Beyond the Tradeoff: Dynamic Selectivity in Ionic Transport and Current Rectification

Abstract

Traditionally, ion-selectivity in nanopores and nanoporous membranes is understood to be a consequence of Debye overlap, in which the Debye screening length is comparable to the nanopore radius somewhere along the length of the nanopore(s). This criterion sets a significant limitation on the size of ion-selective nanopores, as the Debye length is on the order of 1 − 10 nm for typical ionic concentrations. However, the analytical results we present here demonstrate that surface conductance generates a dynamical selectivity in ion transport, and this selectivity is controlled by so-called Dukhin, rather than Debye, overlap. The Dukhin length, defined as the ratio of surface to bulk conductance, reaches values of hundreds of nanometers for typical surface charge densities and ionic concentrations, suggesting the possibility of designing large-nanopore (10 − 100 nm), high-conductance membranes exhibiting significant ion-selectivity. Such membranes would have potentially dramatic implications for the efficiency of osmotic energy conversion and separation techniques. Furthermore, we demonstrate that this mechanism of dynamic selectivity leads ultimately to the rectification of ionic current, rationalizing previous studies showing that Debye overlap is not a necessary condition for the occurrence of rectifying behavior in nanopores.

Pressure-Induced Enlargement and Ionic Current Rectification in Symmetric Nanopores

“…28 Secondly, we demonstrate that pressure induced-fluid flow produces ionic current rectification despite the lack of the usually required geometrical asymmetry in the pore. 5,7 This is opposite to the so far reported role of pressure in reducing ICR in asymmetrical nanopores 18,19 .…”

“…where d is the diameter of the nanopore, L the thickness of the membrane, and σ the bulk conductance of the solution. 33,34 One measure of the nonlinearity in ion transport is the ionic current rectification (ICR) ratio 5,7 which we define as:…”

“…ICR in a nanapore has been shown previously to be controlled by the spatial variation in the axial direction z of the local Dukhin number Du(z), with stronger asymmetry of Du(z) between the pore ends yielding stronger rectification. 7 The Dukhin number measures the relative magnitude of surface to bulk ionic conduction. For a 1:1 electrolyte, and in the absence of Debye layer overlap in the pore, Du(z) = − c+(z)−c−(z) 2(c+(z,r=0)+c−(z,r=0)) , where c ± are the positive and negative ion concentrations, • • • denotes an average over the pore cross-section, and r is the radial coordinate.…”

Light-Enhanced Blue Energy Generation Using MoS2 Nanopores

“…This effect is becoming increasingly important as the pore size increases and helps to maintain good power generation in large nanopores. Along the same line, recent work has analytically shown that strong surface conductance generates a dynamic ion selectivity, which is defined through Dukhin, rather than EDL, overlap and is responsible for the maintenance of good ion selectivity in larger pores 24 .…”

Osmosis, from molecular insights to large-scale applications

“…an asymmetric surface charge or an asymmetric geometry. Such behavior is expected to occur in the regime where the Dukhin number is of order one and asymmetric along the channel 154 : the Dukhin number is defined here as Du = Σ/c s h, where Σ is the surface charge density, c s the bulk salt concentration and h a characteristic channel dimension. It quantifies the importance of surface versus bulk electric conduction.…”