Recycle reactor models for complex electrochemical/chemical reaction systems

The performance of complex electrochemical reaction sequences in recycle plug flow reactors is mathematically modelled. The reactions include successive electron transfers (EE reactions), chemical reaction interposed between successive electron transfers (ECE reactions), simultaneous electron transfers and simultaneous electron transfer and chemical reaction. Both potentiostatic and galvanostatic operations are considered and the effects of important parameters such as mass transport coefficient, recycle ratio and chemical reaction rate in the recycle loop are highlighted. This is done by considering two important electro-organic synthesis reactions, the production ofp-aminophenol and the reduction of oxalic acid to glyoxylic acid.Nomenclature a activity factor - C _ji concentration of species j at reactor inlet - C _j bulk concentration of species j - C _j ^s surface concentration of species j - C _j ^e concentration of component j returned to reactor inlet stream - C _j concentration from reactor outlet - C _je equilibrium concentration - E electrode potential - F Faraday number - i _n partial current density of stepn - i _T total current density - k deactivation rate constant - k _f n forward electrochemical rate constant of stepn - k _b n backward electrochemical rate constant of stepn - k _f forward chemical reaction rate constant - k _r reverse chemical reaction rate constant - k _Lj mass transfer coefficient for species j - k _a forward adsorption rate constant - k _d reverse adsorption rate constant - L reactor length - r recycle ratio - t reaction time - u velocity - Q flow rate - x reactor dimension - _n constant describing potential dependency of reverse reaction rate constant - _n constant describing potential dependency of forward reaction rate constant - _j surface concentration of adsorbed species j - electrode area per unit length - residence time of fluid in recycle loop     

Mechanisms of electroless metal plating. III. Mixed potential theory and the interdependence of partial reactions

Electroless plating reactions are classified according to four overall reaction schemes in which each partial reaction is either under diffusion control or electrochemical control. The theory of a technique based on the observation of the mixed potential as a function of agitation, concentration of the reducing agent and concentration of metal ions is presented. Using this technique it is shown that in electroless copper plating the copper deposition reaction is diffusion-controlled while the formaldehyde decomposition reaction is activation-controlled. Values of the kinetic and mechanistic parameters for the partial reactions obtained by this method and by other electrochemical methods indicate that the two partial reactions are not independent of each other.Nomenclature a Tafel slope intercept - A electrode area - b _M Tafel slope for cathodic partial reaction - b _R Tafel slope for anodic partial reaction - B _M diffusion parameter for CuEDTA^2– complex - diffusion parameter for dissolved oxygen - B _R diffusion parameter for HCHO - C _M bulk concentration of copper ions - bulk concentration of dissolved oxygen - C _R ^a surface concentration of HCHO - C _R bulk concentration of HCHO - D _R diffusion coefficient of HCHO - E electrode potential - E _M thermodynamic reversible potential for the metal deposition reaction - E _M ⁰ standard electrode potential for copper deposition - E _MP mixed potential - E _R thermodynamic reversible potential for reducing agent reaction - E _R ⁰ standard electrode potential for HCHO - F Faraday constant - i _M current density for metal deposition - i _M total cathodic current density - i _M ^k kinetic controlled current density for metal deposition - i _M ⁰ exchange current density for metal deposition - i _M ^D diffusion-limited current density for metal deposition - i _M ^D diffusion-limited current density for total cathodic reactions - current density for oxygen reduction - i _plat plating current density - i _R current density for HCHO oxidation - i _R ⁰ exchange current density for HCHO oxidation - i _R ^D diffusion-limited current density for HCHO oxidation - n _M number of electrons transferred in metal deposition reaction - n _R number of electrons transferred in the HCHO oxidation reaction - R gas constant - T absolute temperature - stoichiometric number - _M transfer coefficient for metal deposition - _R transfer coefficient for HCHO oxidation - _M symmetry factor - number of steps prior to rate determining step - _M overpotential for metal deposition - _R overpotential for HCHO oxidation - v kinematic viscosity - rotation rate of electrode     

