Determination of electrode kinetics by corrosion potential measurements: Zinc corrosion by bromine

An attractive way of determining the electrode kinetics of very fast dissolution reactions is that of measuring the corrosion potential in flowing solutions. This study analyses a critical aspect of the corrosion potential method, i.e., the effect of nonuniform corrosion distribution, which is very common in flow systems. The analysis is then applied to experimental data for zinc dissolution by dissolved bromine, obtained at a rotating hemispherical electrode (RHE). It is shown that in this case the current distribution effect is minor. However, the results also indicate that the kinetics of this corrosion system are not of the classical Butler-Volmer type. This is explained by the presence of a chemical reaction path in parallel with the electrochemical path. This unconventional corrosion mechanism is verified by a set of experiments in which zones of zinc deposition and dissolution at a RHE are identified in quantitative agreement with model predictions. The practical implications for the design of zinc/bromine batteries are discussed.Notation C _i concentration of species i (mol cm^–3) - D _` diffusivity of species i (cm² s^–1) - F Faraday constant - i _j current density of species j (A cm^–2) - i ₀ ^b exchange current density referenced at bulk concentration (A cm^–2) - J , inverseWa number - N - n number of electrons transferred for every dissolved metal atom - P _m Legendre polynomial of orderm - r ₀ radius of dise, sphere, or hemisphere - s stoichiometric constant - t ₊ transference number of metal ion - V _corr corrosion overpotential (V) Greek letters anodic transfer coefficient of Reaction 21b - _a anodic transfer coefficient of metal dissolution - _c cathodic transfer coefficient of metal dissolution - anodic transfer coefficient of zinc dissolution - velocity derivative at the electrode surface - (x) incomplete Gamma function - , exchange reaction order ofM ⁺ⁿ - , inverseWa number - _a activation overpotential (V) - _c concentration overpotential (V) - polar angle (measured from the pole) (rad) - k solution conductivity (^–1 cm^–1) - kinematic viscosity (cm² s^–1) - ₀ solution potential at the electrode surface (V) - rotation rate (s^–1) - * indicates dimensionless quantities     

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     

Potential distribution and electrode stability in a bipolar electrolysis cell

A computational model is presented, which enables the identification of those zones endangered by corrosion in a bipolar electrolysis cell stack. The method consists of two steps: first the potential profile in the electrolyser is computed by numerical solution of the Laplace equation using the finite difference method; then, making use of the Criss-Cobble correspondence principle, this profile is related to the potential-dependent thermodynamic stabilities of the respective metals. This may be a useful tool in the design of intermittently operating electrolysers (for example those powered by solar energy).Nomenclature A metal phase - A _i single A-phase point - B electrolyte phase - B _i single B-phase point - F Faraday constant - h mesh interval (m) - i local current density (A m^–2) - i ₀ exchange current density (A m^–2) - j local current across the double layer (A) - j _iA,j _iB tangential or normal component of the double layer current (A) - K A, B phase conductivity ratio - m molality mol kg^–1 - R gas constant - T absolute temperature (K) - U potential (V) - U ₀ water decomposition voltage (V) - U _tot end plate potential (V) - x, y cartesian coordinates - overrelaxation factor - _a, _c anodic or cathodic overpotential (V) - _A, _B electrical conductivity (^–1 m^–1) - potential (V) - _m local double layer potential, electrode end (V) - _s local double layer potential, electrolyte end (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.     

Application of the trickle tower to problems of pollution control. III. Heavy-metal cyanide solutions

The destruction of CN^– and co-deposition of copper, cadmium, nickel, zinc and lead, both as simple solutions and as mixtures, have been investigated in a number of trickle towers with from 8 to 49 layers of cells. Specific chemical effects due to the formation of cyano-complexes of some of the metals are evident, and it has been found that copper, nickel and cadmium accelerate the destruction of CN^–, at least initially. For simple solutions a previously proposed scaling law is adequate.Nomenclature a length of bipolar element (cm) - c concentration (ppm) - c ⁰ initial concentration (ppm) - K mass transfer coefficient (cm s^–1) - K=K _L effective mass transfer coefficient (cm s^–1) - L wetted perimeter per layer of packing (cm) - p number of layers of cells - t time (s) - v _o volumetric flow rate (cm³ s^–1) - V inventory of solution (cm³) - _L fractional active length - _s reversible potential with respect to main counter reaction (V) - _s ^T potential applied across an element with respect to main counter reaction (V)     

