Kinetics of copper electrodeposition in citrate electrolytes

The kinetics of copper electrocrystallization in citrate electrolytes (0.5M CuSO₄, 0.01 to 2M sodium citrate) and citrate ammonia electrolytes (up to pH 10.5) were investigated. The addition of citrate strongly inhibits the copper reduction. For citrate concentrations ranging from 0.6 to 0.8 M, the impedance plots exhibit two separate capacitive features. The low frequency loop has a characteristic frequency which depends mainly on the electrode rotation speed. Its size increases with increasing current density or citrate concentration and decreases with increasing electrode rotation speed. A reaction path is proposed to account for the main features of the reduction kinetics (polarization curves, current dependence of the current efficiency and impedance plots) observed in the range 0.5 to 0.8 M citrate concentrations. This involves the reduction of cupric complex species into a compound that can be either included as a whole into the deposit or decomplexed to produce the metal deposit. The resulting excess free complexing ions at the interface would adsorb and inhibit the reduction of complexed species. With a charge transfer reaction occurring in two steps coupled by the soluble Cu(I) intermediate which is able to diffuse into the solution, this model can also account for the low current efficiencies observed in citrate ammonia electrolytes and their dependencies upon the current density and electrode rotation speed.Nomenclature b, b ₁, b ₁ ^* Tafel coefficients (V^–1) - bulk concentration of complexed species (mol cm^–3) - (si*) concentration of intermediate C^* atx=0 (mol cm^–3) - C concentration of (Cu Cit H)^2– atx=0 (mol cm^–3) - C C variation due to E - C concentration of complexing agent (Cit)^3- at the distancex (mol cm^–3) - C _o concentrationC atx=0 (mol cm^–3) - C _o C _o variation due to E - Cv _s bulk concentrationC (mol cm^–3) - (Cit H), (Cu), (Compl) molecular weights (g) - C _dl double layer capacitance (F cm^–2) - D diffusion coefficient of (Cit)^3- (cm²s^–1) - D ₁ diffusion coefficient of C^* (cm²s^–1) - E electrode potential (V) - f ₁ frequency in Equation 25 (s^–1) - F Faraday's constant (96 500 A smol^–1) - i, i ₁, i ₁ ^* current densities (A cm^–2) - i i variation due to E - Im(Z) imaginary part ofZ - j - k ₁, k ₁ ^* , K₁, K ₁ ^* , K₂, K rate constants (cms^–1) - K rate constant (s^–1) - K ₃ rate constant (cm³ A^–1s^–1) - R _t transfer resistance (cm²) - R _p polarization resistance (cm²) - Re(Z) real part ofZ - t time (s) - x distance from the electrode (cm) - Z _f faradaic impedance (cm²) - Z electrode impedance (cm²) Greek symbols maximal surface concentration of complexing species (molcm^–2) - thickness of Nernst diffusion layer (cm) - , ₁, ₂ current efficiencies - angular frequency (rads^–1) - electrode rotation speed (revmin^–1) - =K ^–1(s) - _d diffusion time constant (s) - electrode coverage by adsorbed complexing species - (in0) electrode coverage due toC _s - variation due to E     

Generalized analytical expressions for Tafel slope,reaction order and a.c. impedance for the hydrogen evolution reaction (HER): mechanism of HER on platinum in alkaline media

Following the generally accepted mechanism of the HER involving the initial proton discharge step to form the adsorbed hydrogen intermediate, which is desorbed either chemically or electrochemically, generalized expressions for the Tafel slope, reaction order and the a.c. impedance for the hydrogen evolution reaction are derived using the steady-state approach, taking into account the forward and backward rates of the three constituent paths and the lateral interactions between the chemisorbed intermediates. Limiting relationships for the Tafel slope and the reaction order, previously published, are deduced from these general equations as special cases. These relationships, used to decipher the mechanistic aspects by examining the kinetic data for the HER on platinum in alkaline media, showed that the experimental observations can be consistently rationalized by the discharge-electrochemical desorption mechanism, the rate of the discharge step being retarded on inactive platinum compared to the same on active platinum.Nomenclature C _d double-layer capacity (µF cm^–2) - E _rev reversible electrode potential (V) - F Faraday number (96 487 C mol^–1 ) - R gas constant - T temperature (K) - Y _f Faradaic admittance (^–1 cm^–2) - Y _t Total admittance (^–1 cm^–2) - Z _f Faradaic impedance ( cm²) - i _f total current density (A cm^–2) - i _nf nonfaradaic current density (A cm^–2) - j - k ₀ ¹ rate constant of the steps described in Equations 1 to 3 (mol cm^–2 s^–1 ) - j - qmax saturation charge (µC cm^–2) - Laplace transformed expressions for i, and E - _{1 3} symmetry factors for the Equations 1 and 3 - saturation value of adsorbed intermediates (mol cm^–2) - overpotential - coverage by adsorbed intermediates - angular frequency This paper is dedicated to Professor Brian E. Conway on the occasion of his 65th birthday, and in recognition of his outstanding contribution to electrochemistry.     

