TL;DR

This paper develops a new fundamental measure density functional for mixtures of parallel hard cylinders, extending previous models and validating it through comparisons and calculations of phase behavior and correlation functions.

Contribution

It introduces a novel density functional for mixtures of parallel hard cylinders, generalizing existing models and employing a dimensional reduction approach.

Findings

Derived the density functional for mixtures of parallel hard cylinders.

Calculated fluid-fluid demixing spinodals for a binary mixture.

Determined direct correlation functions for the system.

Abstract

We obtain a fundamental measure density functional for mixtures of parallel hard cylinders. To this purpose we first generalize to multicomponent mixtures the fundamental measure functional proposed by Tarazona and Rosenfeld for a one-component hard disk fluid, through a method alternative to the cavity formalism of these authors. We show the equivalence of both methods when applied to two-dimensional fluids. The density functional so obtained reduces to the exact density functional for one-dimensional mixtures of hard rods when applied to one-dimensional profiles. In a second step we apply an idea put forward some time ago by two of us, based again on a dimensional reduction of the system, and derive a density functional for mixtures of parallel hard cylinders. We explore some features of this functional by determining the fluid-fluid demixing spinodals for a binary mixture of cylinders with the same volume, and by calculating the direct correlation functions.