Work

Closed-form hard-sphere thermodynamics under nanoscale confinement: from equations of state to unmixing forces

Year: 2026

Type: preprint

Abstract: Equations of state accurately describe hard-sphere thermodynamics but are generally considered to fail under nanoscale confinement. We show that this failure is geometric rather than thermodynamic: a closed-form, parameter-free mapping from apparent to effective packing fraction restores the accuracy of the Carnahan-Starling equation of state and, with it, the entire analytical thermodynamic framework, including free energies, wall pressures, chemical potentials, and the large-cavity surface response. Applied to overlapping anchored hard-sphere droplets, a geometry inherent to biomolecular force generation, it yields unmixing free energies and full distance-dependent force profiles in quantitative agreement with simulations from the dilute regime to above the bulk freezing transition.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.25629

Authors: Vilar, Jose M. G., Saiz, Leonor

Institutions: Ikerbasque, University of the Basque Country, Instituto Biofisika, University of California, Davis

Language: English

Topic: Phase Equilibria and Thermodynamics

Subfield: Biomedical Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7204483868

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