Adsorption and surface tension of ionic surfactants at the air–water interface: review and evaluation of equilibrium models

A series of old and new equilibrium tension models are reviewed and evaluated for single premicellar ionic surfactants at the air–water interface with or without added salt with a common ion. Several experimental methods used to measure surface tensions, adsorbed densities, and surface potentials are also reviewed. The models are based on the Gibbs adsorption isotherm, and classified as ‘pseudo-nonionic’ when the surface charge is ignored or ‘ionic’ when the surface charge and its electric double layer are accounted for. The former models fit and represent well tension and adsorption density data but are not predictive, primarily because the underlying adsorption isotherms, the Langmuir or the Frumkin, are independent of salinity. Ionic models are to an extent predictive, based on the Davies or a combined Frumkin–Davies isotherm, and provide estimates of the adsorbed density and surface potential. Counterion binding is incorporated in the new models using a fractional binding parameter analogous to that used in micellar models. Certain advanced binding models proposed by Kralchevsky et al., Kalinin and Radke, and Warszyski et al. are also examined. The models are tested with tension data at 25°C for sodium dodecylsulfate (SDS) in the presence of several sodium chloride (NaCl) concentrations. Both the model predictions and the fitted parameter values are evaluated with respect to physical plausibility and overall goodness of fit to the available data. Although the pseudo-nonionic models can fit the data well, the fitted parameters depend strongly on salinity. The more advanced ionic models can fit the data nearly as well as the pseudo-nonionic models, and provide a plausible description of the surface electrostatics. More detailed electrostatic models, and reliable data on both adsorbed densities and surface potentials at the surfactant–water interface are needed for developing more definitive and less empirical models, and for improving further our fundamental understanding of the adsorption and tension behavior of ionic surfactants.