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 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-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     

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     

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 application of the measurement of impedance to the corrosion of dental amalgams

A preliminary experimental investigation of the electrochemical characteristics of a high and a low copper dental amalgam in contact with saline solution has been carried out. The impedance and the corrosion current (in the absence of dissolved oxygen) have been measured at each potential in the near steady state for fresh amalgam surfaces. Analysis of the electrochemical data produces charge transfer resistance, double layer capacity, ohmic resistance and Warburg coefficient curves, which are briefly discussed. The aim of the work is, ultimately, to determine thein vivo corrosion rates and heavy metal ion release from amalgams.Nomenclature a anodic Tafel slope - C _dl differential capacity - D _A diffusion coefficient of A - E potential with respect to SCE electrode - E ₀ standard potential with respect to SCE - i current density - j square root of-1 - R ohmic loss resistance - R _cl charge transfer resistance - Z() impedance - frequency of a.c. potential - diffusion layer thickness - Warburg impedance parameter     

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     

Studies concerning charged nickel hydroxide electrodes I. Measurement of reversible potentials

Reversible potentials (E _R) have been measured for nickel hydroxide/oxyhydroxide couples over a range of KOH concentrations from 0·01–10 M. It is shown that the couples derived from the parent- and-Ni(OH)₂ systems can be distinguished by the relative change in KOH level on oxidation and reduction. In the case of couples derived from the-class of materials a dependence of 0·470 moles of KOH per 2e change is found compared with 0·102 moles of KOH per 2e change for the-class of materials. Couples derived from the- and-Ni(OH)₂ systems can be encountered in a series of activated and de-activated forms having a range of formal potentialsE ₀ . Activated. and de-activated-Ni(OH)₂/-NiOOH couples are found to lie in the range 0·443–0·470 V whilst-Ni(OH)₂/-NiOOH couples lie in the range 0·392–0·440 V w.r.t. Hg/HgO/KOH. It is demonstrated for de-activated,-Ni(OH)₂/-NiOOH couples thatE _R is independent of the degree of oxidation of the nickel cation between states of charge of 25% and 70%. SimilarlyE _R is constant for states of charge between 12% and 60% for activated-Ni(OH)₂/-NiOOH couples. The constant potential regions are considered to be derived from heterogeneous equilibria between pairs of co-existing phases both containing nickel in upper and lower states of oxidation. Differences inE ₀ between the activated and de-activated couples are considered to be related to the degree of order/disorder in the crystal lattice.     

A model of the electrochemical behaviour within a stress corrosion crack

A mathematical model of the electrochemical behaviour within a stress corrosion crack is proposed. Polarization field, crack geometry, surface condition inside the crack, electrochemical kinetics, solution properties and applied stress can be represented by the polarization potential and current, the electrochemical reactive equivalent resistance of the electrode, the change in electrolyte specific resistance and surface film equivalent resistance, respectively. The theoretical calculated results show that (i) when anodic polarization potential is applied, the change in the crack tip potential is small; (ii) when cathodic polarization potential is applied, the crack tip potential changes greatly with the applied potential; (iii) the longer the crack, the smaller the effect of the applied potential on the crack tip potential in both anodic polarization and cathodic polarization conditions. The calculated results are in good agreement with previous experimental results.Notation coordinate, from crack mouth (on the metal surface) to crack tip (cm) - y y = s _L L/(s ₀ – s _L) + L – , function of (cm) - y ₀ y ₀ = s _L L/(s ₀ – s _L) + L (cm) - V polarization potential (V) - galvanic potential of electrode (V) - ₁ galvanic potential of electrolyte (V) - t sample thickness (cm) - w sample width (cm) - S _L crack tip width (cm) - S _o crack mouth width (cm) - L crack length (cm) - s() crack width at position (cm) - _lo specific resistance of electrolyte, as a constant ( cm) - _s specific resistance of metal ( cm) - (, y) specific resistance of electrolyte, varies with potential and crack depth ( cm) - R _b (, y) electrochemical reactive equivalent resistance of electrode, varies with potential and crack depth () - R ₁ electrolyte resistance () - R _s metal resistance () - r(, y) surface film equivalent resistance, varies with potential and crack depth () - r _o surface film equivalent resistance, as a constant () - I _o total polarization current (A) - I net polarization current from integrating 0 to in Fig. 2 (A) - polarization overpotential (V) - _a anodic polarization overpotential (V) - _c cathodic polarization overpotential (V) - Euler's constant     

Electrochemical behaviour of viologen-cyclodextrin inclusion complexes. The case of non-alkyl group substituted viologen

