Secondary Current Distribution Research Articles

Scaling Relationships for Designing Local Bipolar Electrochemical Systems

Bipolar electrochemistry has recently been utilized for many new electrochemical applications from electroanalytics to electrodeposition(1). Bipolar electrochemistry is defined as spatially segregated, equal and opposite reduction and oxidation on an electrically-floating conductor. Passage of current in an electrochemical cell produces an ohmic potential drop through the electrolyte solution. When this potential drop is substantial, and a conductor is in that potential gradient, the path of least resistance for current flow can be through the conductor, inducing bipolar electrochemical reactions. In previous work, we have shown that a rastering microjet electrode system can create a highly localized potential distribution that is useful for localized bipolar electrodeposition(2, 3). The microjet configuration we use is called the scanning bipolar cell (SBC), where a feeder anode is located inside the microjet and a feeder cathode is placed in the far-field electrolyte pool outside the microjet. In the SBC configuration, potential gradients are high right beneath the microjet. If charge transfer resistances are modest, reduction occurs on the conducting substrate and an equal and opposite oxidation takes place in the far-field of the conductor. In short, no direct electrical connection is made to the conducting substrate, but electrodeposition and patterning occurs when the SBC is rastered over the conductor. The SBC has been used to electrodeposit Cu, Ni, Ag, Au, and various transition metal alloys (CuNi, FeNi, CoNi) on copper and gold substrates. In this work, we use finite element method (FEM) computations (axisymmetric geometry shown in Figure 1a) to explore the effects of substrate and microjet geometries and compare to experimental demonstrations. A secondary current distribution is appropriate for SBC computations because the concentration is substantially uniform (limiting current densities exceed 10 A cm-2 in the microjet configuration used here). Computed current density profiles for varying SBC operating conditions shown in Figure 1b demonstrate current localization at the conductive substrate. For a secondary current system, the dimensionless Wagner number relates charge transfer resistances to ohmic resistances of the cell. Bipolar electrochemical systems are engineered to have small Wagner numbers (small charge transfer resistances and large ohmic drops) so that the preferred current pathway is through the conductive electrode. Computations show that ohmic resistance is dominated by the region in the annular gap and charge transfer resistance can be approximated using Tafel kinetics for the local reaction beneath the nozzle. These approximations are for an axisymmetric system on a macroscopically large substrate compared to the microjet. When substrate dimensions are not axisymmetric, or approach dimensions of the microjet, the far-field reaction kinetics can substantially affect this scaling relationship. In addition to substrate scaling, we explore how imperfect nozzle geometries affect ohmic drop and the impact of the feeder cathode on the bipolar behavior. Scale-down of the SBC into nanoscopic dimensions is mainly limited by fabrication and motion control for the microjet. However, given the similarity of the SBC to scanning ion conductance microscopy, which has motion-control and pipette dimensions at sub-micron resolutions, we are confident practical sub-micron systems can be achieved (4).

Analytical and Computational Scaling Relationships for the Coupled Phenomena that Control Local Bipolar Electrochemical Behavior

Bipolar electrochemistry involves intricate coupling of ionic migration in the electrolyte, charge transfer kinetics of the equal and opposite oxidation and reduction chemistries, and the thermodynamic relationship of the bipolar couple. Finite element method simulations are used to explore these coupled phenomena in the scanning bipolar cell (SBC), an experimental system we recently introduced. We generalize simulation results through the development of scaling relationships based on a linearized equivalent circuit model comprised of resistors and a transistor. Accurate analytical expressions are presented for the SBC electrolyte ohmic resistance. Secondary current distribution simulations for two thermodynamically distinct bipolar couples identify the most appropriate linearizations for the charge transfer resistance. In our model, the bipolar redox couple can have a thermodynamic barrier that serves as a gate voltage for switching the transistor that enables or blocks bipolar current flow through the substrate. The resulting resistor-transistor network provides an analytical expression for the bipolar current efficiency, the fraction of applied current participating in bipolar electrochemistry. Simplification of coupled (nonlinear) phenomenon into circuit elements has inevitable inaccuracies, and we explore the origins and size of these systematic errors. The implications of the scaling ideas presented here are generalizable for other purpose-driven bipolar electrochemical systems.

