Some problems in plane elastic dielectrics

Representations of Galerkin type are obtained for the displacement vector, polarization vector and the potential fields in the static plane theory of elastic dielectrics using the method of associated matrices. Fundamental matrix solutions of an infinite elastic dielectric plane subjected to a concentrated body force, electric force and charge density are derived from the singular solutions of harmonic, biharmonic and Helmholtz equations. Using boundary operatorsY, Z, M, the fundamental matrix solutions, and Betti's formulae, a matrix (x, y) is constructed and an integral representation for (u ₁,u ₂,P ₁,P ₂, ) is obtained. Discontinuity theorems are stated for the double layer potential andQ operator of the single layer potential. By means of these theorems, the solutions of interior and exterior boundary value problems are reduced to the solution of a system of five singular integral equations. The index of one of the systems is shown to be zero and it is concluded that Fredholm theorems and its alternatives hold.

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Zusammenfassung Durch Anwendung der Assoziativ-Matrizen-Methode werden Galerkinische Darstellungen für den Verschiebungsvektor, den Polarisierungsvektor und die potentiellen Prüffelder einer statischen ebenen Theorie des elastischen Dielektrikums entwickelt. Von den singulären Lösungen der harmonischen, biharmonischen und Helmholtz-Gleichungen werden grundlegende Matrizenlösungen für das unendliche, ebene und elastische Dielektrikum, das durch konzentrierte Raumkräfte, elektrische Kräfte und Ladungsdichte beansprucht wird, abgeleitet. Unter Verwendung der Randwert-OperatorenY, Z, M, der grundlegenden Matrizen-Lösungen und Betti's Formel, wird eine Spezial-Matrize (x, y) konstruiert und eine Integraldarstellung für (u ₁,u ₂,P ₁,P ₂, ) erhalten. Unstetigkeitssätze werden für das Doppelschicht-Potential und denQ-Operator eines einschichtigen Potentials angeführt. Durch Anwendung dieser Sätze werden die Lösungen der inneren und äusseren Grenzwertprobleme zur Lösung eines Systems von fünf singulären Integralgleichungen reduziert. Der Index eines der Systeme wird als Null bewiesen und es wird die Schlussfolgerung gezogen, dass der Fredholmsche Satz und seine Alternativen fur diese Theorie anwendbar sind.

     

Analysis of peptides and protein digests by reversed phase high performance liquid chromatography–electrospray ionisation mass spectrometry using neutral pH elution conditions

In this study, the advantages of carrying out the analysis of peptides and tryptic digests of proteins under gradient elution conditions at pH 6.5 by reversed-phase liquid chromatography (RP-HPLC) and in-line electrospray ionisation mass spectrometry (ESI-MS) are documented. For these RP separations, a double endcapped, bidentate anchored n-octadecyl wide pore silica adsorbent was employed in a capillary column format. Compared to the corresponding analysis of the same peptides and protein tryptic digests using low pH elution conditions for their RP-HPLC separation, this alternative approach provides improved selectivity and more efficient separation of these analytes, thus allowing a more sensitive identification of proteins at different abundance levels, i.e. more tryptic peptides from the same protein could be confidently identified, enabling higher sequence coverage of the protein to be obtained. This approach was further evaluated with very complex tryptic digests derived from a human plasma protein sample using an online two-dimensional (2D) strong cation-exchange (SCX)-RP-HPLC-ESI-MS/MS system. Again, at pH 6.5, with mobile phases of different compositions, improved chromatographic selectivities were obtained, concomitant with more sensitive on-line electrospray ionisation tandem mass spectrometric (ESI-MS/MS) analysis. As a consequence, more plasma proteins could be confidently identified, highlighting the potential of these RP-HPLC methods with elution at pH 6.5 to extend further the scope of proteomic investigations.     

