Effect of state of charge on impedance spectrum of sealed cells Part II: Lead acid batteries

Alternating current impedance spectroscopy (ACIS) was performed on commercial sealed lead acid batteries. A method previously developed in the literature was modified to determine the state of charge of sealed lead acid cells by obtaining the impedance spectrum in a wide frequency range. The data were sensitive to state of charge at low frequencies. A modified Randles' circuit was used to fit the impedance data. The effect of the state of charge on the equivalent circuit parameters was determined.List of symbols R ohmic resistance of battery () - C _dl double layer capacitance (F) - Q ₁ constant phase element representing double layer capacitance - Q ₂ constant phase element representing Warburg diffusion - O finite diffusion element - R _t charge transfer resistance () - R _s,R _p equivalent series and parallel resistance () - C _s,C _p equivalent series and parallel capacitance (F)     

Impedance parameters and the state-of-charge. II. Lead-acid battery

The determination of the state-of-charge of the lead-acid battery has been examined from the viewpoint of internal impedance. It is shown that the impedance is controlled by charge transfer and to a smaller extent by diffusion processes in the frequency range 15–100 Hz. The equivalent series/parallel capacitance as well as the a.c. phase-shift show a parabolic dependence upon the state-of-charge, with a maximum or minimum at 50% charge. These results are explained on the basis of a uniform transmission-line analog equivalent circuit for the battery electrodes.Nomenclature Battery This word is used synonymous with the word cell - R _p equivalent parallel resistance () - R _s equivalent series resistance () - ¦Z¦ modulus of impedance () - C _p equivalent parallel capacitance (F) - C _s equivalent series capacitance (F) - a.c. phase-shift (radians or degrees) - 2f - f a.c. frequency (Hz) - R resistance of electrolyte solution and separator () - ¯C double layer capacity (F) - W diffusional (Warburg) impedance () - R _t resistance due to polarization () - energy transfer coefficient - T absolute temperature (K) - R gas constant - F Faraday constant - C _O ⁰ bulk concentration of the oxidant - C _R ⁰ bulk concentration of the reductant - D _O diffusion coefficient of the oxidant - D _R diffusion coefficient of the reductant - Warburg coefficient - N number of pores/area - A active area of the electrode (cm²) - S state-of-charge - a anode - c cathode - L inductance - I _o exchange current     

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     

Fundamentals of lead-acid cells. XVII. The a.c. impedance of lead dioxide formed in sulphuric acid on some lead alloys

The impedances of PbO₂ formed on lead and some lead alloys have been measured over a wide range of potential. Conditions were chosen so that well-defined electrode states were obtained. Considerable differences were observed in the behaviour of alloys containing antimony and bismuth. The latter alloying ingredient appears to contribute some semiconducting properties to lead sulphate films formed on PbO₂ by polarizing them at potentials negative to the reversible potential in sulphuric acid.Nomenclature C _L double-layer capacitance - C _X series capacitance - D diffusion coefficient - E potential - R _CT charge-transfer resistance - R electrolyte resistance - Z _D impedance as defined by Equation 1 - Z _F impedance as defined by Equation 2 - Z impedance as defined by Equation 3 - Warburg coefficient - angular frequency     

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     

The impedance of the alkaline zinc-mercuric oxide cell. I. Cell behaviour and interpretation of impedance spectra

