End-group analysis of polymacromonomer formed in the radical polymerization of styrene-type PMMA macromonomers by using 2H NMR spectroscopy

Summary Isotactic (iso-) and syndiotactic (syn-) poly(methyl methacrylate) (PMMA) macromonomers having styrene group as a polymerizable function were polymerized with perdeuterated 2,2-azobisisobutyronitrile in toluene at 60°C. The resultant polymacromonomers were analyzed by ²H NMR spectroscopy to determine the number of initiator fragment in a polymacromonomer chain (N) and initiator efficiency (f). The N values were less than unity (0.500.72), indicating the chain transfer reaction to occur in the radical polymerization of macromonomer. The f values were 0.180.28 and much smaller than that for styrene polymerization (0.50.7). Iso-macromonomer gave larger N and f values than syn- one, suggesting that the tacticity of macromonomer affects the reaction pathway probably owing to the difference in chain mobility between iso- and syn-PMMA chains.     

Single and blended maize volatiles as attractants for diabroticite corn rootworm beetles

Synthetic maize volatiles and analogs dispensed singly and blended were tested for attractiveness to western (WCR, Diabrotica virgifera virgifera) and northern corn rootworm beetles (NCR, D. barberi) in maize fields. Newly identified attractants included syn-benzaldoxime, especially for NCR, and -caryophyllene for WCR females. (±)-Linalool was more effective than was (–)-linalool. Myrcene, (+)--pinene, and (–)--pinene were unattractive. Adding methyl salicylate to (±)-linalool, (+)--terpineol, or -ionone appeared to synergistically increase capture of WCR females, but dispensing the terpenes in binary blends did not. Dose–response data for methyl salicylate, (±)-linalool, and a blend of both compounds confirmed the synergy. -Caryophyllene, but not (–)--pinene, added to the latter blend produced a further synergistic increase in WCR female capture that did not vary with sesquiterpene dose from 1.0 to 100 mg. Indole addition to the same blend caused an increase in WCR female captures indicative of synergy, assuming that each did not individually lure different segments of the WCR female population. The green leaf volatiles (Z)-3-hexenyl acetate and (Z)-3-hexen-1-ol were unattractive alone and had no influence on efficacy of traps baited with 3.3 mg each of (±)-linalool, methyl salicylate, and -caryophyllene. The latter mixture captured about half as many WCR females as did 10 mg of 4-methoxycinnamaldehyde, a potent WCR attractant standard. Substituting -ionone for (±)-linalool yielded a ternary blend that captured more beetles than did the aldehyde and was unaffected by aldehyde addition. Olive oil, which has been used to sustain attractant volatilization, did not affect captures. The results show that the blending of maize volatiles has the potential to greatly improve efficacy of lures having promising applications in corn rootworm population management.     

Deactivation and Regeneration of Spent Three-Way Automotive Exhaust Gas Catalysts (TWC)

The effect of oxidation, oxy-chlorination and reduction treatments at elevated temperatures on the dispersion of palladium (Pd) and rhodium (Rh) for commercially aged three-way automotive exhaust gas catalysts (TWC) has been investigated. The catalytic activity of treated samples was compared with a reference sample, which was taken from the corresponding aged TWC and tested using a mini-cuts reactor simulating real driving conditions. In the case of oxygen, the improvement of the noble metal dispersion on the catalysts was dependent on the noble metal loading and the degree of metal sintering. Adding chlorine to the oxygen atmosphere facilitates the restructuring of the metals with an improved increase in the noble metal dispersion. The temperature and the composition of the gas used during these thermal treatments proved to be of importance not only to increase the metal dispersion, but also to prevent possible losses of noble metals, in the form of volatile MO _x Cl _y compounds. TEM-EDS techniques indicated changes in the size of the largest noble metal agglomerates of up to 100 nm in size after thermal gas treatment. BET porosity and XRD analyses were employed to investigate restructuring of the washcoat and showed a decrease in pore size distribution and an increase in surface area.     

