Sedimentation of a charged colloidal sphere in a charged cavity

An analytical study is presented for the quasisteady sedimentation of a charged spherical particle located at the center of a charged spherical cavity. The overlap of the electric double layers is allowed, and the polarization (relaxation) effect in the double layers is considered. The electrokinetic equations that govern the ionic concentration distributions, electric potential profile, and fluid flow field in the electrolyte solution are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved for a symmetric electrolyte with the surface charge densities of the particle and cavity as the small perturbation parameters. An analytical expression for the settling velocity of the charged sphere is obtained from a balance among the gravitational, electrostatic, and hydrodynamic forces acting on it. Our results indicate that the presence of the particle charge reduces the magnitude of the sedimentation velocity of the particle in an uncharged cavity and the presence of the fixed charge at the cavity surface increases the magnitude of the sedimentation velocity of an uncharged particle in a charged cavity. For the case of a charged sphere settling in a charged cavity with equivalent surface charge densities, the net effect of the fixed charges will increase the sedimentation velocity of the particle. For the case of a charged sphere settling in a charged cavity with their surface charge densities in opposite signs, the net effect of the fixed charges in general reduces/increases the sedimentation velocity of the particle if the surface charge density of the particle has a greater/smaller magnitude than that of the cavity. The effect of the surface charge at the cavity wall on the sedimentation of a colloidal particle is found to increase with a decrease in the particle-to-cavity size ratio and can be significant in appropriate situations.     

The interpretation of solution electrolyte vibrational bands in potential-difference infrared spectroscopy

The influence of ionic migration to and from the surrounding solution reservoir upon potential-difference infrared (PDIR) spectra is examined for some cases involving anionic adsorption in order to elucidate its consequences upon the net potential-induced compositional changes in the thin-layer solution. Representative PDIR spectra for the adsorption of azide anions on gold are compared in the absence and presence of excess alkali perchlorate supporting electrolyte. In the latter, the loss of solution azide in the spectral thin layer upon stepping to a more positive potential, resulting from increased azide adsorption, is accompanied by extensive migration of perchlorate into the thin layer. The form of the spectra induced by potential-dependent azide specific adsorption differs in these two circumstances since in the former the ionic migration between the thin-layer cavity and the solution reservoir necessary for charge compensation is provided by the azide electrolyte itself, whereas in the latter case migration of the supporting electrolyte yields a fixed quantity of azide in the thin layer. The intensities and sign of the PDIR bands arising from solution-phase azide and perchlorate enable the extent of the potential-dependent anionic redistribution in the thin-layer cavity to be quantified. In the absence of added perchlorate, the magnitude of the solution azide band is diminished substantially, inferring that replenishment of the thin-layer solution concentration occurs predominantly via N⁻₃ migration from the surrounding solution reservoir. Similar results were also obtained for cyanate adsorption on gold. The influence of cation as well as anion migration on this thin-layer charge redistribution was examined by employing an infrared-active cation, NH⁺₄, as well as from the addition of H₃O⁺. While the results indicate that cation migration can contribute substantially to this charge redistribution, anion migration typically appears to predominate when specific anion adsorption is encountered. Some general consequences of such ion migration effects to the interpretation of PDIR spectra are noted.     

Electrophoresis of soft particles with charged rigid core coated with pH-regulated polyelectrolyte layer

We present a theoretical study on the electrophoresis of a soft particle with a dielectric charged rigid core grafted with a charge-regulated polyelectrolyte layer. The polyelectrolyte layer possesses either an acidic or a basic functional group and the charge dissociation depends on the local pH and ionic concentration of the electrolyte. The dielectric rigid core is considered to possess a uniform volumetric charge density. The electric potential distribution is determined by computing the Poisson-Boltzmann equation outside the core coupled with a Poisson equation inside the impermeable core along with suitable matching conditions at the core-shell interface. The computed electric field is used to determine the mobility of the particle through an existing analytic expression based on the Debye-Huckel approximation. Our results are found to be in good agreement with the existing solutions for the limiting cases. The influence of the core charge density, ionic concentration, and pH of the electrolyte on the particle mobility is studied for different choice of hydrodynamic penetration length of the polyelectrolyte and dissociation constant of the functional group. The critical value of the pH required to achieve zero mobility is estimated. We find that in a monovalent electrolyte solution, the soft particle with a net negative (positive) charge can have positive (negative) mobility.     

