Homogenization of periodic structures via Bloch decomposition

In this paper, the classical problem of homogenization of elliptic operators in arbitrary domains with periodically oscillating coefficients is considered. Using Bloch wave decomposition, a new proof of convergence is furnished. It sheds new light and offers an alternate way to view the classical results. In a natural way, this method leads us to work in the Fourier space and thus in a framework dual to the one used by L. Tartar [Problemes d'Homogeneisation dans les Equations aux: Derivees Partielles, Cours Peccot au College de Prance, 1977] in his method of homogenization. Further, this technique offers a nontraditional way of calculating the homogenized coefficients which is easy to implement in the computer.

Local environmental structures of Mo in the superionic conducting glass (AgI)(0.6)(Ag2MoO4)(0.4) by anomalous X-ray scattering

The anomalous X-ray scattering (AXS) method using Mo K absorption edges has been employed for obtaining the local structural information of superionic conducting glass having the composition (AgI)(0.6)(Ag2MoO4)(0.4). The possible atomic arrangements in the near-neighbor region of this glass were estimated by coupling the results with the least-squares variational analysis so as to reproduce the differential intensity profile for Mo as well as the ordinary scattering profile. The coordination number of oxygen around Mo is found to be about 4 at the distance of 0.180 mn. This implies that the most probable structural entity in the glass is the MoO4 tetrahedral unit which has been proposed based on infrared spectroscopy. The value of the coordination number of I- around Ag+ is estimated as 4.4 at 0.287 nm, suggesting an arrangement similar to that of crystalline or molten AgI.

Water-mediated ionic interactions in protein structures

It is well known that water molecules play an indispensable role in the structure and function of biological macromolecules. The water-mediated ionic interactions between the charged residues provide stability and plasticity and in turn address the function of the protein structures. Thus, this study specifically addresses the number of possible water-mediated ionic interactions, their occurrence, distribution and nature found in 90% non-redundant protein chains. Further, it provides a statistical report of different charged residue pairs that are mediated by surface or buried water molecules to form the interactions. Also, it discusses its contributions in stabilizing various secondary structural elements of the protein. Thus, the present study shows the ubiquitous nature of the interactions that imparts plasticity and flexibility to a protein molecule.

Micellar structures of dimeric surfactants with phosphate head groups and wettable spacers: A small-angle neutron scattering study

Dimeric or gemini surfactants consist of two hydrophobic chains and two hydrophilic head groups covalently connected by a hydrophobic or hydrophilic spacer. This paper reports the small-angle neutron scattering (SANS) measurements from aqueous micellar solutions of two different recently developed types of dimeric surfactants: (i) bis-anionic C16H33PO4--(CH2)(m)-PO4-C16H33,2Na(+) dimeric surfactants composed of phosphate head groups and a hydrophobic polymethylene spacer, referred to as 16-m-16,2Na(+), for spacer lengths m = 2, 4, 6, and 10, (ii) bis-cationic C16H33N+(CH3)(2)-CH2-(CH2-O-CH2)(p)-CH2-N+ (CH3)(2)C16H33,2Br(-) dimeric surfactants composed of dimethylammonium head groups and a wettable polyethylene oxide spacer, referred to as 16-CH2-p-CH2-16,2Br(-), for spacer lengths p = 1 - 3. The micellar structures of these surfactants are compared with the earlier studied bis-cationic C16H33N+ (CH3)(2)-(CH2)(m)-N+ (CH3)(2)C16H33,2Br(-) dimeric surfactants composed of dimethylammonium head groups and a hydrophobic polymethylene spacer, referred to as 16-m-16,2Br(-). It is found that 16-m-16,2Na(+), similar to 16-m-16,2Br(-), form various micellar structures depending on the spacer length. Micelles an disklike for rn = 2, rodlike for m = 4, and prolate ellipsoidal fur m = 6 and 10. The micelles of 16-CH2-p-CH2-16,2Br(-) are prolate ellipsoidal for all the values of p = 1 - 3. It is also found that micelles of 16-m-16,2Na(+) and 16-CH2-p-CH2-16,2Br(-) are large in comparison to those of 16-in-16,2Br(-) for similar spacer lengths. This is connected with the fact that both in 16-m-16,2Na(+) and 16-CH2-p-CH2-16,2Br(-), the head group or the spacer is more hydrated as compared to that in the 16-m-16,2Br(-). An increase in the hydration of the spacer or the head group increases the screening of the Coulomb repulsion between the charged head groups. This effect has been found to be more pronounced in the dimeric surfactants having wettable spacers. [S1063-651X(99)00303-7].

