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     

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     

The estimation of the residual capacity of sealed lead-acid cells using the impedance technique

The problem of estimating the residual usable energy of a lead-acid cell has been intensified by the introduction of fully sealed units. These rely on the recombination of gaseous oxygen produced during overcharge at the positive electrode with the active material at the negative electrode. This introduction has removed the possibility of electrolyte density measurements, third electrode measurements and restricted residual capacity assessments to the two cell terminals. A method for this process is described using a parameter based on a characteristic frequency. The parameter is also a useful measure of cell ageing.Nomenclature R _SOL Ohmic resistance of cell () - Charge-transfer resistance of positive and negative electrodes () - CL Double-layer capacitance of both positive and negative electrodes (F) - Warburg diffusion (S^–1/2) - C _EXT External series capacitor in analogue Fig. 5 (F) - R _EXT External resistor in parallel withC _EXT in the anologue circuit Fig. 5 () - IND Inductor in Fig. 5 representing the geometrical effects of the cell at high frequencies (Henries) - R _IND External resistor in parallel with IND in the analogue circuit Fig. 5 () - Roughness factor allowing for the porosity of both electrodes     

The impedance of the Ledanché cell. I. The treatment of experimental data and the behaviour of a typical undischarged cell

The impedance spectrum of an undischarged commercial Leclanché cell (Ever Ready type SP11) is presented in the forms of the Sluyters plot and the modified Randies plot. The decomposition of the experimental cell impedances into the component parts has been achieved using a computer. The decomposition process and the component processes representing the overall cell behaviour are described.List of symbols R _s in-phase component of (experimental) electrode impedance - R _t charge transfer resistance referred to nominal area of Zn ( cm²) - 1/(C _s) out-of-phase component of (experimental) electrode impedance - angular frequency (= 2f) - R resistance of electrolyte solution - charge transfer resistance - C _L double layer capacitance - C _DL double layer capacitance of electrode referred to nominal area of Zn (F cm^–2) - j –1 - Warburg coefficient - D factor in Equations 1 and 2 - C _s R _s calculated values ofC _s andR _s (first approximation) - C _s R _s calculated values ofC _s andR _s (refined values taking into account the additional network) - C _s R _s calculated values of C_s andR _s (refined values taking into account porosity) - _x resistive part of additional series component (parallel connection) - C _x capacitance part of additional series component (parallel connection) - D factor in Equations 6 and 7     

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)     

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

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

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)     

Cooperative inclusion of sodium 1-pyrenesulfonate by γ-cyclodextrin

Summary The interaction of -cyclodextrin(-CD) with sodium 1-pyrenesulfonate(PS) was studied spectrophotometrically. -CD was found to cause much larger decrease in the absorption maxima of PS than -CD. The fluorescence spectra of PS in the presence of -CD showed excimer emission, while those of PS with -CD showed only monomer emission, indicating that -CD forms 12 (-CDPS) complexes in which two PS molecules are included in the -CD cavity in a face-to-face fashion. The binding isotherm showed a sigmoidal curve. The association constants were estimated by computer simulation of the binding curve. The 12 (CDPS) complex was found to be much more stable (K=10⁶ M^–1) than the 11 complex (K=1 M^–1). At high concentration of -CD another -CD cooperates in binding two PS molecules, resulting in the formation of a 22 complex.     

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)     

Effect of the type of mullite and certain additives on the sintering process of mullite-zircon specimens

Conclusions The effect of the type of mullite on the sintering process of mullite-zircon specimens was studied. It was shown that using electromelted mullite as chamotte ensures optimum properties. Sintered mullite increases the porosity of the products.The optimum content of the argillaceous binder for obtaining dense and strong specimens was found to be 10%.It was shown that highly refractory oxides intensify (activate) the sintering process of the mullite-zircon products obtained using electromelted mullite and strengthen them to the maximum extent. In this case, their thermal shock resistance remains quite high.The salts of REE have a positive effect on the sintering process of the mullite-zircon specimens at 1650°C and improve their strength; however, in this case, their thermal shock resistance decreases abruptly. The oxides of REE lead to less intense sintering of the mullite-zircon specimens but these additives increase their strength significantly and impart the required thermal shock resistance.The sintering process of the mullite-zircon specimens occurs in the presence of a liquid phase and is accomplished in three stages whose kinetics can be described by the relationships (proportionalities)l/l^1,3, l/l^1/2, and l/l^1/3, respectively.Translated from Ogneupory, No. 8, pp. 12–17, August, 1988.     

