Quantitative description of surface adsorption of surfactant in aqueous solution without the Gibbs equation.

A new equation related to the surface tension and concentration of solute in the surface region is derived and a three-step procedure is proposed to determine the molecular area of surfactants in aqueous solution at saturation of the air-liquid surface. Based on their surface tension data, the molecular areas of hexyl, octyl and decyl trimethylammonium bromide (HTABr, OTABr and DTABr) in aqueous solutions have been calculated and are in agreement with the computational results of density functional theory. Gibbs analysis has also been carried out for these surfactants. As the surface tension data are fitted with the Gibbs equation, it is found that there exist two line segments for both OTABr and DTABr, which lead to two molecular areas for each of them. This arbitrariness indicates that no unique molecular area could be obtained for OTABr and DTABr. As for HTABr, its molecular area obtained with Gibbs analysis is out of the range estimated with density functional theory. These results show the failure of the Gibbs equation.