Effect of ion solvation on the diffuse layer structure in mixed electrolytes

A “solvionic” model of a multicomponent electrochemical system (mixed electrolyte) is considered. An ion in the solution is considered as a point charge rigidly fixed inside its solvation shell. The corresponding equations for the diffuse layer on an ideally polarizable electrode are derived, and an effective method of their numerical solution is formulated. The calculations are performed in order to follow the changes in the diffuse layer structure with variations in the electrode charge and electrolyte composition. Far from the zerocharge potential of solution, the dependences of distributions of solution components over the diffuse layer on the electrode charge radically differ from those within the classic Gouy-Chapman theory. Analytical equations (asymptotics at large electrode charges) for concentrations of solvated ions in the plane of their maximum approach and for their “surface excesses” (diffuse adsorption) are determined. Results of numerical calculations for a 0.2 M LiCl + 0.05 M BaCl₂ solution are plotted.     

Chemico-electromechanical coupling in microporous media

We determine the macroscopic transport properties of isotropic microporous media by volume-averaging the local Nernst-Planck and Navier-Stokes equations in nonisothermal conditions. In such media, the excess of charge that counterbalances the charge deficiency of the surface of the minerals is partitioned between the Gouy-Chapman layer and the Stern layer. The Stern layer of sorbed counterions is attached to the solid phase, while the Gouy-Chapman diffuse layer is assumed to have a thickness comparable to the size of the pores. Rather than using Poisson-Boltzmann distributions to describe the ionic concentrations in the pore space of the medium, we rely on Donnan distributions obtained by equating the chemical potentials of the water molecules and ions between a reservoir of ions and the pore space of the medium. The macroscopic Maxwell equations and the macroscopic linear constitutive transport equations are derived in the vicinity of equilibrium, assuming that the porous material is deformable. In the vicinity of thermodynamic equilibrium, the cross-coupling phenomena of the macroscopic constitutive equations of transport follow Onsager reciprocity. In addition, all the material properties entering the constitutive equations depend only on two textural properties, the permeability and the electrical formation factor.     

Series approach to modeling ion size effects for asymmetric electrolytes in the diffuse double layer

The theory of the diffuse layer for asymmetric electrolytes is reconsidered with emphasis on the effects of ion size on the diffuse layer potential drop and differential capacity. For asymmetric 2:1 and 1:2 electrolytes, this potential drop is expressed in terms of a polynomial with a linear, quadratic, and cubic term in the corresponding estimate in the Gouy-Chapman theory. Optimal polynomial coefficients and model validation for 2:1 electrolytes are provided by least-squares regression of Monte Carlo data obtained for a restricted electrolyte in a primitive solvent. These coefficients are then expressed as simple functions of the parameters commonly associated with the mean spherical approximation. The series approach accurately describes potential drops and differential capacities of the diffuse layer for 2:1 and 1:2 electrolytes for the chosen assumptions.     

Series approach to modeling ion size effects for symmetric electrolytes in the diffuse double layer

An analytical model is developed for the potential drop and differential capacity across the diffuse layer which considers the effects of ion size on these properties. For symmetric electrolytes, this potential drop is expressed in terms of a cubic polynomial in the corresponding estimate in the Gouy-Chapman theory. Optimal polynomial coefficients and model validation for 1:1 and 2:2 electrolytes are provided by fits of Monte Carlo data obtained for a restricted electrolyte in a primitive solvent. Simple relationships between these coefficients and parameters commonly associated with the mean spherical approximation are obtained. It is shown that the series approach accurately describes potential drops and differential capacities of the diffuse layer for 1:1 and 2:2 electrolytes for the chosen assumptions.     

An approach to the method for determination of surface potential on solid/liquid interface: theory

The electrochemical properties on solid particle surfaces in an aqueous system have found wide application in many fields. However, for some of them there are no reliable methods of determination. What is particularly worth mentioning is the surface potentials of solid particles. Though this is a most important property and a most basic parameter in colloid interface electrochemistry, no reliable method for its determination is available yet. In the present paper, based on the diffuse double-layer theory, mathematical relations are constructed between the average concentration of ions positively adsorbed in the diffuse double layer and the surface potential of solid particles, thus transforming the determination of surface potential of solid particles into that of the average concentration of ions in the diffuse double layer, and then by applying the standard relationships of Gouy-Chapman theory, the mathematical relations of the average concentration of ions in the diffuse double layer with surface charge density, electrical field strength at surface, and specific surface area of solid particles are constructed.     

