Dielectric relaxation measurements on nonlinear side-chain polymers

Dynamic dielectric relaxation measurements in the frequency range from 0.001 Hz to 5 kHz have been performed on an amorphous nonlinear optical side-chain polymer, containing the active molecule 4-dimethylamino-4-nitrostilbene as pendant group. The results yielded the relaxation times of the group in the temperature region from 20° below to 40° above the glass-transition temperature of the polymer. The temperature dependence could be described well by the Williams-Landel-Ferry (WLF) equation. It is shown that the relaxation times have a distribution, which could be fit to the form of Cole and Cole with a parameter =0.55. Consequently a substantial part of the active molecules will not be aligned when the polymer is subjected to a poling procedure.     

Pseudo-steady-state solutions for solidification in a wedge

Polubarinova-Kochina's analytical differential equation methodis used to determine the pseudo-steady-state solution to problemsinvolving the freezing (solidification) of wedges of liquidwhich are initially at their fusion temperature. In particular,we consider four distinct problems for wedges which are: freezingwith the same constant boundary temperature, freezing with thesame constant boundary heat fluxes, freezing with distinct constantboundary temperatures and freezing with distinct constant fluxesat the boundaries. For the last two problems, a Heun's differentialequation with an unknown singularity is derived, which in bothcases admits a particularly elegant simple solution for thespecial case when the wedge angle is . The moving boundariesobtained are shown pictorially.     

Influence of rotational diffusion of the Mössbauer spectrum of ultrafine particles in a supercooled liquid

The theory of the Mössbauer line shape of ultrafine particles in a liquid has been developed taking into account both translational and rotational diffusion of the particles. A simple analytical expression has been found for the line shape in the limiting case of fast rotational diffusion. In this limit the line shape appears to be independent of the rotational diffusion constant apart from a constant and a scaling factor. The quadrupole splitting remains visible even in this limiting case in contrast to the case of molecular rotation diffusion spectra. The predictions of the theory are compared with experimental spectra of nanosize iron oxide particles dispersed in supercooled decalin where a rapid decrease of the total area with increasing temperature has been found. The present theory can account for a part of the observed loss of spectral area. It is also demonstrated that the uncertainty in the determination of the total area and diffusion constants from the Mössbauer spectra increases significantly when the rotational diffusion is taken into account.     

Moment methods in Padé approximation: The unitary case

Given a unitary operator T in a Hilbert space H = (H, 〈·, ·〉) convergence results for two sequences of ($\text{(n ? 1)}\text{n)}$ two-point Padé approximants to the function f(z) = 〈(I ? zT)^?1u₀, u₀〉, (u₀ ∈ H, ∥ u₀∥ = 1, z regular for T) are given. An elementary proof is also given of the well-known operator version of the trigonometric moment problem, not using the solution of the classical trigonometric moment problem.     

Structure and reactivity of surface oxides on Pt(110) during catalytic CO oxidation

We present the first structure determination by surface x-ray diffraction during the restructuring of a model catalyst under reaction conditions, i.e., at high pressure and high temperature, and correlate the restructuring with a change in catalytic activity. We have analyzed the Pt(110) surface during CO oxidation at pressures up to 0.5 bar and temperatures up to 625 K. Depending on the pressure ratio, we find three well-defined structures: namely, (i) the bulk-terminated Pt(110) surface, (ii) a thin, commensurate oxide, and (iii) a thin, incommensurate oxide. The commensurate oxide only appears under reaction conditions, i.e., when both and CO are present and at sufficiently high temperatures. Density functional theory calculations indicate that the commensurate oxide is stabilized by carbonate ions (CO3(2-)). Both oxides have a substantially higher catalytic activity than the bulk-terminated Pt surface.     

