Determination of the Rate Constants from Phase Delay Effect in Chemical Reactions

A new method for the determination of rate constant k of a reaction of the type A + X P₁ + P₂ is presented. The method is based on the phase delay between the oscillatory inflow of the parent substance X into the reaction medium and the concentration of the parent substance in the field changing as a result of the reaction, which can be expressed as tan = . A method was used for the determination of the rate constant of the saponification of ethyl acetate (reactant A) with sodium hydroxide (reactant X) at 17°C. Reactant A was used in excess with respect to reactant X, which ensured its constant concentration.     

Fluorescence of lanthanide(III) complexes with aminopolyacetic acids in aqueous solutions

The fluorescence of Eu(III), Gd(III), Tb(III) and Dy(III) ions complexed with aminopolyacetic acids was investigated. The influence of temperature and the dimensions of the ligand molecules and of their electric charge on the intensity of the emission bands is discussed as well as the ratio of the hypersensitive (forbidden) band to the allowed band intensity. On the basis of the fluorescence measurements a simple theoretical model is discussed and certain generalizations concerning the fluorescence of the lanthanides group are derived.

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Fluoreszenz von Lanthaniden(III)-Komplexen mit Aminopolyessigsäuren in wäßrigen Lösungen

Zusammenfassung Die Fluoreszenz von mit Aminopolyessigsäuren komplexierten Eu(III), Gd(III), Tb(III) und Dy(III) Ionen wurde untersucht. Der Einfluß von Temperatur und Größe der Ligandenmoleküle und von deren elektrischer Ladung auf die Intensität der Emissionsbanden wird diskutiert, ebenso das Verhältnis der Intensitäten der hyperempfindlichen und erlaubten Banden. Auf der Basis von Fluoreszenzmessungen wird ein einfaches theoretisches Modell diskutiert und Verallgemeinerungen betreffend der Fluoreszenz der Lanthanidengruppe getroffen.

     

Activation of dimethyl ether with transition metal atoms

The cocondensation of iron or manganese atoms with dimethyl ether at ?196°C leads to organometallic products which upon hydrolysis at 25°C yield a mixture of mainly alkenes and alkanes.     

Theoretische Überlegungen zur Wechselwirkung zwischen verschiedenen Schwingungstypen, 1. Mitt.: Wechselwirkung zwischen Streckschwingungen und Ringwellungsschwingungen (ring-puckering vibrations)

Zusammenfassung Es werden die Folgen der zwei Gleichgewichtszustände bei Ringwellungsschwingungen besprochen. Kopplung zwischen Streckschwingungen mit Deformationsschwingungen einerseits und Ringwellungsschwingungen andererseits muß zu der experimentell beobachteten Abweichung der differentiellen Spektrumsverschiebung führen. Die Frequenzen der Deformationsschwingungen nehmen ab, die der Ringwellungsschwingungen nehmen zu.

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Theoretical discussion of the interaction between different types of vibration, I.: Interaction between stretching and ring-puckering-vibrations

The consequences of the two equilibrium states in ring-puckering vibrations are discussed. Coupling between valence and deformation vibration on the one hand and ring-puckering vibrations on the other has to lead to the experimentally observed irregularity in differential spectrum progression; the deformation frequencies will decrease, and the ring-puckering frequencies will increase.

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Mit 2 Abbildungen     

The Gompertzian curve reveals fractal properties of tumor growth

The normalized Gompertzian curve reflecting growth of experimental malignant tumors in time can be fitted by the power function y(t)=at^b with the coefficient of nonlinear regression r0.95, in which the exponent b is a temporal fractal dimension, (i.e., a real number), and time t is a scalar. This curve is a fractal, (i.e., fractal dimension b exists, it changes along the time scale, the Gompertzian function is a contractable mapping of the Banach space R of the real numbers, holds the Banach theorem about the fix point, and its derivative is 1). This denotes that not only space occupied by the interacting cancer cells, but also local, intrasystemic time, in which tumor growth occurs, possesses fractal structure. The value of the mean temporal fractal dimension decreases along the curve approaching eventually integer values; a fact consistent with our hypothesis that the fractal structure is lost during tumor progression.     

Annealed Ni/Ti/SiC structure analysed by SIMS and GDMS

Depth profile analysis was performed using two mass spectrometry analytical techniques applying argon ion sputtering—secondary ion mass spectrometry (SIMS) and glow discharge mass spectrometry (GDMS). 150 nm Ni/20 nm Ti/4H-SiC structure was prepared by evaporation coating with titanium and nickel. The structure was analysed as prepared and annealed in 600°C in dry N₂. Obtained results allow monitoring several processes present during annealing of Ni/Ti/SiC structures. These are nickel diffusion and its reaction with SiC leading to formation of Ni₂Si, precipitation of carbon and segregation of titanium. Results are also used for comparison of the two analytical techniques used. The techniques base on different ionisation mechanisms. In SIMS, secondary ions are formed at the bombarded surface during ion sputtering process in ultra-high vacuum environment, while in GDMS, ionisation occurs in glow discharge above the eroded surface in low vacuum.     

The construction of the Gilmore–Perelomov coherent states for the Kratzer–Fues anharmonic oscillator with the use of the algebraic approach

By applying the algebraic approach and the displacement operator to the ground state, the unknown Gilmore–Perelomov coherent states for the rotating anharmonic Kratzer–Fues oscillator are constructed. In order to obtain the displacement operator the ladder operators have been applied. The deduced SU(1, 1) dynamical symmetry group associated with these operators enables us to construct this important class of the coherent states. Several important properties of these states are discussed. It is shown that the coherent states introduced are not orthogonal and form complete basis set in the Hilbert space. We have found that any vector of Hilbert space of the oscillator studied can be expressed in the coherent states basis set. It has been established that the coherent states satisfy the completeness relation. Also, we have proved that these coherent states do not possess temporal stability. The approach presented can be used to construct the coherent states for other anharmonic oscillators. The coherent states proposed can find applications in laser-matter interactions, in particular with regards to laser chemical processing, laser techniques, in micro-machinning and the patterning, coating and modification of chemical material surfaces.     

Exact solution of the Schrödinger equation with a new expansion of anharmonic potential with the use of the supersymmetric quantum mechanics and factorization method

The study involves finding exact eigenvalues of the radial Schrödinger equation for new expansion of the anharmonic potential energy function. All analytical calculations employ the mathematical formalism of the supersymmetric quantum mechanics. The novelty of this study is underlined by the fact that for the first time the recurrence formulas for rovibrational bound energy levels have been derived employing factorization method and algebraic approach. The ground state and the excited states have been determined by means of the hierarchy of the isospectral Hamiltonians. The Riccati nonlinear differential equation with superpotentials has been solved analytically. It has been shown that exact solutions exist when the potential and superpotential parameters satisfy certain supersymmetric constraints. The results obtained can be utilized both in computations of quantum chemistry and theoretical spectroscopy of diatomic molecules.