MOLECULAR THEORY OF BENDING ELASTICITY AND BRANCHING OF CYLINDRICAL MICELLES

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 intermicellar junctions (branches). The internal (free) energy of the micelles, before and after a bending deformation and junction for mation, are calculated using mean field theories for the free energies of the molecules constituting these structures. The molecular free en ergies, which depend on the local packing geometries, include the cont ributions of head group repulsion forces, the hydrocarbon-water interf acial energy, and the chain conformational free energy. We find that w hen only the head group and surface contributions to the packing energ y art:taken into account, the one-dimensional bending constant of the micelles is negligibly small, When the chain contribution is included, and when reasonable molecular packing parameters are used, we find th at the persistence length, which is proportional to the bending rigidi ty, is typically a few tens of nanometers. The free energy change asso ciated with the formation of a trijoint intermicellar junction upon th e ''fusion'' of one micellar end cap with the cylindrical body of anot her micelle is found to be small but positive; about 10 k(B)T at room temperature. This conclusion does not refute ?he possibility that inte rmicellar junctions are metastable transients or that their formation may be favored entropically, due either to conformational degeneracy o r excluded volume interactions between micelles. Our conclusions apply to aqueous solutions containing one, single-tail, surfactant species.