Two-dimensional n.m.r. studies of polybutadiene adducts with dihalocarbenes

A variety of two-dimensional (2D) n.m.r. experiments were performed on the adducts of 1,4-polybutadienes (PBD) with difluorocarbene (:CF₂) and fluorochlorocarbene (:CFC1) to assign stereochemical microstructure, carbon types, and syn and anti isomers. A 2D homonuclear ¹⁹F J-correlated (COSY) spectrum of the trans-PBD:CF₂ adducts at complete conversion showed that the geminal fluorines were equivalent in the isotactic and syndiotactic stereochemical triads (AA' singlets), but nonequivalent in the heterotactic triad (AB quartet). The 2D homonuclear ¹⁹F J-resolved experiment confirmed this finding and gave a geminal coupling constant of 160 Hz. Pentad stereosequence fine structure was observed in the 2D spectra but not in the 1D spectra. Editing of carbon types proved difficult by the distortionless enhancement by polarization transfer (d.e.p.t.) pulse sequence (Doddrell, D. M., Pegg, D. T. & Bendall, M. R., J. Magn. Reson., 1982, 48 , 323) for PBD:CFC1 adducts, owing in part to different magnitudes of the ¹J₁₃ scalar coupling constant. A 2D heteronuclear ¹³C-¹H J-resolved experiment was superior and also provided the coupling constants, which ranged from 130 Hz (acyclic methylenes) to 167 Hz (cyclopropyl methines). The identity of syn and anti structures in cis-PBD:CFC1 adducts was rigorously established by a 2D heterocorrelated ¹⁹F-¹H nuclear Overhauser experiment (NOESY). It is noteworthy that the more hindered structure with chlorine syn to the alkyl groups is preferred by 1·65:1. Analysis of a model compound obtained from cis-5-decene gave ³J couplings of 20 and ≤ 3 Hz for the syn and anti compounds, respectively. These couplings were obscured in the 1D polymer spectrum by stereosequence broadening, but their values could be extracted by 2D ¹⁹F-¹H J-resolved spectroscopy.     

The Effect of Hydroxyoxime Isomer Conformation on Metal Extraction in the LIX 63/Versatic 10 Synergistic System

LIX 63 contains an aliphatic α-hydroxyoxime as its active component, with two isomeric forms (anti and syn) being present in a 3:2 ratio in “as supplied” reagent. In the present work, > 90% pure syn hydroxyoxime was isolated from LIX 63. Examination of metal extraction properties in systems containing Versatic 10 with anti and/or syn hydroxyoxime established unequivocally that the syn isomer plays no beneficial role in metal extraction in this synergistic solvent extraction system, thereby excluding the possibility of monodentate coordination of hydroxyoxime. Economic consequences arising from this outcome and the opportunity to maximize reagent utilisation are briefly discussed.     

Separation of heavy metal ions by complexation on poly (N-vinyl imidazole) hydrogels

Summary Poly (N-vinyl imidazole) (PVIm) hydrogels were prepared by -irradiating binary mixtures of N-vinyl imidazole-water in a ⁶⁰Co- source having 4.5 kGy/h dose rate. These hydrogels were characterized with gravimetric and spectrophotometric studies. Hydrogels with equilibrium swelling ratio of 600% in distilled water were used in the metal ion adsorption studies. The effects of pH, equilibration time, and initial metal ion concentration were considered in batch equilibrium study on the chelation of Cu²⁺, Co²⁺, Cd²⁺, and Pb²⁺ ions. Maximum metal ion adsorption were observed at pH=6.0. It has also been observed that the amount of adsorbed metal ions decreased at lower pHs because of protonation of PVIm ring.     

Electrochemical behaviour of copper in trimethyl-n-hexylammonium bis((trifluoromethyl)sulfonyl)amide, an ammonium imide-type room temperature molten salt

The redox behaviour of copper species in an ammonium imide room temperature molten salt was examined to clarify the applicability of the salt to the electroplating media of various metals. Trimethyl-n-hexylammonium bis((trifluoromethyl)sulfonyl)amide (TMHA-Tf₂N), having an electrochemical window of 5.6 V (50 °C), and the corresponding copper(II); salt were used to prepare the solution. In TMHA-Tf₂N media the monovalent copper ion, Cu(I), was stable and Cu metal was oxidized, or corroded, in the presence of Cu(II) species as: Cu²⁺ + Cu 2Cu⁺. Cathodic electrodeposition of copper metal and its anodic dissolution were, thus one-electron reactions and their current efficiencies were almost 100%.     

