Equation of state of hard-disk fluids under single-file confinement

Abstract

The exact transfer-matrix solution for the longitudinal equilibrium properties of the single-file hard-disk fluid is used to study the limiting low- and high-pressure behaviors analytically as functions of the pore width. In the low-pressure regime, the exact third and fourth virial coefficients are obtained, which involve single and double integrals, respectively. Moreover, we show that the standard irreducible diagrams do not provide a complete account of the virial coefficients in confined geometries. The asymptotic equation of state in the high-pressure limit is seen to present a simple pole at the close-packing linear density, as in the hard-rod fluid, but, in contrast to the latter case, the residue is $2$. Since, for an arbitrary pressure, the exact transfer-matrix treatment requires the numerical solution of an eigenvalue integral equation, we propose here two simple approximations to the equation of state, with different complexity levels, and carry out an extensive assessment of their validity and practical convenience vs the exact solution and available computer simulations.

14 pages, 9 figures, 4 appendices; v3: minor changes

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• Canonical partition function and distance dependent correlation functions of a quasi-one-dimensional system of hard disks
• Monte Carlo simulation of Hard-, Square-Well, and Square-Shoulder Disks in narrow channels
• Ordering properties of anisotropic hard bodies in one-dimensional channels
• Competition between shape anisotropy and deformation in the ordering and close packing properties of quasi-one-dimensional hard superellipse fluids
• Exact anisotropic properties of hard spheres in narrow cylindrical confinement
• Orientational ordering and correlations in a quasi-one-dimensional hard-dumbbell fluid
• Algebraic to exponential decay of spatial correlations in one-dimensional and confined hard-core fluids: A Laplace-pole analysis
• Inhomogeneous Diffusion in Confined Colloidal Suspensions
• Hard disks confined within a narrow channel