Electrochemical mass transfer studies in open cavities

Experimental measurements on free convection mass transfer in open cavities are described. The electrochemical deposition of copper at the inner surface of a cathodically polarized copper cylinder, open at one end and immersed in acidified copper sulphate was used to make the measurements. The effects on the rate of mass transfer of the concentration of the copper sulphate, the viscosity of the solution, the angle of orientation, and the dimensions of the cylinder were investigated. The data are presented as an empirical relation between the Sherwood number, the Rayleigh number, the Schmidt number, the angle of orientation and the ratio of the diameter to the depth of the cylinder. Comparison of the results with the available heat transfer data was not entirely satisfactory for a number of reasons that are discussed in the paper.Nomenclature C _b bulk concentration of Cu⁺⁺ (mol cm^–3) - C _b bulk concentration of H₂SO₄ (mol cm^–3) - C _o concentration of Cu⁺⁺ at cathode (mol cm^–3) - C _o concentration of H₂SO₄ at cathode (mol cm^–3) - D cavity diameter (cm) - D diffusivity of CuSO₄ (cm² s^–1) - D diffusivity of H₂SO₄ (cm² s^–1) - Gr Grashof number [dimensionless] (=Ra/Sc) - g acceleration due to gravity (=981 cm s^–2) - H cavity depth (cm) - h coefficient of heat transfer (Wm ^–2 K^–1) - i _L limiting current density (mA cm^–2) - K mass transfer coefficient (cm s^–1) - K ₁,K ₂ parameters in Equation 1 depending on the angle of orientation () of the cavity (see Table 3 for values) [dimensionless] - k thermal conductivity (W m^–1 K^–1) - L ^* characteristic dimension of the system (=D for cylindrical cavity) (cm) - m exponent on the Rayleigh number in Equation 1 (see Table 3 for values) [dimensionless] - Nu Nusselt number (=hL ^* k^–1) [dimensionless] - n exponent on the Schmidt number in Equation 1 (see Table 3 for values) [dimensionless] - Pr Prandtl number (=v/k) [dimensionless] - Ra Rayleigh number (defined in Equation 2) [dimensionless] - Sc Schmidt number (=v/D) [dimensionless] - Sh Sherwood number (=KD/D) [dimensionless] - ^t H⁺ transference number for H⁺ [dimensionless] - ^t Cu⁺⁺ transference number for Cu⁺⁺ [dimensionless] - specific densification coefficient for CuSO₄ [(1/)/C] (cm³ mol^–1) - specific densification coefficient for H₂SO₄ [(1/)/C] (cm³ mol^–1) - k thermal diffusivity (cm² s^–1) - dynamic viscosity of the electrolyte (g cm^–1 s^–1) - kinematic viscosity of the electrolyte (= /)(cm² s^–1) - density of the electrolyte (g cm^–3) - angle of orientation of the cavity measured between the axis of the cavity and gravitational vector (see Fig. 1) [degrees] - parameter of Hasegawaet al. [4] (=(2H/D))5/4 Pr^{– 1/2}) [dimensionless]     

Experimental investigation of the primary and secondary current distribution in a rotating cylinder Hull cell

A rotating cylinder cell having a nonuniform current distribution similar to the traditional Hull cell is presented. The rotating cylinder Hull (RCH) cell consists of an inner cylinder electrode coaxial with a stationary outer insulating tube. Due to its well-defined, uniform mass-transfer distribution, whose magnitude can be easily varied, this cell can be used to study processes involving current distribution and mass-transfer effects simultaneously. Primary and secondary current distributions along the rotating electrode have been calculated and experimentally verified by depositing copper.List of symbols c distance between the cathode and the insulating tube (cm) - F Faraday's constant (96 484.6 C mol^–1) - h cathode length (cm) - i local current density (A cm^–2) - i _L limiting current density (A cm^–2) - i _ave average current density along the cathode (A cm^–2) - i ₀ exchange current density (A cm^–2) - I total current (A) - M atomic weight of copper (63.54 g mol^–1) - n valence - r _p polarization resistance () - t deposition time (s) - V _c cathode potential (V) - Wa _T Wagner number for a Tafel kinetic approximation - x/h dimensionless distance along the cathode surface - z atomic number Greek symbols _a anodic Tafel constant (V) - _c cathodic Tafel constant (V) - solution potential (V) - overpotential at the cathode surface (V) - density of copper (8.86 g cm^–3) - electrolyte conductivity ( cm^–1) - deposit thickness (cm) - _ave average deposit thickness (cm) - surface normal (cm)     

Recovery of pickling effluents by electrochemical oxidation of ferrous to ferric chloride

