Pushing the envelope of the test functions in the Szegö and Avram–Parter theorems

The Szegö and Avram–Parter theorems give the limit of the arithmetic mean of the values of certain test functions at the eigenvalues of Hermitian Toeplitz matrices and the singular values of arbitrary Toeplitz matrices, respectively, as the matrix dimension goes to infinity. The question on whether these theorems are true whenever they make sense is essentially the question on whether they are valid for all continuous, nonnegative, and monotonously increasing test functions. We show that, surprisingly, the answer to this question is negative. On the other hand, we prove the two theorems in a general form which includes all versions known so far.     

Kinetic study on the living/controlled cationic polymerization of p‐methoxystyrene coinitiated by tris(pentafluorophenyl)borane

A kinetic study of the living cationic polymerization of p‐methoxystyrene using 1‐(4‐methoxyphenyl)ethanol ( 1 )/B(C₆F₅)₃ initiating system in a mixture of CH₃CN with CH₂Cl₂ 1:1 (v/v) at room temperature was carried out utilizing a wide variety of conditions. The polymerization proceeded in a living fashion even in the presence of a large amount of water ([H₂O]/[B(C₆F₅)₃] ratio up to 20) to afford polymers whose M_n increased in direct proportion to monomer conversion with fairly narrow MWDs (M_w/M_n ≤ 1.3). The investigation revealed that the rate of polymerization was first‐order in B(C₆F₅)₃ concentration, while a negative order in H₂O concentration close to ?2 was obtained. It was also found that the rate of polymerization decreased with lowering temperature, which could be attributed to a decreased concentration in free Lewis acid, the true coinitiator of polymerization. A mechanistic scheme to explain the kinetic behavior of living p‐methoxystyrene polymerization is proposed, which has been validated by PREDICI simulation on multiple‐data curves obtained by ¹H NMR in situ polymerization experiment. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6928–6939, 2008     

Fast-switching effect using viscous chiral-nematic materials

We report on chiral-nematic mixtures containing viscous chiral dopants, composed of rigid rod-like chiral molecules, in order to solve the problem of backflow in the middle layers of the liquid crystal cells. During the study, the viscoelastic properties of the liquid crystal compositions have been optimised, as well as the helical twisting power of the chiral compounds, the anchoring energy and the pre-tilt angle of alignment materials, the ratio between the cell gap and the helical pitch (d/P₀). After optimisation, we prepared test cells with low operating voltage – from 1.5 till 5.0 V, fast response time (τ_on + τ_off) – less than 1 ms, wide operating temperature range from ?40°C till +100°C, and good thermal stability. It should be noted that the response time of the new electro-optical mode does not strongly depend on the cell gap, which is in contrast to other known operating modes. We have achieved rather linear than quadratic dependence of the response time when changing the thickness of the cell.     

Origin of the nonadhesive properties of fibrinogen matrices probed by force spectroscopy

The deposition of a multilayered fibrinogen matrix on various surfaces results in a dramatic reduction of integrin-mediated cell adhesion and outside-in signaling in platelets and leukocytes. The conversion of a highly adhesive, low-density fibrinogen substrate to the nonadhesive high-density fibrinogen matrix occurs within a very narrow range of fibrinogen coating concentrations. The molecular events responsible for this transition are not well understood. Herein, single-cell and molecular force spectroscopy were used to determine the early steps in the formation of nonadhesive fibrinogen substrates. We show that the adsorption of fibrinogen in the form of a molecular bilayer coincides with a several-fold reduction in the adhesion forces generated between the AFM tip and the substrate as well as between a cell and the substrate. The subsequent deposition of new layers at higher coating concentrations of fibrinogen results in a small additional decrease in adhesion forces. The poorly adhesive fibrinogen bilayer is more extensible under an applied tensile force than is the surface-bound fibrinogen monolayer. Following chemical cross-linking, the stabilized bilayer displays the mechanical and adhesive properties characteristic of a more adhesive fibrinogen monolayer. We propose that a greater compliance of the bi- and multilayer fibrinogen matrices has its origin in the interaction between the molecules forming the adjacent layers. Understanding the mechanical properties of nonadhesive fibrinogen matrices should be of importance in the therapeutic control of pathological thrombosis and in biomaterials science.     

Nondestructive three-dimensional analysis of layered polymer structures with chemical imaging

Three-dimensional (3D) chemical information was obtained by means of a combination of two-dimensional attenuated total reflection Fourier transform infrared (ATR-FT-IR) imaging with a focal plane array detector and variable angle depth profiling. Since the penetration depth of the evanescent wave in ATR spectroscopy is not limited by diffraction, it was possible to resolve thin sandwiched polymer layers nondestructively within a stack of polymer layers. Chemical images were obtained from layers of different thickness of the laminate by moving a custom-made aperture to specific positions on the condenser lens of the ATR accessory. Sequences of absorption images detect the successive appearance of thin, buried layers of polybutylmethacrylate (d(PBMA) = 400 nm) and polycarbonate (d(TMPC) = 300 nm) in different depths of the stack of polymer layers. The depth resolution of variable-angle ATR-FT-IR imaging is sufficiently high to detect surface roughness at the interface between different polymer layers. Two different stacks of polymers with reordered sandwich-layers were imaged simultaneously, demonstrating the potential of variable angle ATR-FT-IR for 3D-imaging of a sample with xyz-heterogeneity, which can be a powerful analytical technique for materials science and biomedical research.     

