Title: surface chemical potential
Long Title: IUPAC Gold Book - surface chemical potential
DOI: 10.1351/goldbook.S06161
Status: current

Definition
Defined by: \[\mu _{i}^{\sigma }=(\frac{\partial A^{\sigma }}{\partial n_{i}^{\sigma }})_{T,A_{\rm{S}},n_{j}^{\sigma }}=(\frac{\partial G^{\sigma }}{\partial n_{i}^{\sigma }})_{T,p,\gamma ,n_{j}^{\sigma }}\] \[\mu _{i}^{\rm{S}}=(\frac{\partial A^{\rm{S}}}{\partial n_{i}^{\rm{S}}})_{T,V^{\rm{S}},A_{\rm{S}},n_{j}^{\rm{S}}}=(\frac{\partial G^{\rm{S}}}{\partial n_{i}^{\rm{S}}})_{T,p,\gamma ,n_{j}^{\rm{S}}}\] where \(A^{\sigma }\) is the surface excess Helmholtz energy, \(G^{\sigma }\) is the surface excess Gibbs energy, \(A^{\rm{S}}\) is the interfacial Helmholtz energy, \(G^{\rm{S}}\) is the interfacial Gibbs energy, and \(A_{\rm{S}}\) is the surface area. The quantities thus defined can be shown to be identical, and the conditions of equilibrium of component \(i\) in the system to be \[\mu _{i}^{\alpha }=\mu _{i}^{\sigma }=\mu _{i}^{\rm{S}}=\mu _{i}^{\beta }\] where \(\mu _{i}^{\alpha }\) and \(\mu _{i}^{\beta }\) are the chemical potentials of \(i\) in the bulk phases $\ce{\upalpha\!}$ and $\ce{\upbeta\!}$. (\(\mu _{i}^{\alpha }\) or \(\mu _{i}^{\beta }\) have to be omitted from this equlibrium condition if component \(i\) is not present in the respective bulk phase.) The surface chemical potentials are related to the Gibbs energy functions by the equations \[G^{\sigma }=\sum _{\begin{array}{c}
i
\end{array}}n_{i}^{\sigma }\ \mu _{i}^{\sigma }\] \[G^{\rm{S}}=\sum _{\begin{array}{c}
i
\end{array}}n_{i}^{\rm{S}}\ \mu _{i}^{\rm{S}}\]

Related Terms
- Gibbs energy: https://goldbook.iupac.org//terms/view/G02629
- chemical potentials: https://goldbook.iupac.org//terms/view/C01032
- surface excess Gibbs energy: https://goldbook.iupac.org//terms/view/S06176
- surface excess Helmholtz energy: https://goldbook.iupac.org//terms/view/S06177

Source
- PAC, 1972, 31, 577. 'Manual of Symbols and Terminology for Physicochemical Quantities and Units, Appendix II: Definitions, Terminology and Symbols in Colloid and Surface Chemistry' on page 602 (https://doi.org/10.1351/pac197231040577)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/S06161/html
- json: https://goldbook.iupac.org/terms/view/S06161/json
- xml: https://goldbook.iupac.org/terms/view/S06161/xml

Citation: Citation: 'surface chemical potential' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.S06161
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Accessed: 2026-07-24T19:09:30+00:00