Cathodic behaviour of antimony (III) species in chloride solutions

Cathodic copper is easily contaminated by antimony in copper electrowinning from chloride solutions even when the antimony concentration in the electrolyte is as low as 2 p.p.m. Reduction potential measurements of copper and antimony species indicate that electrodeposition of antimony is unlikely unless copper concentration polarization exists near the cathode surface. A.c. impedance measurements and the effect of the rotation speed of the disc electrode indicate that the cathodic process mechanism for antimony is complicated. Both diffusion and chemical reactions occurring on the cathode surface supply the electrochemical active antimony species for the cathodic process. Reaction orders of the cathodic process with respect to antimony chloride, hydrogen and chloride ion concentrations are 2, –1 and –1, respectively. A proposed reaction mechanism for the process explains the experimental findings satisfactorily.List of symbols A surface area (cm²) - a_o1, a₁ constants - C concentration (mol cm^–3) - D diffusion coefficient (cm2 s^–1) - E potential (V) - F Faraday constant (Cmol^–1) - f frequency (s^–1) - I current (A) - i current density (A cm^–2) - i _{d 8} limiting diffusion current density due to the diffusion of species O from bulk to the electrode surface and then the subsequent Reac tions 1 and 2 (A cm^–2) - i _{d o} limiting diffusion current density of species O (A CM^–2) - K chemical equilibrium constant - k rate constant (s^–1) - n number of electrons involved in the reaction - Q charge (C) - Q _dl charge devoted to double layer capacitance (C) - Q _f total charge in the forward step of potential step chronocoulometry (C) - Q _r total charge in reverse step of potential step chronocoulometry (C) - t time (s) - sweep rate (V s^–1) Greek symbols amount of species adsorbed per unit area (mol cm^–2) - fraction of adsorption sites on the surface occupied by adsorbate. - ratio of rate constant defined in Equation 1 - _c thickness of reaction layer (cm) - d thickness of diffusion layer (cm) - time (s) - modified time (s^1/2) - kinematic viscosity (cm² s^–1) - angular velocity (s^–1)     

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)     

Potential-pH diagrams for complex systems

A generalized thermodynamic analysis and a geometric interpretation of potential-pH diagrams for multi-element systems are presented. The presence of reactive gases, e.g. CO₂ and SO₂, and complex-forming species, e.g. NH₃ and Cl^–, are expressly considered. The equilibrium state is described by a set of independent formation reactions of all species containing the active redox element, M. The formation reactions are written in terms of a user-specified set of primitive species, e.g. M, H₂O, H⁺,e, X and Y, where X and Y could be CO₂ and Cl^– for example. Some of these primitive species, e.g. M ande, may be virtual species, that is, they do not have an independent existence as separate entities in the reaction mixture. This procedure permits an explicit algebraic solution for the potential-pH diagram. Examples of Pourbaix and predominance diagrams for complex uranium and chromium systems are given. A defined by Equation 41 - a activity - a _M overall activity of redox element M - D maximum dimensionality of diagram - E electrochemical potential - F Faraday's constant - f degrees of freedom - G _f.n ⁰ standard free energy of formation of speciesn - h _i stoichiometric coefficient for H⁺ in generalized formation reaction - M symbol for redox element - M _i symbol forith species containing redox element M - M _X molal concentration of species M _i - [M]_T total dissolved concentration of redox element M - n number of species containing redox element M - P number of phases - P_j symbol for primitive species - p pressure - p _ij stoichiometric coefficient for species P_j in generalized formation reaction - r number of independent reactions - R gas constant - s number of species - t number of primitive species - w _i stoichiometric coefficient for H₂O in generalized formation reaction - [X] molal concentration of X - x _i stoichiometric coefficient for species X in generalized formation reaction - y _i stoichiometric coefficient for species Y in generalized formation reaction - z _i stoichiometric coefficient for electrons in generalized formation reaction - _i atoms of redox element in species M _i (_i v_i ^–1) - activity coefficient - chemical potential - v_i stoichiometric coefficient for species M _i in generalized formation reaction (v_{i i} ^–1) - aq aqueous phase - b, c, d dissolved species (M_b, M_c, M_d) containing redox element M - i ith species, M_i (gaseous, solid or dissolved) containing redox element M - j primitive species - M redox element M - s, t, u, v solid phases (M_s, M_t, M_u, M_v) containing redox element M - o standard state - reference electrode     