A parameter characterizing the geometry of expanded metal. II. Natural convection mass transfer at expanded metal electrodes

Free convective mass transfer rates at vertical electrodes of expanded metal were measured by the electrochemical method. Electrode height and electrolyte concentration were varied and the dependence of the expanded metal on the geometry and on the mesh orientation with respect to the vertical direction was investigated. A single equation was developed to correlate all the results. Besides the generalized dimensionless groups for natural convection the correlation includes a parameter characterizing the geometry of the expanded metal. The correlation also represents free convective mass transfer results obtained by other investigators with vertical mesh electrodes.Nomenclature a width of narrow space - A mean mesh aperture - c ₀ bulk concentration - d cavity diameter - d _p particle diameter - D diffusivity - g acceleration due to gravity - Gr Grashof number =gh³/v² - h electrode height - H cavity depth - k mass transfer coefficient - LD long dimension of expanded metal - R _h hydraulic radius - Sc Schmidt number=/D - SD small dimension of expanded metal - Sh Sherwood number=kh/D - void fraction - kinematic viscosity - density - electrode area per unit volume - electrode area per unit net area     

Mass transfer to planar and expanded metal electrodes in bubble columns

Mass transfer rates at planar electrodes and electrodes of expanded metal placed in the centre of a bubble column were measured. The gas velocity and the physical properties of the electrolytic solutions were varied and different types of expanded metal were investigated. In some cases increases in the mass transfer coefficient over the planar electrode value of more than 100% were obtained. Dimensionless correlations are presented for the different systems.Nomenclature A mean mesh aperture - D diffusivity - D _c column diameter - g acceleration due to gravity - Ga Galileo number =gL ³/v ² - Gr Grashof number =gL ³/v ² - k mass transfer coefficient - L electrode height - r radial position - R column radius - Re Reynolds number =R _h V _s/ - R _h hydraulic radius = / - Sc Schmidt number = /D - Sh Sherwood number =kL/D - V_s superficial velocity - gas void fraction - _M porosity of expanded metal - kinematic viscosity - density - electrode area per unit volume - electrode area per unit net area     

Behaviour of a tall vertical gas-evolving cell. Part I: Distribution of void fraction and of ohmic resistance

Electrolysis of a 22 wt % NaOH solution has been carried out in a vertical tall rectangular cell with two segmented electrodes. The ohmic resistance of the solution between a segment pair has been determined as a function of a number of parameters, such as, current density and volumetric rate of liquid flow. It has been found that the ohmic resistance of the solution during the electrolysis increases almost linearly with increasing height in the cell. Moreover, a relation has been presented describing the voidage in the solution as a function of the distance from the electrodes and the height in the cell.Notation A _e electrode surface area (m²) - a _s parameter in Equation 12 (A^–1) - b _s parameter in Equation 12 - d distance (m) - d _ac distance between the anode and the cathode (m) - d _wm distance between the working electrode and an imaginary separator (m) - F Faraday constant (C mol^–1) - h height from the leading edge of the working electrode corresponding to height in the cell (m) - h _e distance from the bottom to the top of the working electrode (m) - h _s height of a segment of working electrode (m) - I current (A) - I ₂₀ current for segment pair 20 (A) - I _1–19 total current for the segment pairs from 1 to 19 inclusive (A) - I _x-19 total current for the segment pairs fromx to 19 inclusive (A) - i current density A m^–2 - N _s total number of gas-evolving pairs - n ₁ constant parameter in Equation 8 - n _a number of electrons involved in the anodic reaction - n _c number of electrons involved in the cathodic reaction - n _s number of a pair of segments of the segmented electrodes from their leading edges - Q _g volumetric rate of gas saturated with water vapour (m³ s^–1) - Q ₁ volumetric rate of liquid (m³ s^–1) - R resistance of solution () - R ₂₀ resistance of solution between the top segments of the working and the counter electrode () - R _p resistance of bubble-free solution () - R _p,20 R _p for segment pair 20 () - r _s reduced specific surface resistivity - r _s,0 r _s ath=0 - r _s,20 r _s for segment pair 20 - r _s, r _s for uniform distribution of bubbles between both the segments of a pair - r _s,,20 r _s, for segment pair 20 - S _b bubble-slip ratio - S _b,20 S _b at segment pair 20 - S _b,h S _b at heighh in the cell - T temperature (K) - V _m volume of 1 mol gas saturated with water vapor (m³ mol^–1) - v ₁ linear velocity of liquid (m s^–1) - v _1,0 v ₁ through interelectrode gap at the leading edges of both electrodes (m s^–1) - W _e width of electrode (m) - X distance from the electrode surface (m) - Z impedance () - Z real part of impedance () - Z imaginary part of impedance () - resistivity of solution ( m) - _p resistivity of bubble-free solution ( m) - gas volumetric flow ratio - ₂₀ at segment pair 20 - _s specific surface resistivity ( m²) - _{s, p s} for bubble-free solution ( m²) - thickness of Nernst bubble layer (m) - ₀ ath=0 (m) - voidage - _x,0 atx andh=0 - _0,0 voidage at the leading edge of electrode wherex=0 andh=0 - _,h voidage in bulk of solution at heighth - ₂₀ voidage in bubble of solution at the leading edge of segment pair 20     

