Gibbs adsorption equation ($\Gamma =-\frac{1}{k_{B}T}\frac{d\gamma }{d\ln a}$)

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, ${\Gamma }_{\mathrm{mol}}=-(RT{)}^{-1}d\gamma /d\ln a$. A local molecular area estimate is $\Sigma =-k_{B}T/(d\gamma /d\ln a)$. Ionic surfactants can require counterion and activity factors; the simple single-component expression must not be transferred to them without specifying those constraints.