Interaction of a finite quantum system with an infinite quantum system that contains a single one-parameter eigenvalue band

Interaction of a finite quantum system that contains ρ eigenvalues and eigenstates with an infinite quantum system that contains a single one-parameter eigenvalue band is considered. A new approach for the treatment of the combined system is developed. This system contains embedded eigenstates with continuous eigenvalues , and, in addition, it may contain isolated eigenstates with discrete eigenvalues . Two ρ × ρ eigenvalue equations, a generic eigenvalue equation and a fractional shift eigenvalue equation are derived. It is shown that all properties of the system that interacts with the system can be expressed in terms of the solutions to those two equations. The suggested method produces correct results, however strong the interaction between quantum systems and . In the case of the weak interaction this method reproduces results that are usually obtained within the formalism of the perturbation expansion approach. However, if the interaction is strong one may encounter new phenomena with much more complex behavior. This is also the region where standard perturbation expansion fails. The method is illustrated with an example of a two-dimensional system that interacts with the infinite system that contains a single one-parameter eigenvalue band. It is shown that all relevant completeness relations are satisfied, however strong the interaction between those two systems. This provides a strong verification of the suggested method.     

Densities and Volumetric Properties of Binary Mixtures of Formamide with 1-Butanol, 2-Butanol, 1,3-Butanediol and 1,4-Butanediol at Temperatures between 293.15 and 318.15 K

The densities of binary mixtures of formamide (FA) with 1-butanol, 2-butanol, 1,3-butanediol, and 1,4-butanediol, including those of the pure liquids, over the entire composition range were measured at temperatures (293.15, 298.15, 303.15, 308.15, 313.15 and 318.15) K and atmospheric pressure. From the experimental data, the excess molar volume, V _m ^E, partial molar volumes, and , at infinite dilution, and excess partial molar volumes, and , at infinite dilution were calculated. The variation of these parameters with composition and temperature of the mixtures are discussed in terms of molecular interactions in these mixtures. The partial molar expansivities, and , at infinite dilution and excess partial molar expansivities, and , at infinite dilution were also calculated. The V _m ^E values were found to be positive for all the mixtures at each temperature studied, except for FA + 1-butanol which exhibits a sigmoid trend wherein V _m ^E values change sign from positive to negative as the concentration of FA in the mixture is increased. The V _m ^E values for these mixtures follow the order: 1-butanol < 2-butanol < 1,3-butanediol < 1,4-butanediol. It is observed that the V _m ^E values depend upon the number and position of hydroxyl groups in these alkanol molecules.     

Recent developments in Ruddlesden–Popper nickelate systems for solid oxide fuel cell cathodes

Motivated by recent work on the Ruddlesden–Popper material, which was shown to be a superior oxide-ion conductor than conventional solid-oxide fuel cell cathode perovskite materials, we undertook A- and B-site doping studies of the Ruddlesden–Popper nickelate series in an attempt to identify other candidates for cathode application. In this paper, we summarize our most significant results for the and systems and more recently, the higher-order Ruddlesden–Popper phases La _n+1Ni _n O_3n+1 (n=2 and 3), which show greater promise as cathode materials than the n=1 compositions.     

Binuclear cobalt(II/II) and cobalt(II/III) chelates with O<Subscript>2</Subscript>N<Subscript>2</Subscript> ligands: synthesis,structure and magnetic studies

Abstract  The title complexes and have been synthesized in excellent yields by reacting Co(OAc)₂·4H₂O with H₂L¹ and H₂L², respectively, in acetonitrile solution. Here, [L¹]²⁻ and [L²]²⁻ are the deprotonated forms of N,N-bis(2-hydroxybenzyl)-N′,N′-dimethylethylenediamine and N,N-bis(2-hydroxybenzyl)-2-picolylamine, respectively. The crystal structures of and were determined by x-ray crystallography. In , each cobalt atom has distorted trigonal bipyramid geometry, while in , each cobalt atom has distorted octahedral geometry. Variable temperature magnetic moment measurements show weak antiferromagnetic interaction in . The magnetic characterization for is in agreement with the presence of Co(II) and Co(III) centers. Graphical Abstract  The title complexes and have been synthesized in excellent yields by reacting Co(OAc)₂·4H₂O with dianionic N₂O₂ coordinating ligands. In complex 1, each cobalt atom has distorted trigonal bipyramid geometry, while in complex 2, each cobalt atom has distorted octahedral geometry. Variable temperature magnetic moment measurements show weak antiferromagnetic interaction in complex 1. The magnetic characterization for complex 2 is in agreement with the presence of Co(II) and Co(III) centers. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

