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.     

Diffusiophoresis of charged particles and diffusioosmosis of electrolyte solutions

A review is presented on the theoretical basics and recent developments about the diffusiophoresis of charged particles and diffusioosmosis of electrolyte solutions driven by imposed electrolyte concentration gradients with particular emphasis on the principal analytical formulas and their physical interpretations. For diffusiophoresis, migrations of particles with thin polarized electric double layers but arbitrary zeta potentials and with arbitrary double layers but relatively low surface potentials are both discussed in detail, covering not only diffusiophoresis of single particles but also their motions near solid boundaries or other particles. For diffusioosmosis, fluid flows along single plane walls, in micro/nano-channels, and in porous media are considered, in which the solid walls may have arbitrary zeta potentials or surface charge densities, and both the effect of the lateral distribution of the diffuse ions and the relaxation effect in the double layers on the tangential electric field induced by the prescribed electrolyte concentration gradient are included.     

Application of the method of images on electrostatic phenomena in aqueous Al2O3 and ZrO2 suspensions

A new solution for the Poisson equation for the diffuse part of the double layer around spherical particles will be presented. The numerical results are compared with the solution of the well-known DLVO theory. The range of the diffuse layer differs considerably in the two theories. Also, the inconsistent representation of the surface and diffuse layer charge in the DLVO theory do not occur in the new theory. Experimental zeta potential measurements were used to determine the charge of colloidal Al2O3 and ZrO2 particles. It is shown that the calculated charge can be interpreted as a superposition of independent H+ and OH- adsorption isotherms. The corresponding Langmuir adsorption isotherms are taken to model the zeta potential dependence on pH. In the vicinity of the isoelectric point the model fits well with the experimental data, but at higher ion concentrations considerable deviations occur. The deviations are discussed. Furthermore, the numerical results for the run of the potential in the diffuse part of the double layer were used to determine the electrostatic interaction potential between the particles in correlation with the zeta potential measurements. The corresponding total interaction potentials, including the van der Waals attraction, were taken to calculate the coagulation half-life for a suspension with a particle loading of 2 vol%. It is shown that stability against coagulation is maintained for Al2O3 particles in the pH region between 3.3 and 7 and for ZrO2 only around pH 5. Stability against flocculation can be achieved in the pH regime between 4.5 and 7 for Al2O3, while the examined ZrO2 particles are not stable against flocculation in aqueous suspensions.     

Stability of nanodispersions: a model for kinetics of aggregation of nanoparticles

In the course of aggregation of very small colloid particles (nanoparticles) the overlap of the diffuse layers is practically complete, so that one cannot apply the common DLVO theory. Since nanopoarticles are small compared to the extent of the diffuse layer, the process is considered in the same way as for two interacting ions. Therefore, the Br?nsted concept based on the Transition State Theory was applied. The charge of interacting nanoparticles was calculated by means of the Surface Complexation Model and decrease of effective charge of particles was also taken into account. Numerical simulations were performed using the parameters for hematite and rutile colloid systems. The effect of pH and electrolyte concentration on the stability coefficient of nanosystems was found to be more pronounced but similar to that for regular colloidal systems. The effect markedly depends on the nature of the solid which is characterized by equilibrium constants of surface reactions responsible for surface charge, i.e., by the point of zero charge, while the specificity of counterions is described by their association affinity, i.e., by surface association equilibrium constants. The most pronounced is the particle size effect. It was shown that extremely small particles cannot be stabilized by an electrostatic repulsion barrier. Additionally, at the same mass concentration, nanoparticles aggregate more rapidly than ordinary colloidal particles due to thier higher number concentration.     

