The effects of ionic valency and size asymmetry on counterion adsorption

TL;DR

This study investigates how ionic size and valency asymmetry influence counterion adsorption near charged surfaces, deriving analytical models and revealing saturation and layering phenomena in ionic solutions.

Contribution

It provides a generalized Grahame equation and analytical concentration profiles accounting for size and valency asymmetry, extending classical electrostatic models.

Findings

Concentration profiles saturate at high surface charge and large ionic size.

Layered ionic structures form near the surface based on valency-to-size ratio.

Crossover from dilute to saturated regimes depends on surface charge and size asymmetry.

Abstract

We study the effect of asymmetry in solvent and ionic size on the equilibrium properties of multivalent ionic solutions near a charged surface. For a single ionic species in solution, we derive a generalized Grahame equation at the charged surface. For general size ratio between the ions and the solvent, we obtain analytical results for the concentration profiles as a function of the distance from the surface. For weak surface charge and small ion-to-solvent size ratio, the profile follows the classical Poisson-Boltzmann equation in dilute solution conditions. However, for high surface charge and large ionic size, the concentration profile saturates near the surface, leading to distinctive dependencies of the solution properties on the surface charge density and size asymmetry. Furthermore, the crossover between dilute and saturated regimes depends on the surface charge and ionic size asymmetry. We suggest that a solution containing multiple ionic species of different valencies and sizes stratifies close to the surface in the saturation regime. This leads to the formation of layers that are ordered according to the ions' valency-to-size ratio.