Adsorption of an Ideal Gas on a Small Spherical Adsorbent.

Bjørn Strøm,Sondre Schnell,Dick Bedeaux

doi:10.3390/nano11020431

Bjørn Strøm, Sondre Schnell + Show 1 more

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https://doi.org/10.3390/nano11020431

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Abstract

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, , 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 , 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 , and chemical potential . 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.

Highlights

Received: 21 January 2021The objective of the paper is to demonstrate an organized and transparent thermodynamic framework for statistical model development for small systems
The main focus from the thermodynamic side is on the characteristic feature of small systems, namely the effect of size on intensive variables
We do this by first obtaining the characteristic thermodynamic function for the adsorbed phase from nanothermodynamics as introduced by Hill [1,2,3]

Summary

Introduction

Received: 21 January 2021The objective of the paper is to demonstrate an organized and transparent thermodynamic framework for statistical model development for small systems. The main focus from the thermodynamic side is on the characteristic feature of small systems, namely the effect of size on intensive variables. We do this by first obtaining the characteristic thermodynamic function for the adsorbed phase from nanothermodynamics as introduced by Hill [1,2,3]. The close relationship between the subdivision potential and the characteristic feature of small systems is a consequence of the generalization of thermodynamics to small systems, and the framework’s internal structure that follows.

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