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.     

On the Charge Carrier Concentration in Sodium–Calcium Aluminophosphate Glasses

The dc and ac conductivities of the xNa₂O–(35 – x)CaO–7.5Al₂O₃–57.5P₂O₅glasses (mol %) with x= 0–35 are studied in the frequency range from 20 Hz to 1 MHz at different temperatures. It is found that the dc conductivity strongly depends on xonly for glasses with x 10. For glasses with x 5, the dc conductivity is virtually composition independent. The dependence of the ac conductivity plotted on the log(()/_dc) vs. log(/_dc) coordinates is analyzed. The ac conductivity represented in these coordinates depends on xonly for glasses with x 5, in which the dc conductivity does not depend on x. For glasses with xin the range from 10 to 35, all the isotherms of the ac conductivity closely coincide with each other. This result is discussed in the framework of two hypotheses: (1) the conductivity () is determined by the dynamic polarization (of the Maxwell–Wagner type at low frequencies) of the material due to spatial fluctuations of the density of paths providing the migration of sodium ions and (2) the concentration of charge carriers is independent of x.     

Electrochemical behaviour of viologen-cyclodextrin inclusion complexes. The case of non-alkyl group substituted viologen

The electrochemical behavior of non-alkyl substituted viologen, 4,4-dibenzyl bipyridinium (BzV), 4,4-dicyanophenyl bipyridinium (CyV) and -,-,-cyclodextrin (, , -CD) was studied using cyclic voltammetry and a spectroelectrochemical method. It was found that BzV and Fe(CN) ₆ ^4– formed a charge-transfer (CT) complex with a ratio of 21 and the colour of the solution faded with the addition of an electrolyte. This behaviour is the same as in then-heptyl viologen and ferrocyanide system [1]. BzV, -CD and -CD formed an inclusion complex only in the reduced state, whilst BzV and -CD formed an inclusion complex in both the oxidized and the reduced state. An EC scheme in which a chemical reaction follows an electrochemical reaction was considered to predominate in the BzV and -, -CD systems, while a CE scheme in which a chemical reaction preceded an electrochemical reaction predominated in the BzV and -CD system. On the other hand, CyV was found to form an inclusion complex with -, -, -CD in both the oxidized and the reduced states. therefore a CE scheme was considered to predominate in the CyV--, -, -CD systems.     

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).     

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     

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.     

Dynamic mechanical properties of crosslinked polyisoprene under deformation

Summary Molecular motions of elastomers under deformations were observed through dynamic mechanical measurements. Composite master curves of dynamic moduli E and E and loss tangent tan over a wide range of frequency and in a state of elongation were obtained by the time-temperature superposition procedure. It is found that both moduli increase with strain, . The slope of the dispersion curve of E become more gradual with the increase in , while that of E is almost unchanged. The increment of E is generally larger than that of E, which does not agree with the N. W. Tschoegl prediction, E ^* ()=f() E _o ^* (), where E ^* () and E _o ^* () are complex moduli at the strain of and O, respectively, and f() is the function of only . The difference in the strain dependence of E from E was found to correspond to the strain dependence of the equilibrium modulus.     

A wall-jet electrode reactor and its application to the study of electrode reaction mechanisms Part I: Design and construction

A wall jet electrode reactor possessing a laminar flow regime, suitable for mechanistic studies, is reported. This reactor is different from those described in the literature in the size of its working electrode surface area. The reactor is evaluated by means of mass transport-limited current measurements using as a model reaction the reduction of ferricyanide ions at a platinum electrode surface from a 0.01 m K₃Fe(CN)₆-0.01 m K₄Fe(CN)₆ solution containing 1 m KCl as supporting electrolyte. The dependence of the mass transport-limited current on the crucial reactor parameters — the volume flow rate V _f (m³ s^–1), the nozzle diameter a (m) and the radius of the working electrode R (m) — is established and verified by theoretical predictions. The reactor is shown to have the desired wall jet hydrodynamics for: 1.6 × 10^–6 V _f 4.3 × 10^–6 m³ s^–1, 1.5 × 10^–3 a 3 × 10^–3 m and 1.5 × 10^–2 R 2 × 10^–2 m.List of symbols a nozzle diameter (m) - C _A concentration of A in the bulk (mol m^–3) - D _A diffusion coefficient of A (m² s^–1) - F Faraday's constant (C mol^–1) - dynamic viscosity (gm^–1 s^–1) - H distance between the working electrode and the tip of the nozzle (m) - I _lim mass-transport-limited current (A) - k _r constant linking the typical velocity of the wall-jet to the mean velocity in the nozzle - v kinematic viscosity (m² s^–1) - n number of electrons exchanged - density (g m^–3) - R radius of the working electrode (m) - t time (s) - V _f volume flow rate (m^–3 s^–1)     

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     

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)     

Convective Regime of Filtration Combustion of Energetic Materials in a Cocurrent Flow of Their Combustion Products

The convective regime of filtration combustion of energetic materials in a cocurrent flow of their combustion products is studied using a model with extremely simplified kinetics and heat transfer, which shows instability of the process. It is shown that the more accurate twotemperature model describes a steadystate regime. In this regime, the gas temperature on the hot boundary of the heating zone is well below the combustion temperature, and the solidphase temperature is well below the temperature proposed in recent studies on this topic. It is pointed out that the twotemperature approach is unjustified and intragranular nonisothermicity must be taken into account for convective regimes. It is shown that the threetemperature model, which takes into account this effect, does not give a stable steadystate solution.     