Planar electric double layer for a restricted primitive model electrolyte at low temperatures

Monte Carlo simulation and the modified Poisson-Boltzmann theory are used to investigate the planar electric double layer for a restricted primitive model electrolyte at low temperatures. Capacitance as a function of temperature at low surface charge is determined for 1:1, 2:2, 2:1, and 3:1 electrolytes. Negative adsorption can occur for 1:1 electrolytes at low surface charge with low electrolyte concentration. The 1:1 electrolyte diffuse layer potential as a function of surface charge displays a maximum at low densities. At high densities, the diffuse layer potential is negative with a negative slope. The Gouy-Chapman-Stern theory fails in this low-temperature regime, whereas the modified Poisson-Boltzmann theory is fairly successful in this regard.     

Static electrification of solid oxide in liquid metal and electrical double layer at the interface

Static electrification of a solid oxide, say a semiconducting oxide in liquid metal, is mainly due to electron transfer between two phases. Excess electrons in the liquid metal phase provided by the oxide give rise to an electrical double layer at the interface. The electrical double layer may be divided into three parts, an immobile inner layer, a compressed diffuse layer, and a flat layer extending into the bulk liquid metal. Differential potential analysis and the induced emf method were used to measure the potential of the compressed diffuse layer and the excess electron density of the flat layer, respectively. Results show that most oxides in liquid metals carry positive charges on their surfaces and the potentials of the compressed diffuse layer are in the range of 3 to 42 microV. Such a low potential implies that the diffuse layer is considerably compressed. The excess electron densities of the flat layer are on the order of 10(22) electrons/m(3) of Hg and their contributions to surface charges of oxide are in the range of 10(17) to 10(18) charges/m(2) for the oxide/mercury systems with a solid density of 0.3 wt% at room temperature.     

Modification of Surface Forces by Metal Ion Adsorption

Abstract

Sorption of ions may lead to variations in interparticle forces and, thus, changes in the stability of colloidal particles. Chemical interactions between metal ions and colloidal particles modify the molecular structure of the surface, the surface charge, and the electrical potential between colloidal particles. These modifications to the surface and to the electrical double layer due to metal ion sorption are reflected in the interaction force between a particle and another surface, which is measured in this study by atomic force microscopy (AFM). Specifically, AFM is used to investigate the sorption of copper ions from aqueous solutions by silica particles. The influence of metal ion concentration and solution ionic strength on surface forces is studied under transient conditions. Results show that as the metal ion concentration is decreased, charge reversal occurs and a longer period of time is required for the system to reach equilibrium. The ionic strength has no significant effect on sorption kinetics. Furthermore, neither metal concentration nor ionic strength exhibits any effect on sorption equilibria, indicating that for the experimental conditions used in this study, the surface sites of the silica particle are fully occupied by copper ions.     

Mechanisms behind concentration profiles illustrated by charge and concentration distributions around ions in double layers

The mechanisms behind the behaviour of concentration and charge density profiles in diffuse electric double layers are investigated quantitatively for 1:1 and 2:2 electrolytes. This is done by analysing various contributions to the mean force that acts on each ion. The forces are obtained from the calculated ionic charge and concentration distributions around individual ions at various positions in the double layer. These distributions are presented graphically which allows an immediate visual illustration of the mechanisms in action. Some features studied are charge inversion in double layers for divalent aqueous electrolytes, overcompensation of surface charge due to large amounts of physisorbed counterions, ion size effects in the double layer structure and various mechanisms that cause deviations from the predictions of the Poisson–Boltzmann approximation. A major objective of the paper is to present the results in a visual form and explain aspects of modern double layer theory in a simple manner.     

330 - Determination of surface charge of bilayer lipid membranes

The determination of the membrane surface charge is based on the measurement of the surface potential difference at both sides of the bilayer lipid membrane (BLM) connected with the asymmetrical concentration of the electrolyte in both solutions. In the short-circuit regime the intramembrane potential jump is caused by the difference in the two surface potentials. In order to find the intramembrane potential jump the BLM capacitance dependence on voltage was used. In some range of electrolyte concentrations a dependence of the potential jump on the surface charge was found. The charge density was calculated by applying the Gouy-Chapman theory of the diffuse double layer. Surface charges were determined for BLM of common bovine brain lipids, phosphatidylethanolamine, dioleyllecithin and azolectine.     

