Pattern formation and instability of smectic-A filaments grown from an isotropic phase

Pattern formation and instability of smectic-A filaments grown from an isotropic phase have been investigated. The evolution and shape equations for the filaments are derived by a variation of the free energy of the filaments. It is shown from the evolution equation that the length of the filament increases exponentially with time under a cooling process. It is also shown from the shape equation that the existence of the threshold length of the straight filaments for buckling and the global properties of the filaments can be predicted. The theoretical results are demonstrated experimentally in the binary mixture of octyloxycyanobiphenyl with dodecyl alcohol.