Conformational studies of mixed-ligand copper(II) chelates. Crystal and molecular structure of (N,N-dimethyl-N′-ethyl-1,2-diaminoethane-(1-phenyl-1,3,-butanedionato)copper(II) perchlorate

The IR and ligand field spectra and the structure of the mixed-ligand compound [N,N-dimethyl-N′-ethyl-1,2-diaminoethane(1-phenyl-1,3-butanedionato)(perchlorato)copper(II)]), [Cu(dmeen)bzac(OClO3)], are reported. The structure was determined by single crystal X-ray diffraction analysis (triclinic, space group ). The structure is square pyramidal with the apical position occupied by one oxygen of the tetrahedral perchlorato group (distance from copper 2.452(5) Å). The plane of the phenyl ring is tilted forming an angle of 16.72(14)° with the plane of the β-dionato moiety. The nitrogenous base adopts the gauche conformation with torsional angle of 108.72(14)°. The ethyl group is cis oriented relative to the phenyl group, occupying the equatorial position with the vector of the carbon-nitrogen bond forming an angle of 143.9(3)° with the CuNN plane. The interactions of the adjacent axial hydrogen with an oxygen of the perchlorato group result in hydrogen bond formation. The IR spectra reveal that in the solid state the Br− or Cl− displace easily the ClO4− group. The shifts in the ligand field spectra indicate that polar solvents participate in donor-acceptor interactions with the metal centre along an axis perpendicular to the CuN2O2 plane.

Structure and spectra of dichloro(hydroxy-methoxy-di(2-pyridyl)methane)copper(II)

The non-electrolyte dichloro(hydroxy-methoxy-di(2-pyridylmethane)copper(II), resulting from the reaction of di(2-pyridyl)ketone and copper(II) chloride in methanol solution, was isolated and characterized and its structure was determined by X-ray diffraction. The pyridyl nitrogens and the chloride anions virtually from a basal plane in which lies the copper atom, while the oxygen of the methoxy group is in an apical position at a distance of 2.497 (3)Å. The nitrogenous base adopts the boat conformation with the pyridyl rings forming a dihedral angle of 108.72 (14)°. The nearest interatomic copper distance of 3.940(3)Å precludes copper-copper interactions, while the proximity of copper to the out-of-plane chlorine atoms [3.109(3)Å] suggests weakly bound chloro-bridged dimers. Spectral changes indicate that protic molecules displace the methoxy group and water affords the corresponding 1,1-diol.

Reactions of methylvinyl and phenylvinyl ketones with a tricyclic ketone derived from 2-tetralone: characterization of crystalline products by X-ray diffraction

Base catalysed reaction of the tricyclic ketone (6 ⇌ 7) with methylvinyl ketone gave the tetracyclic ketols, 11, 13, 15, 16, and the pentacyclic ketols, 12, 17. With phenylvinyl ketone, the tetracyclic ketol (18) was formed. The stereostructures of the ketols were identified by X-Ray diffraction. The base-catalysed title reactions gave the cyclic ketols and derived compounds shown below whose structures were identified by X-ray diffraction.

Reaction of (±)-1,1′-binaphthyl-2,2′-diyl hydrogen phosphate {(±)-phosH} with copper(II), cobalt(II) and iron(II) compounds; Identification by x-ray diffraction of [Co(CH3OH)4(H2O)2][(+)-phos][(−)-phos]. 2CH3OH·H2O

[Cu2(μO2CCH3)4(H2O)2], [CuCO3·Cu(OH)2], [CoSO4·7H2O], [Co((+)-tartrate)], and [FeSO4·7H2O] react with excess racemic (±)- 1,1′-binaphthyl-2,2′-diyl hydrogen phosphate {(±)-PhosH} to give mononuclear CuII, CoII and FeII products. The cobalt product, [Co(CH3OH)4(H2O)2]((+)-Phos)((−)-Phos) ·2CH3OH·H2O (7), has been identified by X-ray diffraction. The high-spin, octahedral CoII atom is ligated by four equatorial methanol molecules and two axial water molecules. A (+)- and a (−)-Phos− ion are associated with each molecule of the complex but are not coordinated to the metal centre. For the other CoII, CuII and FeII samples of similar formulation to (7) it is also thought that the Phos− ions are not bonded directly to the metal. When some of the CuII and CoII samples are heated under high vacuum there is evidence that the Phos− ions are coordinated directly to the metals in the products.