New catalyst systems for the polymerization of substituted acetylenes: M(CO)6—Lewis acid—hv (M=W,Mo)

Summary A new catalyst system prepared by UV irradiation of a toluene solution of W(CO)₆ and a Lewis acid polymerized phenylacetylene (e.g., polymer yield 50%, M _n 5.0×10⁴ with SnCl₄ (0.5 equivalent to W(CO)₆) as Lewis acid). This catalyst afforded high molecular weight polymers M _n 4×10⁵ – 5×10⁵) from phenylacetylenes with ortho-substituents (e.g., o-Me₃Si and o-CF₃). The Mo(CO)₆-based counterpart was rather effective to acetylenes having electron-withdrawing groups (e.g., ClC Cph). Polymerization of phenylacetylene occurred as well when SnCl₄ was added after UV irradiation of a toluene solution of W(CO)₆ and the monomer; this suggests that the polymerization proceeds via metal carbenes having coordinated SnCl₄.     

Design characteristics of an aluminium-air battery with consumable wedge anodes

An attempt was made to optimize a mechanically rechargeable bipolar-cell battery, exemplified by an aluminium-air battery with self-perpetuating wedge anodes. The optimization involved current density of battery operation and some design parameters such as the anode thickness and the cell dimensions. It was shown that these parameters depend on the energy-to-power ratio selected by the user. The saline electrolyte aluminium-air battery was found to be essentially a low power-density/high energy-density power source. Energy densities of up to over 1500 W h kg^–1 are achievable for low power needs, indicating very long operations between recharging. It was also shown that aluminium should render significantly cheaper electric energy than any of the high-energy density metals.Nomenclature d anode plate thickness (cm) - d _p thickness of end-plates (cm) - d thickness of cell walls (cm) (see Fig. 1) - E energy density (W h kg^–1) - E _B total energy contained in the battery (k W h) - F the Faraday constant 26.8 A h mol^–1 - g _c weight of the air cathode per unit anode area (g cm^–2) - g _e excess electrolyte per unit electrode area (g cm^–2) - g _h weight of the hardware per unit anode area (g cm^–2) - g _m weight of metal per unit electrode area (g cm^–2) - _m g excess of unconsumable metal per unit electrode area (g cm^–2) - g ₀ sum of all the weights except that of consumable metal (g cm^–2) - g _ox weight of oxygen consumed withg _m (g cm^–2) - G total weight of battery (g) - G _m total amount of reserve metal per cell and per cm width (kg cm^–1) - G _m total weight of the wedges (kg) - G _r total weight of the reserve anode container except the metal (kg) - G free energy of oxidation of the metal (kW h mol^–1) - h _a height of the wedge (cm) - h _r reserve anode height (cm) - j current density (mA cm^–2) - J total current drawn from the battery (mA) - n number of electrolyte replacements between anode replacement - n _c number of cells in a battery - M atomic weight of the metal (kg mol^–1) - P power density (W kg^–1) - Q _e cost of metal in the cost of unit energy produced ($ kW^–1 h^–1) - Q _e ⁰ theoretical figure of merit of a metal ($ kW^–1 h^–1) - Q _m cost of metal per unit weight ($ kg^–1) - S _a total anode surface area (cm²) - U cell voltage without ohmic drop (V) - V cell voltage (V) - x width of battery (cm) - z number of electrons exchanged per atom of metal dissolved - interelectrode spacing (cm) - spacing between cover and top of a new reserve anode (cm) - _f material efficiency - _v voltage efficiency - _e conductivity of electrolyte (ohm^–1 cm^–1) - _e electrolyte density (g cm^–3) - _m density of metal (g cm^–3) - _p density of end-plates (g cm^–3) - _w density of cell-walls (g cm^–3)     

Synthesis and Photocatalytic Properties of HTaWO<Subscript>6</Subscript> Intercalated with Oxide Materials

Transition metal oxides (TiO₂, MnO₂, Cr₂O₃, Fe₂O₃, NiO, CuO) were intercalated into the interlayer of HTaWO₆ by (1) hydrothermal reaction on HTaWO₆ with 1 M soluble metal nitrate aqueous solution at 130C for 12 h followed by calcination at 250C for 3 h and (2) sol reaction on HTaWO₆/n-C₃H₇NH₂ precursor with metal oxide sol, followed by UV irradiation. The gallery height of transition metal oxide in the interlayer of HTaWO₆ is changed from 0.42 to 0.71 nm, the band gap energies of intercalated materials are less than 3 eV. HTaWO₆/Cr₂O₃, HTaWO₆/MnO, HTaWO₆/Fe₂O₃, HTaWO₆/NiO and HTaWO₆/CuO porous materials are capable of photocatalytic decomposing methyl orange, and the photocatalytic activity of HTaWO₆/TiO₂ is superior to that of unsupported TiO₂.     