Synthesis of new metal-containing side-chain monomers and polymers

New metal-containing vinyl monomers, hexyl-6-oxy-{4-[4-(4-carboxy cyclopentadienyl manganese tricarbonyl phenyl)phenyl]benzoyloxy}methacrylate and hexyl-6-oxy-{4-[4-(4-ferrocenoyl phenyl)phenyl]benzoyloxy}methacrylate, and the corresponding homopolymers and random copolymers with hydroxy monomer hexyl-6-oxy-{4-[4-(4-hydroxyphenyl)phenyl]benzoyloxy}methacrylate were synthesized. The compounds were characterized by¹H NMR; their thermal behavior was investigated by means of differential scanning calorimetry. Monomers and polymers containing the ferrocene unit melt at lower temperatures than those derived from the cyclopentadienyl managanese tricarbonyl moiety. The melting temperatures of the monomers and polymers ranged from 399 to about 515 K, Both monomers and polymers failed to exhibit mesogenic behavior. Values ofM _n,M _w,M _w/M _n, and degree of polymerization were obtained by gel permeation chromatography. TheM _n ranged from 16,500 for the copolymer containing hexyl-6-oxy-{4-[4-(4-ferrocenoyl phenyl)phenyl] benzoyloxy}methacrylate and hydroxy monomer hexyl-6-oxy-{4-[4-(4-hydroxyphenyl)phenyl]benzoyloxy}methacrylate at a 1:3 ratio to 26,000 for the copolymer containing hexyl-6-oxy-{4-[4-(4-carboxy cyclopentadienyl manganese tricarbonyl phenyl)phenyl]benzoyloxy}methacrylate and hydroxy monomer hexyl-6-oxy-{4-[4-(4-hydroxyphenyl)phenyl]benzoyloxy}methacrylate at a 1:3 ratio.M _w/M _n ranged from 1.6 in the case of the copolymer containing hexyl-6-oxy-{4-[4-(4-carboxy cyclopentadienyl manganese tricarbonyl phenyl)phenyl]benzoyloxy}methacrylate and hydroxy monomer hexyl-6-oxy-{4-[4-(4-hydroxyphenyl)phenyl]benzoyloxy}methacrylate at a 1:3 ratio to 2.2 in the case of poly(hexyl-6-oxy{4-[4-(4-carboxy cyclopentadienyl manganese tricarbonyl phenyl)phenyl]benzoyloxy}methacrylate).     

The impedance of alkaline manganese cells and their relationship to cell performance. III. Correlation with high-rate pulse discharge capacity