Interrelation between the Glass Transition Temperature, Thermal Expansion Coefficient, and Poisson Ratio for Some Glasses in the AV–BVI–CVIISystems

In the framework of the free volume concept, the dependences of _g T _gand T _gon and are considered and the interrelation between the fraction of the fluctuation free volume f _g, Poisson ratio , and Grüneisen lattice parameter for chalcogenide, oxogenide, and oxohalide glasses is discussed. The fluctuation free volume model and the model of soft atomic configurations are compared in terms of anharmonicity of the glasses under investigation.     

Thrust Performance of an Ideal Pulse Detonation Engine

Quasisteady and twodimensional unsteady formulations of the problem on the operation cycle of a pulse detonation engine are derived. A formula for the specific impulse is obtained, and the thrust performance of the engine is calculated. It is found that the thrust performance of this engine for flight Mach numbers M [0; 3.6] and compression ratios p ₂/p ₁ [1; 80] are always higher than those of the ramjet and onespool turbojet. As the compression ratio increases, the advantage of the pulse detonation engine becomes less noticeable.     

Relationship between preferential adsorption coefficient and intrinsic viscosity in ternary systems

Summary The relation proposed between the preferential adsorption coefficient, , and the intrinsic viscosity, ¦¦ ¦¦=¦¦+AK has been applied in this paper to previously published data. This equation is found to be valid in theta condi tions and far away from them. The obtained results are compared to the ones calculated with the Dondos-Benoit equation.     

Studies on electrical conductivity of gamma irradiated polyaniline

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

Preparation of Linear π-Conjugated Coordination Polymers Having Ruthenium(II) Complex in the Main Chain

Soluble -conjugated coordination polymers having a ruthenium(II) complex in the main chain were prepared from a soluble metal complex monomer and a bridging ligand via coordination. Refluxing of an ethanol-water suspension containing (4,4-dinonyl-2,2-bipyridyl)Ru(III) with 2,3-bis(2-pyridyl)pyrazine gave the coordination polymer. The resulting polymer was soluble in common organic solvents. The structure was confirmed by uv/vis spectra and gpc analysis.     

Composition dependence of the oxygen-evolution reaction rate on Ir x Ti1−x O2 mixed-oxide electrodes

Mudcrack-free oxide films of Ir _x Ti_1–x O₂ (0 < x 1) on titanium substrates were obtained, and the effects of the oxide composition on the rate of oxygen-evolution reaction were investigated. At x 0.6, Ir-rich grains appear on the mudcrack-free surface. In the purely single-phase region (0 < x 0.5), the pseudo-capacitive charge is proportional to the surface composition, x _s, and the exchange-current density for the oxygen-evolution reaction increases linearly with x _s at 0.2 x _s 0.5, with an extrapolated intercept at x _s 0.15, below which the oxides are inactive.     

Interaction of methane with surfaces of silica,aluminas and HZSM-5 zeolite. A comparative FT-IR study

Infrared investigations on the interaction of methane with silica, aluminas (, and ) and HZSM-5 zeolite have been carried out. At low temperature (173 K), methane adsorption was observed over these oxides and HZSM-5 zeolite. Our findings featured that the infrared inactive ₁ band (2917 cm^–1) of a gaseous methane molecule became active and shifted to lower frequencies (2900 and 2890 cm^–1) when it adsorbed on the surfaces of these adsorbents. Our results also demonstrate that hydroxyl groups played a very important role in methane adsorption over the acidic oxides and the HZSM-5 zeolite. When interaction between the hydroxyl groups and methane took place, the band shift of the hydroxyl groups varied with different oxides. The strength of the interaction decreased according to the following sequence, Si-OH-Al>Al-OH>Si-OH, which is in accordance with the order of their acidities. At higher temperatures, methane interacted quite differently with various oxides and HZSM-5 zeolite. It has been observed that the hydroxyl groups of silica, -alumina and HZSM-5 zeolite could exchange with CD₄ at temperatures higher than 773K, while those on -alumina could exchange at a temperature as low as 573 K. Another interesting observation was the formation of formate species over Al₂O₃ (both and ) at temperatures higher than 473 K. The formate species would decompose to CO₂, or produce carbonate at much higher temperatures. Formation of formate species was not observed over silica and HZSM-5 under similar conditions, -Al₂O₃ did not adsorb or react with methane in any case.     

Role of plant volatiles in resistance of selected rice varieties to brown planthopper,Nilaparvata lugens (Stål) (Homoptera: Delphacidae)

Rice plant volatiles extracted as steam distillates significantly affected the behavior and biology of the brown planthopper,Nilaparvata lugens (Stål). In a multichoice test, more females settled and fed on tillers of a susceptible rice variety Taichung Native 1 (TN1), sprayed with its own extract or acetone than on TN1 tillers sprayed with the extract of the resistant variety ARC6650 or Ptb33. In another test,N. lugens females ingested significantly more of a 10% sucrose solution mixed with TN1 steam distillate extract than of plain sucrose solution or that mixed with extracts of resistant varieties. Topical application of the extracts of resistant varieties Mudgo, ASD7, Rathu Heenati, Babawee, Ptb33, and ARC6650 caused significantly higher mortality of females than did the TN1 extract. Likewise, significantly more first-instar nymphs died when they were caged on susceptible TN1 plants sprayed with the extracts of resistant varieties than on plants sprayed with TN1 extract. The extract of 60-day-old resistant plants was more toxic than the extract of 30-, 45-, or 100-day-old plants. However, toxicity of the extract from susceptible TN1 remained low at all plant growth stages.Principal Research Scientist (ICIPE), based at International Rice Research Institute (IRRI), P.O. Box 933, Manila, Philippines.     

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