Electrostatic correlations on the ionic selectivity of cylindrical membrane nanopores

Abstract

We characterize the role of electrostatic fluctuations on the charge selectivity of cylindrical nanopores confining electrolyte mixtures. To this end, we develop an extended one-loop theory that can account for correlation effects induced by the surface charge, nanoconfinement of the electrolyte, and interfacial polarization charges associated with the low permittivity membrane. We validate the quantitative accuracy of the theory by comparisons with previously obtained Monte-Carlo simulation data from the literature, and scrutinize in detail the underlying forces driving the ionic selectivity of the nanopore. In the biologically relevant case of electrolytes with divalent cations such as CaCl2 in negatively charged nanopores, electrostatic correlations associated with the dense counterion layer in the channel result in an increase of the pore coion density with the surface charge. This peculiarity analogous to the charge inversion phenomenon remains intact for dielectrically inhomogeneous pores, which indicates that the effect should be observable in nanofiltration membranes or DNA-blocked nanopores characterized by a low membrane permittivity. Our results show that a quantitatively accurate consideration of correlation effects is necessary to determine the ionic selectivity of nanopores in the presence of electrolytes with multivalent counterions.

Beyond Poisson–Boltzmann: fluctuations and fluid structure in a self-consistent theory

“…We now have the main set of equations ready and turn to the analytical solutions of equations (13)- (15) for a simple planar geometry in order to investigate the charge inversion phenomenon [7]. Then we will couple these equations with the Stokes equation and show that charge inversion gives rise to a reversal of electrophoretic DNA mobility [10] and hydrodynamically induced ion currents through cylindrical pores [11].…”

“…One should also note that equations (4) and (5) can be easily generalized to an asymmetrical electrolyte (see e.g. [7]). …”

“…Numerical methods have recently been developed to solve them [6,7,16,18]. In particular, in comparison with the MC simulations, [6] and [7] identified the validity regime of the equations for liquids confined to slit and cylindrical nanopores, respectively. In the following we will discuss the approximate solutions of equations (4)- (6) and their modifications to physically relevant situations, which to some extent also permit analytical calculations.…”

“…Hatlo et al considered the variational formulation of inhomogeneous electrolytes by introducing a restricted self-consistent scheme [5]. In [6,7], one of us (SB) introduced a numerical scheme for the exact solution of the variational equations in slit and cylindrical nanopores. At this point, we should also mention the oneloop treatment of charge correlations that allows the analytical treatment of inhomogeneous electrolytes.…”

Electroneutrality breakdown and specific ion effects in nanoconfined aqueous electrolytes observed by NMR

“…The ion-ion correlations based on electrostatic and ion-specific interactions are predicted to be of crucial importance in nanoconfined electrolytes 33,36,38,42,43 . Although the preferentially adsorbed anions in the nanopores could attract Na þ cations via electrostatic interactions as demonstrated by both the experiments and the simulation, the higher Na þ concentration associated with NaNO 3 electrolyte is not due to the anomalous interfacial affinity of NO 3 À since its concentration is consistent with the ranking of the Hofmeister series, that is, lower than the BF 4 À concentration (Fig.…”