Impact of Head Group Charges, Ionic Sizes, and Dielectric Images on Charge Inversion: A Monte Carlo Simulation Study

Debye-Hückel Free Energy of an Electric Double Layer with Discrete Charges Located at a Dielectric Interface

Poisson-Boltzmann theory provides an established framework to calculate properties and free energies of an electric double layer, especially for simple geometries and interfaces that carry continuous charge densities. At sufficiently small length scales, however, the discreteness of the surface charges cannot be neglected. We consider a planar dielectric interface that separates a salt-containing aqueous phase from a medium of low dielectric constant and carries discrete surface charges of fixed density. Within the linear Debye-Hückel limit of Poisson-Boltzmann theory, we calculate the surface potential inside a Wigner-Seitz cell that is produced by all surface charges outside the cell using a Fourier-Bessel series and a Hankel transformation. From the surface potential, we obtain the Debye-Hückel free energy of the electric double layer, which we compare with the corresponding expression in the continuum limit. Differences arise for sufficiently small charge densities, where we show that the dominating interaction is dipolar, arising from the dipoles formed by the surface charges and associated counterions. This interaction propagates through the medium of a low dielectric constant and alters the continuum power of two dependence of the free energy on the surface charge density to a power of 2.5 law.

On the physics of both surface overcharging and charge reversal at heterophase interfaces

A series of Monte Carlo simulations are employed to reveal the physics of both surface overcharging and charge reversal at a negatively charged dielectric interface exposed to a bulk solution containing a +2:−1 electrolyte in the absence and presence of a monovalent salt.

Electrically Polarized Biomaterials

Electrically polarized biomaterials and their interactions with the surrounding biological environment is important for understanding the host response, growth and inhibition of biological species as well as the long-term fate and performance of the implants. Polarized materials possess electrical charges at the surface due to polar or electret properties. As these surfaces are at the frontier of biological reactions understanding biological interactions at the interface with polarized biomaterials requires a convergence of understanding multiple disciplines. This article discusses progress that has taken place in the fields of surface and interface science, materials science and biomedical device engineering to obtain a better perspective of such interactions.

Charge reversal at a planar boundary between two dielectrics

Despite the ubiquitous character and relevance of the electric double layer in the entire realm of interface and colloid science, very little is known of the effect that surface heterogeneity exerts on the underlying mechanisms of ion adsorption. Herein, computer simulations offer a perspective that, in sharp contrast to the homogeneously charged surface, discrete groups promote multivalent counterion binding, leading to charge reversal but possibly having not a sign change of the electrophoretic mobility. Counterintuitively, the introduction of dielectric images yields a significantly greater accumulation of counterions, which further facilitates the magnitude of charge reversal. The reported results are very sensitive to both the degree of ion hydration and the representation of surface charges. Our findings shed light on the mechanism for charge reversal over a broad range of coupling regimes operating the adsorption of counterions through surface group bridging attraction with their own images and provide opportunities for experimental studies and theoretical development.

Suppression and promotion of charge inversion in the presence of multivalent coions

We report charge inversion using Monte Carlo calculations for a negatively charged surface in aqueous solutions involving coions of different charges and monovalent counterions. It is shown that a rise in the valence of coions at moderate concentrations can substantially promote charge inversion for the surface charge values of biological relevance, regardless of the representation of surface charges but dependent in a nontrivial way on polarization effects resulting from dielectric discontinuity. These obtained characteristics challenge the traditional belief that the coions are generally considered to suppress charge inversion and expose the important role of coions of higher valence in tailoring the effective interactions of biomolecules with the cell membrane.

Self-energy-modified Poisson-Nernst-Planck equations: WKB approximation and finite-difference approaches

We propose a modified Poisson-Nernst-Planck (PNP) model to investigate charge transport in electrolytes of inhomogeneous dielectric environment. The model includes the ionic polarization due to the dielectric inhomogeneity and the ion-ion correlation. This is achieved by the self energy of test ions through solving a generalized Debye-Hückel (DH) equation. We develop numerical methods for the system composed of the PNP and DH equations. Particularly, toward the numerical challenge of solving the high-dimensional DH equation, we developed an analytical WKB approximation and a numerical approach based on the selective inversion of sparse matrices. The model and numerical methods are validated by simulating the charge diffusion in electrolytes between two electrodes, for which effects of dielectrics and correlation are investigated by comparing the results with the prediction by the classical PNP theory. We find that, at the length scale of the interface separation comparable to the Bjerrum length, the results of the modified equations are significantly different from the classical PNP predictions mostly due to the dielectric effect. It is also shown that when the ion self energy is in weak or mediate strength, the WKB approximation presents a high accuracy, compared to precise finite-difference results.

