Ion redistribution in an electric double layer

The structure of a single flat electric double layer (EDL) is studied by grounding a symmetric electrolyte (NaCl), which is in contact with a planar positively corona-treated polypropylene film. Because the profiles of the electrostatic potential distribution and ion distribution in the solution are altered when the solution is grounded, some mobile counterions in the diffuse layer of the electrolyte solution will go into the Helmholtz layer and thus decrease the electric potential psi(a/2) at the Stern plane in order to obtain a new equilibrium. After the system is grounded for a long time, the representation of the electric double layer changes from a Stern model to a Helmholtz model. Theoretical and experimental analyses are given in this study.     

Comparing the Predictions of the Nonlinear Poisson-Boltzmann Equation and the Ion Size-Modified Poisson-Boltzmann Equation for a Low-Dielectric Charged Spherical Cavity in an Aqueous Salt Solution

The ion size-modified Poisson Boltzmann equation (SMPBE) is applied to the simple model problem of a low-dielectric spherical cavity containing a central charge, in an aqueous salt solution to investigate the finite ion size effect upon the electrostatic free energy and its sensitivity to changes in salt concentration. The SMPBE is shown to predict a very different electrostatic free energy than the nonlinear Poisson-Boltzmann equation (NLPBE) due to the additional entropic cost of placing ions in solution. Although the energy predictions of the SMPBE can be reproduced by fitting an appropriatelysized Stern layer, or ion-exclusion layer to the NLPBE calculations, the size of the Stern layer is difficult to estimate a priori. The SMPBE also produces a saturation layer when the central charge becomes sufficiently large. Ion-competition effects on various integrated quantities such the total number of ions predicted by the SMPBE are qualitatively similar to those given by the NLPBE and those found in available experimental results.     

Effect of a Dynamic Stern Layer on the Sedimentation Velocity and Potential in a Dilute Suspension of Colloidal Particles

In this paper the theory of the sedimentation velocity and potential (gradient) in a dilute suspension of charged spherical colloidal particles developed by Ohshima et al. (H. Ohshima, T. W. Healy, L. R. White, and R. W. O'Brien, J. Chem. Soc., Faraday Trans. 2, 80, 1299 (1984)) has been modified to include the presence of a dynamic Stern layer on the particle surfaces. The starting point has been the theory that Mangelsdorf and White (C. S. Mangelsdorf, and L. R. White, J. Chem. Soc., Faraday Trans. 86, 2859 (1990)) developed to calculate the electrophoretic mobility of a colloidal particle allowing for the lateral motion of ions in the inner region of the double layer (dynamic Stern layer). The effects of varying the different Stern layer parameters on the sedimentation velocity and potential are discussed and compared to the case when a Stern layer is absent. The influence of electrolyte concentration and zeta potential of the particles is also analyzed. The results show that regardless of the chosen set of Stern layer and solution parameters, the presence of a dynamic Stern layer causes the sedimentation velocity to increase and the sedimentation potential to decrease, in comparison with the standard case (no Stern layer present). These changes are almost negligible when sedimentation velocity is concerned, but they are very important when it comes to the sedimentation potential. A justification for this fact can be given in terms of an Onsager reciprocal relation, connecting the magnitudes of the sedimentation potential and the electrophoretic mobility. As previously reported, the presence of a dynamic Stern layer exerts a great influence on the electrophoretic mobility of a colloidal particle, and by means of the Onsager relation, the same is confirmed to occur when the sedimentation potential is concerned. Copyright 2000 Academic Press.     

The modelling of solvent structure in the electrical double layer

A Civilized Model electrolyte is one in which the ions and solvent molecules are regarded as distinct molecular species and treated on an equal basis. Recent efforts to use a Civilized Model to study the effects of solvent structure in the properties of the electrical double layer are discussed. By modelling the electrolyte as a simple ion-dipole mixture, it is possible to gain valuable insight in areas such as: 1) the successes and limitations of the Gouy-Chapman-Stern picture; 2) the derivation as opposed to a postulation of the Stern layer; 3) the influence of the charged surface on the magnitudes of the apparent Stern capacities (e.g. the “low” capacitances of the mercury/solution interface vs. the “high” capacitance of inorganic oxides); 4) the effect of solvent structure on the potential profile in the diffuse layer; 5) the interpretation of the electrokinetic potential; and 6) the role of solvent orientation on the x potential.     

