Surface Tension Isotherms as a Competition between Adsorption and Micellization

The air–water surface tension of aqueous surfactant solutions changes with surfactant concentration. Capturing its functional form (the “surface tension isotherm”) has been made challenging not only by the oversimplified conventional assumptions on the mechanisms of (i) surfactant adsorption at the interface and (ii) surfactant self-assembly in the bulk, but also by the lack of a clear theoretical guideline on how to combine (i) and (ii) to obtain an equation for the surface tension isotherm. These difficulties will be overcome by our recent theoretical breakthrough: the gradient of surface tension (with respect to the surfactant concentration) is determined by a competition between surface adsorption and bulk self-assembly of surfactants. The key is the separability of the two contributions, which is enabled by the surfactant concentration at interfacial saturation being below the critical micelle concentration (CMC). This leads to a novel, closed-form, explicit isotherm equation that can fit experimental surface tension data and reveal the underlying competition between (i) and (ii). Unlike previous models, our novel isotherm accounts for interfacial thickness and clarifies the origin of the saturation capacity, while encompassing the results of previous models, including (a) the aggregation number as the ratio of surface tension gradients between sub- and super-CMC regions, (b) the definitions of CMC, and (c) the relationship between CMC and micellization free energy.