Anomalous Diffusion at Liquid Surfaces

Abstract

We study the role of bulk-surface exchange in the diffusion of adsorbed molecules at liquid-solid and liquid-fluid interfaces. For “strong adsorbers” (readsorption time much less than desorption time) we find anomalous surface diffusion on time scales less than the surface retention time: Displacement moments grow as $〈r^q〉\sim t^{\zeta \left(q\right)}$, where $\zeta \left(q\right)=q$ for $q<\mathrm{}1\mathrm{}$, $\zeta \left(q\right)=(q+1\mathrm{})/2\mathrm{}$ for $q>\mathrm{}1\mathrm{}$, and $〈r〉\sim t\ln t$. This superdiffusive behavior arises because molecules execute Lévy walks on the surface, mediated by the liquid bulk.