The characteristics of the effluents from the preparatory pickling step of zinc plating are presented and the various methods of oxidizing ferrous to ferric chloride are briefly considered. An electrochemical oxidation method is proposed to recover these effluents by using an electrochemical cell with three-dimensional electrodes and an anion selective membrane. A near exhausted hydrochloric acid solution was used as catholyte. The experimental data obtained from the proposed cell show a faradic yield of 100% and easy control of the parasitic reactions. The three-dimensional anode was modelled and it is shown that at high values of current only the felt entrance region works efficiently.Nomenclature A membrane surface (cm²) - a specific felt surface (cm^–1) - C concentration difference (mol dm-^–3) - D average diffusion coefficient through the membrane (cm² s^–1) - i _n felt wall flux of species (mol cm^–2 s^–1) - j total current density (A cm^–2) - j ₀ exchange current density (A cm^–2) - j ₁ current density in matrix (A cm^–2) - j ₂ current density in felt solution (A cm^–2) - j _n transfer current density (A cm^–2) - L thickness of felt electrode (cm) - L _m thickness of membrane (cm) - M transport of ferrous and ferric ions through the membrane (mol) - N superficial flux of ion reactant (mol cm^–2 s^–1) - u superficial fluid velocity (cm s^–1) - x distance through felt electrode (cm) - R universal gas constant (8.3143 J mol^–1 K^–1) - T absolute temperature (K) - t time (s) Greek letters _a, _c anodic and cathodic transfer coefficient - local overpotential ( = ₁ – ₂) (V) - conductivity of solution (mS cm^–1) - µ solution viscosity (Pa s) - solution density (g cm^–3) - conductivity of solid matrix (mS cm^–1) - ₁ electrostatic potential in matrix phase (V) - ₂ electrostatic potential in solution (V)     

Impedance of a porous electrode with an axial gradient of concentration

When the impedance is measured on a battery, an inductive impedance is often observed in a high frequency range. This inductance is frequently related to the cell geometry and electrical leads. However, certain authors claimed that this inductance is due to the concentration distribution of reacting species through the pores of battery electrodes. Their argument is based on a paper in which a fundamental error was committed. Hence, the impedance is re-calculated on the basis of the same principle. The model shows that though the diffusion process plays an outstanding role, the overall reaction rate is never completely limited by this process. The faradaic impedance due to the concentration distribution is capacitive. Therefore, the inductive impedance observed on battery systems cannot be, by any means, attributed to the concentration distribution inside the pores. Little frequency distribution is found and the impedance is close to a semi-circle. Therefore depressed impedance diagrams in porous electrodes without forced convection cannot be ascribed to either a Warburg nor a Warburg-de Levie behaviour.Nomenclature A D¦C¦ (mole cm s^–1) - B j+K¦C¦ (mole cm s^–1) - b Tafel coefficient (V^–1) - C(x) Concentration ofS in a pore at depthx (mole cm^–3) - C ₀ Concentration ofS in the solution bulk (mole cm^–3) - C C(x) change under a voltage perturbation (mole cm^–3) - ¦C¦ Amplitude of C (mole cm^–3) - D Diffusion coefficient (cm² s^–1) - E Electrode potential (V) - E Small perturbation inE namely a sine-wave signal (V) - ¦E¦ Amplitude of E(V) - F Faraday constant (96500 A s mol^–1) - F(x) Space separate variable forC - f Frequency in Hz (s^–1) - g(x) KC(x)¦E¦(mole cm s^–1) - I Apparent current density (A cm^–2) - I _st Steady-state current per unit surface of pore aperture (A cm^–2) - j Imaginary unit [(–1)^1/2] - K Pseudo-homogeneous rate constant (s^–1) - K Potential derivative ofK, dK/dE (s^–1 V^–1) - K ^* Heterogeneous reaction rate constant (cm s^–1) - L Pore depth (cm) - n Reaction order - P Reaction product - p Parameter forF(x), see Equation 13 - q Parameter forF(x), see Equation 13 - R _e Electrolyte resistance (ohm cm) - R _p Polarization resistance per unit surface of pore aperture (ohm cm²) - R _t Charge transfer resistance per unit surface of pore aperture (ohm cm²) - S Reacting species - S _a Total surface of pore apertures (cm²) - S ₀ Geometrical surface area - S _p Developed surface area of porous electrode per unit volume (cm² cm^–3) - s Concentration gradient (mole cm^–3 cm^–1) - t Time - U Ohmic drop - x Distance from pore aperture (cm) - Z Faradaic impedance per unit surface of pore aperture (ohm cm²) - Z _x Local impedance per unit pore length (ohm cm³) - z Charge transfer number - Porosity - Thickness of Nernst diffusion layer - Penetration depth of reacting species (cm) - Penetration depth of a.c. signal determined by the potential distribution (cm) - Electrolyte (solution) resistivity (ohm cm) - ₀ Flow of S at the pore aperture (mole cm² s^–1) - Angular freqeuncy of a.c. signal, 2f(s^–1) - Integration constant     

Diffusion-controlled current distributions near cell entries and corners

This paper reports experimental work undertaken to explore diffusion-controlled current distributions immediately downstream of sudden changes in flow cross-sectional area such as may occur at the entry to electrochemical flow cells. Nozzle flows expanding into an axisymmetric circular duct and into a square duct have been investigated using the reduction of ferricyanide ions on nickel micro-electrodes as the electrode process. The spanwise distribution of current has also been studied for the case of the square cell where secondary corner flows are significant.Nomenclature A electrode area (cm²) - c bulk concentration of transferring ions (mol dm^–3) - D cell diameter (cm) - D Diffusion coefficient (cm₂s^–1) - F Faraday number (96 486 C mol^–1) - I limiting electrolysis current (A) - k mass transfer coefficient (cm s^–1) - N nozzle diameter (cm) - u mean fluid velocity (cm s^–1) - x distance downstream from point of entry to cell (cm) - z number of electrons exchanged - electrolyte viscosity (g s^–1 cm^–1) - electrolyte density (g cm^–3) - (Re)_D duct Reynolds number,Du/ - (Re)_N nozzle Reynolds number,Nu/ - (Sc) Schmidt number,/D) - (Sh) Sherwood number,kD/D)     

