A Study of Concentration Polarization on Ion Exchange Membrane Electrodialysis

The concentration polarization phenomena in ion exchange membrane electrodialysis have been studied with single exchange membrane cell. The limiting current densities of Asahi ion-permselective membranes CK-1 and CK-2, Selemion ion-exchange membranes CMV, AMV, DMV and ASV have been measured with Ag-AgCl reversible electrode in various electrolyte solutions under 25°C and constant flow rate. In sodium chloride solution, the cation exchange membrane is easier to occur concentration polarization than the anion exchange membrane. The limiting current density increases as the concentration of solution increases for the same kind of ion exchange membrane. The experimental limiting current densities of Selemion CMV and AMV in NaCl, KCl, MgCl₂, CaCl₂, BaCl₂, Na₂SO₄, NaOH and HCl aqueous solutions are measured. The results show that the limiting current density increases as the ion mobility and diffusivity increase, and is affected by the transference number of ion. For the mixture of electrolyte solution, there are linear relationship between limiting current density and equivalent fraction of electrolytes.     

Electric mass transport of sodium chloride through cation-exchange membrane MK-40 in dilute sodium chloride solutions: A rotating membrane disk study

The polarization properties of an electromembrane system consisting of an MK-40 membrane and a dilute sodium chloride solution are investigated with an experimental apparatus, which includes a rotating membrane disk with a horizontally positioned membrane. For the electrochemical systems of MK-40/0.01 M NaCl and MK-40/0.001 M NaCl, effective ion transport numbers and partial current-voltage curves are determined for sodium and hydrogen ions, and limiting-current densities and the diffusion-layer thickness are calculated as functions of the rotation rate of the membrane disk. The space-charge distribution in the diffusion layer and in the membrane is calculated for various current densities and rotation rates of the membrane. It is shown that when electric-current densities are greater than the limiting value, ion fluxes of the salt increase as a result of a decrease in the effective thickness of the diffusion layer. This decrease is caused by the development of space charge, electroconvection, water dissociation, and the exaltation effect in the region near the membrane. It has been established that in dilute solutions the limiting current is not purely electrodiffusive in nature.     

镉离子在H2SO4溶液中极谱行为的研究

本文研究了在没有动物胶的0.5M H_2SO_4溶液中镉离子的极谱行为,得到了如下的结果:(1)在0.050～20.0mM CdSO_4 0.5M H_2SO_4的十种溶液中测得的电流-电位曲线都有良好的波形、恒定的极限扩散电流和易于确定的半波电位.这些曲线上都没有极谱极大出现;其极限扩散电流(波高)与镉离子的浓度成正比.在镉离子低浓度(0.050～0.20mM)时,半波电位保持不变,在镉离子高浓度(1.00～20.0mM)时,也仅有很小的变化.故镉离子在0.5MH_2SO_4,溶液中的电流-电位曲线可供定量和定性测定之用.(2)镉离子在低浓度时的极谱波是一种可逆波.(3)前人在H_2SO_4溶液中研究镉离子时之所以没有能得到令人满意的极谱行为的原因是他们在H_2SO4溶液中添加了动物胶的缘故.(4)作者从得到的波形良好的电流-电位曲线上,测定了25±0.2℃时镉离子在0.5M H_2SO_4溶液中的扩散电流常数、半波电位和电极反应中得失的电子数.结果如下: i_d/cm~(2/3)t~(1/6)=3.97μA/mM·mg~(2/3)·s~(-1/2) E_(1/2)=-1.011V(0.5M硫酸亚汞电极)=-0.559V(饱和甘汞电极) n=2 这些数据比Lingane的数据,扩散电流常数2.6μA/mM·mg~(2/3)·s~(-1/2)和半波电位-0.59V(饱和甘汞电极)],要合理些.     

