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

Jose M. G. Vilar; Leonor Saiz

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arXiv · 2608.25629

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

Jose M. G. Vilar·Leonor Saiz

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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.

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Jose M. G. Vilar, Leonor Saiz. 2026-08-26. Closed-form hard-sphere thermodynamics under nanoscale confinement: from equations of state to unmixing forces. https://arxiv.org/abs/2608.25629

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