The double layer and ion adsorption at the interface between two non miscible solutions: Part I. Interfacial tension measurements for the water-nitrobenzene tetraalkylammonium bromide systems

The classical treatment of the double layer has been extended to the interface between two immiscible solutions. The model presented is composed of an inner compact layer, characterized by a dipolar potential drop, between two diffuse type layers. The systems studied are composed of C₂ to C₅ quaternary ammonium bromides at partition equilibrium between water and nitrobenzene for which the inner potential difference, for a given electrolyte, is independent, at least in the lower concentration range, of the concentration. Drop weight interfacial measurements and the use of the Gouy-Chapman approach show that the tetraethyl-, tetrapropyl- and tetrabutylammonium ions are not adsorbed within the inner compact layer, and the dipolar potential drop of this layer can then be determined. Tetrapentylammonium ions on the contrary are specifically adsorbed but the amount of adsorbed ions within the compact inner layer cannot be evaluated because of the impossibility, in this case, of determining the dipolar potential drop.     

Hydrolysis versus ion correlation models in electrokinetic charge inversion: establishing application ranges

In this article, we investigate experimentally a wide range of situations where charge inversion (i.e., overcompensation of the surface charge of a colloidal particle by the countercharge) can occur. To that end, the electrophoretic mobility of sodium montmorillonite, silica, and polystyrene latex as functions of pH and concentration of different salts is presented, and conditions are established where charge inversion occurs. The reason for this study is to provide experimental evidence for distinguishing between two existing models for the explanation of charge inversion. One of these is the specific adsorption of ions located in the Stern layer in combination with a Gouy-Chapman diffuse part of the double layer. The other ion-correlation theories explain the phenomenon in terms of purely physical arguments based on Coulombic pair interactions between ions and surface charges and on excluded volume effects. In distinguishing between these two interpretations, the influence of the pH plays a central role because of its effect on the hydrolysis of multivalent cations. In our experiments, it is found that although 1-2 and 2-2 electrolytes provoke a decrease in the absolute values of the electrophoretic mobilities when their concentration in solution is increased, they never lead to charge inversion, whatever the surface charge or the pH. However, in the case of salts of trivalent cations, electrokinetic charge reversal is often observed above a certain critical electrolyte concentration. In addition, the extent of overcharging increases when the concentration is raised above the critical value. This trend occurs for any system in which the surface charge is pH-independent, as in polystyrene latex and montmorillonite. Most of the results presented here are compatible with the specific adsorption of hydrolyzed metal ions as the main driving force for charge inversion. At low pH, when the hydrolysis of trivalent cations is likely to be absent, overcharging can be attributed to ion correlation effects.     

Inner- and outer-sphere complexation of ions at the goethite-solution interface

Formation of inner- and outer-sphere complexes of environmentally important divalent ions on the goethite surface was examined by applying the charge distribution CD model for inner- and outer-sphere complexation. The model assumes spatial charge distribution between the surface (0-plane) and the next electrostatic plane (1-plane) for innersphere complexation and between the 1-plane and the head end of the diffuse double layer (2-plane) for the outersphere complexation. The latter approach has been used because the distance of closest approach to a charged surface may differ for different ions. The surface structural approach implies the use of a Three-Plane model for the compact part (Stern layer) of solid-solution interface, which is divided into two layers. The thickness of each layer depends on the capacitance and the local dielectric constant. The new approach has been applied to describe the adsorption of magnesium, calcium, strontium, and sulfate ions. It is shown that the concept can successfully describe the development of surface charge in the presence of Ca(+2), Mg(+2), Sr(+2), and SO4(-2) as a function of loading, pH, and salt level, and also the shift in the isoelectric point (IEP) of goethite. The CD modeling revealed that, for the conditions studied, magnesium is mainly adsorbed as a bidentate innersphere complex, calcium can be a combination of bidentate innersphere and a monodentate inner- or outer-sphere complexes, and strontium is probably adsorbed as an outersphere complex. Sulfate is present as a mixture of inner- and outer-sphere monodentate complexes. Outersphere complexation is less pH dependent than innersphere complexation. The CD model predicts that the outersphere complexation of divalent cations and anions is relatively favorable at respectively low and high pH. Increase of ion loading favors the formation of innersphere complexes.     