On the special values of monic polynomials of hypergeometric type

Special values of monic polynomials y _n (s), with leading coefficients of unity, satisfying the equation of hypergeometric type

Kinetics and Equilibria for Complex Formation between Palladium(II) and Chloroacetate

Kinetics and equilibria for the formation of a 1:1 complex between palladium(II) and chloroacetate were studied by spectrophotometric measurements in 1.00 mol HClO₄ at 298.2 K. The equilibrium constant, K, of the reaction

Volumetric Properties of Binary Mixtures of Acetonitrile and Chloroalkanes at 25°C and Atmospheric Pressure

Excess molar volumes for binary mixtures of acetonitrile + dichloromethane, acetonitrile + trichloromethane, and acetonitrile + tetracloromethane at 25°C have been used to calculate partial molar volumes , excess partial molar volumes , and apparent molar volumes of each component as a function of composition. The V _m ^Evalues are negative over the entire composition range for the systems studied. The applicability of the Prigogine–Flory–Patterson theory was explored. The agreement between theoretical and experimental results is satisfactory for the systems with dichloromethane and tetrachloromethane. For the unsymmetrical behavior of the system with trichloromethane, however, the agreement is poor.     

Removal of Nitrogen and Organic Matter in a Radial-Flow Aerobic-Anoxic Immobilized Biomass Reactor Used in the Posttreatment of Anaerobically Treated Effluent

This work reports on the removal of organic matter and nitrogen in a radial-flow aerobic-anoxic immobilized biomass (RAIB) reactor fed with domestic sewage pretreated in a horizontal-flow anaerobic immobilized biomass (HAIB) reactor. Polyurethane foam was used as support material for biomass attachment in both reactors. In batch experiments, a first-order kinetic model with residual concentration represented the organic matter removal rate, whereas nitrogen conversion followed a pseudo-first-order reaction in series model, with kinetic constants k ₁ (ammonium to nitrite) and k ₂ (nitrite to nitrate) of 0.25 and 6.62 h⁻¹, respectively. The RAIB reactor was operated in continuous-flow mode and changes in the airflow rate and hydraulic retention time were found to interfere in the apparent kinetic constants to the nitritation (k ₁) and nitratation (k ₂). Nitrification and denitrification were achieved in the partially aerated RAIB reactor operating with hydraulic retention times of 3.3 h and 2.7 h in the aerobic and anoxic zones, respectively. Ethanol was added in the anoxic zone of the reactor to promote denitrification. The effluent flow of the RAIB reactor presented a COD of 52 mg l⁻¹, and concentrations of 2 mg , 1.24 mg and 3.46 mg .     

Synthesis and characterization of poly(lactic acid) and glucosamine-formaldehyde/dodecylbenzenesulfonate composite films

The composite films of poly(lactic acid) (PLA) doped with glucosamine(Gluc)-formaldehyde(FA) polymer/sodium dodecylbenzenesulfonate (SDBS) complexes at 1–5 wt% were synthesized to demonstrate striking improvement of their structural and mechanical properties. The polymer complexes were obtained by the hydrothermal polymerization of Gluc and FA at a molar ratio of 1:2 in the presence of SDBS. The atomic ratios of S in to N in (=S/N) in the polymer complexes limitedly range from 0.52 to 0.69, indicating that the complexation develops through the nonstoichiometric reaction between groups of (Gluc-FA) polymer and ones of SDBS and 31–48% of the groups remain unbound. The PLA composite film doped with 1 wt% (Gluc-FA)/SDBS showed the elongation-at-break of as large as 194% compared with 37% for PLA film, together with an appreciable increase of the crystallites size (D ₂₀₀) of PLA from 21.8 to 33.3 nm.     

