A model of the electrochemical behaviour within a stress corrosion crack

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

Effects of gas bubbles on the current and potential profiles within porous flow-through electrodes

This paper presents a mathematical model to calculate the distributions of currenti(x), potentialE(x), gas void fraction (x) and pore electrolyte resistivity (x) within porous flow-through electrodes producing hydrogen. It takes into consideration the following effects: (i) the kinetics of the interfacial charge transfer step, (ii) the effect of the non-uniformly generated gas bubbles on the resistivity of the gas-electrolyte dispersion within the pores of the electrode (x) and (iii) the convective transport of the electrolyte through the pores. These effects appear in the form of three dimensional groups i.e.K=i _o L where i_o is the exchange current density, is the specific surface area of the electrode andL its thickness.= ⁰ L where ⁰ is the pore electrolyte resistivity and =/Q where is a constant, =tortuosity/porosity of the porous electrode andQ is the superficial electrolyte volume flow rate within it. Two more dimensionless groups appear: i.e. the parameter of the ohmic effect =K/b and the kinetic-transport parameterI=K. The model equations were solved fori(x),E(x), (x) and (x) for various values of the above groups.Nomenclature specific surface area of the bed, area per unit volume (cm^–1) - b RT/F in volts, whereR is the gas constant,T is the absolute temperature (K) - B =[1–(I ² Z/4)], Equation 9a - C =(1–B ²), Equation 9b - E(L) potential at the exit face (V) - E(0) potential at the entry face (V) - E(x) potential at distancex within the electrode (V) - E _rev reversible potential of the electrochemical reaction (V) - F Faraday's constant, 96500 C eq^–1 - i _o exchange current density of the electrode reaction (A cm^–2 of true surface area) - i(L) current density at the exit face (A cm^–2 of geometrical cross-sectional area of the packed bed) - I K =i _oL(/Q) (dimensionless group), Equation 7d - K =i _oL, effective exchange current density of the packed bed (A cm^–2) Equation 7a - L bed thickness (cm) - q tortuosity factor (dimensionless) - Q superficial electrolyte volume flow rate (cm³ s^–1) - x =position in the electrode (cm) - Z =exp [(0)], Equation 7f - transfer coefficient, =0.5 - =K/b=(i ₀ L ⁰ L)/b (dimensionless group) Equation 7e - (x) gas void fraction atx (dimensionless) - = ⁰ L, effective resistivity of the bubble-free pore electrolyte for the entire thickness of the electrode ( cm²) - (0) polarization at the entry face (V) - (L) polarization at the exit face (V) - =q/, labyrinth factor - constant (cm³ C^–1), Equation 3a - =/Q (A ^–1) conversion factor, Equation 3b - porosity of the bed - (x) effective resistivity of the gas-electrolyte dispersion within the pores ( cm) - ⁰ effective resistivity of the bubble-free pore electrolyte ( cm)     

An investigation of some Schiff bases as corrosion inhibitors for austenitic chromium–nickel steel in H2SO4

The corrosion inhibition of austenitic chromium–nickel steel by two Schiff bases, N-(1-toluidine)salicylaldimine and N-(2-hydroxyphenyl)salicylaldimine, was investigated in sulphuric acid medium. The effect of concentration and temperature on inhibition properties was determined. It was found that when the concentrations of inhibitor were increased the inhibition efficiencies () and surface coverage () increased. Some thermodynamic parameters such as free energy of adsorption, G _ads, and enthalpy, H, were determined for the Schiff bases. Experimental results agree with the Temkin isotherm for N-(1-toluidine)salicylaldimine, but the Langmuir isotherm is more appropriate for N-(2-hydroxyphenyl)salicylaldimine.     

