Simple one-dimensional interaction systems with superexponential relaxation times

Finite one-dimensional random processes with local interaction are presented which keep some information of a topological nature about their initial conditions during time, the logarithm of whose expectation grows asymptotically at least asM ³, whereM is the size of the setR _M of states of one component. ActuallyR _M is a circle of lengthM. At every moment of the discrete time every component turns into some kind of average of its neighbors, after which it makes a random step along this circle. All these steps are mutually independent and identically distributed. In the present version the absolute values of the steps never exceed a constant. The processes are uniform in space, time, and the set of states. This estimation contributes to our awareness of what kind of stable behavior one can expect from one-dimensional random processes with local interaction.Partially supported by NSF grant #DMS-932 1216.     

Quantum decay of supercurrent in thin superconducting wires

Quantum fluctuations cause a decay of the supercurrent in thin superconducting wires making them resistive even at very low temperatures. We derive a microscopic effective action formalism that goes beyond the usual TDGL approach and study quantum fluctuations of the superconducting order parameter at all temperatures belowT _C . We calculate the quantum phase slip rate in thin superconducting wires, demonstrate the importance of dissipation in a quantum phase slip process, and evaluate the resistanceR(T) of the wire. In very thin wires the effect is well observable, even at zero temperature.     

Synthesis, X-ray diffraction studies, and DFT calculations on hexacoordinated germanium derivatives: the case of germaspirobis(ocanes)

Synthesis of the title compounds, viz. [RN(CH2CHR'O)2]2Ge (1, R = Me, R' = H; 2, R = Me, R' = Ph; 3, R = Ph, R' = H), by the reaction of 2 equiv of corresponding dialkanolamines RN(CH2CHR'OH)2 (4, R = Me, R' = H; 5, R = Me, R' = Ph; 6, R = Ph, R' = H) with (AlkO)4Ge is reported. Composition and structures of all novel compounds were established by 1H and 13C NMR spectroscopy and mass spectrometry as well as elemental analysis data. The single-crystal X-ray diffraction of 2 has clearly indicated the presence of two transannular interactions Ge<--N in the compound. N atoms are cis-orientated. The compound 3 possesses long Ge...N distances. The structural data obtained from geometry optimizations by DFT calculations on 1-3 reproduces experimental results. Both cis- and trans-isomers were studied, and cis-configuration was found to be more thermodynamically stable for all three compounds. The transition states for possible cis <--> trans rearrangement processes in 1-3 were calculated. The properties of the Ge-O and Ge<--N bonds in 1-3 were analyzed by the AIM approach. The interactions between the Ge atom and N atoms as well as O atoms possess predominantly ionic character.     

Synthesis and Structural Characterisation of Two Copper(II) Complexes of <Emphasis Type="Italic">N</Emphasis>-(1-acetyl-2-propylidene) (2-pyridylmethyl) amine

Two new complexes [CuBr(C₁₁H₁₃N₂O)] (1) and [Cu(NCO)(C₁₁H₁₃N₂O)] (2) containing the tridentate Schiff base ligand, N-(1-acetyl-2-propylidene)(2-pyridylmethyl) amine which is the 1:1 condensation product of acetylacetone and 2-aminomethylpyridine, have been synthesised and characterised by elemental analysis, IR and electronic spectra, electrochemical study and single crystal X-ray diffraction study. Crystal structures reveal that the copper atom in both the complexes are in square geometry formed by the N₂O donor set of the Schiff base and a bromine atom in 1 and one cyanate ligand in 2. Both bromide and isocyanate ligands act in a terminal monodentate fashion.     

Solid State Supramolecular Complexes [Hg<Subscript>6</Subscript>As<Subscript>4</Subscript>](CuX<Subscript>3</Subscript>)<Subscript>2</Subscript> (X <Emphasis Type="Bold">=</Emphasis> Cl,Br): One-Dimensional Helical Guest in a Three-Dimensional Host Framework

Two new supramolecular complexes, [Hg₆As₄](CuBr₃)₂ (1) and [Hg₆As₄](CuCl₃)₂ (2), have been synthesized and their crystal structures have been determined. Compound 1 crystallizes in the monoclinic system, space group I2/a (No. 15), with the unit cell dimensions a = 14.884(3), b = 9.358(2), c = 20.413(4) Å, β=92.88(3)°, and Z = 6. The crystal structure is comprised of the three-dimensional [Hg₆As₄]⁴⁺ polycationic framework hosting one-dimensional 6-step helical (CuBr guest chains built of the [CuBr₄] tetrahedra sharing two of their vertexes. The complex 2 exhibits a distorted variant of the same type of crystal structure (space group I2/a, a = 14.690(1), b = 9.1851(7), c = 20.285(1) Å, β=92.170(1), and Z = 6) that is characterized by a multifarious positioning of the guest anions in the cavities of the perfectly ordered [Hg₆As₄]⁴⁺ host framework. Structures of the title supramolecular assemblies and the previously reported silver-containing analogue [Hg₆As₄](AgCl₃)₂ are discussed taking into account the principles of host–guest complementarity.     

