987 resultados para Lebesgue Constants
Resumo:
Possible structures for Al2W and AlW2 clusters and their anions were presented and studied by use of density functional theory B3LYP at various spin multiplicities. The proposed three structures are triangular form with C-2v symmetry; linear structure with D (infinity h) symmetry; and linear structure with C (infinity v) symmetry. The calculated results indicate that structures with C-2v symmetry are the most stable for both neutral clusters and their anions. For Al2W, C-2v Symmetry at spin multiplicity 5 is the ground state, while for its anion, doublet is the lowest. For AlW2 and its anion, doublet and triplet are the ground states, respectively.
Resumo:
A new phase of monoclinic BaTb2Mn2O7 with extra superlattice lines in addition to the usual orthorhombic X-ray diffraction patterns was prepared and a Rietveld refinement was applied to analyze the crystal structure using X-ray powder diffraction data at room temperature. The refined lattice parameters were a = 0.54918(8) nm, b = 2.0149(5) nm, c = 0.54922(9) nm, and beta = 90.62degrees with the space group A2/m (no. 12). The MnO6 oxygen octahedron has distortion and tilts around a-axis by about 7degrees each other in the reverse direction.
Resumo:
Equilibrium geometries, vibrational frequencies and dissociation energies of the second row transition metal dimers (from Y-2 to Cd-2 except Tc-2) ere studied by use of density functional methods B3LYP, BLYP, B3PW91, BHLYP, BP86, B3P86, SVWN, MPW1PW91 and PBE1PBE. The accuracy DFT methods is found to be highly dependent on the functional employed, in particular for vibrational frequency and dissociation energy. In most cases, the predicted bond distance is in general agreement with experiment and previous theoretical results. For van der Waals dimer Cd-2, B3LYP and BLYP have excellent performance in predicting the bond distance. For Ag-2, all density functional methods used in this study perform well in producing the bond distance, vibrational frequency and dissociation energy.
Resumo:
Ground state geometries were searched for transition metal trimers Sc-3, Y-3, La-3, Lu-3, Ti-3, Zr-3, and Hf-3 by density functional methods. For all the studied trimers, our calculation indicates that the ground state geometries are either equilateral triangle (Zr-3 and Hf-3) or near equilateral triangle (Ti-3, Sc-3, Y-3, La-3, and Lu-3). For rare earth trimers Sc-3, Y-3, La-3, and Lu-3, isosceles triangle (near equilateral triangle) at quartet state is the ground state. Isosceles triangle at doublet state is the competitive candidate for the ground state. For Zr-3 and Hf-3, equilateral triangle at singlet state is the most stable. For Ti-3, isosceles triangle (near equilateral triangle) at quintet state gives the ground state. For Sc-3, Zr-3, and Hf-3, where experimental results are available, the predicted geometries are in agreement with experiment in which the ground state is equilateral triangle (Zr-3) or fluxional (Sc-3 and Hf-3). For Y-3, the calculated geometry is in agreement with experimental observation and previous theoretical study that Y-3 is a bent molecule for the ground state.
Resumo:
Equilibrium geometries, vibrational frequencies and dissociation energies of hafnium dimer and trimer were studied by density functional methods B3LYP, BLYP, B3PW91, BHLYP, BP86, B3P86, mPW1PW91 and PBE1PBE. The results indicate that singlet is the ground state both for hafnium dimer and for trimer. For hafnium dimer, the calculated bond distance is less sensitive to the methods used. Except at BHLYP level, the calculated vibrational frequency is comparable to the experimental value. For hafnium trimer, equilateral triangle with D-3h symmetry is slightly favored compared with isosceles triangle with C-2v, symmetry except at BHLYP level. This conclusion is in agreement with experiment in which the ground state of Hf-3 is fluxional and low-spin or closed shell is preferred.
Resumo:
La-2, Yb-2, and Lu-2 have been studied by use of the density-functional methods B3LYP, BLYP, B3PW91, BHLYP, BP86, B3P86, MPW1PW91, and PBE1PBE. In these density-functional methods, the exchange functional is from either Becke's three-parameter HF-DFT hybrid exchange functional (B3), pure DFT exchange functional of 1988 (B), a modification of the half-and-half HF/DFT hybrid method (BH), Perdew-Wang 1991 (PW91), or Barone's modified PW91 (MPW1), while the correlation functional is from either Lee, Yang, and Parr (LYP), Perdew-Wang 1991 (PW91), or Perdew 86 (P86). PBE1PBE is the generalized-gradient-approximation exchange-correlation functional of Perdew, Burke, and Ernzerhof. For La-2, the calculated bond distance is in reasonable agreement with the experiment, but the calculated vibrational frequency is underestimated significantly compared with the experiment. Only BP86 and B3P86 have the best performance in reproducing the experimental dissociation energy for La-2. For the van der Waals dimer Yb-2, three functionals, B3LYP, BLYP, and BHLYP have excellent performance in reproducing the spectroscopic constants compared with both the experiment and previous theoretical studies.
