Adsorption of Large Ions from an Electrolyte Solution: A Modified Poisson-Boltzmann Equation

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...

We study the ionic distribution near a charged surface. A new method for performing Monte Carlo simulations in this geometry is discussed. A theory is then presented that allows us to accurately reproduce the density profiles obtained in the simulations. In the weak-coupling regime, a theory accounts for the ion-image interactions, leading to a modified Poisson-Boltzmann equation. When the correlations between the ions are significant, a strong-coupling theory is used to calc...

The study of the electrical double layer lies at the heart of colloidal and interfacial science. The standard mean-field Poisson-Boltzmann (PB) theory is incapable of modeling many phenomena originated from ion correlation. An important example is charge inversion or overcharging of electrical double layers in multivalent electrolyte solutions. Existing theories aiming to include correlations cannot capture the nonmonotonic dependence of charge inversion on salt concentration...

We present a modified Poisson-Boltzmann model that adds steric repulsion of ions, providing an approximation to ion-ion correlations. Controlled by specific ion sizes, this steric contribution provides a concentration cap. Importantly, the steric contribution to the total free energy is comparable in size to the electrostatic contribution and exceeds the classical energy $1/2CV^2$. Capacitance varies non-monotonically with voltage, with a maximum near 0.2-0.3V depending on th...

This chapter deals with charged polymers (polyelectrolytes) in solution and at surfaces. The behavior of polyelectrolytes is markedly different from that of neutral polymers. In bulk solutions, i.e. disregarding the surface effect, there are two unique features to charged polymers: first, due to the presence of long-ranged electrostatic repulsion between charged monomers, the polymer conformations are much more extended, giving rise to a very small overlap concentration and h...

When ions are crowded, the effect of steric repulsion between ions (which can produce oscillations in charge density profiles) becomes significant and the conventional Poisson-Boltzmann (PB) equation should be modified. Several modified PB equations were developed but the associated total ionic charge density has no oscillation. This motivates us to derive a general model of PB equations called the PB-steric equations with a parameter $\Lambda$, which not only include the con...

When ions are crowded, the effect of steric repulsion between ions becomes significant and the conventional Poisson--Boltzmann (PB) equation (without steric effect) should be modified. For this purpose, we study the asymptotic limit of steady state Poisson--Nernst--Planck equations with steric effects (PNP-steric equations). By the assumptions of steric effects, we transform steady state PNP-steric equations into a PB equation with steric effects (PB-steric equation) which ha...

Model macroion solutions next to a charged wall show interface \textit{true overcharging}, charge reversal and inversion, and layering. Macroion layering is present, even if the wall or the macroparticle are \textit{uncharged} or if the wall and macroions are like-charged. An effective long-range attractive force between the adsorbed macroions is implied. The results are obtained through an integral equation theory and a new extended Poisson-Boltzmann theory, and are in accor...

Within the framework of a Modified Poisson-Boltzmann theory accounting for steric effects of microions, we prove analytically that the effective pair interactions between like-charge colloids immersed in a confined electrolyte are repulsive. Our approach encompasses and extends previously known results to the case of complete confinement, and further incorporates the finite size of the microions which is absent in the standard Poisson-Boltzmann theory.

Ionic solutions are often regarded as fully dissociated ions dispersed in a polar solvent. While this picture holds for dilute solutions, at higher ionic concentrations, oppositely charged ions can associate into dimers, referred to as Bjerrum pairs. We consider the formation of such pairs within the nonlinear Poisson-Boltzmann framework, and investigate their effects on bulk and interfacial properties of electrolytes. Our findings show that pairs can reduce the magnitude of ...