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

Abstract

Poisson-Boltzmann (PB) theory is the classic approach to soft matter electrostatics which has been applied to numerous problems of physical chemistry and biophysics. Its essential limitations are the neglect of correlation effects and of fluid structure. Recently, several theoretical insights have allowed the formulation of approaches that go beyond PB theory in a systematic way. In this topical review we provide an update on the developments achieved in self-consistent formulations of correlation-corrected Poisson-Boltzmann theory. We introduce the corresponding system of coupled nonlinear equations for both continuum electrostatics with a uniform dielectric constant and a structured solvent, a dipolar Coulomb fluid, including nonlocal effects. While the approach is only approximate and also limited to corrections in the so-called weak fluctuation regime, it allows to include physically relevant effects, as we show for a range of applications of these equations.

Electrostatic charge-charge and dipole-dipole interactions near the surface of a medium with screening non-locality (Review Article)

“…(29) and (38). We note that the obtained power-law asymptotics of the charge-charge and dipole-dipole interactions near the metal surface differs much from the exponential screening in the bulk of the Thomas-Fermi metal: exp ( ) L −κ [88].…”

“…It is remarkable that even the crude description of molecules in the framework of classical electrostatics as interacting point dipoles mirrored in the classical perfect-metal substrate mimics the complicated densityfunctional quantum-mechanical picture successfully enough at large distances between them [34][35][36]. One should note that the non-local electrostatics turned out to be useful for bulk-condensed-matter problems as well [37,38].…”

Beyond Poisson–Boltzmann: Numerical Sampling of Charge Density Fluctuations

“…where the solvent is not uniform, but made of freely orientable dipoles to represent water molecules, or even more refined ones. 13,[20][21][22] In the canonical ensemble, the Hamiltonian and partition function of the system are given in (4).…”

Implicit Solvation Methods for Catalysis at Electrified Interfaces

“…An account for the corresponding ion correlations requires in general field theoretical approaches, using loop expansions, which lead to substantially more complicated expressions than in PB theory. 207,208 A promising, more approximate approach by Bazant et al instead leads to a simple correction of the mean-field electrostatic potential energy, cf. eq.…”