Transition layer thickness in microlaminar deposits

A theoretical analysis was carried out on the change of composition of a deposit obtained by the dual pulse method of forming laminar metal foils, with transition from a low current to a high current pulse, both in the galvanostatic and the potentiostatic mode of deposition. It was shown that the existence of a transition layer of varying composition between a layer of pure metal 1 and a layer consisting predominantly of the metal 2 is an inherent consequence of the electrochemical process, primarily because of an induction period in the concentration polarization with respect to ions of metal 1. The importance of this transition layer increases as the thickness of the layers of the two metals decreases. Eventually this limits the possibility of obtaining a sharp boundary between the layers, when the nanometre region of layer thickness is reached. Equations are given for calculating the deposition current density and rate of stirring of the electrolyte which provide a deposit of a required level of metal 1 in the layer of metal 2, as well as a required sharpness of the boundary between two layers. Experimental proof of the correctness of the analysis was sought. It was found that significant changes in the properties of the deposit occur in the same range of layer thickness in which the transition of the composition takes places.Nomenclature _c,1, a_c,2 transfer coefficient of the cathodic processes - C interfacial capacitance - C₁, C₂ concentration of the ions of metals 1 and 2 at the interface r - C ₀ ¹ , C ₀ ² concentration of ions of the metals 1 and 2 in solution - D ₁ diffusion coefficient for the diffusion of ions of the metal 1 - E _r,1,E _r,2 reversible potentials of metals 1 and 2, respectively - F the Faraday constant - J ₀ ¹ ,J ₀ ² exchange current density of the metals 1 and 2, respectively - M ₁,M ₂ atomic weights of the metals 1 and 2, respectively - kinematic viscosity of solution - ₁, ₂ densities of the metals 1 and 2 respectively - rotation speed (r.p.s.) - z number of electrons exchanged in the deposition process 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.     

Synthesis of new metal-containing side-chain monomers and polymers

New metal-containing vinyl monomers, hexyl-6-oxy-{4-[4-(4-carboxy cyclopentadienyl manganese tricarbonyl phenyl)phenyl]benzoyloxy}methacrylate and hexyl-6-oxy-{4-[4-(4-ferrocenoyl phenyl)phenyl]benzoyloxy}methacrylate, and the corresponding homopolymers and random copolymers with hydroxy monomer hexyl-6-oxy-{4-[4-(4-hydroxyphenyl)phenyl]benzoyloxy}methacrylate were synthesized. The compounds were characterized by¹H NMR; their thermal behavior was investigated by means of differential scanning calorimetry. Monomers and polymers containing the ferrocene unit melt at lower temperatures than those derived from the cyclopentadienyl managanese tricarbonyl moiety. The melting temperatures of the monomers and polymers ranged from 399 to about 515 K, Both monomers and polymers failed to exhibit mesogenic behavior. Values ofM _n,M _w,M _w/M _n, and degree of polymerization were obtained by gel permeation chromatography. TheM _n ranged from 16,500 for the copolymer containing hexyl-6-oxy-{4-[4-(4-ferrocenoyl phenyl)phenyl] benzoyloxy}methacrylate and hydroxy monomer hexyl-6-oxy-{4-[4-(4-hydroxyphenyl)phenyl]benzoyloxy}methacrylate at a 1:3 ratio to 26,000 for the copolymer containing hexyl-6-oxy-{4-[4-(4-carboxy cyclopentadienyl manganese tricarbonyl phenyl)phenyl]benzoyloxy}methacrylate and hydroxy monomer hexyl-6-oxy-{4-[4-(4-hydroxyphenyl)phenyl]benzoyloxy}methacrylate at a 1:3 ratio.M _w/M _n ranged from 1.6 in the case of the copolymer containing hexyl-6-oxy-{4-[4-(4-carboxy cyclopentadienyl manganese tricarbonyl phenyl)phenyl]benzoyloxy}methacrylate and hydroxy monomer hexyl-6-oxy-{4-[4-(4-hydroxyphenyl)phenyl]benzoyloxy}methacrylate at a 1:3 ratio to 2.2 in the case of poly(hexyl-6-oxy{4-[4-(4-carboxy cyclopentadienyl manganese tricarbonyl phenyl)phenyl]benzoyloxy}methacrylate).     

