Electrical resistance of polybenzimidazole membranes

Measurements of electrical resistance were made on several polybenzimidazole membranes prepared for use in reverse osmosis. In contact with 1 M KCl, different samples had resistances which ranged from 0.087 to 22 cm². Smaller ranges of resistance were seen with membranes in contact with 36% H₂SO₄ (0.022 to 0.030 cm²) and 40% KOH (0.0063 to 0.096 cm²). With all three electrolytes, however, increasing resistance followed increasing salt rejection measured under reverse osmosis conditions. This offers a rapid and convenient diagnostic test for reverse osmosis performance of the membranes.     

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)     

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)     

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     

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     

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     

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     

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.     

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)     

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     

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)     

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).     

Effective conductivities of an FeS positive in LiCl-KCl eutectic electrolyte at different states of charge

The effective conductivities of an FeS positive electrode in an Li-Al/FeS cell were determined for different states of charge and discharge in LiCl-KCl eutectic electrolyte at 450° C. The data obtained experimentally were compared with those obtained in 67.4 mol% LiCl-KCl electrolyte and theoretically predicted profiles. The electrode resistance profiles indicate that precipitation of KC1, in addition to formation of Li₂S, in the positive electrode causes high internal resistance and limits the discharge capacity.Nomenclature C _i,b Bulk concentration of speciesi outside the electrode (mol cm^–3) - C _i,p Concentration of speciesz in the pore solution (mol cm^–3) - D _i Diffusion coefficient of speciesi (cm² sec^–1) - F Faraday's constant (96 487 C equiv^–1) - I Current density (A cm^–1) - k _j Conductivity ratio defined ask _j /k _c - K _m,j Conductivity ratio defined asK _m,j /k _c - L Electrode thickness per unit volume (cm) - R _i,diffu Rate of concentration change of speciesi due to diffusion (mol s^–1cm^–3) - R _i,migra Rate of concentration change of speciesi due to migration (mol s^–1 cm^–3) - R _i,precip Rate of concentration change of speciesi due to precipitation (mol s^–1cm^–3) - R _i,reac Rate of concentration change of speciesi due to reaction (mol s^–1cm^–3) - t Time (s) - t _i ^Cl Transference number of speciesi relative to Cl^– - ¯ _j Molar volume ofj (cm³mol^–1) - w _LiCl Mass fraction of LiCl - x _i Mole fraction of speciesi - (x _LiCl)_KCl,sat Mole fraction of LiCl in LiCl-KCl electrolyte saturated with KC1 - (x _LiCl)_LiCl,sat Mole fraction of LiCl in LiCl-KCl electrolyte saturated with LiCl - _i Rate constant of production or consumption of speciesi - Void fraction or porosity - _j Volume fraction of solid phasej - _ps Volume fraction of precipitated salt - K _c Conductivity of continuous phase, e.g. electrolyte (^–1 cm^–1) - k _j Conductivity of solid phasej (^–1 cm^–1) - K _m,j Effective conductivity for a mixture of conductive solid phasej and the electrolyte at a given volume fraction of phasej (^–1 cm^–1) - Density of electrolyte (g cm^–3) - Effective conductivity of FeS electrode at a state of discharge (^–1 cm^–1) - Effective resistivity of FeS electrode at a state of discharge ( cm)     

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)     

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.     

Microwave absorption measurements of the electrical conductivity of small particles

A microwave absorption technique based on cavity perturbation theory is shown to be applicable for electrical conductivity measurements of both a small, single-crystal particle and finely divided powder samples when values fall in either the low (<0.1 ^–1 cm^–1) or the intermediate (0.1 100 ^–1 cm^–1) conductivity region. The results here pertain to semiconductors in the latter region. If the skin depth of the material becomes significantly smaller than the sample dimension parallel to theE-field, an appreciable error can be introduced into the calculated conductivity values; however, this discrepancy is eliminated by correcting for the field attenuation associated with the penetration depth of the microwaves. A modification of this approach utilizing the skin depth allows a first-order correction to be applied to powder samples which results in the accurate measurement of absolute values, and results with doped Si powders are compared to values obtained from one small single particle using this microwave technique as well as reported DC values determined with single crystals. The use of this microwave absorption technique with small particles having high surface/volume ratios, such as catalyst supports and oxide catalysts, under controlled environments can provide fundamental information about adsorption and catalytic processes on such semiconductor surfaces. An application to a ZnO powder demonstrates this capability.     

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.     

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.     

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     

Emissivity of carbon disulfide explosive combustion products

Conclusions Anomalous values occur in the emissivity of explosion products of carbon disulfide-oxygen mixtures at relatively low pressures also (p₀=0.03 atm). While within the spectral range of SO+OSO₂+h recombination radiation (280–370 nm), in accordance with the results of [2, 3] the value exceeds unity, on the wings of the radiation band ()1.If nitrogen oxide is employed as an oxidizer instead of oxygen, the limiting emissivity becomes anomalously high in the spectral range of the chemiluminescent reaction NO+ONO₂+h.It is proposed that at low CS₂/O₂ mixture pressure the radiation spectrum wings are connected with electron energy levels of SO₂ molecules populated by the mechanisms of thermal multistep activation, due to which their density is less than the thermodynamic equilibrium value.Chernogolovka. Translated from Fizika Goreniya i Vzryva, No. 5, pp. 108–114, September–October, 1978.