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 surface excess Helmholtz energy, $G^{\sigma }$ is the surface excess Gibbs energy, $A^{\text{S}}$ 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 chemical potentials 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 Gibbs energy functions by the equations $$G^{\sigma }=\sum _{\begin{array}{c}i\end{array}}{n}_i^{\sigma }{\mu }_i^{\sigma }$$ $$G^{\text{S}}=\sum _{\begin{array}{c}i\end{array}}{n}_i^{\text{S}}{\mu }_i^{\text{S}}$$