On the relationship between charge distribution, surface hydration, and the structure of the interface of metal hydroxides

The double layer structure of metal (hydr)oxides is discussed. Charge separation may exist between the minimum distance of approach of electrolyte ions and the DDL domain. The corresponding capacitance value of the outer Stern layer is similar to the capacitance value of the inner Stern layer. The extended Stern model implicitly supports a hydration structure at the near-surface with some discrete layering of water and electrolyte ions. The significance of dipole orientation is analyzed theoretically. Dipole theory in combination with a calculated ion charge distribution is compared with the experimental overall charge distribution. Ion charge distribution for various oxyanions has been calculated applying the Brown bond valence concept to the geometry of surface complexes that have been optimized with MO/DFT calculations. The comparison is done in detail for silicic acid adsorption on goethite. In addition, results are discussed for arsenite, carbonate, sulfate, and phosphate, using the same approach. The dipole correction depends on the charge introduced in a neutral surface by ion adsorption, which differs for the various ions studied. The fractional correction factor phi derived for the experimental data agrees with the theoretical value phi(m)=0.17+/-0.02. On an absolute scale, the dipole corrections are usually limited to the range about 0-0.15 v.u. The CD values calculated with MO/DFT are not particularly sensitive (approximately 0.03 v.u.) to the precise Fe-octahedral geometry, which suggests that a calculated CD is a reasonable approximation in ion adsorption modeling for ill-defined Fe-oxides like HFO and natural Fe oxide materials of soils.     

Introducing interacting diffuse layers in TLM calculations: a reappraisal of the influence of the pore size on the swelling pressure and the osmotic efficiency of compacted bentonites

The truncation of the Gouy-Chapman diffuse part in compacted clay-rocks and bentonite is introduced into the electrical triple-layer model (TLM) recently developed by P. Leroy and A. Revil [J. Colloid Interface Sci. 270 (2004) 371]. The new model is used to explain the dependence of the osmotic efficiency and the swelling pressure as functions of the mean pore size of the medium, determined from the porosity and the specific surface. The truncation of the diffuse layer introduces a new variable in the system of equations to be solved, the electrical potential at the midplane between adjacent charged surfaces. This new variable is evaluated through a Taylor expansion of the electrical potential. The present model is able to capture the variation of the osmotic efficiency and the swelling pressure with the mean pore size. The partition of counterions between the Stern layer and the diffuse layer as a function of the pore size calculated by the TLM also shows a good consistency with the model. This implies that more than 90% of the counterions are located in the Stern layer.     

pH-Regulated nanopore conductance with overlapped electric double layers

There has been a significant growth of interest in single nanopore ionic devices that could control the transport of ions and rectify ionic current. To improve the advance of relevant nanofluidic devices, a model is derived for the first time to investigate the zeta potential and ionic conductance of a cylindrical nanopore with overlapped electric double layer as functions of pH, salt concentration as well as the Stern layer capacitance. The developed model is validated by the experimental data of the nanopore conductance. Results show that in addition to the magnitudes, the relevant behaviors of zeta potential and conductance of the nanopore might be significantly influenced by the Stern layer.     

Strong and weak points in the interpretation of colloid stability

Lyophobic dispersions can be stabilized against aggregation by electrostatic repulsion or by “steric” repulsion caused by the presence of large molecules at the interfaces. Theories of colloid stability are briefly reviewed.Strong and weak points in the present interpretations are pointed out. Two important weak points in the interpretation of electrostatic stabilization are: 1) the assumption that the zeta potential and the Stern potential are about identical, and 2) the apparent lack of influence of the particle size on the rate of slow coagulation.A list of areas where new experiments and/or further development of theories are expected to be profitable closes the paper. In several of these areas a combination of a fluid mechanical and a colloid chemical approach is called for.     

