ORIENTATIONAL DEPENDENCE OF THE SURFACE FREE-ENERGY OF THE L(ALPHA)-L(3) INTERFACE

Geometrical, topological, and energetical properties on an interface b etween the lamellar L(alpha) and the isotropic sponge phase L(3) are c onsidered. The sponge phase shows a characteristic interbilayer separa tion d(3) that is larger than the interbilayer separation d(alpha) in the L(alpha) phase. This feature controls the experimentally observed phenomenon of orientational epitaxy (Quilliet, C.; Blanc, C.; Kleman, M. Phys. Rev. Lett. 1996, 77, 522) that keeps the lamellar L(alpha) bi layers tilted with respect to the interface. We discuss the concentrat ion profile near the interface, the geometry of smooth matching betwee n the bilayers of both phases and estimate the surface tension of the L(alpha)-L(3) interface at equilibrium orientation of layers. The ener gy needed to deviate the layers from the equilibrium orientation (''an choring'' energy) is calculated using the Frenkel-Kontorova dislocatio n model. The model also predicts faceting, which is observed experimen tally. Both the surface tension and anchoring energies are of the orde r of K/d(alpha), where K is the bend elastic constant. The role of lay er undulation in tangential anchoring is discussed and illustrated exp erimentally. Finally, an outcome of the theory is that the orientation is related to the topological parameter of the sponge phase (coordina tion number of the passages introduced by Forte et al., J. Phys. (Pari s) 1988, 49, 511).