Teaching Nano-Thermodynamics: Gibbs Energy of Single-Component Nanoparticles

Jindřich Leitner,David Sedmidubský

doi:10.12691/wjce-5-6-4

Jindřich Leitner, David Sedmidubský

Open Access

https://doi.org/10.12691/wjce-5-6-4

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Abstract

Much attention has been paid to thermodynamic modeling of nanosystems. A common approach consists in addition of a surface/interface term to the Gibbs energy of bulk materials and application of general conditions of equilibrium. Some discrepancy still remains dealing with the expression for surface contribution to molar Gibbs energy and chemical potential of components. It is shown, that due to the nonextensive nature of the surface area, these contributions are different for molar and partial molar quantities. The consistent expressions for the molar Gibbs energy and chemical potential of a single-component spherical nanoparticle are put forward along with the simple derivation of the Kelvin and Gibbs-Thomson equations.

Highlights

Much attention has been paid to calculation of phase diagrams of nanoalloys [1,2,3,4,5] as well as calculation of equilibrium constants of chemical reactions in nanosystems [6,7,8,9]
A common approach consists in addition of a surface/interface term to the Gibbs energy of bulk materials and application of general conditions of equilibrium in a closed system at constant temperature and pressure, namely equality of chemical potentials of individual components in coexisting phases or zero Gibbs energy of reaction
Two quite similar but diverse terms are used for the surface contribution to Gibbs energy of spherical nanoparticles of radius r, namely

Summary

Introduction

Much attention has been paid to calculation of phase diagrams of nanoalloys [1,2,3,4,5] as well as calculation of equilibrium constants of chemical reactions in nanosystems [6,7,8,9]. Two quite similar but diverse terms are used for the surface contribution to Gibbs energy of spherical nanoparticles of radius r, namely. This apparent controversy has been a subject of discussion and has been referred in a number of recently published papers [10,11,12,13,14,15]. The purpose of our contribution is to correctly derive relations for the molar Gibbs energy and chemical potential of single-component spherical nanoparticle and explain this apparent discrepancy. The relation for chemical potential of nanoparticle is used for simple elucidation of the Kelvin and Gibbs-Thomson equations

Homogeneous Functions

Total Gibbs Energy of Nanoparticle

Molar Gibbs Energy of Nanoparticle

Applications for Gas-liquid and Solid-liquid Equilibria

Conclusion