Theoretical description of the electrical double layer for a mixture of n ionic species with arbitrary size and charge asymmetries. I. Spherical geometry

Abstract

In this work, we propose a theoretical finite element description of the ionic profiles of a general mixture of n species of spherical charged particles dissolved in an implicit solvent, with arbitrary size and charge asymmetries, neutralizing a spherical macroion. This approach aims to close the gap between the nano- and the micro-scales in macroion solutions, taking into account the ion correlations and ionic excluded volume effects consistently. When these last two features are neglected, the classical non-linear Poisson–Boltzmann theory for n ionic species—with different ionic closest approach distances to the colloidal surface—is recovered as a limit case. As a proof of concept, we study the electrical double layer of an electroneutral mixture of oppositely charged colloids and small microions, with an asymmetry 1:333 in size and 1:10 in valence, in salt-free and added salt environments. Our theoretical approach displays a good agreement regarding the ionic profiles, the integrated charge, and the mean electrostatic potential obtained from molecular dynamics simulations with explicit-sized microions. Although the non-linear Poisson–Boltzmann colloid–colloid and colloid–microion profiles differ notably from those obtained via molecular dynamics simulations with explicit small-sized ions, the associated mean electrostatic potential agrees well with the corresponding explicit microion simulations.

Application of the symmetric Poisson–Boltzmann theory to a model colloidal mixture

“…SPB calculations were carried out at the parameters of the HNC/MSA study and MD simulations of Elisea-Espinoza et al 23 for a PM colloidal system. The details of the SPB calculation are given in ref.…”

“…10,29. Two systems were considered by Elisea-Espinoza et al , 23 (i) a 4 component system of two colloid species and their respective counterions and (ii) a 6 component system, being the previous system (i) with a supporting electrolyte. The description of the different components is given in Table 1, and the values of T and ε r are 298 K and 78.5 respectively.…”

“…A suitable 4- or 6-species model to compare with has been recently studied by Elisea-Espinoza, Gonzalez-Tovar and Guerrero-García. 23 They have considered a molecular dynamics (MD) simulation and hypernetted chain/mean spherical approximation (HNC/MSA) study of a 4 component PM mixture of 2 colloids plus their counterions, and with an additional supporting aqueous electrolyte, a 6-component mixture. Their paper has provided us with a chance to compare our SPB structural properties with simulation and HNC/MSA predictions of a 4- or 6-component system.…”

“…Their paper has provided us with a chance to compare our SPB structural properties with simulation and HNC/MSA predictions of a 4- or 6-component system. This work of Elisea-Espinoza et al 23 is important in the sense of it using both simulation and theory to calculate the structural properties of colloidal mixtures up to 6 components. A drawback is that only very low concentrations of the colloid and salt were treated.…”

“…A brief resume of the techniques used to solve the equations numerically is also given. In Section 3 details of the SPB predicted structures of the 4 or 6-component colloidal systems and a comparative assessment of the same vis-à-vis the MD simulation data 23 are given. Finally in Section 4 some concluding remarks are made.…”