Hydrophobic Surface Properties in Ionic Micelle Using Ellipsoid of Revolution Model

Abstract
oday the micelle model of surfactant in ellipsoid of revolution form with small aspect ratio is developed. On condition that the molecule in micelle nucleus is packed densely and the charge on its surface is arranged evenly, the hydrophobic properties of this micelle, such as magnitude and fraction of free hydrophobic surface, ionicity, surface tension and corresponding surface energy were determined. There are two Laplace’s equations (fundamental and generalized) were used for surface tension calculation. Laplace’s generalized (differential) equation is integrated in quadratures. All the results are represented in the reduced form as the function of aspect ratio and aggregation number of ellipsoidal micelle. At the equilibrium state of the micellar transition “sphere – ellipsoid” with small aspect ratio of the ellipsoid the minimum of the micelle surface energy were determined. Verification of the results is carried out by the example of the micellar aqueous solution of sodium decyl sulfate.

Keywords: ionic micelle, hydrophobic properties, surface tension, ellipsoid of revolution, Laplace’s equations