Leaf surface chemicals fromNicotiana affecting germination ofPeronospora tabacina (adam) sporangia

A bioassay was used to evaluate the effects of cuticular leaf components, isolated fromN. tabacum, N. glutinosa (accessions 24 and 24a), and 23other Nicotiana species, on germinationof P. tabacina (blue mold). The leaf surface compounds included- and-4,8,13,-duvatriene-l,3-diols (DVT-diols), (13-E)-labda-13-ene-8-,15-diol (labdenediol), (12-Z)-labda-12,14-diene-8-ol (cis-abienol), (13-R)-labda-8,14-diene-13-ol (manool), 2-hydroxymanool, a mixture of (13-R)-labda-14-ene-8,13-diol (sclareol), and (13-S)-labda-14-ene-8,13-diol (episclareol), and various glucose and/or sucrose ester isolates. The above in acetone were applied onto leaf disks of the blue moldsusceptibleN. tabacum cv. TI 1406, which was then inoculated with blue mold sporangia. Estimated IC₅₀ values (inhibitory concentration) were 3.0g/cm² for-DVT-diol, 2.9/cm² for-DVT-diol, 0.4g/cm² for labdenediol and 4.7g/cm² for the sclareol mixture. Manool, 2-hydroxymanool, andcis-abienol at application rates up to 30g/cm² had little or no effect on sporangium germination. Glucose and/or sucrose ester isolates from the cuticular leaf extracts of 23Nicotiana species and three different fractions fromN. bigelovii were also evaluated for antimicrobial activity at a concentration of 30g/cm². Germination was inhibited by >20% when exposed to sugar esters isolated fromN. acuminata, N. benthamiana, N. attenuata, N. clevelandii, andN. miersii, and accessions 10 and 12 ofN. bigelovii. These results imply that a number of compounds may influence resistance to blue mold in tobacco.     

Experimental investigation of the primary and secondary current distribution in a rotating cylinder Hull cell

A rotating cylinder cell having a nonuniform current distribution similar to the traditional Hull cell is presented. The rotating cylinder Hull (RCH) cell consists of an inner cylinder electrode coaxial with a stationary outer insulating tube. Due to its well-defined, uniform mass-transfer distribution, whose magnitude can be easily varied, this cell can be used to study processes involving current distribution and mass-transfer effects simultaneously. Primary and secondary current distributions along the rotating electrode have been calculated and experimentally verified by depositing copper.List of symbols c distance between the cathode and the insulating tube (cm) - F Faraday's constant (96 484.6 C mol^–1) - h cathode length (cm) - i local current density (A cm^–2) - i _L limiting current density (A cm^–2) - i _ave average current density along the cathode (A cm^–2) - i ₀ exchange current density (A cm^–2) - I total current (A) - M atomic weight of copper (63.54 g mol^–1) - n valence - r _p polarization resistance () - t deposition time (s) - V _c cathode potential (V) - Wa _T Wagner number for a Tafel kinetic approximation - x/h dimensionless distance along the cathode surface - z atomic number Greek symbols _a anodic Tafel constant (V) - _c cathodic Tafel constant (V) - solution potential (V) - overpotential at the cathode surface (V) - density of copper (8.86 g cm^–3) - electrolyte conductivity ( cm^–1) - deposit thickness (cm) - _ave average deposit thickness (cm) - surface normal (cm)     

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

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

Effect of the particle size on the activity of MoO x C y catalysts for the isomerization of heptane

