Calculations on the effect of gas evolution on the current-overpotential relation and current distribution in electrolytic cells

Gas evolution during electrode reactions has several effects on the electrode behaviour. One of these effects is the nonuniform increase of the resistivity of the electrolyte with the resultant increase of IR drop through the solution and the distortion of current distribution. Calculations of these effects are presented for an electrode built of vertical blades. This geometry has the peculiarity that it allows the inclusion of linear polarization and gas effects in the treatment, without the necessity to use numerical or approximate solutions of the differential equations. It is shown that the system parameters can be combined into a single dimensionless parameter to describe those aspects of the electrode behaviour which depend on the gas evolution. The parameters examined include the geometry of the electrode, the polarization resistance, gas bubble rise velocity, and solution resistivity. Expressions are given for optimization of the electrode geometry to achieve minimum overpotential.Nomenclature b Polarization resistance ( cm²) - C Constant, =RT( + t)/lPtFs (A^–1cm) - E(x) Potential of the solution at pointx (V) - f _av Average volume fraction of gas (dimensionless) - (fy) Volume fraction of gas at heighty (dimensionless) - f(Y) Volume fraction of gas at reduced heightY (dimensionless) - F Faraday number (coulomb mol^–1) - h Height of the electrode (cm) - i Nominal current density of the electrode =I _T/hw (A cm^–2) - i(y) Local electrode current density at heighty (A cm^–2) - i(Y) Local electrode current density at reduced heightY (A cm^–2) - i _f(x) Faradaic current density at pointx (A cm^–2) - i _f(X) Faradaic current density at reduced lengthX (A cm^–2) - i _f,av Average faradaic current density in the slot=I _s/2hl(Acm^–2) - I _s Total current entering one slot (A) - I _T Total current flowing to the electrode (A) - I(x) Current flowing in the solution phase of one slot at pointx (A) - k Constant, = (2/b)^1/2 (cm^–1) - K Dimensionless parameter =hRT(2/b)^1/2/4lPzFs, or = 1–(1–iCh)^1/4 - l Horizontal length of the slot (cm) - n Number of slots on the electrode (dimensionless) - p Pressure of gas liberated on the electrode (assumed to be independent of height) (atm) - R Universal gas constant (cm³ atm K^–1 mol^–1) - s Bubble rise velocity (cm s^–1) - t Thickness of the blades (cm) - T Temperature of the gas (K) - dV(y) Volume of gas present in a volume element of the slot (cm³) - w Width of the electrode (cm) - x Horizontal distance from the back plate (cm) - X Reduced horizontal distance =x/l (dimensionless) - y Vertical distance from the bottom of the electrode (cm) - Y Reduced vertical distance =y/h (dimensionless) - z Number of Faradays needed to produce one mole of gas (mol^–1) - Width of a slot (blade spacing) (cm) - Measured overpotential of the electrode =(l)(V) - (x) Overpotential at pointx (V) - Resistivity of gas free electrolyte ( cm) - (y) Resistivity of gas filled electrolyte at, heighty ( cm).     

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     

Unsteady mass transfer in turbulent flow close to a rotating cylinder

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

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)     

Mass and momentum transfer enhancement due to electrogenerated gas bubbles

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

Synthesis, Characterization and Optimum Reaction Conditions of Oligo-N, N′-bis (2-hydroxy-1-naphthalidene) Thiosemicarbazone

The oxidative polycondenzation reaction conditions of N, N-bis (2-hydroxy-1-naphthalidene) thiosemicarbazone (HNTSC) using air oxygen, H₂O₂ and NaOCl were studied in an aqueous alkaline medium between 50–90°C. Oligo-N, N-bis (2-hydroxy-1-naphthalidene) thiosemicarbazone was characterized by ¹H-NMR, FT-IR, UV-Vis, size exclusion chromatography (SEC) and elemental analysis techniques. Solubility testing of oligomer was investigated using organic solvents such as DMF, THF, DMSO, methanol, ethanol, CHCl₃, CCl₄, toluene acetonitrile, ethyl acetate, concentrated H₂SO₄ and an aqueous alkaline solution. Using NaOCl, H₂O₂ and air O₂ oxidants, conversion to oligo-N, N-bis (2-hydroxy-1-naphthalidene) thiosemicarbazone (OHNTSC) of N, N-bis (2-hydroxy-1-naphthalidene) thiosemicarbazone was found to be 85, 80 and 76%, respectively, in an aqueous alkaline medium. According to the SEC analyses, the number-average molecular weight, weight-average molecular weight and polydispersity index values of OHNTSC synthesized were found to be 1050 gmol^–1 1715 gmol^–1 and 1.63, using NaOCl, and 2137, 2957 gmol^–1 and 1.38, using air O₂ and 2155 gmol^–1 4164 gmol^–1 and 1.93, using air H₂O₂, respectively. Also, TG analysis was shown to be unstable of oligo-N, N-bis (2-hydroxy-1-naphthalidene) thiosemicarbazone against thermo-oxidative decomposition. The weight loss of OHNTSC was found to be 97.29% at 900°C.     

