## 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]