Electrode heat balances of electrochemical cells: application to NaCl electrolysis

This paper deals with a method of estimating single electrode heat balances during the electrolysis of molten NaCl-ZnCl₂ in a cell using a-alumina diaphragm. By measuring the thermoelectric power of the thermogalvanic cells: (T) Na/-alumina/NaCl-ZnCl₂/-alumina/Na(T+dT) and (T) C,Cl₂/NaCl-ZnCl₂/Cl₂,C(T+dT) the single electrode Peltier heat for sodium deposition and for chlorine evolution at 370° C were estimated to be –0.026±0.001 JC^–1 and+0.614±0.096 J C^–1, respectively.     

Interfacial behaviour of various liquid electrode/β″-alumina systems

Three different liquid electrode/sodium-alumina interfaces were investigated. The NaNO₃/-alumina interface displays ohmic behaviour although the resistance is somewhat larger than expected. The sodium/-alumina interface exhibits asymmetric resistance with respect to d.c. current flow. Cyclic voltammetry results suggest that a Na₂O film is being modified electrochemically during the sweeps. When a sodium amalgam electrode is utilized, the film, if it is present, has very little effect. The asymmetric resistance is not observed and there is good agreement between d.c. and a.c. resistances after only a small amount of sodium deposition.     

Effects of chloride, bromide and iodide ions on internal stress in films deposited during high speed nickel electroplating from a nickel sulfamate bath

The effects of chloride, bromide and iodide additions on the internal stress developed in nickel films deposited during high speed electroplating from nickel sulfamate baths operated close to the nickel ion limiting current density were investigated. The variations in internal strain in the films were detected in situ using a resistance wire-type strain gauge placed on the reverse side of the copper substrate. The film resistance on the as-plated electrodes was measured using an electronic current interrupter technique. The effects of chloride, bromide, and iodide additions could be classified into two groups: (a) chloride and bromide ions, and (b) iodide ions. For chloride and bromide additions over the concentration range of 0.1 to 0.5M, the nickel deposits exhibited a block- and pyramid-like texture with a (200) crystal orientation. The internal tensile stress developed in 20m thick nickel films deposited in the presence of these two halides was as low as 140–170MPa. Conversely, for additions of iodide, at iodide concentrations greater than 0.1M the deposited nickel exhibited a fine granular texture of disordered crystal orientation. The internal tensile stress developed in 20m thick nickel films deposited from these latter baths tended to rise with increasing iodide concentration to values considerably higher than those observed at similar concentrations of NiCl₂ or NiBr₂.     

The use of alkali carbonates in carbon concentration cells

The feasibility of using alkali carbonates as electrolytes in carbon concentration cells has been investigated. The following cell was set up: The test electrode (LHS) was a carbon-permeable-iron membrane in contact with a gaseous or liquid metal environment whose carbon activity could be varied. Experiments involving argon and liquid sodium environments at 970 K showed that the potential of the-Fe test electrode was a function of its carbon activity.The potential of the electrode,-Fe, C ¦ CO ₃ ^2– , was also measured as a function of carbonate ion activity and current.It was concluded that the predominant electrode reaction at the iron electrode was reversible and involved carbon and carbonate species or species with which they were in equilibrium.     

Electrosynthesis of 4,4′-dinitroazobenzene on PbO2 electrodes

Parameters which affect the electrosynthesis of 4,4-dinitroazobenzene from p-nitroaniline on platinum and PbO₂ electrodes were investigated and optimum conditions were determined. Maximum conversion efficiency for electrosynthesis was 95% with a pure -PbO₂ electrode. It was found that the electrocatalytic activity of a PbO₂ electrode depends upon its / ratio and its degree of crystallinity. The effects of the added base and water on the conversion efficiency were also elucidated.     

