Variational approach in weighted Sobolev spaces to scattering by unbounded rough surfaces

We consider the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface which is assumed to lie within a finite distance of some plane. The paper is concerned with the study of an equivalent variational formulation of this problem set in a scale of weighted Sobolev spaces. We prove well-posedness of this variational formulation in an energy space with weights which extends previous results in the unweighted setting [S. Chandler-Wilde and P. Monk, SIAM J. Math. Anal., 37 (2005), pp. 598–618] to more general inhomogeneous terms in the Helmholtz equation. In particular, in the two-dimensional case, our approach covers the problem of plane wave incidence, whereas in the three-dimensional case, incident spherical and cylindrical waves can be treated. As a further application of our results, we analyze a finite section type approximation, whereby the variational problem posed on an infinite layer is approximated by a variational problem on a bounded region.

Transition metal clusters on graphite

The topic of this work is 3d transition metals deposited on graphite. Spin-polarised density-functional calculations are used to obtain the magnetic moments of deposited adatoms and dimers. Interatomic potentials are also deduced. These are used in molecular dynamics simulations to study cluster formation and to investigate cluster morphology.

Impacts of epigeic, anecic and endogeic earthworms on metal and metalloid mobility and availability

The introduction of earthworms into soils contaminated with metals and metalloids has been suggested to aid restoration practices. Eisenia veneta (epigeic), Lumbricus terrestris (anecic) and Allolobophora chlorotica (endogeic) earthworms were cultivated in columns containing 900 g soil with 1130, 345, 113 and 131 mg kg1 of As, Cu, Pb and Zn, respectively, for up to 112 days, in parallel with earthworm-free columns. Leachate was produced by pouring water on the soil surface to saturate the soil and generate downflow. Ryegrass was grown on the top of columns to assess metal uptake into biota. Different ecological groups affected metals in the same way by increasing concentrations and free ion activities in leachate, but anecic L. terrestris had the greatest effect by increasing leachate concentrations of As by 267%, Cu by 393%, Pb by 190%, and Zn by 429% compared to earthworm-free columns. Ryegrass grown in earthworm-bearing soil accumulated more metal and the soil microbial community exhibited greater stress. Results are consistent with earthworm enhanced degradation of organic matter leading to release of organically bound elements. The degradation of organic matter also releases organic acids which decrease the soil pH. The earthworms do not appear to carry out a unique process, but increase the rate of a process that is already occurring. The impact of earthworms on metal mobility and availability should therefore be considered when inoculating earthworms into contaminated soils as new pathways to receptors may be created or the flow of metals and metalloids to receptors may be elevated.

Application of interpolymer complexation to coat solid and soft surfaces

Water-soluble polymers are often capable of forming interpolymer complexes in solutions and at interfaces, which offers an excellent opportunity for surface modification. The complex formation may be driven by H-bonding between poly(carboxylic acids) and non-ionic polymers or by electrostatic attraction between oppositely-charged polyelectrolytes. In the present communication the following applications of interpolymer complexation in coating technologies will be considered: (1) Complexation between poly(acrylic acid) and non-ionic polymers via H-bonding was used to coat glass surfaces. It was realised using layer-by-layer deposition of IPC on glass surfaces with subsequent cross-linking of dry multilayers by thermal treatment. Depending on the glass surface functionality this complexation resulted in detachable and non-detachable hydrogel films; (2) Electrostatic layer-by-layer self-assembly between glycol chitosan and bovine serum albumin (BSA) was used to coat magnetic nanoparticles. It was demonstrated that the native structure of BSA remains unaffected by the self-assembling process.

Rigid ferrocenophane and its metal complexes with transition and alkaline-earth metal ions

The rigid [6]ferrocenophane, L-1, was synthesised by condensation of 1,1'-ferrocene dicarbaldehyde with trans-1,2-diaminocyclohexane in high dilution at r.t. followed by reduction. When other experimental conditions were employed, the [6,6,6]ferrocenephane (L-2) was also obtained. Both compounds were characterised by single crystal X-ray crystallography. The protonation of L-1 and its metal complexation were evaluated by the effect on the electron-transfer process of the ferrocene (fc) unit of L-1 using cyclic voltammetry (CV) and square wave voltammetry (SWV) in anhydrous CH3CN solution and in 0.1 M (Bu4NPF6)-Bu-n as the supporting electrolyte. The electrochemical process of L-1 between 300 and 900 mV is complicated by amine oxidation. On the other hand, an anodic shift from the fc/fc(+) wave of L-1 of 249, 225, 81 and 61 mV was observed by formation of Zn2+, Ni2+, Pd2+ and Cu2+ complexes, respectively. Whereas Mg2+ and Ca2+ only have with L-1 weak interactions and they promote the acid-base equilibrium of L-1. This reveals that L-1 is an interesting molecular redox sensor for detection of Zn2+ and Ni2+, although the kinetics of the Zn2+ complex formation is much faster than that of the Ni2+ one. The X-ray crystal structure of [(PdLCl2)-Cl-1] was determined and showed a square-planar environment with Pd(II) and Fe(II) centres separated by 3.781(1) angstrom. The experimental anodic shifts were elucidated by DFT calculations on the [(MLCl2)-Cl-1] series and they are related to the nature of the HOMO of these complexes and a four-electron, two-orbital interaction.

