## 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 Aσ is the surface excess Helmholtz energy, Gσ is the surface excess Gibbs energy, AS is the interfacial Helmholtz energy, GS is the interfacial Gibbs energy, and AS 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 µ i α and µ i β are the chemical potentials of i in the bulk phases α and β. (µ i α or µ i β 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 $G^{\sigma }=\sum _{\begin{array}{c} i \end{array}}n_{i}^{\sigma }\ \mu _{i}^{\sigma }$ $G^{\text{S}}=\sum _{\begin{array}{c} i \end{array}}n_{i}^{\text{S}}\ \mu _{i}^{\text{S}}$
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 (https://doi.org/10.1351/pac197231040577)