Confined systems and the modified virial theorem from semiclassical considerations

We show that two simple semiclassical strategies, one based on the Wilson–Sommerfeld rule and the other on the uncertainty principle, yield the exact modified form of the virial theorem for confined systems. An alternative, easier quantum mechanical route to arrive at this result is also sketched. Pilot calculations on confined oscillators reveal decisive trends. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Brownian motion of nonlinear oscillators: The projection operator method and its application to a double-well-potential oscillator

A projection operator method is presented, which provides the most efficient way for calculating the stationary behavior of nonlinear Brownian motion. A continued-fraction expansion of the Fourier-Laplace transform of the displacement correlation function or the spectral density is used. This method utilizes a successive optimization procedure on the nonlinear terms and includes the method of statistical linearization as the lowest order approximation. A systematic way to calculate the continued fraction numerically up to sufficient order for convergence is developed, which enables us to obtain the spectral density of a system previously uncomputable.Numerical computations of the spectral density of a nonlinear oscillator with a double-well potential are presented and compared with the results obtained by statistical linearization.This work was supported in part by the National Science Foundation under Grant CHE 75-20624.     

Electrolytic Co3O4 for thin-layer anodes of lithium-ion batteries

Electrolytic (e) cobalt oxide of a spinel structure, e-Co₃O₄, is obtained from the sulfate and nitrate (aqueous, water-alcohol) solutions containing Co²⁺ with the aim of using it in thin-layer anodes of lithium-ion batteries. The physicochemical and structural properties of the synthesized compounds are examined using thermal and x-ray diffraction analyses, absorption IR spectroscopy, and atomic force microscopy. The electrochemical characteristics of e-Co₃O₄ are determined in breadboards of lithium power sources and in the lithiumion system LiCoO₂/e-Co₃O₄.     

Strong coupling expansion for classical statistical dynamics

We discuss the simple, randomly driven systemdx/dt = –x –x³ +f(t), wheref(t) is a Gaussian random function or stirring force with f(t)f(t) = (t – t). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's functions as power series in (1/R)ⁿ, whereR is the internal Reynolds number ()^1/2/, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonianp ²/2 +m ² x ²/2 +vx ⁴ +x ⁶/2, we evaluate the path integral on a lattice by assuming that thex ⁶ term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(a)^1/3, wherea is the lattice spacing. Using Padé approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.Supported financially by the National Science Foundation and the U.S. Department of Energy.     

Oscillatory reduction of bromate by aspirin in acidic aqueous solution

Summary The experimental behavior of the uncatalyzed Belousov - Zhabotinsky reaction between aspirin and bromate in acidic media in the batch reactor has been studied for the first time. Aspirin is an interesting substrate because it is one of the most used medicines. The medical aspirin behaves also in an oscillatory manner with bromate. The oscillating process was investigated under aerobic and anaerobic conditions. The complex dynamic behavior has been observed in the mixed aspirin - vitamin C - _BrO3 - H₂SO₄ system.     

制备纳米V2O5的新方法及其电化学性能的研究

目前对锂离子电池正极材料的研究主要为达到如下目标而进行:高的比容量和能量密度,良好的循环性和寿命,资源丰富、价格便宜以及环境友好。已进行了广泛研究的LiCoO_2、LiNiO_2、LiMn_2O_4等锂离子电池正极材料,虽然具有较高的电压平台、良好的稳定性和寿命,但其容量相对较低和价格较高限制了其进一步的应用和发展。     

Cathode of a fuel cell with a solid polymer electrolyte: Calculating overall currents in the presence of a gas-diffusion layer

Mathematical apparatus, which makes it possible to perform calculations of the current-voltage characteristics of cathodes of fuel cells with a solid polymer electrolyte in conditions where there are present extraneous diffusion restrictions is proposed. In so doing, the partial pressure of oxygen and the absolute pressure of gas in the gas chamber may assume any values. First of all presented are the results of calculations of the current-voltage characteristics intrinsic to active layers of the air and oxygen cathodes, which are performed under the assumption that the extraneous diffusion restrictions are absent altogether. Thereafter, in the same conditions (at the same parameters that characterize the active layer of a cathode), obtained are results of a calculation of the current-voltage characteristics inherent in the air and oxygen cathodes in the presence of extraneous diffusion restrictions. Afterward there is performed an analysis of the way a gas-diffusion layer restricts the process of generation of current in a cathode and of what measures should be taken in order for the extraneous diffusion restrictions to become less significant.     