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 (–)     

Calculation of Temperature Dependences of the Viscosity and Volume Relaxation Time for Oxide Glass-Forming Melts from Chemical Composition and Dilatometric Glass Transition Temperature

The relaxation parameter K _sthat is equal to the ratio of the viscosity to the Kohlrausch volume relaxation time _s is analyzed. It is shown that this parameter can be evaluated from the temperature T ₁₃(corresponding to a viscosity of 10¹³P) and the glass transition temperature T ₈ ⁺determined from the dilatometric heating curve. The maximum error of the estimate with due regard for experimental errors is equal to ±(0.4–0.5)logK _sfor strong glasses and ±(0.6–0.8)logK _sfor fragile glasses, which, in both cases, corresponds to a change in the relaxation times with a change in the temperature by ±(8–10) K. It is revealed that the viscosity, the Kohlrausch volume relaxation time _s , and the shear modulus Gof glass-forming materials in silicate, borate, and germanate systems satisfy the relationship log( _s G/) 1. The procedure for calculating the temperature dependences of the viscosity and the relaxation times in the glass transition range from the chemical composition and the T ₈ ⁺temperature for glass-forming melts in the above systems is proposed. The root-mean-square deviations between the calculated and experimental temperatures T ₁₁and T ₁₃are equal to ±(6–8) K for all the studied (silicate, borate, germanate, and mixed) oxide glass-forming systems. The proposed relationships can be useful for evaluating the boundaries of the annealing range and changes in the properties and their temperature coefficients upon cooling of glass-forming melts.     