X-ray diffraction study of the influence of temperature on the structural correlations of poly(2-hydroxypropyl ether of bisphenol A)

The X-ray diffraction pattern of glassy poly(2-hydroxypropyl ether of bisphenol A) is studied at room temperature on oriented samples in order to associate its different peaks to different structural correlations. On the other hand, X-ray diffraction patterns have been obtained at different temperatures from Tg − 50 K up to Tg + 50 K for the above-mentioned polymer. Attention has been paid to the evolution with temperature of the position of the wide diffraction maximum corresponding to interchain correlations in the polymer. The temperature evolution of this parameter shows a marked discontinuity just at the glass transition temperature.

Diffraction from thermotropic copolyester molecules

Analytical expressions for the meridional scattering from highly oriented random copolyesters are presented. These procedures are utilised in developing the relationship of the features in the diffraction pattern to compositions and relative lengths of the constituent monomer units. The difference between the scattering patterns for random and block copolymers are discussed. The theory is applied to an example of a liquid crystal froming random copolyester.

Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the $p$-version

Plane wave discontinuous Galerkin (PWDG) methods are a class of Trefftz-type methods for the spatial discretization of boundary value problems for the Helmholtz operator $-\Delta-\omega^2$, $\omega>0$. They include the so-called ultra weak variational formulation from [O. Cessenat and B. Després, SIAM J. Numer. Anal., 35 (1998), pp. 255–299]. This paper is concerned with the a priori convergence analysis of PWDG in the case of $p$-refinement, that is, the study of the asymptotic behavior of relevant error norms as the number of plane wave directions in the local trial spaces is increased. For convex domains in two space dimensions, we derive convergence rates, employing mesh skeleton-based norms, duality techniques from [P. Monk and D. Wang, Comput. Methods Appl. Mech. Engrg., 175 (1999), pp. 121–136], and plane wave approximation theory.

Plane wave approximation of homogeneous Helmholtz solutions

In this paper, we study the approximation of solutions of the homogeneous Helmholtz equation Δu + ω 2 u = 0 by linear combinations of plane waves with different directions. We combine approximation estimates for homogeneous Helmholtz solutions by generalized harmonic polynomials, obtained from Vekua’s theory, with estimates for the approximation of generalized harmonic polynomials by plane waves. The latter is the focus of this paper. We establish best approximation error estimates in Sobolev norms, which are explicit in terms of the degree of the generalized polynomial to be approximated, the domain size, and the number of plane waves used in the approximations.

Plane wave approximation in linear elasticity

We consider the approximation of solutions of the time-harmonic linear elastic wave equation by linear combinations of plane waves. We prove algebraic orders of convergence both with respect to the dimension of the approximating space and to the diameter of the domain. The error is measured in Sobolev norms and the constants in the estimates explicitly depend on the problem wavenumber. The obtained estimates can be used in the h- and p-convergence analysis of wave-based finite element schemes.

2D hexagonal mesoporous platinum films exhibiting biaxial, in-plane pore alignment

The synthesis of 2D hexagonal mesoporous platinum films with biaxial, in-plane pore alignment is demonstrated by electrodeposition through an aligned lyotropic liquid crystal templating phase. Shear force is used to align a hexagonal lyotropic liquid crystalline templating phase of an inexpensive and a commercially available surfactant, C16EO10, at the surface of an electrode. Electrodeposition and subsequent characterisation of the films produced shows that the orientation and alignment of the phase is transferred to the deposited material. Transmission electron microscopy confirms the expected nanostructure of the films, whilst transmission and grazing incidence small angle X-ray scattering analysis confirms biaxial, in plane alignment of the pore structure. In addition further electrochemical studies in dilute sulfuric acid and methanol show that the pores are accessible to electrolyte solution as indicated by a large current flow; the modified electrode therefore has a high surface area, that catalyses methanol oxidation, and the pores have a very large aspect ratio (of theoretical maximum 2 × 105). Films with such aligned mesoporosity will advance the field of nanotechnology where the control of pore structure is paramount. The method reported is sufficiently generic to be used to control the structure and order of many materials, thus increasing the potential for the development of a wide range of novel electronic and optical devices.