The transient behaviour of a class of semicontinuous tank electrolysers

The transient behaviour and figures of merit of an isothermal electrolyser consisting of a perfectly mixed-flow compartment and a batch compartment separated by an ion-selective membrane are analysed by means of its governing balance equations solved on a microcomputer.Nomenclature c acid concentration - E conversion of the oxidized to the reduced species at the cathode - F Faraday's constant (96487 C mol^–1) - i current density - K cost of operation - k ₁,k ₂ cost coefficients (specific costs) - Q _s charge density; its sample regression - S _O initial slope of the conversion-time curve (Fig. 3) - t time - t _H transport (transference) number of hydronium ions - V magnitude of the imposed voltage - x ₁ ⁰ magnitude of the inlet concentration of the oxidized species - w acid concentration in the anolyte - lumped parameter, defined as 1+^k m ^A/Q _c - sample linear regression parameters (Table 5) - fractional concentration of the oxidized species defined as (concentration — surface concentration)/concentration - _c mean residence time defined asV _c /Q _c Special symbols MU arbitrary monetary unit - * steady-state The majority of symbols is defined in Table 1.     

Significance of logarithmic throwing index: a theoretical approach

An expression for the metal distribution ratio in electroplating systems as a function of the primary current density ratioL in the formM=L [W(1–r)/(1+K)] is derived.W,r andK are three dimensionless parameters related to the current efficiency ratio, the concentration polarization and activation polarization during the metal discharge. The function [W(1–r)/1+K] is compared with 1/A, the logarithmic throwing index empirically determined by Chin. The metal distribution ratio calculated by the use of the above formula is compared with the experimentally observed values. The close agreement between the two within an accuracy of 10% proves the validity of the equation derived. The logarithmic throwing power of electroplating systems is thus confirmed on theoretical grounds.Nomenclature A Logarithmic Throwing Index —inverse of the slope of the plot of logM versus logL - b Tafel slope. Slope of the equation =a + b logi - d_n Current efficiency in percent for metal deposition at near cathode - d _f Current efficiency in percent for metal deposition at far cathode - E The overall cell potential - E _n The potential drop in the electrolyte between the anode and near cathode - E _f The potential drop in the electrolyte between the anode and far cathode - e _a Dynamic anode potential - e _n Dynamic potential at the near cathode at a current densityi _n - e _f Dynamic potential at the far cathode at a current densityi _n - f a fraction = - i The average current density (A dm^–2) - i _n The primary current density at the near cathode when there is no polarization(A dm^–2) - i _f The primary current density at the far cathode when there is no polarization(A dm^–2) - i _n The secondary current density at the near cathode (A dm^–2) - i _f The secondary current density at the far cathode (A dm^–2) - i _{H n} The partial cathode current density at the near cathode for parallel cathodic reactions other than metal discharge (A dm^–2) - i _{H f} The partial cathode current density at the far cathode for parallel cathodic reactions other than metal discharge (A dm^–2) - i _{M n} The partial cathode current density for metal discharge at the near cathode - i _{M f} The partial cathode current density for metal discharge at the far cathode - K A dimensionless parameter =b/2.3E _f - l Linear Ratio =l _f/l _n ori _n i _f - l _n Linear distance of the near cathode (cm) - l _f Linear distance of the far cathode (cm) - M Metal distribution ratio - m _n Weight of metal deposited on the near cathode - m _f Weight of metal deposited on the far cathode - R Secondary current distribution ratio=i _n/i_f - r A dimensionless parameter related toK andf and given byf=(1/L) ^r/K - W A dimensionless parameter related current efficiency ratioR ^W–1 =d _n/d_f - Specific resistivity of the electrolyte( cm^–2) - _n The overpotential at the near cathode (V) - _f The overpotential at the far cathode - i ₀ The exchange current density     