The extent to which the initial impedance characteristics of a batch of LR6 alkaline manganese cells determine their life and therefore capacity during a typical 2 A/10 s pulse discharge regime has been investigated, and the importance of thermodynamic factors have also been considered. It is shown that the potential drop (E-V _pulse) for the initial discharge cycle can be calculated approximately from a knowledge of the initial internal resistance value, and the recovery voltage,V _rec, can be calculated using a simple thermodynamic theory for the homogeneous phase discharge of -MnO₂. During subsequent cycles the polarization of the cathode-can assembly remains approximately constant at 300 mV while that of the anode-separator system increases progressively from 100 mV to >300 mV. The constancy of the former parameter can be attributed to constancy in the cathode contribution to the internal resistance, whereas the changes in the latter can be ascribed to increases in anode resistance polarization and anode concentration polarization. Minimization of cell internal resistance and anode polarization are therefore of primary concern if cell performance is to be maximized.Nomenclature E initial open-circuit voltage - V _pulse cell voltage att=10 s - V _pulse cell voltage att=10 s for the first pulse - V _rec open-circuit voltage at the end of a 50-s recovery period - V total polarization of the cell - V _A anode polarization (anode-separator system) - V _C cathode polarization (cathode-can assembly) - ohmic polarization - _NT charge-transfer polarization - _C concentration polarization - R _i cell internal resistance - R _e electrolyte resistance - R _part ^cath contact resistance between cathode particles or within the particles themselves - R ^cath effective resistance of cathode-can assembly - R _i ^cath contact resistance at the interface between the nickel oxide phase and the cathode (MnO₂ + graphite mixture) - R _phase ^cath resistance of the nickel oxide phase on the surface of the nickel-plated steel positive current collector (cell can) - R ₂ ^cath contact resistance at the interface between the nickel oxide layer on the can surface and the can itself - R high frequency intercept on complex plane impedance diagram - R diameter of the complex plane impedance semicircle - f ^* characteristic frequency at the top of the complex plane semicircle - C effective parallel capacitance in the equivalent circuit for a cell attributed to the cathode-can assembly - c _MnO2 concentration of MnO₂ at any point in the discharge - cMnO ₂ ⁰ maximum MnO₂ concentration at 100% efficiency - c _MnOOH concentration of MnOOH at any point in the discharge - c _MnOOH ⁰ maximum MnOOH concentration at 100% efficiency - proton-electron spatial correlation coefficient - I total current - i _R current through resistanceR - i _c current through capacitor - V _p voltage drop across parallel R-C circuit - A anode - C cathode - obs observed - calc calculated     

Unsteady mass transfer in turbulent flow close to a rotating cylinder

Electrodiffusional methods of studying unsteady turbulent mass transfer involved measurement of a transient current characteristicI() after step polarization of a rotating annular cylindrical 46 mm dia electrode at a fixed rotational velocity atRe=(2–9)×10⁴ andSc=2.4×10³. The potassium ferri-ferrocyanide system with NaOH background electrolyte was used. An initial asymptote at 0 served as a test. The similarity of the normalized transfer coefficientK ₊=/u _* with respect to the Reynolds number demonstrated turbulent flow development. Tests were aimed at determining the powern in the approximate law of attenuation of turbulent diffusionD _t in they-direction normal to the wallD _t/v=by ₊ ⁿ .A numerical solution of the unsteady turbulent diffusion equation obtained as a set of lg ()=f() curves for 3n4 with an interval 0.2, where ()=I/I()_#x2212;1 has been achieved.Notation I diffusion current - C C ₀ andC _p concentration, concentration in the bulk liquid and polymer concentration, respectively - C _f drag of a Newtonian fluid - time - U linear velocity - v kinematic viscosity - angular velocity - j flow - y ₊ yu _*/v, ₊ = u _* ² and =(1-C/C ₀), dimensionless quantities This paper was presented at the Workshop on Electrodiffusion Flow Diagnostics, CHISA, Prague, August 1990.     

Weak Gel Behaviour of Poly(vinyl alcohol)-Borax Aqueous Solutions

Thermal transition of PVA-borax aqueous gels with a PVA concentration of 60 g/L and a borax concentration of 0.28 M was investigated at temperatures ranging from 15 to 60C using static light scattering (SLS), dynamic light scattering (DLS), and dynamic viscoelasticity measurements. Three relaxation modes, i.e. two fast and one slow relaxation modes, were observed from DLS measurements. Two fast relaxation modes located around 10^–310¹ sec, with one fast mode (_f1) being scattering vector q-dependent and the other fast mode (_f2, with _f2>_f1) being q-independent. The _f1 mode was attributed to the gel mode whilst the _f2 mode could be due to the hydrodynamics of intra-molecular hydrophobic domains formed by uncharged segments of polymer backbones. The slow relaxation mode with relaxation time located around 10¹10³ sec in DLS data was due to the motion of aggregated clusters and was observed only at temperatures above 40C. The amplitude and relaxation time of slow mode decrease as temperature is increased from 40 to 60C. At temperatures below 40C, no slow relaxation mode was observed. The SLS measurements showed PVA-borax-water system had fractal dimensions D _f2.4 and D _f2.0 as temperature was below and above 40C, respectively. The simple tilting test indicated gel behaviour for the PVA-borax aqueous system at temperatures below 40C with a creep flow after a long time exposure in the gravity field. But the dynamic viscoelasticity measurements demonstrated a solution behaviour for PVA/borax/water at temperatures below 40C, the critical gel point behaviour for G() and G() was not observed in this system as those reported for chemical crosslinked gels. These results suggest that the PVA-borax aqueous system is a thermoreversible weak gel.     

