Numerical Study of Rayleigh–Benard Instability of a Binary Electrolyte in a Cell with Plane Parallel Electrodes Taking into Account the Space Charge

An electrochemical system consisting of two plane horizontal electrodes of the same metal and the interelectrode space filled with solution of a salt of this metal is considered. The conditions of emergence of Rayleigh–Benard convective instability in this system are investigated using a numerical method. Two reasons for the instability are taken into account: the buoyant force and the electrical force caused by a very small space charge formed near the electrode, at which the electrochemical reaction proceeds at the limiting diffusion current. The instability emergence conditions are characterized by critical values of two parameters corresponding to the aforementioned forces. The mutual effect of these forces on the instability emergence and an essential role of the ratio between the diffusion coefficients of electrolyte cations and anions are revealed.     

Onset of natural convection in the electrochemical cell with horizontal electrodes under non-steady-state conditions: A numerical study

The disturbance of mechanical equilibrium of stagnant electrolyte containing three types of ions and the onset of natural convection in the electrochemical cell with plane horizontal electrodes under the non-steady-state conditions are studied theoretically. The Navier-Stokes equations in the Boussinesq approximation, the equations of ionic transfer of electrolyte components, which is caused by diffusion, convection, and migration, and the electroneutrality condition were used as the mathematical model of the process. Using the numerical simulation, the regularities of the onset of natural convection of electrolyte solution with the formation of convective cells are studied. The effect of transport properties of solution on the critical time of onset of convection and on the time before the current starts to increase due to the onset of natural convection, on the sizes and shape of convective cells and the mass-transfer rate is investigated by the example of cathodic deposition of metal at the limiting current.     

Study of a Solvated Adsorbed Gelatin Layer Using a Modified Force Microscope

The interaction energies between gelatin-coated surfaces at various electrolyte and pH conditions are reported. The surfaces are of glass and are negatively charged under all conditions used here. Gelatin is a polyampholyte, with an isoelectric pH (IEP) of approximately 4.9. At low pH the gelatin molecules have a net positive charge, and thus the polyampholyte tends to adsorb with a relatively flat conformation. As the pH is increased the strong attractive interaction between the surface and the polyampholyte decreases as more negative charges and then fewer positive charges appear on the polyampholyte, and so the gelatin extends away from the surface. On changing electrolyte concentrations after adsorption no effect was seen at the IEP, but the layer was observed to swell at more alkaline pHs. This is consistent with the net minimum charge situation on the polymer under these conditions. Changing the adsorption conditions was seen to have an effect, and this is attributed to the different affinities of the gelatin chain to the surface depending on the solution chemistry. Results obtained when the gelatin was initially adsorbed on one surface or two were similar, suggesting that the gelatin transfers rapidly from one surface to another. The importance of adsorption conditions as well as current conditions is discussed. Copyright 1999 Academic Press.     

Electrostatic interaction of ion-penetrable membranes. Effects of ionic solubility

An analytic, approximate expression for the electrostatic interaction between two membranes immersed in an electrolyte solution is derived on the basis of a simple membrane model. This model assumes that the membrane has a surface layer in which charged groups are uniformly distributed and that electrolyte ions can penetrate into the surface layer. The partition coefficients of cations and anions between the solution and the surface layer, which are related to their solubilities in the surface layer, may be different from unity.The electrostatic interaction depends on the ionic partition coefficients between the solution and the surface layer, and the relative permittivity of the surface layer, as well as on the membrane-fixed charges, the electrolyte concentration in the solution, and the surface layer thickness. It is shown, in particular, that even where the charge layer has no fixed charges, the electrostatic interaction force can be produced if the solubilities of cations and anions are different in the surface layer.     

Donnan permselectivity in layer-by-layer self-assembled redox polyelectrolye thin films

Redox polyelectrolyte multilayers have been assembled with use of the layer-by-layer (LBL) deposition technique with cationic poly(allylamine) modified with Os(bpy)(2)ClPyCHO (PAH-Os) and anionic poly(styrene)sulfonate (PSS) or poly(vinyl)sulfonate (PVS). Different behavior has been observed in the formal redox potential of the Os(II)/Os(III) couple in the polymer film with cyclic voltammetry depending on the charge of the outermost layer and the electrolyte concentration and pH. The electrochemical quartz crystal microbalance (EQCM) has been used to monitor the exchange of ions and solvent with the external electrolyte during redox switching. At low ionic strength Donnan permselectivity of anions or cations is apparent and the nature of the ion exclusion from the film is determined by the charge of the topmost layer and solution pH. At high electrolyte concentration Donnan breakdown is observed and the osmium redox potential approaches the value for the redox couple in solution. Exchange of anions and water with the external electrolyte under permselective conditions and salt and water under Donnan breakdown have been observed upon oxidation of the film at low pH for the PAH-Os terminating layer. Moreover, at high pH values and with PVS as the terminating layer EQCM mass measurements have shown that cation release was masked by water exchange.     