Flow-through and flow-by porous electrodes of nickel foam Part III: theoretical electrode potential distribution in the flow-by configuration

This paper deals with the theoretical potential distribution within a flow-by parallelepipedic porous electrode operating in limiting current conditions in a two-compartment electrolytic cell. The model takes into account the influence of the counter-electrode polarization and of the separator ohmic resistance. The results show that the design of the porous electrode requires the knowledge of the solution potential distribution within the whole cell volume.Nomenclature a _c specific surface area per unit volume of electrode - C ₀ entrance concentration (y=0) - C _s exit concentration (y=y ₀) - E electrode potential (= _M – _S ) - E _o equilibrium electrode potential - F Faraday number - i current density - mean mass transfer coefficient - K parameter [a _ea zFi _oa/(_a RT)]^1/2 - L porous electrode thickness - n number of terms in Fourier serials - P specific productivity - Q volumetric flow-rate - mean flow velocity based on empty channel - V constant potential - V _R electrode volume - x thickness variable - X conversion - y length variable - y ₀ porous electrode length - z number of electrons in the electrochemical reaction Greek symbols parameter - parameter - ionic electrolyte conductivity in pores - _S solution potential - _M matrix potential ( _M = constant) - parameter [=n/y ₀ - parameter [=+K] - overpotential Suffices a anodic - c cathodic - eq equilibrium - s separator - S solution     

Kinetics and mechanism for the hydrothermal decomposition of sodium amalgam promoted on graphite electrodes containing iron

The kinetics for the hydrothermal decomposition of sodium amalgam was studied in the presence of water and caustic soda on graphite electrodes containing iron.Regression analysis of over 1000 data points in a linear regression analysis yielded the following rate expression, explaining 89% of the variance in the data, leaving 11% of the variance unexplained: r=–d(Na)/dt=187.8 (T)^–2/3 exp (– 196.9/RT) (Na)^3/4 (NaOH)^–1/5.The decomposition rate of sodium amalgam is strongly limited by the rate of diffusion of sodium metal atoms in the mercury, and also the activity of water at the active cathodic sites on the catalyst. The activation energy for charge transfer for this process is low at 196.9 cal mol^–1 or 8.5 mV.The range of variables studied was: temperature –25, 50 and 85° C; caustic concentration –10, 30 and 50 wt.%; amalgam concentration –0.1,0.2 and 0.3 mol.%, and finally with iron concentrations in the graphite matrix of – 215.9, 929.5 and 6180 ppm.List of symbols R 1.987 cal (K mol)^–1 = ideal gas law constant - ¯R M-M distance between nearest neighbours in the crystal lattice of the electrode used to calculate the Madelung constant - r i/nF = –d(Na)/dt = reaction rate giving loss of amalgam in mol min^–1 - T (273 + ° C) = absolute temperature (K) - (Na) C _Na = moll^–1 = concentration of sodium in mercury - (NaOH) C _NaOH = moll^–1 = concentration of sodium hydroxide in water solution - Z⁺, Z^– charges on cation and anion, respectively - (M) active centre on the iron promoter catalyst - i total net current density - i ₊ anode partial current density - i _– cathode partial current density - i ₀ exchange current density, ati ₊ =i _– =i ₀, where 0, and the mutually compensating anodic and cathodic current densities are present at the equilibrium potential - overpotential on the electrode,E-E ⁰ - A Arrhenius coefficient, constant - diffusion coefficient of sodium metal in mercury in cm² min^–1 - ¯K rate constant, temperature and activation energy dependent - k rate constant, independent of temperature and activation energy - a _Na (Na) =C _Na = activity of sodium in mercury and to a good approximation equal to its concentration - a _w activity of water in presence of caustic - x distance normal to the catalyst surface (cm) - dx change in distance normal to the catalyst surface - t time at which sample is collected and reaction is quenched - t₀ initial time zero - a, b the order of the reaction, or the exponential power to which the concentration is raised, as opposed to the molecularity of the reaction, or the molecules/collision. The order is empirical and the molecularity is theoretical - Y ln(- d [Na]/dt) = lnk +nlnTE _a/RT +aln(Na) +bln(NaOH), the linear least squares curve fitting program equation - B _0,1,2,3,4 coefficients for the linear least squares curve fitting program - x _i sample measurementi - d x _i-¯X = deviation from the average - standard deviation, d²/¯n - ² variance, or the mean squared deviation from the mean, d ²/¯n - ¯X arithmetic mean,x ₁ +x ₂ + ... x_n/¯n - ¯n total number of measurements.     

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)     

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     

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

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

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.     