Joule heating induced local electrodeposition for microelectronic circuits

A fundamental study is performed for local electrodeposition of copper utilizing thermal potential induced by Joule heating. The feasibility of the process for microelectronic applications is assessed by both experiment and mathematical modeling. The results of the investigation show that (i) a copper wire is coated under conditions of a.c. 50 Hz Joule heating in electrolyte containing 1.0 M CuSO₄ and 0.5m H₂SO₄ with relatively high deposition rate of about 0.4 µm min^–1, (ii) the Joule heating current should be kept below the boiling point of the solution to realize uniform deposition, and (iii) results of calculations by the present model based on one-dimensional heat conduction agree well with experimental results.Nomenclature D diameter of wire (m) - D ₀ initial diameter of wire (m) - F Faraday constant (96 487 C mol¹ ) - g acceleration due to gravity (9.807 m s²) - Gr Grashof number - H thickness of electrodeposit (m) - I current (A) - i ₀ exchange current density (Am^–2) - i _n current density normal to electode (Am^–2) - J current density (I/S) (Am^–2) - L length of wire (m) - M molar concentration of electrolyte (mol dm^–3 or M) - m atomic weight (kg mol^–1) - n number of electrons participating - n unit normal vector to boundary - Nu Nusselt number - Pr Prandtl number - q heat per unit volume (W m^–3) - R universal gas constant (8.314 3 J mol^–1 K^–1) - (r, z) cylindrical coordinate (m) - S cross section of wire (m²) - T temperature (K) - T ₀ fixed temperature at both ends of wire (K) - T _y temperature of electrolyte (K) - t time (s) - x longitudinal coordinate over wire (m) Greek symbols heat transfer coefficient (W m^–2 K^–1 - _a,c anodic (a) and cathodic (c) transfer coefficient - thermal expansion coefficient of solution (K^–1) - specific heat (J kg^–1K^–1) - potential (V) - _e electrode potential (V) - thermal conductivity (W m^–1 K^–1 ) - _y ionic conductivity of electrolyte (^–1m^–1) - _e electronic conductivity of electrode (^–1 m^–1) - kinematic viscosity (m²s^–1) - surface overpotential ( _e – ) (V) - time constant (s) - density (kg m^–3) This work was presented at The 7th International Microelectronics Conference, Yokohama, Japan (1992).     

The hydrodynamics of a magnetoelectrolytic cell

The characteristics of induced flow in a cylindrical magnetoelectrolytic cell under the influence of uniform and non-uniform magnetic fields are analysed. Experimental surface velocity values are predicted with reasonable accuracy by magnetohydrodynamic models incorporating open-channel flow concepts.Nomenclature A, D parameters in Equation 7 [Gak equation] - B magnetic flux density vector;B _r,B _z its radial and axial components;B ₀ its magnitude, ¯B its average magnitude - B ₁ (pr) auxiliary function in the annular Hankel transform technique (Equation 6) - e unit vectors in the cylindrical coordinate system with componentse _r,e _o,e _z - F magnitude of the MHD force density in the-direction - f _c friction coefficient of energy loss due to curvature - g acceleration due to gravity - H height of the electrodes in electrolytic cell - h _f energy head loss due to friction - h _c energy head loss due to curvature - I electric current flow - J electric current density vector - K lumped parameter;K=IB _o/2H - K _f,K _c K factors in terms of friction and curvature losses - k geometric shape factor,R/r _o - P pressure - p annular Hankel transform parameter - R radius of the outer electrode - r _o radius of the inner electrode - r radius measured from the centre of the electrolytic cell - V _gq velocity in the-direction - ¯V its average - _n regression coefficients in Equation 13 - dynamic viscosity of electrolyte - gn kinematic viscosity of electrolyte - density of electrolyte - (p) function defined in Equation 8a - (r) surface profile function (Equation 29)     

