Tracer‐diffusion in quenched lamellar phases

A theory is presented to describe the tracer‐diffusion properties of surfactant molecules embedded in quenched, disordered lamellar phases, such as those encountered in concentrated solutions and melts of block copolymers. We demonstrate that for weak anisotropy of the local diffusion tensor Dij, the average diffusion coefficient of an isotropically disordered sample is slightly larger than (1/3)∑iDii and is independent of the geometrical and statistical details of the quenched pattern. For large anisotropy of Dij, transport of a tracer molecule will in general become dependent on the population and type of topological defects that characterize the quenched sample and thus on its preparation and history. In such instances, sub‐diffusive transport can be achieved.