Numerical Study of Electroconvective Instability of Binary Electrolyte in a Cell with Plane Parallel Electrodes

Electroconvective instability of a binary electrolyte in a cell with plane parallel electrodes is studied using a numerical method. When a direct current is passed through the cell, a space charge and an electrical force acting upon the solution form under certain conditions. If the electric force density reaches a critical value, convective instability emerges in the cell, leading to the formation of nonequilibrium dissipative structures similar to Rayleigh–Benard cells in a nonuniformly heated liquid. The critical parameter _crit, at which instability emerges in the system, is determined. Dependences of _crit on the ratio between the diffusion coefficients for electrolyte cations and anions and on the current passed through solution are determined.     

Electrical potential distribution over the bilayer lipid membrane due to amphiphilic ion adsorption

Potential drops at the boundary of the bilayer lipid membrane (BLM) due to amphiphilic anion (dodecylsulfate) adsorption have been investigated. The magnitude of these drops was determined by different experimental methods: inner field compensation (IFC), electrophoretic mobility and current relaxation (tetraphenylboron and dipicrylamine were taken as probe anions).The boundary potential (BP) drops (IFC method) do not depend on the electrolyte concentration for neutral membranes. The ζ-potential values in the same conditions are considerably smaller than the BP drops measured by the IFC method. The potential drops, determined with the help of the initial BLM conductivity changes (current relaxation method) coincide with the BP drops (IFC method). The adsorption of amphiphilic ions leads to a decrease in the rate constant of the movement of hydrophobic ions through the BLM (current relaxation method).To explain the results obtained, it is suggested that a potential drop due to amphiphilic ion adsorption is located not only in the diffuse double layer, but also in a layer inside the membrane. The latter is not screened by electrolyte solution ions and could not be registered by the electrophoretic method.     

Electroinitiated graft copolymerization

A technique has been developed for initiating a graft copolymerization electrochemically. A copoly(styrene/vinylbenzophenone) linear copolymer was prepared to serve as the electroactive starting material. The benzophenone sites on this molecule are readily activated at the cathode. Macroradical ions result from the direct transfer of electrons to benzophenone groups of the electroactive backbone polymer. In solution in N,N-dimethylformamide with tetraethylammonium perchlorate (TEAP) as supporting electrolyte the passage of current produced a dark blue solution similar to that observed with radical anions obtained with benzophenone directly. When monomer such as acrylonitrile or methyl methacrylate was added, a graft copolymer was formed. Electrolysis of solutions of the backbone polymer in tetrahydrofurn (THF), with sodium tetraphenylboride as supporting electrolyte, produced relatively stable, persistent macroradical anions and, under appropriate conditions, the reddish-violet macrodianions. Both types initiated graft copolymerization of acrylonitrile and methyl methacrylate. Graft copolymers were characterized by gel permeation chromatography (GPC), infrared (IR), and solvent extraction. High grafting efficiency (i. e., free from homopolymer) can be obtained under appropriate conditions. Suitable mechanisms are proposed, compared, and discussed.     

The limiting current of electrochemical reaction in the binary electrolyte in the rotating electrochemical cell

A rotating cylindrical electrochemical cell with a plane ring electrode on its cover containing a binary electrolyte was considered. The equation for the diffusion limiting current density on the ring electrode was derived ignoring the effect of Coriolis force. The solution of transfer equations by the Karman method at the limiting current in the cell allowed us to analyze the effect of Coriolis force on the boundary layer thickness and to determine the conditions, under which the Coriolis force may be ignored.     

Limiting current in a redox system on a vertical electrode under conditions of natural convection

The problem of calculating the limiting current in a redox system on a vertical plane electrode under the natural convection conditions is solved. By way of example, the reaction of ferrocyanide oxidation on platinum in a solution containing a mixture of potassium ferrocyanide and ferricyanide (in excess). An equation for the effective Rayleigh number determining the limiting current is derived by Kármán’s method with allowance made for the migration current of an indifferent electrolyte. Limiting currents in the electrochemical system under study are determined experimentally. The calculated and measured limiting currents are compared.     

Converse flexoelectric effect in homeotropic nematic layers with asymmetric surface anchoring

The dc electric field-induced deformations of conducting flexoelectric nematic layers were studied numerically. Asymmetric boundary conditions expressed by different anchoring strengths on the limiting surfaces were assumed. Nematic material was characterised by negative dielectric anisotropy. Both signs of the sum of flexoelectric coefficients were taken into account. The electric properties of the layer were described in terms of a weak electrolyte model. Mobility of cations was assumed to be one order of magnitude lower than that of anions. Quasi-blocking electrode contacts were assumed. The threshold voltages for the deformations and the director distributions in the deformed layers were calculated for low, moderate and high ion concentrations. The director distributions were also determined. The results show that asymmetry caused by difference between the anchoring strengths and by difference between mobilities of anions and cations lead to two threshold values for a given layer corresponding to two polarities of the bias voltage. Additionally, the values of both thresholds depend on the sign of the flexoelectric parameter. In every case under consideration, the threshold is significantly lowered when the ion concentration is high.     