A charge-scaling implementation of the variational electrostatic projection method

Two new charge-scaling methods for efficient modeling of the solvated macromolecular environment in hybrid QM/MM calculations of biological reactions are presented. The methods are extensions of the variational electrostatic projection (VEP) method, and allows a subset of atomic charges in the external environment to be adjusted to mimic, in the active dynamical region, the electrostatic potential and field due to the large surrounding macromolecule and solvent. The method has the advantages that it offers improved accuracy, does not require the use of a three-dimensional grid or auxiliary set of fitting points, and requires only minor molecular simulation code modifications. The VEP-cs and VEP-RVM+cs methods are able to attain very high accuracy (relative force errors of 10(-7) or better with appropriate choice of control parameters), and take advantage of a recently introduced set of high-order discretization schemes and Gaussian exponents for boundary element solvation and VEP methods. The methods developed here serve as potentially powerful tools in the arsenal of computational techniques used in multiscale computational modeling problems.     

Effect of Electrolyte Concentration on the Stern Layer Thickness at a Charged Interface

The chemistry and physics of charged interfaces is regulated by the structure of the electrical double layer (EDL). Herein we quantify the average thickness of the Stern layer at the silica (SiO₂) nanoparticle/aqueous electrolyte interface as a function of NaCl concentration following direct measurement of the nanoparticles’ surface potential by X‐ray photoelectron spectroscopy (XPS). We find the Stern layer compresses (becomes thinner) as the electrolyte concentration is increased. This finding provides a simple and intuitive picture of the EDL that explains the concurrent increase in surface charge density, but decrease in surface and zeta potentials, as the electrolyte concentration is increased.     

The influence of stern layer conductance on the dielectrophoretic behavior of latex nanospheres

The influence of the Stern layer conductance on the dielectrophoretic behavior of sub-micrometer-sized latex spheres is examined. The dielectrophoretic response of the particles is measured and analyzed in terms of a model of surface conductance divided into discrete components related to the structure of the double layer. The effect of both co- and counterions in the bulk solution on the Stern layer conductance is demonstrated.     

The water-amorphous silica interface: analysis of the Stern layer and surface conduction

To explain why dynamical properties of an aqueous electrolyte near a charged surface seem to be governed by a surface charge less than the actual one, the canonical Stern model supposes an interfacial layer of ions and immobile fluid. However, large ion mobilities within the Stern layer are needed to reconcile the Stern model with surface conduction measurements. Modeling the aqueous electrolyte-amorphous silica interface at typical charge densities, a prototypical double layer system, the flow velocity does not vanish until right at the surface. The Stern model is a good effective model away from the surface, but cannot be taken literally near the surface. Indeed, simulations show no ion mobility where water is immobile, nor is such mobility necessary since the surface conductivity in the simulations is comparable to experimental values.     

Two components of boundary potentials at the lipid membrane surface: electrokinetic and complementary methods studies

Bilayer lipid membranes (BLM) are commonly used as models for cell membranes to study their interactions with inorganic ions and molecules of biological importance. In this work the principal electrostatic effects at the BLM surface are demonstrated by two methods: by the inner membrane field compensation (IFC) which is applied to planar BLM and sensitive to changes in the total boundary potential; and by electrokinetic measurements in liposome suspensions, sensitive to diffuse (surface) component of this potential. The difference in these two potentials allows us to conclude on changes in the dipole component of the boundary potential caused by structural changes at the membrane–water interface. No difference in the experimental data of both methods was observed for Be²⁺ and other divalent cation adsorption to unchanged phosphatidyl choline (PC) membranes. These data are in a good agreement with the Gouy–Champan–Stern (GCS) theory of diffuse double layer. This theory gives the value of binding constants for Be²⁺ about 400 M⁻¹ and 10⁴ M⁻¹ for DPPC liposomes in the liquid and solid states of the lipids, respectively. Clear isotope effects for normal and heavy water solutions of Be²⁺ were observed both by the electrostatic measurements and by differential scanning calorimetry. In contrast to PC, the electrostatic potentials induced by Be²⁺ and Gd³⁺ adsorption to membranes from phosphatidyiserine (PS) show the difference between the data of mentioned methods — total boundary potential changes are much higher in comparison to the surface potential. Dipole potential changes (about 150 mV) caused by changes in PS head group orientation may be more important in this specific case.     

Effects of Stern layer conductance on electrokinetic energy conversion in nanofluidic channels

A thermo-electro-hydro-dynamic model is developed to analytically account for the effects of Stern layer conductance on electrokinetic energy conversion in nanofluidic channels. The optimum electrokinetic devices performance is dependent on a figure of merit, in which the Stern layer conductance appears as a nondimensional Dukhin number. Such surface conductance is found to significantly reduce the figure of merit and thus the efficiency and power output. This finding may explain why the recently measured electrokinetic devices performances are far below the theoretical predictions where the effects of Stern layer conductance have been ignored.     