An electrochemical model for reduction of MnO2 with Fe2+ ions

The reduction kinetics of MnO₂ by Fe²⁺ ions in acidic solution have been studied. The effects of stirring rate, particle size, temperature, Fe²⁺ and H⁺ concentrations have been investigated. Diffusional resistances are negligible above 900 r.p.m. and the rate is controlled by electrochemical reaction. A mixed-potential model developed to describe metallic corrosion has been used in combination with the shrinking core model to explain the reaction kinetics. The overall reaction has been written in terms of cathodic and anodic half-cell reactions. The Tafel equation has been used as a starting point to derive a rate equation. A value of 0.5 has been obtained for charge transfer coefficients, which implies the existence of symmetrical charge barriers. The kinetics of the cathodic reduction reaction are first order with respect to the proton concentration.Nomenclature D diffusion coefficient (cm² s^–1) - D _i impeller diameter (cm) - D _T reactor diameter (cm) - d ₀ initial particle diameter (m) - E e.m.f. between platinum and saturated calomel electrode (V) - F Faraday constant - e electrode potential (V) - e _j liquid-junction potential (V) - k _a rate constant of anodic half-cell reaction - k _c rate constant of cathodic half-cell reaction - k ₁ Mass transfer coefficient (cm s^–1) - m ₀ amount of MnO₂ charged in the reactor (g) - M Molecular weight of MnO₂ - N Stirring speed (r.p.m.) - Re _s Reynolds number for stirring (ND _i ²/) - Re _p Reynolds number for particle (d ^4/31/3/) - Sc Schmidt number (/D) - Sh Sherwood number (k ₁ d/D) - V Reaction volume (dm³) - X Conversion factor Greek letters _i stoichiometric coefficient of reactant i in Equation 1 - stirring energy per unit volume - kinematic viscosity (cm² s^–1) - time required for complete conversion (min)     

The active dissolution of tin in acidic chloride electrolyte solutions — a rotating disc study

The anodic dissolution of tin in acidic chloride electrolyte has been investigated using the rotating disc technique. The dissolution reaction has a Tafel slope of 64 ±5 mV dec^–1 after the effects of diffusion are eliminated. The order of reaction with respect to Cl^– ion has been found to be unity. The measured currents were also found to depend onC _H+. The suggested mechanism involves quasi-reversible charge transfer.A possible explanation is given for the observed current-time behaviour at low anodic current densities.Notation i Current density - i ₍₎ Current density at infinite rotation speed - i _d ,Cl^– Limiting current density due to Cl^– diffusion - C _cl ^– Concentration of chloride ion - C _H+ Concentration of hydrogen ion - d ₀ Diffusion coefficient of oxidised species - k _b Rate constant for reduction of oxidised species - Kinematic viscosity - Angular velocity - Anodic transfer coefficient - Rate constant at standard equilibrium potential - Direction of reaction     

A particulate vortex bed cell for electrowinning: operational modes and current efficiency

The process of electrowinning of copper ions from dilute solutions has been used as a model system to assess the performance of a vortex bed cell with a three-dimensional cathode of conducting particles. Experiments were carried out under three conditions: with constant cell voltage, with constant cell current throughout the process and with exponential decrease of the operating current with time in order to underfollow the limiting current. Results from a batch recirculating system indicate that exponential decrease of operating current with time effects an improvement in current efficiency over a wide range of concentration.Nomenclature specific surface area of particles (cm^–1) - C, C _i concentration of Cu²⁺ ions at the momentt, and initial concentration, respectively (M) - d _p particle diameter (cm) - F Faraday number (96 487 A s mol^–1) - i current density (Am^–2) (calculated for the surface area of the particles) - i _av average current density obtained in the constant cell voltage process (Am^–2) - I _L(t),I _L o limiting current at timet, and initial limiting current, respectively (A) - k _L mass transfer coefficient (cm s^–1) - n number of electrons transferred in the process - Q volumetric flow rate (dm³ s^–1) - R universal gas constant (J mol^–1 K^–1) - t time (s) - T temperature (K) - U cell voltage (V) - V volume of electrolyte (cm³) - v _o volume of particles (cm³) - overpotential (V) - _e current efficiency - , _o bed porosity and porosity of the fixed bed, respectively - =V/Q residence time (s) - see Fig. 2     