Molybdenum trioxide samples having apparent particle sizes (APS) of 5 and 20 .m were partially reduced under flow of a mixture of H₂/n-heptane during 4 h. X-ray diffraction and Raman spectroscopy showed the typical structural transformation of MoO₃ into MoO_xC_y and MoO₂. These structural changes occur preferentially on the {0k0} planes. After the reduction treatment the resulting materials, having surface areas of 23 and 53 m²/g, were evaluated in the isomerization of n-heptane at 643 K and 18.5 bar. The catalyst with an APS of 20 .m showed a maximum conversion around 70%, while for the catalyst with an APS of 5 .m the maximum conversion was 34%. The lower activity of the 5 .m MoO_xC_y catalyst seems to be related to a faster rate of formation of oxygen vacancies and rearrangement of the lattice into a more stable and less active structure in the case of small-size particles, due to a higher concentration of terminal Mo=O bonds along the a- and b-axes, which facilitate the electrophilic attack by hydrogen on the (010) plane.     

Performance of Ni/MgO–AN catalyst in high pressure CO2 reforming of methane

The catalytic activity of 8.8 wt Ni/MgO–AN prepared from alcogel derived MgO was studied for the dry reforming of methane under high pressure (1.5 MPa). The catalyst showed a self-stabilization process during the reaction that lasted for 50 h, in which the catalytic activity decreased with increasing the reaction time on stream (TOS) up to 12 h, and then became stabilized thereafter. The activity decline during the initial 12 h of the reaction was found closely related to an increase in the amount of carbon deposits on the catalyst, which also became stabilized after the catalyst had served the reaction for 12 h. Comprehensive characterizations of the coked catalyst with Temprature programmed hydrogenation (TPH), X-ray photoelectron spectroscopy (XPS) and X-ray diffractometer (XRD) techniques revealed two kinds of carbon deposits (-carbon and -carbon) on the used catalyst. The -carbon deposits were found to be produced from CH4 decomposition while the -carbon deposits from CO disproportionation. It was revealed that the accumulation of -carbon deposits was a key cause for the activity decline and the self-stabilized catalysis during the initial 12 h of the high-pressure reaction. Moreover, it was also observed that an unavoidable sintering of metallic Ni particles from 6.5 to 11 nm, which happened within the very first hour of the reaction, was not directly related to the catalyst stability.     

Potential distribution and electrode stability in a bipolar electrolysis cell

A computational model is presented, which enables the identification of those zones endangered by corrosion in a bipolar electrolysis cell stack. The method consists of two steps: first the potential profile in the electrolyser is computed by numerical solution of the Laplace equation using the finite difference method; then, making use of the Criss-Cobble correspondence principle, this profile is related to the potential-dependent thermodynamic stabilities of the respective metals. This may be a useful tool in the design of intermittently operating electrolysers (for example those powered by solar energy).Nomenclature A metal phase - A _i single A-phase point - B electrolyte phase - B _i single B-phase point - F Faraday constant - h mesh interval (m) - i local current density (A m^–2) - i ₀ exchange current density (A m^–2) - j local current across the double layer (A) - j _iA,j _iB tangential or normal component of the double layer current (A) - K A, B phase conductivity ratio - m molality mol kg^–1 - R gas constant - T absolute temperature (K) - U potential (V) - U ₀ water decomposition voltage (V) - U _tot end plate potential (V) - x, y cartesian coordinates - overrelaxation factor - _a, _c anodic or cathodic overpotential (V) - _A, _B electrical conductivity (^–1 m^–1) - potential (V) - _m local double layer potential, electrode end (V) - _s local double layer potential, electrolyte end (V)     

The Effect of Metal Ratios in Graphene-Supported PdCoNi Anodic Electrocatalysts on Catalytic Property for Enhanced Methanol Electrooxidation

The various metal ratios of PdCoNi/G nanocomposites (PdCoNi/G 6:1:1, 6:3:3, 6:4.5:1.5, 6:1.5:4.5, and 6:9:9) supported on graphene were synthesized using a chemical reduction of metal compounds and graphite oxide with a strong reducing agent under N₂ conditions without calcinations to improve the electrocatalytic performance for methanol electrooxidation. SEM, EDX, XRD, XPS, and XANES were used to study the physical and chemical properties of all electrocatalysts. The composition of PdCoNi/G electrocatalysts was in the form of palladium metal, cobalt oxides, and nickel oxide. The electrocatalysis activity of methanol oxidation in 1 M KOH was investigated by cyclic voltammetry and chronoamperometry. It was found that PdCoNi/G (6:1:1) nanocomposite enhanced the catalytic activity. The relative potential showed the highest current density (17.27 mA/cm²) and negative potential (??0.065 V) in the catalyst studies. In addition, PdCoNi/G (6:1:1) nanoncomposite presented the best intermediate poisoning tolerance for the methanol oxidation of all synthesized electrocatalysts. These confirmed that PdCoNi/G (6:1:1) is very promising for applications in direct methanol fuel cell (DMFC).

