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.