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

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

Cathodic behaviour of antimony (III) species in chloride solutions

Cathodic copper is easily contaminated by antimony in copper electrowinning from chloride solutions even when the antimony concentration in the electrolyte is as low as 2 p.p.m. Reduction potential measurements of copper and antimony species indicate that electrodeposition of antimony is unlikely unless copper concentration polarization exists near the cathode surface. A.c. impedance measurements and the effect of the rotation speed of the disc electrode indicate that the cathodic process mechanism for antimony is complicated. Both diffusion and chemical reactions occurring on the cathode surface supply the electrochemical active antimony species for the cathodic process. Reaction orders of the cathodic process with respect to antimony chloride, hydrogen and chloride ion concentrations are 2, –1 and –1, respectively. A proposed reaction mechanism for the process explains the experimental findings satisfactorily.List of symbols A surface area (cm²) - a_o1, a₁ constants - C concentration (mol cm^–3) - D diffusion coefficient (cm2 s^–1) - E potential (V) - F Faraday constant (Cmol^–1) - f frequency (s^–1) - I current (A) - i current density (A cm^–2) - i _{d 8} limiting diffusion current density due to the diffusion of species O from bulk to the electrode surface and then the subsequent Reac tions 1 and 2 (A cm^–2) - i _{d o} limiting diffusion current density of species O (A CM^–2) - K chemical equilibrium constant - k rate constant (s^–1) - n number of electrons involved in the reaction - Q charge (C) - Q _dl charge devoted to double layer capacitance (C) - Q _f total charge in the forward step of potential step chronocoulometry (C) - Q _r total charge in reverse step of potential step chronocoulometry (C) - t time (s) - sweep rate (V s^–1) Greek symbols amount of species adsorbed per unit area (mol cm^–2) - fraction of adsorption sites on the surface occupied by adsorbate. - ratio of rate constant defined in Equation 1 - _c thickness of reaction layer (cm) - d thickness of diffusion layer (cm) - time (s) - modified time (s^1/2) - kinematic viscosity (cm² s^–1) - angular velocity (s^–1)     

Computer simulation of high-discharge-rate battery systems

Simulations were carried out for a proposed two-dimensional high-discharge-rate cell under load with an interelectrode gap of the order of 100 m. A finite difference program was written to solve the set of coupled, partial differential equations governing the behaviour of this system. Cell dimensions, cell loads, and kinetic parameters were varied to study the effects on voltage, current and specific energy. Trends in cell performance are noted, and suggestions are made for development of cells to meet specific design criteria. Modelling difficulties are discussed and suggestions are made for improvement.Nomenclature A surface area of unit cell (cm²) - A _k conductivity parameter (cm^{2 –1} mol^–1) - b Tafel slope (V) - c concentration (mol cm^–3) - c ₀ concentration of bulk electrolyte (mol cm^–3) - D diffusivity (cm² s^–1) - D _h lumped diffusion parameter (J s cm^–2 mol^–1) - D _s lumped diffusion coefficient (A cm² mol^–1) - E rest potential of electrode (V) - F Faraday constant (96 500 C mol^–1) - i current density (A cm^–2) - I total current for unit cell (A) - i ₀ exchange current density (A cm^–2) - N flux of charged species (mol cm² s^–1) - R gas constant (8.314 J mol^–1 K^–1) - R _ext resistance external to cell () - t time (s) - T temperature (K) - t ₀ transference number - u mobility (cm² mol J^–1 s^–1) - V volume of an element in the cell (cm³) - V _ext voltage external to cell (V) - z charge on an ion - _c concentration overpotential (V) - _s surface overpotential (V) - conductivity (^–1 cm^–1) - stoichiometric coefficient - electric potential in solution (V)     

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.     