Non-equilibrium electric surface phenomena

Non-equilibrium aspects of traditional electrokinetic phenomena (electrophoresis, electroosmosis, streaming potential, sedimentation potential), electrostatic interaction of particles and new electrokinetic phenomena are considered. The significance of non-equilibrium electric surface phenomena for many major areas of modern colloid science (characterization of colloids, membrane science, transport phenomena and separation, particle interaction and coagulation) is established.The study of non-equilibrium electric surface phenomena is connected with the validation of the standard electrokinetic model (SEM), the development of a non-standard model and the development of an extensive programme of disperse system characterization based on integrated electrokinetic investigations. Experimental and theoretical studies of systems with a smooth, non-porous impermeable surface (mica in Anderson's experiments, and quartz microcapillaries with a molecule-smooth surface in Churaev's experiments) have shown that usually there are no significant difficulties in interpreting electrokinetic investigations despite the possible anomaly in the water structure near the surface and the possibility of maximum shear stress (yield stress), i.e. the anomalous viscosity and decreased dissolving power with respect to ions. However, systems which do not satisfy the conditions of the SEM are widely distributed, owing to the porosity, roughness or permeability of the boundary layer of the surface of the solid body which simultaneously belongs to the solid and liquid phases. In this layer, enclosed between the outer Helmholtz plane and the slipping plane, the motion of the liquid strongly slows down and the tangential flow of ions is characterized purely by the mobility which is close to the normal. Thus, a general property of a non-standard electrokinetic model is the presence of an anomalous (additional) surface conductivity in excess of the surface conductivity determined according to Bikerman's equation based on the ζ -potential alone.Confidence in modelling the electrokinetic phenomena has grown with the development of methods for modifying the surface such that its properties approach those of the SEM (Bijsterbosch and co-workers; Saville and co-workers).Extension of the particle characterization concept requires the measurement of both the mobile charge and the electrokinetic charge and from this an estimate of the thickness of the additional conductivity zone can be made. With the additional measurement of a titratable charge, it is possible to estimate the ion distribution between the dense and diffuse parts of the double layer (DL) and to estimate the decreased mobility of ions in the Stern layer or in the immobilized part of the DL.Quantitative laws governing the interaction of particles and corresponding to the non-standard model substantially differ from the traditional laws described by the DVLO theory as applied to the SEM. This is also true for adsorption properties which are characterized without sufficient reason by means of the ζ-potential. Therefore both the development of models of interaction and adsorption of ions, allowing for the non-standard electrokinetic model, and the extension of the particle characterization programme to integrated investigations of electric surface phenomena are required.Further generalization of the theory of electrokinetic phenomena is achieved. In addition to the surface charge another variety of surface force can be the origin of the electrokinetic phenomena.     

THEORETICAL MODELING OF IONIC SURFACTANT ADSORPTION ON MINERAL OXIDE SURFACES

A model for the adsorption of ionic surfactants on oppositely charged solid surfaces of uniform charge density is developed. The model is based on the assumption that, on the solid surface, adsorbed surfactant monomers, monolayered and bilayered surfactant aggregates of different sizes and specifically adsorbing ions of added electrolyte constitute a mixture of hard discs. It means that only excluded area interactions between the surface discs are taken into account. To avoid a rapid two-dimensional condensation of the adsorbed surfactant the potential energy per molecule in the surface aggregates, which is a sum of chemical and electrostatic interactions, is assumed to decrease linearly with the increasing aggregate size. The electrostatic interactions of ionic species with the charged solid surface are described in terms of the Guy-Chapman theory of the double layer formation. The appropriate equations for adsorption isotherms of surfactant and electrolyte ions are derived and used to predict the experimental adsorption isotherms of DTAB on the precipitated silica at two different salt concentrations in the aqueous solution, On the basis of the obtained results the evolution of the adsorbed phase structure and the charge of silica particles with an increasing surface coverage is discussed.     

