Flow-induced molecular orientation of amphiphile monolayers: incorporation of hexatic elasticity into Ericksen-Leslie theory.

By introducing the local lattice elasticity into the pure Ericksen-Leslie (EL) theory which only considers the deformation of the director, we developed a more general theory for understanding the behaviors of hexatic liquid crystal under flow. In the cases of amphiphilic monolayers in tilted phases (L2 and L'2), the exact solutions of the new EL equation in two types of flow, pure extension and simple shear, explain well most of the features of flow-induced tilt azimuth orientation observed by Fuller's group [Science, 274, 233 (1996)] and Schwartz's group [Nature (London) 410, 348 (2001)]. In particular, the "shear band" domain generated by flow discovered by the former is proved theoretically as the result of two-dimensional Wulf construction in L2 and L'2 phases.