Oxygen transport at porous air electrodes: Experimental

Porous carbon air electrodes have been operated in fully developed and laminar channel flow and their limiting current density measured with variations in the air velocity, the electrode length and the air channel thickness. The results are placed on a theoretical basis, using a theoretical model previously developed for the two extreme conditions of a thin mass transfer boundary layer in the air channel and complete oxygen exhaustion. The implications of the results on cell design are discussed.     

Flow-through and flow-by porous electrodes of nickel foam Part III: theoretical electrode potential distribution in the flow-by configuration

This paper deals with the theoretical potential distribution within a flow-by parallelepipedic porous electrode operating in limiting current conditions in a two-compartment electrolytic cell. The model takes into account the influence of the counter-electrode polarization and of the separator ohmic resistance. The results show that the design of the porous electrode requires the knowledge of the solution potential distribution within the whole cell volume.Nomenclature a _c specific surface area per unit volume of electrode - C ₀ entrance concentration (y=0) - C _s exit concentration (y=y ₀) - E electrode potential (= _M – _S ) - E _o equilibrium electrode potential - F Faraday number - i current density - mean mass transfer coefficient - K parameter [a _ea zFi _oa/(_a RT)]^1/2 - L porous electrode thickness - n number of terms in Fourier serials - P specific productivity - Q volumetric flow-rate - mean flow velocity based on empty channel - V constant potential - V _R electrode volume - x thickness variable - X conversion - y length variable - y ₀ porous electrode length - z number of electrons in the electrochemical reaction Greek symbols parameter - parameter - ionic electrolyte conductivity in pores - _S solution potential - _M matrix potential ( _M = constant) - parameter [=n/y ₀ - parameter [=+K] - overpotential Suffices a anodic - c cathodic - eq equilibrium - s separator - S solution     

The behaviour of porous electrodes in a flow-by regime—I. theoretical study

A mathematical model is presented to describe the behaviour of three-dimensional electrodes operating under limiting current conditions. Principal results are the effect of electrolyte resistivity, hydrodynamic and cell geometrical parameters on the distribution of the electrolyte potential and overpotential inside the structure. The most pertinent parameters of the electrode and application to the design of a reactor having perpendicular directions of current and electrolyte flow are given.     

A comparison between flow-through and flow-by porous electrodes for redox energy storage

An economic comparison is made between electrode configurations for flow redox battery applications: (i) the flow-through configuration (current parallel to the fluid flow) and (ii) the flow-by configuration (current perpendicular to the fluid flow). Steady-state computer models are developed for each electrode system. These models are used to predict current density, cell voltage, and power density over a complete cycle (charge and discharge). The economic comparison is made by optimizing each configuration with respect to an objective function appropriate for redox battery applications. Only the variable costs are considered. The results of the optimization show that the flowbby configuration is superior. The flow-through configuration not only yields a lower return on investment, but it is impractical due to a requirement of extremely low flow rates (Re < 0.001). Its failure is due to current flow (and ohmic potential drop) in the same direction as the fluid flow.     

Flow-through and flow-by porous electrodes of nickel foam Part IV: experimental electrode potential distributions in the flow-through and in the flow-by configurations

Experimental distributions of the solution potential in flow-through and flow-by porous electrodes of nickel foam operating in limiting current conditions are presented. These are in good agreement with the corresponding theoretical distributions. In the case of a flow-by configuration used in a two-compartment cell, the experiments confirm the validity of the models, presented in Part III, which take into account the presence of a separator (ceramic porous diaphragm or ion exchange membrane).Nomenclature a _e specific surface area per unit volume of electrode - C ₀ entrance ferricyanide concentration (y=0) - D molecular diffusion coefficient of ferricyanide - E _e cathode potential - F Faraday number - mean (and local) mass transfer coefficient - L electrode thickness - L _s-L separator thickness - m number of sheets of foam in a stack - n number of terms in Fourier series - Q volumetric flow-rate - r _s ohmic specific resistance of the separator - mean flow velocity based on empty channel - V constant potential - X conversion - x coordinate for the electrode thickness - y coordinate for the electrode length - y ₀ length of the porous electrode - z number of electrons in the electrochemical reaction Greek symbols parameter - parameter - ionic electrolyte conductivity - _sc solution potential in the pores of the cathode - _M matrix potential ( _sc = constant) - parameter [=n/y ₀] - electrolyte density - mean porosity - kinematic viscosity - E _c potential drop in the porous cathode - potential drop defined in Fig. 5 Indices c cathodic - o electrolyte alone - s separator     

Flow-through and flow-by porous electrodes of nickel foam. I. Material characterization

