Bulk-mediated Surface Diffusion on a Cylinder in the Fast Exchange Limit

Abstract

In various biological systems and small scale technological applications particles transiently bind to a cylindrical surface. Upon unbinding the particles diffuse in the vicinal bulk before rebinding to the surface. Such bulk-mediated excursions give rise to an effective surface translation, for which we here derive and discuss the dynamic equations, including additional surface diffusion. We discuss the time evolution of the number of surface-bound particles, the effective surface mean squared displacement, and the surface propagator. In particular, we observe sub-and superdiffusive regimes. A plateau of the surface mean-squared displacement reflects a stalling of the surface diffusion at longer times. Finally, the corresponding first passage problem for the cylindrical geometry is analysed.

Non-Brownian Interfacial Diffusion: Flying, Hopping, and Crawling

“…Qualitatively, this suggests that molecular trajectories associated with surface diffusion should contain long “Lévy” flights. Theorists later provided a complete solution of this problem on a flat surface and on a cylinder, − validating the basic findings and extending their relevance. − While these theoretical predictions were rigorous and detailed, they proved difficult to confirm empirically given the experimental methods available at the time.…”

Mapping the diffusion pattern of 1O2 along DNA duplex by guanine photooxidation with an appended biphenyl photosensitizer

“…Diffusion of 1 O 2 along a DNA duplex can be generalized as the diffusion of particles on the surface of a cylinder. Diffusion of particles on a cylindrical surface has been described to go through the combination of adsorption, crawling, desorption, bulk diffusion, and rebinding 38 . The desorbed particles have to travel a much longer distance before rebinding than that can be reached by the crawling particles in the same timescale.…”

“…This study would provide the information about the traveling behavior of 1 O 2 along DNA duplexes in more detail than ever, thereby offering clues to overcome the low reactivity of type-II photooxidation of ON in a DNA- and/or RNA-targeting PDT by attaching BP at the most appropriate position of ON, where the target G would be most efficiently and selectively oxidized. In addition, the study could be a unique experimental demonstration of the diffusion of a particle along a cylindrical surface in molecular level, which is a challenging subject in diffusion science 38 .…”