Isotherm predicted from Gouy-Chapman theory

The deviations from the Szyszkowski-Langmuir adsorption theory have led to the proposal of a munber of models for the equihbrium adsorption of surfactants at the gas-Uquid interface. The aim of this paper is to critically analyze the theories and assess their applicabihty to the adsorption of both ionic and nonionic surfactants at the gas-hquid interface. The thermodynamic approach of Butler [14] and the Lucassen-Reynders dividing surface [15] will be used to describe the adsorption layer state and adsorption isotherm as a function of partial molecular area for adsorbed nonionic surfactants. The traditional approach with the Gibbs dividing surface and Gibbs adsorption isotherm, and the Gouy-Chapman electrical double layer electrostatics will be used to describe the adsorption of ionic surfactants and ionic-nonionic surfactant mixtures. The fimdamental modeling of the adsorption processes and the molecular interactions in the adsorption layers will be developed to predict the parameters of the proposed models and improve the adsorption models for ionic surfactants. Finally, experimental data for surface tension will be used to validate the proposed adsorption models. 

Figure 5. Isotherm predicted from the Gouy-Chapman theory (with low-potential approximation) for Na+-Ca2+ exchange on a charged solid.

While the linear adsorption isotherms of Figure 4 are illustrative only, they are not inconsistent with reality. The simplest theory of the electrical double layer, the Gouy-Chapman approximation, predicts that if the pH is not far from the isoelectric point, the charge represented by counter ions in the diffuse double layer is related to the surface potential as follows (4, 52, 86) ... 

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