Application of Local Backside Contacts for Structuring of Silicon with Anodization: Simulation and Experiments

Anodization of silicon can be used as a structuring process with adjustable anisotropy by control of charge flow through the silicon substrate with local electrodes placed on the substrate. In this work, for the first time the secondary current distribution model for anodization of p-type silicon with backside local contacts (electrodes) is presented and compared to experiments. Additionally, a novel idea of active backside contacts is worked out. Influences of backside electrode positions on the etch form is investigated to achieve spatial control of the current distribution during anodization process. Possibilities and limitations of the developed method with locally distributed backside contacts for shape control during silicon anodization are discussed.

Finite element modeling of silver electrodeposition for evaluation of thickness distribution on complex geometries

The paper reveals benefits of multi-disciplinary computer simulation and parametric studies in the design of silver plating process for improved coating distribution. A finite element model of direct current silver plating is experimentally validated for an Assaf panel without agitation. The model combines tertiary current distribution with Butler–Volmer electrode kinetics and computational fluid dynamics at a very low flow-rate. The effect of charge transfer coefficients on the throwing power of the process is quantified for the studied geometry, and variation of cathodic current density and exchange current density is investigated. A simpler model based on secondary current distribution is employed to quantify the effect of electrolyte conductivity on the throwing power of the process. A model combining tertiary current distribution and computational fluid dynamics has been developed and experimentally validated for simulation of complex telecom component electroplating in agitated electrolyte. The effect of current density on the process throwing power is quantified. Recommendations regarding modeling methodology and the effect of electrochemical and process parameters on the thickness distribution have been developed.

A Direct Numerical Method of Lines Approach for Predicting Primary and Secondary Current Density Distributions: Linear and Nonlinear Boundary Conditions

A direct numerical method of lines approach is presented for solving Laplace’s equation to obtain primary and secondary potential and current density distributions in electrochemical cells. Steady-state heat transfer in solids is governed by Laplace’s equation and has been solved directly by various numerical methods such as the successive over-relaxation method and the implicit alternative direction method (see e.g., Carnahan et al., 1969). Another method that has been used to solve Laplace’s equation is the method of false transients (Schiesser, 1991, 1994). In this method, one adds a time derivative of the dependent variable to Laplace’s equation, uses finite differences to approximate the spatial derivatives, and then solves the resulting system of equations by the method of lines (Davis, 1984; Schiesser, 1991, 1994; Rice and Do, 1995; Schiesser and Silebi, 1997; Cutlip and Shacham, 1998; Constantinides and Mostoufi, 1999;Taylor, 1999; Subramanian and White, 2000a). In our earlier paper, we presented a method for solving Laplace’s equation using a semi analytical method of lines. This method consists of using a central difference approximation for the second-order derivative in one of the spatial directions followed by solving analytically the resulting system of second-order differential equations by an analytical method. That is, the system of second-order, two-point boundary value problems are solved analytically by casting them in first-order form. As of today, solvers have developed to a point where the resulting two point boundary value problems in y (when discretization is used in x) can be directly and efficiently solved numerically. We present and analyze the results of this approach, called Numerical two dimensional method of lines for analyzing current distributions in Hull cell and other geometries of interest for electrochemical engineers. Another key point is that instead of finite difference methods, staggered grid and finite volume methods with variable node spacing in x gives much superior results even compared to state of the art finite element software such as COMSOL. Acknowledgements The work presented herein was funded in part by the Clean energy institute at the University of Washington, Seattle. References Carnahan, B., Luther, H.A., Wilkes, J.O., 1969. Applied Numerical Methods. Wiley, New York.Schiesser, W.E., 1991. The Numerical Method of Lines. Academic Press, New York.Schiesser, W.E., 1994. Computational mathematics in Engineering and Applied Science: ODEs, DAEs and PDEs. CRC Press, Boca Raton.Schiesser, W.E., Silebi, C.A., 1997. Computational Transport Phenomena. Cambridge UniversityPress, New York.Davis, M.E., 1984. Numerical Methods and Modeling for Chemical Engineers. Wiley, New York.Rice, R.G., Do, D.D., 1995. Applied mathematics and modelling for chemical Engineers. John Wiley& Sons Inc., New York.Constantinides, A., Mostoufi, N., 1999. Numerical Methods for Chemical Engineers with Matlab Applications. Prentice-Hall, New Jersey.Cutlip, M.B., Shacham, M., 1998. The numerical method of lines for partial differential equations. CACHE News 47, 18–21.Taylor, R., 1999. Engineering computing with maple: solution of PDEs via method of lines. CACHE News 49, 5–8.Taylor, R., Krishna, R., 1993. Multi Component Mass Transfer. Wiley, New York.Subramanian, V.R., White, R.E., 2000a. Solving differential equations with maple. Chemical Engineering Education 34, 328–336.Subramanian, V.R., White, R.E., 2000b. A semianalytical method for predicting primary and secondary current density distributions: linear and non-linear boundary conditions. Journal of Electrochemical Society 147 (5), 1636–1644.Subramanian, V.R., White, R.E., 2004. Semianalytical method of lines for solving elliptic partial differential equations. Chemical Engineering Science 59, 781–788.