Resumo:
Bond distances, vibrational frequencies and dissociation energies for the ground state of Lu-2 were studied by density functional methods B3LYP, B3PW91, BLYP, BHLYP, BP86, B3P86, MPW1PW91, PBE1PBE and SVWN with CEP-121G and SDD basis sets. Singlet state is predicted to be the most stable. CEP-121G has a better overall performance than SDD. At CEP-121G basis set, all density functional methods used in this study perform well in reproducing the spectroscopic constants.
Resumo:
Two series of tensile tests with constant crosshead speeds (ranging from 5 to 200 mm/min) and tensile relaxation tests (at strains from 0.03 to 0.09) were performed on low-density polyethylene in the subyield region of deformations at room temperature. Mechanical tests were carried out on nonannealed specimens and on samples annealed for 24 h at the temperatures T = 50, 60, 70, 80, and 100 degreesC. Constitutive equations were derived for the time-dependent response of semicrystalline polymers at isothermal deformations with small strains. A polymer is treated as an equivalent heterogeneous network of chains bridged by temporary junctions (entanglements, physical crosslinks, and lamellar blocks). The network is thought of as an ensemble of mesoregions linked with each other. The viscoelastic behavior of a polymer is modeled as a thermally induced rearrangement of strands (separation of active strands from temporary junctions and merging of dangling strands with the network). The viscoplastic response reflects sliding of junctions in the network with respect to their reference positions driven by macrostrains. Stress-strain relations involve five material constants that were found by fitting the observations.
Resumo:
Three series of tensile tests with constant cross-head speeds (ranging from 5 to 200 mm/min), tensile relaxation tests (at strains from 0.03 to 0.09) and tensile creep tests (at stresses from 2.0 to 6.0 MPa) are performed on low-density polyethylene at room temperature. Constitutive equations are derived for the time-dependent response of semicrystalline polymers at isothermal deformation with small strains. A polymer is treated as an equivalent heterogeneous network of chains bridged by temporary junctions (entanglements, physical cross-links and lamellar blocks). The network is thought of as an ensemble of meso-regions linked with each other. The viscoelastic behavior of a polymer is modelled as thermally-induced rearrangement of strands (separation of active strands from temporary junctions and merging of dangling strands with the network). The viscoplastic response reflects mutual displacement of meso-domains driven by macro-strains. Stress-strain relations for uniaxial deformation are developed by using the laws of thermodynamics. The governing equations involve five material constants that are found by fitting the observations. Fair agreement is demonstrated between the experimental data and the results of numerical simulation.
Resumo:
Electrospray ionization tandem mass spectrometry (ESI-MSn) and the phase solubility method were used to characterize the gas-phase and solution-phase non-covalent complexes between rutin (R) and alpha-, beta- and gamma-cyclodextrins (CDs). The direct correlation between mass spectrometric results and solution-phase behavior is thus revealed. The order of the 1:1 association constants (K-c) of the complexes between R and the three CDs in solution calculated from solubility diagrams is in good agreement with the order of their relative peak intensities and relative collision-induced dissociation (CID) energies of the complexes under the same ESI-MSn condition in both the positive and negative ion modes. Not only the binding stoichiometry but also the relative stabilities and even binding sites of the CD-R complexes can be elucidated by ESI-MSn. The diagnostic fragmentation of CD-R complexes, with a significant contribution of covalent fragmentation of rutin leaving the quercetin (Q) moiety attached to the CDs, provides convincing evidence for the formation of inclusion complexes between R and CDs. The diagnostic fragment ions can be partly confirmed by the complexes between Q and CDs. The gas-phase stability order of the deprotonated CD-R complexes is beta-CD-R > alpha-CD-R > gamma-CD/R; beta-CD seems to bind R more strongly than the other CDs.