Analysis of the inductance influence on the measured electrochemical impedance

The high-frequency region of the impedance diagram of an electrochemical cell can be deformed by the inductance of the wiring and/or by the intrinsic inductance of the measuring cell. This effect can be noticeable even in the middle frequency range in the case of low impedance systems such as electrochemical power sources. A theoretical analysis of the errors due to inductance effects is presented here, on the basis of which the admissible limiting measuring frequency can be evaluated. Topology deformations due to the effect of inductance in the case of a single-step electrochemical reaction are studied by the simulation approach. It is shown that an inductance can not only change the actual values of the parameters (electrolytic resistance, double layer capacitance, reaction resistance), but can also substantially alter the shape of the impedance diagram, this leading to erroneous structure interpretations. The effect of the size and surface area of the electrode on its intrinsic inductance is also evaluated.Nomenclature A linear dimension of the surface area confined by the circuit (cm) - C _D double layer capacitance (F) - C _M measured capacitance - d diameter of the mean effective current line (mm) - f _max limiting (maximum) frequency of measurement (Hz) - K ₁,K ₂ shape coefficients with values of 2×10^–9 and 0.7 for a circle, and 8×10^–9 and 2 for a square (dimensionless) - L intrinsic inductance of the electrochemical cell assumed as an additive element (H) - R _E electrolyte resistance () - R _M measured resistance () - R _P reaction resistance () - r ₀ specific resistance ( cm) - S electrode surface area (cm²) - T _c time constant (s) - Z impedance () - Z _lm imaginary component of the impedance without accounting for the influence of inductance () - Z _lm imaginary component of the impedance accounting for the influence of the additive inductance () - shape coefficient; =1 for a square and =^1/2/2 for circle (dimensionless) - _L relative complex error due to the influence of inductance (dimensionless) - _L ^A relative amplitude error due to inductance (%) - ^L relative phase error due to inductance (%) - ratio between the effective inductance time constant and the capacitive time constant (dimensionless) - angular frequency (s^–1) - _R characteristic frequency at which the inductive and capactive parts of the imaginary component of impedance are equal (s^–1)     

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.     

Lamellar Morphology of Poly(3-hydroxybutyrate)/Poly(ethylene oxide) Blends as Studied via Small Angle X-ray Scattering

The lamellar morphology of a melt-miscible blend consisting of two crystalline constituents, poly(3-hydroxybutyrate) (PHB) and poly(ethylene oxide) (PEO) have been investigated by means of small angle X-ray scattering (SAXS). The blend was a crystalline/amorphous system when temperatures lay between the melting point of PEO (ca. T _m ^PEO=60C) and that of PHB (ca. T _m ^PHB=170C), while it became a crystalline/crystalline system below T _m ^PEO. The crystalline microstructures of the blends were induced by two types of crystallization history, i.e. one-step and two-step crystallizations. In the one-step crystallization, the blends were directly quenched from the melt to room temperature to allow simultaneous PHB and PEO crystallization. The two-step crystallization involved first cooling to 70C to allow PHB crystallization for 72 h followed by cooling to room temperature (ca. 19C) to allow PEO crystallization. In the crystalline/crystalline state, two scattering peaks have been observed in the Lorentz-corrected SAXS profiles, irrespective of the crystallization histories, meaning that crystallization created separate PHB and PEO lamellar stack domains. One-step crystallization yielded lamellar stack domains containing almost pure PHB and PEO lamellae. Two-step crystallization generated almost pure PHB lamellar domains and the PEO lamellar domains with inserted PHB lamellae. In the crystalline/amorphous state, the composition dependence of the amorphous layer thickness (l _a), the presence of zero-angle scattering, and the volume fraction of the PHB lamellar stack (_s) revealed that both one-step and two-step crystallizations, generated the interfibrillar segregation morphology, where the extent of interfibrillar segregation of amorphous PEO increased with increasing PEO content.     