Probing the limits of steric constraints in the oligomerization of copper(I) complexes: structures of two sterically congested oligomers

Oligomeric copper(I) clusters are formed by the insertion reaction of copper(I) aryloxides into heterocumulenes. The effect of varying the steric demands of the heterocumulene and the aryloxy group on the nuclearity of the oligomers formed has been probed. Reactions with copper(I)2-methoxyphenoxide and copper(I)2-methylphenoxide with PhNCS result in the formation of hexameric complexes hexakis[N-phenylimino(aryloxy)methanethiolato copper(I)] 3 and 4 respectively. Single crystal X-ray data confirmed the structure of 3. Similar insertion reactions of CS2 with the copper(I) aryloxides formed by 2,6-di-tert-butyl-4-methylphenol and 2,6-dimethylphenol result in oligomeric copper(I) complexes 7 and 8 having the (aryloxy)thioxanthate ligand. Complex 7 was confirmed to be a tetramer from single crystal X-ray crystallography. Reactions carried out with 2-mercaptopyrimidine, which has ligating properties similar to N-alkylimino(aryloxy)methanethiolate, result in the formation of an insoluble polymeric complex 11. The fluorescence spectra of oligomeric complexes are helpful in determining their nuclearity. Ir has been shown that a decrease in the steric requirements of either the heterocumulene or aryloxy parts of the ligand can compensate for steric constraints acid facilitate oligomerization. (C) 1999 Elsevier Science Ltd. All rights reserved.

Spectral asymptotics of the Helmholtz model in fluid-solid structures

A model representing the vibrations of a coupled fluid-solid structure is considered. This structure consists of a tube bundle immersed in a slightly compressible fluid. Assuming periodic distribution of tubes, this article describes the asymptotic nature of the vibration frequencies when the number of tubes is large. Our investigation shows that classical homogenization of the problem is not sufficient for this purpose. Indeed, our end result proves that the limit spectrum consists of three parts: the macro-part which comes from homogenization, the micro-part and the boundary layer part. The last two components are new. We describe in detail both macro- and micro-parts using the so-called Bloch wave homogenization method. Copyright (C) 1999 John Wiley & Sons, Ltd.

Structures of the catalytic site mutants D99A and H48Q and the calcium-loop mutant D49E of phospholipase A(2)

Crystal structures of the active-site mutants D99A and H48Q and the calcium-loop mutant D49E of bovine phospholipase A(2) have been determined at around 1.9 Angstrom resolution. The D99A mutant is isomorphous to the orthorhombic recombinant enzyme, space group P2(1)2(1)2(1), The H48Q and the calcium-loop mutant D49E are isomorphous to the trigonal recombinant enzyme, space group P3(1)21, The two active-site mutants show no major structural perturbations. The structural water is absent in D99A and, therefore, the hydrogen-bonding scheme is changed. In H48Q, the catalytic water is present and hydrogen bonded to Gln48 N, but the second water found in native His48 is absent. In the calcium-loop mutant D49E, the two water molecules forming the pentagonal bipyramid around calcium are absent and only one O atom of the Glu49 carboxylate group is coordinated to calcium, resulting in only four ligands.

Synthesis and structures of oxyanion encapsulated copper(I)-dppm complexes (dppm = bis(diphenylphosphino) methane)