The electrical double layer of micelles in ionic surfactant solutions in the presence of a background electrolyte: 1. Diluted micellar solutions of sodium dodecyl sulfate

The structure of the electrical double layer (EDL) of micelles in dilute micellar solutions in the presence of a background electrolyte is studied within the framework of the Gouy-Chapman-Stern theory. On the basis of the Stern isotherm for counterion adsorption, conditions of electroneutrality, and the Gauss condition at the interface between the diffuse and dense parts of EDL, three equations are derived for the electrostatic potentials of the surface of micelle cores and the diffuse part of EDL as well as for the potential of the specific adsorption of counterions. Model parameters are verified by the example of sodium dodecyl sulfate (SDS). Potentials of the diffuse part of EDL, the degree of binding of counterions with micelles, and the specific adsorption potential are calculated from the experimental data on the potential of the surface of SDS micelle cores and their sizes, critical micellization concentration, aggregation numbers, and the constants of premicellar association. The specific adsorption potential of SDS is found to be ?(4.6 ± 0.1)?, where ? is the product of Boltzmann’s constant and absolute temperature. The specific adsorption potential is independent of the background electrolyte concentration, remains constant within the determination error of the parameters, and substantially contributes to the formation of EDL of micelles.     

Dielectrophoretic behavior of latex nanospheres: low-frequency dispersion

The electrostatic manipulation of nanoparticles using nonuniform electric fields (dielectrophoresis) has proved a useful method of investigating the movement of charge around colloidal particles. While previous work has explained many of the ways in which particle behavior deviates from that predicted by classical Maxwell-Wagner interfacial polarization theory, there exists an additional, anomalous polarization mechanism observed in media of high conductivity, causing an unexpected observation of positive dielectrophoresis. Here this is suggested that this may be explained in terms of the polarization of the Stern layer.     

The conditions governing the specific adsorption of counter-ions in the interaction of two parallel plate-like colloidal particles

Frens and Overbeek have proposed that during the Brownian collision of two colloidal particles in a hydrophobic sol, the surface charge density due to potential-determining (p.d.) ions remains virtually unchanged. It is argued here that the cause of this behaviour is the low concentration of p.d. ions in the diffuse layer. However, equilibrium can be maintained with respect to counter-ions adsorbed into the Stern region from the supporting electrolyte, because the concentration of such electrolyte in the dispersion medium is considerably greater than that of p.d. ions.A general expression is quoted from earlier work for the electric double layer interaction between two parallel plate-like particles in the case where surface charge due to p.d. ions is fixed, but where counter-ions adsorbed into the Stern region can equilibrate with ions of the same species in the diffuse layer. Incorporating discreteness-of-charge and ion-size effects into the adsorption isotherm of the counter-ions, the double layer interaction energy of the two plates is calculated at contact of the two outer Helmholtz planes (o.h.p.'s). It is shown that although this energy exceeds the classical expression obtained by assuming the potential at the o.h.p. to be independent of plate separation, it remains finite.     

Computational study of the structure and behavior of aqueous mixed system sodium unsaturated carboxylate-dodecyltrimethylammonium bromide

The mixed surfactant system sodium 10-undecenoate (SUD)-dodecyltrimethylammonium bromide (DTAB) was studied by computational simulation to determine the composition and structure of the mixed microstructures. Results were contrasted with experimental data obtained from literature and our own laboratory. The modelization predicts spherical or cylindrical micelles with a preferential composition of SUD-DTAB of about 1:2, while the system predicts a lamellar structure with a proportion of 1:1 when SUD is replaced by the saturated soap sodium undecanoate. The model also predicts the deep inclusion of bromide ions in the micelle Stern layer. All predictions were in agreement with previous experimental results.     

The Dielectrophoretic Behavior of Submicron Latex Spheres: Influence of Surface Conductance

An analysis of the dielectrophoretic crossover frequency as a function of medium conductivity has been made for submicron spheres with different surface functionalities. It is shown that the AC electrokinetic behavior of the particles can be explained by modeling the surface conductivity of the particle as the sum of two surface conductance components: one due to charge motion behind the slip plane (the Stern layer) and the other due to charge motion in front of the slip plane.