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)     

Mass and momentum transfer enhancement due to electrogenerated gas bubbles

The effect of electrogenerated gas bubbles with simultaneous bulk liquid flow on the mass and momentum transfer at a wall of an electrolytic cell is experimentally determined. The local mass transfer coefficient and electrolyte shear stress are obtained using two types of microelectrodes imbedded in the channel wall. The influence of the most important parameters (electrolyte velocity, position along the wall, gas electrogeneration rate) on the transfer enhancement is studied and an analogy between mass and momentum transfer in the presence of bubbles is clearly demonstrated from the experimental results. The comparison with classical correlations, valid for systems involving natural turbulence, shows the higher energetic efficiency of devices where the turbulence is artificially generated by electrolytic gas bubbles.Nomenclature A constant parameter in Equation 3 - ¯C time averaged value of the concentration of a reacting species - c ₀ molar concentration in the bulk of the solution - d microelectrode diameter - d _e hydraulic equivalent diameter - D molecular diffusion coefficient - D _t turbulent diffusivity of mass transfer - f/2 friction factor, =/gr¯v ² - h channel thickness - I _g electrogeneration rate - i _g electrogeneration current density - i _l limiting current density on a microelectrode imbedded in the conducting wall - i_l limiting current density on a microelectrode imbedded in the inert wall - k _d local mass transfer coefficient - k local mass transfer coefficient on a microelectrode in the non-conducting wall - N _M specific mass flux near an interface - Re Reynolds number, = (¯vd _e)/v - s velocity gradient, = (¯v _x/y)y = o - s ⁺ dimensionless velocity gradient, =sd ²/D - Sc Schmidt number, =v/D - Sh Sherwood number, = (k _d x)/D - St Stanton number, =k _d/¯v - ¯v, ¯v _x electrolyte velocity - v ^* friction velocity, = (/)^1/2 - v ⁺ normalized velocity, =¯v _x /v ^* - x axial coordinate - y coordinate perpendicular to the wall - y ⁺ dimensionless length = (yv ^*)/v Greek letters parameter defined in Equation 8 - boundary layer thickness - ⁺ dimensionless form of , = (s/v)^1/2 - , _x electrolyte shear stress - dynamic viscosity - kinematic viscosity - _t momentum transfer diffusivity - specific gravity - ² variance of the fluctuations ofi _L ori _L Paper presented at the International Meeting on Electrolytic Bubbles organized by the Electrochemical Technology Group of the Society of Chemical Industry, and held at Imperial College, London, 13–14 September 1984.     

Effects of gas bubbles on the current and potential profiles within porous flow-through electrodes