Electrokinetic ion transport in confined micro‐nanochannel

In this paper, a confined micronanochannel is presented to concentrate ions in a restricted zone. A general model exploiting the Poisson–Nernst–Plank equations coupled with the Navier–Stokes equation is employed to simulate the electrokinetic ion transport. The influences of the micronanochannel dimension and the surface charge density on the potential distribution, the ion concentration, and the fluid flow are investigated. The numerical results show that the potential drop depends mainly on the nanochannel, instead of the confined channel. Both decreasing the width and increasing the length enhance the ion enrichment performance. For a given nanochannel, ultimate value of ion concentration may be determined by the potential at the center point of the nanochannel. The study also shows that the enrichment stability can be improved by increasing the micronanochannel width, decreasing the micronanochannel length and reducing the surface charge density.     

Electrostatic contribution to the ion solvation energy: cavity effects

Ion solvation process has been analysed for the spherically symmetrical system where an ion is located inside a cavity surrounded by an isotropic nonlocal dielectric medium. It has been proven that for any dielectric properties of the medium, the electric field outside the cavity as well as the ion solvation energy depend only on the total ion charge but not of the particular distribution of the ion charge density inside the cavity. These characteristics remain unchanged if the charge is displaced from the external boundary of the cavity into it. Analytical formulas for them have been derived for a particular model of the nonlocal dielectric function. Comparison of results for the solvation energy on the basis of this new theory and of the conventional approach (disregarding the existence of the cavity) shows a significant difference between their predictions if the ion charge is displaced inside the ion cavity.     

Note on nonaqueous electrokinetic transport in charged porous media

A model for electrokinetic transport in charged capillaries is compared with experiments using nonaqueous lithium chloride solutions. The electrokinetic parameters considered are the pore fluid conductivity and the concentration potential. Methanol/water mixtures were the solvent, and track-etched mica membranes with a well-characterized pore structure were the porous medium. The electrolyte concentrations used were such that the Debye lengths of solutions in pores ranged from much smaller to much larger than the radius of pores. The space-charge model is found to be capable of qualitatively describing the trend of the electrokinetic data, but as expected, at higher concentrations the model fails, probably because the assumption that ion—ion interactions are negligible no longer holds. The experimental results show that the pore fluid conductivity depends strongly on the dielectric constant of the solvent, that the absolute value of the pore wall charge tends to decrease with the lowering of the solvent dielectric constant, and that the wall charge tends to increase with the concentration of the chloride ion.     

Titanium Dioxide/Electrolyte Solution Interface: Electron Transfer Phenomena

Electron transfer between a titanium dioxide/electrolyte solution interface has been studied. As found by other researchers of similar interfaces (TiO(2)- and ZnO-electrolyte solution), a slow consumption of OH(-) ions takes place in this type of interface. A theoretical model has been developed for calculating the change in the Fermi energy of both electrolyte solution and semiconductor, showing that ion consumption from the solution is favoured by the decrease of the difference between their Fermi energies. A kinetic constant (upsilon) is found to characterise the consumption process, its value increasing with electrolyte and semiconductor mass concentrations. Furthermore, this process may be used to estimate the point of zero charge of a titanium dioxide colloidal dispersion. Copyright 2000 Academic Press.     

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.     

