Faradaic Current Density Research Articles

A numerical study of the equilibrium and nonequilibrium diffuse double layer in electrochemical cells

A numerical solution of the Nernst-Planck and Poisson equations is presented. The equations are discretized in a finite difference scheme using the method of lies on variable spatial and temporal grids. A Gear’s stiffly stable predictmector integration procedure which automatically adjusts the order of the predictor and corrector equations (and the step size) to ensure the accuracy of the results is incorporated. Some advantages of our approach over more classical ones are discussed. The numerical solution is applied to the study of the equilibrium and nonequilibrium diffuse electrical double layer (EDL) at the metal electrode/electrolyte solution interface. The prescription of this layer is similar to that used in the classical Gouy-Chapman theory. Electrode kinetics are described by the Butler-Volmer equation. Concentration, faradaic and displacement electric current densities, and electric potential profdea as functions of time a- the cell thickness, and partiahly in the EDL regions at the metal electrode/solution interfaces, are obtained. Two physical problems are studied: (i) the formation of the equilibrium EDL, and (ii) the transient response of the system to an electrical perturbation. Thew examplea illustrate the potential applications of the numerical method. Numerical techniques for the solution of transport problems in electrochemistry have contributed significantly to the analysis of many complex processes which are difficult to deal with using more conventional approaches. Though other techniques like the boundary element method are experiencing an increasing popularity,’ fmite differences2J has been one of the most widely used in electrochemistry since the pioneering work by Feldberg!.s The need for numerical solutions appears in a multitude of problems of practical interest, e.g., transport phenomena described by diffusional type or second-order parabolic PDEs (partial differential equations) subjected to temporal boundary conditions,*J diffusion-migration situations involving the coupled, nonlinear Nemst-Planck and Poisson equations,b10 convective diffusion problems in electrochemical cell~,~J etc. Modern numerical solutions to the Nemst-Planck and Poisson equations in electrochemical cells including electrical double layer (EDL) effects seem to be lacking.’ We present, here, a numerical solution of these equations for a system consisting of three ions

The electrochemical oxidative dimerization of methane

The electrochemical oxidative dimerization of methane to give C 2 hydrocarbon species was investigated in solid oxide fuel cells (SOFCs) possessing the general configuration: CH 4, (anode) electrocatalyst/ZrO 2(8m/oY 2O 3)/La 0.9Sr 0.1MnO 3, O 2(air). Perovskite anode electrocatalysts shown to possess activity towards promoting the subject reaction included Sm 0.5Ce 0.5CuO 3, Tb 0.8Sm 0.2CuO 3, Gd 0.9Th 0.1CuO 3, Gd 0.9Na 0.1MnO 3 and Th 0.8Yb 0.2NiO 3. An inverse linear dependence was found for methane conversion to C 2 species on both perovskite electrocatalyst molecular volumes and their lattice-ionic free volumes. These observations suggested that anode electrocatalyst activity towards promoting C 2 synthesis may be either dependent upon lattice spacings or on their intrinsic ionic transport properties, both of which might be expected to be related to the lattice metal-oxygen bonding energy. The maximum partial Faradaic current densities at copper based perovskite were found to exhibit a linear dependence to the experimentally determined magnetic moments, consistent with an increasing population of Cu 3+ sites, favoring stabilization of reactive surface O - species.

Electrochemical Natural Gas Conversion to More Valuable Species

The electrochemical oxidative dimerization of methane to give hydrocarbon species was investigated in solid oxide fuel cells possessing the general configuration Perovskite anode electrocatalysts shown to possess activity toward promoting the subject reaction included , , , , and . Maximum partial faradaic current densities at active perovskite anode electrocatalysts for promoting the subject reaction were found to be directly correlatable to their calculated oxygen binding energies on the perovskite surface, where increasing binding energies were found to favor higher rates for electrochemical partial methane oxidation. Increasing surface oxygen binding energies at perovskite anode electrocatalysts were found to correlate with increasing perovskite lattice free volumes with electrochemical measurements, supporting increasing surface oxygen binding energies and perovskite lattice‐free volumes as leading to enhanced rates for the subject reaction. As a consequence, synergism was found between experimentally determined perovskite anode electrocatalyst activities, their calculated surface oxygen binding energies, and lattice ionic‐free volumes.

