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.     

Mass transfer in the rotating electrochemical cell with vertical cylindrical electrodes: the effect of rotational rate and cell geometry on the limiting current density

The mass transfer in the rotating electrochemical cell with vertical cylindrical electrodes containing a binary electrolyte is theoretically studied. The Navier-Stokes equations in the rotating system of coordinates, the equations of ionic transfer of electrolyte components, which is caused by diffusion, convection, and migration, and the condition of electroneutrality are used as the mathematic model of the process. The effects of centrifugal force and Coriolis force are studied by using the numerical simulation; the effect of geometry of electrochemical cell on the limiting mass transfer rate is determined.     

Numerical Modeling of Steady-State Ion Transfer in Electrochemical Systems with Allowance for Migration

Numerical methods that are used for modeling steady-state ion transfer in electrochemical systems and account for the diffusion, migration, and convection are analyzed. An economical method for calculating steady-state processes is designed. The method splits a set of coupled equations of ion transfer and the electroneutrality conditions. The splitting is done in each iteration step by successively calculating distributions of the electric field potential and the electrolyte component concentrations. Techniques for approximate solution of redetermined set of difference equations used for calculating electric fields are analyzed. On the basis of this analysis, a novel technique is put forth, which ensures a minimum deviation from electroneutrality. Results of computational experiments are presented.     

A new approach to micropatterning: application of potential-assisted ion transfer at the liquid-liquid interface for the local metal deposition

A new approach to micropatterning is demonstrated. The approach is based on driving an electrochemical process at the solid-liquid interface through the formation of a flux of ions from a micropipet that is held in close proximity to the surface. The flux of ions is generated by the so-called potential assisted ion transfer at the interface between two immiscible electrolyte solutions (ITIES). As a model system, the local deposition of silver was examined. Specifically, a constant potential, which was applied to a micropipet filled with an aqueous solution of silver ions, caused the transfer of Ag(+) into the outer nitrobenzene (NB) solution that consisted of an electrolyte, tetrabutylammonium tetrakis[4-chlorophenyl]borate (TBATPBCl). To facilitate the transfer of silver ions a macrocyclic ligand, that is, dibenzo-24-crown-8 (DB24C8), was added to the organic phase. The Faradaic current of this micro-ITIES was used as a means of controlling the tip-surface distance in scanning electrochemical microscopy (SECM) and depositing silver microstructures on a gold substrate.     

Model and experimental studies of gravitational convection in an electromembrane cell

The model and experimental studies of the effect of gravitational convection on transport processes in an electromembrane cell are carried out. A model of an unsteady process of binary electrolyte transfer in moderately dilute solutions in an electromembrane cell for underlimiting current modes with allowance made for the natural and forced convection is built in the form of a system of two-dimensional equations of Navier-Stokes, Nernst-Planck, thermal conductivity, and electric current continuity. The dynamics of the appearance and development of vortex structures that arise in response to operation of gravitational archimedian forces is considered as well as their effect on the transfer of salt ions. Chronoampero- and chronopotentiograms obtained in an experimental study of desalination channels in electromembrane systems are interpreted.     

Finite difference method of simulation of non-steady-state ion transfer in electrochemical systems with allowance for migration

Finite difference methods of the second order of accuracy are elaborated for numerical calculation of non-steady-state ion transfer, which is caused by diffusion, migration, and convection in the unidimensional electrochemical systems. The methods of decoupling a set of coupled continuity equations of the electrolyte species are proposed, which ensures that the discrete equations are consistent with the initial differential equations and the electroneutrality condition is rigorously met. The methods of approximation of the boundary conditions of the second order temporal and spatial accuracy and the method of decoupling the transfer equations in the boundary nodes are elaborated. The explicit, fully implicit, and semi-implicit finite difference schemes are elaborated. For semi-implicit schemes, two versions of difference equation closure are proposed, which assure the unambiguity of determination of the distribution of electrical potential. Comparison analysis of the accuracy of elaborated finite difference methods of calculation of non-steady-state ion transfer is performed.     

Flux decline during cross flow membrane filtration of electrolytic solution in presence of charged nano-colloids: a simple electrokinetic model

An electrokinetic transport based approach for quantification of reversible flux decline due to the concentration polarization of an electrolyte solution in presence of charged colloids is presented. The model envisions the electrolyte transport across a charged cake or gel layer as transport of ions through charged cylindrical capillaries. This model is coupled with the standard theory of concentration polarization during cross flow membrane filtration. The analysis is carried out entirely in terms of generalized, non-dimensional variables. A dimensionless group termed as the scaled gel layer resistance evolves from the analysis, which accounts for the electrical properties of the charged nano-colloids and the electrolyte solution. A parametric study is performed to elucidate the coupled influence of mass transfer, membrane resistance, gel resistance, and electrical properties of the gel-electrolyte polarized layer. The effects of these parameters are examined on the filtration performance through the model equations.     

