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Article

Adsorption of an Ideal Gas on a Small Spherical Adsorbent

1
Department of Materials Science and Engineering, Faculty of Natural Sciences, Norwegian University of Science and Technology, NTNU, NO-7491 Trondheim, Norway
2
Porelab, Department of Chemistry, Norwegian University of Science and Technology, NTNU, NO-7491 Trondheim, Norway
*
Author to whom correspondence should be addressed.
Academic Editor: Abdelhamid Elaissari
Nanomaterials 2021, 11(2), 431; https://doi.org/10.3390/nano11020431
Received: 21 January 2021 / Revised: 4 February 2021 / Accepted: 6 February 2021 / Published: 9 February 2021
(This article belongs to the Special Issue Nanoscale Thermodynamics)
The ideal gas model is an important and useful model in classical thermodynamics. This remains so for small systems. Molecules in a gas can be adsorbed on the surface of a sphere. Both the free gas molecules and the adsorbed molecules may be modeled as ideal for low densities. The adsorption energy, Us, plays an important role in the analysis. For small adsorbents this energy depends on the curvature of the adsorbent. We model the adsorbent as a sphere with surface area Ω=4πR2, where R is the radius of the sphere. We calculate the partition function for a grand canonical ensemble of two-dimensional adsorbed phases. When connected with the nanothermodynamic framework this gives us the relevant thermodynamic variables for the adsorbed phase controlled by the temperature T, surface area Ω, and chemical potential μ. The dependence of intensive variables on size may then be systematically investigated starting from the simplest model, namely the ideal adsorbed phase. This dependence is a characteristic feature of small systems which is naturally expressed by the subdivision potential of nanothermodynamics. For surface problems, the nanothermodynamic approach is different, but equivalent to Gibbs’ surface thermodynamics. It is however a general approach to the thermodynamics of small systems, and may therefore be applied to systems that do not have well defined surfaces. It is therefore desirable and useful to improve our basic understanding of nanothermodynamics. View Full-Text
Keywords: adsorption; nanothermodynamics; small-system; size-dependent; thermodynamics; statistical mechanics; ideal gas; nanoparticles adsorption; nanothermodynamics; small-system; size-dependent; thermodynamics; statistical mechanics; ideal gas; nanoparticles
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MDPI and ACS Style

Strøm, B.A.; Bedeaux, D.; Schnell, S.K. Adsorption of an Ideal Gas on a Small Spherical Adsorbent. Nanomaterials 2021, 11, 431. https://doi.org/10.3390/nano11020431

AMA Style

Strøm BA, Bedeaux D, Schnell SK. Adsorption of an Ideal Gas on a Small Spherical Adsorbent. Nanomaterials. 2021; 11(2):431. https://doi.org/10.3390/nano11020431

Chicago/Turabian Style

Strøm, Bjørn A., Dick Bedeaux, and Sondre K. Schnell. 2021. "Adsorption of an Ideal Gas on a Small Spherical Adsorbent" Nanomaterials 11, no. 2: 431. https://doi.org/10.3390/nano11020431

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