The effect of the gas void distribution on the ohmic resistance during water electrolytes

Due to the presence of gas bubbles on the electrode surface and in the interelectrode gap during water electrolysis, the ohmic resistance in the cell increases. The main aim of this investigation is to obtain insight into the effect of the gas void distribution on the ohmic resistance in the electrolysis cell. The gas void distribution perpendicular to the electrode surface has been determined at various current densities, solution flow velocities and heights in the cell, taking high speed motion pictures. From these measurements it follows that two bubble layers can be distinguished. The current density distribution and the ohmic resistance in the electrolysis cell have been determined using a segmented nickel electrode. The current density decreases at increasing height in the cell. The effect is more pronounced at low solution flow velocities and high current densities. A new model to calculate the ohmic resistance in the cell is proposed.Nomenclature A _l electrolyte area (m²) - c constant (–) - d _wm distance between the working electrode and the diaphragm resp. the tip of the Luggin capillary (m) - E voltage of an operating cell (V) - f gas void fraction (–) - F Faraday constant (C/mol) - f ₀ gas void fraction at the electrode surface (–) - f _b gas void fraction in the bulk electrolyte (–) - h height from the bottom of the working electrode (m) - h _r reference height (= 1 cm) (m) - H total height of the electrode (m) - i current density (A m^–2) - i _av average current density (A m^–2) - i _r reference current density (= 1 kA m^–2) (A m^–2) - R resistance () - R specific resistance (_m) - R unit surface resistance (m²) - R ₁ resistance of the first bubble layer () - R ₂ resistance of the second bubble layer () - R _cell ohmic resistance in the cell () - R _b bubble radius (m) - s _l degree of screening by bubbles in the electrolyte (–) - _l liquid flow velocity (m s^–1) - _{1, r} reference liquid flow velocity (= l m s^–1) (m s^–1) - V _M molar gas volume (m³ mol^–1) - w width of the electrode (m) - x distance from the electrode surface (m) - thickness of the bubble layer adjacent to the electrode (m) - number of bubbles generated per unit surface area and unit time (m^–2 s^–1) Paper presented at the International Meeting on Electrolytic Bubbles organised by the Electrochemical Technology Group of the Society of Chemical Industry, and held at Imperial College, London, 13–14 September 1984.     

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     

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     

Cathodic reduction of hypochlorite during reduction of dilute sodium chloride solution