A mathematical model for platinum/ PTFE/porous nickel fuel cell oxygen diffusion electrodes

This paper describes the cylindrical agglomerate model for oxygen/alkali gas diffusion electrodes fabricated from platinum, PTFE and porous nickel. Corrections for the increase in hydroxyl ion concentration with increasing current density have been made to the original model of Brown and Horve. Changes in performance by variation of the bulk structural parameters, e.g. agglomerate radius, porosity and tortuosity, have been studied. Theoretical modes of electrode decay have been explored.List of symbols Transfer coefficient - C Concentration of O₂ in elec trolyte mol cm^–3 - C _i Concentration of O₂ atr = R mol cm^–3 - C _o Concentration of O₂ in electrolyte atr = mol cm^–3 - Diffusion coefficient of O₂ in KOH cm² sec^–1 - Film thickness cm - E Overpotential of the electrode V - F Faraday's constant - i Electrode current density A cm^–2 - i _a Current per agglomerate A - I ₁(Z) First order Bessel function - I ₀(Z) Zero order Bessel function - j Local current density A cm^–2 - j _o Exchange current density A cm^–2 - L Agglomerate length (catalyst thickness) cm - N Number of electrons in rate determining step - N _a Number of agglomerates per cm² of electrode - Potential drop along ag glomerate V - _L Potential drop at L_a V - r Radial direction - R Radius of agglomerate cm - R _o Gas constant - Density of platinum g cm^–3 - S _g Surface area per gram cm² g^–1 - Solubility coefficient of O₂ mol cm^–3 - _m Electrolyte conductivity (ohm cm)^–1 - T Absolute temperature °K - _a Axial tortuosity - Porosity of platinum in the agglomerate - _r Aadial tortuosity of the agglomerate - W Catalyst loading g cm^–2 - x Axial direction     

Long service life IrO2/Ta2O5 electrodes for electroflotation

Ti/IrO₂-Ta₂O₅ electrodes prepared by thermal decomposition of the respective chlorides were successfully employed as oxygen evolving electrodes for electroflotation of waste water contaminated with dispersed peptides and oils. Service lives and rates of dissolution of the Ti/IrO₂-Ta₂O₅ electrodes were measured by means of accelerated life tests, e.g. electrolysis in 0.5M H₂SO₄ at 25°C and j = 2 A cm^–2. The steady-state rate of dissolution of the IrO₂ active layer was reached after 600–700 h (0.095 g Ir h^–1 cm^–2) which is 200–300 times lower than the initial dissolution rate. The steady-state rate of dissolution of iridium was found to be proportional to the applied current density (in the range 0.5–3 A cm^–2 ). The oxygen overpotential increased slightly during electrolysis (59–82 mV for j = 0.1 A cm^–2 ) and the increase was higher for the lower content of iridium in an active surface layer. The service life of Ti/IrO₂ (65 mol%)-Ta₂O₅ (35 mol%) in industrial conditions of electrochemical devices was estimated to be greater than five years.List of symbols a constant in Tafel equation (mV) - b slope in Tafel equation (mV dec^–1) - E potential (V) - f mole fraction of iridium in the active layer - j current density (A cm^–2) - l number of layers - m _Ir content of iridium in the active layer (mg cm^–2) - r dissolution rate of the IrO₂ active layer (g Ir h^–1 cm^–2) - T _c calcination temperature (°C) - _{O 2} oxygen overpotential (mV) - _{O 2} difference in oxygen overpotential (mV) - _A service life in accelerated service life tests (h) - _S service life in accelerated service life tests related to 0.1 mg Ir cm^–2 (h) - _p polarization time in accelerated service life tests (h)     

A mass transfer model for the autocatalytic dissolution of a rotating copper disc in oxygen saturated ammonia solutions