The impedances of small (2400 mA h) alkaline Zn-HgO cells have been measured in the range 10 kHz-0.001 Hz at various states of charge from fully charged to fully discharged. The behaviour of the cell conforms to that expected for rate control by charge transfer at the zinc electrode and diffusion in solution. At low frequencies there is a relaxation in the diffusive circuit elements which ultimately results in a complete suppression of the capacitative component of the impedance at zero frequency. The low-frequency behaviour is analogous to convective diffusion and is due to the effective distance between the electrodes being small compared with the characteristic length (D/)^1/2. The magnitude of the charge transfer resistance is the best measure of the state of charge.Nomenclature a effective electrode separation - C _DL double-layer capacitance of cell - C _R capacitative component of cell impedance - C concentration difference - D percentage discharge in Equation 12 - D _i diffusion coefficient of speciesi - R ohmic resistance of cell - R _R resistive component of cell Faradaic impedance - Ui constant defined by Equation 10 - Z total cell impedance - Z _F cell Faradaic impedance - Z _F cell impedance modified for porosity effect - Z _x cell impedance of Faradaic component plus double layer - cell Warburg coefficient (slope ofR _R and 1/C _Rversus su}-1/2) - _C Warburg coefficient calculated fromC _r values - _i cell Warburg coefficient for speciesi - Warburg coefficient calculated fromR _R values - dihedral angle of tail of Sluyters plot (after coming-off high-frequency semicircle) - angular frequency     

Kinetics and mechanism of the Al(iii)/Al electrode reaction in cryolite-alumina melts

Using the relaxation method (RM) with galvanostatic perturbation and electrochemical impedance spectroscopy (EIS), exchange current densities and activation parameters were determined for the electrode reaction on the aluminium electrode in pure cryolite melt and in cryolite-alumina melts with the addition of 2–12 wt % Al₂O₃. In all these melts a three step electrode process was observed, comprising a preceding chemical reaction followed by two charge transfer steps. The exchange current densities for two charge transfer steps were determined as a function of temperature, together with the equilibrium constant of the preceding chemical reaction and its kinetic and diffusion impedance. The third step was found to be independent of diffusion and of the concentration of alumina, whereas the second step showed mixed characteristics. The exchange current densities were of the order of 5–15 A cm^–2.

Abbreviations

List of symbols A electrode area (cm²) - A, B, C coefficients of Equation 12 (V) - C _dl double layer capacitance (F) - c concentration (mol cm^–3) - D _O; D _R diffusion coefficients of the oxidized and reduced ionic species (cm² S^–1) - E _A activation energy (kJ mol^–1) - F Faraday constant (C mol^–1) - j exchange current density (A cm^–2. - K equilibrium constant (dimensionless) - k sum of the forward (k ₁) and backward (k ₂) rate constants (s^–1) - k ₀ standard rate constant (cm s^–1) - L ₁, L ₂ high frequency and low frequency inductances (H) - L _out outer inductance (H) - R _el electrolyte resistance () - n number of electrons (dimensionless) - R molar gas constant (J mol^–1 K^–1) - R _ct charge transfer resistance () - s ₁, s ₂ angular frequencies (s^–1) - T temperature (K) - t time (s) - Z complex impedance () - Z, Z real and imaginary parts of the complex impedance () - Z _w Warburg diffusion impedance ( s^–1/2) Greek symbols _c overall cathodic transfer coefficient (dimensionless) - , coefficients in Equation 12 (s^–1/2) - coefficient in Equation 12 (s^–1) - overpotential (V) - angular frequency (s^–1) - _O, _R Warburg coefficients of the oxidized and reduced ionic species ( s^–1/2)     

Dielectric properties of anodic oxide layers on tantalum

The dielectric properties of the anodically formed oxide layers on tantalum in contact with electrolyte were analysed by measuring the frequency and temperature dependence of the impedance. It has been found that the frequency dependence of the series capacitance and resistance component of the impedance in the audio frequency range are in accordance with Young's relation. In order to explain such behaviour the electrical resistivity is assumed to vary exponentially with distance through the oxide layer. This variation can be ascribed to the occurrence of the exponential change of oxygen vacancies in the anodic layer during the growth of the oxide layer. The activation energy was obtained from the temperature dependence of the series capacitance. In the paper the unsimplified Young's relations have been proved to be K-K transformable.Nomenclature C _s series capacitance (F) - R _s series resistance () - f frequency of applied signal (Hz) - x integration variable of frequency (Hz) - A area (cm²) - K characteristic length (cm^–1) - d oxide layer thickness (cm) - y distance through oxide (cm) - a _C slope of linear part of 1/C _s against logf plot (Equation 5) - a _R slope of linear part ofR _s against 1/f plot (Equation 3) - relative permittivity of oxide layer - (y) resistivity at distancey ( cm) - (0) resistivity on positiony=0 ( cm) - (d) resistivity on positiony=d ( cm) - T absolute temperature (K) - k Boltzmann constant (eV K^–1) - activation energy (eV) - z complex variable,z=x+iy, - Res residue     

