= Gibbs adsorption equation
{c}
{title2=$\Gamma=-\frac1{k_BT}\frac{d\gamma}{d\ln a}$}
= Gibbs adsorption isotherm
{c}
{synonym}
For the simple one-solute interface convention, <surface excess> per molecule is related to the derivative of <surface tension> $\gamma$ with respect to the logarithm of solute activity $a$ by the displayed equation. For ideal dilute behavior one may use concentration ratios in place of activity ratios. In molar units, $\Gamma_{\rm mol}=-(RT)^{-1}d\gamma/d\ln a$. A local molecular area estimate is $\Sigma=-k_BT/(d\gamma/d\ln a)$. Ionic surfactants can require counterion and activity factors; the simple single-component expression must not be transferred to them without specifying those constraints.
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