Limiting current density and water dissociation in bipolar membranes

The behaviour of bipolar membranes in NaCl and Na₂SO₄ solutions is discussed. The membranes are characterized in terms of their limiting current densities. Below the limiting current density the electric current is carried by salt ions migrating from the transition region between the anion and the cation exchange layer of the bipolar membrane. In steady state these ions are replaced by salt ions transported from the bulk solutions into the transition region by diffusion and migration due to the fact that the ion-exchange layers are not strictly permselective. When the limiting current density is exceeded, the salt transport from the transition region can no longer be compensated by the transport into the region and a drastic increase in the membrane resistance and enhanced water dissociation is observed. This water dissociation is described as being a combination of the second Wien effect and the protonation and deprotonation of functional groups in the membrane. The limiting current density is calculated from a mass balance that includes all components involved in the transport. The parameters used in the mathematical treatment are the diffusion coefficients of salt ions and water, the ion mobilities in the membrane, the fixed charge densitiy of the membrane, the pK_b values of the functional groups and the solution bulk concentrations.     

Charge transfer between two immiscible electrolyte solutions: Part VI. Polarographic and voltammetric study of picrate ion transfer across the water/nitrobenzene interface

The transfer of the picrate ion across the interface between two immiscible electrolyte solutions, 0.05 M LiCl in water and 0.05 M tetrabutylammonium tetraphenylborate in nitrobenzene was investigated by electrolysis with the electrolyte dropping electrode and by cyclic voltammetry. Under the conditions of the experiments the charge-transfer process is controlled solely by diffusion. The maximum which appears on the polarogram of the picrate ion close to the limiting current can be suppressed by the addition of a surface-active substance (gelatine). The diffusion coefficients of the picrate ion in the aqueous and nitrobenzene phase were determined from the limiting polarographic current and from the peak current on the cyclic voltammogram. The value of the formal potential of the charge-transfer reaction, which was calculated from the half-wave potential or from the peak potential, is in good agreement with that inferred from the extraction data.     

Electrochemistry of nanopore electrodes in low ionic strength solutions

The steady-state voltammetric behavior of truncated conical nanopore electrodes (20-200 nm orifice radii) has been investigated in low ionic strength solutions. Voltammetric currents at the nanopore electrode reflect both diffusive and migrational fluxes of the redox molecule and, thus, are strongly dependent on the charge of the redox molecule and the relative concentrations of the supporting electrolyte and redox molecule. In acetonitrile solutions, the limiting current for the oxidation of the positively charged ferrocenylmethyltrimethylammonium ion is suppressed at low supporting electrolyte concentrations, while the limiting current for the oxidation of the neutral species ferrocene is unaffected by the ionic strength. The dependence of the limiting current on the relative concentrations of the supporting electrolyte and redox molecule is accurately predicted by theory previously developed for microdisk electrodes. Anomalous values of the voltammetric half-wave potential observed at very small nanopore electrodes (<50 nm radius orifice radii) are ascribed to a boundary potential between the pore interior and bulk solution (i.e., a Donnan-type potential).     

Mass transport and effective diffusion coefficient in the reduction of hydrogen ions from aqueous sulfuric acid solutions: Numerical modeling

This work presents results of the numerical solution to a system of equations of material balance and the movement of particles in solution under the influence of the forces of diffusion, migration, and convection, which describe the process of mass transport during the reduction of hydrogen ions at a rotating disk electrode from aqueous sulfuric acid solutions with and without excess supporting electrolyte. Results of the calculations show that the diffusion kinetics of hydrogen ion reduction can be observed only with measurements in dilute (≤10^?3 M) sulfuric acid solutions with an excess of indifferent supporting electrolyte. For more acidic solutions it is necessary to take into account the simultaneous diffusion of hydrogen and bisulfate ions. In the study of the regularities of hydrogen ion reduction in sulfuric acid solutions with a sulfate supporting electrolyte, it is necessary to take into account that with excess supporting electrolyte, the limiting current of hydrogen reduction is caused solely by the diffusion of bisulfate ions, but for small concentration ratios of the supporting electrolyte to acid, the influence of migration effects is significant.     