First and second thermodynamic mixing functions of ethylbenzene+n-nonane, +n-decane,and+n-dodecane at 25 and 45°C

Isothermal compressibilities _T and isobaric thermal expansion coefficients _p have been determined for mixtures of ethylbenzene+n-nonane, +n-decane, and +n-dodecane at 25 and 45°C in the whole range of composition. The excess functions and have been obtained at each measured mole fraction. The first one is zero for ethylbenzene +n-nonane, positive for ethylbenzene +n-decane, and +n-dodecane and increases with chain length n of the n-alkane. The function is positive for the three studied systems and nearly constant with n. Both mixing functions increase slightly with temperature. From this measurement and supplementary literature data of molar heat capacities at constant pressure C _P , the isentropic compressibilities _S, the molar heat capacities at constant volume C _V and the corresponding mixing functions have been calculated at 25°C. Furthermore, the pressure dependence of excess enthalpy H ^B , at zero pressure and at 25°C has been obtained from our experimental results of and experimental literature values for excess volume V ^E .     

Electrochemical study of the thermodynamics and kinetics of hydrophilic ion transfers across water | <Emphasis Type="Italic">n</Emphasis>-octanol interface

Thermodynamics and kinetics of hydrophilic ion transfers across water|n-octanol (W|OCT) interface have been electrochemically studied by means of novel three-phase and thin-film electrodes. Three-phase electrodes used for thermodynamics measurements comprise edge plane pyrolytic graphite, the surface of which was partly modified with an ultrathin film of OCT, containing hydrophobic lutetium bis(tetra-tert-butylphthalocyaninato) (Lu[tBu₄Pc]₂) as a redox probe. The transfers of anions and cations from W to OCT were electrochemically driven by reversible redox transformations of Lu[tBu₄Pc]₂ to chemically stable lipophilic monovalent cation and anion , respectively. Upon reduction of Lu[tBu₄Pc]₂, the transfers of alkali metal cations from W to OCT have been studied for the first time, enabling estimation of their Gibbs transfer energies. For kinetic measurements, a thin-film electrode configuration has been used, consisting of the same electrode covered completely with a thin layer of OCT that contained the redox probe and a suitable electrolyte. Combining the fast and sensitive square-wave voltammetry with thin-film electrodes, the kinetics of , , and Cl⁻ transfers have been estimated. Dedicated to Professor Dr. Yakov I. Tur’yan on the occasion of his 85th birthday.     

Solubility of Oxygen in Some 1-1, 2-1, 1-2, and 2-2 Electrolytes as a Function of Concentration at 25°C

The solubility of oxygen has been measured in a number of electrolytes [(LiCl, KCl, RbCl, CsCl, NaF, NaBr, NaI, NaNO₃, KBr, KI, KNO₃, CaCl₂, SrCl₂, BaCl₂, Li₂SO₄, K₂SO₄, Mn(NO₃)₃)] as a function of concentration at 25°C. The solubilities, mol (kg-H₂O)^–1, have been fitted to a function of the molality m (standard deviation < 3mol-kg^–1)

Solubility of Rhodochrosite (MnCO3) in NaCl Solutions

The solubility of rhodochrosite (MnCO₃) at 25°C under constant carbon dioxide partial pressure p(CO₂) was determined in NaCl solutions as a function of ionic strength I. The dissolution of MnCO₃(s) for the reaction

Kinetics and mechanism of the oxidation of hydrogen peroxide by the octacyanotungstate(V) ion in alkaline aqueous media