Synthesis,spectroscopy, and X-ray crystal structures of copper(II) complexes of the tridentate ONS ligand formed by condensation of 4,4,4-trifluoro-1-(2-thienyl)-2,4-butanedione with S-benzyldithiocarbazate

A new tridentate ONS ligand, H₂L, has been synthesized by condensing thenoyltrifluoroacetone(4,4,4-trifluoro-1-(2-thienyl)-2,4butaneanedione) with S-benzyldithiocarbazate and its structure determined by X-ray diffraction. In the solid state, the Schiff base exists as the ketoamine-thioketo tautomer but in solution and in the presence of copper(II), it converts to the enol-thiol form and deprotonates to give copper(II) complexes of formula, [CuL] and [CuLL¹] (L = doubly deprotonated form of the ligand; L¹ = py, bipy or phen] which have been characterized by magnetic, spectroscopic, and X-ray diffraction studies. An X-ray crystallographic analysis shows that [CuL(py)] has a square-planar geometry with the ligand coordinated to the copper(II) center via the enolate oxygen, the azomethinic nitrogen and the thiolate sulfur, the fourth coordination position being occupied by pyridine. The [CuL(bipy)] complex is five-coordinate with a structure close to square-pyramidal in which the Schiff base acts as a doubly deprotonated tridentate ONS ligand and bipy is bidentate.     

Synthesis of polypyrrole nanoparticles and its grafting with silica gel for selective binding of chromium(VI)

Polypyrrole nanoparticles of desired structure have been synthesized through simple micelle technique. It is then grafted with functionalized silica gel to develop a novel organic-inorganic hybrid material. The role of dimethyl dichloro silane (coupling agent) in grafting is demonstrated. The nanoparticles are characterized by TEM, SEM and TGA. Grafting reactions are evaluated by spectral (FTIR) analysis and chemical test. The Cr(VI) binding behavior of the composite is studied in various pH of the medium. The selectivity in binding Cr(VI) is monitored. The metal ion adsorption capacity and surface area of the material are found to be 38 mg/g and 235 m²/g, respectively.     

粘滑混合边界条件下平面边界前的Stokes流动

对具有粘滑混合边界条件的平面边界,建立一个Stokes流动的一般性定理,利用双调和函数A与调和函数B,表示了3维Stokes流动的速度场和压力场.关于无滑动平面边界前Stokes流动的早期定理,成为该一般性定理的一个特例.进一步地,从一般性定理导出了一个推论,根据该Stokes流函数,给出了粘滑边界条件时刚性平面轴对称Stokes流动问题的解,得到了流体作用在边界上的牵引力和扭矩公式.给出了一个说明性的例子.     

Mechanisms of TiO2 nanoparticle transport in porous media: role of solution chemistry, nanoparticle concentration, and flowrate

The controlled self-assembly of multi-components in one system represents the capability integrating intermolecular interactions and functions of components and is believed the key procedure leading to multifunctional materials finally. In pursuing this goal, we used a double-chain cationic surfactant with a benzoic acid group at the end of one tail to encapsulate Keggin-type polyanion clusters via electrostatic interaction, obtaining uniform supramolecular hybrid reverse micelles, which served as hydrogen-bonding donors. Five pyridine derivatives containing conjugated and non-conjugated groups were chosen as hydrogen-bonding acceptors to bind with reverse micelles. Through mixing with these components according to chemical stoichiometry, the hybrid reverse micelle changed to a new self-assembly precursor through intermolecular hydrogen bonding. The as-prepared reverse micelles bearing conjugated pyridine groups exhibit supramolecular liquid crystal properties, which were characterized by differential scanning calorimetry, polarizing optical microscopy, and X-ray diffraction. The length and number of the alky chain in the pyridine derivatives, as well as the charges of polyoxometalates were also studied with regard to the liquid crystal structure. The synergistic effect of among three components was analyzed, and the liquid crystal properties could be conveniently adjusted through the modification of the hydrogen-bonding acceptor components.     