This paper deals with the characterization of three nickel foams for use as materials for flow-through or flow-by porous electrodes. Optical and scanning electron microscope observations were used to examine the pore size distribution. The overall, apparent electrical resistivity of the reticulated skeleton was measured. The BET method and the liquid permeametry method were used to determine the specific surface area, the values of which are compared with those known for other materials.Nomenclature a _e specific surface area (per unit of total volume) (m^–1) - a _s specific surface area (per unit of solid volume) (m^–1) - (a _e)_BET specific surface area determined by the BET method (m^–1) - (a _e)_Ergun specific surface area determined by pressure drop measurements (m^–1) - mean pore diameter (m) - mean pore diameter determined by optical microscopy (m) - mean pore diameter using Ergun equation (m) - e thickness of the skeleton element of the foam (m) - G grade of the foam (number of pores per inch) - P/H pressure drop per unit height of the foam (Pa m^–1) - r electrical resistivity ( m) - R _h hydraulic pore radius (m) - T tortuosity - mean liquid velocity (m s^–1) Greek symbols mean porosity - circularity factor - dynamic viscosity (kg m^–1 s^–1) - liquid density (kg m^–3) - pore diameter size dispersion     

The behaviour of porous electrodes in a flow-by regime—II. experimental study

An experimental study of the effectiveness of three-dimensional electrodes working under limiting current conditions and the experimental potential distributions in reactors where the directions of current and electrolyte flow are perpendicular is presented. The analytical solution presented in Part I is experimentally tested for packed bed electrodes of nickel sphericalparticles using the reduction of ferricyanide ions as the electrochemical reaction. Good agreement is observed for a range of reactors having various geometric dimensions, flow rates and reactant concentrations.     

Multiscale modeling of ion transport in porous electrodes

Ion transport through nanoporous materials is of fundamental importance for the design and development of filtration membranes, electrocatalysts, and electrochemical devices. Recent experiments have shown that ion transport across porous materials is substantially different from that in individual pores. Here, we report a new theoretical framework for ion transport in porous materials by combining molecular dynamics (MD) simulations at nanopore levels with the effective medium approximation to include pore network properties. The ion transport is enhanced with the combination of strong confinement and dominating surface properties at the nanoscale. We find that the overlap of electric double layers and ion–water interaction have significant effects on the ionic distribution, flux, and conductance of electrolytes. We further evaluate the gap between individual nanopores and complex pore networks, focusing on pore size distribution and pore connectivity. This article highlights unique mechanisms of ion transport in porous materials important for practical applications.     

Flow-through and flow-by porous electrodes of nickel foam. II. Diffusion-convective mass transfer between the electrolyte and the foam

The work described here concerns the diffusion-convective mass transfer to flow-through and flow-by porous electrodes of nickel foam. Empirical correlations giving the product of the mass transfer coefficient and the specific surface areaa _e of the material as a function of the pressure drop per unit electrode height and as a function of the grade characterizing the foam are proposed. The performance of various materials are compared in terms of vs the mean linear electrolyte flow velocity.Nomenclature a _e specific surface area (per unit of total volume of electrode) (m^–1) - A, B Ergun law coefficients determined in flow-by configuration - A, B Ergun law coefficients determined in flow-through configurationA, A (Pa m^–3 s²);B, B (Pa m² s^–1) - C _E entering concentration of ferricyanide ions (mole m^–3) - D molecular diffusion coefficient (m² s^–1) - F Faraday number (C mol^–1) - G grade of the foams - I _L limiting current (A) - mean mass transfer coefficient (m s^–1) - n number of stacked foam sheets in the electrode - P/H pressure drop per unit of height (Pa m^–1) - Q _v volumetric electrolyte flow rate (m³ s^–1) - Re Reynolds number - Sc Schmidt number - Sh Sherwood number - T mean tortuosity of the foam pores - mean electrolyte velocity (m s^–1) - V _R electrode volume (m³) - X conversion - dynamic viscosity (kg m^–1 s^–1) - v number of electrons in the electrochemical reaction - v kinematic viscosity (m² s^–1)     

Simultaneous reactions at disk and porous electrodes

Advances in electrochemical engineering are reviewed, and the methodology of the analysis of electrochemical systems is outlined. Examples illustrative of current research concern simultaneous reactions for flow-through porous electrodes and the more fundamental system of a rotating disk electrode. Here the undesirable side reaction is the formation of dissolved hydrogen, and the main reaction is the deposition of copper from sulfuric acid solutions. Distributions of reaction rate, concentration, and potential describe the detailed system behavior. The side reaction is responsible for the poorly defined limiting-current plateau on the disk electrode and provides a limit for the maximum flow rate at which good recovery can be achieved with the porous electrode.     