Excluded volume driven counterion condensation inside nanotubes in a concave electrical double layer model

The physical properties of organic nanotubes attract increasing attention due to their potential benefit in technology, biology and medicine. We study the effect of ion size on the electrical properties of cylindrical nanotubes filled with electrolyte solution within a modified Poisson-Boltzmann (PB) approach. For comparison purposes, small hollow nanospheres filled with electrolyte solution are considered. The finite size of the particles in the inner electrolyte solution is described by the excluded volume effect within a lattice statistics approach. We found that an increased ion size reduces the number of counterions near the charged inner surface of the nanotube, leading to an enlarged electrostatic surface potential. The concentration of counterions close to the inner surface saturates for higher surface charge densities and larger ions. In the case of saturation, the closest counterion packing is achieved, all lattice sites near the surface are occupied and an actual counterion condensation is observed. By contrast, the counterion concentration at the axis of the nanotube steadily increases with increasing surface charge density. This growth is more pronounced for smaller nanotube radii and larger ions. At larger nanotube radii for small ion size counterion condensation may also be observed according to the Tsao criterion, i.e. the counterion concentration at the centre is independent of the number of counterions in the system. With decreasing radius the Tsao condensation effect is shifted towards physiologically unrealistic surface charge densities.     

Confinement free energy of flexible polyelectrolytes in spherical cavities

A weakly charged flexible polyelectrolyte chain in a neutral spherical cavity is analyzed by using self-consistent field theory within an explicit solvent model. Assuming the radial symmetry for the system, it is found that the confinement of the chain leads to creation of a charge density wave along with the development of a potential difference across the center of cavity and the surface. We show that the solvent entropy plays an important role in the free energy of the confined system. For a given radius of the spherical cavity and fixed charge density along the backbone of the chain, solvent and small ion entropies dominate over all other contributions when chain lengths are small. However, with the increase in chain length, chain conformational entropy and polymer-solvent interaction energy also become important. Our calculations reveal that energy due to electrostatic interactions plays a minor role in the free energy. Furthermore, we show that the total free energy under spherical confinement is not extensive in the number of monomers. Results for the osmotic pressure and mean activity coefficient for monovalent salt are presented. We demonstrate that fluctuations at one-loop level lower the free energy and corrections to the osmotic pressure and mean activity coefficient of the salt are discussed. Finite size corrections are shown to widen the range of validity of the fluctuation analysis.     

Intrinsic charge and Donnan potentials of grafted polyelectrolyte layers determined by surface conductivity data

In order to characterize grafted polyelectrolyte layers based on electrokinetic measurements a theory of the surface conductivity Ksigma was developed, starting from the model of thick polyelectrolyte layers with uniform segment distribution and dissociable groups with an unknown pK value. According to this model the inner part of the polyelectrolyte layer adjacent to the substrate is considered to be isopotential while the potential decay occurs in a zone near the solution side of the layer. A simple equation for the Donnan potential psiD as a function of pH, pK, electrolyte concentration C0, and volume charge density rho was obtained. In the derived equation Ksigma is directly related to psiD while the other terms have less influence on the magnitude of Ksigma and can be accounted for in a second approximation using psiD as determined from the measured Ksigma. Evaluation of the suggested model indicates that Ksigma measurements provide an effective method to characterize polyelectrolyte layers by analyzing the dependence of psiD on pH and C0: The magnitude of Ksigma yields information about the surface charge at complete dissociation of the ionizable groups. The dependence of Ksigma on pH and C0 can be used for the determination of the pK value of the dissociating functions and the segment volume fraction of the polyelectrolyte can be estimated using the measured value of rho.     

Influence of steric, electric, and dielectric effects on membrane potential

The membrane potential arising through nanofiltration membranes separating two aqueous solutions of the same electrolyte at identical hydrostatic pressures but different concentrations is investigated within the scope of the steric, electric, and dielectric exclusion model. The influence of the ion size and the so-called dielectric exclusion on the membrane potential arising through both neutral and electrically charged membranes is investigated. Dielectric phenomena have no influence on the membrane potential through neutral membranes, unlike ion size effects which increase the membrane potential value. For charged membranes, both steric and dielectric effects increase the membrane potential at a given concentration but the diffusion potential (that is the high-concentration limit of the membrane potential) is affected only by steric effects. It is therefore proposed that membrane potential measurements carried out at high salt concentrations could be used to determine the mean pore size of nanofiltration membranes. In practical cases, the membrane volume charge density and the dielectric constant inside pores depend on the physicochemical properties of both the membrane and the surrounding solutions (pH, concentration, and chemical nature of ions). It is shown that the Donnan and dielectric exclusions affect the membrane potential of charged membranes similarly; namely, a higher salt concentration is needed to screen the membrane fixed charge. The membrane volume charge density and the pore dielectric constant cannot then be determined unambiguously by means of membrane potential experiments, and additional independent measurements are in need. It is suggested to carry out rejection rate measurements (together with membrane potential measurements).     

