Anomalous diffusion in elongated micelles and its Lévy flight interpretation

(Received 6 June 1991, accepted in final form 3 September 1991)

Abstract
We have observed anomalously enhanced self (tracer) diffusion in systems of polymer-like, breakable micelles. We argue that it provides the first experimental realization of a random walk for which the second moment of the jump size distribution fails to exist ("Lévy flight"). The basic mechanism is the following: due to reptation, short micelles diffuse much more rapidly than long ones. As time goes on, shorter and shorter micelles are encountered by the tracer, and hence the effective diffusion constant increases with time. We discuss in detail the fact that this anomalous régime only exists in a certain range of concentration and temperature. The theoretical dependence of the asymptotic diffusion constant on concentration is in quite good agreement with the experiment.