A The Gibbs Adsorption Equation

The Gibbs adsorption equation, in its most general form (Gibbs, 1928), 

The surface excess concentration is defined here as the excess, per unit area of interface, of the amount of any component actually present in the system over that present in a reference system of the same volume in which the bulk concentrations in the two phases remain uniform up to a hypothetical (Gibbs) dividing surface. 

For solutions consisting of the solvent and only one solute, dy = —RT(Todln ao + Ty/ln a ), where subscripts 0 and 1 refer to the solvent and the solute, respectively. For dilute solutions (10-2 M or less) containing only one nondissociating surface-active solute, the activity of the solvent and the activity coefficient of the solute can both be considered to be constant and the mole fraction of the solute xi may be replaced by its molar concentration C. Thus 

Since FA- = TB- Ii to maintain electroneutrality and aA+ aB- = C x/ without significant error, 

For mixtures of two different surfactants, the value of n for the mixture, mix = n X + 112X2, where nx, and n2 are the n values for individual surfactants 1 and 2 of the mixture and X and X2 their respective mole fractions at the interface (equation 2.46). 

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