Diffusion in Confined Geometries

• Published in: Chemphyschem Vol. 10; no. 1; pp. 45 - 54
• Main Authors: Burada, P. Sekhar, Hänggi, Peter, Marchesoni, Fabio, Schmid, Gerhard, Talkner, Peter
• Format: Journal Article
• Language: English
• Published: Weinheim WILEY-VCH Verlag 12.01.2009; WILEY‐VCH Verlag; Wiley
• Subjects: Algorithms; Brownian motion; Chemistry; Colloidal state and disperse state; Diffusion; entropy; Exact sciences and technology; General and physical chemistry; Ion Channels - chemistry; Ion Transport; Models, Theoretical; Molecular Conformation; Physical and chemical studies. Granulometry. Electrokinetic phenomena; single-file diffusion; transport; Structure function; Confinement; Fluctuations; single-file diffusion; Segregation; Contact interaction; Mobility; Suspension; Entropy; Geometry; Brownian motion; Particle; Chemical reaction; Dynamics; Particle interaction; Resonance; Thermodynamic properties; Diffusion; Transport
• ISSN: 1439-4235; 1439-7641; 1439-7641
• DOI: 10.1002/cphc.200800526

Diffusive transport of particles or, more generally, small objects, is a ubiquitous feature of physical and chemical reaction systems. In configurations containing confining walls or constrictions, transport is controlled both by the fluctuation statistics of the jittering objects and the phase space available to their dynamics. Consequently, the study of transport at the macro‐ and nanoscales must address both Brownian motion and entropic effects. Herein we report on recent advances in the theoretical and numerical investigation of stochastic transport occurring either in microsized geometries of varying cross sections or in narrow channels wherein the diffusing particles are hindered from passing each other (single‐file diffusion). For particles undergoing biased diffusion in static suspension media enclosed by confining geometries, transport exhibits intriguing features such as 1) a decrease in nonlinear mobility with increasing temperature or also 2) a broad excess peak of the effective diffusion above the free diffusion limit. These paradoxical aspects can be understood in terms of entropic contributions resulting from the restricted dynamics in phase space. If, in addition, the suspension medium is subjected to external, time‐dependent forcing, rectification or segregation of the diffusing Brownian particles becomes possible. Likewise, the diffusion in very narrow, spatially modulated channels is modified via contact particle–particle interactions, which induce anomalous sub‐diffusion. The effective sub‐diffusion constant for a driven single file also develops a resonance‐like structure as a function of the confining coupling constant. A tight squeeze: The mathematical formalism for modelling the diffusion of a Brownian particle immersed in a confined suspension fluid (picture) is outlined. Particle transport along a channel subject to stationary pumping is described. A review of results for the diffusion of a single file along a periodically corrugated channel (picture, bottom) is presented.