Copper(I)-dppm complexes encapsulating the oxyanions ClO4-, NO3-, CH3C6H4CO2-, SO42-, and WO42- have been synthesized either by reduction of the corresponding Cu(II) salts and treatment with dppm, or by treating the complex [Cu-2(dppm)(2)(dmcn)(3)](BF4)(2) (1) (dmcn = dimethyl cyanamide) with the respective anion. The isolated complexes [Cu-2(dppm)(2)(dmcn)(2)(ClO4)] (ClO4) (2), [Cu-2(dppm)(2)(dmcn)(2)(NO3)] (NO3) (3), Cu-2(dppm)(2)(NO3)(2) (4), [Cu-2(dppm)(2)(CH3C6H4CO2)(2)]dmcn.2THF (5), Cu-2(dppm)(2)(SO4) (6), and [Cu-3(dppm)(3)(Cl)(WO4)] 0.5H(2)O (7) have been characterized by IR, H-1 and P-31{H-1} NMR, UV-vis, and emission spectroscopy. The solid-state molecular structure of complexes 1, 2, 4, and 7 were determined by single-crystal X-ray diffraction. Pertinent crystal data are as follows: for 1, monoclinic P2(1)/c, a = 11.376(10) Angstrom, b = 42.503(7) Angstrom, c = 13.530(6) Angstrom, beta = 108.08(2)degrees, V = 6219(3) Angstrom(3), Z = 4; for 2, monoclinic P2(1)/c, a = 21.600(3) Angstrom, b = 12.968(3) Angstrom, c = 23.050(3) Angstrom, beta = 115.97(2)degrees, V = 5804(17) Angstrom(3), Z = 4; for 4, triclinic , a = 10.560(4) Angstrom, b = 10.553(3) Angstrom, c = 22.698(3) Angstrom, alpha = 96.08(2)degrees, beta = 96.03(2)degrees, gamma = 108.31(2)degrees, V = 2362(12) Angstrom(3), Z = 2; and for 7, orthorhombic P2(1)2(1)2(1), a = 14.407(4) Angstrom, b = 20.573(7) Angstrom, c = 24.176(6) Angstrom, V = 7166(4) Angstrom(3), Z = 4. Analyses of the crystallographic and spectroscopic data of these complexes reveal the nature of interactions between the Cu-I-dppm core and oxyanion. The anchoring of the oxyanion to the Cu-n(dppm)(n) unit is primarily through coordination to the metal, but the noncovalent C-H ... O interactions between the methylene and phenyl protons of the dppm and oxygen atoms of the oxyanion play a significant role. The solid-state emission spectra for complexes 1-6 are very similar but different from 7. In CDCl3 solution, addition of ClO4- or NO3- (as their tetrabutylammonium salts) to 1 establishes a rapid equilibrium between the anion-complexed and uncomplexed forms. The association constant values for ClO4- and NO3- have been estimated from the P-31{H-1} NMR spectra.

Tensile flow behaviour of 2.25Cr-1Mo ferritic steel base metal and simulated heat affected zone structures of 2.25Cr-1Mo weld joint

Tensile tests in the temperature range 298 to 873 K have been performed on 2.25Cr-1Mo base metal and simulated heat affected zone (HAZ) structures of its weld joint, namely coarse grain bainite, fine grain bainite and intercritical structure. Tensile flow behaviour of all the microstructural conditions could be adequately described by the Hollomon equation (sigma = K-1 epsilon(n1)) at higher (> 623 K) temperatures. Deviation from the Hollomon equation was observed at low strains and lower (< 623 K) temperatures. The Ludwigson modification of Hollomon's equation, sigma = K-1 epsilon(n1) + exp (K-2 + n(2) epsilon), was found to describe the flow curve. In general, the flow parameters n(1), K-1, n(2) and K-2 were found to decrease with increase in temperature except in the intermediate temperature range (423 to 623 K). Peaks/plateaus were observed in their variation with temperature in the intermediate temperature range coinciding with the occurrence of serrated flow in the load-elongation curve. The n(1) Value increased and the K-1 value decreased with the type of microstructure in the order: coarse grain bainite, fine grain bainite, base metal and intercritical structure. The variation of nl with microstructure has been rationalized on the basis of mean free path (MFP) of dislocations which is directly related to the inter-particle spacing. Larger MFP of dislocations lead to higher strain hardening exponents n(1).

Molecular self-assembly of cadmium-triazolate complexes via hydrogen bonding: Synthesis, structures and photoluminescent properties

Two new cadmium coordination polymers namely Cd(HAmTrz-COO)(4)(NH4+)(2)] 1; and Cd(HAmTrz)(2)I-2](n) 2; (HAmTrz-COOH = 3-amino-1,2,4-triazole-5-carboxylic acid), have been prepared based on HAmTrz-COOH as ligand. The crystal structures of 1 and 2 have been determined by single-crystal X-ray diffraction technique. In coordination-complex 1 four triazole ligands coordinate via N1 nitrogen leading to a tetrahedral geometry around cadmium ion, while in 2 the ligand prefers to coordinate to the metal in a bidentate bridging mode. The structures of both the coordination polymers can be envisaged as 3D hydrogen bonded networks. Thermogravimetric analysis shows that 2 is more stable than 1 owing to different coordination numbers of cadmium atoms. Photoluminescence properties of both the compounds have been investigated in the solid state. (C) 2011 Elsevier B.V. All rights reserved.