Behaviour of a tall vertical gas-evolving cell Part II: Distribution of current

Vertical electrolysers with a narrow electrode gap are used to produce gases, for example, chlorine, hydrogen and oxygen. The gas voidage in the solution increases with increasing height in the electrolyser and consequently the current density is expected to decrease with increasing height. Current distribution experiments were carried out in an undivided cell with two electrodes each consisting of 20 equal segments or with a segmented electrode and a one-plate electrode. It was found that for a bubbly flow the current density decreases linearly with increasing height in the cell. The current distribution factor increases with increasing average current density, decreasing volumetric flow rate of liquid and decreasing distance between the anode and the cathode. Moreover, it is concluded that the change in the electrode surface area remaining free of bubbles with increasing height has practically no effect on the current distribution factor.Notation A _e electrode surface area (m²) - A _e,s surface area of an electrode segment (m²) - A _{e, 1–19} total electrode surface area for the segments from 1 to 19 inclusive (m²) - A _e,a anode surface area (m²) - A _e,a,h A _e,a remaining free of bubbles (m²) - A _e,e cathode surface area (m²) - A _e,c,h A _e,c remaining free of bubbles (m²) - a ₁ parameter in Equation 7 (A^–1) - B current distribution factor - B _r B in reverse position of the cell - B _s B in standard position of cell - b _a Tafel slope for the anodic reaction (V) - b _c Tafel slope for the cathodic reaction (V) - d distance (m) - d _ac distance between the anode and the cathode (m) - d _wm distance between the working electrode and an imaginary membrane (m) (d _wm=0.5d _wt=0.5d _ac) - d _wt distance between the working and the counter electrode (m) - F Faraday constant (C mol^–1) - h height from the leading edge of the working electrode corresponding to height in the cell (m) - h _e distance from the bottom to the top of the working electrode (m) - I current (A) - I _s current for a segment (A) - I ₂₀ current for segment pair 20 (A) - I _1–19 total current for the segment pairs from 1 to 19 inclusive (A) - i current density (A m^–2) - i _av average current density of working electrode (A m^–2) - i _b current density at the bottom edge of the working electrode (A m^–2) - i ₀ exchange current density (A m^–2) - i _0,a i ₀ for anode reaction (A m^–2) - i _l current density at the top edge of the working electrode (A m^–2) - n ₁ parameter in Equation 15 - n _s number of a pair of segments of the segmented electrodes from their leading edges - Q _g volumetric rate of gas saturated with water vapour (m³ s^–1) - Q ₁ volumetric rate of liquid (m³ s^–1) - R resistance of solution () - R ₂₀ resistance of solution between the top segments of the working and the counter electrode () - R _p resistance of bubble-free solution () - R _p,20 R _p for segment pair 20 () - r _s reduced specific surface resistivity - r _s,0 r _s ath=0 - r _s,20 r _s for segment pair 20 - r _s, r _s for uniform distribution of bubbles between both the segments of a pair - r _s,,20 r _s, for segment pair 20 - T temperature (K) - U cell voltage (V) - U _r reversible cell voltage (V) - v ₁ linear velocity of liquid (m s^–1) - v _1,0 v ₁ through interelectrode gap at the leading edges of both electrodes (m s^–1) - x distance from the electrode surface (m) - gas volumetric flow ratio - ₂₀ at segment pair 20 - specific surface resistivity ( m²) - _t at top of electrode ( m²) - _p for bubble-free solution ( m²) - _b at bottom of electrode ( m²) - thickness of Nernst bubble layer (m) - ₀ ath=0 (m) - _{0,i 0} ati - voidage - _x,0 atx andh=0 - _0,0 voidage at the leading edge of electrode wherex=0 andh=0 - _0,0 ati _b - _0,0 ati=i _t - _,h voidage in bulk of solution at heighth - _,20 voidage in bubble of solution at the leading edge of segment pair 20 - _lim maximum value of _0,0 - overpotential (V) - _a anodic overpotential (V) - _c cathodic overpotential (V) - _h hyper overpotential (V) - _h,a anodic hyper overpotential (V) - _h,c cathodic hyper overpotential (V) - fraction of electrode surface area covered by of bubbles - _a for anode - _c for cathode - resistivity of solution ( m) - _p resistivity of bubble-free solution ( m)     

Analysis of the inductance influence on the measured electrochemical impedance

The high-frequency region of the impedance diagram of an electrochemical cell can be deformed by the inductance of the wiring and/or by the intrinsic inductance of the measuring cell. This effect can be noticeable even in the middle frequency range in the case of low impedance systems such as electrochemical power sources. A theoretical analysis of the errors due to inductance effects is presented here, on the basis of which the admissible limiting measuring frequency can be evaluated. Topology deformations due to the effect of inductance in the case of a single-step electrochemical reaction are studied by the simulation approach. It is shown that an inductance can not only change the actual values of the parameters (electrolytic resistance, double layer capacitance, reaction resistance), but can also substantially alter the shape of the impedance diagram, this leading to erroneous structure interpretations. The effect of the size and surface area of the electrode on its intrinsic inductance is also evaluated.Nomenclature A linear dimension of the surface area confined by the circuit (cm) - C _D double layer capacitance (F) - C _M measured capacitance - d diameter of the mean effective current line (mm) - f _max limiting (maximum) frequency of measurement (Hz) - K ₁,K ₂ shape coefficients with values of 2×10^–9 and 0.7 for a circle, and 8×10^–9 and 2 for a square (dimensionless) - L intrinsic inductance of the electrochemical cell assumed as an additive element (H) - R _E electrolyte resistance () - R _M measured resistance () - R _P reaction resistance () - r ₀ specific resistance ( cm) - S electrode surface area (cm²) - T _c time constant (s) - Z impedance () - Z _lm imaginary component of the impedance without accounting for the influence of inductance () - Z _lm imaginary component of the impedance accounting for the influence of the additive inductance () - shape coefficient; =1 for a square and =^1/2/2 for circle (dimensionless) - _L relative complex error due to the influence of inductance (dimensionless) - _L ^A relative amplitude error due to inductance (%) - ^L relative phase error due to inductance (%) - ratio between the effective inductance time constant and the capacitive time constant (dimensionless) - angular frequency (s^–1) - _R characteristic frequency at which the inductive and capactive parts of the imaginary component of impedance are equal (s^–1)     