Theory and Experiments for Generalization of the Scanning Bipolar Cell for Patterning of Diverse Metals

The Scanning Bipolar Cell (SBC) is a novel system using bipolar electrochemistry for micro-scale patterning without needing to connect the power supply to the substrate. Bipolar electrochemistry, defined as spatially segregated, equal and opposite reduction and oxidation on an electrically-floating conductor, has been understood for several decades but has recently seen a renaissance for many new electrochemical applications (1). The main driving force for bipolar electrochemistry is the ohmic potential drop through the electrolyte solution during the passage of current in an electrochemical cell. The scanning bipolar cell was modified from an electrodeposition tool we call “Electrochemical Printing” (EcP). EcP jets electrolyte through a microcapillary nozzle with an upstream anode onto a conductive substrate that is cathodically polarized using an electrical connection. In this system, the ohmic potential drop beneath the microcapillary wall is designed to be large compared to charge transfer overpotential (small Wagner number), creating a localized current on the macroscopically polarized substrate. The large ohmic potentials typical of EcP make this system ideal for bipolar electrochemical applications and is easily modified when, instead of using the substrate as a cathode, it is allowed to float, and a new “feeder” cathode is placed distant from the microjet (Figure 1a attached) (2). In this configuration localized and controllable electrodeposition occurs on the macroscopic conductive substrate without direct electrical contact. The concept for the scanning bipolar cell was first validated experimentally and computationally using the reversible copper redox couple, where copper deposits were patterned on a sacrificial copper substrate while copper in the far-field oxidized (2). The equal and opposite nature of bipolar electrochemistry provided a restructuring of the copper substrate, where the amount of material etched in the far-field was also locally deposited beneath the nozzle. Secondary current distribution computations evaluated the coupling between the ohmic and charge transfer resistances and determined relative current pathways through the system. We have further generalized the design guidelines for operating the SBC to include a wide range of electrodepositable materials such as nickel, gold, and silver. The design guidelines for the SBC depend on the nobility and electrochemical reversibility of the material. Tailoring the far-field electrochemical reaction to that of the local reduction is also essential for successful bipolar electrodeposition. Nickel is ideal for patterning with the SBC because it behaves irreversibly by forming a passivating oxide film, protecting the deposit from subsequent electrochemical oxidation. For reversible materials, such as copper, any previously patterned material can be electrochemically oxidized during subsequent deposition. This creates an added challenge for electrolyte design in order to create systems where the undesired copper oxidation is secondary to the far-field oxidation chemistry. To overcome this challenge we design pseudo-stable baths, where the equilibrium potential of the reducing agent (ascorbic acid) is slightly lower than that of the material being deposited. Figure 1b shows an optical micrograph of copper patterned on a gold substrate with ascorbic acid providing the bipolar oxidation in the far-field. Essentially, this is an electroless deposition bath that does not function well because of the low thermodynamic driving force. Nonetheless, the ascorbic acid oxidation is thermodynamically preferential to copper etching, so there is a window for the desired chemistry (ascorbic acid oxidation) to occur without the undesired chemistry (copper oxidation) occurring. This window also determines how fast we can drive the electrochemical reactions. Figure 1c shows an optical micrograph where the applied current is 10x larger than in 1b for the same electrolyte formulation, providing enough substrate polarization to do both undesired copper etching and ascorbic acid oxidation. Scaling relationships for the SBC have been studied via simulations, and scale-down limitations center around nozzle fabrication and motion control. However, the SBC functions similarly to scanning ion conductance microscopy (SICM), which has pipette dimensions and motion-control with nanometer resolutions. We are confident that electrolyte design characteristics at the micron-scale can be applied to sub-micron systems with smaller resolution and control (3). We have shown how modifying our pre-existing EcP technology for bipolar electrochemistry provides a platform for patterning without electrical connections to the substrate. Co-design of the electrochemical cell, electrolyte, and substrate is critical to engineering effective bipolar electrochemical systems.

