MODELING SOLUTION ENTROPY IN THE THEORY OF MICELLIZATION

In order to develop an equilibrium theory of surfactant solutions, one needs to estimate the entropy of the system consisting of the solvent, singly dispersed surfactant molecules and aggregates of all possible sizes and shapes. No fundamental approach for estimating this entropy taking into account such variations in the size, shape, flexibility and compactness of the constituent species is available in the literature. Currently available theories use entropy estimates that may lack a priori justification, but with the anticipation of obtaining useful practical results. The four widely used entropy estimates are based on the ideal solution model, the gas-like translation model, the Flory-Huggins model, and the translational entropy model. In this paper, we explore the consequences of using these entropy models to predict the properties of solutions in which globular and rodlike micelles are present. Specifically, we compare the theoretical predictions of the CMC, the average aggregation number of the micelles, the size polydispersity, the dependence of micelle size on concentration, the critical constants for incipient phase separation, the spinodal line and the osmotic compressibility resulting from the different entropy models. Our analysis shows that the different entropy estimates lead to widely differing predictions of aggregation characteristics and solution phase behavior. All four entropy estimates employed in the literature lead to predictions that disagree with one or more of the experimentally observed solution characteristics. We find however, that a simple modification to the translational entropy model based on the fact that the surfactant solution is a liquid and not gas-like, brings all theoretical predictions into consistency with the experiments.