Sodium chloride solutions of concentration 15 and 30 g dm^–3 were electrolysed in a flow-through electrolyser with a titanium/TiO)₂/RuO₂ anode at current densities 1059–4237 A m^–2. The current yield for the reduction of hypochlorite on a stainless steel cathode was found to be 13–32% at 7 g dm^–3 NaClO, in agreement with that calculated on the basis of the Stephan-Vogt theory. Migration of ions was taken into account, the diameter of hydrogen bubbles was set equal to 0.04 mm and the coverage of the electrode with the bubbles was estimated as = 0.897. The results of calculations show that the reduction rate of hypochlorite at low NaCl concentrations is lowered by migration. Literature data for the reduction of hypochlorite are in accord with the current yield calculated on the basis of the Stephan-Vogt theory using = 0.787 and = 0.949.List of symbols C _i ^o concentration of species i in the bulk (mol m^–3) - C _i ^s concentration of species i at the cathode surface (mol m^–3) - d _B bubble diameter (m) - D _e equivalent diameter (characteristic dimension) (m) - D _i diffusion coefficient of species i (m² s^–1) - f _G gas evolution efficiency - F Faraday constant (96 487 C mol^–1) - j total current density (Am^–2) - j _B current density for gas evolution (Am^–2) - j _{c, lim} limiting current density for cathodic reduction of ClO^– (A m^–2) - j _{c, r} critical current density (A m^–2) - L length of electrode (m) - M migration correction factor - n _B number of electrons exchanged in gas evolution - n _ClO ^– number of electrons exchanged in reduction of ClO^– - N _i flux of species i (mol m^–2 s^–1) - Q charge passed (C) - P _t total gas pressure (Pa) - Re Reynolds number (Equation 14) - Re _B Reynolds number (Equation 17) - Sc Schmidt number (Equation 13) - Sh Sherwood number (Equation 12) - Sh _B Sherwood number (Equation 15) - T absolute temperature (K) - u _i mobility of ion i (m² s^–1 V^–1) - _B fictitions linear velocity of gas formation (ms^–1) - _el rate of electrolyte flow (ms^–1) - V volume of the electrolyte in the system (m³) - V _{H 2} content of hydrogen in gas phase (%) - V _{O 2} content of oxygen in gas phase (%) - y _i current yield (differential) for production of species i (%) - y _r current yield (differential) for reduction of ClO^– and ClO ₃ ^– (%) - Y _ClO–,r current yield (differential) for reduction of CIO^– (%) - Y _i integral current yield for production of species i (%) - z _i charge number of ion i Greek symbols thickness of Nernst diffusion layer (m) - _c thickness of convective diffusion layer (m) - _B thickness of diffusion layer controlled by gas evolution (m) - dynamic viscosity (m² s^–1) - time (s) - coverage of electrode surface with gas bubbles - Galvani potential (V) - correction function (Equation 11)     

Mass transfer and electrocrystallization analyses of nanocrystalline nickel production by pulse plating

A comparison between the experimental process parameters employed for the pulse plating of nanocrystalline nickel and the solution-side mass transfer and electrokinetic characteristics has been carried out. It was found that the experimental process parameters (on-time, off time and cathodic pulse current density) for cathodic rectangular pulses are consistent and within the physical constraints (limiting pulse current density, transition time, capacitance effects and integrity of the waveform) predicted from theory with the adopted postulates. This theoretical analysis also provides a means of predicting the behaviour of the process subject to a change in the system, kinetic and process parameters. The product constraints (current distribution, nucleation rate and grain size), defined as the experimental conditions under which nanocrystalline grains are produced, were inferred from electrocrystallization theory. High negative overpotential, high adion population and low adion surface mobility are prerequisites for massive nucleation rates and reduced grain growth; conditions ideal for nanograin production. Pulse plating can satisfy the former two requirements but published calculations show that surface mobility is not rate-limiting under high negative overpotentials for nickel. Inhibitors are required to reduce surface mobility and this is consistent with experimental findings. Sensitivity analysis on the conditions which reduce the total overpotential (thereby providing more energy for the formation of new nucleation sites) are also carried out. The following lists the effect on the overpotential in decreasing order: cathodic duty cycle, charge transfer coefficient, Nernst diffusion thickness, diffusion coefficient, kinetic parameter () and exchange current density.Nomenclature A constant employed in Fig. 8, (nFi₀)/(RT _e C _a)(s^–1) - B constant in Equation 38 (V²) - C cation concentration (molcm^–3) - C _a capacitance of double layer (µFcm^–2) - C _s cation surface concentration (molcm^–3) - C _s ^* dimensionless cation surface concentration, C _s/C (–) - C cation bulk concentration (molcm^–3) - D diffusion coefficient of cation (cm²s^–1) - E total applied potential (V) - E ⁰ standard cell potential (V) - F Faraday constant (Cmol^–1) - function defined in Appendix C(–) - Fr frequency of waveform (Hz) - f _i,p function defined in Appendix C for pth period (–) - f _i, function defined in Appendix C for p period (–) - G _j function defined in Appendix B (–) - gi function defined in Appendix B (–) - i current density (Acm^¨) - i _ac unsteady fluctuating a.c. current density (Acm^–2) - i _c capacitance current density (Acm^–2) - i _dc steady time-averaged d.c. current density (Acm^–2) - i _F Faradaic current density (Acm^–2) - i _lim limiting d.c. current density (Acm^–2) - i ₀ exchange current density (Acm^–2) - i _PL limiting pulse current density, i ₁{Cs = 0 at t = (p – 1) T + t ₁(Acm^–2) - i ₁ cathodic pulse current density (Acm^–2) - i ₂ relaxed or low current pulse current density (Acm^–2) - iin anodic pulse current density (Acm^–2) - i ^* dimensionless current density, i/|i _lim| (–) - i ₀ ^* dimensionless exchange current density, i _dc/|i _lim| (–) - i _dc ^* dimensionless steady time-averaged d.c. current density, i _dc/|i _lim| (–) - i _PL ^* dimensionless limiting cathodic pulse current density, i _PL/|i _lim| (–) - i _PL,p ^* dimensionless limiting pulse current density at pth period, i ₁(C _s = 0)/|i _lim| (–) - i _PL, ^* dimensionless limiting pulse current density for p , i ₁(C _s = 0)/|i _lim| (–) - i ₁ ^* dimensionless cathodic pulse current density, i ₁/|i _lim| (–)     