This paper presents a mathematical model to calculate the distributions of currenti(x), potentialE(x), gas void fraction (x) and pore electrolyte resistivity (x) within porous flow-through electrodes producing hydrogen. It takes into consideration the following effects: (i) the kinetics of the interfacial charge transfer step, (ii) the effect of the non-uniformly generated gas bubbles on the resistivity of the gas-electrolyte dispersion within the pores of the electrode (x) and (iii) the convective transport of the electrolyte through the pores. These effects appear in the form of three dimensional groups i.e.K=i _o L where i_o is the exchange current density, is the specific surface area of the electrode andL its thickness.= ⁰ L where ⁰ is the pore electrolyte resistivity and =/Q where is a constant, =tortuosity/porosity of the porous electrode andQ is the superficial electrolyte volume flow rate within it. Two more dimensionless groups appear: i.e. the parameter of the ohmic effect =K/b and the kinetic-transport parameterI=K. The model equations were solved fori(x),E(x), (x) and (x) for various values of the above groups.Nomenclature specific surface area of the bed, area per unit volume (cm^–1) - b RT/F in volts, whereR is the gas constant,T is the absolute temperature (K) - B =[1–(I ² Z/4)], Equation 9a - C =(1–B ²), Equation 9b - E(L) potential at the exit face (V) - E(0) potential at the entry face (V) - E(x) potential at distancex within the electrode (V) - E _rev reversible potential of the electrochemical reaction (V) - F Faraday's constant, 96500 C eq^–1 - i _o exchange current density of the electrode reaction (A cm^–2 of true surface area) - i(L) current density at the exit face (A cm^–2 of geometrical cross-sectional area of the packed bed) - I K =i _oL(/Q) (dimensionless group), Equation 7d - K =i _oL, effective exchange current density of the packed bed (A cm^–2) Equation 7a - L bed thickness (cm) - q tortuosity factor (dimensionless) - Q superficial electrolyte volume flow rate (cm³ s^–1) - x =position in the electrode (cm) - Z =exp [(0)], Equation 7f - transfer coefficient, =0.5 - =K/b=(i ₀ L ⁰ L)/b (dimensionless group) Equation 7e - (x) gas void fraction atx (dimensionless) - = ⁰ L, effective resistivity of the bubble-free pore electrolyte for the entire thickness of the electrode ( cm²) - (0) polarization at the entry face (V) - (L) polarization at the exit face (V) - =q/, labyrinth factor - constant (cm³ C^–1), Equation 3a - =/Q (A ^–1) conversion factor, Equation 3b - porosity of the bed - (x) effective resistivity of the gas-electrolyte dispersion within the pores ( cm) - ⁰ effective resistivity of the bubble-free pore electrolyte ( cm)     

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     

On the characterization of oxygen recombination in sealed lead-acid batteries

For characterizing the oxygen cycle in sealed lead-acid batteries the technological terms oxygen recombination efficiency and oxygen recombination conditions are introduced and their different meanings explained. Numerical values are calculated or estimated from plots of overpressure against time. Emphasis is placed on investigations of the influence of technological parameters on oxygen recombination conditions.Nomenclature F Faraday constant - D diffusion coefficient - L solubility coefficient - A effective surface area on the negative electrode covered with an electrolyte film - diffusion layer thickness - p _{O 2} oxygen partial pressure - p _{H 2} hydrogen partial pressure - I _OC overcharging current (defined negative) - I _{O 2red} oxygen reduction current - I _{H 2ev} hydrogen evolution current - I _{PhSO 4red} cathodic formation (recharge) current - P _{O 2}(St) steady-state P_{O 2} - p _{O 2} quasi steady-state p_{O 2} - R gas constant - T temperature - V gas space volume - (I_OC–I_{O 2red}–I_{H 2ev}) - viscosity - d electrode distance - l crack length - p electrolyte density     

On the mechanism of electroless plating. I. Oxidation of formaldehyde at different electrode surfaces

To elucidate the mechanism of electroless plating solutions with formaldehyde as the reductant, the anodic oxidation of formaldehyde in alkaline medium was studied. The influence of electrode material, pH and potential was investigated. The experimental results can be explained by a mechanism in which methylene glycol anion (CH₂OHO^–) is dehydrogenated at the electrode surface, yielding adsorbed hydrogen atoms. The atomic hydrogen can either be oxidized to water or be desorbed as a gas. Kinetic rate laws for these two reactions are given. Electroless copper, platinum and palladium solutions behave according to the mechanism.Nomenclature E applied potential - E _a activation energy of adsorption - E _d activation energy of desorption (=–H+E _a) - E _eq equilibrium potential of the reversible hydrogen reaction at a given pH - F Faraday's constant - –H heat of adsorption - i ⁰ apparent exchange current density for the reversible hydrogen reaction - i ₀ exchange current density for the reversible hydrogen reaction - k rate constant for the desorption of hydrogen - L _s heat of atomization - R gas constant - T absolute temperature - ₇ rate of oxidation of hydrogen atoms - ₈ rate of desorption of hydrogen - transfer coefficient (0.5) - overpotential (=E–E _eq) - fraction of the surface covered by hydrogen atoms - _M work function of metal M - potential of the outer Helmholtz layer relative to the bulk of the electrolyte     

