Dynamic Surface Tension of Polydisperse Surfactant Solutions: A Pseudo-Single-Component Approach

A method for treating both the equilibrium and dynamic surface tension of polydisperse surfactant solutions is introduced and explored. The model is expressed in terms of a pseudo-single-surfactant approximation, where the polydisperse mixture is treated as if it were a pure single-component surfactant. The theory presented is based on the Langmuir adsorption isotherm and suggests that polydisperse surfactants behave as pseudo-single surfactants at equilibrium but diverge from the pseudo-single approach under certain dynamic conditions. Parametric studies provide further insight, suggesting that the dynamic surface tension of polydisperse solutions approaches the pseudo-single-surfactant approximation when competition for interfacial area by surfactant molecules is absent. For systems where competitive adsorption is present, surface tension generally equilibrates more slowly. Finally, the static and dynamic surface tensions of the Tergitol 15-S- n series, an important commercial grade nonionic surfactant, are analyzed in terms of the pseudo-single-surfactant approach. It is observed that the Szyszkowski surface tension equation satisfactorily approximates the equilibrium surface tension for all Tergitols at concentrations below the critical micelle concentration. The pseudo-single-surfactant approach provides a good prediction of dynamic surface tension for the lower Tergitols (15-S-5, 15-S-7, and 15-S-9), but fails to capture the slow equilibration observed in higher Tergitols (15-S-12, 15-S-15, and 15-S-20). This observation is rationalized in terms of the expected lower surface activity of the higher Tergitols.