Mathematical model of electromigration allowing the deviation from electroneutrality

The structure of the double layer on the boundary between solid and liquid phases is described by various models, of which the Stern–Gouy–Chapman model is still commonly accepted. Generally, the solid phase is charged, which also causes the distribution of the electric charge in the adjacent diffuse layer in the liquid phase. We propose a new mathematical model of electromigration considering the high deviation from electroneutrality in the diffuse layer of the double layer when the liquid phase is composed of solution of weak multivalent electrolytes of any valence and of any complexity. The mathematical model joins together the Poisson equation, the continuity equation for electric charge, the mass continuity equations, and the modified G-function. The model is able to calculate the volume charge density, electric potential, and concentration profiles of all ionic forms of all electrolytes in the diffuse part of the double layer, which consequently enables to calculate conductivity, pH, and deviation from electroneutrality. The model can easily be implemented into the numerical simulation software such as Comsol. Its outcome is demonstrated by the numerical simulation of the double layer composed of a charged silica surface and an adjacent liquid solution composed of weak multivalent electrolytes. The validity of the model is not limited only to the diffuse part of the double layer but is valid for electromigration of electrolytes in general.     

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.     

Foam films stabilized by dodecyl maltoside. 1. Film thickness and free energy of film formation

Foam films stabilized by a sugar-based nonionic surfactant, beta-dodecyl maltoside, are investigated. The film thickness and the film contact angle (which is formed at the transition between the film and the bulk solution) are measured as a function of NaCl concentration, surfactant concentration, and temperature. The film thickness measurements provide information about the balance of the surface forces in the film whereas the contact angle measurements provide information about the specific film interaction free energy. The use of the glass ring cell and the thin film pressure balance methods enables studies under a large variety of conditions. Thick foam films are formed at low electrolyte concentration. The film thickness decreases (respectively the absolute value of the interaction film free energy increases) with the increase of the electrolyte concentration according to the classical DLVO theory. This indicates the existence of a repulsive double layer electrostatic component of the disjoining pressure. An electrostatic double layer potential of 16 mV was calculated from the data. A decrease of the film thickness on increase of the surfactant concentration in the solution is observed. The results are interpreted on the basis of the assumption that the surface double layer potential originates in the adsorption of hydroxyl ions at the film surfaces. These ions are expelled from the surface at higher surfactant concentration.     

Sedimentation of a concentrated dispersion of composite colloidal particles

The sedimentation of a concentrated spherical dispersion of composite particles, where a particle comprises a rigid core and a membrane layer containing fixed charge, is investigated theoretically. The dispersion is simulated by a unit cell model, and a pseudo-spectral method based on Chebyshev polynomials is adopted to solve the problem numerically. The influences of the thickness of double layer, the concentration of particles, the surface potential of the rigid core of a particle, and the amount of fixed charge in the membrane layer on both the sedimentation potential and the sedimentation velocity are discussed. Several interesting results are observed; for example, depending upon the charged conditions on the rigid core and in the membrane layer of a particle, the sedimentation potential might have both a local maximum and a local minimum and the sedimentation velocity can have a local minimum as the thickness of double layer varies. Also, the sedimentation velocity can have a local maximum as the surface potential varies. We show that the sedimentation potential increases with the concentration of particles. The relation between the sedimentation velocity and the concentration of particles, however, depends upon the thickness of double layer.     

The temperature effect on electrokinetic properties of the silica–polyvinyl alcohol (PVA) system

The influence of polyvinyl alcohol (PVA) adsorption on the structure of the diffuse layer of silica (SiO₂) in the temperature range 15–35 °C was examined. The microelectrophoresis method was used in the experiments to determine the zeta potential of the solid particles in the absence and presence of the polymer. The adsorption of PVA macromolecules causes the zeta potential decrease in all investigated SiO₂ systems. Moreover this, decrease is the most pronounced at the highest examined temperature. Obtained results indicate that the conformational changes of adsorbed polymer chains are responsible for changes in electrokinetic properties of silica particles. Moreover, the structure of diffuse layer on the solid surface with adsorbed polymer results from the following effects: the presence of acetate groups in PVA chains, the blockade of silica surface groups by adsorbed polymer and the shift of slipping plane due to macromolecules adsorption.     

