Analytical Study of Discrete Optical Breathers in Spiral Polymer Chain

Physico‐mechanical properties of polymers in solid state, in particular conditions of their structural transformations, are substantially defined by existence and mobility of elementary nonlinear excitations. The localized oscillatory excitations (breathers), which have been revealed earlier in crystalline polyethylene alongside with topological solitons, turn out to be significant for thermodynamic studies as well as for investigation of energy transfer. We consider analytically the breathers in more complex crystalline polytetrafluoroethylene. It is shown that introduction of adequate variables allows to construct the continuum model describing spatially localized excitations with several internal degrees of freedom. Characteristic parameters of breathers and conditions of their mobility are defined.

     

The effect of substrate roughness on the static friction of CuO nanowires

The dependence of static friction on surface roughness was measured for copper oxide nanowires on silicon wafers coated with amorphous silicon. The surface roughness of the substrate was varied to different extent by the chemical etching of the substrates. For friction measurements, the nanowires (NWs) were pushed by an atomic-force microscope (AFM) tip at one end of the NW until complete displacement of the NW was achieved. The elastic bending profile of a NW during this manipulation process was used to calculate the ultimate static friction force. A strong dependence of static friction on surface roughness was demonstrated. The real contact area and interfacial shear strength were estimated using a multiple elastic asperity model, which is based on the Derjaguin–Muller–Toporov (DMT) contact mechanics. The model included vertical elastic flexure of NW rested on high asperities due to van der Waals force.     

The 57Fe Synchrotron Mössbauer Source at the ESRF

The design of a ⁵⁷Fe Synchrotron Mössbauer Source (SMS) for energy‐domain Mössbauer spectroscopy using synchrotron radiation at the Nuclear Resonance beamline (ID18) at the European Synchrotron Radiation Facility is described. The SMS is based on a nuclear resonant monochromator employing pure nuclear reflections of an iron borate (⁵⁷FeBO₃) crystal. The source provides ⁵⁷Fe resonant radiation at 14.4 keV within a bandwidth of 15 neV which is tunable in energy over a range of about ±0.6 µeV. In contrast to radioactive sources, the beam of γ‐radiation emitted by the SMS is almost fully resonant and fully polarized, has high brilliance and can be focused to a 10 µm × 5 µm spot size. Applications include, among others, the study of very small samples under extreme conditions, for example at ultrahigh pressure or combined high pressure and high temperature, and thin films under ultrahigh vacuum. The small cross section of the beam and its high intensity allow for rapid collection of Mössbauer data. For example, the measuring time of a spectrum for a sample in a diamond anvil cell at ～100 GPa is around 10 min, whereas such an experiment with a radioactive point source would take more than one week and the data quality would be considerably less. The SMS is optimized for highest intensity and best energy resolution, which is achieved by collimation of the incident synchrotron radiation beam and thus illumination of the high‐quality iron borate crystal within a narrow angular range around an optimal position of the rocking curve. The SMS is permanently located in an optics hutch and is operational immediately after moving it into the incident beam. The SMS is an in‐line monochromator, i.e. the beam emitted by the SMS is directed almost exactly along the incident synchrotron radiation beam. Thus, the SMS can be easily utilized with all existing sample environments in the experimental hutches of the beamline. Owing to a very strong suppression of electronic scattering for pure nuclear reflections (～10^?9), SMS operation does not required any gating of the prompt electronic scattering. Thus, the SMS can be utilized in any mode of storage ring operation.     

Many faces of stickiness in Hamiltonian systems

We discuss the phenomenon of stickiness in Hamiltonian systems. By visual examples of billiards, it is demonstrated that one must make a difference between internal (within chaotic sea(s)) and external (in vicinity of KAM tori) stickiness. Besides, there exist two types of KAM-islands, elliptic and parabolic ones, which demonstrate different abilities of stickiness.     

Stereoselective recognition of vicinal diamines with a Zn(II) complex

Zn(II) complex of L (N,N'-bis(2-pyridylmethyl)-N,N'-dimethyl-trans-1,2-diaminocyclohexane) binds chiral vicinal diamines (1,2-diphenylethylenediamine (dpen) and 1,2-diaminocyclohexane (dach)) stereoselectively. Crystallographic studies reveal that the ternary complex has the C2 symmetric cis-alpha topology. 1H NMR shows that the R,R form of the tetradentate zinc complex binds rapidly and reversibly to the R,R form of the diamine over the S,S form with a stereoselectivity of about 5:1. Although the diamine exchange rate is rapid it is slower than the NMR time scale, and distinct signals for the diastereomeric complexes are observed when racemic mixtures of the host and guest molecules are mixed. Origin of stereoselectivity is discussed in terms of steric effects.     

Bethe-Sommerfeld conjecture for periodic operators with strong perturbations

We consider a periodic self-adjoint pseudo-differential operator H=(?Δ) ^m +B, m>0, in ? ^d which satisfies the following conditions: (i) the symbol of B is smooth in x, and (ii) the perturbation B has order less than 2m. Under these assumptions, we prove that the spectrum of H contains a half-line. This, in particular implies the Bethe-Sommerfeld conjecture for the Schrödinger operator with a periodic magnetic potential in all dimensions.     