Investigations in platinum metal group electrochemistry: II The Pd(II)-Pd° reduction

The Norbide boron carbide electrode has been satisfactorily applied to polarographic studies of Pd(II)–Pd° and some other systems involving deposition of metal. By its means the following thermodynamic and kinetic data have been established: standard oxidation-reduction potentials, Pd²⁺–Pd°, 0.91 V; Ag⁺–Ag°, 0.805 V; stability constants, PdCl ₄ ^2– , log ₄, 9·38; logK ₄, 1·44; Pd(SO₄) ₂ ^2– , log ₂, 3·16; activation energies, Pd²⁺–Pd°:Q _D, 18·6; Q°, 188 kJ mole^–1. Analytical applications have been briefly examined.List of symbols A Area of the working electrode - (A°) Apparent frequency factor of the Arrhenius relationship - n Nominally the product of the transfer coefficient, , and the number of electrons,n, involved in an electrochemical process. In practice it is the value obtained from the slopeRT/anF of the lineE v. ln(i ₁–i)/i orv. ln(i ₁–i) - _j Product of dissociation constants of successive complexes:K ₁×K ₂×...×K _j - C ₀ Bulk concentration in the aqueous phase of species undergoing electrochemical reduction or oxidation - D ₀ Diffusivity of that species in the aqueous phase immediately adjacent to the electrode surface - Thickness of a diffusion layer - E _1/2 Half-wave potential, at whichi=i ₁/2 in a polarographic wave of the formE=E _1/2+RT/anF ln(i ₁–i)/i - E _mid Potential at whichi=i ₁/2 in a wave of the formE=E _mid+RT/anF ln(i ₁–i)/i - E _1/2 Displacement of half-wave potential caused by complexing of reducing species - _1/2 Overpotential at the half-wave potentialE _1/2 - _mid Overpotential atE _mid - f Activity coefficient, e.g.f _Pd ^2+(x=0) the activity coefficient of Pd²⁺ species in the aqueous phase at the electrode surface - i ₁ Limiting current - i Current at any stage of the electro-chemical processes governed byE v. ln(i ₁–i)/i relationships - j Number of complexing ligands associated with a cation—e.g. for PdCl ₃ ^– =3 - Q Arrhenius activation energy of the electrochemical process of a reduction at a working electrode [8] - Q _D Arrhenius activation energy of the diffusion stage of an electrochmical reduction [8]     

Applications of magnetoelectrolysis

A broad overview of research on the effects of imposed magnetic fields on electrolytic processes is given. As well as modelling of mass transfer in magnetoelectrolytic cells, the effect of magnetic fields on reaction kinetics is discussed. Interactions of an imposed magnetic field with cathodic crystallization and anodic dissolution behaviour of metals are also treated. These topics are described from a practical point of view.Nomenclature 1, 2 regression parameters (-) - B magnetic field flux density vector (T) - c concentration (mol m^–3) - c bulk concentration (mol m^–3) - D diffusion coefficient (m² s^–1) - d _e diameter of rotating disc electrode (m) - E electric field strength vector (V m^–1) - E _i induced electric field strength vector (V m^–1) - E _g electrostatic field strength vector (V m^–1) - F force vector (N) - F Faraday constant (C mol^–1) - H magnetic field strength vector (A m^–1) - i current density (A m^–2) - i _L limiting current density (A m^–2) - i _L ⁰ limiting current density without applied magnetic field (A m^–2) - I current (A) - I _L limiting current (A) - j current density vector (A m^–2) - K reaction equilibrium constant - k reaction velocity constant - k _b Boltzmann constant (J K^–1) - _{m 1}, m ₂ regression parameters (-) - n charge transfer number (-) - q charge on a particle (C) - R gas constant (J mol^–1 K^–1) - T temperature (K) - t time (s) - V electrostatic potential (V) - v particle velocity vector (m s^–1) Greek symbols transfer coefficient (–) - velocity gradient (s^–1) - _MS potential difference between metal phase and point just inside electrolyte phase (OHP) - diffusion layer thickness (m) - ₀ hydrodynamic boundary layer thickness without applied magnetic field (m) - density (kg m^–3) - electrolyte conductivity (^–1 m^–1) - magnetic permeability (V s A^–1 m^–1) - kinematic viscosity (m² s^–1) - vorticity     

Determination of electrode kinetics by corrosion potential measurements: Zinc corrosion by bromine