ChemInform Abstract: Electrochemical Reduction of Carbon Dioxide at in situ Electrodeposited Copper.

AbstractHigh faradaic efficiencies and current densities for the electrochemical reduction of CO2 to both CH4 and C2H4 are achieved at Cu deposited in situ on glassy carbon from an aqueous CuSO4/KHCO3 electrolyte.

On the Electrochemical Reduction of Carbon Dioxide at In Situ Electrodeposited Copper

High faradaic efficiencies and current densities for the electrochemical reduction of to both and are reported at in situ deposited copper on glassy carbon electrodes in aqueous . At 8.3 mA/cm2 the cumulative yield for and can be essentially faradaic. At 25 mA/cm2 the overall efficiency for these two products was 79%. The proposed reduction mechanism does not appear to involve the direct electrochemical reduction of , but proceeds through the reaction of weakly adsorbed with electrochemically generated chemisorbed hydrogen at the copper surface. Subsequent reduction of this reduced species probably leads to bridged groups which can be desorbed to give either carbon monoxide or reduced further to give and .

Effect of electrolyte properties on current efficiency of bipolar packed bed electrodes.

Electric current densities via different pathways and current efficiencies were evaluated in a bipolar packed bed electrode cell of 0.1m × 0.1m in cross section and 0.2m in height. The particulate electrodes were cylindrical ferrite pellets 6mm in diameter and 6mm long. The bypass current density was dependent on electrical conductivity of electrolyte, solid holdup, cell configuration and cell voltage. The Faradaic current density under the mass transfer-controlling condition was simulated with the mass transfer coefficient in packed bed, the ratio of effective area to surface area of each pellet, solid holdup and depolarizer concentration. The overall current efficiency was expressed as a function of bypass current density, Faradaic current density and actual current efficiency. Introduction of inert gas bubbles increased the maximum current efficiency by about 15%.

The replacement of Fick's laws by a formulation involving semidifferentiation

The mathematical operation of semidifferentiation enables the concentration of an electroactive species at the surface of an electrode to be related straightforwardly to the faradaic current density. This relationship holds irrespective of the degree of reversibility of the electrode reaction and is not restricted to diffusion-controlled situations. This concept provides an improved starting point for the prediction of voltammetric relationships, compared with the classical Fick's law approach, in that only one additional condition (representing the electrical signal applied to the cell) is needed to characterize the experiment. This contrasts with the classical approach in which a number of simultaneous partial differential equations need to be solved. In addition, as illustrated in the examples cited, the greater simplicity of the new approach permits a generalization of voltammetric concepts and suggests improved experimental techniques. Specifically, we have uncovered a novel method of elucidating electrochemical kinetics.

Kinetics of the Deposition and Dissolution of Silver

Galvanostatic measurements, made on spherical silver electrodes in highly purified aqueous acid solutions of silver perchlorate at current densities up to 10 amp cm—2, gave overpotential as a function of time and Faradaic current density at constant total current. Variables were total current density, concentration of silver ions and state of the electrode surface. The theory of the surface diffusion kinetics was developed to encompass high current density regions and the surface adion concentration (cad0) evaluated. A theoretical analysis of the steady state of surface diffusion control of the metal-ion exchange reaction shows that the current is distributed nonuniformly between growing sites, with constant potential over the electrode surface. An equation previously developed by Rojter, Juza, and Polujan has been modified and shown to be applicable to galvanostatic transients when the transfer reaction is rate controlling. The symmetry factor β, of electrode kinetics, is shown to be potential dependent, and, in systems of sufficiently high i0 values, to tend to zero at high overpotential. This results in a limiting current density for a transfer controlled process. The tendency towards such a current was observed and shown to be quantitatively consistent with the discussion of β.