Article
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On How to Measure the Subdivision Potential in Nanothermodynamics
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)
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.v1 Bedeaux, D.; Kjelstrup, S. On How to Measure the Subdivision Potential in Nanothermodynamics. Preprints 2024, 2024020742. https://doi.org/10.20944/preprints202402.0742.v1
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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