An attractive way of determining the electrode kinetics of very fast dissolution reactions is that of measuring the corrosion potential in flowing solutions. This study analyses a critical aspect of the corrosion potential method, i.e., the effect of nonuniform corrosion distribution, which is very common in flow systems. The analysis is then applied to experimental data for zinc dissolution by dissolved bromine, obtained at a rotating hemispherical electrode (RHE). It is shown that in this case the current distribution effect is minor. However, the results also indicate that the kinetics of this corrosion system are not of the classical Butler-Volmer type. This is explained by the presence of a chemical reaction path in parallel with the electrochemical path. This unconventional corrosion mechanism is verified by a set of experiments in which zones of zinc deposition and dissolution at a RHE are identified in quantitative agreement with model predictions. The practical implications for the design of zinc/bromine batteries are discussed.Notation C _i concentration of species i (mol cm^–3) - D _` diffusivity of species i (cm² s^–1) - F Faraday constant - i _j current density of species j (A cm^–2) - i ₀ ^b exchange current density referenced at bulk concentration (A cm^–2) - J , inverseWa number - N - n number of electrons transferred for every dissolved metal atom - P _m Legendre polynomial of orderm - r ₀ radius of dise, sphere, or hemisphere - s stoichiometric constant - t ₊ transference number of metal ion - V _corr corrosion overpotential (V) Greek letters anodic transfer coefficient of Reaction 21b - _a anodic transfer coefficient of metal dissolution - _c cathodic transfer coefficient of metal dissolution - anodic transfer coefficient of zinc dissolution - velocity derivative at the electrode surface - (x) incomplete Gamma function - , exchange reaction order ofM ⁺ⁿ - , inverseWa number - _a activation overpotential (V) - _c concentration overpotential (V) - polar angle (measured from the pole) (rad) - k solution conductivity (^–1 cm^–1) - kinematic viscosity (cm² s^–1) - ₀ solution potential at the electrode surface (V) - rotation rate (s^–1) - * indicates dimensionless quantities     

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)     

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     

Anionic synthesis of ω-1,1-diphenylethylene-terminated polystyrene macromonomers. Rational synthesis of ABC hetero three-armed-star-branched polymers

Summary Polystyrene macromonomers with terminal 1,1-diphenylethylene functionality were prepared by the reaction of one equivalent of poly(styryl)lithium with 1,4-bis (l-phenylethenyl)benzene (PDDPE). The macromonomer functionalities were determined by ¹H NMR [(vinyl CH₂)=5.4 ppm] and UV spectroscopy (_max=260 nm). The stoichiometric linking reaction of poly(styryl)lithium (M_n=15.3x10³ g/mol) with an -1,1-diphenylethylene-terminated polystyrene macromonomer (M_n=5.4x10³ g/mol) followed by addition of styrene monomer has been used to prepare a hetero three-armed, star-branched polymer with M_n=5.8x10⁴ g/mol (5,400-15,300-37,300). The g value ([]b/[]l) was equal to 0.92.     

Surface treatment for mitigation of hydrogen absorption and penetration into AISI 4340 steel and Inconel 718 alloy

It is shown that the underpotential deposition of zinc on AISI 4340 steel and Inconel 718 alloys inhibits the hydrogen evolution reaction and the degree of hydrogen ingress. In the presence of monolayer coverage of zinc on the substrate surfaces, the hydrogen evolution current densities are reduced 46% and 68% compared with the values obtained on bare AISI 4340 steel and Inconel 718 alloy, respectively. As a consequence, the underpotential deposition of zinc on AISI 4340 steel and Inconel 718 alloy membrane reduces the steady state hydrogen permeation current density by 51% and 40%, respectively.List of symbols C _S surface hydrogen concentration (mol cm^–3) - D hydrogen diffusion coefficient (cm² S^–1) - E potential (V) - E _pdep predeposition potential (V) - F Faraday constant (96 500 C mol^–1) - i current density (A cm^–2) - i _a HER current density in the absence of predeposition of zinc (A cm^–2) - i ₀ exchange current density (A cm^–2) - i _p HER current density in the presence of predeposition of zinc (A cm^–2) - j _t transition hydrogen permeation current density (A cm^–2) - j _o initial hydrogen permeation current density (A cm^–2) - j steady state hydrogen permeation current density (A cm^–2) - k thickness dependent absorption-adsorption constant (mol cm^–3) - L membrane thickness (cm) - Q _max maximum charge required for one complete layer of atoms on a surface (C cm^–2) - t time (s) Greek symbols _c cathodic transfer coefficient, dimensionless - _H hydrogen surface coverage, dimensionless - _Zn zinc surface coverage, dimensionless - work function (eV) - = t D/L ² (dimensionless time)     

