Titratable macroions in multivalent electrolyte solutions: Strong coupling dressed ion approach

Electrostatic interactions between charge regulated spherical macroions

We study the interaction between two charge regulating spherical macroions with dielectric interior and dissociable surface groups immersed in a monovalent electrolyte solution. The charge dissociation is modelled via the Frumkin-Fowler-Guggenheim isotherm, which allows for multiple adsorption equilibrium states. The interactions are derived from the solutions of the mean-field Poisson-Boltzmann type theory with charge regulation boundary conditions. For a range of conditions we find symmetry breaking transitions from symmetric to asymmetric charge distribution exhibiting annealed charge patchiness, which results in like-charge attraction even in a univalent electrolyte-thus fundamentally modifying the nature of electrostatic interactions in charge-stabilized colloidal suspensions.

Charge regulation of a surface immersed in an electrolyte solution

In this paper, we investigate theoretically a model of charge regulation of a single charged planar surface immersed in an aqueous electrolyte solution. Assuming that the adsorbed ions are mobile in the charged plane, we formulate a field theory of charge regulation where the numbers of adsorbed ions can be determined consistently by equating the chemical potentials of the adsorbed ions to that of the ions in the bulk. We analyze the mean-field treatment of the model for electrolyte of arbitrary valences, and then beyond, where correlation effects are systematically taken into account in a loop expansion. In particular, we compute exactly various one-loop quantities, including electrostatic potentials, ion distributions, and chemical potentials, not only for symmetric (1, 1) electrolyte but also for asymmetric (2, 1) electrolyte, and make use of these quantities to address charge regulation at the one-loop level. We find that correlation effects give rise to various phase transitions in the adsorption of ions, and present phase diagrams for (1, 1) and (2, 1) electrolytes, whose distinct behaviors suggest that charge regulation, at the one-loop level, is no longer universal but depends crucially on the valency of the ions.

Interactions between zwitterionic membranes in complex electrolytes

We investigate the electrostatic interactions of zwitterionic membranes immersed in mixed electrolytes composed of mono- and multivalent ions. We show that the presence of monovalent salt is a necessary condition for the existence of a finite electrostatic force on the membrane. As a result, the mean-field membrane pressure originating from the surface dipoles exhibits a nonuniform salt dependence, characterized by an enhancement for dilute salt conditions and a decrease at intermediate salt concentrations. On addition of multivalent cations to the submolar salt solution, the separate interactions of these cations with the opposite charges of the surface dipoles makes the intermembrane pressure more repulsive at low membrane separation distances and strongly attractive at intermediate distances, resulting in a discontinuous like-charge binding transition followed by the membrane binding transition. By extending our formalism to account for correlation corrections associated with large salt concentrations, we show that membranes of high surface dipole density immersed in molar salt solutions may undergo a membrane binding transition even without the multivalent cations. Hence, the tuning of the surface polarization forces by membrane engineering can be an efficient way to adjust the equilibrium configuration of dipolar membranes in concentrated salt solutions.

Like-charge polymer-membrane complexation mediated by multivalent cations: One-loop-dressed strong coupling theory

We probe the electrostatic mechanism driving adsorption of polyelectrolytes onto like-charged membranes upon the addition of tri- and tetravalent counterions to a bathing monovalent salt solution. We develop a one-loop-dressed strong coupling theory that treats the monovalent salt at the electrostatic one-loop level and the multivalent counterions within a strong-coupling approach. It is shown that the adhesive force of the multivalent counterions mediating the like-charge adsorption arises from their strong condensation at the charged membrane. The resulting interfacial counterion excess locally maximizes the screening ability of the electrolyte and minimizes the electrostatic polymer grand potential. This translates into an attractive force that pulls the polymer to the similarly charged membrane. We show that the high counterion valency enables this adsorption transition even at weakly charged membranes. Additionally, strongly charged membranes give rise to monovalent counterion-induced correlations and intensify the interfacial multivalent counterion condensation, strengthening the complexation of the polymer with the like-charged membrane, as well as triggering the orientational transition of the molecule prior to its adsorption. Finally, our theory provides two additional key features as evidenced by previous adsorption experiments: first, the critical counterion concentration for polymer adsorption decreases with the rise of the counterion valency and, second, the addition of monovalent salt enhances the screening of the membrane charges and suppresses monovalent counterion correlations close to the surface. This weakens the interfacial multivalent counterion condensation and results in the desorption of the polymer from the substrate.

An improved theory of the electric conductance of ionic solutions based on the concept of the ion-atmosphere's smaller-ion shell

Although the electric conductivity of ionic solutions is of great importance in science and technology, complete understanding of the physical factors and principles underlying ion and charge transport in solution has so far been missing. The Debye-Hückel-Onsager (DHO) theory of the equivalent ionic conductivity (λi for single ion i, Λ for a binary electrolyte) is a limiting law of only a few electrolyte valence families, and its extension to solution of finite concentration has not been entirely successful; at most, it has led to semiempirical expressions of λi or Λ vs. concentration (c), incorporating adjustable parameters of no clear physical meaning. Improving the description of the ion atmosphere and including in the conductivity model the smaller-ion shell (SiS) of this atmosphere (D. Fraenkel, Mol. Phys., 2010, 108, 1435) allow now an extension of the DHO theory to a "DHO-SiS" theory that offers analytic expressions for λi and Λ as a function of c without adjustable parameters. The fit with experiment is very good, often excellent, for many electrolytes of the various valence families. λi values can be converted to single-ion activity coefficients, γis, suggesting that the latter ionic factors do have physical validity, contrary to what many literature sources claim. Together with the recently proposed theory of the limiting conductivities, λ0i and Λ0 (D. Fraenkel, Mol. Phys., 2018, 116, 2271), the new theory offers a simple and comprehensive ion conductivity treatment that improves upon existing theoretical treatments, with λi and Λ expressed by ionic sizes instead of λ0i and Λ0.

Interactions between charged particles with bathing multivalent counterions: experiments vs. dressed ion theory

We compare the recent experimentally measured forces between charged colloidal particles, as well as their effective surface potentials (surface charge) in the presence of multivalent counterions in a bathing monovalent salt solution, with the predictions of the dressed ion theory of strongly charged colloidal systems. The benchmark for comparison is provided by the DLVO theory and the deviations from its predictions at small separations are taken as an indication of the additional non-DLVO attractions that can be fitted by an additional phenomenological exponential term. The parameters characterizing this non-DLVO exponential term as well as the dependencies of the effective potential on the counterion concentration and valency predicted by the dressed ion theory are well within the experimental values. This suggests that the deviations from the DLVO theory are probably caused by ion correlations as formalized within the dressed ion theory.