RESUMO

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.

Assuntos

Coloides , Eletricidade , Íons , Eletricidade Estática , Solventes

RESUMO

The capacitive compactness has been introduced very recently [G. I. Guerrero-García et al., Phys. Chem. Chem. Phys. 20, 262-275 (2018)] as a robust and accurate measure to quantify the thickness, or spatial extension, of the electrical double layer next to either an infinite charged electrode or a spherical macroion. We propose here an experimental/theoretical scheme to determine the capacitive compactness of a spherical electrical double layer that relies on the calculation of the electrokinetic charge and the associated mean electrostatic potential at the macroparticle's surface. This is achieved by numerically solving the non-linear Poisson-Boltzmann equation of point ions around a colloidal sphere and matching the corresponding theoretical mobility, predicted by the O'Brien and White theory [J. Chem. Soc., Faraday Trans. 2 74, 1607-1626 (1978)], with experimental measurements of the electrophoretic mobility under the same conditions. This novel method is used to calculate the capacitive compactness of NaCl and CaCl2 electrolytes surrounding a negatively charged polystyrene particle as a function of the salt concentration.

RESUMO

The spatial extension of the ionic cloud neutralizing a charged colloid or an electrode is usually characterized by the Debye length associated with the supporting charged fluid in the bulk. This spatial length arises naturally in the linear Poisson-Boltzmann theory of point charges, which is the cornerstone of the widely used Derjaguin-Landau-Verwey-Overbeek formalism describing the colloidal stability of electrified macroparticles. By definition, the Debye length is independent of important physical features of charged solutions such as the colloidal charge, electrostatic ion correlations, ionic excluded volume effects, or specific short-range interactions, just to mention a few. In order to include consistently these features to describe more accurately the thickness of the electrical double layer of an inhomogeneous charged fluid in planar geometry, we propose here the use of the capacitive compactness concept as a generalization of the compactness of the spherical electrical double layer around a small macroion (González-Tovar et al., J. Chem. Phys. 2004, 120, 9782). To exemplify the usefulness of the capacitive compactness to characterize strongly coupled charged fluids in external electric fields, we use integral equations theory and Monte Carlo simulations to analyze the electrical properties of a model molten salt near a planar electrode. In particular, we study the electrode's charge neutralization, and the maximum inversion of the net charge per unit area of the electrode-molten salt system as a function of the ionic concentration, and the electrode's charge. The behaviour of the associated capacitive compactness is interpreted in terms of the charge neutralization capacity of the highly correlated charged fluid, which evidences a shrinking/expansion of the electrical double layer at a microscopic level. The capacitive compactness and its first two derivatives are expressed in terms of experimentally measurable macroscopic properties such as the differential and integral capacity, the electrode's surface charge density, and the mean electrostatic potential at the electrode's surface.

RESUMO

The current rectification displayed by solid-state p-n semiconductor diodes relies on the abundance of electrons and holes near the interface between the p-n junction. In analogy to this electronic device, we propose here the construction of a purely ionic liquid-state electric rectifying heterojunction displaying an excess of monovalent cations and anions near the interface between two immiscible solvents with different dielectric properties. This system does not need any physical membrane or material barrier to show preferential ion transfer but relies on the ionic solvation energy between the two immiscible solvents. We construct a simple device, based on an oil/water interface, displaying an asymmetric behavior of the electric current as a function of the polarity of an applied electric field. This device also exhibits a region of negative differential conductivity, analogous to that observed in brain and heart cells via voltage clamp techniques. Computer simulations and mean field theory calculations for a model of this system show that the application of an external electric field is able to control the bulk concentrations of the ionic species in the immiscible liquids in a manner that is asymmetric with respect to the polarity or direction of the applied electric field. These properties make possible to enhance or suppress selective ion transport at liquid-liquid interfaces with the application of an external electric field or electrostatic potential, mimicking the function of biological ion channels, thus creating opportunities for varied applications.

RESUMO

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.