Reactor engineering models of complex electrochemical reaction schemes. III. Galvanostatic operation of parallel reactions in batch reactors

Batch electrochemical reactor models for parallel reaction sequences are developed for cells operating galvanostatically. Independent and dependent parallel reactions and a parallel-series reaction scheme are considered and emphasis is placed on the development of analytical expressions to predict reactor behaviour. Electro-organic synthesis reactions such as the production of betaalanine and glyoxylic acid are considered as examples. Experimental data for the electro-oxidation of aqueous oxalic acid and glyoxylic acid solutions are shown to be in reasonable agreement with the reaction analysis.Nomenclature a Parameter defined in Equation 21 - C _j ^s Surface concentration of species j - C _j Bulk concentration of species j - C _jo Initial concentration of species j - C _Bmax Maximum concentration of species B - CE Current efficiency - E Electrode potential - F Faraday constant - i _p Partial current density of step p of reaction scheme - i _t Total current density - k _fp Forward electrochemical rate constant of step p - k _Lj Mass transfer coefficient for species j - K _L Dimensionless mass transfer parameter - n _p Number of electrons in step p of reaction scheme - S Electrode area - t Reaction time - V Batch reactor volume - _p Constant describing potential dependency of reaction rate constant of reaction step p - Y ₁,Y ₂,Y ₃ Effective overall resistance factors - _g Dimensionless reaction time for galvanostatic operation - _p Dimensionless reaction time for potentiostatic operation     

Effect of gas evolution on mass transfer in an electrochemical reactor

Experiments were conducted to study the effect of gas bubbles generated at platinum microelectrodes, on mass transfer at a series of copper strip segmented electrodes strategically located on both sides of microelectrodes in a vertical parallel-plate reactor. Mass transfer was measured in the absence and presence of gas bubbles, without and with superimposed liquid flow. Mass transfer results were compared, wherever possible, with available correlations for similar conditions, and found to be in good agreement. Mass transfer was observed to depend on whether one or all copper strip electrodes were switched on, due to dissipation of the concentration boundary layer in the interelectrode gaps. Experimental data show that mass transfer was significantly enhanced in the vicinity of gas generating microelectrodes, when there was forced flow of electrolyte. The increase in mass transfer coefficient was as much as fivefold. Since similar enhancement did not occur with quiescent liquid, the enhanced mass transfer was probably caused by a complex interplay of gas bubbles and forced flow.List of symbols A electrode area (cm²) - a constant in the correlation (k = aRe ^m , cm s^–1) - C _{R, bulk} concentration of the reactant in the bulk (mol^–1 dm^–3) - D diffusion coefficient (cm² s^–1) - d _h hydraulic diameter of the reactor (cm) - F Faraday constant - Gr Grashof number =gL ³/² (dimensionless) - g gravitational acceleration (cm s^–2) - i _g gas current density (A cm^–2) - i _L mass transfer limiting current density (A cm^–2) - k mass transfer coefficient (cm s^–1) - L characteristic length (cm) - m exponent in correlations - n number of electrons involved in overall electrode reaction, dimensionless - Re Reynolds number =Ud _h^–1 (dimensionless) - Sc Schmidt number = D ^–1 (dimensionless) - Sh Sherwood number =kLD ^–1 (dimensionless) - U mean bulk velocity (cm s^–1) - x distance (cm) - _N equivalent Nernst diffusion layer thickness (cm) - kinematic viscosity (cm² s^–1) - density difference = (_L – ), (g cm^–3) - _L density of the liquid (g cm^–3) - average density of the two-phase mixture (g cm^–3) - void fraction (volumetric gas flow/gas and liquid flow)