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 $〈{r}^{q}〉\ensuremath{\sim}{t}^{\ensuremath{\zeta}(q)}$, where $\ensuremath{\zeta}(q)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}q$ for $q<1$, $\ensuremath{\zeta}(q)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(q+1)/2$ for $q>1$, and $〈r〉\ensuremath{\sim}t\mathrm{ln}t$. This superdiffusive behavior arises because molecules execute L\'evy walks on the surface, mediated by the liquid bulk.