A model for bipolar current leakage in cell stacks with separate electrolyte loops

A model predicting leakage current in a bipolar battery stack is presented. This model applies current balance and potential balance equations to a stack and treats the electrolyte, manifold and membrane separator as resistance elements in an electric circuit analog. This results in a set of linear difference equations with constant coefficients. Leakage currents in stacks made up of different numbers of cells are predicted and the effect of each resistance component on stack performance is investigated.Nomenclature C _j j=1 ... 5, constants in Equations 24–29, defined in the Appendix - D _j j=1 ... 5, constants in Equations 25–29, defined in the Appendix - E difference operator, Ef _n=f _n+1 - I _L load current (A) - K manifold current, anodie (A) - L manifold current, cathodic (A) - N number of cells in the bipolar stack - R _A lateral electrolyte resistance, anodic () - R _C lateral electrolyte resistance, cathodic () - R _e1 electrolyte resistance, anodic () - R _e2 electrolyte resistance, cathodic () - R _MA manifold resistance, anodic () - R _MC manifold resistance, cathodic () - R _s membrane resistance () - V ₀ cell potential (V) - i ₁ battery current, anodic (A) - i ₂ battery current, cathodic (A) - k leakage current, anodic (A) - l leakage current, cathodic (A) - r _j j=1 ... 5, roots of the characteristic equation, solved in the Appendix     

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)     

The impedance of the alkaline zinc-manganese dioxide cell. II. An interpretation of the data

The impedance of small alkaline zinc-manganese dioxide cells has been interpreted in terms of a controlling charge-transfer and diffusion process at the zinc electrode throughout the early stages of discharge. After about 20% of the available charge has been removed, it becomes necessary to include the manganese dioxide electrode circuit components. This network has the circuit elements for charge transfer and a proceeding chemical reaction. The Warburg component for the manganese dioxide electrode need not be considered since the effective area considerably exceeds that of the zinc. The relative areas are confirmed by the magnitudes of the circuit element components. The decomposition of the impedance data has been successfully accomplished as far as 80% discharge; after this point cells show considerable differences from cell to cell, especially in the low-frequency range, which makes a confident interpretation difficult. It is considered that this is due to the loss of the physical definition of the system.Nomenclature C _m,C _z double-layer capacitances of MnO₂ and Zn electrodes, respectively - C _X,R _X parallel branch accounting for current density varying with fractional electrode coverage - R resistance of electrolyte - V open-circuit voltage of cell - Z, Z, Z impedance of cell,resistive component ofZ and reactive component ofZ, respectively - _m, _z transfer resistance of MnO₂ and Zn electrodes, respectively - , _R, _C in Warburg equation:Z _W = ^–1/2(1–i) orZ _W = _R^–1/2– i_Cco^–1/2     

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     

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)     

Influence of current distribution on electrode potentials in bipolar water electrolysis cells of the ‘sandwich’ type