The electrochemical behavior of non-alkyl substituted viologen, 4,4-dibenzyl bipyridinium (BzV), 4,4-dicyanophenyl bipyridinium (CyV) and -,-,-cyclodextrin (, , -CD) was studied using cyclic voltammetry and a spectroelectrochemical method. It was found that BzV and Fe(CN) ₆ ^4– formed a charge-transfer (CT) complex with a ratio of 21 and the colour of the solution faded with the addition of an electrolyte. This behaviour is the same as in then-heptyl viologen and ferrocyanide system [1]. BzV, -CD and -CD formed an inclusion complex only in the reduced state, whilst BzV and -CD formed an inclusion complex in both the oxidized and the reduced state. An EC scheme in which a chemical reaction follows an electrochemical reaction was considered to predominate in the BzV and -, -CD systems, while a CE scheme in which a chemical reaction preceded an electrochemical reaction predominated in the BzV and -CD system. On the other hand, CyV was found to form an inclusion complex with -, -, -CD in both the oxidized and the reduced states. therefore a CE scheme was considered to predominate in the CyV--, -, -CD systems.     

Laminar radial flow electrochemical reactors. I. Flow fields

The velocity fields of three laminar radial flow electrochemical reactors are modeled using numerical and semi-analytical techniques. The capillary gap cell configuration is modeled using Galerkin finite element (GFEM) analysis and the asymptotic form of its velocities presented. An approximate asymptotic expression for entry length is also derived and compared to predicted entry lengths from the GFEM. Qualitative agreement is achieved. Two areas of flow separation are observed, their location being a function of gap width, flow Reynolds number (Re) and inlet pipe diameter. The rotating electrolyzer (REL) flow field is also simulated with the GFEM model. The insensitivity of the REL radial velocity profiles as a function of flow rate is shown. The shape of the radial velocity profiles and the degree of separation of the radial velocity jets are shown to be determined by the Taylor number (being the ratio of half-gap width over the theoretical boundary layer thickness). The asymptotic entry length solution is shown to provide a better estimate for this cell than for the capillary gap cell. Unlike the previous cells the pump cell shows less asymptotic behavior and is therefore more difficult to simulate. The GFEM approach is usually too costly for this cell and therefore perturbation techniques are applied. The resulting semi-analytical solution adequately represents laminar pump cell velocity profiles over a broad range of parameter values and is very short and easy to implement. One high Taylor number simulation is performed using the GFEM and the previously reported decoupling of electrodic mass transfer is interpreted via velocity profiles.Nomenclature a gap width - Q volumetric flow rate (m³ s^–1) - r dimensionless radius - R radius (m) - Re Reynolds number (v _c a/v) - Re _gap gap Reynolds number (a ²/v) - Re rotational Reynolds number (R ₀ ² /v) - Sc Schmidt number (v/D) - spin dimensionless group (Equation 8) - t time (s) - v _c characteristic velocity (m s^–1) two defined: for FEM analysis it wasQ/b ² for Perturbation analysis 6Q/(2R _in a) - v _r dimensionless radial velocity - v _z dimensionless axial velocity - v dimensionless azimuthal velocity - V velocity (m s^–1) - z dimensionless axial distance Greek symbols Taylor number (Equation 7) - ratio of characteristic lengths (a/R _o ) - viscosity (kg m^–1 s) - constant - density (kg m^–3) - azimuthal direction - kinematic viscosity (m² s^–1) - angular velocity (rad s^–1)     

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

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

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.     

Comparison between the impedance spectra of Li/SOCl2 batteries obtained using the time and the frequency domain measurement techniques

A comparison between the impedance spectra of Li/SOCl₂ batteries obtained in the time and frequency domains is reported. It is demonstrated that by averaging over several responses the accuracy in the time domain is greatly improved. On the other hand, it was found that the time domain technique caused nonlinearity in the system response even at very small amplitudes of excitation (for example corresponding to a potential drop of 30 mV). The method is useful for routine characterization of the quality of galvanic cells in industrial production. The accuracy compared with market-available impedance spectrometers operating in the frequency domain is satisfactory (±10%), the price being much lower.Nomenclature g _i parameters of model frequency response - g _id parametersg _i obtained by deconvolution - g _ir parametersg _i obtained by frequency domain method - H frequency response - H _m model frequency response - H _r reference frequency response - i(t) excitation current - I() Fourier transform of thei(t) - Im imaginary part - j imaginary unit - M Number of independent measurements - N number of samples - Re real part - R resistance - R ₀ ohmic resistance - T sampling time - u(t) response voltage - U() Fourier transform ofu(t) - dispersion factor - angular frequency - () phase spectrum - _a relative amplitude error - _gi relative error ofg _i - average relative amplitude error - _p relative phase error - average relative phase error - ₀ mean relaxation time     

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)     

