Rectification in synthetic conical nanopores: A one-dimensional Poisson-Nernst-Planck model

Kosińska, I. D.; Goychuk, Igor; Kostur, Marcin; Schmid, Gerhard; Hänggi, Peter

doi:10.1103/physreve.77.031131

Cited by 138 publications

(125 citation statements)

References 35 publications

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“…For instance, entropic effects on the rectification efficiency of the conical nanopores of Siwy and co-workers have been analyzed by Kosinska et al ͑2008͒. However, in-pore diffusion in a liquid suspension requires a fully 3D analysis of the pumping mechanism, which sets the basis for the fabrication of more complicated ionic devices ͑Stein et van der Heyden et al, 2004͒.…”

Section: B Artificial Nanoporesmentioning

confidence: 99%

Artificial Brownian motors: Controlling transport on the nanoscale

2009

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In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with unbiased external input signals, deterministic and random alike, can assist directed motion of particles at submicron scales. In such cases, one speaks of "Brownian motors." In this review the constructive role of Brownian motion is exemplified for various physical and technological setups, which are inspired by the cellular molecular machinery: the working principles and characteristics of stylized devices are discussed to show how fluctuations, either thermal or extrinsic, can be used to control diffusive particle transport. Recent experimental demonstrations of this concept are surveyed with particular attention to transport in artificial, i.e., nonbiological, nanopores, lithographic tracks, and optical traps, where single-particle currents were first measured. Much emphasis is given to two-and three-dimensional devices containing many interacting particles of one or more species; for this class of artificial motors, noise rectification results also from the interplay of particle Brownian motion and geometric constraints. Recently, selective control and optimization of the transport of interacting colloidal particles and magnetic vortices have been successfully achieved, thus leading to the new generation of microfluidic and superconducting devices presented here. The field has recently been enriched with impressive experimental achievements in building artificial Brownian motor devices that even operate within the quantum domain by harvesting quantum Brownian motion. Sundry akin topics include activities aimed at noise-assisted shuttling other degrees of freedom such as charge, spin, or even heat and the assembly of chemical synthetic molecular motors. This review ends with a perspective for future pathways and potential new applications.

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Section: B Artificial Nanoporesmentioning

confidence: 99%

Artificial Brownian motors: Controlling transport on the nanoscale

2009

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“…The entropic nature of this term leads to a genuine dynamics which is distinctly different from that observed when the potential is of energetic origin [17]. It has been shown that the FJ equation can provide a very accurate description of entropic transport in channels of varying cross-section [17,18,19]. However, the derivation of the FJ equation entails a tacit approximation: The particle distribution in the transverse direction is assumed to equilibrate much faster than in the main (unconstrained) direction of transport.…”

Section: Introductionmentioning

confidence: 99%

Entropic particle transport in periodic channels

et al. 2008

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The dynamics of Brownian motion has widespread applications extending from transport in designed micro-channels up to its prominent role for inducing transport in molecular motors and Brownian motors. Here, Brownian transport is studied in micro-sized, two dimensional periodic channels, exhibiting periodically varying cross sections. The particles in addition are subjected to an external force acting alongside the direction of the longitudinal channel axis. For a fixed channel geometry, the dynamics of the two dimensional problem is characterized by a single dimensionless parameter which is proportional to the ratio of the applied force and the temperature of the particle environment. In such structures entropic effects may play a dominant role. Under certain conditions the two dimensional dynamics can be approximated by an effective one dimensional motion of the particle in the longitudinal direction. The Langevin equation describing this reduced, one dimensional process is of the type of the Fick-Jacobs equation. It contains an entropic potential determined by the varying extension of the eliminated channel direction, and a correction to the diffusion constant that introduces a space dependent diffusion. Different forms of this correction term have been suggested before, which we here compare for a particular class of models. We analyze the regime of validity of the Fick-Jacobs equation, both by means of analytical estimates and the comparisons with numerical results for the full two dimensional stochastic dynamics. For the nonlinear mobility we find a temperature dependence which is opposite to that known for particle transport in periodic potentials. The influence of entropic effects is discussed for both, the nonlinear mobility and the effective diffusion constant.

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“…The driven transport of charged particles across bottlenecks (Burada et al 2009), such as ion transport through artificial nanopores or artificial ion pumps (Siwy et al 2005;Kosinska et al 2008) or in biological channels (Berezhkovskii & Bezrukov 2005), are more familiar systems where diffusive transport is regulated by entropic barriers. Similarly, the operation of artificial Brownian motors and molecular machines also relies on a mutual interplay among diffusion and binding action by energetic or, more relevant in the present context, entropic barriers (Derenyi & Astumian 1998;Astumian & Hänggi 2002;Reimann & Hänggi 2002;Burada et al 2009;).…”

Section: Introductionmentioning

confidence: 99%

Entropic transport: a test bed for the Fick–Jacobs approximation

Burada

Schmid

Hänggi

2009

Phil. Trans. R. Soc. A.

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Biased diffusive transport of Brownian particles through irregularly shaped, narrow confining quasi-one-dimensional structures is investigated. The complexity of the higher dimensional diffusive dynamics is reduced by means of the so-called Fick-Jacobs approximation, yielding an effective one-dimensional stochastic dynamics. Accordingly, the elimination of transverse, equilibrated degrees of freedom stemming from geometrical confinements and/or bottlenecks causes entropic potential barriers that the particles have to overcome when moving forward noisily. The applicability and the validity of the reduced kinetic description are tested by comparing the approximation with Brownian dynamics simulations in full configuration space. This non-equilibrium transport in such quasi-one-dimensional irregular structures implies, for moderate-to-strong bias, a characteristic violation of the Sutherland-Einstein fluctuation-dissipation relation.

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Rectification in synthetic conical nanopores: A one-dimensional Poisson-Nernst-Planck model

Cited by 138 publications

References 35 publications

Artificial Brownian motors: Controlling transport on the nanoscale

Artificial Brownian motors: Controlling transport on the nanoscale

Entropic particle transport in periodic channels

Entropic transport: a test bed for the Fick–Jacobs approximation

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