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Surface chemical potentials

Surface chemica1 potentials are defined by


The quantities thus defined can be shown to be identical, and the conditions of equilibrium of component $ i$ in the system to be

$\displaystyle {\mu}^{\alpha}_i = {\mu}^{\sigma}_i = {\mu}^s_i = {\mu}^{\beta}_i, $

where $ {\mu}^{\alpha}_i$ and $ {\mu}^{\beta}_i$ are the chemical potentials of $ i$ in the bulk phases $ {\alpha}$ and $ {\beta}$. ( $ {\mu}^{\alpha}_i$ or $ {\mu}^{\beta}_i$ has to be omitted from this equilibrium 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

$\displaystyle G^{\sigma}$ $\displaystyle =$ $\displaystyle {\sum}_in^{\sigma}_i{\mu}^{\sigma}_i,$  
$\displaystyle G^s$ $\displaystyle =$ $\displaystyle {\sum}_in^s_i{\mu}^s_i.$