Scaling Behavior of Bipolar Nanopore Rectification with Multivalent Ions

Abstract

We present a scaling behavior of a rectifying bipolar nanopore as a function of the parameter ξ = R P /(λ z if ), where R P is the radius of the pore, λ is the characteristic screening length of the electrolyte filling the pore, and z if = z + |z − | is a scaling factor that makes scaling work for electrolytes containing multivalent ions (z + and z − are cation and the anion valences). By scaling we mean that the rectification of the pore (defined as the ratio of currents in the forward and reversed biased states) depends on pore radius, concentration, c, and ion valences via the parameter ξ implicitly. This feature is based on the fact that rectification depends on the voltage-sensitive appearance of depletion zones that, in turn, depend on the relation of R P to the rescaled screening length λ z if . In this modeling study, we use the Poisson-Nernst-Planck (PNP) theory and a particle simulation method, the Local Equilibrium Monte Carlo (LEMC). The latter can compute ion correlations that are ignored in the mean-field treatment of PNP and that are very important for multivalent ions (we show results for 1:1, 2:1, 3:1, and 2:2 electrolytes). In addition to the z if factor, we show that one must choose a screening length appropriate to the system, in our case the Debye length for λ for PNP and the screening length given by the Mean Spherical Approximation for LEMC.

Rectification of bipolar nanopores in multivalent electrolytes: effect of charge inversion and strong ionic correlations

“…where j i (r) is the ionic flux, c i (r) is the concentration, and , as in our earlier works. [30,29,31,36] These particular choices do not qualitatively affect our conclusions.…”

“…That work [36] was performed for various combinations of R pore , c, and z i at fixed surface charge σ = 1 e/nm 2 (the charge pattern was then ±σ ). Here, we fix pore radius and salt concentration and change surface charge for various z + : z − electrolytes.…”

“…Here, we fix pore radius and salt concentration and change surface charge for various z + : z − electrolytes. While our focus was on scaling in our previous work, [36] here we concentrate on the σ -dependence and the anomalous response of the nanopore to the presence of multivalent ions.…”

Modeling the Device Behavior of Biological and Synthetic Nanopores with Reduced Models

“…The radial distribution of the ions is important because it determines the behavior of the axial profiles. This was discussed in detailed in our recent studies [ 50 , 52 ].…”

“…Why do reduced models work well for some biological ion channels and synthetic nanopores What are reduced models and what defines a “good” reduced model? Our attempt to answer these questions is based on the knowledge accumulated over 20 years [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 ] of modeling and computing permeation and selectivity in ion channels and nanopores.…”