Studies on electrical conductivity of gamma irradiated polyaniline

Summary de electrical conductivity at surface of -irradiated polyaniline (PAn) has been studied. EPR spectroscopic results indicate that the variation of spin concentration is consistent with the increase of _de. Electrical conductivity (_de) versus temperature (T) characteristics of unirradiated and irradiated PAn were performed, which demonstrate that the unirradiated curve can fit to ln_deT₁, while the irradiated curve fit to ln_deT_1/4.     

Kinetics and mechanism of anodic oxidation of chlorate ion to perchlorate ion on lead dioxide electrodes

The kinetics and mechanism of anodic oxidation of chlorate ion to perchlorate ion on titanium-substrate lead dioxide electrodes have been investigated experimentally and theoretically. It has been demonstrated that the ionic strength of the solution has a marked effect on the rate of perchlorate formation, whereas the pH of the solution does not influence the reaction rate. Experimental data have also been obtained on the dependence of the reaction rate on the concentration of chlorate ion in the solution at constant ionic strength. With these data, diagnostic kinetic criteria have been deduced and compared with corresponding quantities predicted for various possible mechanisms including double layer effects on electrode kinetics. It has thus been shown that the most probable mechanisms for anodic chlorate oxidation on lead dioxide anodes involve the discharge of a water molecule in a one-electron transfer step to give an adsorbed hydroxyl radical as the rate-determining step for the overall reaction.Nomenclature anodic energy transfer coefficient - ₂ potential of outer Helmholtz plane with respect to solution - _M potential of metal with respect to solution - dielectric constant of solution - ₂ permittivity of free space - faradaic efficiency for anodic chlorate oxidation - A adsorbed intermediate in Reaction 2 - B bulk species in Reaction 2 - c _A concentration of A at outer Helmholtz plane - c _B concentration of B at outer Helmholtz plane - c _B ⁰ concentration of B in bulk - c _ClO3 ^– /0 concentration of ClO ₃ ^– in bulk - c _ClO4 ^– /0 concentration of ClO ₄ ^– in bulk - E electrode potential corrected for ohmic drop - E _a electrode potential as measured against reference electrode - E _s ⁰ standard electrode potential of Reaction 2 - E _z potential of zero charge of the anode in test solution - F Faraday constant - f F/(RT) - I _t current at anode - I _OER current used for oxygen evolution reaction at anode - I current used for chlorate oxidation (=I _t–I _OER) at anode - i _t I _t/anode area - i _OER I _OER/anode area - i I/anode area - J total concentration of (uni-univalent) electrolytes in solution - K ₂ integral capacitance of compact part of double layer - K _s standard rate constant for Reaction 2, corrected for double layer effects - n _s number of electrons involved in Reaction 2 - p ln(–i)/lnc _ClO3 ^– /0 - q _M charge density on metal surface - Q ₁ quantity of electricity passed in given time interval - Q _OER quantity of electricity required for oxygen evolution reaction in given time interval - R ohmic resistance between anode and Luggin tip - R gas constant - r ln(–i)/lnJ - s ln(–i)/ pH - T absolute temperature - t ln(–i)/E - u (₂ RT/2)^1/2 - V volume of gases evolved in given time interval - V _H volume of hydrogen evolved in given time interval - Z _B charge on species B     

Calorimetric,X-ray and infra-red investigations on poly(hexamethylene adipamide)

Summary In dependence on crystallization conditions three ranges with different crystal structure and heat of fusion were found by DSC,WAXS,and IR for unoriented PA 6.6 samples of densities between 1.10 and 1.17gcm^–3: Range I:_I triclinic, _c ^I =1.225 gcm^–3,H _M ^I = 235 Jg^–1. Range II:_II triclinic, _c ^II =1.165 gcm^–3, H _M ^II =185 Jg^–1. Range III:Continuous variation from _c ^I ,H _M ^I to _c ^II , H _M ^II . _a=1.095 gcm^–3 is independent of crystallization. conditions. The transition between _I and _II is probably due to changes of the chain conformation.     