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     

Influence of charge and discharge of electric double layer in pulse plating

In pulse plating the useful values of the on and off times are limited by the rate of charging and discharging, respectively, of the electrical double layer at the electrode-solution interface. The charging and discharging times are calculated as a function of the relevant parameters (pulse current density, exchange current densityi ₀, capacitanceC of the double layer and others). Simple, approximate relationships are also presented for the case in which no experimental values fori ₀ andC are available. In order to quantify the damping of the Faradaic current the concept of degree of flattening is introduced to describe the extent of the capacitive effects. The influence of a high degree of flattening on some deposit properties is illustrated by examples.Nomenclature a zF/RT - A proportionality factor between current and potential - C capacitance of the electric double layer - E potential - i current density - i ₀ exchange current density - i _C capacitive current density - i _F Faradaic current density - i _m average current density in pulsed current - i _p pulsed current density - i _t total current density (i _C+i _F) - Q charge - T used inRT = temperature in K - T pulse length - T interval between two pulses (off time) - t _c charging time of the double layer (up to 99% ofi _P) - t _c ^* charging time of the double layer (withj _F=0 during the charge) - t _c ^** charging time of the double layer (up to 98.2% of _a, and constant resistance for electron transfer) - t _d discharging time of the double layer (fromi _F=0.999i _p to 0.01i_p) - t _n time interval corresponding to the nth increment of potential - z number of charges per ion - transfer coefficient - overpotential of the electrode - _a activation overpotential - _a, activation overpotential byi _F =i _p      

Electrochemical removal of copper ions from very dilute solutions

A device for concentrating electropositive cations using porous, fixed, flow-through, carbon electrodes is described. A feed of 667g of copper per ml of solution was reduced to less than 1g of copper per ml of solution. The flow rate was 0.20 cm³/cm²/min through a bed 6 cm thick. Capital cost for the cell is the controlling factor. A preliminary economic analysis indicates that the value of copper recovered will more than pay for the installation and operation of the cell, even for fairly small units.List of Symbols a area per unit volume, cm^–1 - c _o copper concentration of feed, mol/cm³ - c _b averaged, bulk copper concentration within porous cathode, mol/cm³ - c _b ^L copper concentration in cathode effluent, mol/cm³ - D diffusion coefficient of copper ions, cm²/s - F Faraday constant, 96,487 coul/equiv - i ₂ superficial or overall electrical current density in catholyte solution, A/cm² - i _T total, overall current density to cathode, A/cm² - I total current, mA - k _m mass transfer coefficient, cm/s - L thickness of the cathode, cm - n number of electrons transferred in electrode reaction, 2 - Sc Schmidt number/D, dimensionless - t time to plug cathode with copper, s - v superficial or approach velocity of catholyte solution, cm/s - VDP potential of saturated calomel reference electrode in catholyte effluent relative to the cathode, V - VA potential of anode relative to cathode, V - y distance from entrance of cathode toward cathode backing plate, cm - ak _m/v, cm^–1 - nFv ² c _o/ak _m K, V - void fraction, dimensionless - k effective or superficial electrical conductivity of catholyte, mho/cm - k° electrical conductivity of feed solution, mho/cm - viscosity of feed solution, g/cm-s - density of feed solution, g/cm³ - ₂ potential in the solution, V - particle shape factor, 0.86 for flakes, dimensionless     

