The effect of olefinic terminal chains on the mesomorphic properties of 4,4'-disubstituted diphenyldiacetylenes

New diphenyldiacetylenes of the type with A, B = H and/or F; m = 0, 1; n = 1-4; and X = C n H 2n + 1 , F, CF 3 or CN were synthesized and their mesomorphic properties determined by hot stage polarizing microscopy and DSC. When m = 0, all of these compounds showed only a nematic phase except when X = CF 3 when both nematic and smectic A phases were seen. Both clearing and melting temperatures were higher than those reported for substitution with the corresponding alkyl chains but the much larger increase in clearing temperatures produced considerably wider nematic phases. Eutectic mixtures of a few of these olefins yielded nematic materials also having much wider temperature ranges and higher clearing temperatures than the eutectic mixtures of the alkyl compounds, while retaining their high birefringence and low viscosities. Such materials are of interest for beam-steering devices.

Four of the diacetylenes with m = 1 ( A, B = H) were also prepared ( X = C 6 H 13 , F, n = 2, 3). When X was C 6 H 13 ( n = 2), the nematic range was smaller in the 2- than in the 1-olefin but wider than in the alkyl series. When X = F, either no nematic phase or a monotropic one was observed, whereas the 1-olefins gave a much wider nematic phase. Both transition temperatures were lower than those for the corresponding 1-olefin and alkyl analogues. The compound with X = C 6 H 13 and n = 2 had a melting temperature below room temperature.     

Integrable models for vicious and friendly walkers

We consider random walks of two essentially different classes of random walkers, namely, of vicious and friendly ones, on one-dimensional lattices with periodic boundary conditions. The walkers are called vicious since, arriving at a lattice site, they annihilate not only one another but all the remaining walkers as well. On the contrary, an arbitrary number of friendly walkers can share the same lattice sites. It is shown that a natural model describing the behavior of friendly walkers is an integrable model of the boson type. A representation of the generating function for the number of the lattice paths performed by a fixed number of friendly walkers for a certain number of steps is obtained. Bibliography: 22 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 335, 2006, pp. 59–74.     

New Heat-Resistant Polyimidates Derived from Bisphenols and Mono- and Dicarboxylic Acid Imidoyl Chlorides

New polyimidates were prepared from bisphenols and mono- and dicarboxylic acid imidoyl chlorides. The structures of the polymers were determined, and their physicochemical, chemical, and thermal properties were studied. The possibility of preparing film and compression materials with good mechanical characteristics from these polymers was examined.     

Relaxing local modes and the theory of low-frequency Raman scattering in glasses

Raman scattering in glasses is investigated theoretically. The experimental Raman spectra of glasses exhibit a low-frequency peak (at ～10 cm^?1) that, as a rule, is attributed to vibrational modes of nanometer-sized structural units (nanocrystallites). It is established that the elastic moduli of nanocrystallites must necessarily be dependent on their sizes due to the Laplace pressure effect. A theory of the low-frequency peak is constructed using a realistic size distribution function of nanocrystallites with allowance made for the Laplace pressure effect and the dissipation of vibrational energy. Within this theory, the shape of the low-frequency peak and its evolution with temperature can be analyzed quantitatively. The proposed approach offers a physical interpretation of the experimental data and provides insight into the relation of the characteristic nanocrystallite sizes to the elastic moduli and surface tension coefficients of materials.     

Numerical study of simultaneous natural convection heat transfer from both surfaces of a uniformly heated thin plate with arbitrary inclination

 Numerical studies were conducted to investigate the natural convection heat transfer around a uniformly heated thin plate with arbitrary inclination in an infinite space. The numerical approach was based on the finite volume technique with a nonstaggered grid arrangement. For handling the pressure–velocity coupling the SIMPLE-algorithm was used. QUICK scheme and first order upwind scheme were employed for discretization of the momentum and energy convective terms respectively. Plate width and heating rate were used to vary the modified Rayleigh number over the range of 4.8×10⁶ to 1.87×10⁸. Local and average heat transfer characteristics were compared with regarding to the inclination angle. The empirical expressions for local and average Nusselt number were correlated. It has been found that for inclination angle less than 10^∘, the flow and heat transfer characteristics are complicated and the average Nusselt number can not be correlated by one equation while for inclination angle larger than 10^∘, the average Nusselt number can be correlated into an elegant correlation. Received on 18 April 2001 / Published online: 29 November 2001