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     

Durability and thermal cycling of Ni/YSZ cermet anodes for solid oxide fuel cells

The long-term properties of Ni/yttria stabilized zirconia (YSZ) cermet anodes for solid oxide fuel cells were evaluated experimentally. A total of 13 anodes of three types based on two commercial NiO powders were examined. The durability was evaluated at temperatures of 850 C, 1000 C and 1050 C over 1300 to 2000h at an anodic d.c. load of 300mA cm^–2 in hydrogen with 1 to 3% water. The anode-related polarization resistance, R _P, was measured by impedance spectroscopy and found to be in the range of 0.05 to 0.7 cm². After an initial stabilization period of up to 300h, R _P varied linearly with time within the experimental uncertainty. At 1050 C no degradation was observed. At 1000 C a degradation rate of 10 m cm² per 1000 h was found. The degradation rate was possibly higher at 850 C. A single anode was exposed to nine thermal cycles from 1000 to below 100 C at 100 C h^–1. An increase in R _P of about 30m cm² was observed over the first two cycles. For the following thermal cycles R _P was stable within the experimental uncertainty.     

Syntheses and Properties of Aromatic Polyimides Based on 1,1-Bis[4-(4-aminophenoxy)phenyl]-1-phenyl-2,2,2-trifluoroethane and 1,1-Bis[4-(4-aminophenoxy)phenyl]-1-phenylethane

A series of fluorinated polyimides were prepared from 1,1-bis[4-(4-aminophenoxy)phenyl]-1-phenyl-2,2,2-trifluoroethane with various aromatic tetracarboxylic dianhydrides via a conventional two-step procedure. These polyimides were amorphous in nature and afforded flexible and tough films. Some polyimides derived from less stiff dianhydrides were soluble in polar organic solvents. The glass-transition temperatures (T _g) of these polyimides ranged from 252 to 324C, and softening temperatures (T _s) stayed in the 254322C range. Decomposition temperatures (T _d) at 10% weight loss all occurred above 569C in both air and nitrogen atmospheres. For a comparative study, another series of analogous polyimides based on 1,1-bis[4-(4-aminophenoxy)phenyl]-1-phenylethane were also pepared and characterized.     

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.     

Modelling of time-dependent performance criteria in a three-dimensional cell system during batch recirculation copper recovery

A three-dimensional electrode cell with cross-flow of current and electrolyte is modelled for galvanostatic and pseudopotentiostatic operation. The model is based on the electrodeposition of copper from acidified copper sulphate solution onto copper particles, with an initial concentration ensuring a diffusion-controlled process and operating in a batch recycle mode. Plug flow through the cell and perfect mixing of the electrolyte in the reservoir are assumed. Based on the model, the behaviour of reacting ion concentration, current efficiency, cell voltage, specific energy consumption and process time on selected independent variables is analysed for both galvanostatic and pseudopotentiostatic modes of operation. From the results presented it is possible to identify the optimal values of parameters for copper electrowinning.List of symbols a specific surface area (m^–1) - A cross-sectional area (mu²) - a _a Tafel constant for anode overpotential (V) - a _II Tofel constant for hydrogen evolution overpotential (V) - b _a Tafel coefficient for anode overpotential (V decade^–1) - b _H Tafel coefficient for hydrogen evolution overpotential (V decade^–1) - C _e concentration at the electrode surface (m) - C _L cell outlet concentration (m) - C ₀ cell inlet concentration (m) - C ₀ ⁰ initial cell inlet concentration att = 0 (m) - d _p particle diameter (m) - e, e _p current efficiency and pump efficiency, respectively - E specific energy consumption (Wh mol^–1) - E solution phase potential drop through the cathode (V) - F Faraday number (C mol^–1) - h interelectrode distance (m) - i, i _L current density and limiting current density, respectively (A m^–2) - I, I _L current and limiting current, respectively (A) - I _H partial current for hydrogen evolution (A) - k _L mass transfer coefficient (m s^–1) - L bed height (m) - l bed depth (m) - M molecular weight (g mol^–1) - N power per unit of electrode area (W m^–2) - n exponent in Equation 19 - P pressure drop in the cell (N m^–2) - Q electrolyte flow rate (m³ h^–1) - R Universal gas constant (J mol^–1 K^–1) - r _e electrochemical reaction rate (mol m^–2 h^–1) - t _c critical time for operating current to reach instantaneous limiting current (s) - t _p process time to reach specified degree of conversion (s) - T temperature (K) - u electrolyte velocity (m s^–1) - U total cell voltage (V) - U ₀ reversible decomposition potential (V) - U _ohm ohmic voltage drop between anode and threedimensional cathode (V) - V volume of electrolyte (m³) - z number of transferred electrons Greek letters ratio of the operating and limiting currents - _{A, a} anodic activation overpotential (V) - _{c, e} cathodic concentration overpotential (V) - bed voidage - _H void fraction of hydrogen bubbles in cathode - constant (Equation 2) - ₀ electrolyte conductivity (ohm^–1 m^–1) - v electrolyte kinematic viscosity (m² s^–1) - _d diaphragm voltage drop (V) - _H voltage drop due to hydrogen bubble containing electrolyte in cathode (V) - electrolyte density (kg m^–3) - _p particle density (kg M^–3) - reservoir residence time (s)     

