The non-dominance of counterions in charge-asymmetric electrolytes: non-monotonic precedence of electrostatic screening and local inversion of the electric field by multivalent coions

Abstract

The asymptotic convergence of the thermodynamic and structural properties of unequally-sized charge-symmetric ions in strong electric fields was postulated more than thirty years ago by Valleau and Torrie as the dominance of counterions via the non-linear Poisson–Boltzmann theory [Valleau and Torrie, J. Chem. Phys., 1982, 76, 4623]. According to this mean field prescription, the properties of the electrical double layer near a highly charged electrode immersed in a size-asymmetric binary electrolyte converge to those of a size-symmetric electrolyte if the properties of counterions are the same in both instances. On the other hand, some of the present authors have shown that, in fact, counterions do not dominate the electrical properties of a spherical macroion in the presence of unequally-sized ions, symmetric in valence, if ion correlations and ionic excluded volume effects are taken into account consistently. These ingredients are neglected in the classical Poisson–Boltzmann picture. In the present work, we show the occurrence of the non-dominance of counterions in the opposite scenario, that is, when ions are equally-sized but asymmetric in valence. This is performed in the presence of highly charged colloidal surfaces of spherical and planar geometries for different ionic volume fractions. In addition to the phenomenon of non-dominance of counterions, our simulations and theoretical data also exhibit a non-monotonic order or precedence in the mean electrostatic potential, or electrostatic screening, at the Helmholtz plane of a charged colloid. This interesting behaviour is analyzed as a function of the coion's valence, the ionic volume fraction, and the charge and size of the colloidal particle. All these phenomena are explained in terms of the decay of the electric field near the colloidal surface, and by the appearance of a local inversion of both the electric field and the integrated surface charge density of the colloidal particle in the presence of monovalent counterions and multivalent coions.