Selective Electrocatalytic Hydrogenation of trans-2-Allyl-6-methyl(allyl, phenyl)-1,2,3,6-tetrahydropyridines on the Nickel and Copper Cathodes

It is shown that the electrocatalytic hydrogenation (ECH) of trans-2-allyl-6-R-1,2,3,6-tetrahydropyridines (R = Me, All, Ph) on a nickel cathode (Ni_disp/Ni) in 40-% aqueous DMF in the presence of excess AcOH yields products of total hydrogenation of all double bonds—relevant trans-2-propyl-6-R₁-piperidines (R₁ = Me, Pr, Ph). Selective hydrogenation of terminal double bonds of allyl substituents in piperideines under study with the retention of the intracycle double bond may be realized on a copper cathode (Cu_ann), provided the stoichiometric ratio between AcOH and the initial substance is observed exactly. In either case, at points of maximum selectivity of ECH processes, the ratio c _AcOH/c _ini = n+ 1, where nis the number of hydrogenated bonds. The difference in the ECH mechanisms on the Cu_ann and Ni_disp/Ni cathodes is discussed. The results of hydrogenation of the trans-2-allyl-6-R-1,2,3,6-tetrahydropyridines at the Cu_ann and Ni_disp/Ni cathodes confirm the general character of regularities discovered earlier during ECH of citral.     

Methane polymerization with a hollow cathode: Influence of the cathode metal

Methane, mixed with argon, has been polymerized by means of a hollow-cathode discharge system. Two types of cathodes were studied; one was made of a solid solution of 81% tungsten and 19% platinum, while the other was of pure tungsten. Under identical operating conditions, a higher polymer yield was found in the case of the platinum cathode (90% against 70% for tungsten). The work function of the solid solution was estimated to be 6.3 eV, compared with 4.4 eV for tungsten. In terms of the data available, the thermionic current, which is the main source of energetic electrons, is about one order of magnitude lower for the solid solution cathode when compared with the tungsten cathode thermionic current. However, the polymer yield observed is higher in the former case. The concentration of the CH species in the hollow cathode was found to differ greatly for the cathodes tested and was about 5 times higher in the case of tungsten-platinum cathodes. Since no excited platinum vapor could be detected in the gas phase, the increase in CH concentration was attributed to a catalytic effect of the cathode inside surface. An evaluation of the plasma polymer deposition rate yields 70 nm·s^–1 for the platinum-tungsten type hollow cathode and 42 nm·s^–1 for the tungsten one. In both cases, the deposition rate is much higher than those obtained from the most widely used methods for plasma polymer deposition (0.10–1.0 nm·s^–1) implying methane-argon mixtures, and is comparable to the results obtained with a new type of plasma polymer deposition reactor described in the literature.     

Allowed transitions in silicon isoelectronic ions

Dipole‐allowed transitions have been studied for the first few members of the Si isoelectronic sequence. Transition energies, oscillator strengths, transition probabilities and quantum defect values have been estimated for the low‐ and high‐lying excited states of s and d symmetries up to the principal quantum number n=7 for these 3p open shell ions from P⁺ to Cr¹⁰⁺. Time‐dependent coupled Hartree–Fock (TDCHF) theory has been utilized to calculate such transition properties. Most of the results for transition energies, oscillator strengths, and transition probabilities for higher excited states are new. The transition energies for low‐lying excited states agree well with experimental data wherever available. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001