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

¹ Institute for Theoretical Physics NSC KIPT, Akademicheskaya st.1, 61108 Kharkov, Ukraine and Max-Planck Institute for Physics of Complex Systems, Nöthnitzer Str. 38, D-01187 Dresden, FRG
² Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
³ MEMPHYS - Center for Biomembrane Physics, Department of Physics, Chemistry, and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
⁴ Institut für Physik, Humboldt Universität zu Berlin, Newtonstraße 15, D-12489 Berlin, FRG
⁵ Institute for Physics & Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany and Department of Physics, Technical University of Tampere, FI-33101 Tampere, Finland

^⋆ Corresponding author. E-mail: rmetzler@uni-potsdam.de

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.