Persistence vectors and higher moment tensors of polyoxyalkanes

Statistical mechanical averages of vectors and tensors characterizing the spatial configurations of polyoxymethylene (POM) and polyoxyethylene (POE) chains, i.e., the chain vector r connecting the ends of the chain and the tensors formed from this vector, are evaluated in internal reference frames attached to the first two bonds of each chain as functions of its length. Convergences of the persistence vectors a ≡ 〈 r 〉 with chain length to their limits a _∞ are delineated. For POE, the orientation of a _∞ with respect to the X₁ axes (the direction of the first bond) depends markedly on the choice of the initial bond and hence also on the internal frame of reference. Cartesian tensors up to fourth rank formed from the displacement vector ρ = r ? a are evaluated for n = 4–1922 bonds for POM and n = 3–300 bonds for POE. The second moment tensor 〈ρρ^T〉 calculated for POM is nearly cylindrically symmetric about the axis perpendicular to the plane of the first two bonds. Corresponding symmetry is absent in POE. Correlation with the freely jointed chain is investigated for the components of the tensors of fourth rank formed from the reduced vector \documentclass{article}\pagestyle{empty}\begin{document} $\tilde \rho = \left\langle {\rho \rho ^{\rm T} } \right\rangle ^{ - 1/2} \rho $\end{document}. Use of the equivalent chain model for this purpose is validated for POE but not for POM, even at n = 2000 bonds. At the limit 1/n = 0, the parameter m, representing the number of bonds of the real chain equivalent to one of the model, is estimated to be ca. 31 for POM. For POE a value of m = 10.3 ± 1.3 holds for n > 20 for all components. Results are compared with those calculated previously for polymethylene, poly(dimethylsiloxane) and polypeptides. The fact that values of m derived by analysis of moments are larger than those obtained in the usual manner by fitting the model chain to 〈r²〉₀ and r_max for the real chain demonstrates the inadequacy of artificial models for the representation of the real chain.     

Modified Wave Operators for Maxwell-Schrödinger Equations in Three Space Dimensions

We study the scattering theory for the Maxwell-Schrödinger equations under the Coulomb gauge and the Lorentz gauge conditions in three space dimensions. These equations belong to the borderline between the short range case and the long range one. We prove the existence of modified wave operators for those equations for small scattered states with no restriction on the support of the Fourier transform of them. Communicated by Vincent Rivasseau submitted 14/11/02, accepted: 29/04/03     

Measurement of soil/dust arsenic by gas phase chemiluminescence

A gas phase chemiluminescence (GPCL)-based method for trace measurement of arsenic has been recently described for the measurement of arsenic in water. The principle is based on the reduction of inorganic As to AsH₃ at a controlled pH (the choice of pH governs whether only As(III) or all inorganic As is converted) and the reaction of AsH₃ with O₃ to produce chemiluminescence (Idowu et al., Anal. Chem. 78 (2006) 7088-7097). The same general principle has also been used in postcolumn reaction detection of As, where As species are separated chromatographically, then converted into inorganic As by passing through a UV photochemical reactor followed by AsH₃ generation and CL reaction with ozone (Idowu and Dasgupta, Anal. Chem. 79 (2007) 9197-9204). In the present paper we describe the measurement of As in different soil and dust samples by serial extraction with water, citric acid, sulfuric acid and nitric acid. We also compare parallel measurements for total As by induction coupled plasma mass spectrometry (ICP-MS). As(V) was the only species found in our samples. Because of chloride interference of isobaric ArCl⁺ ICP-MS analyses could only be carried out by standard addition; these results were highly correlated with direct GPCL and LC-GPCL results (r² = 0.9935 and 1.0000, respectively). The limit of detection (LOD) in the extracts was 0.36 μg/L by direct GPCL compared to 0.1 μg/L by ICP-MS. In sulfuric acid-based extracts, the LC-GPCL method provided LODs inferior to those previously observed for water-based standards and were 2.6, 1.3, 6.7, and 6.4 μg/L for As(III), As(V), dimethylarsinic acid (DMA) and monomethylarsonic acid (MMA), respectively.     

Aromaticity and π-bond covalency: prominent intermolecular covalent bonding interaction of a Kekulé hydrocarbon with very significant singlet biradical character

An anthracene-linked bisphenalenyl Kekulé molecule with very significant singlet biradical character has shown a prominent covalent bonding interaction between molecules in a molecular aggregate. High aromatic stabilization energy in the anthracene linker is responsible for the significant singlet biradical character.     

Shape and topology optimization based on the phase field method and sensitivity analysis

This paper discusses a structural optimization method that optimizes shape and topology based on the phase field method. The proposed method has the same functional capabilities as a structural optimization method based on the level set method incorporating perimeter control functions. The advantage of the method is the simplicity of computation, since extra operations such as re-initialization of functions are not required. Structural shapes are represented by the phase field function defined in the design domain, and optimization of this function is performed by solving a time-dependent reaction diffusion equation. The artificial double well potential function used in the equation is derived from sensitivity analysis. The proposed method is applied to two-dimensional linear elastic and vibration optimization problems such as the minimum compliance problem, a compliant mechanism design problem and the eigenfrequency maximization problem. The numerical examples provided illustrate the convergence of the various objective functions and the effect that perimeter control has on the optimal configurations.     

Nuclear field shift effect in isotope fractionation of thallium

Environmental transport of Tl is affected by redox reaction between Tl(I) and Tl(III) and ligand exchange reactions of them. In order to deepen the knowledge of Tl chemistry, we investigated fractionation of Tl stable isotopes (²⁰³Tl and ²⁰⁵Tl) in a chemical exchange system. Tl isotopes were fractionated in a liquid–liquid extraction system, in which aqueous and organic phases are hydrochloric acid solution and dichloroethane including a crown ether, respectively. After purification by ion-exchange chemistry, the isotope ratio of ²⁰⁵Tl/²⁰³Tl in equilibrated aqueous phase was measured precisely by multiple-collector–inductively-coupled-plasma–mass-spectrometry. A large isotope fractionation >1 ‰ was found. Electronic structures of possible Tl species (hydrated Tl⁺, Tl³⁺, and Tl chlorides) were calculated by ab initio methods, and the isotope fractionation factor was theoretically obtained. The isotope fractionation via intramolecular vibrations was calculated to be much smaller than the experimental result. The isotope fractionation via isotopic change in nuclear volume, named the nuclear field shift effect, was calculated to be >1 ‰ in Tl(I)–Tl(III) redox systems and/or ligand exchange systems of Tl(III). The nuclear field shift effect was found to be the major origin of Tl isotope fractionation.