Determination of limiting current density for different electrodialysis modules

Limiting current density of ammonium nitrate solution in laboratory-, pilot-, and industrial-scale electrodialysis modules were determined to provide a method for the prediction of the limiting current density of ammonium nitrate solutions at any conditions. The current-voltage curve was measured in each case and the limiting current density was evaluated using the dependence of the derivative, dI/dU, on the electric current, I. The limiting current was determined as a current at which the derivative dI/dU equals zero. The developed method enables not only the prediction of the limiting current density but the limiting cut and limiting flux can be determined concurrently at any linear flow velocity of the diluate and inlet ammonium nitrate concentration. It could help to prevent working in the overlimiting region and to avoid undesirable decrease of current efficiency and pH changes. The limiting cut is the maximal cut that can be obtained at certain linear flow velocity and module geometry irrespective of the inlet ammonium nitrate concentration and it is very useful information when designing a new electrodialysis unit for specific application.     

Polarographic reduction of pyridinium ion in pyridine tetraethylammonium perchlorate as background electrolyte

Tetraethylammonium perchlorate, compared to lithium perchlorate as background electrolyte for the reduction of pyridinium ion in pyridine, is effective over a wider potential range, but is more difficult to obtain in a pure state; slight amounts of impurities do not, however, affect the pyridinium wave. The pyridinium wave produced in 0.1 M Et₄NClO₄ may occur at a more negative potential than the main pyridinium wave in 0.1 M LiClO₄, depending on the source of the pyridinium ion, but still appears to be due to a diffusion-controlled reduction, whose limiting current is linearly proportional to concentration; the prewave observed in LiCl0₄ background generally does not appear in Et₄NClO₄ background. Specific differences in the effect of Li(I), Na(I) and Et₄N(I) background cation appear to be due to electrocapillary phenomena and perhaps to the extent of solvation of the ions. The constancy of current for solutions containing acetic acid with added acetate, pyridinium nitrate with added nitrate, and benzoic acid with added benzoate indicate that the pyridinium reduction is independent of anion concentration.     

Exaltation effects in the metal electrodeposition from acid electrolytes

The exaltation of mass transfer of discharging cations, caused by the concurrent hydrogen evolution from acidified solutions, results in a sharp increase in the metal deposition rate. In this case the limiting process rate depends linearly on the hydrogen evolution current density; it depends but weakly on the solution agitation and temperature. Under the electrolysis of solutions containing weak acids as a supporting electrolyte, the higher the acid formation constant, the more pronounced is the dependence of the electrodeposition limiting rate on the hydrogen current density. When microelectrodes are used, the varying of the background acid nature may affect the hydrogen evolution rate markedly, while the metal electrodeposition rate mainly depends on the cell voltage. When metals are electrodeposited from complex anions, the parallel hydrogen evolution hinders the mass transfer; this process depends on the anion stability constant and charge, all other conditions being the same. The found peculiarities can be used in the inversion voltammetry for the lowering of the metal detection limit, improving of the analysis selectivity, and time saving.     

Mechanism of charging and supercharging molecules in electrospray ionization

The origin of the extent of charging and the mechanism by which multiply charged ions are formed in electrospray ionization have been hotly debated for over a decade. Many factors can affect the number of charges on an analyte ion. Here, we investigate the extent of charging of poly(propyleneimine) dendrimers (generations 3.0 and 5.0), cytochrome c, poly(ethylene glycol)s, and 1,n-diaminoalkanes formed from solutions of different composition. We demonstrate that in the absence of other factors, the surface tension of the electrospray droplet late in the desolvation process is a significant factor in determining the overall analyte charge. For poly(ethylene glycol)s, 1,n-diaminoalkanes, and poly(propyleneimine) dendrimers electrosprayed from single-component solutions, there is a clear relationship between the analyte charge and the solvent surface tension. Addition of m-nitrobenzyl alcohol (m-NBA) into electrospray solutions increases the charging when the original solution has a lower surface tension than m-NBA, but the degree of charging decreases when this compound is added to water, which has a higher surface tension. Similarly, the charging of cytochrome c ions formed from acidified denaturing solutions generally increases with increasing surface tension of the least volatile solvent. For the dendrimers investigated, there is a strong correlation between the average charge state of the dendrimer and the Rayleigh limiting charge calculated for a droplet of the same size as the analyte molecule and with the surface tension of the electrospray solvent. A bimodal charge distribution is observed for larger dendrimers formed from water/m-NBA solutions, suggesting the presence of more than one conformation in solution. A similar correlation is found between the extent of charging for 1,n-diaminoalkanes and the calculated Rayleigh limiting charge. These results provide strong evidence that multiply charged organic ions are formed by the charged residue mechanism. A significantly smaller extent of charging for both dendrimers and 1,n-diaminoalkanes would be expected if the ion evaporation mechanism played a significant role.     

