Isomorphous substitutions of rare earth elements for calcium in synthetic hydroxyapatites

Polycrystalline hydroxyapatites Ca(10-x)REE(x)(PO(4))(6)(OH)(2-x)O(x) were synthesized and studied by X-ray powder diffraction, infrared absorption, diffuse-reflectance spectroscopy, and thermogravimetry. The solubility limits x(max) of rare earth elements (REE) in Ca hydroxyapatites decreases with an increasing REE atomic number from x(max) = 2.00 for La, Pr, and Nd to x(max) = 0.20 for Yb at 1100 °C. Refinements of X-ray diffraction patterns by the Rietveld method show that REE atoms substitute for Ca preferentially at the Ca(2) sites of the apatite structure. The substitution decreases the Ca(2)-O(4) atomic distances in the calcium coordination polyhedra and increases the Ca(2)-O(1,2,3) distances. This observation shows that interatomic distances depend not only on radii of the ions involved in the substitution but also on their charges.     

N-phosphorylated imidazolium salts as precursors to 2- and 5-phosphorylated imidazoles and new imidazol-2-ylidenes featuring the PNCN unit

It has been experimentally proven that the reaction of 1- or 1,2-disubstituted imidazoles with diorganylphosphorus(III) halides proceeds via initial formation of N-phosporylated imidazolium salts. Treatment of these salts with strong bases results in phosphorylation of the parent imidazoles at the 2- or 5-positions, correspondingly. In a previous case, imidazol-2-ylidenes are formed as intermediates. With both N1 and N3 atoms bearing sterically demanding or/and π-donating groups, deprotonation of 1,3-disubstituted imidazolium salts with NaN(SiMe(3))(2) afforded new stable N-phosphorus-substituted Arduengo-type carbenes.     

Hydrodynamic,optical, and electrooptical properties of macromolecules of third-generation cylindrical dendrimers in chloroform and dichloroacetic acid

Acrylic polymers containing side dendrons of the third generation based on L-aspartic acid have been studied via the methods of molecular hydrodynamics, dynamic and static light-scattering, optics, and electrooptics. There are marked differences in hydrodynamic and optical properties of the macromolecules under study and previously examined polymers with side dendrons of first and second generations. In the range of degrees of polymerization from 10 to 40, these macromolecules possess an extremely low shape asymmetry. Experiments demonstrate the predominant orientation of end side dendrons along the main molecular chain. In chloroform solutions, the orientation of macromolecules in hydrodynamic and electric fields occurs according to the large-scale mechanism. In dichloroacetic acid, the hydrodynamic dimensions of macromolecules decrease, an effect that is accompanied by an increase in the kinetic flexibility of polymer chains.     

The role of the covalent interaction in the formation of the electronic structure of Au- and Cu-intercalated graphene on Ni(111)

A study is reported of the role played by covalent interaction in the coupling of graphene formed on Ni(111) to the Ni substrate and after intercalation of Au and Cu monolayers underneath the graphene. Covalent interaction of the graphene π states with d states of the underlying metal (Ni, Au, Cu) has been shown to bring about noticeable distortion of the dispersion relations of the graphene electronic π states in the region of crossing with d states, which can be described in terms of avoided-crossing effects and formation of bonding and antibonding d-π states. The overall graphene coupling to a substrate is mediated by the energy and occupation of the hybridized states involved. Because graphene formed directly on the Ni(111) surface has only bonding-type occupied states, the coupling to the substrate is very strong. Interaction with intercalated Au and Cu layers makes occupation of states of the antibonding and bonding types comparable, which translates into a weak resultant overall coupling of graphene to the substrate. As a result, after intercalation of Au atoms, the electronic structure becomes similar to that of quasi-free-standing graphene, with linear dispersion of π states at the K point of the Brillouin zone and the Dirac point localized close to the Fermi level. Intercalation of Cu atoms under the graphene monolayer results, besides generation of covalent interaction, in a slight charge transport, with a partial occupation of the previously unoccupied π* states and the Dirac point shifted by 0.35 eV toward increasing binding energy.     

Nonlinear Green’s functions in smectics

A solution of the problem of the strain of smectics subjected to a localized force has been proposed. An increase in the force is accompanied by a change from a linear increase in the strain amplitude to a square-root increase.     

Temperature-Abnormal Diffusivity in underdamped spatially periodic systems

A theoretical model of temperature-anomalous diffusion has been developed on the basis of computer calculation results. It has been shown that the behavior of diffusion in underdamped spatially periodic systems is anomalous in a certain force range: the diffusivity increases unlimitedly with a decrease in the temperature. Analytical expressions have been found for the width and position of this range depending on the friction coefficient and other parameters of the system. Scaling dependences of the diffusivity and mobility of particles on the friction coefficient have been obtained.     

Direct and inverse multichannel scattering problems

We consider small oscillations of a system of pairwise interacting particles in an external field near a stable equilibrium. The system is assumed to consist of finitely many channels, i.e., semi-infinite linear chains of particles, attached to a scatterer, which is a finite system of interacting particles. Direct and inverse scattering problems are considered. In particular, an algorithm finding characteristics of the channels on the basis of scattering data is given.     

On the asymptotic nonlinearity in smectics

Isolated sources of deformation in smectics for which the problem of determining the displacement field is significantly nonlinear at arbitrarily long distances even for a small action amplitude are indicated. Nonlinear asymptotic expressions can be determined in some cases.     

Determination of eigenvalues and discontinuous eigenfunctions of the system of equations of elasticity theory

Discretization algorithms are developed for the problem of eigenvalues and discontinuous eigenfunctions of the operator of elasticity theory. The operator is considered in a region with a clamped boundary. Error bounds of the approximate solution are obtained. Model examples are solved.Institute of Cybernetics of the Ukrainian Academy of Sciences. Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 74, pp. 38–45, 1992;