surface chemical potential

https://doi.org/10.1351/goldbook.S06161
Defined by: \[\mu _{i}^{\sigma }=(\frac{\partial A^{\sigma }}{\partial n_{i}^{\sigma }})_{T,A_{\text{S}},n_{j}^{\sigma }}=(\frac{\partial G^{\sigma }}{\partial n_{i}^{\sigma }})_{T,p,\gamma ,n_{j}^{\sigma }}\] \[\mu _{i}^{\text{S}}=(\frac{\partial A^{\text{S}}}{\partial n_{i}^{\text{S}}})_{T,V^{\text{S}},A_{\text{S}},n_{j}^{\text{S}}}=(\frac{\partial G^{\text{S}}}{\partial n_{i}^{\text{S}}})_{T,p,\gamma ,n_{j}^{\text{S}}}\] where \(A^{\sigma }\) is the @S06177@, \(G^{\sigma }\) is the @S06176@ \(A^{\text{S}}\) is the interfacial Helmholtz energy, \(G^{\text{S}}\) is the interfacial Gibbs energy, and \(A_{\text{S}}\) 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 \[\mu _{i}^{\alpha }=\mu _{i}^{\sigma }=\mu _{i}^{\text{S}}=\mu _{i}^{\beta }\] where \(\mu _{i}^{\alpha }\) and \(\mu _{i}^{\beta }\) are the @C01032@ of \(i\) in the bulk phases α and β. (\(\mu _{i}^{\alpha }\) 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 @G02629@ functions by the equations \[G^{\sigma }=\sum _{\begin{array}{c} i \end{array}}n_{i}^{\sigma }\ \mu _{i}^{\sigma }\] \[G^{\text{S}}=\sum _{\begin{array}{c} i \end{array}}n_{i}^{\text{S}}\ \mu _{i}^{\text{S}}\]
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 [Terms] [Paper]