The Effect of Temperature,Agitation and Content of Gold on the Thickness of Electroplated Gold at Various Current Densities

The effect of temperature, agitation, and content of gold in the solution on the thickness of electroplated gold at various current densities can be easily explained by their effect on the limiting current. Diffusion coefficient of aurocyanide ion, thickness of diffusion layer, and the activity of aurocyanide ion in the bulk solution are the three major factors to affect the limiting current. It was found that the change of temperature will affect both diffusion coefficient and thickness of diffusion layer. However, the thickness of diffusion layer is mainly determined by the means of agitation.     

Electrolysis with electrolyte dropping electrode: II. Basic properties of the system

In a theoretical discussion the conditions have been pointed out where an interface of two immiscible electrolyte solution behaves as an equilibrium system metal ion-metallic electrode, as an ideally polarized electrode and as an electrode under faradaic current flow. The basic equations for current-electrical potential difference across the interface have been deduced for the cases of ion as well as electron transfer.Experimentally, various base electrolyte systems were studied, the most advantageous among these are LiCl in water+tetrabutylammonium tetraphenylborate in nitrobenzene and MgCl₂ in water+tetrabutylammonium dicarbollyl cobaltate in nitrobenzene. S-shaped polarographic curves were observed with the tetramethylammonium ion. The limiting current is directly proportional to concentration. The limiting currents are somewhat higher than those predicted by the Ilkovi? equation which has been ascribed to the tangential movement of the interface.     

Numerical investigation of the current transition regimes in nanochannels

The concentration polarization phenomena and its effects represent one of the main challenges for the optimal operation of many nanofluidic systems. A numerical investigation of the different electric current transition regimes observed during the concentration polarization phenomena in nanochannels is performed. This included a 2D‐axisymmetric simulation of the nanofluidic system (reservoir‐nanochannel‐reservoir). From these simulations, a novel mechanism is discovered that explains that different current transition regimes. This driving mechanism involves the applied electric field penetration while the convective flow mechanism is found to be negligible. This differs with the classical statement that the mixing process with less depleted areas initiated by an electrokinetic vortex instability starts the overlimiting regime. Additionally, the numerical approach allows us to identify new characteristics of the linear‐limiting transition such as source‐like and saddle‐like points of the electric field streamlines. The three voltage–current regimes (linear, limiting and overlimiting) are explained by observing and quantifying changes in electric field, potential, ion concentration and ion concentration gradients within the system.     

Current efficiency and titration efficiency in coulometric titrations with electrogenerated ceric ion determination of iodide

The current efficiency for the electrogeneration of cerie ion at a platinum anode falls considerably below 100% at both very small and at large current densities in both sulfuric and perchloric acid media. The maximal current efficiency is about 99.8%.Iodide ion can be titrated to iodine with an error of only about +0.3%, even under conditions where the cerie ion generation efficiency is only 98%. High titration efficiency, in spite of poor efficiency for ceric ion generation, is obtained because iodine is oxidized to iodate ion at a potential slightly in advance of the potential at which cerous ion is oxidized. Since the electrogenerated iodate ion oxidizes iodide ion only a minor fraction of the total quantity of electricity results from ceric ion generation, so the effect of its inefficient generation is greatly minimized. Satisfactory titrations of iodide ion to iodine can be performed without any cerous salt present, provided the generating current density is smaller than the limiting current density for oxidation of iodine to iodate ion.     

