Fluids confined in wedges and by edges: From cluster integrals to thermodynamic properties referred to different regions

TL;DR

This paper explores how the geometry of confining vessels, like wedges and edges, influences the thermodynamic properties of fluids, providing analytic relations and examining low-density behaviors for different regions and geometries.

Contribution

It derives analytic relations for line thermodynamic properties in wedge and edge geometries as functions of dihedral angle, unifying the treatment of these regions and analyzing low-density behaviors.

Findings

Analytic relations between thermodynamic properties and dihedral angle.

Unified approach for edges and wedges.

Low-density behavior of confined hard sphere fluids.

Abstract

Recently, new insights in the relation between the geometry of the vessel that confines a fluid and its thermodynamic properties were traced through the study of cluster integrals for inhomogeneous fluids. In this work I analyze the thermodynamic properties of fluids confined in wedges or by edges, emphasizing on the question of the region to which these properties refer. In this context, the relations between the line-thermodynamic properties referred to different regions are derived as analytic functions of the dihedral angle $\alpha$ , for $0<\alpha<2\pi$ , which enables a unified approach to both edges and wedges. As a simple application of these results, I analyze the properties of the confined gas in the low-density regime. Finally, using recent analytic results for the second cluster integral of the confined hard sphere fluid, the low density behavior of the line thermodynamic properties is analytically studied up to order two in the density for $0<\alpha<2\pi$ and by adopting different reference regions.