Mean-field beyond mean-field: the single particle view for moderately to strongly coupled charged fluids

Relaxation dynamics of two interacting electrical double-layers in a 1D Coulomb system

We consider an out-of-equilibrium one-dimensional model for two electrical double-layers. With a combination of exact calculations and Brownian dynamics simulations, we compute the relaxation time (τ) for an electroneutral salt-free suspension, made up of two fixed colloids, withNneutralizing mobile counterions. ForNodd, the two double-layers never decouple, irrespective of their separationL; this is the regime of like-charge attraction, whereτexhibits a diffusive scaling inL²for largeL. On the other hand, for evenN,Lno longer is the relevant length scale for setting the relaxation time; this role is played by the Bjerrum length. This leads to distinctly different dynamics: forNeven, thermal effects are detrimental to relaxation, increasingτ, while they accelerate relaxation forNodd. Finally, we also show that the mean-field theory is recovered for largeNand moreover, that it remains an operational treatment down to relatively small values ofN(N> 3).

One-dimensional colloidal model with dielectric inhomogeneity

We consider a one-dimensional model allowing analytical derivation of the effective interactions between two charged colloids. We evaluate exactly the partition function for an electroneutral salt-free suspension with dielectric jumps at the colloids' position. We derive a contact relation with the pressure that shows there is like-charge attraction, whether or not the counterions are confined between the colloids. In contrast to the homogeneous dielectric case, there is the possibility for the colloids to attract despite the number of counterions (N) being even. The results are shown to recover the mean-field prediction in the limit N→∞.

Electroosmotic Flow Grows with Electrostatic Coupling in Confining Charged Dielectric Surfaces

In this work, the effects of polarization of confining charged planar dielectric surfaces on induced electroosmotic flow are investigated. To this end, we use dissipative particle dynamics to model solvent and ionic particles together with a modified Ewald sum method to model electrostatic interactions and surfaces polarization. A relevant difference between counterions number density profiles, velocity profiles, and volumetric flow rates obtained with and without surface polarization for moderate and high electrostatic coupling parameters is observed. For low coupling parameters, the effect is negligible. An increase of almost 500% in volumetric flow rate for moderate/high electrostatic coupling and surface separation is found when polarizable surfaces are considered. The most important result is that the increase in electrostatic coupling substantially increases the electroosmotic flow in all studied range of separations when the dielectric constant of electrolytes is much higher than the dielectric constant of confining walls. For the higher separation simulated, an increase of around 340% in volumetric flow rate when the electrostatic coupling is increased by a factor of two orders of magnitude is obtained.

Osmotic stress and pore nucleation in charged biological nanoshells and capsids

A model system is proposed to investigate the chemical equilibrium and mechanical stability of biological spherical-like nanoshells in contact with an aqueous solution with added dissociated electrolyte of a given concentration. The ionic chemical equilibrium across the permeable shell is investigated in the framework of an accurate Density Functional Theory (DFT) that incorporates electrostatic and hardcore correlations beyond the traditional mean-field (e.g., Poisson-Boltzmann) limit. The accuracy of the theory is tested by a direct comparison with Monte Carlo (MC) simulations. A simple analytical expression is then deduced which clearly highlights the entropic, electrostatic, and self-energy contributions to the osmotic stress over the shell in terms of the calculated ionic profiles. By invoking a continuum mean-field elastic approach to account for the shell surface stress upon osmotic stretching, the mechanical equilibrium properties of the shell under a wide variety of ionic strengths and surface charges are investigated. The model is further coupled to a continuum mechanical approach similar in structure to a Classical Nucleation Theory (CNT) to address the question of mechanical stability of the shells against a pore nucleation. This allows us to construct a phase diagram which delimits the mechanical stability of capsids for different ionic strengths and shell surface charges.

Electric double layers with surface charge modulations: Exact Poisson-Boltzmann solutions

Poisson-Boltzmann theory is the cornerstone for soft matter electrostatics. We provide exact analytical solutions to this nonlinear mean-field approach for the diffuse layer of ions in the vicinity of a planar or a cylindrical macroion. While previously known solutions are for homogeneously charged objects, the cases worked out exhibit a modulated surface charge-or equivalently, surface potential-on the macroion (wall) surface. In addition to asymptotic features at large distances from the wall, attention is paid to the fate of the contact theorem, relating the contact density of ions to the local wall charge density. For salt-free systems (counterions only), we make use of results pertaining to the two-dimensional Liouville equation, supplemented by an inverse approach. When salt is present, we invoke the exact two-soliton solution to the 2D sinh-Gordon equation. This leads to inhomogeneous charge patterns, that are either localized or periodic in space. Without salt, the electrostatic signature of a charge pattern on the macroion fades exponentially with distance for a planar macroion, while it decays as an inverse power law for a cylindrical macroion. With salt, our study is limited to the planar geometry and reveals that pattern screening is exponential.

Ionic size effects on the Poisson-Boltzmann theory

In this paper, we develop a simple theory to study the effects of ionic size on ionic distributions around a charged spherical particle. We include a correction to the regular Poisson-Boltzmann equation in order to take into account the size of ions in a mean-field regime. The results are compared with Monte Carlo simulations and a density functional theory based on the fundamental measure approach and a second-order bulk expansion which accounts for electrostatic correlations. The agreement is very good even for multivalent ions. Our results show that the theory can be applied with very good accuracy in the description of ions with highly effective ionic radii and low concentration, interacting with a colloid or a nanoparticle in an electrolyte solution.

Strong-coupling theory of counterions between symmetrically charged walls: from crystal to fluid phases

We study thermal equilibrium of classical pointlike counterions confined between symmetrically charged walls at distance d. At very large couplings when the counterion system is in its crystal phase, a harmonic expansion of particle deviations is made around the bilayer positions, with a free lattice parameter determined from a variational approach. For each of the two walls, the harmonic expansion implies an effective one-body potential at the root of all observables of interest in our Wigner strong-coupling expansion. Analytical results for the particle density profile and the pressure are in good agreement with numerical Monte Carlo data, for small as well as intermediate values of d comparable with the Wigner lattice spacing. While the strong-coupling theory is extended to the fluid regime by using the concept of a correlation hole, the Wigner calculations appear trustworthy for all electrostatic couplings investigated. Our results significantly extend the range of accuracy of analytical equations of state for strongly interacting charged planar interfaces.