Gas transport in tight porous media: Gas kinetic approach

We describe the flow of gas in a porous medium in the kinetic regime, where the viscous flow structure is not formed in separate pores. Special attention is paid to the dense kinetic regime, where the interactions within the gas are as important as the interaction with the porous medium. The transport law for this regime is derived by means of the gas kinetic theory, in the framework of the model of “heavy gas in light one”. The computations of the gas kinetic theory are confirmed by the dimension analysis and a simplified derivation revealing the considerations behind the kinetic derivation. The role of the thermal gradient in the transport law is clarified.     

Criterion of completeness of electrolysis at flow porous electrodes

An equation is presented which allows the calculation of the critical solution flow velocity corresponding to complete reaction controlled by diffusion at flow porous electrodes. The equation has been experimentally confirmed with good accuracy for the mass transport-controlled reaction of the reduction of K₃Fe(CN)₆ at flow porous electrodes composed of fine platinum screens and of gilded graphite granules described in the literature. If the critical flow velocity can be determined experimentally, the equation may be used for the determination of the specific surface of the electrode or the diffusion coefficient of the process. In this way the specific surfaces of graphite electrodes have been determined, which also enabled the calculation of mass transfer coefficients and dimensionless correlations for the Sherwood Number andj _D-factor.List of symbols A/t' Empirical constant in Equation 5 - B Empirical constant in Equation 5 - d _p Particle diameter (cm) - D Diffusion coefficient (cm²s^–1) - j _D j _D -factor,j _D =(Sh)(Re)^–1(Sc)^–1/3 - k Coefficient of mass transfer (cm s^–1) - L Electrode height (cm) - M log₁₀e=0.4343 - r Pore radius (cm) - r ₁ Coefficient of correlation - R Limiting degree of conversion - R _c Critical limiting degree of conversion - R _c Average critical limiting degree of conversion - (Re) Reynolds Number, (Re)=ud _p / - R _h Hydraulic radius (cm) - s Specific surface (cm^–1) - (Sc) Schmidt Number, (Sc)=/D - Average Schmidt Number - (Sh) Sherwood Number, (Sh)=kd _p /D - T Absolute temperature (K) - u Superficial flow velocity (cm s^–1) - u _c Critical superficial flow velocity (cm s^–1) - w Interstitial flow velocity (cm s^–1) - Void fraction - Dynamic viscosity (poise) - Dimensionless parameter - Kinematic viscosity (cm²s^–1)     

Sonovoltammetry at platinum electrodes: surface phenomena and mass transport processes

Application of simultaneous ultrasound to representative solution-phase reversible voltammetric couples produce a step-shaped voltammogram at platinum electrodes of both macro and micro dimensions. The limiting current increases with ultrasonic power, but is not markedly affected by ultrasonic frequency in the 20–800kHz region. In contrast the complex voltammetry of a platinized platinum electrode surface within the hydrogen adsorption regime in aqueous acid medium is very little affected by sonication. Factors affecting the reproducibility of sonoelectrochemical experiments when employing ultrasonic sources are discussed.Author to whom correspondence should be addressed     

Free-convective ionic mass transport at inclined circular disk electrodes

Electrochemical mass transport rates at circular disk electrodes and at arbitrary inclination angles, α, formed between the cathode and the horizontal were measured. The results can be correlated by the general regression relationship

for O° ≤ α ≤ 170° and 2.5 × 10⁸ < Ra_L < 6.3 × 10⁹, using the distance between electrodes, L, as the characteristic length. The range of the exponents n, m is $\text{1}\text{4}$–$\text{1}\text{3}$ and C(α) varies from 0.33 to 0.39.     

Effect of radial diffusion on the polarization at porous flow-through electrodes

The effect of radial diffusion on the polarization of porous flow-through electrodes has been investigated with the aid of a mathematical model. The proposed model takes into consideration the rates of mass transfer in the axial direction by convection and in the radial direction by diffusion as well as charge transport in the pore electrolyte and electron transfer kinetics at the electrode-electrolyte interface. Normalization of the variables gave rise to dimensionless groups pertinent to the kinetic, ohmic and radial diffusion effects. These are respectively,I the reversibility index, Δ the parameter of ohmic effect andψ the parameter of radial diffusion. The latter (ψ=2φ/Sh) is the ratio of two other dimensionless groups. With this formulation, larger values ofψ correspond to more predominant control of the electrode behaviour by radial diffusion. The same is also true for the parameter of ohmic effect Δ. Solutions have been obtained for two limiting cases: negligible and signifcant potential drop in the pore electrolyte. In both cases, equations have been derived which give the quantitative (highly non-linear) effect ofψ on the current-polarization relations. In the case of a significant ohmic potential drop in the pore electrolyte, it was found that the controlling parameter is the product Δψ The two variables seem to give a synergistic effect since, at large Δ values a certain change inψ has a more pronounced effect on the polarization than the corresponding change at lower Δ values. Qualitative and quantitative tests of some aspects of the model are reported using the electrochemical reduction of copper ions from acid copper sulphate solutions at a packed bed of copper particles. Satisfactory agreement was obtained.     