Summary The oxidation of H₂O₂ by [W(CN)₈]^3– has been studied in aqueous media between pH 7.87 and 12.10 using both conventional and stopped-flow spectrophotometry. The reaction proceeds without generation of free radicals. The experimental overall rate law, , strongly suggests two types of mechanisms. The first pathway, characterized by the pH-dependent rate constant k _s, given by , involves the formation of [W(CN)₈· H₂O₂]^3–, [W(CN)₈· H₂O₂·W(CN)₈]^6– and [W(CN)₈· HO]^3– intermediates in rapid pre-equilibria steps, and is followed by a one-electron transfer step involving [W(CN)₈·HO]^3– (k _a) and its conjugate base [W(CN)₈·O]^4– (k _b). At 25 °C, I = 0.20 m (NaCl), the rate constant with H _a =40±6kJmol^–1 and S _a =–151±22JK^–1mol^–1; the rate constant with H _b =36±1kJmol^–1 and S _b =–136±2JK^–1mol^–1 at 25 °C, I = 0.20 m (NaCl); the acid dissociation constant of [W(CN)₈·HO]^3–, K ₅ =(5.9±1.7)×10^–10 m, with and is the first acid dissociation constant of H₂O₂. The second pathway, with rate constant, k _f, involves the formation of [W(CN)₈· HO₂]^4– and is followed by a formal two-electron redox process with [W(CN)₈]^3–. The pH-dependent rate constant, k _f, is given by . The rate constant k ₇ =23±6m ^–1 s ^–1 with and at 25°C, I = 0.20 m (NaCl).     

Reaction of hydrogen atoms with dimethyldisulfide

Hydrogen atoms, generated by the mercury (³P₁) sensitization of H₂, were allowed to react with dimethyldisulfide in the temperature range of 25–155°C. The only retrievable product is methanethiol, formed in the primary metathetical reaction \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm H} + {\rm CH}_3 {\rm SSCH}_3 {\rm CH}_3 {\rm SH} + {\rm CH}_3 {\rm S} $\end{document}. The intermediacy of thiyl radicals was clearly demonstrated in experiments carried out in the presence of ethylene where one of the major products detected was ethyl methyl sulfide, formed via CH₃S + C₂H₅ → CH₃SC₂H₅. The major fate of the CH₃S radical is recombination and disproportionation, and the yield of methanethiol formed via disproportionation contributes less than 5% to the total thiol yield. The rate coefficient of step 1, from competition with the reaction \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm H} + {\rm C}_{\rm 2} {\rm H}_{\rm 4} {\rm C}_{\rm 2} {\rm H}_5 $\end{document}, is k₁ = (5.7 ± 1.2) × 10¹² exp[? (100 ± 100)/RT] cm³/mol sec.     

Unified treatment of complete orthonormal sets of nonrelativistic,quasirelativistic and relativistic sets of spinor wave functions,and Slater spinor orbitals in coordinate,momentum and four-dimensional spaces

Using the properties of tensor spherical harmonics introduced by the author in previous paper (Guseinov, Phys Lett A 372:44, 2007) and complete orthonormal scalar basis sets of nonrelativistic -exponential type orbitals ( -ETO), - momentum space orbitals ( -MSO) and z ^α-hyperspherical harmonics (z ^α-HSH) for particles with spin s = 0 the new analytical relations for the quasirelativistic and relativistic spinor wave functions and Slater spinor orbitals in coordinate, momentum and four-dimensional spaces are derived, where α = 1, 0, −1, −2,.... The 2-component quasirelativistic and 4-component relativistic spinor wave functions obtained are complete without the inclusion of the continuum. The relativistic spinor wave function sets and Slater spinor orbitals are expressed through the corresponding quasirelativistic spinor wave functions and Slater spinor orbitals, respectively. The analytical formulas for overlap integrals over quasirelativistic and relativistic Slater spinor orbitals with the same screening constants in coordinate space are also derived.     

