Diffraction by finite-size crystalline bundles of single wall nanotubes

We calculate the diffraction spectrum of finite-size crystalline bundles of single wall carbon nanotubes (SWNT). The general profile of the spectrum as well as the width and position of the (1 0) diffraction peaks of the 2-D lattice of bundles depend on the tubes symmetry, distribution of tubes diameters and diameter of the bundles. Consequently, any attempt to derive the mean-diameter of the tubes from a diffraction spectrum requires to consider the diameters distribution of the tubes and the size of the bundles. Experimental diffraction profiles of various single wall nanotubes samples are well fitted by the calculated spectra. Received 16 December 1998     

Effect of local molecular structure on the chain-length dependence of the electronic properties of thiophene-based pi-conjugated systems

Three series of thiophene-based pi-conjugated oligomers built with different combinations of thiophene cycles and double bonds have been synthesized and characterized. The analysis of the chain length dependence of the electronic, electrochemical, and vibrational properties of the three series of oligomers has been carried out using cyclic voltammetry, UV-vis, IR, and Raman spectroscopies. These various investigations provide consistent results showing that incorporation of ethylenic linkages in an oligothiophene structure leads to a faster decrease of the HOMO-LUMO gap with chain extension due to the combined effects of enhanced planarity and lower overall aromatic character of the system. Although the incorporation of two consecutive double bonds in the system leads to a stabilization of the dicationic state, this structural modification does not produce the expected further decrease of the HOMO-LUMO gap at large chain extension. This phenomenon is discussed on the basis of an interplay between aromaticity and bond length alternation.     

Synthesis and Diels-Alder Reactions of a New Kind of Chiral Dienophiles: Cyclic Vinyl-p-tolylsulfilimines

A new kind of chiral dienophiles, cyclic vinyl-p-tolylsulfilimines (2a and 2b), were obtained from the corresponding (Z)-sulfinylacrylonitriles with HBF(4) and methanol. The asymmetric Diels-Alder reaction of optically pure 2a with cyclopentadiene under mild thermal or catalyzed conditions afforded only the endo-4a adduct with complete endo and pi-facial selectivities. The ability of the sulfilimine moiety to enhance the dienophilic reactivity of the double bond is similar to that of the sulfinyl group.     

Zeros of the Whittaker function associated to Coulomb waves

The zeros in the complex z plane of the Whittaker function W_c/z,µ(z),closely related to spherical waves in the quantum-mechanicalCoulomb problem, are investigated for varying real values ofthe parameters c and µ     

Lamellar bridged silsesquioxanes: self-assembly through a combination of hydrogen bonding and hydrophobic interactions

The synthesis of four bis(trialkoxysilylated) organic molecules capable of self-assembly--(EtO)3Si(CH2)3NHCONH-(CH2)n-NHCONH(CH2)3Si(OEt)3 (n = 9-12)--associating urea functional groups and alkylidene chains of variable length is described. These compounds behave as organogelators, forming supramolecular assemblies thanks to the intermolecular hydrogen bonding of urea groups. Whereas fluoride ion-catalysed hydrolysis in ethanol in the presence of a stoichiometric amount of water produced amorphous hybrids, acid-catalysed hydrolysis in an excess of water gave rise to the formation of crystalline lamellar hybrid materials through a self-organisation process. The structural features of these nanostructured organic/inorganic hybrids were analysed by several techniques: attenuated Fourier transformed infrared (ATR-FTIR), solid-state NMR spectroscopy (13C and 29Si), scanning and transmission electron microscopy (SEM and TEM) and powder X-ray diffraction (PXRD). The reaction conditions, the hydrophobic properties of the long alkylidene chains and the hydrogen-bonding properties of the urea groups are determining factors in the formation of these self-assembled nanostructured hybrid silicas.     

Far- and mid-infrared of crystalline 2,2'-bithiophene: ab initio analysis and comparison with infrared response

Infrared intramolecular vibrations and lattice modes in the crystalline phase of 2,2'-bithiophene (2T) are investigated using the direct method combined with density functional theory (DFT)-based total energy calculations. For the first time, the far- and mid-infrared responses have been calculated from the Gamma-point modes and the Born effective charge tensors of the 2T crystalline phase. The relative good agreement between the calculated and experimental infrared spectra allows us to assign the origin of the main features of the experimental spectra, which is of particular interest in the far-infrared domain. These assignments are useful for understanding all the properties of the 2T crystalline phase in which phonon-phonon and electron-phonon interactions play an important role.     

Raman modes of index-identified freestanding single-walled carbon nanotubes

Using electron diffraction on freestanding single-walled carbon nanotubes, we have determined the structural indices (n,m) of tubes in the diameter range from 1.4 to 3 nm. On the same freestanding tubes, we have recorded Raman spectra of the tangential modes and the radial breathing mode. For the smaller diameters (1.4-1.7 nm), these measurements confirm previously established radial breathing mode frequency versus diameter relations and would be consistent with the theoretically predicted proportionality to the inverse diameter. However, for extending the relation to larger diameters, either a yet unexplained environmental constant has to be assumed, or the linear relation has to be abandoned.     

Phonon density of states of single-wall carbon nanotubes

The vibrational density of states of single-wall carbon nanotubes (SWNT) was obtained from inelastic neutron scattering data from 0 to 225 meV. The spectrum is similar to that of graphite above 40 meV, while intratube features are clearly observed at 22 and 36 meV. An unusual energy dependence below 10 meV is assigned to contributions from intertube modes in the 2D triangular lattice of SWNT bundles, and from intertube coupling to intratube excitations. Good agreement between experiment and a calculated density of states for the SWNT lattice is found over the entire energy range.