Mean First-Passage Time of Surface-Mediated Diffusion in Spherical Domains |
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| Authors: | O Bénichou D S Grebenkov P E Levitz C Loverdo R Voituriez |
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| Institution: | 1.Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), case courrier 121,Université Paris 6,Paris Cedex,France;2.Laboratoire de Physique de la Matière Condensée (UMR7643),CNRS – Ecole Polytechnique,Palaiseau Cedex,France;3.Laboratoire Poncelet (UMI 2615),CNRS – Independent University of Moscow,Moscow,Russia |
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| Abstract: | We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain,
for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. The presented
approach is based on an integral equation which can be solved analytically. Numerically validated approximation schemes, which
provide more tractable expressions of the mean first-passage time are also proposed. In the framework of this minimal model
of surface-mediated reactions, we show analytically that the mean reaction time can be minimized as a function of the desorption
rate from the surface. |
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