Electrostatic interaction in the presence of dielectric interfaces and polarization-induced like-charge attraction

Electrostatic polarization is important in many nano- and micro-scale physical systems such as colloidal suspensions, biopolymers, and nanomaterials assembly. The calculation of polarization potential requires an efficient algorithm for solving 3D Poisson's equation. We have developed a useful image charge method to rapid evaluation of the Green's function of the Poisson's equation in the presence of spherical dielectric discontinuities. This paper presents an extensive study of this method by giving a convergence analysis and developing a coarse-graining algorithm. The use of the coarse graining could reduce the number of image charges to around a dozen, by 1-2 orders of magnitude. We use the algorithm to investigate the interaction force between likely charged spheres in different dielectric environments. We find the size and charge asymmetry leads to an attraction between like charges, in agreement with existing results. Furthermore, we study three-body interactions and find, in the presence of an external interface, that the interaction force depends on the curvature of the interface and performs a nonmonotonic electrostatic force.

Computational evidence of two driving mechanisms for overcharging in an electric double layer near the point of zero charge

We have adopted an ensemble Monte Carlo simulation method to systematically verify two physical driving mechanisms responsible for overcharging which refers to the adsorption of an effective charge onto a like-charged planar surface around the point of zero charge within the primitive model of mixed electrolytes with varying salt concentrations. One is electrostatic in character dominated by dielectric images and the other is purely entropic in origin by ionic size asymmetry effects, of which the former has never been reported both theoretically and experimentally and the latter could be interpreted satisfactorily in terms of available theoretical approaches. The electrostatically driven mechanism is found to critically depend on the ionic sizes while the entropically driven mechanism occurs with almost the same efficiency in a relative wide range of surface charge density. Depending on the delicate interplay between charge and steric correlations, the two distinct driving mechanisms may cooperatively give rise to a more pronounced overcharging process.

Simulation of an electrical double layer model with a low dielectric layer between the electrode and the electrolyte

We report Monte Carlo simulation results for double layers of 1:1 and 2:1 electrolytes near an electrode with an inner layer that has a dielectric constant, ε(2), smaller than that of the electrolyte, ε(3). The electrolyte is modeled in the implicit solvent framework (primitive model), while the electrode is a metal electrode in this study (ε(1) → ∞). The charged hard sphere ions are not allowed to enter into the inner layer. We show that the capacitance of the inner layer is C(δ) = ε(0)(ε(2) + ε(3))/2δ, where δ is the thickness of the inner layer. This result is different from that obtained from solutions of the Poisson-Boltzmann equation (ε(0)ε(2)/δ), indicating that interpretation of experimental data with a fitted ε(2) dielectric constant of the inner layer must be done using a different equation. We also show that the properties of the diffuse layer are not independent of the value of ε(2), which is a usual assumption of the Poisson-Boltzmann theory. This is mainly because the repulsive image charges repel both the counterions and the co-ions, while the electrode charge attracts the counterions and repels the co-ions.

Dressed counterions: polyvalent and monovalent ions at charged dielectric interfaces

We investigate the ion distribution and overcharging at charged interfaces with dielectric inhomogeneities in the presence of asymmetric electrolytes containing polyvalent and monovalent ions. We formulate an effective "dressed counterion" approach by integrating out the monovalent salt degrees of freedom and show that it agrees with results of explicit Monte Carlo simulations. We then apply the dressed counterion approach within the framework of the generalized strong-coupling theory, valid for polyvalent ions at low concentrations, which enables an analytical description for salt effects as well as dielectric inhomogeneities in the limit of strong Coulomb interactions. Limitations and applicability of this theory are examined by comparing the results with simulations.