Limiting Current in Iodine–Iodide System on Vertical Electrode under Conditions of Natural Convection

The limiting current of the triiodide reduction on a vertical plane electrode in solutions containing excess potassium iodide is calculated by the Karman method for natural-convection conditions. Equations for the average and local limiting currents (which depend on the electrode height), the boundary layer thickness, and the vertical component of the fluid velocity are derived. The average limiting currents, experimentally determined as functions of concentrations of solution components and electrode's height, are compared to calculated values.     

Application of the rotated dropping mercury electrode to the analysis of mixtures of electroactive substances

The use of poylacrylamide is recommended instead of gelatin as an ideal maximum suppressor to be employed with both the rotated dropping mercury electrode (RODE) and conventional dropping electrode (DME). It is retained at the mercury surface over the entire potential range and does not combine with heavy metals. Reproducibility of the measurement of the residual current and that of the limiting current at the RDME were studied, and it was found that accurate determinations of a single constituent (±2%) are possible at concentrations as low as 1 to 2.10^-5M. The variation of the limiting current with potential is much greater at the RDME than at the DME. This effect must be considered in the analysis of a mixture of electroactive species at the RDME. Method have been discussed for making the proper correction for a preceding wave when a limiting current of a mixture of constituents is measured. Because of its high sensitivity and good reproducibility of results, the RDME is recommended for the analysis of solutions containing one or more electroactive species at concentrations less than 10^-4M.     

Theoretical investigation on confinement of ions in a cube‐shaped ion trap

The confinement of ions in a cube‐shaped ion trap and the mathematical formalism governing the behavior of ions in the trap is investigated theoretically. Afterwards, the stability regions are computed using the fourth‐order Rung–Kutta method. Consequently, the influence of the direction of ions, injected into the trap from its center on the stability region, is numerically discussed. Moreover, the maximum angle of injection with respect to the vertical axis of the cube for which the ions could be confined in the trap without invoking any direct current component of voltage (henceforth referred to as limiting angle) was calculated. Strong linear correlation between the angle of injection and the ratio of the stability region areas is confirmed. A nonlinear feature of a cube‐shaped ion trap is demonstrated with a focus on the equations of motion for an ion confined into the trap. It is worthwhile to note that the stability region of our cubic ion trap, which has its own boundary conditions and electrodynamics, has been theoretically investigated for the first time. Besides, the limiting angle as well as the aforementioned strong linear correlation has not been reported in the literature previously. Copyright © 2015 John Wiley & Sons, Ltd.     

Influence of the convective term in the Nernst-Planck equation on properties of ion transport through a layer of solution or membrane

The one-dimensional boundary-value problem of steady-state ion transport, which takes into account the convective component, is formulated and solved in terms of the Nernst-Planck model. This problem is investigated in connection with the diffusion layer, which is understood in a broad sense. This can be the diffusion layer as it is usually understood, i.e., located adjacent to a hydraulically permeable membrane. In another context it can be regarded as a capillary connecting two reservoirs filled with solutions of different concentration or as an uncharged macropore permeating the membrane and separating two solutions. Finally, the solution to the problem is applied to the membrane itself, which is represented as a quasi-homogeneous gel. In the latter case, a virtual electroneutral solution in local equilibrium with a small volume of membrane is considered. The problem is investigated in dimensionless form as a function of the Peclet number. It is shown that the Peclet number is numerically equal to the absolute value of the dimensionless convection velocity. The limiting current, concentration profiles, distributions of the field strength and potential, and effective transport numbers are analyzed as functions of the convective component.     

Mathematical modeling of cyclic voltammetry for EC<Subscript>2</Subscript> reaction

The non-steady-state concentration for an EC reaction at planar electrode is derived. The analytical expression for the concentration for EC reaction is reported for small and large value of reaction rate. The asymptotic expression for the non-steady-state current for EC reaction is also derived. The analytical solutions for normalized current response were formulated using the method of Laplace transformation. The concentration and current are compared with available limiting case results, and are found to be in good agreement.