A mathematical model of mass transfer processes during autocatalytic dissolution of metallic copper in oxygen-containing ammonia solutions using the rotating disc technique is presented. The model is based on the equations of steady state convective diffusion with volumetric mass generation terms and boundary conditions of the third kind, in more generalized form, at the disc surface and of the first kind in the bulk solution. The boundary value problem was solved numerically using the finite difference method with variable mesh spacing. Comparison of calculated and experimental results indicates that the model quantitatively represents the measurements. The rate of the reaction Cu(II)+Cu2Cu(I) determines the overall rate of the process.Nomenclature A rotating disc surface area, (cm²) - B dimensionless constant,B=k ₃ c ₁ ^{0 –1} - c _i concentration of speciesi, c _i=c _i(y) (mol cm^–3) - c _i ⁰ concentration of species i in the bulk of solution,c _i ⁰ =c _i ⁰ (t) (mol cm^–3) - c _{i, 0} concentration of species i at the disc surface,c _i,0=c _i (y=0) (mol cm^–3) - C _i concentration ratio,C _i=c _i/c _i ⁰ ,C _i=C _i() - C _i ⁰ concentration ratio (in the bulk of solution),C _i=c _i ⁰ /c _i ⁰ - C _i,0 concentration ratio (at the disc surface),C _i,0=c _i,0/c _i ⁰ - D _i molecular diffusivity of species i (cm² s^–1) - h space increment,h==(/v)^1/2y, dimensionless - j _i mass flux of species i (mol cm^–2 s^–1) - k _i first-order reaction rate constant (cm s^–1 or cm³ mol^–1 s^–1) - K _i,j diffusivity ratio,K _i,j=D _i/D _j, dimensionless - M number of space increments - n _i total number of moles of Cu(II) entering the bulk of solution referred to the unit disc surface area (mol cm^–2) - rate of production of species i by the chemical reaction (mol cm^–3 s^–1) - Sc _i Schmidt number,Sc _i=v _i/D _i - t time, (s) - t time increment (s) - v fluid velocity vectorv=(u, v, w) (cm s^–1) - V volume of solution (cm³) - W ₁,W ₂ dimensionless group,W ₁=(K _3,2/D ₁) (v/)^1/2,W ₂ = (K _1,2/D ₂(v/)^1/2 - x ₁ coordinates,l=1, 2, 3 - y axial coordinate (perpendicular to the disc surface) - y space increment (cm) Greek letters nabla operator - kinematic viscosity of solution (cm² s^–1) - _i stoichiometric coefficients - disc angular velocity (s^–1) - dimensionless axial coordinate, =(/v)^1/2 y - dimensionless space increment, =(/v)^1/2y     

Mechanism of copper-nickel alloy electrodeposition

The codeposition kinetics of copper and nickel alloys in complexing citrate ammonia electrolytes has been investigated by means of polarization and electrochemical impedance techniques. It is confirmed that the two-step discharge of the complexed cupric species Cu(II)Cit is diffusion-controlled during the alloy deposition, resulting in an increase in the nickel content of the alloy with electrode polarization. Impedance spectra are also consistent with a two-step discharge of Ni(II) cations involving an intermediate adsorbate, Ni(I)_ads, originating from the reversible first step. A reaction model is developed for the parallel discharge of Cu(II)Cit and Ni(II) in which the reactions for nickel deposition are catalysed by active sites permanently renewed at the surface of the growing alloy. The surface density of these sites, slowly nucleated from Ni(I)_ads and included in the deposit, varies with the electrode polarization, thus generating a low-frequency feature specific of Cu–Ni codeposition. This reaction model reproduces to a reasonable extent the potential dependence of the partial current densities for nickel and copper discharge, the current dependence of the alloy nickel content and also most of the experimental relaxation processes observed on impedance spectra.Nomenclature b ₁,b ₂,b ₃,b ₃ b ₄,b ₅,b ₇ Tafel coefficients (V^–1) - C concentration of Cu(II)Cit at distancex (mol cm^–3) - [Cu(II)] bulk concentration of Cu(II)Cit (mol cm^–3) - C ₀ concentration of Cu(II)Cit atx=0 (mol cm^–3) - C* concentration of Cu(I)Cit atx=0 (mol cm^–3) - C ₀, C* variations inC ₀,C* due to E - (Cu), (Ni) molecular weights (g) - C _dl double layer capacitance (F cm^–2) - D diffusion coefficient of Cu(II)Cit (cm² s^–1) - E electrode potential (V) - f frequency (s^–1) - F Faraday (constant 96 487 A s mol^–1) - g interaction factor between adsorbates - i,i _Cu,i _Ni current densities (A cm^–2) - Im(Z) imaginary part ofZ - j (–1)^1/2 - k mass transfer coefficients (cm s^–1) - K ₁,K ₃ rate constants (cm s^–1) - K ₂ rate constants (s^–1) - K ₃,K ₄,K ₅,K ₆,K ₇ rate constants (cm^–2 s^–1) - [Ni(II)] bulk concentration of NiSO₄ (mol cm^–3) - R _t charge transfer resistance ( cm²) - Re(Z) real part ofZ - t time (s) - x distance from the electrode (cm) - Z _F faradaic impedance ( cm²) - Z electrode impedance - maximal surface concentration of Ni(I)_ads intermediates (mol cm^–1) - nickel content in the deposited alloy (wt %) - thickness of Nernst diffusion layer (cm) - ₁ electrode coverage by adsorbed Ni(I)_ads intermediate - ₂ electrode coverage by active sites - ₁, ₂ variations in ₁, ₂ die to E - * =K ₂ ^–1 (s) - _d diffusion time constant (s) - ₁ time constant relative to ₁ (s) - ₂ time constant relative to ₂ (s) - angular frequency (rad s^–1) - electrode rotation speed (rev min^–1)     