Isotropic magnetic exchange between anisotropic Yb(III) ions. Study of Cs3Yb2Cl9 and Cs3Yb2Br9 crystals

Despite the prevalent belief about a strong anisotropy of the magnetic exchange in rare-earth compounds, Cs3Yb2Cl9 and Cs3Yb2Br9 crystals are found to exhibit fully isotropic exchange coupling between Yb3+ ions. In this article, we attempt to reveal the physical origin of this surprising feature. Our theoretical consideration is based on a model of the kinetic exchange between two octahedrally coordinated Yb3+ ions in their ground Kramers doublet states. It is shown that a mechanism of kinetic exchange involving intercenter electron hopping between 4f orbitals of two Yb3+ ions in a face-shared binuclear unit results in fully isotropic antiferromagnetic exchange coupling, while a mechanism in which the electron jumps from the 4f to the 5d orbital gives rise to a highly anisotropic interaction. Comparison of these results with the experimental data along with qualitative arguments regarding the relative significance of these two contributions to the overall exchange indicate that, in face-shared Yb3+ binuclear units, the 4f <--> 4f mechanism plays a dominant role.     

Selection of anion exchangers for detoxification of dilute-acid hydrolysates from spruce

Six anion-exchange resins with different properties were compared with respect to detoxification of a dilute-acid hydrolysate of spruce prior to ethanolic fermentation with Saccharomyces cerevisiae. The six resins encompassed strong and weak functional groups as well as styrene-, phenol-, and acrylic-based matrices. In an analytical experimental series, fractions from columns packed with the different resins were analyzed regarding pH, glucose, furfural, hydroxymethylfurfural, phenolic compounds, levulinic acid, acetic acid, formic acid, and sulfate. An initial adsorption of glucose occurred in the strong alkaline environment and led to glucose accumulation at a later stage. Acetic and levulinic acid passed through the column before formic acid, whereas sulfate had the strongest affinity. In a preparative experimental series, one fraction from each of six columns packed with the different resins was collected for assay of the fermentability and analysis of glucose, mannose, and fermentation inhibitors. The fractions collected from strong anion-exchange resins with styrene-based matrices displayed the best fermentability: a sevenfold enhancement of ethanol productivity compared with untreated hydrolysate. Fractions from a strong anion exchanger with acrylic-based matrix and a weak exchanger with phenol-based resin displayed an intermediate improvement in fermentability, a four- to fivefold increase in ethanol productivity. The fractions from two weak exchangers with styrene- and acrylic-based matrices displayed a twofold increase in ethanol productivity. Phenolic compounds were more efficiently removed by resins with styrene-and phenol-based matrices than by resins with acrylic-based matrices.     

Probing photoelectrochemical processes in Au-CdS nanoparticle arrays by surface plasmon resonance: application for the detection of acetylcholine esterase inhibitors

The photoelectrochemical charging of Au-nanoparticles (NP) in a Au-nanoparticle/CdS-nanoparticle array assembled on a Au-coated glass surface is followed by means of surface plasmon resonance (SPR) spectroscopy upon continuous irradiation of the sample. The charging of the Au-NPs results in the enhanced coupling between the localized surface plasmon of the Au-NP and the surface plasmon of the bulk surface, leading to a shift in the plasmon angle. The charging effect of the Au-NPs is supported by concomitant electrochemical experiments in the dark. Analysis of the results indicates that ca. 4.2 electrons are associated with each Au-nanoparticle under steady-state irradiation. The photoelectrochemical charging effect of the Au-NPs in the Au-CdS NP array is employed to develop a SPR sensor for acetylcholine esterase inhibitors.     

Sn19.3Cu4.7As22I8: a new clathrate-I compound with transition-metal atoms in the cationic framework

Sn19.3Cu4.7As22I8, a new clathrate-I compound with a cationic host framework containing transition metals, has been synthesized, and its crystal structure has been determined. It crystallizes in the cubic space group Pmn with a unit cell parameter a = 11.1736(3) angstroms and Z = 1 (R = 0.031 for 329 independent reflections and 22 variables). Tin, copper, and arsenic form the cationic clathrate framework hosting the guest iodine anions in cages of two different shapes. Sn19.3Cu4.7As22I8 does not contain vacancies in the framework but reveals three partially occupied positions of the metal atoms, leading to the formation of Sn-Sn and Sn-Cu bonds that differ in length. The 119Sn M?ssbauer spectrum confirms the local environment of tin atoms. The hyperfine constants obtained from the M?ssbauer spectra for different cationic tin clathrates are discussed. Electron diffraction and electron microscopy reveal that the splitting affects the short-range ordering but does not lead to a superstructure. Though containing a transition metal, Sn19.3Cu4.7As22I8 is diamagnetic, and its composition corresponds to the Zintl formalism.