Applications of magnetoelectrolysis

A broad overview of research on the effects of imposed magnetic fields on electrolytic processes is given. As well as modelling of mass transfer in magnetoelectrolytic cells, the effect of magnetic fields on reaction kinetics is discussed. Interactions of an imposed magnetic field with cathodic crystallization and anodic dissolution behaviour of metals are also treated. These topics are described from a practical point of view.Nomenclature 1, 2 regression parameters (-) - B magnetic field flux density vector (T) - c concentration (mol m^–3) - c bulk concentration (mol m^–3) - D diffusion coefficient (m² s^–1) - d _e diameter of rotating disc electrode (m) - E electric field strength vector (V m^–1) - E _i induced electric field strength vector (V m^–1) - E _g electrostatic field strength vector (V m^–1) - F force vector (N) - F Faraday constant (C mol^–1) - H magnetic field strength vector (A m^–1) - i current density (A m^–2) - i _L limiting current density (A m^–2) - i _L ⁰ limiting current density without applied magnetic field (A m^–2) - I current (A) - I _L limiting current (A) - j current density vector (A m^–2) - K reaction equilibrium constant - k reaction velocity constant - k _b Boltzmann constant (J K^–1) - _{m 1}, m ₂ regression parameters (-) - n charge transfer number (-) - q charge on a particle (C) - R gas constant (J mol^–1 K^–1) - T temperature (K) - t time (s) - V electrostatic potential (V) - v particle velocity vector (m s^–1) Greek symbols transfer coefficient (–) - velocity gradient (s^–1) - _MS potential difference between metal phase and point just inside electrolyte phase (OHP) - diffusion layer thickness (m) - ₀ hydrodynamic boundary layer thickness without applied magnetic field (m) - density (kg m^–3) - electrolyte conductivity (^–1 m^–1) - magnetic permeability (V s A^–1 m^–1) - kinematic viscosity (m² s^–1) - vorticity     

Partial oxidation of methane to synthesis gas

Partial oxidation of methane to synthesis gas has been carried out over a number of transition metal catalysts under a range of conditions. It is found that the metals Ni, Ru, Rh, Pd, Ir and Pt, either supported on alumina or present in mixed metal oxide precursors, will bring the system to equilibrium. The yield of CO and H2 improves with increasing temperature in the range 650–1050 K, and decreases with increasing pressure between 1 and 20 atm. An excellent yield (92%) is obtained with a 421 N₂CH₄O₂ ratio at 1050 K and atmospheric pressure, with a space velocity of 4×10⁴ hour^–1.     

Kinetics and mechanism of anodic oxidation of chlorate ion to perchlorate ion on lead dioxide electrodes

The kinetics and mechanism of anodic oxidation of chlorate ion to perchlorate ion on titanium-substrate lead dioxide electrodes have been investigated experimentally and theoretically. It has been demonstrated that the ionic strength of the solution has a marked effect on the rate of perchlorate formation, whereas the pH of the solution does not influence the reaction rate. Experimental data have also been obtained on the dependence of the reaction rate on the concentration of chlorate ion in the solution at constant ionic strength. With these data, diagnostic kinetic criteria have been deduced and compared with corresponding quantities predicted for various possible mechanisms including double layer effects on electrode kinetics. It has thus been shown that the most probable mechanisms for anodic chlorate oxidation on lead dioxide anodes involve the discharge of a water molecule in a one-electron transfer step to give an adsorbed hydroxyl radical as the rate-determining step for the overall reaction.Nomenclature anodic energy transfer coefficient - ₂ potential of outer Helmholtz plane with respect to solution - _M potential of metal with respect to solution - dielectric constant of solution - ₂ permittivity of free space - faradaic efficiency for anodic chlorate oxidation - A adsorbed intermediate in Reaction 2 - B bulk species in Reaction 2 - c _A concentration of A at outer Helmholtz plane - c _B concentration of B at outer Helmholtz plane - c _B ⁰ concentration of B in bulk - c _ClO3 ^– /0 concentration of ClO ₃ ^– in bulk - c _ClO4 ^– /0 concentration of ClO ₄ ^– in bulk - E electrode potential corrected for ohmic drop - E _a electrode potential as measured against reference electrode - E _s ⁰ standard electrode potential of Reaction 2 - E _z potential of zero charge of the anode in test solution - F Faraday constant - f F/(RT) - I _t current at anode - I _OER current used for oxygen evolution reaction at anode - I current used for chlorate oxidation (=I _t–I _OER) at anode - i _t I _t/anode area - i _OER I _OER/anode area - i I/anode area - J total concentration of (uni-univalent) electrolytes in solution - K ₂ integral capacitance of compact part of double layer - K _s standard rate constant for Reaction 2, corrected for double layer effects - n _s number of electrons involved in Reaction 2 - p ln(–i)/lnc _ClO3 ^– /0 - q _M charge density on metal surface - Q ₁ quantity of electricity passed in given time interval - Q _OER quantity of electricity required for oxygen evolution reaction in given time interval - R ohmic resistance between anode and Luggin tip - R gas constant - r ln(–i)/lnJ - s ln(–i)/ pH - T absolute temperature - t ln(–i)/E - u (₂ RT/2)^1/2 - V volume of gases evolved in given time interval - V _H volume of hydrogen evolved in given time interval - Z _B charge on species B     