Numerical Solution of the Problem of the Limiting Current for the Copper Electrodeposition from a Solution of Cupric Sulfate and Sulfuric Acid in Conditions of Natural Convection

Equations for a boundary layer, written in self-similar variables, are integrated numerically to obtain distributions of concentration of ions Cu²⁺, H⁺, and SO₄ ^2–; a hydrodynamic velocity; partial currents of electrolyte components; and the limiting current of copper deposition and determine the Rayleigh number for the system under consideration. The results are compared with an approximate analytical solution obtained earlier.     

Electrokinetic flow in a planar slit covered by an ion-penetrable charged membrane

The electrokinetic flow of an electrolyte solution in a planar slit covered by an ion-penetrable charged membrane layer is analyzed theoretically. An approximate analytical expression for the spatial variation in the electrical potential is derived, and the electroosmotic velocity, the total electric current, and the streaming potential of the system under consideration are evaluated. The effects of epsilon' (relative permittivity of liquid phase/relative permittivity of membrane layer), eta' (viscosity of liquid phase/viscosity of membrane layer) and the valence of anions (coions) on the volumetric flow rate and total current are examined. We show that the effect of the valence of cations (counterions) on the volumetric flow rate is less significant than that of epsilon' and that of eta'. However, the effect of epsilon' on the total current is less significant than that of the valence of cations and that of eta'. The variation of total current as a function of ionic strength is found to have a local minimum, regardless of whether a pressure gradient is applied or not. The absolute streaming potential has a local maximum as the concentration of fixed charge varies, which was not found in previous studies.     

Studies on erosion of silicone rubber exposed to partial arc discharges

The effect of electrolyte conductivity on the partial arc discharge development between two electrolyte electrodes on a silicone rubber sheet surface was investigated. Tests were executed by placing the salt-waterlogged glass-filter paper on a silicone rubber sheet to simulate a polluted electrolyte layer, and partial arc discharges with a constant current value of 10 mA were observed. It was found that the formation of an arc channel and a temperature distribution on the sample surface varied with the electrolyte conductivity. In addition, the relation between the electrolyte conductivity and the weight loss due to the heat erosion of specimens was also investigated by a 3D morphological observation and a simulated calculation. The partial arc discharge did significantly not influence on the sample surface erosion under serious polluted conditions. In contrast, the severest erosion appeared under the light pollution with comparatively lower conductivity of the electrolyte electrodes.     

Numerical Simulation of Rayleigh–Bènard Instability in Solutions Containing Ions of Three Types

The conditions for appearance of a Rayleigh–Benard instability (RBI) induced by a constant current between two horizontal electrodes in solution containing electroactive ions and indifferent electrolyte (system with three kinds of ions) are analyzed. It is taken into account that all the components take part in the formation of buoyant forces. The problem is solved for a stationary case (as an expansion to a series by a small parameter), and then equations for low perturbations are solved by the Galerkin method. The calculation is performed with a program that accounts for any number of members in a Galerkin expansion. A diagram is obtained, which determines conditions for the RBI emergence in terms of ratios of partial Raleigh numbers. The ratio of diffusion coefficients for supporting cations and anions significantly affects position of the boundary dividing ranges of convective stability and RBI in a diagram of nonequilibrium phase transitions.     

In situ surface plasmon resonance measurements of self-assembled monolayers of ferrocenylalkylthiols under constant potentials.

A commercial system for surface plasmon resonance (SPR) possessing a batch-type flow channel has been simply modified so as to conduct in situ SPR measurements under polarization of an Au sensor chip at constant potentials. The modified instrument can monitor electrochemical reactions of monolayer materials with high stability and high reproducibility. The redox reaction of a self-assembled monolayer (SAM) of 6-ferrocenyl-1-hexanethiol (FcHT) induced the resonance angle shifts, the magnitudes of which accorded with the Nernst equation. The measurements in electrolyte solutions containing different electrolyte anions revealed that the SPR measurements detected ion pairing of electrolyte anions with oxidized FcHT. In cases of measurements in alkylsulfonic acid solution, simulation of the results based on the N-layer model has clarified that alkylsulfonate anions make an assembled layer on the FcHT SAM.     