A new access to Gibbs energies of transfer of ions across liquid|liquid interfaces and a new method to study electrochemical processes at well-defined three-phase junctions

Droplets of polar and nonpolar aprotic solvents containing dissolved electroactive species can be easily attached to paraffin-impregnated graphite electrodes. When the electrode with the attached droplet is introduced into an aqueous electrolyte solution, the electrochemical reactions of the dissolved species can be elegantly studied. Provided the droplet does not contain a dissolved electrolyte, the electrochemical reaction will be confined to the very edge of the three-phase junction droplet|graphite|aqueous electrolyte. When a neutral species is oxidised, two pathways are possible: the oxidised species can remain in the droplet and anions will be transferred from the aqueous solution to the organic solvent, or the oxidised species may leave the droplet and enter the aqueous solution. Depending on the nature of the dissolved species, the nature of the organic solvent, the presence or absence of appropriate anions and cations in the two liquid phases, very different reaction pathways are possible. The new approach allows studies of ion transfer between immiscible solvents to be performed with a three-electrode potentiostat. Electrochemical determinations of the Gibbs energy of ion transfer between aqueous and nonpolar nonaqueous liquids are possible, whereas conventional ion transfer studies require the presence of a dissociated electrolyte in the organic phase. The new method considerably widens the spectrum of accessible ions.     

Electrochemical and electrocatalytic stability of Prussian blue/Berlin green redox transformation in Prussian blue-polypyrrole composite films

Redox transformation of Prussian blue to Berlin green (PB/BG) in Prussian blue-polypyrrole (PB-PPy) composites synthesized via original one-step method has been studied. It was shown that the nature of anion and composition of background electrolyte play an important role for both the stability and the shape of electrochemical response of composite film during redox transfer of Prussian blue to Berlin green. Nitric acid, phosphoric acid, malic acid and citric acid 0.05 N (eq/L) solutions and the same acids partially neutralized with 0.01 N KOH were used as electrolyte to study the role of potassium ions presence in solution. The most stable electrochemical response of PB/BG redox transfer was obtained for the nitrate anions containing solutions in the presence of potassium ions. Nevertheless, the stability of the electrochemical transformation PB/BG in composite films in other media is enough to detect the sulphite ions content in wine samples via electrocatalytic reaction at the potentials of PB/BG redox transformation.

     

A comparative study of the anion transfer kinetics across a water/nitrobenzene interface by means of electrochemical impedance spectroscopy and square-wave voltammetry at thin organic film-modified electrodes

The kinetics of the transfer of a series of hydrophilic monovalent anions across the water/nitrobenzene (W/NB) interface has been studied by means of thin organic film-modified electrodes in combination with electrochemical impedance spectroscopy and square-wave voltammetry. The studied ions are Cl-, Br-, I-, ClO4-, NO3-, SCN-, and CH3COO-. The electrode assembly comprises a graphite electrode (GE) covered with a thin NB film containing a neutral strongly hydrophobic redox probe (decamethylferrocene or lutetium bis(tetra-tert-butylphthalocyaninato)) and an organic supporting electrolyte. The modified electrode is immersed in an aqueous solution containing a supporting electrolyte and transferring ions, and used in a conventional three-electrode configuration. Upon oxidation of the redox probe, the overall electrochemical process proceeds as an electron-ion charge-transfer reaction coupling the electron transfer at the GE/NB interface and compensates ion transfer across the W/NB interface. The rate of the ion transfer across the W/NB interface is the limiting step in the kinetics of the overall coupled electron-ion transfer reaction. Moreover, the transferring ion that is initially present in the aqueous phase only at a concentration lower than the redox probe, controls the mass transfer regime in the overall reaction. A rate equation describing the kinetics of the ion transfer that is valid for the conditions at thin organic film-modified electrodes is derived. Kinetic data measured with two electrochemical techniques are in very good agreement.     

三元杂质砷锑钴对锌电沉积阴极过程的影响

采用电化学研究方法探讨了在锌电积过程中砷、锑、钴杂质对阴极极化过程的单一和共同影响,得出了单一杂质和三元杂质对锌电积过程影响的动力学方程及参数,并对其极化机理进行了研究.结果表明,含一元杂质的ZnSO4/H2SO4溶液的动力学参数与理论值基本一致,而含三元的ZnSO4/H2SO4溶液的传递系数α要比理论值小,说明杂质的存在及其含量的大小、品种的多少对锌电积影响程度不同.     

Numerical Modeling of Non-Steady-State Ion Transfer in Electrochemical Systems with Allowance for Migration

Numerical methods that are used for modeling non-steady-state ion transfer in electrochemical systems and account for the diffusion, migration, convection, and homogeneous chemical reactions are analyzed. It is shown that the violation of the electroneutrality condition (ENC) in the process of numerical solution is due to the difference equations being inconsistent with the initial differential equations. Difference schemes for numerical calculation of transfer processes, which make it possible to split a set of coupled equations, are designed and conditions for their stability are determined. The explicit difference scheme is self-consistent, i.e. it ensures that ENC is rigorously met. In the implicit difference scheme, ENC is probably violated when splitting the set of equations. To restore electroneutrality of the medium, it is proposed to use a physically substantiated analytical relation for the space charge relaxation under the action of a strong electric field.     