New polyisobutylene based model ionomers

Three-arm star polyisobutylene ionomers (¯M_n=8800) with terminal SO₃ M (M=K or Ca²) groups were synthesized and their mechanical properties investigated. Compression molded films displayed high elongations, i.e., -1000% for Ca² ionomers with lower values for the K counterions. Strain induced crystallinity was observed at higher elongations. Mechanical properties in general compared favorably with conventional covalently linked rubbery networks and were comparable and in some cases superior to EPDM-based ionomers carrying randomly distributed SO₃ M groups.For the first two parts see Proceedings, 28th IUPAC Macromolecular Symposium, Amherst, MA, July 11–16, 1982, p. 905 and 906     

Cooperative inclusion of sodium 1-pyrenesulfonate by γ-cyclodextrin

Summary The interaction of -cyclodextrin(-CD) with sodium 1-pyrenesulfonate(PS) was studied spectrophotometrically. -CD was found to cause much larger decrease in the absorption maxima of PS than -CD. The fluorescence spectra of PS in the presence of -CD showed excimer emission, while those of PS with -CD showed only monomer emission, indicating that -CD forms 12 (-CDPS) complexes in which two PS molecules are included in the -CD cavity in a face-to-face fashion. The binding isotherm showed a sigmoidal curve. The association constants were estimated by computer simulation of the binding curve. The 12 (CDPS) complex was found to be much more stable (K=10⁶ M^–1) than the 11 complex (K=1 M^–1). At high concentration of -CD another -CD cooperates in binding two PS molecules, resulting in the formation of a 22 complex.     

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

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

Behaviour of a tall vertical gas-evolving cell. Part I: Distribution of void fraction and of ohmic resistance

Electrolysis of a 22 wt % NaOH solution has been carried out in a vertical tall rectangular cell with two segmented electrodes. The ohmic resistance of the solution between a segment pair has been determined as a function of a number of parameters, such as, current density and volumetric rate of liquid flow. It has been found that the ohmic resistance of the solution during the electrolysis increases almost linearly with increasing height in the cell. Moreover, a relation has been presented describing the voidage in the solution as a function of the distance from the electrodes and the height in the cell.Notation A _e electrode surface area (m²) - a _s parameter in Equation 12 (A^–1) - b _s parameter in Equation 12 - d distance (m) - d _ac distance between the anode and the cathode (m) - d _wm distance between the working electrode and an imaginary separator (m) - F Faraday constant (C mol^–1) - h height from the leading edge of the working electrode corresponding to height in the cell (m) - h _e distance from the bottom to the top of the working electrode (m) - h _s height of a segment of working electrode (m) - I current (A) - I ₂₀ current for segment pair 20 (A) - I _1–19 total current for the segment pairs from 1 to 19 inclusive (A) - I _x-19 total current for the segment pairs fromx to 19 inclusive (A) - i current density A m^–2 - N _s total number of gas-evolving pairs - n ₁ constant parameter in Equation 8 - n _a number of electrons involved in the anodic reaction - n _c number of electrons involved in the cathodic reaction - n _s number of a pair of segments of the segmented electrodes from their leading edges - Q _g volumetric rate of gas saturated with water vapour (m³ s^–1) - Q ₁ volumetric rate of liquid (m³ s^–1) - R resistance of solution () - R ₂₀ resistance of solution between the top segments of the working and the counter electrode () - R _p resistance of bubble-free solution () - R _p,20 R _p for segment pair 20 () - r _s reduced specific surface resistivity - r _s,0 r _s ath=0 - r _s,20 r _s for segment pair 20 - r _s, r _s for uniform distribution of bubbles between both the segments of a pair - r _s,,20 r _s, for segment pair 20 - S _b bubble-slip ratio - S _b,20 S _b at segment pair 20 - S _b,h S _b at heighh in the cell - T temperature (K) - V _m volume of 1 mol gas saturated with water vapor (m³ mol^–1) - v ₁ linear velocity of liquid (m s^–1) - v _1,0 v ₁ through interelectrode gap at the leading edges of both electrodes (m s^–1) - W _e width of electrode (m) - X distance from the electrode surface (m) - Z impedance () - Z real part of impedance () - Z imaginary part of impedance () - resistivity of solution ( m) - _p resistivity of bubble-free solution ( m) - gas volumetric flow ratio - ₂₀ at segment pair 20 - _s specific surface resistivity ( m²) - _{s, p s} for bubble-free solution ( m²) - thickness of Nernst bubble layer (m) - ₀ ath=0 (m) - voidage - _x,0 atx andh=0 - _0,0 voidage at the leading edge of electrode wherex=0 andh=0 - _,h voidage in bulk of solution at heighth - ₂₀ voidage in bubble of solution at the leading edge of segment pair 20     

