The synthesis of mesogenic polymers provoked by molecular mobility. polysiloxanarylenes

An approach to the synthesis of potentially thermotropic liquid crystalline polymers based on parallel investigation of their molecular mobility was realized. The initial idea was provoked by the observation that there exists some correspondence of molecular mobility data and the ability of a polymer to form a liquid crystalline phase. Previously this phenomenon was demonstrated on the example of a series of thermotropic main chain polymers with flexible dimethylsiloxane spacers of variable length. The relation between the structure of the main chain and local molecular mobility of different fragments was investigated in a series of regular polysiloxane-silarylenes containing rigid aromatic sequences. Molecular mobility was studied by dielectric spectroscopy in solution and in solid state. The structure of the main chain has been changed by variation of the repeated fragments' length, substituents and joint groups. The data of molecular mobility and their conformity with the chain structure were used for directed synthetic search of desired mesogenic polymers.     

Korn's Inequalities for Junctions of Spatial Bodies and Thin Rods

The dependence on the small parameter ε of constants in Korn's inequalities is investigated for domains which are obtained by joining thin rods to an elastic spatial body. The external ends of the rods are clamped. The asymptotic accuracy of the derived inequalities is achieved by certain distribution of weight multipliers and powers of ε in L₂-norms of displacements and their derivatives while the introduced weights differ for longitudinal and transversal components of displacement fields in the rods. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.     

Ab initio simulation of paramagnetic NMR spectra: the 31P NMR in oxovanadium phosphates

A theoretical analysis of the temperature-dependent (31)P NMR signals for the ambient pressure vanadyl pyrophosphate AP-(VO)(2)P(2)O(7) and the oxovanadium hemihydrate hydrogenophosphate VO(HPO(4)).0.5H(2)O phases is reported. The ab initio calculation of the magnetic exchange parameters and the hyperfine constants gives access to an original ab initio simulation of NMR spectra. Such a strategy allows one to clarify the crystallographic nature of the different experimentally studied phases. For the vanadyl pyrophosphate ambient pressure structure, our simulations strongly support the presence of a monoclinic phase. Based on this assumption, hyperfine constants are extracted from the fit of the experimental data. These values are directly compared to the ab initio ones.     

Breaking the phonon bottleneck in semiconductor nanocrystals via multiphonon emission induced by intrinsic nonadiabatic interactions

We observe ultrafast 1P-to-1S intraband relaxation in PbSe and CdSe nanocrystals (NCs) that have distinct energy spectra. While ultrafast dynamics in CdSe NCs has typically been interpreted in terms of electron-hole energy transfer, this mechanism is not active in PbSe NCs because of sparse densities of states in the conduction and valence bands. Our observations of temperature activation and confinement-enhanced relaxation in PbSe NCs can be explained by efficient multiphonon emission triggered by nonadiabatic electron-phonon interactions and are indicative of large, size-dependent, intraband Huang-Rhys parameters.     

Remarkable enhancement of reactivity of carbonyl compounds for polymerizations with non-activated aromatic hydrocarbons

Reaction of carbonyl compounds bearing electron-withdrawing substituents with non-activated aromatic hydrocarbons proceeds selectively in trifluoromethanesulfonic acid (TFSA) at room temperature to give linear, high-molecular-weight polymers.     

Artificial boundary conditions on polyhedral truncation surfaces for three-dimensional elasticity systemsConditions aux limites artificielles sur des surfaces polyhédrales de troncature pour des systèmes d'élasticité tridimensionalle

For a three-dimensional exterior problem in the framework of anisotropic elasticity, artificial boundary conditions are constructed on a polyhedral truncation surface. These conditions do not need an explicit formula for the fundamental matrix. An approach to adapt the shape of truncation surfaces to the shape of the enclosed cavity is discussed. To cite this article: S. Langer et al., C. R. Mecanique 332 (2004).     

Self adjoint extensions of differential operators in application to shape optimizationExtensions autoadjointes d'opérateurs différentiels et application à l'optimisation de forme

Two approaches are proposed for the modelling of problems with small geometrical defects. The first approach is based on the theory of self adjoint extensions of differential operators. In the second approach function spaces with separated asymptotics and point asymptotic conditions are introduced, and the variational formulation is established. For both approaches the accuracy estimates are derived. Finally, the spectral problems are considered and the error estimates for eigenvalues are given. To cite this article: S.A. Nazarov, J. Sokolowski, C. R. Mecanique 331 (2003).