Scanning tunnelling microscopic images of the surface ordering of the liquid crystal 4-n-octyl-4'-cyanobiphenyl

Images of the surface ordering of 4-n-octyl-4'-cyanobiphenyl, a room temperature smectic liquid crystal deposited upon graphite, have been obtained by scanning tunnelling microscopy. The microscope was operated in air using the constant-current mode. Under certain tunnelling conditions it has been possible to resolve both the aliphatic and aromatic parts of the molecule, and to observe individual benzene rings. Two previously unreported conformations have been observed: an overlapping bilayer structure with spacing 3.7 nm, and a monolayer structure with spacing 2.4 nm. The latter structure may represent the first visual evidence for a surface polar ordered structure.     

Constraints on the number of maximal independent sets in graphs

A maximal independent set of a graph G is an independent set that is not contained properly in any other independent set of G. Let i(G) denote the number of maximal independent sets of G. Here, we prove two conjectures, suggested by P. Erdös, that the maximum number of maximal independent sets among all graphs of order n in a family Φ is o(3^n/3) if Φ is either a family of connected graphs such that the largest value of maximum degrees among all graphs of order n in Φ is o(n) or a family of graphs such that the approaches infinity as n → ∞.     

Rotation Part of the Dielectric Permittivity of Water Vapor for Different Spectral Line Profiles

We estimate the possible influence of spectral line profile (Lorentz profile, Van Vleck–Weisskopf profile, and profile obtained by solving kinetic equation) on the rotation part of the dielectric permittivity of water-vapor monomers. Spectral regions corresponding to long-wavelength (static) and high-frequency (optical) limiting cases as well as regions in close proximity to resonances of various intensities are considered. The studied effects are compared with the corresponding effects on water-vapor absorption coefficient, which are related to factors determining the line-shape structure.     

Kinetic study of n-heptane oxidation

The oxidation of n-heptane has been studied in a jet-stirred flow reactor in the temperature range 950–1200 K at atmospheric pressure for a wide range of fuel-oxygen equivalence ratios (0.2 to 2.0). A chemical kinetic reaction mechanism developed from previous studies on smaller hydrocarbons and extended to C₆ and C₇ species was used to reproduce the experimental data. Good agreement between computed and measured concentrations of major chemical species was obtained for the entire range of experimental conditions. Sensitivity analyses were carried out to identify the reactions having the greatest influence on the modeling results. The major reaction paths for n-heptane consumption and for the formation of the main products have been identified. In addition n-heptane ignition delays behind a reflected shock wave measured by other investigators were used to validate the present reaction mechanism at higher temperature and pressure.     

Liquid crystal side chain polysiloxanes containing various proportions of non-mesogenic units

Recent studies have established that side chain polymeric liquid crystals composed of mesogenic and non-mesogenic side groups keep their liquid-crystalline properties even for a low proportion of mesogens. We show that the detailed structures of three kinds of new diluted liquid crystal polysiloxanes depend on the nature of the co-substituent as well as on the proportion of the silicon sites occupied by the mesogenic groups. Mixtures of these systems with low molar mass liquid crystals were also investigated in terms of compatibility and/or stabilization of smectic A phases.