High voltage supercapacitors using hydrated graphene film in a neutral aqueous electrolyte

The potential stability windows of chemical converted graphene in different aqueous electrolyte solutions were investigated for the first time. Based on this result, a supercapacitor with a high voltage and long cycle-life was prepared with the hydrated graphene films in the neutral aqueous solution at the maximum voltage of 1.6 and even 1.8 V. The electrochemical performance of the obtained sample was systematically investigated by cyclic voltammetry, galvanostatic charge/discharge and electrochemical impedance spectroscopy. According to the cyclic voltammetry, hydrated graphene film can still retain rectangular shape at the high scan rate of 0.5 V/s in the neutral aqueous electrolyte. At a galvanostatic charge/discharge rate of 1 or 200 A/g, the specific capacitance of 202.3 or 138.1 F/g was delivered, respectively. Furthermore, the EIS results also confirm its fast neutral ion diffusion and high operating frequency of 9.34 Hz.     

Colloidal Supercapattery: Redox Ions in Electrode and Electrolyte

Redox chemistry is the cornerstone of various electrochemical energy conversion and storage systems, associated with ion diffusion process. To actualize both high energy and power density in energy storage devices, both multiple electron transfer reaction and fast ion diffusion occurred in one electrode material are prerequisite. The existence forms of redox ions can lead to different electrochemical thermodynamic and kinetic properties. Here, we introduce novel colloid system, which includes multiple varying ion forms, multi‐interaction and abundant redox active sites. Unlike redox cations in solution and crystal materials, colloid system has specific reactivity‐structure relationship. In the colloidal ionic electrode, the occurrence of multiple‐electron redox reactions and fast ion diffusion leaded to ultrahigh specific capacitance and fast charge rate. The colloidal ionic supercapattery coupled with redox electrolyte provides a new potential technique for the comprehensive use of redox ions including cations and anions in electrode and electrolyte and a guiding design for the development of next‐generation high performance energy storage devices.     

Enhancing Capacity Performance by Utilizing the Redox Chemistry of the Electrolyte in a Dual‐Electrolyte Sodium‐Ion Battery

A strategy is described to increase charge storage in a dual electrolyte Na‐ion battery (DESIB) by combining the redox chemistry of the electrolyte with a Na⁺ ion de‐insertion/insertion cathode. Conventional electrolytes do not contribute to charge storage in battery systems, but redox‐active electrolytes augment this property via charge transfer reactions at the electrode–electrolyte interface. The capacity of the cathode combined with that provided by the electrolyte redox reaction thus increases overall charge storage. An aqueous sodium hexacyanoferrate (Na₄Fe(CN)₆) solution is employed as the redox‐active electrolyte (Na‐FC) and sodium nickel Prussian blue (Na_x‐NiBP) as the Na⁺ ion insertion/de‐insertion cathode. The capacity of DESIB with Na‐FC electrolyte is twice that of a battery using a conventional (Na₂SO₄) electrolyte. The use of redox‐active electrolytes in batteries of any kind is an efficient and scalable approach to develop advanced high‐energy‐density storage systems.     

