Predicting Surface Tensions of Surfactant Solutions from Statistical Mechanics

The importance of surfactants to various industries necessitates a predictive understanding of their surface tension and adsorption behavior in terms of molecular characteristics. Previous models are highly empirical, require fitting parameters, and have limited applicability at various temperatures. Here, we provide a surface tension model based on statistical mechanics that (1) is thermodynamically consistent, (2) provides a higher predictive power, wherein surface tension can be calculated for any tail length, concentration, and temperature from molecular parameters, and (3) provides a physical understanding of the important molecular interactions at play. This model is applicable to both nonionic and ionic surfactants, where the effects of the electric double layer have been taken into account in the latter case. For nonionic surfactants, we were able to extend our model to predict dynamic surface tension as well. We have validated our model with tensiometry experiments for various surfactants, concentrations, and temperatures. In addition, we have validated our model with a diverse set of literature data, wherein agreement within a few mN M^-1 and a correct prediction of phase change behavior is shown. The model could enable a more informed design of surfactant systems and serve as the theoretical basis for theory on more complex surfactant systems such as mixtures.