Defect chemistry and oxygen transport of (La0.6Sr0.4 − xMx)0.99Co0.2Fe0.8O3 − δ, M = Ca (x = 0.05, 0.1), Ba (x = 0.1, 0.2), Sr: Part II: Oxygen transport

This paper is the second part of a two part series, where the effects of varying the A-site dopant on the defect chemistry and transport properties of the materials (La_0.6Sr_0.4 ? xM_x)_0.99Co_0.2Fe_0.8O_3 ? δ, M = Sr, Ca (x = 0.05, 0.1), Ba (x = 0.1, 0.2) (LSMFC) have been investigated. In part I, the findings on the defect chemistry were reported, while the oxygen transport properties are reported here in part II. In the investigated material series, the amount of divalent dopant has been kept constant, while Sr ions have been substituted with Ca ions (smaller ionic radius) or Ba ions (larger ionic radius). The size difference induces different strains into the crystal structure in each composition. The possibility of simple relationships between various crystal strain parameters and the transport properties were analyzed. Oxygen pump controlled permeation experiments and a surface sensitive electrolyte probe were used to extract the permeability and surface resistance, r_s. The highest permeability was found for (La_0.6Sr_0.3Ca_0.1)_0.99Co_0.2Fe_0.8O_3 ? δ. The apparent activation energy of the permeability was 78 kJ/mol. The inverse surface resistance, r_s^? 1, also had an activated behavior with an activation energy close to 180 kJ/mol for most of the materials. A reversible transition to an abnormally low r_s was found in (La_0.6Sr_0.3Ca_0.1)_0.99Co_0.2Fe_0.8O_3 ? δ at T > 1223 K.     

Orthogonal rational functions and modified approximants

Let {α _n | _n ^∞ be a sequence in the open unit disk in the complex plane and let $(\overline {\alpha _k } |\alpha _k | = - 1$ when α _k =0. Let μ be a positive Borel measure on the unit circle, and let {φ _n } _n ^∞ be the orthonormal sequence obtained by orthonormalization of the sequence {B _n } _n ^∞ with respect to μ. Let {ψ _n } _n ^∞ be the sequence of associated rational functions. Using the functions φ _n , ψ _n and certain conjugates of them, we obtain modified Padé-type approximants to the function $$F\mu (z) = \int\limits_{ - \pi }^\pi {\frac{{t + z}}{{t - z}}} d\mu (\theta ), (t = e^{i\theta } ).$$      

A reactive rhodium(I) carbonyl dithiolate and the formation of acyl and hydride species

The rhodium(I) complex [Rh(CO)(PEt₃)(mnt)]^? (mnt = maleonitriledithiolate) reacts with a variety of alkyl halides to form acyl complexes isolated in the presence of excess PEt₃ as five-coordinate species of formula [Rh(COR)(PEt₃)₂(mnt)]. The structure of the complex for R = n-Pr has been determined by an X-ray analysis, and is found to be a square-based pyramid with the acyl group in the apical position. Addition of HClO₄ to the rhodium(I) anion in the presence of excess PEt₃ yields rhodium(III) hydride, [RhH(CO)(PEt₃)₂(mnt)], while addition of acid to the rhodium(I) complex in CH₃CN solution with ethylene present leads slowly to formation of an acyl complex which is isolated as [Rh(COEt)(PEt₃)₂(mnt)] upon phosphine addition. A novel alkyl group migration from the acyl carbon to a donor S atom is also observed in monophosphine systems.     

Orthogonal Rational Functions and Nested Disks

In Akhiezer's book [“The Classical Moment Problem and Some Related Questions in Analysis,” Oliver & Boyd, Edinburghasol;London, 1965] the uniqueness of the solution of the Hamburger moment problem, if a solution exists, is related to a theory of nested disks in the complex plane. The purpose of the present paper is to develop a similar nested disk theory for a moment problem that arises in the study of certain orthogonal rational functions. Let {α_n}^∞_n=0be a sequence in the open unit disk in the complex plane, let

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( /|α_k|=−1 whenα_k=0), and let

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We consider the following “moment” problem: Given a positive-definite Hermitian inner product ·, · on × , find a non-decreasing functionμon [−π, π] (or a positive Borel measureμon [−π,π)) such that

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In particular we give necessary and sufficient conditions for the uniqueness of the solution in the case that If this series diverges the solution is always unique.