Insights from Monte Carlo simulations on charge inversion of planar electric double layers in mixtures of asymmetric electrolytes

Abstract

Monte Carlo simulations of a planar negatively charged dielectric interface in contact with a mixture of 1:1 and 3:1 electrolytes are carried out using the unrestricted primitive model under more realistic hydrated ion sizes. Two typical surface charge densities are chosen to represent the systems from the weak to strong coupling regimes. Our goal is to determine the dependence of the degree of charge inversion on increasing concentration of both mono- and trivalent salts and to provide a systematic study on this peculiar effect between short-range and electrostatic correlations. The numerical results show that addition of monovalent salt diminishes the condensation of trivalent counterions due to either the favorable solvation energy or the available space constraints. As the concentration of trivalent salt increases, on the other hand, the inclusion of the ionic size and size asymmetry results in a damped oscillatory charge inversion at low enough surface charge and another counterintuitive surface charge amplification. It is proposed that both of the anomalous events in the weak coupling regime are thought to be entropic in origin which is completely different from the electrostatic driven charge inversion in the strong coupling regime. In addition, the electrostatic images arising from the dielectric mismatch lead to a decaying depletion effect on the structure of double layer with growing salt concentration in the case of low charged interface but have no effect at high surface charge values. The microscopic information obtained here points to the need for a more quantitative theoretical treatment in describing the charge inversion phenomenon of real colloidal systems.

Structure of the nanobubble clusters of dissolved air in liquid media

“…This leads to the situation when the value of e |Q(r)| /εrkT becomes smaller than unity for large values of (r − R) and, hence, the density ρ(r) of the screening ionic charge for such values of (r − R) should be described by the Debye-Huckel law, i.e., should be ∼ (1/r) exp [−κ (r − R)], where κ is defined by (30). On the other hand, in accordance with numerical simulations [106][107][108], the decrease in ρ(r) for small values of (r − R) must be much more rapid, but smooth. On the basis of these two features of the behavior of density ρ(r), our model of screening stems from the representation of ρ(r) in the entire range of (r − R) in the form…”

“…It is important that the sign reversal of charge Q(r) always occurs not jump-wise, as follows from the concepts of the formation of a two-dimensional liquid formed by the basic ions and counter-ions, but as a result of a smooth approaching Q(r) to zero for r → R + r, where r is the scale of considerable decrease in the volume density of counter-ions near the particle surface (in the immediate vicinity of the surface their density is maximal, but finite). Thus, the results of [106][107][108] indicate that, first, the inversion effect is indeed of the threshold type with respect to the parameter B. Second, the charge inversion occurs not at the particle surface proper, but as a result of a gradual mixing of counter-ions with basic ions upon an increase in (r − R).…”

“…Note that qualitatively similar results are summarized in Refs. [107,108], but in these works the authors considered the planar negatively charged surface. It is important that the sign reversal of charge Q(r) always occurs not jump-wise, as follows from the concepts of the formation of a two-dimensional liquid formed by the basic ions and counter-ions, but as a result of a smooth approaching Q(r) to zero for r → R + r, where r is the scale of considerable decrease in the volume density of counter-ions near the particle surface (in the immediate vicinity of the surface their density is maximal, but finite).…”

“…5 The total charge Q(r) and the charge density ρ(r) in the liquid surrounding the bubston of radius R. The bubston charge Q 0 is negative. The curve for Q(r) was modeled to have the same form as the corresponding graphs for the symmetric 1: 1 electrolyte solution in works [106][107][108] the remaining part of this distribution (r < a c ) is spherically symmetric as before. Such a pattern is widely used in theoretical treatment of electrophoresis, see, e.g., [109].…”

“…According to the results obtained by these authors, the screening of the inverted charge can be successfully described on the basis of the Poisson-Boltzmann equation. An important step in explaining the details of the charge inversion effect were the publications [106][107][108], which described the results of numerical calculating aimed at the study of the structure of the screening ionic shell of a strongly charged macro-particle in an aqueous salt solution. For instance, in the study [106] a strongly charged macroparticle (a macro-ion) with the charge |Q 0 | = 20e, and the binary (Z: Z = 2: 2 or 1: 1) ionic salt solution were analyzed.…”