(Electrodeposition Division Research Award) The Scanning Bipolar Cell: Design Principles for Patterning of Diverse Metals without Contact to the Substrate

Bipolar electrochemistry has recently been utilized for many new electrochemical applications from electroanalytics to electrodeposition (1). Bipolar electrochemistry is defined as spatially segregated, equal and opposite reduction and oxidation on an electrically-floating conductor. Passage of current in an electrochemical cell produces an ohmic potential drop through the electrolyte solution. When this potential drop is substantial, and a conductor is in that potential gradient, the path of least resistance for current flow can be through the conductor, inducing bipolar electrochemical reactions. Here we describe how to transform the electrodeposition method we call “Electrochemical Printing” (EcP) so it can function as a scanning bipolar cell. EcP uses a microjet cell configuration with an upstream anode and the substrate to be patterned is the cathode. Localized electrodeposition occurs when the ohmic potential drop is large compared to charge transfer overpotential, i.e. when there is a small Wagner number. Our existing EcP tool can serve as a scanning bipolar cell (Figure 1a attached) when, instead of using the substrate as a cathode, it is allowed to float, and a new “feeder” cathode is placed distant from the microjet. Ohmic potential drop beneath the microjet induces bipolar electrochemistry. With carefully engineered electrolytes, localized and controllable electrodeposition occurs on the floating substrate, without direct electrical contact. The concept for the scanning bipolar cell (SBC) was validated with the highly reversible copper chemistry, performing localized deposition beneath the nozzle while a copper substrate oxidized in the far-field (2). Figure 1b shows an optical micrograph of the copper on copper system, patterned with the SBC operated over a range of fly heights and applied currents. Secondary current distribution computations were used to determine the relative current flow pathways through the electrolyte and extent of bipolar electrochemistry through the substrate. We describe the electrolyte and operating principles for patterning a wide range of materials with the SBC. Our design guidelines depend on the nobility, kinetics, and reversibility of the material deposited, and importantly, tailoring the far-field oxidation chemistry redox potential to that of the species being deposited. Figure 1c shows an optical micrograph of nickel deposits patterned on a gold substrate at varying tool operating conditions. Here, the oxidation chemistry to complete the couple on the floating substrate is ascorbic acid. In this system, both nickel reduction and ascorbic acid oxidation behave irreversibly. For reversible materials, such as copper, any previously patterned copper material can be effectively erased during subsequent patterning, since the equal and opposite oxidation can be metal etching on the floating substrate. This challenge is overcome by designing pseudo-stable electrolyte formulations, similar to electroless deposition baths, that protect the material from being further oxidized. Figure 1d depicts an optical micrograph of copper patterned on a gold substrate using ascorbic acid for the far-field oxidation chemistry. The electrolyte here was designed so that the equilibrium potential of ascorbic acid is marginally higher than that of copper, creating a slightly unstable formulation, but where ascorbic acid oxidation is preferential to copper etching, allowing the pattern to be retained. The SBC scaling behavior has been studied, and is mainly limited by fabrication and motion control for the microjet. However, given the similarity of the SBC to scanning ion conductance microscopy, which has motion-control and pipette dimensions at sub-micron resolutions, we are confident practical sub-micron systems can be achieved (3). We have shown that bipolar electrochemical patterning requires careful co-design of the electrolyte, substrate, and SBC, but it is possible to achieve patterning of diverse materials. The scanning bipolar cell represents a new class of remote control electrochemistry.

Analytical representations of the spread harmonic measure density.