Fluidized bed electrodes Part IV. Electrodeposition of copper in a fluidized bed of copper-coated spheres

The effective resistivity of the discontinuous metal phase in a fluidized bed copper electrode is derived from measurements of the potential distribution in the solution. The values are similar to those which have been previously observed for a fluidized bed of silver-coated particles and are compared with a theoretical expression based on a model of charge sharing during single particle elastic collisions. It is shown that the metal resistivity follows the predicted dependence on bed expansion and solution resistivity; the constant of proportionality is, however, different and this is attributed to a stagnation zone close to the feeder electrode. Such a stagnant zone is also indicated by comparison of the experimental and theoretically predicted distribution of potential in the metal phase.The diffusion controlled removal of copper from 10^–4 M copper sulphate is also shown to follow the theoretically predicted behaviour; the mass transfer coefficient indicates a high degree of turbulence within the bed. It is shown that scale-up factors of the order of 300 can be achieved in the processing of such dilute solutions. In view of the relatively high resistivity of the metal phase it is suggested that practical systems would arrange for a current and fluid flow to be at right angles to each other.Glossary A surface area per unit volume of electrode (cm^–1) - C double layer capacity (Farads cm^–2) - c ₀ concentration (moles cm^–3) - D diffusion coefficient (cm² s^–1) - F the Faraday (coulombs mole^–1) - I total current (A cm^–2) - i local current density (A cm^–2) - i _o exchange current density (A cm^–2) - K _m mass transfer coefficient (cm s^–1) - n equivalents per mole - R gas constant (volt coulomb deg^–1 mole^–1) - r particle radius (cm) - T absolute temperature - u superficial solution velocity (cm s^–1) - V voidage - v _p mean particle velocity (cm s^–1) - x distance from feeder in direction of current flow (cm) - electrochemical transfer coefficient for an anodic reaction - Young's modulus (dynes cm^–2) - Solution-metal diffusion layer thickness (cm) - electrode length normalized w.r.t. the static bed length - local overpotential (volts) - characteristic length (cm) - solution-particle density difference (g cm^–3) - _m effective specific resistivity of the discontinuous metal phase ( cm) - _s effective specific resistivity of the solution phase ( cm) - _m metal potential (volts) - _s solution potential (volts)     

Calculation of mean current densities in a two rotating disc electrodes system

A theoretical relationship for mass transfer in the laminar flow region of streaming in a rotating electrolyser was derived by the method of similarity of the diffusion layer for electrodes placed sufficiently far from the rotation axis. The obtained relationship was compared with the known equations valid for systems with axial symmetry. The mean current densities were found from the numerical solution of the convective diffusion equation by the finite-element method and were compared with experimental results.Nomenclature a constant, exponent - c concentration - c ₀ concentration in the bulk phase - C _ij matrix coefficient - D diffusion coefficient - F Faraday constant, 96487 C mol^–1 - h interelectrode distance - j current density - mean current density - J mass flux density - L _j base function - n number of transferred electrons in electrode reaction - n _r outer normal to the boundary - mass flux - N number of nodal points in an element - Q volume rate of flow - mean volume rate of flow - r radial coordinate - r ₀ inner electrode radius - r _l outer electrode radius - r _v radius of inlet orifice - r _d outer disc radius - v _r radial velocity component - v _z normal velocity component - z normal coordinate - thickness of the layer in which the equation of convective diffusion is solved - boundary of the integration domain - thickness of the diffusion layer - _N thickness of the Nernst diffusion layer - v kinematic viscosity - angular velocity - surface Criteria Re _chan channel Reynolds numberQ/hv - Re _loc local Reynolds number,Q/(r + r ₀) - local Reynolds number at mean electrode radius,Q/v(r ₁ +r ₀) - Re _rot rotation Reynolds number, r _d ² /v - modified rotation Reynolds number at mean electrode radius, (r ₁+r ₀)²/4v - Ré _rot modified rotation Reynolds number, (r+r ₀)²/4v - Sc Schmidt number,v/D - Sh _r local Sherwood number,j(r-r ₀)/nFDc _o - mean Sherwood number, - Ta Taylor number,h(/v)^1/2     