On the effects of ion-wall chemical association on the electric double layer: a density functional approach for the restricted primitive model at a charged wall

We describe a density functional theory for the restricted primitive model of ionic fluid at a charged wall with active sites to which ions can bond. The theory is an extension of our recent approach [Pizio et al., J. Chem. Phys. 121, 11957 (2004)] and is focused in the effects of specific adsorption of ions on the wall, besides the electrostatic phenomena. In order to solve the problem, we use the first-order thermodynamic perturbation theory of chemical association developed by Wertheim [J. Chem. Phys. 87, 7323 (1987)]. The microscopic structure of the electric double layer and the amount of adsorbed charge are investigated. Also, the temperature dependence of capacitance is analyzed. The capacitance depends on the kind of ions that form associative bonds with the surface sites and is determined by a net charge acting on the diffuse layer. The shape of the temperature dependence of capacitance essentially depends on the association energy and the density of bonding sites.     

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.     

Charge dependence of adsorption energy of ions at electrodes

Analysis of the energetic and geometric characteristics of the inner part of the electrical double layer has been carried out in the presence of the specific adsorption of ions accompanied by change in the dimensions and dielectric properties of the inner layer. On the basis of the formulae for the electrochemical potential of the adsorbed ion on the electrode surface and for the components of the inner layer capacity, the equations of the Frumkin isotherm and of its parameters have been derived. It has been shown that, in general, the Frumkin isotherm is non-linear at the given electrode charge and the charge dependence of the adsorption equilibrium constant has a parabolic form. The results of the corresponding theoretical calculations have been compared with the experimental data obtained by the study of the specific adsorption of tetra-alkylammonium cations on a bismuth electrode in ethanolic and aqueous solutions. Good agreement of the experimental results with those calculated theoretically confirm the validity of the equations derived.     

The electrical double layer for a fully asymmetric electrolyte around a spherical colloid: an integral equation study

The hypernetted chain/mean spherical approximation (HNC/MSA) integral equation for a totally asymmetric primitive model electrolyte around a spherical macroparticle is obtained and solved numerically in the case of size-asymmetric systems. The ensuing radial distribution functions show a very good agreement when compared to our Monte Carlo and molecular-dynamics simulations for spherical geometry and with respect to previous anisotropic reference HNC calculations in the planar limit. We report an analysis of the potential versus charge relationship, radial distribution functions, mean electrostatic potential, and cumulative reduced charge for representative examples of 1:1 and 2:2 salts with a size-asymmetry ratio of 2. Our results are collated with those of the modified Gouy-Chapman (MGC) and unequal radius modified Gouy-Chapman (URMGC) theories and with those of HNC/MSA in the restricted primitive model (RPM) to assess the importance of size-asymmetry effects. One of the most striking characteristics found is that, contrary to the general belief, away from the point of zero charge the properties of an asymmetric electrical double layer (EDL) are not those corresponding to a symmetric electrolyte with the size and charge of the counterion, i.e., counterions do not always dominate. This behavior suggests the existence of a new phenomenology in the EDL that genuinely belongs to a more realistic size-asymmetric model where steric correlations are taken into account consistently. Such novel features cannot be described by traditional mean-field theories such as MGC, URMGC, or even by enhanced formalisms, such as HNC/MSA, if they are based on the RPM.     

Revelation of Nonideal Properties of the Diffuse Layer Near the Surface of a Charged Electrode

It is shown that the charge dependence of the difference between reciprocal differential capacitances for two La₂(SO₄)₃concentrations at the same charge qreliably reveals that properties of the diffuse layer at |q| of 1 to 2 C/cm²are not ideal. Experimental values of the capacitance of Hg, Tl–Ga, and Cd–Ga electrodes in La₂(SO₄)₃aqueous solutions suggest that this phenomenon is adequately described by the Gonzalez–Sanz theory, which links activity coefficients of ions in the diffuse layer with the average stoichiometric activity coefficient in the electrolyte and the electrode charge.     

