surface chemical potential

Defined by:

$μ i σ = ( ∂ A σ ∂ n i σ ) T , A S , n j σ = ( ∂ G σ ∂ n i σ ) T , p , γ , n j σ$

$μ i S = ( ∂ A S ∂ n i S ) T , V S , A S , n j S = ( ∂ G S ∂ n i S ) T , p , γ , n j S$

where $A σ$ is the surface excess Helmholtz energy, $G σ$ is the surface excess Gibbs energy $A S$ is the interfacial Helmholtz energy, $G S$ is the interfacial Gibbs energy, and $A S$ 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

$μ i α = μ i σ = μ i S = μ i β$

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

$G σ = ∑ i n i σ μ i σ$

$G S = ∑ i n i S μ i S$

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