Incorporation of excluded-volume correlations into Poisson-Boltzmann theory

Abstract

We investigate the effect of excluded volume interactions on the electrolyte distribution around a charged macroion. First, we introduce a criterion for determining when hard-core effects should be taken into account beyond standard mean field Poisson-Boltzmann (PB) theory. Next, we demonstrate that several commonly proposed local density functional approaches for excluded volume interactions cannot be used for this purpose. Instead, we employ a non-local excess free energy by using a simple constant weight approach. We compare the ion distribution and osmotic pressure predicted by this theory with Monte Carlo simulations. They agree very well for weakly developed correlations and give the correct layering effect for stronger ones. In all investigated cases our simple weighted density theory yields more realistic results than the standard PB approach, whereas all local density theories do not improve on the PB density profiles but on the contrary, deviate even more from the simulation results.

Continuum molecular electrostatics, salt effects, and counterion binding—A review of the Poisson–Boltzmann theory and its modifications

“…60 Now, we will consider modifications of the PBE which are simpler than the Borukhov's theory but also account for the saturation of ionic concentration. The Borukhov expression for ionic concentrations (Eq.…”

Dissecting electrostatic screening, specific ion binding, and ligand binding in an energetic model for glycine riboswitch folding

“…PB theory has been successfully applied to predict the composition of the ion atmosphere and ion induced folding of nucleic acids Draper 1999, 2000;Grilley et al 2006;Bai et al 2007Bai et al , 2008Chu et al 2007), although limitations in its accuracy are also known; in particular, the neglect of ion size and ion-ion correlations (Antypov et al 2005;Chu et al 2007;Bai et al 2008;Chu et al 2008;Grochowski and Trylska 2008). Under the simplifying assumption that the U-to-M transition does not involve specific ion binding, we can compute the purely electrostatic contributions to the free energy by calculating the dependence of the PB energies on salt concentration for the U and M states: To solve the PB equation and to compute properties such as the composition of the ion atmosphere or electrostatic energies, it is necessary to define the geometry and charge distribution of the molecular conformations of interest.…”

Ion-Specific Excluded-Volume Correlations and Solvation Forces

“…Consequently, ion structure and double-layer forces between adjacent surfaces are oscillatory and highly salt specific [2,[6][7][8][9][10][11][12]. In this context, the ion-specific restabilization of dispersions of colloids [13,14], proteins [15], and clays [16] in dense electrolytes is not understood and loosely assigned to the class of short-ranged ''solvation forces'' [2].Although local extensions to PB are appealing due to their simplicity [4,17], it has been demonstrated that even the simplest nonlocal extension in the framework of density functional theory (DFT) is far superior in describing the oscillatory structure of (size-symmetric and additive) hard-sphere ions close to a hard surface [18]. Surprisingly, the efforts towards a more realistic (and ion-specific) approach to steric effects in PB theory stopped at this level of ''primitive models'' [1] and a few issues remain: effectively, ions are not hard-sphere-like but interact with an oscillatory pair potential due to dispersion and hydration effects [9,19].…”