Characterization of reticulate,three — dimensional electrodes

A study has been made of the mass transfer characteristics of a reticulate, three-dimensional electrode, obtained by metallization of polyurethane foams. The assumed chemical model has been copper deposition from diluted solutions in 1 M H₂SO₄. Preliminary investigations of the performances of this electrode, assembled in a filter-press type cell, have given interesting results: with 0.01 M CuSO₄ solutions the current density is 85 mA cm^–2 when the flow rate is 14 cm s^–1.List of symbols a area for unit volume (cm^–1) - C copper concentration (mM cm^–3) - c _L copper concentration in cathode effluent (mM cm^–3) - c ₀ copper concentration of feed (mM cm^–3) - C ₀ ⁰ initial copper concentration of feed (mM cm^–3) - d pore diameter (cm) - D diffusion coefficient (cm²s^–1) - F Faraday's constant (mcoul me _q ^–1 ) - i electrolytic current density on diaphragm area basis (mA cm^–2) - I overall current (mA) - K _m mass transfer coefficient (cm s^–1) - n number of electrons transferred in electrode reaction (me_q mM^–1) - P ] volumetric flux (cm³s^–1) - Q total volume of solution (cm³) - (Re) Reynold's number - S section of electrode normal to the flux (cm²) - (Sc) Schmidt's number - (Sh) Sherwood's number - t time - T temperature - u linear velocity of solution (cm s^–1) - V volume of electrode (cm³) - divergence operator - void fraction - u/K _m a(cm) - electrical specific conductivity of electrolyte (^–1 cm^–1) - _S potential of the solution (mV) - density of the solution (g cm^–3) - v kinematic viscosity (cm²s^–1)     

Meniscus shape and lateral wetting at the hanging meniscus rotating disc (HMRD) electrode

The hanging meniscus rotating disc (HMRD) electrode is a configuration in which a cylinder of the electrode material is used without an insulating mantle. We have recently shown that the hydrodynamic behaviour of the HMRD is similar to that of the conventional rotating disc electrode and that this configuration can also be used to study the kinetics of simple charge transfer reactions. In this paper experimental data on the change of meniscus shape upon meniscus height and rotation for different electrode materials are presented and analysed in relation to lateral wetting and stability.List of symbols A electrode area (cm²) - C ₀ ^* bulk concentration (mol cm^–3) - D ₀ diffusion coefficient (cm²s^–1) - f force on a cylinder supporting a hanging meniscus (dyn) - F Faraday (96 500 Cmol^–1) - g gravitational acceleration (cm s^–2) - h height (cm) - h _m meniscus height (cm) - h ₀ critical meniscus height (cm) - i total current (A) - i _L limiting current (A) - i _max kinetic current (A) - k proportionality constant (cm^–1) - K dimensionless constant - n number of electrons exchanged - R _eff effective radius of the electrode (cm) - R ₀ geometric radius of the electrode (cm) - V volume of the meniscus above the general level of the liquid surface (cm³) Greek letters ₀ thickness of hydrodynamic boundary layer (cm) - surface tension (dyn cm^–1) - kinematic viscosity (cm²s^–1) - density difference between the liquid and its surrounding fluid (gcm^–3) - _C normal contact angle - _L local contact angle 0_L + 90° - electrode rotation rate (s^–1)     

Natural convection mass transfer at horizontal screens

The free convection mass transfer behaviour of horizontal screens has been investigated experimentally using an electrochemical technique involving the measurement of the limiting currents for the cathodic deposition of copper from acidified copper sulphate solutions. Screen diameter and copper sulphate concentration have been varied to provide a range ofSc.Gr from 22×10⁸ to 26×10¹⁰. Under these conditions, the data for a single screen are correlated by the equation:Sh=0.375(Sc.Gr)^0.305 Results have been compared with previous work on free convection at horizontal solid surfaces where mass transfer coefficients are somewhat lower.Mass transfer coefficients have been measured also for arrays of closely spaced parallel horizontal screens. The mass transfer coefficient was found to decrease with the number of screens forming the array.Symbols and units A area of mass transfer surface, cm² - C _b bulk concentration of ionic species, mol cm^–3 - D diffusivity, cm²s^–1 - F Faraday number, 96494 C g [equiv^–1] - Z number of electrons involved in the reaction - I _L limiting current, A - K mass transfer coefficient, cm s^–1 - Sh Sherwood number, dK/D - Sc Schmidt number,/D or/D - Gr Grashof numbergd ³/ ² _s - solution dynamic viscosity, g cm s^–1 - solution kinematic viscosity, cm² s^–1 - solution density, g cm^–3 - density difference between bulk solution and electrode/solution interface, g cm^–3 - _s solution density at electrode/solution interface, g cm^–3 - d screen diameter, cm - g gravitational acceleration, cm s^–2 On leave of absence, Chemical Engineering Department, Alexandria University, Alexandria, Egypt.     