Simultaneous underpotential deposition of lead and thallium on polycrystalline silver-III

Simultaneous underpotential deposition of lead and thallium from a tartrate medium on a polycrystalline silver electrode is reported. Results of cyclic voltammetric investigations of the effects of concentration and sweep rate on the codeposition behaviour are discussed. Further investigations of the codeposition behaviour through voltammetric experiments using programmed potential inputs are described and discussed in terms of formation of a two-dimensional alloy. Finally, the validity of the existing models of electrochemical phase formation has been investigated under the codeposition conditions.Nomenclature I _pn nondimensional peak current - E _pn nondimensional peak potential - E _/12n nondimensional half-peak width - Q _M charge due to UPD coverage of metal M (Ccm^–2) - t _d holding time (s) - sweep rate (V s^–1) - E potential (V) - instantaneous nucleation growth rate constant     

Mathematical modelling of electrode growth

It is known that during electrodeposition or dissolution electrode shape change depends on the local current density (Faraday's law in differential form). Assuming that concentration gradients in the bulk of the solution may be neglected, the current distribution in an electrochemical system can be modelled by a Laplace equation (describing charge transport) with nonlinear boundary conditions caused by activation and concentration overpotentials on the electrodes. To solve this numerical problem, an Euler scheme is used for the integration of Faraday's law with respect to time and the field equation is discretized using the boundary element method (BEM). In this way, and by means of a specially developed electrode growth algorithm, it is possible to simulate electrodeposition or electrode dissolution. In particular, attention is paid to electrode variation in the vicinity of singularities. It is pointed out that the angle of incidence between an electrode and an adjacent insulator becomes right (/2). This is confirmed by several experiments.List of symbols x _i coordinates of a point i belonging to a boundary (m) - t time (s) - h thickness variation at a point belonging to an electrode (m) - M molecular weight (kgmol^–1) - m specific weight (kgm^–3) - z charge of an ion (C) - F Faraday's constant (C mol^–1) - R _a2 impedance of the linearized activation overvoltage on cathode (S2 cm^–2) - efficiency of the reaction - electric conductivity (^–1 m^–1) - U electric potential (V) - rate of mechanical displacement of a point (m s^–1) - V applied potential on an electrode (V) - W Wagner number defined as the ratio of the mean impedance of the reaction and the mean ohmic resistance of the cell given by L/ with L a characteristic length of the cell. - overvoltage (V) - ₁ overvoltage on anode (V) - ₂ overvoltage on cathode (V)     

Hydrodynamic effects on the efficiency of porous flow-through electrodes

Hydrodynamic conditions in porous flow-through electrodes are discussed with special emphasis on radial diffusion effects on the efficiency of reactant conversion. The effect of porosity and tortuosity on the conversion efficiency are also considered. It is shown experimentally that radial diffusion limits the electrode efficiency for(L)=vr ²/2DL>0.5 and normal porosity and tortuosity values; q1. For(L)<0.5, the electrode works with 100% efficiency.A porous flow-through electrode is divided, in the most general case, into three regions: (a) velocity entrance length h0.2vr²/v in which a steady velocity profile is developing; (b) diffusional entrance lengthHvr ²/2D for which(x)=vr ²/2Dx1; in this region a radial diffusional concentration profile is developing andh is usually much smaller thanH; (c) the region where the velocity and concentration profiles are fully developed. Only in region (c) does the electrode operate with 100% efficiency. In regions (a) and (b) radial diffusion limits the electrode efficiency.     

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.