Graphical Abstract

Schematic illustration of the synthesis of PdCoNi metal nanocomposites (various metal ratios) supported on graphene (a) oxidation of graphite to GO and (b) reduction between GO and metal compounds with NaBH₄ as a reducing agent.

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The application of renewal theory to anodic dissolution processes

The oscillatory behaviour of a certain class of dissolution processes involving anodic dissolution of a metal and the formation of a passivating substance is analysed in terms of renewals via isomorphism with a Type I counter in queuing theory.Nomenclature E(X) statistical expectation of random variableX - E _i expected frequency in theith class of observation (due to a postulated probability distribution) - m renewal number - N _t number of renewals in time period (0,t) - O _i observed frequency in theith class observation - R(t) renewal function (Equation 3) - T _m time lapsed until themth renewal - t time - density parameter of the experimental probability density function - (u) Gaussian probability density function of random variableu - ² chi-square statistic     

Polymer Nanocomposite Hydrogels with Improved Metal Adsorption Capacity and Swelling Behavior: Influence of Spirulina Immobilization onto Montmorillonite Clay

Polacrylamide nanocomposite hydrogels were prepared by in situ free radical polymerization reaction in presence of Spirulina microalgae, which is immobilized in montmorillonite clay (Sp-MMT). The nanocomposite hydrogel having 1 wt.% Sp-MMT clay was found to have desired exfoliated structure, maximum swelling and improved thermal stability. It also showed maximum metal adsorption capacity, which is about 312% higher than that of neat PAAm hydrogel at the highest metal concentration. The presence of Spirulina's porous network structure where all potential binding sites are under receptive position was found to be responsible for the dramatic increase in the metal adsorption and swelling behavior.     

Model of the isotropic anode in the molten carbonate fuel cell

An Isotropic one-dimensional model is proposed for the porous anode of a molten carbonate fuel cell, requiring the thickness of the electrolyte film in the pores as the only one adjustable parameter. The solution of the model equations is presented in a general form and calculations are made by approximation. The wetting of the whole electrode inner surface by the electrolyte is assumed. The model shows that, practically, the current is generated in a thin reaction zone in the electrode. The model may be fitted well to the experimental polarization curves [4], when 0.057 m is the electrolyte film thickness.Nomenclature a _i,b _i,c _i electrode reaction orders - c _k molar concentration of thekth gas component at the electrode/electrolyte interface - c _k equilibrium molar concentration of thekth gas component - d parameter in Equation 21 - D _k diffusion coefficient of thekth component - F Faraday's constant - H _k Henry's constant of thekth component - i Faradaic current density - i ₀ exchange current density - i _k ^lim limiting current density of thekth reagent - j _e,j _m ionic and electronic current density, respectively - j _T total anodic current density - k rate constant in Equation 19 - l electrode thickness - p _k partial pressure of thekth component - PD penetration depth - Q parameter, defined by Equation 41 - R gas constant - S specific internal surface of the electrode - T temperature - V _E relative electrolyte volume in the electrode - x dimensionless coordinate,x=z/l - Z _F (i) function slope at zero current - Z total electrode impedance per unit area of electrode - symmetry coefficient - electrolyte film thickness - overpotential - ₀, ₁ overpotentials at the gas/electrode (x=0) and the electrode/electrolyte (x=1) interfaces, respectively - , dummy variables of the integration - _m measured overpotential - k _E,k _M specific electrolyte and electrode metal conductivity, respectively - k _e ^eff ,k _M ^eff effective electrolyte and electrode metal conductivity, respectively - v stoichiometric number - tortuosity factor - _E, _M electrolyte and electrode metal potentials, respectively - ^eq equilibrium electrode metal-electrolyte potential difference