Sylvio May , Yardena Bohbot and Avinoam Ben-Shaul, 'Molecular Theory of Bending Elasticity and Branching of Cylindrical Micelles', accepted in J.Phys.Chem.
Two structural-thermodynamic characteristics of cylindrical, wormlike, micelles in dilute solution are studied using a molecular-level model: a) the bending elasticity of the micelles, and b) their tendency to form inter-micellar junctions (branches). The internal (free) energy of the micelles, before and after a bending deformation and junction formation, are calculated using mean field theories for the free energies of the molecules constituting these structures. The molecular free energies, which depend on the local packing geometries, include the contributions of head group repulsion forces, the hydrocarbon-water interfacial energy and the chain conformational free energy. We find that when only the head group and surface contributions to the packing energy are taken into account the one-dimensional bending constant of the micelles is negligibly small. When the chain contribution is included, and using reasonable molecular packing parameters, we find that the persistence length, which is proportional to the bending rigidity, is typically a few tens of nanometers. The free energy change associated with the formation of a tri-joint inter-micellar junction upon the ``fusion'' of one micellar end cap with the cylindrical body of another micelle, is found to be small but positive; about 10 kT at room temperature. This conclusion does not refute the possibility that inter-micellar junctions are metastable transients, or that their formation may be favored entropically, due either to conformational degeneracy or excluded volume interactions between micelles. Our conclusions apply to aqueous solutions containing one, single-tail, surfactant species.