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     

Electrolysis by intermittent potential

The application of an intermittent potential yields the maximum rate of electrolysis under non-d.c., mass transfer controlled conditions. A numerical solution was obtained to calculate the average current density under the intermittent potential condition. It is shown that the maximum rate of electrolysis for the intermittent potential case and consequently for all non-d.c. cases cannot exceed that under d.c. conditions.List of symbols c concentration of the reacting ion - c concentration of the reacting ion in the bulk - C dimensionless concentration defined in Equation 6 - D diffusion coefficient - (i _d.c.)₁ the d.c. limiting current density - ( _t)₁ average limiting current density under intermittent potential conditions - t time - z axial co-ordinate Greek _{n 1},_{n 3} coefficients of the series in Equations 1 - _{n 2} 12,13 and 16 - Nernst diffusion layer thickness - dimensionless axial co-ordinate defined in Equation 6 - ₁, _c constants defined in Equation 14 - _{n 2} constant defined in Equation 15 - dimensionless time defined in Equation 6 - ₁, _c dimensionless on-period and cycle period, respectively Deceased     

Mass transport in a weakly stratified electrochemical cell

A study of natural convection in an electrochemical system with a Rayleigh number of the order 10¹⁰ is presented. Theoretical and experimental results for the unsteady behaviour of the concentration and velocity fields during electrolysis of an aqueous solution of a metal salt are given. The cell geometry is a vertical slot and the reaction kinetics is governed by a Butler-Volmer law. To reduce the effects of stratification, the flush mounted electrodes are located (symmetrically) in the middle parts of the vertical walls. It is demonstrated, both theoretically and experimentally, that a weak stratification develops after a short time, regardless of cell geometry, even in the central part of the cell. This stratification has a strong effect on the velocity field, which rapidly attains boundary layer character. Measured profiles of concentration and vertical velocity at and above the cathode are in good agreement with numerical predictions. For a constant cell voltage, numerical computations show that between the initial transient and the time when stronger stratification reaches the electrode area, the distribution of electric current is approximately steady.List of symbols a _i left hand side of equation system - b _i right hand side of equation system - c concentration (mol m^–3) - c dimensionless concentration - c _i concentration of species i' (mol m^–3) - c₀ initial cell concentration (300 mol m^–3) - c ₀ dimensionless initial cell concentration - c_wall concentration at electrode surface (mol m^–3) - dx increment solution vector in Newton's method - D _i diffusion coefficient of species i (m² s^–1) - D ₁ 0.38 × 10^–9 m² s^–1 - D ₂ 0.82 × 10^–9 m² s^–1 - D effective diffusion coefficient of the electrolyte (0.52 × 10^–9 m² s^–1) - _x unit vector in the vertical direction - _y unit vector in the horizontal direction - F Faraday's constant (96 487 A s mol^–1) - g acceleration of gravity (9.81 m s^–2) - i dummy referring to positive (i = 1) or negative (i = 2) ion - f current density (A m^–2) - f dimensionless current density - i₀ exchange current density (0.01 A m^–2) - J _ij Jacobian of system matrix - L length of electrode (0.03 m) - N _i transport flux density of ion i (mol m^–2 s^–1) - n unit normal vector - p pressure (Nm^–2) - p dimensionless pressure - R gas constant molar (8.31 J K^–1 mol^–1) - R _i residual of equation system - Ra Rayleigh number gL ³ c ₀/D (2.54 × 101¹⁰) - S _c Schmidt number /D (1730) - t time (s) - t dimensionless time - T temperature (293 K) - velocity vector (m s^–1) - dimensionless velocity vector - U characteristic velocity in the vertical direction - V _± potential of anode and cathode, respectively - x spatial coordinate in vertical direction (m) - x dimensionless spatial coordinate in vertical direction - x solution vector for c, and - y spatial coordinate in horizontal direction (m) - y dimensionless spatial coordinate in horizontal direction - z _i charge number of ion i Greek symbols symmetry factor of the electrode kinetics, 0.5 - volume expansion coefficient (1.24 × 10^–4 m³ mol^–1) - _s surface overpotential - constant in equation for the electric potential (–5.46) - _s diffusion layer thickness - scale of diffusion layer thickness - constant relating c/y to the Butler-Volmer law (0.00733) - kinematic viscosity (0.9 × 10^–6 m2 s^–1)     

Ethynylene-disilanylene copolymers

Polymers of structure (SiR₂SiR₂-C C-SiR₂SiR₂-C C) _n , in which ethynylene units alternate with disilylene units, have been prepared by two routes: (a) condensation of dichlorodisilanes with dilithium derivatives of 1,2-diethynyldisilanes and (b) ring-opening polymerization of strained cyclic disilanylene-acetylnes, (SiR₂SiR₂C C)₂. The polymers display UV absorption near 240 nm indicative of – conjugation between the Si₂ and the C C moieties. Polymers with R=R=n-Bu or R=n-Bu, R=Ph, undergo solid-state transitions to form liquid crystalline mesophases resembling those observed for many poly(silylenes). Single crystals were obtained for the polymer with R=R=CH₃, by precipitation from dilute cyclohexane solution. The solid-state properties and structures of this family of polymers are discussed.This paper was presented at the Second International Topical Workshop, Advances in Silicon-Based Polymer Science.