Metal-directed assembly of large dinuclear copper(II) dithiocarbamate macrocyclic complexes

The synthesis of a range of dinuclear Cu(II) dithiocarbamate (dtc)-based macrocycles and their characterisation are described. By carefully tuning the size of the aromatic spacer, cavities of different dimensions can be designed. The length and flexibility of the chosen spacer group dictates the intermetallic distance and hence the degree of communication between the two metal centres as evidenced by electrochemical and EPR experiments. This is illustrated by crystallographic evidence that show the macrocycles can host guests (such as CH2Cl2) or can fold and form unexpected Cu(I) dtc clusters.

The synthesis of dicobalt and dinickel complexes of trimethylsilylethynyl-1, 2-dihydrofullerene; characterisation by n.m.r. and structure of the first acyclic metal fullerene derivative: molecular structure of [η2-{2-H-1-(Me3SiC ≡ C)-C60}Ni2(η-C5H5)2]

The synthesis and characterisation of the complexes [η2-{2-H-1-(Me3SiC ≡ C)-C60}Co2(CO)6] (2)} and [η-2-{2-H-1-(Me3SiC ≡ C)-C60}Ni2η-C5H5)2] (3)} is reported, together with a single-crystal molecular structure for (3). This provides the first structural data for an acyclic metal derivative of [60]-fullerene.

Metal complexes with atropisomeric sulfur ligands in asymmetric hydroformylation X-ray structure of [Rh2(μ-biphes)(cod)2] (H2biphes = 4,4′-biphenanthrene-3,3′-dithiol)

The addition of the atropisomeric racemic sulfur compound 4,4′-biphenanthrene-3,3′-dithiol (H2 biphes) to a dichloromethane solution of [{M(μ-OMe)(cod)}2] (M = Rh, Ir, cod = cycloocta-1,5-diene) afforded the dithiolate-bridged complexes [{Rh2(μ-biphes)(cod)2}n] (n = 2 5 or n = 1 6) and [{Ir2(μ-biphes)(cod)2}n]·nCH2Cl27. When 1,1′-binaphthalene-2,2′-dithiol (H2 binas) reacted with [{Ir(μ-OMe)(cod)}2], complex [Ir2(μ-binas)(cod)2] 8 was obtained. Complexes 5 and 6 reacted with carbon monoxide to give the dinuclear tetracarbonyl complex [Rh2(μ-biphes)(CO)4] 9. The reaction of 9 with PR3 provided the mixed-ligand complexes [{Rh2(μ-biphes)(CO)2(PR3)2}2] · xCH2Cl2 (R = Ph, x = 2 10, C6H11, x = 1 11) and [{Rh2(μ-biphes)(CO)3(PR3)}2] · CH2Cl212 (R = OC6H4But-o). The crystal structure of 6 was determined by X-ray diffraction. Reaction of the dithioether ligand Me2biphes with [Rh(cod)2]ClO4 in CH2Cl2 solution afforded the cationic complex [Rh(cod)(Me2biphes)]ClO4 · CH2Cl213. Asymmetric hydroformylation of styrene was performed using the complexes described. The extent of aldehyde conversion ranges from 53 to 100%, with selectivities towards branched aldehydes in the range 51 to 96%. The enantioselectivities were quite low and did not exceed 20%.

Preparation of transition metal complexes of bicyclo[2.2.1]hept-5-ene-2-carboxylic acid (C7H9CO2H) and X-ray crystal structure of [Cu2?(±)-endo-μ-O2CC7H9?4 (CH3OH)2]·2CH3OH

Metathesis reactions were used to prepare a range of dicopper(II), monocopper(I), diruthenium(II, III), dimolybdenum(II,II) and dirhodium(II,II) complexes of either racemic or resolved forms of endo- and exo-bicyclo[2.2.1]hept-5-ene-2-carboxylic acid (C7H9CO2H). The X-ray crystal structure of [Cu2{(±)-endo-μ-O2CC7H9}4(CH3OH)2]·2CH3OH shows the two copper(II) ions bridged by two (+)-endo-bicyclo[2.2.1]hept-5-ene-2-carboxylate anions and two (−)-endo-bicyclo[2.2.1]hept-5-ene-2-carboxylate anions. Methanol molecules occupy the two trans axial sites, and there are also two methanol molecules hydrogen bonded to opposite carboxyl oxygens.