We study the spread harmonic measure that characterizes the spatial distribution of reaction events on a partially reactive surface. For Euclidean domains in which Brownian motion can be split into independent lateral and transverse displacements, we derive analytical formulas for the spread harmonic measure density and analyze its asymptotic behavior. This analysis is applicable to slab domains, general cylindrical domains, and a half-space. We investigate the spreading effect due to multiple reflections on the surface, and the underlying role of finite reactivity. We discuss further extensions and applications of analytical results to describe Laplacian transfer phenomena such as permeation through semipermeable membranes, secondary current distribution on partially blocking electrodes, and surface relaxation in nuclear magnetic resonance.

Multiphysics coupling simulation of RDE for PCB manufacturing

Purpose– The purpose of this paper is to optimize experimental parameters and gain further insights into the plating process in the fabrication of high-density interconnections of printed circuit boards (PCBs) by the rotating disc electrode (RDE) model. Via metallization by copper electrodeposition for interconnection of PCBs has become increasingly important. In this metallization technique, copper is directly filled into the vias using special additives. To investigate electrochemical reaction mechanisms of electrodeposition in aqueous solutions, using experiments on an RDE is common practice.Design/methodology/approach– An electrochemical model is presented to describe the kinetics of copper electrodeposition on an RDE, which builds a bridge between the theoretical and experimental study for non-uniform copper electrodeposition in PCB manufacturing. Comsol Multiphysics, a multiphysics simulation platform, is invited to modeling flow field and potential distribution based on a two-dimensional (2D) axisymmetric physical modeling. The flow pattern in the electrolyte is determined by the 2D Navier–Stokes equations. Primary, secondary and tertiary current distributions are performed by the finite element method of multiphysics coupling.Findings– The ion concentration gradient near the cathode and the thickness of the diffusion layer under different rotating velocities are achieved by the finite element method of multiphysics coupling. The calculated concentration and boundary layer thicknesses agree well with those from the theoretical Levich equation. The effect of fluid flow on the current distribution over the electrode surface is also investigated in this model. The results reveal the impact of flow parameters on the current density distribution and thickness of plating layer, which are most concerned in the production of PCBs.Originality/value– By RDE electrochemical model, we build a bridge between the theoretical and experimental study for control of uniformity of plating layer by concentration boundary layer in PCB manufacturing. By means of a multiphysics coupling platform, we can accurately analyze and forecast the characteristic of the entire electrochemical system. These results reveal theoretical connections of current density distribution and plating thickness, with controlled parameters in the plating process to further help us comprehensively understand the mechanism of copper electrodeposition.

Computational modeling of anodic current distribution and anode shape change in aluminium reduction cells

In aluminium reduction cells, the profile of a new carbon anode changes with time before reaching a steady state shape, since the anode consumption rate, depending on the current density normal to anode surfaces, varies from one region to another. In this paper, a two-dimension model based on Laplace equation and Tafel equation was built up to calculate the secondary current distribution, and the shift of anode shape with time was simulated with arbitrary Lagrangian-Eulerian method. The time it takes to reach the steady shape for the anode increases with the enlargement of the width of the channels between the anodes or between the anode and the sidewall. This time can be shortened by making a sloped bottom or cutting off the lower corners of the new anode. Forming two slots in the bottom surface increases the anodic current density at the underside of the anode, but leads to the enlargement of the current at the side of the anode.

Simulation of current distribution along a planar electrode under turbulent flow conditions in a laboratory filter-press flow cell

A theoretical analysis of primary, secondary and limiting current distributions along the planar nickel electrode of a laboratory filter-press flow cell has been carried out using previous data on the reduction of Fe(CN)63− ions in an aqueous 0.1moldm−3 Na2CO3 electrolyte at 293K. The primary current distribution decreased at the inlet and outlet of the cell and became uniform away from the entrance and exit. The secondary current distribution predominated along the electrode; edge effects appearing only at the corners of the electrolyte compartment. The limiting current distribution presented higher edge effects compared to those experienced under secondary current distribution due to jet flow in the inlet section of the electrolyte compartment. The limiting current density incorporated numerically calculated local flow velocities under turbulent flow conditions which were simulated by solving a Reynolds averaged Navier-Stokes (RANS) equation, expressed in terms of turbulent viscosity and a standard turbulence model.