Glycolate adsorption at gold and platinum electrodes: A theoretical and in situ spectroelectrochemical study

The adsorption of glycolate anions at sputtered gold thin-film electrodes was studied in perchloric acid solutions by cyclic voltammetry experiments combined with in situ Surface Enhanced Raman Scattering (SERS) and Surface Enhanced Infrared Reflection Absorption Spectroscopy under attenuated total reflection conditions (ATR-SEIRAS). Theoretical harmonic vibrational frequencies and band intensities obtained from B3LYP/LANL2DZ,6-31+G(d) calculations for glycolate species adsorbed on Au clusters with (1 1 1) orientation were used to interpret the experimental spectra. Vibrational data confirm the bidentate bonding of glycolate anions through the oxygen atoms of the carboxylate group, in a bridge configuration with the OCO plane perpendicular to the metal surface. The DFT calculations show no significant effect of the total charge of the metal cluster-adsorbate adduct on the vibrational frequencies of adsorbed glycolate species. The infrared experimental study is extended to platinum films electrochemically deposited onto sputtered gold thin-film electrodes showing the potential-dependent formation of adsorbed CO upon dissociative adsorption of glycolate anions. As in the case of gold, the reversible adsorption of glycolate anions takes place in a bidentate configuration as predicted by DFT calculations for glycolate adsorbed on Pt(1 1 1) clusters. At low glycolic acid concentration, the in situ ATR-SEIRA spectra evidence the formation of adsorbed oxalate as reaction intermediate.     

Effect of composition on the performance of cermet electrodes. Experimental and theoretical approach

This work aims to analyse the behaviour of cermet electrodes as a function of their composition, i.e. the ratio between ionic and electronic conducting particles. This is an important parameter to be considered to obtain maximum performance from this type of electrode, which is currently under study for application in oxygen sensors and solid oxide fuel cells. Experimental results of overall electrode resistance, including both ohmic and activation polarisation effects, have been obtained through electrochemical impedance spectroscopy measurements of Pt/YSZ electrodes in air. The results compare favourably with the theoretical predictions for several compositions above the percolation threshold of the electronic conductor. For this reason, the model is a useful tool for the design of optimised cermet electrodes; in particular, the experimental data show that maximum performance is attained for compositions very close to the percolation threshold of the electronic conductor, and this is in very good agreement with the modelling results.     

Inverse approach to quantify multi-physicochemical properties of porous electrodes for solid oxide fuel cells

Porous electrodes are critical components of solid oxide fuel cells (SOFCs). The quantification of electrode properties is very significant for high fidelity modeling and underlying mechanism studies. In this research, an inverse approach is presented to determine multi-physicochemical properties of electrodes using cell polarization performance measurements and repulsive particle swarm optimization technique, without resorting to porous microstructure features, e.g., porosity, tortuosity, pore size. The mathematical model is developed using a proton conducting button cell test stand as the physical base and employed for inverse analysis. The approach is demonstrated using both simulated results and practical measurements. This research provides a new approach for practical SOFC analysis.     

Oxygen electrocatalysis on ultra-thin porous coating rotating ring/disk platinum and platinum-cobalt electrodes in alkaline media

This work discusses the electrocatalysis of the oxygen reduction reaction (ORR) in alkaline media on ultra-thin porous coating electrodes formed by Pt and Pt-Co particles dispersed on carbon (Pt/C and Pt-Co/C, 1:1, 1:3, 1:5, 1:8 Pt:Co atomic proportion). XANES (X-ray absorption near edge structure) analysis was carried out in situ to examine the electronic properties of the Pt and Co atoms. X-ray diffraction was employed to estimate the catalyst particle size and to characterize the crystalline structure. The electrochemical techniques considered were cyclic voltammetry and steady state polarization, which were made using the standard rotating ring/disk electrode. Values of the kinetic parameters of the ORR obtained at the lower Pt/C ratios indicated participation of carbon in the catalysis of the reaction, leading to the formation of large amounts of HO₂⁻. At low overpotentials, the catalytic activity per mass of Pt obtained from mass-transport corrected Tafel plots for the 20 wt.% Pt-Co/C materials with lower Co contents are close that of the standard 20 wt.% Pt/C catalyst.