Application of an external contactless conductivity detector for the analysis of beverages by microchip capillary electrophoresis

Quantitative total ionic analysis of alcoholic and nonalcoholic beverages was performed by microchip capillary electrophoresis with external contactless conductivity detection. An electrolyte solution consisting of 10.5 mM histidine, 50 mM acetic acid, and 2 mM 18-crown-6 at pH 4.1 was used for the determination of NH(4) (+), K(+), Ca(2+), Na(+), and Mg(2+). Fast analysis of Cl(-), NO(3) (-), and SO(4) (2-) was achieved in 20 mM 2-(N-morpholino)ethanesulfonic acid /histidine electrolyte solution at pH 6.0 and the simultaneous separation of up to 12 inorganic and organic anions was performed in a solution containing 10 mM His and 7 mM glutamic acid at pH 5.75. Limits of detection ranged from 90 to 250 mug/L for inorganic cations and anions, and from 200 to 2000 mug/L for organic anions and phosphate. Calibration curves showed linear dependencies over one to two orders of magnitude when the stacking effect was minimized by injecting standard solutions prepared in background electrolyte solutions. Total analysis times of 35 and 90 s were achieved for the determination of 5 inorganic cations and for the simultaneous determination of 12 inorganic and organic anions, respectively, which represents a considerable reduction of analysis time compared to conventional separation methods used in food analysis.     

On the theory of steady-state electrodiffusion

The problem of the electrical field strength distribution outside the boundary layer under on passing of steady-state current through electrolyte is considered. The solution is obtained as a small-parameter reciprocal-power expansion; however, the expansion of the solution in terms of positive powers of this parameter, by using of the method of splicing of asymptotic solutions, is divergent. For the region under consideration, an expression for the field strength is obtained, which differs from the corresponding expression obtained from the electrical neutrality conditions.     

Quantitative SNIFTIRS studies of (bi)sulfate adsorption at the Pt(111) electrode surface

Subtractively normalized interfacial Fourier transform infrared reflection spectroscopy (SNIFTIRS) was applied to study (bi)sulfate adsorption on a Pt(111) surface in solutions of variable pH while maintaining a constant total bisulfate/sulfate ((bi)sulfate) concentration without the addition of an inert supporting electrolyte. The spectra were recorded for both the p- and s-polarizations of the IR radiation in order to differentiate between the IR bands of the (bi)sulfate species adsorbed on the electrode surface from those species located in the thin layer of electrolyte. The spectra recorded with p-polarized light consist of the IR bands from both the species adsorbed at the electrode surface and those present in the thin layer of electrolyte between the electrode surface and ZnSe window whereas the s-polarized spectra contain only the IR bands from the species located in the thin layer of electrolyte. A new procedure was developed to calculate the angle of incidence and thickness of the electrolyte between the Pt(111) electrode surface and the ZnSe IR transparent window. By combining these values with the knowledge of the optical constants for Pt, H(2)O and ZnSe, the mean square electric field strength (MSEFS) at the Pt(111) electrode surface and for thin layer of solution were accurately calculated. The spectra recorded using s-polarization were multiplied by the ratio of the average MSEFS for p- and s-polarizations and subtracted from the spectra recorded using p-polarization in order to remove the IR bands that arise from the species present within the thin layer cavity. In this manner, the resulting IR spectra contain only the IR bands for the anions adsorbed on the Pt(111) electrode surface. The spectra of adsorbed anions show little change with respect to the pH ranging from 1 to 5.6. This behavior indicates that the same species is predominantly adsorbed on the metal surface for this broad range of pH values and the results suggest that sulfate is the most likely candidate for this adsorbate.     

Modification of ion-exchange membrane used for separation of protons and metallic cations and characterization of the membrane by current-voltage curves

The ionic transport properties of several cations (H(+), Na(+), and Zn(2+)) across sulfonated ion-exchange membranes modified with an amine were investigated by the measurement of current-voltage curves to determine the effect of the surface modification of the membrane. The membrane was modified by chlorosulfonation and amination with a diamine (N,N-dimethylethylenediamine) and an amine (isoamylamine) to form a sulfonamide bond between amine groups and the surface layer. In the case of the modification with the diamine, the terminal amine was protonated in acidic media or quaternized with methyl iodide. The presence of a positively charged layer on the two sides of the membrane strongly decreased the limiting current flowing across the membrane in the presence of a 1:1 electrolyte such as HCl or HNO(3) due to an increase of the resistance of the membrane. In the case of divalent cations such as Na(+) and Zn(2+), electrostatic repulsion also contributes to the decrease of the limiting current. The presence of divalent anions seems to increase the limiting current somewhat due to their preconcentration within the cationic layer, which facilitates their subsequent transport across the membrane. When only one face of the membrane was modified, the current-voltage measurements showed that the membrane did not behave like a bipolar membrane. For one-side (under forward polarization) and two-side modified membranes, counterions are slightly blocked in the membrane by the cationic layer, which led to a decrease of the membrane conductivity during electrodialysis.