Numerical Simulation of the Primary, Secondary and Tertiary Potential Distribution on Porous Cathode in a Flow-through Packed Bed Reactor. Influence of Thickness, Concentration and Hydrodynamics in Porous Media

Packed bed electrodes can be used for electrochemical recovery of heavy metals from a variety of industrial and laboratory model solutions. The packed bed electrode forms a porous flow-through (Figure 1) configuration providing large surface area usually depleting the concentration of several metal ions below 0.1 ppm. For design porpoises of these electrodes, it is necessary to study the influence of geometry (cathode thickness), flow rate and concentration on potential distribution.Numerical simulations of primary, secondary and tertiary current distributions on the porous cathode of a packed bed electrochemical reactor (Figure 1) were calculated. For primary and secondary current distribution, Laplace equations with its respective boundary conditions (constant potential for primary current distribution and charge transfer kinetics described by a Tafel approximation in secondary current distribution) were evaluated using the finite element method. For tertiary current distribution, the influence of hydrodynamics was taken in account, considering Navier-Stokes model with Brinkman extension for porous media. Once Brinkman equations was solved and local velocity distributions were obtained, local mass transfer coefficients were evaluated by means of following relationship: Kma=cvb where Km is local mass transport coefficient, a is the specific area, v is local velocity, c and b are empirical constants taken from literature. The effects of flow rate, ion concentration, matrix conductivity and thicknes on the distribution of current on porous cathode are analyzed. Results of current distribution obtained by Nava et. al 2008 [1] enable comparisons with the simulations.

Simulation of Current Distribution Under Turbulent Flow Conditions in a Laboratory Filter-Press Flow Cell

A theoretical analysis of primary, secondary and tertiary current distributions along a planar nickel electrode in a laboratory filter-press flow cell has been carried out using the reduction of Fe(CN)6 3 − ions in a sodium carbonate electrolyte as a model reaction system. The primary current distribution decreased at the inlet and outlet of the cell and became uniform away from the entrance and exit. The secondary current distribution predominated throughout the electrode; edge effects appearing only at the corners of the cell. The tertiary current distribution presented higher edge effects compared to those experienced under secondary current distribution due to jet flow at the inlet of the cell. The limiting current density incorporated numerically calculated local flow velocities under turbulent flow which were simulated by solving the Reynolds averaged Navier-Stokes (RANS) equation, expressed in terms of turbulent viscosity and a standard turbulence model.

Numerical simulation of the primary, secondary and tertiary current distributions on the cathode of a rotating cylinder electrode cell. Influence of using plates and a concentric cylinder as counter electrodes

Numerical simulations of primary, secondary and tertiary current distributions on the cathode of a rotating cylinder electrode (RCE) cell, using four-plate, six-plate, and a concentric cylinder as counter electrodes, were calculated using the finite element method. Copper electrodeposition from an acidic sulfate electrolyte is used as a test system. Charge transfer kinetics is described by a Tafel approximation while mass transport is considered using a Nernstian diffusion layer expression. The importance of using plates and concentric counter electrodes on RCE cathode is demonstrated. The effects of applied current density and electrode rotation speed on the distribution of current on RCE cathode are analyzed. Electrodeposition experiments with copper enable comparisons with the simulations.

Measurements and Simulations of Electrochemical Impedance Spectroscopy of a Three-Electrode Coin Cell Design for Li-Ion Cell Testing

A 2-D mathematical model of the secondary current distribution in a three-electrode cell is used in order to understand distortion of impedance spectra influenced by the position of the reference electrode (RE) in a cell when one electrode extends past the other. The cell setup consists of a modified coin cell, i.e., working and counter electrodes face each other, and a RE is positioned behind the counter electrode (CE) that has a small hole in it to allow for electrolyte access. This configuration shows large distortion of WE and CE impedance data when taken against the RE. The WE/RE impedance is underestimated and contains a negative impedance contribution from the CE whereas the CE/RE impedance is overestimated and contains a positive impedance contribution from the WE. As supported by simulations, the distortions arise from a radial ionic current flowing from the WE toward the edge of the CE hole, and are minimized through an increase of the electrolyte conductivity, an increase of the separator thickness, or a decrease of the hole size in the CE. The distortions nearly disappear when an additional hole is included in the WE that is perfectly aligned with the hole in the CE. These results should be considered whenever designing a 3-electrode cell where the RE is not sandwiched between the two other electrodes.