Spherical polymer brushes under good solvent conditions: molecular dynamics results compared to density functional theory

A coarse grained model for flexible polymers end-grafted to repulsive spherical nanoparticles is studied for various chain lengths and grafting densities under good solvent conditions by molecular dynamics methods and density functional theory. With increasing chain length, the monomer density profile exhibits a crossover to the star polymer limit. The distribution of polymer ends and the linear dimensions of individual polymer chains are obtained, while the inhomogeneous stretching of the chains is characterized by the local persistence lengths. The results on the structure factor of both single chain and full spherical brush as well as the range of applicability of the different theoretical tools are presented. Finally, a brief discussion of the experiment is given.     

Variation in the regioselectivity of levulinic acid bromination in ionic liquids

The reaction of levulinic acid and its esters with bromine in ionic liquids results in the formation of 3-bromo derivatives as the major products and not the 5-bromo substituted isomers, which are typically formed in organic solvents. The bromination of levulinic acid in ionic liquids in the presence of urea leads to the formation of 5-bromolevulinic acid.     

NaAlF4: Preparation, crystal structure and thermal stability

The compound NaAlF₄ has been obtained in the form of thin fibrous crystals or fine colorless powder by condensation at 18 °C of vapors arising over chiolite Na₅Al₃F₁₄ or NaCaAlF₆, heated up to 800 °C. Thermal stability has been investigated by the methods of thermal analysis and high temperature X-ray diffraction. When heated in air, NaAlF₄ is stable up to 390-400 °C, then there is an exothermal solid state decay into Na₅Al₃F₁₄(s) and AlF₃(s). At higher temperature Na₅Al₃F₁₄(s) decays into Na₃AlF₆(s) and NaAlF₄(g). The crystal structure (space group Cmcm, a=3.6124(1) Å, b=14.9469(7) Å, c=5.2617(3) Å, V=284.10 Å³) has been determined by X-ray powder diffraction method. In the crystal structure of NaAlF₄ the octahedrons [AlF₆] are joined through vertices and form corrugated layers, sodium ion layers being located between them. The distances between the atoms of Al-F are in the range 1.791-1.814 Å, and those for Na…F are in the range 2.297-2.439 Å. In spite of limited thermal stability of the crystal form, the compound NaAlF₄ is the main component of the gas mixture over solid and molten salts in the ternary system NaF-AlF₃-CaF₂ and participates in chemical transformations between the phases at high temperature.     

The influence of the conditions of the anodic formation and the thickness of Ag(I) oxide nanofilm on its semiconductor properties

The anodic formation of Ag(I) oxide nanofilms on polycrystalline silver and Ag–Au alloys as well as on low-index single crystals of silver in 0.1?М KOH was examined. By the methods of photocurrent i _ph and photopotential E _ph measurements, the n-type conductivity of Ag₂O film was established. Since the film (6–120 nm) is thinner than the space charge region, the dependence of photocurrent and photopotential appears on the film thickness L: i _ph ~L and E _ph ~L ². The transition from polycrystalline silver to single crystals as well as the addition of a small amount of gold (X _Au?≤?4 at.%) into the silver lattice decreases the degree of deviation from the stoichiometric composition Ag₂O. The parameters of Ag₂O film (optical absorption coefficient α, donor defects concentration N _D, space charge region W, and Debye’s length of screening L _D) depend on the index of a crystal face of silver, volume concentration of gold X _Au in the alloy, and film-formation potential E. At Е?=?0.52 V, the sequences of variation of these parameters correlate with the reticular density sequence. The growth of the potential disturbs these sequences. The band gap in Ag₂O formed on Ag_poly, Ag_hkl, and Ag–Au is 2.32, 2.23, and 2.19 eV. Flat band potential in Ag(I) oxide, formed on Ag_poly in 0.5 M KOH is 0.37 V. The appearance of the clear dependence between the state of the oxide/metal interface and the structure-sensitive parameters of semiconductor Ag(I) oxide phase allows considering the anodic formation of Ag₂O on Ag as a result of the primary direct electrochemical reaction, not of the precipitation from the near-electrode layer.     

Novel Ionophores for Barium‐Selective Electrodes: Synthesis and Analytical Characterization

A novel way of synthesis is developed for the Ba²⁺ selective neutral Ionophore 2a : 2,2′‐[1,2‐phenylenebis(oxyethane‐2,1‐diyloxy)]bis(N‐benzyl‐N‐phenylacetamide) and its methyl ( 2b ), buthyl ( 2c ), and hexyl ( 2d ) derivatives. Ba²⁺ selective electrodes based on Ionophores 2a – d are compared with those with commonly used Ionophore 1 : N,N,N′,N′‐tetracyclohexyl‐oxybis(o‐phenyleneoxy) diacetamide. It is shown that Ionophores 2a – d , particularly 2b , are superior for measurements of Ba²⁺ in the presence of Ca²⁺, and in acidic solutions. Segmented sandwich membrane studies suggest formation of complexes IL₂²⁺ for Ba²⁺, Ca²⁺ and Mg²⁺ ions with Ionophore 2b , while H⁺ ions apparently form complexes H₂L²⁺. The values of the complex formation constants are consistent with the selectivity coefficients.