Polarization of a diffuse soft particle subjected to an alternating current field

The polarization of a diffuse soft particle submerged in an aqueous electrolyte and subjected to a uniform alternating electric field is theoretically analyzed with the standard electrokinetic model (the Poisson-Nernst-Planck equations). The particle consists of a rigid uncharged core and a charged diffuse polyelectrolytic shell (soft layer) permeable to ions and solvent. Our focus is on the impact of the characteristics of the soft layer including the Donnan potential, the soft layer thickness, and the friction coefficient of the soft layer on the dipole coefficient, characterizing the strength of the polarization. Under the limits of thin double layers and thin polyelectrolytic shells, approximate analytical expressions to evaluate the dipole moment coefficients are derived for high-frequency and low-frequency ranges, respectively. The analytical results are compared and agree favorably with those numerically computed by the standard model. Interestingly, we discover that when the double layer is comparable to the soft layer the dipole moment behaves qualitatively differently at different Donnan potentials. When the Donnan potential is small, the dipole moment decreases as the double layer increases. In contrast, at large Donnan potentials, the dipole moment increases with the increase in the double layer. The distinct responses to Donnan potentials are attributed to the impact of the associated double layer on the charge distribution of mobile ions inside the soft layer. The theoretical model provides a fundamental basis for interpreting the polarization of heterogeneous systems, including environmental or biological colloids or microgel particles.     

Ionic liquid ion sources: suppression of electrochemical reactions using voltage alternation

The problem of electrochemical decomposition due to extraction of single polarity ions from a novel ionic liquid ion source (ILIS) is solved by periodically alternating the voltage source so that the potential difference that appears across the double layer formed between the emitter conductive material and the liquid is maintained below the electrochemical window limit, thus eliminating electronic reactions. The ionic liquid EMI-BF(4) is used to externally wet a solid tungsten emitter, establishing a physical boundary with a certain liquid-metal contact area. Theoretical and experimental evidence suggests that this area is close to the effective surface involved in the double layer charging dynamics. The extent of this surface is relatively large, thus increasing the net capacitance and consequently the double layer charging time, demonstrating that low frequency voltage alternation of the order of 1 Hz is enough to obtain clean and reliable ion emission.     

Studies of the coagulation of lyophobic sols by „neutralising“ ions

The slow coagulation of lyophobic sols by electrolytes that may reduce the surface potential by precipitating, chelating or neutralising the adsorbed peptising ion, is described; and the experimental results are explained by an extension of the earlier relations derived from theVerwey-Overbeek theory of stability. Low concentrations of electrolyte—up to ten per cent of the final coagulation value—mainly reduce the stability of dialysed sols by compression of the double layer, while further addition leads to a rapid fall in stability due to reduction of the surface potential. The coagulation of undialysed sols is mainly caused by reduction of surface potential at all concentrations of electrolyte. The coagulation of undialysed sols by precipitating, etc. electrolytes may be equated to the removal of a corresponding amount of the adsorbed peptising ions; and the final coagulation value (for rapid coagulation) then approximately measures the total peptising ion concentration.     

The sedimentation potential in a dilute suspension

During the sedimentation of charged particles immersed in an ionic solution, a gradient of electric potential forms. The gradient reflects the surface potential of the particles, moderated by the screening effect of the diffuse charge. In the theory developed here the fact that the net current is zero is used to derive an expression for the gradient which is free of ambiguities associated with the shape of the averaging volume, one of the shortcomings of the previous theory. The general expression also differs from those derived by previous investigators who summed the dipole fields for each particle, a procedure which leads to expressions that fail to satisfy the constraint on the current. The effect of the macroscopic field on the sedimentation velocity is found to be significant when the double layer is thick. Changes in the sedimentation coefficient are also reflected in the Brownian diffusivity of suspended particles but here the effect appears less significant.