Bounded step superdiffusion in an oriented hexagonal phase.

Fluorescence recovery after pattern photobleaching is used to measure the self-diffusion of surfactant molecules, along cylinders and perpendicular to their main axis in an oriented hexagonal lyotropic phase. Unexpectedly, while the motion along cylinders is diffusive, a superdiffusive behavior is observed in the direction perpendicular to the cylinder axis. Moreover, varying the lattice parameter, we found that the perpendicular diffusion time is governed only by the number of cylinders to cross, providing experimental evidence for superdiffusion with a bounded step length.