Adsorption of surfactants at air/solution interfaces: theoretical description of adsorption equilibrium based on a model of clustering of the surfactant molecules at the air/solution interface

On the basis of the scaled particle theory, a new theoretical approach is developed for adsorption of surfactants capable of forming two-dimensional aggregates at the air/solution interface. The adsorption layer is treated as a mixture of oblate aggregates of various dimensions, interacting via excluded area interactions. A five-parameter equation for the adsorption isotherm is developed, and then integrated to obtain the surface tension isotherm. Experimental surface tension data of a series of n-alkyldimethylphosphine oxides are used for comparison with the equation derived. The numerical best-fit analysis suggests the formation of small aggregates at the air/solution interface for these surfactants. The model parameters obtained while fitting best the model equation to the experimental data show a linear correlation with the alkyl chain length of the surfactant.