Features of the adsorption of Naproxen on the chiral stationary phase (S,S)-Whelk-O1 under reversed-phase conditions

Using elution chromatography, we studied the adsorption mechanism of the Naproxen enantiomers on the chiral stationary phase (S,S)-Whelk-O1, from buffered methanol–water solutions. We propose an adsorption mechanism that assumes monolayer adsorption of the more retained enantiomer and the associative adsorption of the less retained one. The effects of the mobile phase composition on the adsorption of Naproxen are discussed. The combination of an elevated column temperature and of the use of an acidic mobile phase led to the degradation of the column and caused a major loss of its separation ability. The use of a moderately acidic mobile phase at temperature slightly above ambient did not produce rapid severe damages but, nevertheless, hampered the experiments and caused a slow gradual deterioration of the column.     

Radiogenic argon distribution within a mineral grain: implications for dating of hydrothermal mineral-forming event in Sludyanka complex, Siberia, Russia

Usually, in age-determination procedures, the experimenter is interested in the mean concentrations of parent and daughter substances. However, the structure of a solution of the Fick's diffusion equation enables one to specify a procedure, allowing, through macroscopic experiments, one to determine the distribution of radiogenic argon (as well as any of other isotopes) within a mineral grain. Argon, influenced in the geological past by a metamorphic event, has a half-sinusoidal distribution, whereas argon preserved in geological time has a rectangular distribution. The ratio of the quantity of argon of the first type to the total argon is called an alpha-factor. It is believed that this coefficient can be of great interest for geochronological studies, being a symptom of virtual Ar losses and the time instant, at which they happened. A laboratory procedure and a mathematical algorithm to determine the alpha-factor are developed. As an example, a determination of the alpha-factor on a vein-phlogopite from the well-studied Sludyanka deposit, Southern Baikal, Siberia, Russia, is described. Rb-Sr isochron age on phlogopite-calcite-apatite paragenetic assemblage yielded 460+/-7 Ma and is constrained by U-Pb zircon ages of 471+/-1 and 447+/-2 Ma, respectively, on an emplacement of early syenites and monzonites and later 'post-phlogopitic' pegmatites [E.B. Salnikova, S.A. Sergeev, A.B. Kotov, S.Z. Yakovleva, R.H. Steiger, L.Z. Reznitskiy, E.P. Vasil'ev. U-Pb zircon dating of granulite metamorphism in the Sludyanskiy complex, Eastern Siberia. Gondwana Res., 1, 195-205 (1998). L.Z. Reznitskii, G.P. Sandimirova, Y.A. Pakhol'chenko, S.V. Kuznetsova. The Rb-Sr age of phlogopite deposits in Sludyanka, southern Baikal region. Dokl. Earth Sci., 367, 711-713 (1999). L.Z. Reznitskii, A.B. Kotov, E.B. Salnikova, E.P. Vasil'ev, S.Z. Yakovleva, V.P. Kovach, A.M. Fedoseenko. The age and time span of the origin of phlogopite and lazurite deposits in the Southwestern Baikal area: U-Pb geochronology. Petrology, 8, 66-76 (2000).]. In this study, the phlogopite gave an apparent K-Ar age of 365.6+/-10.4 Ma which has no geological meaning. The alpha-factor of 0.27 was derived from a laboratory kinetic experiment. The age determined by the rectangularly distributed argon corresponded to alphax0.129 nmm3/g (total radiogenic argon in the sample)=94.17 nmm3/g, and an age of approximately 274 Ma (e.g. a period without any argon losses). Here, at the first sight, we deal with common argon losses not conjugated with any geological event, because after 447 Ma only lower temperature (in a range of 50-300 degrees C) hydrothermal processes were recorded. A paragenetic phlogopite-bearing vein mineral, hyalophane, having a disturbed Rb-Sr isotopic system, however, yielded 40Ar/39Ar subplateau age of 271+/-2 Ma [V.V. Ivanenko, M.I. Karpenko, M.A. Litsarev. Age of the Sludyanka phlogopite deposits (in Russian; data of the 39Ar-40Ar method). In Geological Series 5, pp. 92-98, Izvestiya Akademii Nauk SSSR, Moskva (1990).], marking similar timing of the K-Ar isotopic system closure. This indicates that K-Ar isotopic system in the phlogopite was not closed (or was partially reset) long after its crystallisation and closing of the Rb-Sr system, in spite of the fact that the crystal was not affected by processes having temperatures above the accepted closure temperatures for micas. There seems to have acted an exchange mechanism of OH-groups between surrounding fluid and hydrocrystal structure. Thus the argon loss did not occur, spontaneously, but argon particles seem to have been captured and carried to the mineral surface by vacancies formed during displacements of OH-groups.     

Paramagnetic intermediates in the photoinduced reaction between dodecamethylcyclohexasilane and 9,10-phenanthraquinone: Time-resolved CIDNP study

The reaction between dodecamethylcyclohexasilane (Me₂Si)₆1 and 9,10-phenanthraquinone 2 has been studied by means of CIDNP method. In the polar solvent, the photodecomposition of 1 is shown to proceed via triplet radical ion pair formed by phenanthraquinone radical anion and cyclohexasilane radical cation. Its transformation leads to the cyclic reaction product - 10-membered cyclic dioxahexasilecine 8 - formally resulting from the addition of linear 1,6-silicon-centered biradical Si(Me)₂-Si₄(Me₂)₄-(Me)₂Si to CO bonds of quinone. Product 8 is unstable, after several hours it converts to dioxasilole 4 via sequential repeated elimination of dimethylsilylenes 3.