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Synergistic extraction of zinc(IT) and cadmium(11) from hydrochloric acid solution with primary amine N1923 and neutral organophosphorus derivatives Cyanex 923 and Cyanex 925 is the focus of this paper. Extraction mechanisms are discussed as well as how the acidity of the aqueous phase, the composition of the organic phase, and the experimental temperature affect the rates of extraction of metal ions. Differences between synergistic efficiency of Zn(II) and Cd(II) with mixtures of primary amines N1923 and either Cyanex 923 or Cyanex 925 are observed. The equilibrium constants, the composition, and the formation constants of the extracted complexes as well as the values of the thermodynamic functions are calculated. According to the synergy coefficient formula, the synergy effect on the extraction of Zn(II) is in the following order:N1923 + Cyanex 925 > N1923 + Cyanex 923 This order is reversed in the case of cadmium(II). For the same synergistic system, the extraction rate follows the order: Zn(II) > Cd(II). Furthermore, the stereochemical structures of the various extractants and their effect on metal ion extraction rate are also investigated.
Resumo:
The extractions of the selected rare earths (Sc, Y, La and Gd) from hydrochloric acid solutions have been investigated using bis(2,4,4-trimethylpentyl)-mono thiophosphinic acid (Cyanex 302, HL) in heptane as an extractant. The results demonstrate that the extractions of rare earths occur via the following reaction: Sc(OH)(2+) + 2[(HL)(2)]((O)) double left right arrow [Sc(OH)L-2 (.) 2(HL)]((O)) + 2H(+) Y3+ + 3[(HL)(2)]((O)) double left right arrow [Y(HL2)(3)]((O)) + 3H(+) La(OH)(2)(+) + 3[(HL)(2)](O) double left right arrow [La(OH)(2)L (.) 5(HL)]((O)) + H+ Gd(OH)(2+) + 3[(HL)(2)]((O)) double left right arrow [Gd(OH)L-2 (.) 4(HL)]((O)) + 2H(+) The pH(1/2) values and equilibrium constants of the extracted complexes have been deduced by taking into account the aqueous phase complexation of the metal ion with hydroxyl ligands and plausible complexes extracted into the organic phase. According to the pH(1/2) values, it is possible to realize mutual separation among Sc(III), Y(III), La(III) and Gd(III) with Cyanex 302 by controlling aqueous acidity.
Resumo:
The species and their formation constants in the ternary, systems were obtained by the Scogs2 software from potentiometric titration data. The Comics software was used to calculate the distribution of species in the ternary systems. MLXH, MLXH2 and MLXH3 are the common species in these systems. The coordination behaviors of the rare earths are very similar and their stability is closely matched. The ternary rare earth complexes are more stable than the corresponding ternary complexes of calcium. The ternary zinc complex with glutamine as the secondary ligand is more stable than the corresponding complexes of rare earths, but the ternary complex with alanine as the secondary ligand shows an inverse trend. The distributions of species in the ternary systems vary with pH changing. A prediction can be made that exogenous rare earths can affect the species of Ca and Zn in human body.
Resumo:
Scanning probe lithography (SPL), employing the tip of an atomic force microscope to mechanically pattern various materials in nanoscale region has provided a simple but significant method for making nanostructures. We use this technique for the lithography of several kinds of substrate surfaces. The tip performance has been found to be a crucial factor in the lithographic process. Four types of cantilevers are employed in nanolithography, including standard silicon nitride (DNP), tapping mode(TM) etched silicon (TESP(W)), uncoated silicon cantilever (NSC21/50) and conductive platinum/iridium-coated probe. Results demonstrate that tips with smaller spring constants can not be used for physically scribing and nanomanipulating in our experiment. The possible mechanism of our experiment is discussed.
Resumo:
The coordination reactions during the solvent extraction of cerium(IV) and fluorine(l) from mixed nitric acid and hydrofluoric acid solutions by di-(2-ethylhexyl)-2-ethylhexylphosphonate, L (DEHEHP) in heptane have been investigated. The extraction data have been analyzed by graphical methods taking into account all plausible species extracted into the organic phase. Different variables influencing the extraction of Ce(IV), such as the concentrations of nitrate ions, hydrofluroric acid, nitric acid, and extractant have been studied. The results demonstrate that DEHEHP can extract not only Ce(NO3)(4) as Ce(NO3)4.2L and HF as HF (.) H2O (.) L, but both together as Ce(HF)(NO3)(4) (.) L. The extraction equilibrium equations are determined according to slope analysis and IR spectra. The equilibrium constants of the extracted complexes have been calculated, taking into account complexation between the metal ion and inorganic ligands in the aqueous phase and all plausible complexes extracted into the organic phase. It is also shown that boric acid, which was added into the mixed solutions to complex with F(I) is not extracted by DEHEHP, and neither does it affect the extraction of cerium(IV) and HF, nor change the extraction mechanism.