Shape-selective alkylation of biphenyl over mordenite: cerium exchanged sodium mordenite and unmodified H-mordenite with low SiO2/Al2O3 ratio

Liquid phase isopropylation of biphenyl with propylene was studied over a cerium exchanged sodium mordenite (Ce/NaM25) and a H-mordenite (HM25) with the same SiO₂/Al₂O₃ ratio of 25. Shape-selective catalysis occurred to give 4,4-diisopropylbiphenyl (4,4-DIPS) in high selectivity over Ce/NaM25 under any propylene pressures. HM25 gave 4,4-DIPS shape-selectively under high propylene pressures. However, the reaction was severely deactivated at a conversion of ca. 60% under such a low pressure as 0.8 kg/cm² because of coke formation in the pore. The yields of 4-isopropylbiphenyl (4-IPBP) and 4,4-DIPB decreased with the increase of those of 3-IPBP and 3,4-DIPB because of non-selective alkylation and isomerization at external acid sites that are alive in spite of severe deactivation. No significant isomerization of 4,4-DIPB over Ce/NaM25 was observed even at low propylene pressure. In the case of HM25, the isomerization of 4,4-DIPB to 3,4-DIPB occurred significantly under low propylene pressures, while it decreased under high pressure. These differences are ascribed to the differences of nature of acid sites between Ce/NaM25 and HM25 zeolites.     

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     

Flow-through and flow-by porous electrodes of nickel foam Part IV: experimental electrode potential distributions in the flow-through and in the flow-by configurations

Experimental distributions of the solution potential in flow-through and flow-by porous electrodes of nickel foam operating in limiting current conditions are presented. These are in good agreement with the corresponding theoretical distributions. In the case of a flow-by configuration used in a two-compartment cell, the experiments confirm the validity of the models, presented in Part III, which take into account the presence of a separator (ceramic porous diaphragm or ion exchange membrane).Nomenclature a _e specific surface area per unit volume of electrode - C ₀ entrance ferricyanide concentration (y=0) - D molecular diffusion coefficient of ferricyanide - E _e cathode potential - F Faraday number - mean (and local) mass transfer coefficient - L electrode thickness - L _s-L separator thickness - m number of sheets of foam in a stack - n number of terms in Fourier series - Q volumetric flow-rate - r _s ohmic specific resistance of the separator - mean flow velocity based on empty channel - V constant potential - X conversion - x coordinate for the electrode thickness - y coordinate for the electrode length - y ₀ length of the porous electrode - z number of electrons in the electrochemical reaction Greek symbols parameter - parameter - ionic electrolyte conductivity - _sc solution potential in the pores of the cathode - _M matrix potential ( _sc = constant) - parameter [=n/y ₀] - electrolyte density - mean porosity - kinematic viscosity - E _c potential drop in the porous cathode - potential drop defined in Fig. 5 Indices c cathodic - o electrolyte alone - s separator     

The vinylation of bromobiphenyls using homogeneous nickel catalysts

The vinylation of 4-bromo-4-hydroxybiphenyl and ethyl acrylate was studied using the catalyst NiCl₂-H₂O/PPh₃ in the presence of inorganic base. Ethyl 4-(4-hydroxyphenyl)cinnamate was formed as vinylation product with a selectivity as high as 98%. The effect of solvent, ligand and base for some halides was examined to show the applicability of the catalyst system.     

Living cationic polymerization of vinyl ethers with a functional group

Summary Living polymerizations of 2-vinyloxyethyl methacrylate and 2-vinyloxyethyl cinnamate were successfully performed with a mixture of hydrogen iodide and iodine (HI/I₂) as an initiating system in toluene at –15 to –40 °C, Although the two monomers have an unsaturated ester pendant group, their living polymerizations proceeded exclusively via the vinyloxyl group without undesirable side reactions of the pendant group. The product polymers had a very narrow molecular weight distribution (Mw/Mn 1.1), and {Mn} directly proportional to monomer conversion. For both vinyloxyethyl monomers, the addition of a new feed of monomer to a polymerization mixture led to an increase in polymer molecular weight which was again proportional to the conversion.     

