Acetylenic and diacetylenic liquid-crystalline monomers: towards ordered conjugated polymers

Abstract

Acetylenic and diacetylenic mesomorphic monomers have been prepared in order to obtain long conjugated polymers able to give high non-linear optical hyperpolarizabilities. Here we report the synthesis of such monomers incorporating cholesteryl and methoxybiphenyl groups; their structural and thermal behaviour are described. The occurrence of mesophases in the acetylenic and diacetylenic derivatives is discussed as a function of the spacer length and of the size of the mesogen moiety. The diacetylenic derivatives containing the methoxybiphenyl groups do not exhibit any liquid-crystalline behaviour but are able to polymerize under U.V. radiation.     

Structural study of the smectic phases of several 4-cyanoalkoxybenzylidene-4'-alkylanilines

Abstract

A series of 4-cyanoalkoxybenzylidene-4'-alkylanilines (CN-nO. m; n = 3, 4, 6 and m = 4, 5, 8) have been synthesized. Their thermotropic liquid-crystalline polymorphism has been investigated using optical microscopy, differential scanning calorimetry and dilatometry. Nematic, smectic A and smectic B mesophases have been identified. The structure of the smectic phases has been studied with X-ray diffraction. Depending upon the compound and the temperature, the smectic layers have been found to be either single (A₁) or double (A₂) layers of molecules. Unexpected from a simple comparison with the well-known behaviour of the very similar nO. m smectogens, which belong to the class of the so-called symmetric and therefore exhibit single-layered smectics only, this structural behaviour has been interpreted to mean the importance of the dipole interactions of the terminal cyano groups. For CN-60.8, a transition has been detected at 64°C between the single and double layered structure.     

A limiting distribution for maxima of discrete stationary triangular arrays with an application to risk due to avalanches

In this paper, we generalize earlier work dealing with maxima of discrete random variables. We show that row-wise stationary block maxima of a triangular array of integer valued random variables converge to a Gumbel extreme value distribution if row-wise variances grow sufficiently fast as the row-size increases. As a by-product, we derive analytical expressions of normalising constants for most classical unbounded discrete distributions. A brief simulation illustrates our theoretical result. Also, we highlight its usefulness in practice with a real risk assessment problem, namely the evaluation of extreme avalanche occurrence numbers in the French Alps.     

Thermosolutal mixed convection and flow-reversal in an inclined parallel-plate channel

The steady-state laminar mixed convection of a binary gas mixture in a parallel-plate channel is investigated. The channel walls are subjected to different combinations of first-type thermal and solutal boundary conditions and different wall inclinations have been considered. A second-order accurate control-volume based numerical scheme is used for the resolution. In parallel with the numerical investigation, the governing conservation equations are also simplified for fully developed conditions and are shown to be controlled by a single parameter. An exact analytical solution is obtained for the main flow variables and transfer rates and serves as a validation tool for the numerical model. In addition, it establishes a criterion based on the two Grashof numbers, the Reynolds number and the channel inclination for the existence of a reversed flow.