Numerical simulation of current distribution along the boron-doped diamond anode of a filter-press-type FM01-LC reactor during the oxidation of water

This work shows a theoretical analysis of primary and secondary current distributions along a boron-doped diamond (BDD) anode of a filter-press-type FM01-LC reactor. Hydroxyl radical formation via water discharge was used as a test system. Microelectrolysis studies confirm that hydroxyl radicals are formed at potentials between 2.3V⩽E⩽2.75V vs. SHE and that at higher potentials oxygen evolution reaction (OER) occurs. Primary current distribution is more uniform away from the curved corners of the cell, originated by the spacer between electrodes; however, the current distribution values at the corners and near to them, differ with a magnitude order of 1×10−5; hence, primary current distribution at BDD anode in the FM01-LC reactor can be considered uniform. Secondary current distribution at different over potential values of 1.7, 1.9 and 2.15V, respectively, did not show border effects. Attenuation of secondary current distribution is associated to kinetic parameters of water discharge on BDD and appropriate cell design. The importance of secondary current distribution for the production of hydroxyl radicals on BDD anode, to avoid OER, is discussed.

Optimization of a Molten Salt Electrolytic Bath Geometry for Rare Earth Metal Recovery using a Finite Element Method

For a recycling procedure for rare earths from spent hydrogen absorbing alloys by rare earths electrodeposition in a molten salt, the electrolytic bath and the cathode accessories have been optimized by evaluating the appropriate secondary current distribution using finite element method (FEM) computer simulation. The desirable cathode dish as an accessory was designed to prevent drops of less adherent electrodeposits, which improved the current density distribution compared with an a priori determined one. In the bath optimization, a reciprocal proportionality of the difference between the maximum and minimum current densities vs. the ratio of volume to surface area (or electrolyte volume) was found. It was found by FEM that if a resistive floating mass is assumed on the electrolyte surface, the observed necking in the electrodeposit near the electrolyte surface can be analyzed.

Simulation study of tertiary current distributions on rotating electrodes

The tertiary current distributions on rotating electrodes have been studied by using the numerical simulation method. An acid copper sulphate electrolyte composed of 0·3M CuSO4 and 1·9M H2SO4 was used within an electrochemical cell of practical dimensions. The rotating disc had a diameter of 6 mm, within which the working electrode with diameter of 3 mm was located at the bottom centre of the disc. The distributions of ion concentrations were obtained by two-dimensional fluid flow simulation and the solution of mass transport equations based on axial symmetry. The calculated concentration boundary layer thicknesses agree well with those obtained from the Levich equation. It is found that the tertiary current distribution on the working electrode is affected by the rotating velocity of the electrode, even if currents are considerably below the limiting current. The effect disappears with the increase in rotating velocity up to 1000 rev min−1 in comparison with the secondary current distribution. The tertiary current distributions for three types of working electrode have been calculated and an improved shape of working electrode is proposed. Since the working electrode is normally used for electrochemical measurements, e.g. polarisation characteristics, which are applied for the calculation of current distribution in the present work, the present study would provide beneficial results to improve the accuracy of measurements.

Methodology for measuring current distribution effects in electrochromic smart windows

Electrochromic (EC) devices for use as smart windows have a large energy-saving potential when used in the construction and transport industries. When upscaling EC devices to window size, a well-known challenge is to design the EC device with a rapid and uniform switching between colored (charged) and bleached (discharged) states. A well-defined current distribution model, validated with experimental data, is a suitable tool for optimizing the electrical system design for rapid and uniform switching. This paper introduces a methodology, based on camera vision, for experimentally validating EC current distribution models. The key is the methodology's capability to both measure and simulate current distribution effects as transmittance distribution. This paper also includes simple models for coloring (charging) and bleaching (discharging), taking into account secondary current distribution with charge transfer resistance and ohmic effects. Some window-size model predictions are included to show the potential for using a validated EC current distribution model as a design tool.

Self-powered electroporation using a singularity-induced nano-electroporation configuration

This study demonstrates the feasibility of creating a self-powered (galvanic) electroporation device using the singularity-induced nano-electroporation configuration. Using this configuration, the electric field in a galvanic electrochemical cell can be amplified and used for electroporation. A secondary current distribution model of a self-powered electroporation device shows that the device can create both reversible and irreversible electroporation-inducing electric field magnitudes, and generate a small amount of power.