Syntheses and optical properties of <Emphasis Type="Italic">α</Emphasis>- and <Emphasis Type="Italic">β</Emphasis>-cyano-poly(<Emphasis Type="Italic">p</Emphasis>-phenylene vinylene) derivatives

Two light emitting molecules with the cyano group at different positions on the vinylene i.e., 2,5-bis(2-thienyl-1-cyanovinyl)-1-(2_-ethylhexyloxy)-4-methoxybenzene (-TPT) and 2,5-bis(2-thienyl-2-cyanovinyl)-1-(2-ethylhexyloxy)-4-methoxybenzene (-TPT), and corresponding polymers, i.e., poly[2,5-bis(2-thienyl-1-cyanovinyl)-1-(2-ethylhexyloxy)-4-methoxybenzene] (denoted as P1) and poly[2,5-bis(2-ethienyl-2-cyanovinyl)-1-(2-ethylhexyloxy)-4-methoxybenzene] (denoted as P2) were synthesized. -TPT and -TPT, respectively, were blended into two host polymers, poly(methyl methacrylate (PMMA) and poly(9-vinylcarbazole) (PVK), to study the optical properties of the dopants in different host polymer matrices. Although -TPT and -TPT have the same backbone structure, their optical properties are much different. The PL emission maximum ( _max) of -TPT was found blue-shifted, compared with that of -TPT, while the PL intensity of -TPT was stronger than that of -TPT. Concentration effect in the optical properties was found, 1 wt% of -TPT in PVK had the maximum fluorescent emission.The PL maximum peak wavelengths for polymer films (P1 and P2) were found red-shifted; while their PL intensities were weaker when compared with those of blends.     

Calculation of the Viscosity of Glass-Forming Melts: VI. The R2O–B2O3–SiO2and RO–B2O3–SiO2Ternary Borosilicate Systems

A method for calculating the viscosity from composition and temperature for melts in the R _m O _n –B₂O₃–SiO₂systems is proposed. The change in the concentrations of structural groups depending on the melt composition is taken into account in calculations. The results of calculations are compared with the experimental data available in the literature on the viscosity of 1200 melts with the use of the SciGlass information system. The root-mean-square deviation between the experimental and calculated characteristic temperatures varies from 30 K (for the glass transition temperature and the Littleton point) to 50 K (for a viscosity of 10⁴P).     

Studies concerning charged nickel hydroxide electrodes. II. Thermodynamic considerations of the reversible potentials

In this paper the thermodynamics of mixing are applied to account for the independence of the discharge potential of the nickel hydroxide electrode as a function of nickel oxidation state. The constant potential region is considered to arise from the formation of a pair of co-existing solid solutions having a composition predetermined by the magnitude of the interactions between the oxidized and reduced species. From considerations of the excess-energy terms, it can be shown for a symmetrical potential/ composition profile, that the constant potential region is identical with the standard potentialE ₀. The influence of asymmetry on the changes inE ₀ are discussed. Consideration has also been made of the influence of dissociation of oxidized and/or reduced species on the potential determining equations. The removal of n-type defects from the nickel(II)-rich phase on discharge is considered to be responsible for the observed secondary discharge plateau at potentials 300 mV more cathodic than normal. This non-equilibrium behaviour can be explained in terms of a mixed pn-semiconducting material.List of symbols E electrode potential at constant pH(V) - E ₀ standard electrode potential (V) - R the gas constant (J K^–1 mole^–1) - F the Faraday constant (C g-equiv^–1) - T the absolute temperature (K) - ^aH⁺ proton activity in the electrolyte - a _z activity of oxidized species z - a _y activity of reduced species y - _H+ chemical potential of the proton - _e chemical potential of the electron - _z ^o standard chemical potential of species z - _z chemical potential of species z - _y ^o standard chemical potential of species y - _y chemical potential of species y - _H,e chemical potential of the proton/electron pair - x _y orx mole fraction of reduced species y - x _z mole fraction of oxidized species z - G _M total free energy of mixing (J mole^–1) - G _R free energy of reaction (J mole^–1) - G _I free energy of mixing under ideality (J mole^–1) - G _E excess free energy (J mole^–1) - A,A _i andB _i interaction energy parameters (J mole^–1) - x _u mole fraction of y in co-existing phase u - x _v mole fraction of y in co-existing phase v - _y activity coefficient of undissociated reduced species y - _z activity coefficient of undissociated oxidized species z - _y ^± mean ionic activity coefficient of y - _z ^± mean ionic activity coefficient of z - _y activity coefficient of y in phase u - _z ^u activity coefficient of z in phase u - _y ^v activity coefficient of y in phase v - _z ^v activity coefficient of z in phase v - I current (A) - S cross-sectional area (cm²) - L conductor length (cm)     

