Aggregation energies of nonionic micelles calculated via pair potentials

Abstract

The aggregation energies of two different forms of nonionic isolated micelles belonging to a binary oil-in-water system were calculated by using pairwise central potentials. One of the micelles is an elongated form (the spherocylinder); the other one is a flat form (the square tablet). The spherocylinder and the square tablet degenerate into the same spherical micelle at low aggregation numbers, whereas they form elongated cylinders and lamellae, respectively, at very high aggregation numbers. Both forms are of particular importance in some nematic systems involving a phase transition. The interaction energy among the polar heads of the amphiphilic molecules was calculated using a central Lennard-Jones potential. The interaction energy among the hydrocarbon chains in the micelle bulk was calculated via a phenomenological potential model. The calculations were performed considering a wide range of values of the parameters involved (i.e. polar head diameter, chain length). The entropic contribution to the aggregation free energy is similar for both micelles, and so their relative stability depends principally on the aggregation energy. The micelle aggregation energy depends strongly on the aggregation number and other geometrical parameters for both forms. The present results are consistent with those obtained using the surfactant parameter model, which permits the evaluation of the elastic bending energy of the micelle membrane for both forms.