Exact equilibrium properties of square-well and square-shoulder disks in single-file confinement

Abstract

This study investigates the (longitudinal) thermodynamic and structural characteristics of single-file confined square-well and square-shoulder disks by employing a mapping technique that transforms the original system into a one-dimensional polydisperse mixture of nonadditive rods. Leveraging standard statistical-mechanical techniques, exact results are derived for key properties, including the equation of state, internal energy, radial distribution function, and structure factor. The asymptotic behavior of the radial distribution function is explored, revealing structural changes in the spatial correlations. Additionally, exact analytical expressions for the second virial coefficient are presented. The theoretical results for the thermodynamic and structural properties are validated by our Monte Carlo simulations.

arXiv comment17 pages, 16 figures; v2: new Appendix A added, inclusion of the transverse correlation degree, plus other changes

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• Exploring anisotropic pressure and spatial correlations in strongly confined hard-disk fluids. Exact results
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• 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