A mathematical model for platinum/ PTFE/porous nickel fuel cell oxygen diffusion electrodes

This paper describes the cylindrical agglomerate model for oxygen/alkali gas diffusion electrodes fabricated from platinum, PTFE and porous nickel. Corrections for the increase in hydroxyl ion concentration with increasing current density have been made to the original model of Brown and Horve. Changes in performance by variation of the bulk structural parameters, e.g. agglomerate radius, porosity and tortuosity, have been studied. Theoretical modes of electrode decay have been explored.List of symbols Transfer coefficient - C Concentration of O₂ in elec trolyte mol cm^–3 - C _i Concentration of O₂ atr = R mol cm^–3 - C _o Concentration of O₂ in electrolyte atr = mol cm^–3 - Diffusion coefficient of O₂ in KOH cm² sec^–1 - Film thickness cm - E Overpotential of the electrode V - F Faraday's constant - i Electrode current density A cm^–2 - i _a Current per agglomerate A - I ₁(Z) First order Bessel function - I ₀(Z) Zero order Bessel function - j Local current density A cm^–2 - j _o Exchange current density A cm^–2 - L Agglomerate length (catalyst thickness) cm - N Number of electrons in rate determining step - N _a Number of agglomerates per cm² of electrode - Potential drop along ag glomerate V - _L Potential drop at L_a V - r Radial direction - R Radius of agglomerate cm - R _o Gas constant - Density of platinum g cm^–3 - S _g Surface area per gram cm² g^–1 - Solubility coefficient of O₂ mol cm^–3 - _m Electrolyte conductivity (ohm cm)^–1 - T Absolute temperature °K - _a Axial tortuosity - Porosity of platinum in the agglomerate - _r Aadial tortuosity of the agglomerate - W Catalyst loading g cm^–2 - x Axial direction     

Some theoretical considerations on the design of a practical anode in an electrochemical reactor

A theoretical analysis of the membrane current distribution is carried out for a typical three-compartment electrolyser in order to point out the effects of geometry on the design of mesh anodes. The factors considered here include the introduction of an insulated border, the perforation of the anode, the finite conductivity of the substrate, and the introduction of a bus bar connection between the anode and the current lead. It is recommended that no insulated border be introduced, since, while reducing the anode area and consequently its cost, it leads to a nonuniform membrane current distribution and hence decreases membrane efficiency. Also, titanium is found to be a suitable substrate for the anode in spite of its relatively low conductivity.Nomenclature a Dummy variable in Equation 3 - b Border width - b ^* Effective border width - f Fraction of open area in electrode - F _B Parameter defined by Equation 4 - F _p Parameter defined by Equation 8 - F _be Parameter defined by Equation 15 - I Total cell current - i Local current density on the membrane at a point - i Current density along the membrane far from the border - _loc Average value of current density over a small portion of the membrane - _cell Average value of current density over the whole membrane - Average value of current density on membrane far from the border - i _max Maximum value of current density on membrane - _loc,max Maximum value of _loc on membrane due to electrode and bus bar resistance effects - i _p Maximum value of current density over a single electrode perforation - j (–1)^1/2 - l _p Characteristic length of mesh - L Dimension of anode in the direction of bus bar orientation - L Dimension of anode in the direction perpendicular to bus bar - L Width of bus bar - s Interelectrode gap - s ₁ Membrane to anode gap - R Electrolyte and membrane resistance - x _b Coordinate along length of bus bar - x _B Coordinate in border effect analysis - x _e Coordinate along electrode in the analysis of its resistance effect - x _P Coordinate in perforation effect analysis - _b Bus bar thickness - _e Electrode thickness - _b Bus bar resistivity - _e Electrode resistivity - _em Resistivity of metal in electrode - _b Potential at a point on the bus bar - _e Potential at a point on the electrode - ¯ _e Average potential over the electrode - _max Potential at the current source - _cath Potential at the equipotential cathode     