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     

Weak Gel Behaviour of Poly(vinyl alcohol)-Borax Aqueous Solutions

Thermal transition of PVA-borax aqueous gels with a PVA concentration of 60 g/L and a borax concentration of 0.28 M was investigated at temperatures ranging from 15 to 60C using static light scattering (SLS), dynamic light scattering (DLS), and dynamic viscoelasticity measurements. Three relaxation modes, i.e. two fast and one slow relaxation modes, were observed from DLS measurements. Two fast relaxation modes located around 10^–310¹ sec, with one fast mode (_f1) being scattering vector q-dependent and the other fast mode (_f2, with _f2>_f1) being q-independent. The _f1 mode was attributed to the gel mode whilst the _f2 mode could be due to the hydrodynamics of intra-molecular hydrophobic domains formed by uncharged segments of polymer backbones. The slow relaxation mode with relaxation time located around 10¹10³ sec in DLS data was due to the motion of aggregated clusters and was observed only at temperatures above 40C. The amplitude and relaxation time of slow mode decrease as temperature is increased from 40 to 60C. At temperatures below 40C, no slow relaxation mode was observed. The SLS measurements showed PVA-borax-water system had fractal dimensions D _f2.4 and D _f2.0 as temperature was below and above 40C, respectively. The simple tilting test indicated gel behaviour for the PVA-borax aqueous system at temperatures below 40C with a creep flow after a long time exposure in the gravity field. But the dynamic viscoelasticity measurements demonstrated a solution behaviour for PVA/borax/water at temperatures below 40C, the critical gel point behaviour for G() and G() was not observed in this system as those reported for chemical crosslinked gels. These results suggest that the PVA-borax aqueous system is a thermoreversible weak gel.     

Synthesis of ternary Li–Mn–O phase at a temperature of 260 ∘C and electrochemical lithium insertion into the oxide

A lithium–manganese oxide, Li _x MnO₂ (x=0.30.6), has been synthesized by heating a mixture (Li/Mn ratio=0.30.8) of electrolytic manganese dioxide (EMD) and LiNO₃ in air at moderate temperature, 260 C. The formation of the Li–Mn–O phase was confirmed by X-ray diffraction, atomic absorption and electrochemical measurements. Electrochemical properties of the Li–Mn–O were examined in LiClO₄-propylene carbonate electrolyte solution. About 0.3 Li in Li _x MnO₂ (x=0.30.6) was removed on initial charging, resulting in characteristic two discharge plateaus around 3.5V and 2.8V vs Li/Li⁺. The Li _x MnO₂ synthesized by heating at Li/Mn ratio=0.5 demonstrated higher discharge capacity, about 250mAh (g of oxide)^–1 initially, and better cyclability as a positive electrode for lithium secondary battery use as compared to EMD.