Computer simulation of high-discharge-rate battery systems

Simulations were carried out for a proposed two-dimensional high-discharge-rate cell under load with an interelectrode gap of the order of 100 m. A finite difference program was written to solve the set of coupled, partial differential equations governing the behaviour of this system. Cell dimensions, cell loads, and kinetic parameters were varied to study the effects on voltage, current and specific energy. Trends in cell performance are noted, and suggestions are made for development of cells to meet specific design criteria. Modelling difficulties are discussed and suggestions are made for improvement.Nomenclature A surface area of unit cell (cm²) - A _k conductivity parameter (cm^{2 –1} mol^–1) - b Tafel slope (V) - c concentration (mol cm^–3) - c ₀ concentration of bulk electrolyte (mol cm^–3) - D diffusivity (cm² s^–1) - D _h lumped diffusion parameter (J s cm^–2 mol^–1) - D _s lumped diffusion coefficient (A cm² mol^–1) - E rest potential of electrode (V) - F Faraday constant (96 500 C mol^–1) - i current density (A cm^–2) - I total current for unit cell (A) - i ₀ exchange current density (A cm^–2) - N flux of charged species (mol cm² s^–1) - R gas constant (8.314 J mol^–1 K^–1) - R _ext resistance external to cell () - t time (s) - T temperature (K) - t ₀ transference number - u mobility (cm² mol J^–1 s^–1) - V volume of an element in the cell (cm³) - V _ext voltage external to cell (V) - z charge on an ion - _c concentration overpotential (V) - _s surface overpotential (V) - conductivity (^–1 cm^–1) - stoichiometric coefficient - electric potential in solution (V)     

Modelling of gas-evolving electrolysis cells. III. TheiR drop at gas-evolving electrodes

Based on a potentiostatic interrupter technique theiR drop of the bubble layer in front of gas-evolving electrodes of various shapes has been investigated. At small plane electrodes the dependency ofiR drop on electrode inclination has been studied for hydrogen, oxygen and chlorine evolution. In all systems a slightly up-faced orientation results in a gas bubble layer structure of minimumiR drop. Also for expanded metal electrodes of different shapes theiR drop across the electrode diaphragm gap has been studied. The fractional open cross-section and the inclination angle of the electrode blades have been identified as important parameters with respect to the gas diverting effect. These tendencies have also been confirmed for a pilot cell of 1 m height.Nomenclature b' Tafel slope (V) - c ₀ double layer capacity (F cm^–2) - d thickness (cm) - E electrode potential (V) - F Faraday number (96487 As mol^–1) - i current density (A cm^–2) - R area resistance ( cm²) - R gas constant (8.3144 Ws deg^–1 mol^–1) - T temperature (K) - t time (s) - u _g ⁰ superficial gas velocity (cm s^–1) - u _sw swarm velocity (cm s^–1) - U voltage (V) Greek symbols inclination angle (^o) - symmetry factor (1) - _g gas voidage (1) - _m maximum gas voidage. (1) - overvolgate (V) - electrolyte conductivity (S cm^–1) - _g number of electrons (1) Paper presented at the 2nd International Symposium on Electrolytic Bubbles organized jointly by the Electrochemical Technology Group of the Society of Chemical Industry and the Electrochemistry Group of the Royal Society of Chemistry and held at Imperial College, London, 31st May and 1st June 1988.     

Electrical conductivities of aqueous ZnSO4−H2SO4 solutions

Conductivities of aqueous ZnSO₄–H₂SO₄ solutions are reported for a wide range of ZnSO₄ and H₂SO₄ concentrations (ZnSO₄ concentrations of 01.2 M and H₂SO₄ concentrations of 02 M) at 25°C, 40°C and 60°C. The results indicate that the solution conductivity at a given ZnSO₄ concentration is controlled by the H₂SO₄ (H⁺) concentration. The variation of the specific conductivity with ZnSO₄ concentration is complex, and depends on the H₂SO₄ concentration. At H₂SO₄ concentrations lower than about 0.25 M, the addition of ZnSO₄ increases the solution conductivity, likely because the added Zn²⁺ and SO ₄ ^2– ions increase the total number of conducting ions. However, at H₂SO₄ concentrations higher than about 0.25 M, the solution conductivity decreases upon the addition of ZnSO₄. This behaviour is attributed to decreases in the amount of free water (through solvation effects) upon the addition of ZnSO₄, which in turn lowers the Grotthus-type conduction of the H⁺ ions. At H₂SO₄ concentrations of about 0.25 M, the addition of ZnSO₄ does not appreciably affect the solution conductivity, possibly because the effects of increasing concentrations of Zn²⁺ and SO ₄ ^2– ions are balanced by decreases in Grotthus conduction.Nomenclature a ion size parameter (m) - a ^* Bjerrum distance of closest approach (m) - C stoichiometric concentration (mol m^–3 or mol L^–1) - I ionic strength (mol L^–1) - k constant in Kohlrausch's law - M molar concentration (mol L^–1) - T absolute temperature (K) - z _i electrochemical valence of speciesi (equiv. mol^–1) - z (z _–|z _–|)^1/2=2 for ZnSO₄ - z ₊ valence of cation in salt (=+2 for Zn²⁺) - z _– valence of anion in salt (=–2 for SO ₄ ^2– ) Greek letters fraction of ZnSO₄ dissociated - specific conductivity (^–1 m^–1) - ^expt measured specific conductivity (^–1 m^–1) - equivalent conductivity (^–1 m² equiv.^–1) - equivalent conductivity at infinite dilution (^–1 m² equiv.^–1) - ⁰ equivalent conductivity calculated using Equation 2 (^–1 m² equiv.^–1) - _cale measured equivalent conductivity (^–1 m² equiv.^–1) - _expt equivalent conductivity of ioni at infinite dilution (^–1 m² equiv.^–1) - reciprocal of radius of ionic cloud (m^–1) - viscosity of solvent (Pa s) - dielectric constant - ± mean molar activity coefficient - density (g cm^–3)     

