Closed-form hard-sphere thermodynamics under nanoscale confinement: from equations of state to unmixing forces
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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BibTeX
@misc{vilar2026closedform,
title = {{Closed-form hard-sphere thermodynamics under nanoscale confinement: from equations of state to unmixing forces}},
author = {Jose M. G. Vilar and Leonor Saiz},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.25629},
eprint = {2608.25629},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.25629},
}
RIS
TY - UNPB
TI - Closed-form hard-sphere thermodynamics under nanoscale confinement: from equations of state to unmixing forces
AU - Jose M. G. Vilar
AU - Leonor Saiz
PY - 2026
DA - 2026/08/26
PB - arXiv
DO - 10.48550/arxiv.2608.25629
UR - https://arxiv.org/abs/2608.25629
AB - 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.
ER -