The estimation of the residual capacity of sealed lead-acid cells using the impedance technique

The problem of estimating the residual usable energy of a lead-acid cell has been intensified by the introduction of fully sealed units. These rely on the recombination of gaseous oxygen produced during overcharge at the positive electrode with the active material at the negative electrode. This introduction has removed the possibility of electrolyte density measurements, third electrode measurements and restricted residual capacity assessments to the two cell terminals. A method for this process is described using a parameter based on a characteristic frequency. The parameter is also a useful measure of cell ageing.Nomenclature R _SOL Ohmic resistance of cell () - Charge-transfer resistance of positive and negative electrodes () - CL Double-layer capacitance of both positive and negative electrodes (F) - Warburg diffusion (S^–1/2) - C _EXT External series capacitor in analogue Fig. 5 (F) - R _EXT External resistor in parallel withC _EXT in the anologue circuit Fig. 5 () - IND Inductor in Fig. 5 representing the geometrical effects of the cell at high frequencies (Henries) - R _IND External resistor in parallel with IND in the analogue circuit Fig. 5 () - Roughness factor allowing for the porosity of both electrodes     

Current distribution in a two-dimensional narrow gap cell composed of a gas evolving electrode with an open part

On the basis of the observation of gas bubbles evolved by electrolysis, a two-dimensional vertical model cell composed of electrodes with open parts for releasing gas bubbles to the back side is proposed. The model cell consists of two layers. One layer forms a bubble curtain with a maximum volume fraction of gas bubbles in the vicinity of the working electrode with open parts. The other. being located out of the bubble layer, is a convection layer with a small volume fraction distributed in the vertical direction under forced convection conditions. The cell resistance and the current distribution were computed by the finite element method when resistivity in the back side varied in the vertical direction along the cell. The following three cases for overpotential were considered: no overpotential, overpotential of the linear type and overpotential of the Butler-Volmer type. It was found that the cell resistance was determined not only by the interelectrode gap but also by the percentage of open area and in some cases by the superficial surface area. The cell resistance varied only slightly with the distribution of the bubble layer in the back side.Nomenclature b linear overpotential coefficient given byb=/i - C proportionality constant given by Equation 15 - d ₁ distance between front side of working electrode and separator - d ₂ thickness of separator - F Faraday constant - I total current per half pitch - i current density at working electrode - i ₀ exchange current density - L length of a real electrolysis cell - n number of electrons transferred in electrode reaction - O _p percentage of open area given by Equation 1 - p pitch, i.e. twice the length of the unit cell, defined by 2(BC) in Fig. 4 - q thickness of bubble curtain, defined by (AM) in Fig. 4 - R gas constant - r _t total cell resistance - r unit-cell resistance defined by (V – V _eq)/I - r _rs residue ofr from sum ofr ₀ andr - r ₀ ohmic resistance of solution when0 _p=0 - r resistance due to overpotential when0 _p=0 - s electrode surface ratio or superficial surface area given by Equation 2 for the present model - T absolute temperature - t thickness of working electrode defined by EF in Fig. 4 - V cell voltage - V _eq open circuit potential difference between working and counter electrodes - solution velocity in cell - ₀ solution velocity at bottom of cell - w width of working electrode, defined by 2(DE) in Fig. 4 - x abscissa located on cell model - y ordinate located on cell model - anodic transfer coefficient - linear overpotential kinetic parameter defined byb/[_bc(p/2)] - d infinitesimally small length on the boundary - volume fraction of gas bubbles in cell - dimensionless cell voltage defined bynF(V – V _eq)/RT - overpotential at working electrode - Butler-Volmer overpotential kinetic parameter defined by [nFi _0bc(p/2)]/RT - coordinate perpendicular to boundary of model cell - ₁ resistivity of bubble-free solution - ₂ resistivity of separator - _bc resistivity of bubble curtain - potential in cell     

Note of the estimation of the Θ temperature and Ψ parameter from the critical temperature data

Summary Critical values of the polymer volume fraction _2,c and the interaction parameter _c have been computed for the case that the equation for the chemical potential of solvent contains terms _{c 2} ³ and _{c 2} ⁴ in addition to ₂ ² . For 0 _c 1/3, the limits for infinite chain length are _2,c = 0 and _c = 0.5. Quite different results are obtained for _c > 1/3, _2,c being finite and _c lower than 1/2. Conclusions for the estimation of the temperature and the entropy-of-dilution parameter are discussed.     

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