On How to Measure the Subdivision Potential in Nanothermodynamics

Dick Bedeaux; Signe Kjelstrup

doi:10.20944/preprints202402.0742.v2

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preprints.org > physical sciences > thermodynamics > doi: 10.20944/preprints202402.0742.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

On How to Measure the Subdivision Potential in Nanothermodynamics

Dick Bedeaux

^* and

Signe Kjelstrup

Version 1 : Received: 12 February 2024 / Approved: 13 February 2024 / Online: 15 February 2024 (03:10:31 CET)
Version 2 : Received: 28 February 2024 / Approved: 4 March 2024 / Online: 6 March 2024 (04:15:04 CET)

How to cite: Bedeaux, D.; Kjelstrup, S. On How to Measure the Subdivision Potential in Nanothermodynamics. Preprints 2024, 2024020742. https://doi.org/10.20944/preprints202402.0742.v2 Bedeaux, D.; Kjelstrup, S. On How to Measure the Subdivision Potential in Nanothermodynamics. Preprints 2024, 2024020742. https://doi.org/10.20944/preprints202402.0742.v2

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MDPI and ACS Style

Bedeaux, D.; Kjelstrup, S. On How to Measure the Subdivision Potential in Nanothermodynamics. Preprints 2024, 2024020742. https://doi.org/10.20944/preprints202402.0742.v2

APA Style

Bedeaux, D., & Kjelstrup, S. (2024). On How to Measure the Subdivision Potential in Nanothermodynamics. Preprints. https://doi.org/10.20944/preprints202402.0742.v2

Chicago/Turabian Style

Bedeaux, D. and Signe Kjelstrup. 2024 "On How to Measure the Subdivision Potential in Nanothermodynamics" Preprints. https://doi.org/10.20944/preprints202402.0742.v2

Abstract

We discuss a central concept of nanothermdynamics; the subdivision potential. We explain how it can be measured or calculated for some typical ensembles, as this has been disputed in the literature. We proceed to discuss its meaning for particular systems, and predict scaling laws for three ensembles. The laws depend on the small system geometry in a predictable way for an ideal gas model with surface adsorption. We provide new equations which relate the subdivision potential to experimental investigations, and give expressions for grand canonical ensembles of spheres, cylinders, slit pores and fluids confined in porous media. The subdivision potential is not compatible with the popular Hadwiger theorem in geometry, and can therefore not be described by a Minkowski set of variables. It is equivalent to Gibbs descriptions when shape- and size variables are defined.

Keywords

Nanothermodynamics; Subdivision potential; Porous media; Shape dependence; Scaling laws

Subject

Physical Sciences, Thermodynamics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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