A particulate vortex bed cell for electrowinning: operational modes and current efficiency

The process of electrowinning of copper ions from dilute solutions has been used as a model system to assess the performance of a vortex bed cell with a three-dimensional cathode of conducting particles. Experiments were carried out under three conditions: with constant cell voltage, with constant cell current throughout the process and with exponential decrease of the operating current with time in order to underfollow the limiting current. Results from a batch recirculating system indicate that exponential decrease of operating current with time effects an improvement in current efficiency over a wide range of concentration.Nomenclature specific surface area of particles (cm^–1) - C, C _i concentration of Cu²⁺ ions at the momentt, and initial concentration, respectively (M) - d _p particle diameter (cm) - F Faraday number (96 487 A s mol^–1) - i current density (Am^–2) (calculated for the surface area of the particles) - i _av average current density obtained in the constant cell voltage process (Am^–2) - I _L(t),I _L o limiting current at timet, and initial limiting current, respectively (A) - k _L mass transfer coefficient (cm s^–1) - n number of electrons transferred in the process - Q volumetric flow rate (dm³ s^–1) - R universal gas constant (J mol^–1 K^–1) - t time (s) - T temperature (K) - U cell voltage (V) - V volume of electrolyte (cm³) - v _o volume of particles (cm³) - overpotential (V) - _e current efficiency - , _o bed porosity and porosity of the fixed bed, respectively - =V/Q residence time (s) - see Fig. 2     

High performance copper oxide cathodes for high temperature solid-oxide fuel cells

The cathodic polarization characteristics of CuO and YBa₂Cu₃O_7- electrodes were studied in the temperature range 600 to 800°C and at oxygen partial pressures ranging from 10^–4 to 0.21 atm. The activity of oxygen reduction on a CuO electrode is closely related to the electronic conductivity and the oxygen ion vacancy density in the surface layer of the electrode. The oxygen ion vacancies created in CuO by doping with Li and the modification of the electronic conductivity by adding Ag provide a new way of enhancing the activity of an oxide electrode for oxygen reduction. It is demonstrated that the rate limiting steps for oxygen reduction at high overpotential and low overpotential are oxygen adsorption and charge transfer on CuO, respectively.List of symbols F Faraday constant - f F/RT - i current - i₀ exchange current - k ⁰ intrinsic rate constant of charge transfer - N() electron density with an energy level E - n number of electrons - R gas constant T temperature Greek letters transfer coefficient - conductivity - overpotential - energy level     

Liquid-phase mass transfer enhancement by gas evolution at inclined plates

The limiting current technique has been employed to determine mass transfer coefficients at vertical and inclined plates with stirring by coplanar electrochemical oxygen evolution. Orientation of the plate has been varied from –45 (down-facing inclined position) to +45 (up-facing inclined position) at ten intervals. At a constant oxygen evolution rate, maximum mass transfer enhancement was achieved at down-facing inclined orientations where (the angle from vertical) is small. The inclination angle at which mass transfer attained its highest value depended on the oxygen evolution rate and is given by _max =a + 10.96 logI _g whereI _g (mA) is the electrochemical current for the oxygen evolution.For the range of the inclination angle, 0 _max, the relationship between the mass transfer coefficient and can be represented byK =K _o +aK _o(sin )^0.3 whereK _o is the mass transfer coefficient at the vertical plate.