Mass transfer studies at iron felts

Mass transfer has been studied at flow-through iron felts using the reduction of ferricyanide or copper cementation on iron as test reactions. Empirical correlations between a modified Sherwood number and the Reynolds number are proposed. Comparisons of the mass-transfer performance of iron felts with other three-dimensional structures are made.List of symbols a ₃ specific surface area per unit felt volume (m^–1) - A empty cross-section of the reactor (m²) - C concentration (mol m^–3) - C ₀ inlet concentration (mol m^–3) - d _h hydraulic diameter (m) - e fibre thickness (m) - E electrode potential (V) - D diffusion coefficient (m²s^–1) - F Faraday constant (A s mol^–1) - i current density (A m^–2) - I total current (A) - I _L limiting current (A) - J _m mass transfer j-factor=(k/v)Sc ^2/3 - K mass transfer coefficient (m s^–1) - l fibre width (m) - L electrode thickness (m) - Re Reynolds number - vd _h/ - Re modified Reynolds number - vl/ - Sc Schmidt number = /D - Sh modified sherwood number = ka _e l ²/D - t time (s) - T Temperature (K) - superficial liquid flow velocity (m s^–1) Greek characters void fraction - dynamic viscosity (kg m^–1 s^–1) - kinematic viscosity (m² s^–1) - ₃ charge number of the electrode reaction - iron density (kg m^—) - _a apparent density of the felt (kg m^–3) - _m residence time of the reservoir (s)     

Molybdenum nitride for the direct decomposition of NO

The physico-chemical properties of passivated -Mo₂N have been investigated. The material showed high activities for NO direct decomposition: nearly 100% NO conversion and 95% N₂ selectivity were achieved at 450C. The amount of O₂ taken up by -Mo₂N increased with temperature rise and reached 3133.9 molg^–1 at 450C; we conclude that there formation of Mo₂O_xN_y occurred. This oxygen-saturated -Mo₂N material was catalytically active: NO conversion and N₂ selectivity were 89 and 92% at 450C. We found that by means of H₂ reduction at 450C, Mo₂O_xN_y could be reduced back to -Mo₂N and the oxidation/reduction cycle is repeatable; such a behaviour and the high oxygen capacity (3133.9 molg^–1) of -Mo₂N suggest that -Mo₂N is a promising catalytic material for automobile exhaust purification.     

Synthesis,electroconductivity and third-order nonlinear optical property of poly(2-isopropoxy-5-methoxy-1,4-phenylenevinylene)

Summary Asymmetrically disubstituted poly(2-isopropoxy-5-methoxy-1,4-phenylene-vinylene), PIMPV, was prepared in thin films via organic-soluble precursor polymer method. These polymer films could be easily stretched up to 7 times, and the drawn films of the PIMPV could be doped with FeCl₃ and I₂ to give conductivities of 26.9 and 11.3 Scm^-1, respectively. The third-order nonlinear optical susceptibility of the polymer was determined using third harmonic generation(THG) method at 1907 nm, fundamental wavelength. Measured ⁽³⁰⁾ (-3: , , ) value was 3.7x10^-12 esu.     

Diffusion-controlled current distributions near cell entries and corners

This paper reports experimental work undertaken to explore diffusion-controlled current distributions immediately downstream of sudden changes in flow cross-sectional area such as may occur at the entry to electrochemical flow cells. Nozzle flows expanding into an axisymmetric circular duct and into a square duct have been investigated using the reduction of ferricyanide ions on nickel micro-electrodes as the electrode process. The spanwise distribution of current has also been studied for the case of the square cell where secondary corner flows are significant.Nomenclature A electrode area (cm²) - c bulk concentration of transferring ions (mol dm^–3) - D cell diameter (cm) - D Diffusion coefficient (cm₂s^–1) - F Faraday number (96 486 C mol^–1) - I limiting electrolysis current (A) - k mass transfer coefficient (cm s^–1) - N nozzle diameter (cm) - u mean fluid velocity (cm s^–1) - x distance downstream from point of entry to cell (cm) - z number of electrons exchanged - electrolyte viscosity (g s^–1 cm^–1) - electrolyte density (g cm^–3) - (Re)_D duct Reynolds number,Du/ - (Re)_N nozzle Reynolds number,Nu/ - (Sc) Schmidt number,/D) - (Sh) Sherwood number,kD/D)     