The potential and current density distributions in a bipolar electrolytic cell for water electrolysis were computed and the solution given as a matrix product. This makes a rapid and simple evaluation of the load-bearing capacity of such a cell possible, taking into consideration the resistance of the bipolar plate and the supply lines, the reciprocal position and gaps of the current bars and the relative resistance characteristics of the two electrodes. At the same time, the electrochemical process was included by means of Tafel parameters. The variation in these data has been given in a dimensionless form and is discussed in detail.Nomenclature a lower anodic current density (Am^–2) - a _A,a _K Tafel constants (V) - b width of the system (m) - b _A,b _K Tafel constants (V decade^–1) - C ₁,C ₂,C ₃,C ₄ D ₁,D ₂,D ₃,D ₄ integral constants - d _A thickness of the anode (m) - d _B thickness of the bipolar plate (m) - d _C thickness of the cathode (m) - d _S thickness of the conductive bars (m) - E _A,E _C local anode or cathode potential (V) - E _A ⁰ ,E _C ⁰ anodic or cathodic potential reference point (V) - e _AC,E _KC local electrochemical potentials (V) - E _AC ⁰ ,E _KC ⁰ standard potentials (V) - h electrode gap (m) - i electrochemical current density (A m^–2) - I, I _tot total current (A) - I _A,I _C local current flow through the anode or cathode (A) - I ₁,I ₂ subcurrents (A) - K constant (m^–2) - K ₁ constant (V) - K ₂ constant (m²) - K ₁₀ dimensionless potential constant - L distance between conductive bars (m) - R _s R ₁,R ₂ supply line resistance () - s distance between bipolar plate and electrode (m) - u _A,U _C dimensionless local anode or cathode potential - U _s potential difference - x coordinate length (m) - x _i a fixed value ofx - y dimensionless standardized length coordinate - y _i a fixed value ofy - z upper current density (Am^–2) - , , _A, _C, dimensionless parameter, cf. Equations 17a, b, 18a-g - _A specific electrical resistance of anode (m) - _B specific electrical resistance of bipolar plate (m) - _C specific electrical resistance of cathode (m) - _E specific electrical resistance of electrolyte with diaphragm (m) - _S specific electrical resistance of conductive bars (m)     

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     

On the nature of the ‘induction period’ during the electrowinning of zinc from nickel containing sulphate electrolytes

As a result of detailed voltammetric, impedance, electron microscopic and opticalin situ investigations of the peculiarities encountered in zinc electrowinning from nickel-containing acid electrolytes, a model for the induction period is proposed and its dependence on the process conditions is elucidated. The model is based on the screening effect of hydrogen bubbles formed on the nickel-rich regions of the cathode which give rise to local galvanic cells.Nomenclature C electrode capacitance - C _dl double layer capacitance - C _Ni volume concentration of Ni²⁺ ions - d diameter of the circle along which the hydrogen bubble is attached to the surface - D _Ni diffusion coefficient of Ni²⁺ ion - E _ze potential of zero charge - f ^* frequency at the apex of the capacitance loop - F Faraday constant - F _c capillary force - F _h hydrostatic force - g acceleration due to gravity - q specific mass of the liquid - h height of the hydrogen bubble - R electrolyte resistance - R _t charge transfer resistance - V volume of the gas phase - thickness of the diffusion layer - wetting angle at the metal-solution-gas interface - ₁₂, ₂₃, ₁₃ surface tensions between: solid-liquid, liquid-gas and solid-gas phases, respectively - kinematic viscosity - rotation speed of the cathode The first results were presented at the International Conference on Base Metals Technology, 8–10 February, 1989, Jamshedpur, India.     

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)     

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

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

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.     

Durability and thermal cycling of Ni/YSZ cermet anodes for solid oxide fuel cells

The long-term properties of Ni/yttria stabilized zirconia (YSZ) cermet anodes for solid oxide fuel cells were evaluated experimentally. A total of 13 anodes of three types based on two commercial NiO powders were examined. The durability was evaluated at temperatures of 850 C, 1000 C and 1050 C over 1300 to 2000h at an anodic d.c. load of 300mA cm^–2 in hydrogen with 1 to 3% water. The anode-related polarization resistance, R _P, was measured by impedance spectroscopy and found to be in the range of 0.05 to 0.7 cm². After an initial stabilization period of up to 300h, R _P varied linearly with time within the experimental uncertainty. At 1050 C no degradation was observed. At 1000 C a degradation rate of 10 m cm² per 1000 h was found. The degradation rate was possibly higher at 850 C. A single anode was exposed to nine thermal cycles from 1000 to below 100 C at 100 C h^–1. An increase in R _P of about 30m cm² was observed over the first two cycles. For the following thermal cycles R _P was stable within the experimental uncertainty.