Viscoelasticity in the diffuse electric double layer

The electroacoustical impedance of the quartz crystal microbalance (QCM) in contact with aqueous electrolyte solutions was measured using the transfer function method in a flow injection system . Measurements of both components of the impedance of the QCM, the resistance R and the inductive reactance XL, have been performed for modified and bare gold and silver surfaces and for different concentrations of several aqueous electrolyte solutions. For the experimental concentration range of 0-50 mM, unexpectedly the QCM impedance does not follow the Kanazawa equation, as is usual for bulk newtonian liquids. This behavior indicates the presence of a nanometric sized viscoelastic layer between the piezoelectric crystal and the bulk electrolyte solution. This layer can only be identified as the Gouy-Chapman diffuse double layer (DDL). Its elasticity and viscosity have been estimated by the measurement of R and XL. The viscoelasticity of the DDL appears to be independent of the chemical nature of the surface and of the solution viscosity but strongly dependent on the surface charge, the bulk electrolyte concentration and the dielectric constant of the solvent.     

Assessment of ion size effects in the diffuse double layer with use of an integral equation approach

An analytical expression is developed for the potential drop across the diffuse layer phi(d) in terms of a cubic polynomial in the corresponding estimate in the Gouy-Chapman approximation, phi(d)(GC). The coefficients of this polynomial are defined in terms of the MSA volume fraction eta and the reciprocal distance parameter Gamma. The resulting expression is shown to describe the Monte Carlo estimates of phi(d) obtained in a primitive level simulation of diffuse layer properties.     

Accounting for diffuse layer ions in triple-layer models

The triple-layer model is one of the most widely used surface complexation models for adsorption on mineral surfaces. In current implementations, the accounting of ions in the diffuse layer may be neglected, resulting in a charge imbalance in the modeled solution as well as errors in mass balance, particularly in low ionic strength solutions when mineral-specific surface area is large. This paper introduces an internally consistent scheme for modeling diffuse layer ions in the triple-layer model. Model calculations illustrate the difference between the proposed and previous implementations using an idealized example. The guarantee of charge balance on both sides of the interface assures that pH is accurately modeled. This may be important in reactive transport simulations, such as modeling adsorption in low ionic strength variable charge soil solutions.     

A new generalization of the standard electrokinetic model

We present a new generalization of the standard electrokinetic model based on the assumption that there is a thin layer surrounding the suspended particle where the equilibrium ion density is not determined by the Gouy-Chapman distribution, while the standard model applies outside this layer. Our approach differs from existing models in that we consider that the surface layer is made both of free ions (mostly counterions) and of the fixed ions that constitute the charge of the particle. Furthermore, the free ion density is determined by appropriate boundary conditions without considering any adsorption isotherms. Finally, the fluid is allowed to freely flow inside the layer, only hindered by the presence of the fixed charges and the adhesion condition on the surface of the particle. We show that this generalization leads to results that qualitatively differ from those obtained using existing models: instead of always decreasing, the electrophoretic mobility can actually increase with the anomalous surface conductivity. This could make it possible to use our model for the interpretation of a broader set of experimental data, including those cases when the measured mobility is higher than predicted by the standard model.     

"中性"粘土矿物对非水溶液中有机碱的吸附

理想品格中无同晶转换，因而不带层电行的中性粘土矿物（即：1：1型的高岭石，板状蛇纹石和2：1型的叶蜡石，滑石）对非极性有机溶剂中有机碱（偶氮苯化合物，pKa＝1.5-5.0）的吸附等温线均属于Langmuir型，且吸附在矿物表面的有机碱均由其碱型变为酸型.偶氮苯化合物的pKa越大，被吸附的量越多在溶剂为正己烷和二硫化碳时粘土的吸附能力比溶剂为苯时高.这些结果说明不带层电行的粘土矿物表面存在着酸位.蒙脱石的酸位数量明显地储存于阳离子种类，但在Na＋、Ca2＋、Mg2＋饱和的条件下高岭石的改位数量几乎相同.随着相对湿度的增加;两矿物对甲基黄的吸附量均减少，但减少的方式明显不同、因此1：1型高岭石和2：1型叶蜡石一样，也具有与蒙脱石不同的表面酸性起源。