Effect of multivalent ions on electroosmotic flow in micro- and nanochannels

In this work, the effect of multivalent ions on electroosmotic flow is investigated for multiple electrolyte components. The cases studied include incorporating Ca2+ and HPO4(2-) and other monovalent ions, such as K+ and H2PO4-, into an aqueous NaCl solution. The governing equations are derived and solved numerically. The boundary conditions for the governing equations are obtained from the electrochemical equilibrium requirements. In comparison with monovalent ions, the results show that in micro- and nanochannels having fixed surface charges, multivalent counterions, even in very small amounts, reduce electroosmotic flow significantly, while the multivalent co-ions have little effect on the electroosmotic flow. Due to the enhanced ion-wall interactions multivalent counterions compose the majority of ions in the electric double layer (EDL), causing a decrease of net charge at the surface.     

Diffusioosmosis and electroosmosis of electrolyte solutions in fibrous porous media

The steady diffusioosmotic and electroosmotic flows of an electrolyte solution in the fibrous porous medium constructed by a homogeneous array of parallel charged circular cylinders are analyzed under conditions of small Peclet and Reynolds numbers. The imposed electrolyte concentration gradient or electric field is constant and can be oriented arbitrarily with respect to the axes of the cylinders. The thickness of the electric double layers surrounding the cylinders is assumed to be small relative to the radius of the cylinders and to the gap width between two neighboring cylinders, but the polarization effect of the diffuse ions in the double layers is incorporated. Through the use of a unit cell model, the appropriate equations of conservation of the electrochemical potential energies of ionic species and the fluid momentum are solved for each cell, in which a cylinder is envisaged to be surrounded by a coaxial shell of the fluid. Analytical expressions for the diffusioosmotic and electroosmotic velocities of the bulk electrolyte solution as functions of the porosity of the ordered array of cylinders are obtained in closed form for various cases. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made. In the limit of maximum porosity, these results can be interpreted as the diffusiophoretic and electrophoretic velocities of an isolated circular cylinder caused by the imposed electrolyte concentration gradient or electric field.     

Transient natural convection induced by electrodeposition of Li+ ions onto a lithium metal vertical cathode in propylene carbonate

Transient natural convection caused by Li⁺ electrodeposition at constant current along a vertical Li metal cathode immersed in a 0.5 M LiClO₄–PC (propylene carbonate) electrolyte was compared with that by Cu²⁺ ion electrodeposition in aqueous CuSO₄ solution. The concentration profile of the Li⁺ ions was measured in situ by holographic interferometry. The interference fringes start to shift with time at a higher current density. The concentration boundary layer thickness for Li⁺ ions was successfully determined. With the progress of electrodeposition, the density difference between the electrolyte at the cathode surface and the bulk electrolyte increased to induce upward natural convection of the electrolyte. The electrolyte velocity was measured by monitoring the movement of tracer particles. The measured transient behavior of the ionic mass and momentum transfer rates normalized with respect to the steady-state value was numerically analyzed. Transient natural convection along a vertical cathode due to Li metal electrodeposition can be reasonably explained by boundary layer theory, similar to the case of Cu electrodeposition in aqueous CuSO₄ solution.     

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.     

Structural and mathematical models for pressure-dependent electrodiffusion of an electrolyte through heterogeneous ion-exchange membranes: Pressure-dependent electrodiffusion of NaOH through the MA-41 anion-exchange membrane

Structural and mathematical models are proposed for describing electrolyte transport through heterogeneous anion-exchange membranes under conditions of pressure-dependent electrodiffusion. The idea that mesopores and macropores are present in the membrane provides the basis for the structural model. The Nernst-Planck equations with a convective term are used to describe ion transport in the solution filling the pores. Results of the solution to the mathematical problem and the experimental investigations demonstrate the possibility of decreasing the transport numbers of sodium ions through an anion-exchange membrane by applying a pressure gradient in the same direction as the electrolyte diffusion flux in the membrane.     

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

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

Relaxation of the electrical double layer after an electron transfer approached by Brownian dynamics simulation

In this paper, the dynamical properties of the electrochemical double layer following an electron transfer are investigated by using Brownian dynamics simulations. This work is motivated by recent developments in ultrafast cyclic voltammetry which allow nanosecond time scales to be reached. A simple model of an electrochemical cell is developed by considering a 1:1 supporting electrolyte between two parallel walls carrying opposite surface charges, representing the electrodes; the solution also contains two neutral solutes representing the electroactive species. Equilibrium Brownian dynamics simulations of this system are performed. To mimic electron transfer processes at the electrode, the charge of the electroactive species are suddenly changed, and the subsequent relaxation of the surrounding ionic atmosphere are followed, using nonequilibrium Brownian dynamics. The electrostatic potential created in the center of the electroactive species by other ions is found to have an exponential decay which allows the evaluation of a characteristic relaxation time. The influence of the surface charge and of the electrolyte concentration on this time is discussed, for several conditions that mirror the ones of classical electrochemical experiments. The computed relaxation time of the double layer in aqueous solutions is found in the range 0.1 to 0.4 ns for electrolyte concentrations between 0.1 and 1 mol L(-1) and surface charges between 0.032 and 0.128 C m(-2).