Helical structures: The geometry of protein helices and nanotubes

In nature, helical structures arise when identical structural subunits combine sequentially, the orientational and translational relation between each unit and its predecessor remaining constant. A helical structure is thus generated by the repeated action of a screw transformation acting on a subunit. A plane hexagonal lattice wrapped round a cylinder provides a useful starting point for describing the helical conformations of protein molecules, for investigating the geometrical properties of carbon nanotubes, and for certain types of dense packings of equal spheres.

Sulfates of organic diamines: hydrogen-bonded structures and properties

In order to investigate the supramolecular hydrogen-bonded networks and other structural features exhibited by compounds containing an organic cation and an inorganic anion, sulfates of the organic diamines, ethylenediamine (I), 1,3-diaminopropane (II), piperazine (III), and 1,4-diazabicyclo[2.2.2]octane (DABCO) (IV) have been prepared investigated by X-ray crystallography. While II, III, and IV crystallize in the centrosymmetric space group, Pbca, P2(1)/n, Pbcn, respectively, I crystallizes in the non-centrosymmetric space group, P4(1) exhibiting chirality and weak NLO properties. I-IV exhibit different types of supramolecular H-bonded networks involving the organic cation and the SO42- anion. The nature and strength of the H-bonding network vary from one compound to another, with the strongest network found in piperazinium sulfate, III, and the weakest in II. While in III, water molecules form part of the H-bonded network, they are present as guest molecules in the channels of IV. Thermal stability of the compounds as well as the infrared spectra reflect the stabilities of these H-bonded solids. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

Supramolecular hydrogen-bonded structures in organic amine squarates

Structures of monohydrogen squarates of methylamine, ethylenediamine, 1,3-diaminopropane, 1,4-diaminobutane, 1,5-diaminopentane, N,N'-diemethylpiperazine and N,N,N,N-tetramethylguanidine have been studied in detail. The supramolecular hydrogen-bonded molecular networks are formed by the monoanion of squaric acid by itself or in association with the parent acid. Three types of hydrogen-bonded motifs are observed in these compounds, namely a liner chain, a cyclic dimer and a cyclic tetramer. These hydrogen-bonded motifs formed by the squaric acid species interact with the amine through N-H...O hydrogen-bonding and give rise to predominantly layered structures, while some of them also exhibit three-dimensional structures. Two of the monohydrogen squarate structures also exhibit pi-pi interactions between two squarate rings. The various hydrogen-bonding parameters in the amine squarates are discussed at length. (C) 2002 Elsevier Science B.V. All rights reserved.

Transformations of two-dimensional layered zinc phosphates to three-dimensional and one-dimensional structures

Transformations of the layered zinc phosphates of the compositions [C6N4H22](0.5) [Zn-2 (HPO4)(3)], I, [C3N2H12][Zn-2 (HPO4)(3)], II and [C3N2OH12][Zn-2 (HPO4)(3)], III, containing triethylenetetramine, 1,3-diaminopropane, and 1,3-diamino-2-hydroxypropane, respectively, have been investigated under different conditions. On heating in water, I transforms to a one-dimensional (1-D) ladder and a three-dimensional (3-D) structure, while II gives rise to only a two-dimensional (2-D) layered structure. In the transformation reaction of I with zinc acetate, the same ladder and 3-D structures are obtained along with a tubular layer. Under similar conditions II gives a layered structure formed by the joining of two ladder motifs. III, on the other hand, is essentially unreactive when heated with water and zinc acetate, probably because the presence of the hydroxy group in the amine which hydrogen bonds to the framework. In the presence of piperazine, I, II and III give rise to a four-membered, corner-shared linear chain which is likely to be formed via the ladder structure. In addition, 2-D and 3-D structures derived from the 1-D linear chain or ladder structures are also formed. The primary result from the study is that the layers produce 1-D ladders, which then undergo other transformations. It is noteworthy that in the various transformations carried out, most of the products are single-crystalline.

Encapsulated and hollow closed-cage structures of WS2 and MoS2 prepared by laser ablation at 450–1050°C

Encapsulated and hollow closed-cage onion-like structures of WS2 and MoS2 were prepared by laser ablation of the corresponding layered structures in argon atmosphere at four varied temperatures. A detailed study for WS2 indicates that only metal-filled onion-like structures are produced at temperatures Tless-than-or-equals, slant650°C, whereas a mixture of metal-filled and hollow structures are produced at Tgreater-or-equal, slanted850°C. The encapsulated metal is identified to be predominantly the metastable β phase of tungsten. Very short tube-like or elongated polyhedral structures are also obtained at high temperatures.