Determination of decamethylcyclopentasiloxane in river and estuarine sediments in the UK

Robust analytical procedures for the measurement of decamethylcyclopentasiloxane (D₅) in river and estuarine sediments and their application in determining environmental concentrations in the UK are presented for the first time in this work. Novel approaches to minimise commonly reported artefacts are utilised, improving the confidence in the concentrations of D₅ reported. Accelerated solvent extraction (ASE) and liquid–solid extraction methods are compared. Both methods use on-column injection gas chromatography/mass spectrometry (GC/MS). Measurements of D₅ concentrations in sediments sampled from the river Great Ouse and from the Humber estuary (UK) are also reported. ASE was suitable to measure concentrations of D₅ in sediments obtained from the river Great Ouse, UK (186–1450 ng g⁻¹, dry weight) and octamethyltetracyclosiloxane (D₄, 12–24 ng g⁻¹, dry weight). C₁₂ linear alkybenzene (C₁₂ LAB), which can be used as a chemical marker for sewage effluent related emissions, was also measured in this analysis. Liquid–solid extraction was optimised to provide more confidence in the lower D₅ concentrations measured in the Humber estuary, UK (49–256 ng g⁻¹, dry weight). A Limit of quantitation (LOQ) for D₅ of 57–110 and 4 ng g⁻¹ dry weight was determined for ASE and liquid–solid extraction, respectively.     

Density functional theory study of the structure and energetics of negatively charged oligopyrroles

First‐principles calculations are used to investigate the electronic properties of negatively charged n‐pyrrole oligomers with n = 2–18. Chains of neutral oligomers are bent, whereas the negatively charged oligomers become almost planar due to accumulation of negative charge at the end monomers. Isomers of short oligomers (n < 6) display negative electron affinity although the corresponding anions are energetically stable. For longer oligomers with n ≥ 6, the electron affinity is small and positive, slowly increasing with oligopyrrole length. Doping of 12‐pyrrole with lithium atoms shows that negative oxidation states are possible due to electron transfer from dopant to oligomer at locations close to dopant. These 12‐pyrrole regions support extra negative charge and exhibit a local structural change from benzenoid to quinoid structure in the C? C backbone conjugation. Comparison between neutral and doped polypyrrole (PPy) indicates that doped polymers displays a substantial depletion of the band gap energy and the appearance of dopant‐based bands in the gap for a 50% per monomer doping level. It is predicted that Li‐doped PPy is not metallic. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Ensemble and Single Molecule Studies on the Use of Metallic Nanostructures to Enhance the Intrinsic Emission of Enzyme Cofactors

We present a strategy for enhancing the intrinsic emission of the enzyme cofactors flavin adenine dinucleotide (FAD), flavin mononucleotide (FMN) and nicotinamide adenine dinucleotide (NADH). Ensemble studies show that silver island films (SIFs) are the optimal metal enhanced fluorescence (MEF) substrates for flavins and gave emission enhancements of over 10-fold for both FAD and FMN. A reduction in the lifetime of FAD and FMN on SIFs was also observed. Thermally evaporated aluminum films on quartz slides were found to be the optimal MEF substrate for NADH and gave a 5-fold increase in the emission intensity of NADH. We present finite-difference time-domain (FDTD) calculations that compute the enhancement in the radiated power emitting from an excited state dipole emitting in the wavelength range of NADH in close proximity to an aluminum nanoparticle, and a dipole emitting in the emission wavelength of flavins next to a silver nanoparticle. These calculations confirm that aluminum serves as the optimal MEF substrate for NADH and silver was the optimal MEF substrate for flavins. This is because the plasmon resonance properties of aluminum lie in the UV-blue regime and that of silver lie in the visible region. We also present the results of single molecule studies on FMN which show SIFs can both significantly enhance the intrinsic emission from single FMN molecules, significantly reduce their lifetimes and also significantly reduce FMN blinking. This is the first report of the observation of MEF from cofactors both at the ensemble and single molecule level. We hope this study will serve as a platform to encourage the future use of metallic nanostructures to study cofactors using their intrinsic fluorescence to directly monitor enzyme binding reactions without the need of extrinsic labeling of the molecules.