An impedance method for the characterization of porous carbons

A method is proposed whereby electrode impedance data may be analysed to yield information about the structure and composition of porous electrode materials. The method is more suitable for comparative investigations than as a technique for obtaining absolute values of the total surface area of a porous solid in contact with an electrolyte.List of symbols A Surface area of the electrode (cm²) - A Apparent specific area of the electrode material (cm²/cm³) - C _dl Capacitance per unit area (F cm^–2) - C Capacitance per unit pore length (F cm^–1) - E ₀ Potential at pore orifice (V) - i ₀ Current at pore orifice (Amp) - l Depth of penetration of signal (cm) - l ₀ Length of pore (cm) - R Resistance of electrolyte per unit pore length (cm^–1) - r Pore radius (cm) - Z ₁ Capacitative impedance per unit pore-length ( cm) - Z ₀ Impedance of pore () - = (R/Z ₁)^1/2 Reciprocal penetration depth (cm^–1) - Electrolyte resistivity ( cm) - 2f wheref = frequency (Hz)     

Turbulent mass transfer in small radius ratio annuli

Mass transfer in annuli for both fully developed laminar and turbulent flow conditions has been studied with respect to available experimental data. It is shown that prediction of the Sherwood number for the inner annular wall based on the hypothesis of coincidence of the zero shear stress position for laminar and turbulent flows leads to serious error in the case of small radius ratio. Also it is shown that in contrast with plain tubes the curvature in small radius ratio annuli should be taken into account for the case of small Reynolds numbers. In consequence, the well-known Leveque equation can be used for the calculation of the mass transfer coefficient in annuli only under certain conditions. Possibilities of electrodiffusion diagnostics for the precise determination of the zero shear stress position in annuli are discussed.List of symbols A cross-section flow area (m²) - a =r ₁/r ₂ annular radius ratio (–) - mean fluctuation and bulk concentration (mol m^–3) - D molecular diffusivity (m²s^–1) - d _b hydraulic diameter (m) - f,f ₁,f ₂ overall, inner and outer wall friction factors (–) - f = ₁/ near wall velocity gradient (s^–1) - pressure drop per unit of length (Pam^–1) - K _L average mass transfer coefficient (ms^–1 ) - k =r ₀/r _0,L ratio of zero shear stress position in turbulent and laminar flows (–) - L mass transfer surface length (m) - L _D diffusion leading edge length (m) - L _ent diffusion entrance length (m) - P _W wetted perimeter (m) - Re =U _av d _h/ Reynolds number (–) - r radial distance from conduit axis (m) - r ₀,r _o,L radial distance of zero shear stress position in turbulent and laminar flows (m) - r ₁,r ₂ radius of inner and outer annular cylinders (m) - Sc = /D molecular Schmidt number (–) - Sh =K _L d _h/D Sherwood number (–) - U _av average liquid velocity (ms^–1) - u,u mean and fluctuation axial velocity (ms^–1) - , mean and fluctuation radial velocity (ms^–1) - y = r – r ₁ distance from the inner wall (m) - y = (/₁)^1/2 dynamic length (m) - Z distance in direction of the flow (m) Greek symbols _D diffusion layer thickness (m) - µ dynamic viscosity (Pa s) - kinematic viscosity (m²s^–1) - density (kgm^–3) - shear stress (Pa) - _W wall shear stress for tube and plate channel (Pa) - ₁, ₂ wall shear stress for inner and outer annular cylinders (Pa) - Geometrical factor with respect to k-function (–) - _R, _K geometrical factor with respect to Rothfus or Kays-Leung equations (–) - ratio of radial distance of zero shear stress position to outer radius in laminar flow (–)     

Novel and Ideal Zirconium-Based Dense Membrane Reactors for Partial Oxidation of Methane to Syngas

A novel and ideal dense catalytic membrane reactor for the reaction of partial oxidation of methane to syngas (POM) was constructed from the stable mixed conducting perovskite material of BaCo_0.4Fe_0.4Zr_0.2O_3– and the catalyst of LiLaNiO/-Al₂O₃. The POM reaction was performed successfully. Not only was a short induction period of 2 h obtained, but also a high catalytic performance of 96–98% CH₄ conversion, 98–99% CO selectivity and an oxygen permeation flux of 5.4–5.8 mlcm^–2min^–1 (1.9–2.0 molm^–2S^–1Pa^–1) at 850°C were achieved. Moreover, the reaction has been steadily carried out for more than 2200 h, and no interaction between the membrane material and the catalyst took place.