Anomalous diffusion of surface-active species at liquid-fluid and liquid-solid interfaces

(Received 23 February 1994, accepted 1 April 1994)

Abstract
We study the role of bulk-surface exchange in the density relaxation kinetics and selfdiffusion of surface-active molecules at liquid surfaces. In " strongly adsorbing " systems, relaxation occurs through bulk-mediated effective surface diffusion characterized by one-step distributions with long tails ; molecules execute Lévy walks on the surface. Correspondingly, at times before particles are finally lost to the bulk, surface displacement r is non-Fickian and exhibits anomalous scaling : moments grow as , where for q < 1, for q > 1 and ln t. The width of an initially localized density disturbance increases linearly in time with a " speed " c which is universally related to other observables. Numerical simulations confirm the family of exponents , and reproduce the observable c. We consider a simple example where end-functionalised macromolecules adsorb at a solid surface, finding where s is the surface " stickiness " parameter. At liquid-fluid interfaces viscoelastic effects compete. For sub-micron scales, we argue that self-diffusion will typically remain dominated at high coverages by the anomalous bulk-mediated mechanism, while surface viscoelasticity will dominate the relaxation of density perturbations.