Equation for the incomplete mean temperature density matrix. Application to diffusion in NQR

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 53–56, April, 1989.     

Theory of the singular quantum oscillator

We propose a number of arguments in favor of reevaluating the theory of a quantum oscillator described by the Hamiltonian H=–d²/dx² + 2²x² + x^–2(=2m=1). We propose that functions ₊(x) which continuously reduce to even harmonic oscillator solutions in the 0 limit be taken as the even solutions of the Hamiltonian in the –1/4 < < 3/4 range. In this scheme the problem becomes truly one-dimensional such that even and odd parity energy levels alternate, whereas the usual approach leads to parity degeneracy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 85–89, October, 1989.     

Possible mechanism of metal ion extraction from aqueous solutions by fibrous polypropylene

Peculiarities of the extraction of metal ions from aqueous solutions by fibrous polypropylene have been investigated. It has been found that metal ion adsorption proceeds owing to the existence of a gas-liquid-hydrophobic polymer boundary line. The process mechanism has been discussed.     

Analysis of products of the industrial synthesis of ethylene oxide by two-dimensional gas chromatography using packed capillary columns

Procedures for separating products of the synthesis of ethylene oxide by two-column gas chromatography using both conventional capillary PLOT columns and packed capillary columns of a new type bearing microparticulated adsorbents are proposed. A combination of packed capillary columns with a microthermostat reduces both separation time and the size of the chromatographic system, which becomes compatible with microreactors. The short time of analysis enables the control over the work of a series of microreactors in a cyclic mode using one chromatographic system.     

Quantum dynamics of H2 formation on a graphite surface through the Langmuir Hinshelwood mechanism

We have studied the formation of the H2 molecule on a graphite surface, when both H atoms are initially physisorbed. The graphite surface is assumed to be planar, and a model potential is obtained in a semiempirical way to reproduce the experimental properties of H physisorption on graphite. The reaction probability has been computed in the case when the angular momentum of the relative H-H motion lies parallel to the surface plane. Three-dimensional wave packet calculations have been performed for collision energies ranging from 2 to 50 meV. It is shown that the reaction occurs with a significant probability and produces the H2 molecule with a considerable amount of vibrationnal energy. A simple mechanical model is presented, where desorption of the nascent H2 molecule results from two successive binary elastic collisions.     

3, 3, 3-Trifluoropropyl(methyl)cyclosiloxanes

The influence of the number of 3, 3, 3-trifluoropropyl(methyl)siloxane links (/) in the cyclotetrasiloxanes _mD_4-m, where D represents the dimethylsiloxane link and m=0–4, on the rearrangement of these compounds in acetone solution under the action of sodium siloxanolate has been studied. The rearrangement takes place with the formation of a linear polysiloxane the degradation of which yields, in addition to the initial ring, cyclosiloxanes with a different structure. The rate of rearrangement of _mD_4-m and of the formation of a linear polysiloxane rises with an increase in m from 0 to 3. The equilibrium concentration of the linear polysiloxane formed from _mD_4-m is inversely proportional to m. Results have been obtained on the kinetics of the formation of the cyclosiloxanes _mD_n, where m=0–5, n=0–5, and m+n=3–6, in the rearrangement of the rings D₃, ₂D₂, ₃D, and ₄. The reactivity of the siloxane links rises in the sequence (CH₃)₂Si-O-Si(CH₃)₂ < (CF₃CH₂CH₂)-(CH₃) Si-O-Si(CH₃)₂ <(CF₃CH₂CH₂) (CH₃)Si-O-Si(CH₃) (CH₂CH₂CF₃) . Because of the negative inductive effect transferred through the siloxane links, the 3, 3, 3-trifluoropropyl groups strongly activate the siloxane ring with respect to nucleophiiic reagents.For part I, see [3].     

2-Diphenylphosphinoyloxybenzaldehyde 4-Nitrophenyl-, 4-Phenyl-1-phthalazinyl-, and Aroylhydrazones and Thiosemicarbazone

Condensation of aryl- and aroylhydrazines and thiosemicarbazide with 2-diphenylphosphinoyloxybenzaldehyde results in formation of the corresponding hydrazones and thiosemicarbazone. The products give rise to conformational equilibrium between rotational and Z,E isomers, which is strongly displaced toward the E,E',Z' isomer and is determined by the nature of substituent in the hydrazine fragment.