A parametric study of copper deposition in a fluidized bed electrode

The behaviour of a fluidized bed electrode of copper particles in an electrolyte of deoxygenated 5×10^–1 mol dm^–3Na₂SO₄–10^–3mol dm^–3H₂SO₄ containing low levels of Cu(II), is described as a function of applied potential, bed depth, flow rate, particle size range, Cu(II) concentration and temperature. The observed (cross sectional) current densities were more than two orders of magnitude greater than in the absence of the bed, and current efficiencies for copper deposition were typically 99%.No wholly mass transport limited currents were obtained, due to the range of overpotentials within the bed. The dependence of the cell current on the experimental variables (excluding temperature) was determined by regression analysis. The values of exponents for some of the variables are close to those expected, while others (for concentration and flow rate) reveal interactions between the experimental parameters. Nevertheless the values of the correlation coefficient matrix are low (except for the term relating expansion and flow rate), so that cross terms may be neglected in modelling the system at the first level of approximation.Nomenclature d mean particle diameter (mm) - E electrode potential, ( _m– _s)_r+(x) (V vs ref) wherer denotes the value of ( _m- _s) at the reversible potential - I (membrane) current density (A m^–2) - L static bed depth (mm) - M concentration of electroactive species (mol dm^–3) - T catholyte temperature (K) - u catholyte flow rate (mm s^–1) - x distance in the bed from the feeder electrode atx=0 - XL expanded bed depth (mm) - bed expansion (fraction of static bed depth) - _m metal phase potential (V) - _s solution phase potential (V) - _m metal phase resistivity (ohm m) - _s solution phase effective resistivity (ohm m) - overpotential (V)     

Characterization of electroless Ni-Mo-P/SnO2/Ti electrodes for oxygen evolution in alkaline solution

Ni-Mo-P alloy electrodes, prepared by electroless plating, were characterized for application to oxygen evolution. The rate constants were estimated for oxygen evolution on electrodes prepared at various Mo-complex concentrations. The surface area and the crystallinity increase with increasing Mo content. The electrochemical characteristics of the electrodes were identified in relation to morphology and the structure of the surface. The results show that the electroless Ni-Mo-P electrode prepared at a Mo-complex concentration of 0.011 m provided the best electrocatalytic activity for oxygen evolution.List of symbols b Tafel slope (mV dec^–1) - b F/RT (mV^–1) - F Faraday constant (96 500 C mol^–1) - j current density (mA cm^–2) - k₁ reaction rate of Reaction 1, (mol^–1 cm³ s^–) - k ₁ = k₁C _OH ^–(mol cm^–2 s^–1) - k ₁₀ rate constant of Reaction 1 at = 0 (mol cm^–2 s^–1) - k_c1 rate constant of Reaction 2 (mol^–1 cm³ s^–1) - k _c1 = k_c1C _{H 2O} (mol cm^–2 s^–1) - k_c2 rate constant of chemical Reaction 3 (mol^–1 cm² s^–1) - k _c2 = k_c2² (mol cm^–2 s^–1) - k_c3 rate constant of Reaction 4 (mol^–1 cm² s^–1) - Q _a anodic capacity (mC) - Q _c cathodic capacity (mC) - R gas constant (8.314 J mol^–1 K^–1) - R _ct charge transfer resistance ( cm²) - R _ads charge transfer resistance due to adsorption effect ( cm²) - C _d1 double layer capacity (mF cm^–2) - _{C ads} double layer capacity due to adsorption effect (mF cm^–2) - T temperature (K) Greek symbols anodic transfer coefficient - _{O 2} oxygen overpotential (mV) - saturation concentration of surface oxide on nickel (mol cm^–2)     

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)