On the use of the hypothesis of local electroneutrality in colloidal suspensions for the calculation of their dielectric properties

The validity of the hypothesis of electroneutrality outside the double layer of a suspended particle with an applied ac electric field is analyzed. It is shown that the electrolyte solution remains electroneutral for distances greater than a few Debye lengths from the particle surface only when the diffusion coefficients of the two ion species are identical. On the contrary, in the general case, a volume charge density around the particle builds up, which extends to distances that are proportional to the square root of the effective diffusion coefficient value divided by the frequency. These distances can easily attain many particle radii. Numerical results for both uncharged and charged suspended particles are presented, and a correction to existing analytical expressions for the field-induced ion distributions around uncharged particles (J. Phys. Chem. 2004, 108, 8397) is given. While the charge densities far from the particle are usually very weak, it is shown that they strongly contribute to the dipole coefficient value and, therefore, to the calculated values of the permittivity and conductivity increments. The errors that would be committed if these charge densities were ignored, assuming local electroneutrality and determining the dipole coefficient at a few Debye lengths from the particle surface, are analyzed and shown to be substantial.     

C.I. Reactive Orange 16-dodecylpyridinium chloride interactions in electrolytic solutions

The effect of electrolytes on the interaction between an anionic dye and a cationic surfactant was investigated spectrophotometrically in submicellar concentration range at certain temperature. The spectral change of the azo dye C.I. Reactive Orange 16 (RO16) exhibits a high sensitivity to the polarity of dye's environment. Dodecylpyridinium chloride (DPC) affects the electronic absorption spectra of dye solution that is dye-surfactant interaction results formation of complex and therefore a decrease in maximum absorption spectra (1.577 at 494 nm). The electrolyte cations cause an increase of the absorbance of DPC-RO16 ion-pair complex in the following order: Ca(2+)>Na(+)>NH(4)(+)>K(+)>Mg(2+), also for electrolyte anions Br(-)>Cl(-)>SO(4)(2-). Furthermore, this order can be changeable with increasing electrolyte concentration. The increase on absorbance value with increasing electrolyte concentration is explained as charge screening. The increase or decrease on absorption spectra of RO16-DPC solution depends on concentration range of the electrolyte added. As an increase on absorbance value with increasing electrolyte concentration is explained as charge screening, a decrease in this value for higher concentration of electrolyte is attributed as the charge of micelle shape.     

Diffusiophoresis in a suspension of charge-regulating colloidal spheres

An analytical study of diffusiophoresis in a homogeneous suspension of identical spherical charge-regulating particles with an arbitrary thickness of the electric double layers in a solution of a symmetrically charged electrolyte with a uniform prescribed concentration gradient is presented. The charge regulation due to association/dissociation reactions of ionogenic functional groups on the particle surface is approximated by a linearized regulation model, which specifies a linear relationship between the surface charge density and the surface potential. The effects of particle-particle electrohydrodynamic interactions are taken into account by employing a unit cell model, and the overlap of the double layers of adjacent particles is allowed. The electrokinetic equations that govern the electric potential profile, the ionic concentration distributions, and the fluid flow field in the electrolyte solution surrounding the particle in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved with the equilibrium surface charge density (or zeta potential) of the particle as the small perturbation parameter. Closed-form formulas for the diffusiophoretic velocity of the charge-regulating sphere correct to the second order of its surface charge density or zeta potential are derived. Our results indicate that the charge regulation effect on the diffusiophoretic mobility is quite sensitive to the boundary condition for the electric potential specified at the outer surface of the unit cell. For the limiting cases of a very dilute suspension and a very thin or very thick electric double layer, the particle velocity is independent of the charge regulation parameter.     

Dressed ion theory of size-asymmetric electrolytes: effective ionic charges and the decay length of screened Coulomb potential and pair correlations

The effects of ionic size asymmetry on long-range electrostatic interactions in electrolyte solutions are investigated within the primitive model. Using the formalism of dressed ion theory we analyze correlation functions from Monte Carlo simulations and the hypernetted chain approximation for size asymmetric 1:1 electrolytes. We obtain decay lengths of the screened Coulomb potential, effective charges of ions, and effective permittivity of the solution. It is found that the variation of these quantities with the degree of size asymmetry depends in a quite intricate manner on the interplay between the electrostatic coupling and excluded volume effects. In most cases the magnitude of the effective charge of the small ion species is larger than that of the large species; the difference increases with increasing size asymmetry. The effective charges of both species are larger (in absolute value) than the bare ionic charge, except for high asymmetry where the effective charge of the large ions can become smaller than the bare charge.