μ-Peroxo-μ-oxo-bis[bis(trimethylsilylmethyl)tin]: the first structurally characterised main-group metal η2-peroxide, a formal tin analogue of an ozonide

The title compound is the first µ-η2-peroxodimetallic species to be characterised for a main group metal, possessing a long peroxo O–O bond, and large C–Sn–C angles, and is an unexpected product from the oxidation of [SnR2][R = CH(SiMe3)2], with a structure analogous to an organic ozonide.

Metal cluster expansion by addition of low valent group 14 reagents: III. Reaction of bis[bis(trimethylsilyl)methyl]tin with M3(CO)12 or its derivatives (M = Fe, Ru, or Os): the crystal and molecular structures of M3(μ-SnR2)2(CO)10(R = CH(SiMe3)2; M = Ru or Os)

The stannylene [SnR2] (R = CH(SiMe3)2) reacts in different ways with the three dodecacarbonyls of the iron triad: [Fe3(CO)12] gives [Fe2(CO)8(μ-SnR2)], [Ru3(CO)12] gives the planar pentametallic cluster [Ru3(CO)10(μ-SnR2)2], for which a full structural analysis is reported, while [Os3(CO)12] fails to react. Different products are also obtained from three nitrile derivatives: [Fe3-(CO)11(MeCN)] gives [Fe2(CO)6(μ-SnR2)2], which has a structure significantly different from that of known Fe2Sn2 clusters, [Ru3(CO)10(MeCN)2] gives the pentametallic cluster described above, while [Os3(CO)10(MeCN)2] gives the isostructural osmium analogue, which shows the unusual feature of a CO group bridging two osmium atoms.

Metal cluster expansion by addition of low-valent group 4B reagents: crystal and molecular structure of [Os3SnH2(CO)10{CH(SiMe3)2}2]; a compound with hydrogen bridging osmium and tin

Cluster expansion of [Os3H2(CO)10] with [SnR2][R = CH(SiMe3)2] take place in high yield to give [Os3SnH2(CO)10R2], the first closed triosmium–main-group metal cluster to be structurally characterized; a novel feature is the presence of a hydrogen atom bridging the tin atom and one of the osmium atoms.

Synthesis and X-ray crystal and molecular structure of tetrakis(2,2-dimethyl-1-phenylethenyl)chromium(IV), the first structurally-characterised homoleptic alkenyl compound of a transition metal

The title compound, the first homoleptic Group 6A metal alkenyl, has been prepared from CrCl3·3(thf), and its properties, including X-ray crystal structure determination, are reported.

Unsaturated σ-hydrocarbyl transition-metal complexes. Part 4. Crystal and molecular structure of trans-chlorobis(diethylphenylphosphine)-(phenylethynyl)platinum(II) and comments on the relative trans influence of various carbon ligands

The molecular structure of trans-[PtCl(CCPh)(PEt2Ph)2] has been determined by X-ray diffraction methods. The crystals are monoclinic, space group P21, with a= 12.359(3), b= 13.015(3), c= 9.031(2)Å, β= 101.65(2)°, and Z= 2. The structure has been solved by the heavy-atom method and refined by full-matrix least squares to R 0.046 for 1 877 diffractometric intensity data. The crystals contain discrete molecules in which the platinum coordination is square planar. The phenylethynyl group is non-linear, with a Pt–CC angle of 163(2)°. Selected bond lengths are Pt–Cl 2.407(5) and Pt–C 1.98(2)Å. The structural trans influences of CCPh, CHCH2, and CH2SiMe3 ligands in platinum(II) complexes are compared; there is only a small dependence on hybridization at the ligating carbon atom.

Unsaturated σ-hydrocarbyl transition-metal complexes. Part 3. Crystal and molecular structure of trans-chlorobis(diethylphenylphosphine)(vinyl)platinum(II)

The molecular structure of trans-[PtCl(CHCH2)(PEt2Ph)2] has been determined by X-ray diffraction methods. The crystals are orthorhombic, space group Pbcn, with a= 10.686(2), b= 13.832(4), c= 16.129(4)Å, and Z= 4. The structure has been solved by the heavy-atom method and refined by full-matrix least squares to R 0.044 for 1 420 diffractometric intensity data. The crystals contain discrete molecules in which the platinum co-ordination is square planar. The Pt–Cl bond vector coincides with a crystallographic diad axis about which the atoms of the vinyl group are disordered. Selected bond lengths (Å) are Pt–Cl 2.398(4), Pt–P 2.295(3), and Pt–C 2.03(2). The Pt–CC angle is 127(2)°. From a survey of the available structural data it is concluded that there is little, if any, back donation from platinum to carbon in platinum–alkenyl linkages.