Improvement of the electrochemical properties of “as-grown” boron-doped polycrystalline diamond electrodes deposited on tungsten wires using ethanol

The electrochemical properties of boron-doped diamond (BDD) polycrystalline films grown on tungsten wire substrates using ethanol as a precursor are described. The results obtained show that the use of ethanol improves the electrochemistry properties of “as-grown” BDD, as it minimizes the graphitic phase upon the surface of BDD, during the growth process. The BDD electrodes were characterized by Raman spectroscopy, scanning electronic microscopy, cyclic voltammetry (CV), and electrochemical impedance spectroscopy (EIS). The boron-doping levels of the films were estimated to be ∼10²⁰ B/cm³. The electrochemical behavior was evaluated using the and redox couples and dopamine. Apparent heterogeneous electro-transfer rate constants were determined for these redox systems using the CV and EIS techniques. values in the range of 0.01–0.1 cm s⁻¹ were observed for the and redox couples, while in the special case of dopamine, a lower value of 10⁻⁵ cm s⁻¹ was found. The obtained results showed that the use of CH₃CH₂OH (ethanol) as a carbon source constitutes a promising alternative for manufacturing BDD electrodes for electroanalytical applications.     

Behavior of (La,Sr)CoO3- and La2NiO4-based ceramic anodes in alkaline media: compositional and microstructural factors

The behavior of dense ceramic anodes made of perovskite-type (x = 0.30–0.70; y = 0–0.05; z = 0–0.20) and K₂NiF₄-type (Me = Co, Cu; x = 0–0.20) indicates significant influence of metal hydroxide formation at the electrode surface on the oxygen evolution reaction (OER) kinetics in alkaline solutions. The overpotential of cobaltite electrodes was found to decrease with time, while cyclic voltammetry shows the appearance of redox peaks characteristic of Co(OH)₂/CoOOH. This is accompanied with increasing effective capacitance estimated from the impedance spectroscopy data, because of roughening of the ceramic surface. The steady-state polarization curves of in the OER range, including the Tafel slope, are very similar to those of model Co(OH)₂–La(OH)₃ composite films where the introduction of lanthanum hydroxide leads to decreasing electrochemical activity. La₂NiO₄-based anodes exhibit a low electrochemical performance and poor stability. The effects of oxygen nonstoichiometry of the perovskite-related phases are rather negligible at high overpotentials but become significant when the polarization decreases, a result of increasing role of oxygen intercalation processes. The maximum electrocatalytic activity to OER was observed for A-site-deficient , where the lanthanum content is relatively low and the Co⁴⁺ concentration determined by thermogravimetric analysis is highest compared to other cobaltites. Applying microporous layers made of template-synthesized nanocrystalline leads to an improved anode performance, although the effects of microstructure and thickness are modest, suggesting a narrow electrochemical reaction zone. Further enhancement of the OER kinetics can be achieved by electrodeposition of cobalt hydroxide- and nickel hydroxide-based films. Dedicated to Professor Dr. Yakov I. Tur’yan on the occasion of his 85th birthday.     

4<Emphasis Type="Italic">p</Emphasis><Superscript>2</Superscript> resonances in photoionization from 4<Emphasis Type="Italic">s</Emphasis>4<Emphasis Type="Italic">p</Emphasis> levels in neutral zinc

In neutral zinc the 4p ² configuration lies above the 3d ¹⁰4s ionization limit and its levels become perturbers in the continuum. Lines have been identified in the Zn I spectrum for the multiplet, whereas no lines have been found for transitions to 4p ^{2 1} D or ¹ S. In this paper, cross sections for photoionization from 4s4p levels are reported that reveal the positions and widths of the 4p ² resonances. Calculations were performed using the multiconfiguration Hartree-Fock (MCHF) and B-spline R-matrix (BSR) method. Results from Breit–Pauli calculations that ignore the background continua are also presented. Included in the latter are energies for the levels and transition data (transition energies, line strengths, f-values, and A-rates) for all E1 transitions between these levels. Transition energies and the agreement in the length and velocity values, particularly for allowed transitions, indicate the accuracy of the computational model. Line widths are compared with other estimates. Contribution to the Serafin Fraga Memorial Issue.