Impedance of a porous electrode with an axial gradient of concentration

When the impedance is measured on a battery, an inductive impedance is often observed in a high frequency range. This inductance is frequently related to the cell geometry and electrical leads. However, certain authors claimed that this inductance is due to the concentration distribution of reacting species through the pores of battery electrodes. Their argument is based on a paper in which a fundamental error was committed. Hence, the impedance is re-calculated on the basis of the same principle. The model shows that though the diffusion process plays an outstanding role, the overall reaction rate is never completely limited by this process. The faradaic impedance due to the concentration distribution is capacitive. Therefore, the inductive impedance observed on battery systems cannot be, by any means, attributed to the concentration distribution inside the pores. Little frequency distribution is found and the impedance is close to a semi-circle. Therefore depressed impedance diagrams in porous electrodes without forced convection cannot be ascribed to either a Warburg nor a Warburg-de Levie behaviour.Nomenclature A D¦C¦ (mole cm s^–1) - B j+K¦C¦ (mole cm s^–1) - b Tafel coefficient (V^–1) - C(x) Concentration ofS in a pore at depthx (mole cm^–3) - C ₀ Concentration ofS in the solution bulk (mole cm^–3) - C C(x) change under a voltage perturbation (mole cm^–3) - ¦C¦ Amplitude of C (mole cm^–3) - D Diffusion coefficient (cm² s^–1) - E Electrode potential (V) - E Small perturbation inE namely a sine-wave signal (V) - ¦E¦ Amplitude of E(V) - F Faraday constant (96500 A s mol^–1) - F(x) Space separate variable forC - f Frequency in Hz (s^–1) - g(x) KC(x)¦E¦(mole cm s^–1) - I Apparent current density (A cm^–2) - I _st Steady-state current per unit surface of pore aperture (A cm^–2) - j Imaginary unit [(–1)^1/2] - K Pseudo-homogeneous rate constant (s^–1) - K Potential derivative ofK, dK/dE (s^–1 V^–1) - K ^* Heterogeneous reaction rate constant (cm s^–1) - L Pore depth (cm) - n Reaction order - P Reaction product - p Parameter forF(x), see Equation 13 - q Parameter forF(x), see Equation 13 - R _e Electrolyte resistance (ohm cm) - R _p Polarization resistance per unit surface of pore aperture (ohm cm²) - R _t Charge transfer resistance per unit surface of pore aperture (ohm cm²) - S Reacting species - S _a Total surface of pore apertures (cm²) - S ₀ Geometrical surface area - S _p Developed surface area of porous electrode per unit volume (cm² cm^–3) - s Concentration gradient (mole cm^–3 cm^–1) - t Time - U Ohmic drop - x Distance from pore aperture (cm) - Z Faradaic impedance per unit surface of pore aperture (ohm cm²) - Z _x Local impedance per unit pore length (ohm cm³) - z Charge transfer number - Porosity - Thickness of Nernst diffusion layer - Penetration depth of reacting species (cm) - Penetration depth of a.c. signal determined by the potential distribution (cm) - Electrolyte (solution) resistivity (ohm cm) - ₀ Flow of S at the pore aperture (mole cm² s^–1) - Angular freqeuncy of a.c. signal, 2f(s^–1) - Integration constant     

A chemically regenerative redox fuel cell

A novel chemically regenerative redox fuel cell is described. The electrode reactions are based on the following redox reactions: cathodic reaction: anodic reaction: VO ₂ ⁺ +2H⁺+e VO²⁺+H₂O (E ₀ +1V), SiW₁₂O ₄₀ ^5– SiW₁₂O ₄₀ ^4– +e (E ₀ 0V). Regeneration of the oxidant by direct oxidation with O₂ was achieved by using the soluble heteropoly acid catalysts, H₃PMo₁₂O₄₀ or H₅PMo₁₀V₂O₄₀, whereas regeneration of the tungstosilicic acid, H₃SiW₁₂O₄₀, was accomplished by direct reduction with H₂ utilizing small amounts of Pt, Pd, Rh, Ru or the soluble Pd-4, 4, 4, 4'-tetrasulphophthalocyanine complex as catalysts. Some aspects of the regeneration kinetics and their influence on the overall performance of the redox fuel cell are discussed.