A homologous series of shape-persistent V-shaped molecules has been designed to form the biaxial nematic phase. Phenyleneethynylene moieties are attached to a bent fluorenone unit to create an apex angle of about 90u, which is determined from the single crystal structure. Two mesogens, one symmetric and another unsymmetric, have been synthesized by attaching a cyano group to one or both of the peripheral phenyl units, respectively. These groups introduce local dipoles essential for the formation of the nematic phases. The tendency to form a crystalline phase is reduced by laterally substituted hexyloxy chains which allow the nematic phase to be supercooled to a glassy state. Two of the three fluorenone derivatives exhibit a transition from the uniaxial nematic to the biaxial nematic phase. This transition has an undetectably small transition enthalpy, but the X-ray diffraction, polarizing optical microscopy, and conoscopy reveal the presence of the biaxial order in the low temperature nematic phase. Results and discussion SynthesisAn optimised strategy, shown in Scheme 1, was applied for the synthesis of unsymmetric phenyleneethynylene oligomers. The key precursor in the synthesis scheme is the 4-bromo-2,5dihydroxyiodobenzene 3. 13 After etherification with hexylbromide, unsymmetric compound 5 can be synthesised using a
We systematically investigate the sound modes of momentum dissipated holographic systems.In particular, we focus on the Einstein-linear axions and the Einstein-Maxwell-dilaton-axion theories in four-dimensional bulk spacetime dimensions. The sound velocities of the two theories are computed respectively and the sound attenuation of the Einstein-Maxwell-axion theory is also calculated analytically. We also obtain numeral dispersion relations in the two theories which match with our analytical results. Our results show that the sound velocity of the Einstein-Maxwelldilaton theory with additional linear axion fields is equivalent to that of 2 + 1 -dimensional Banados-Teitelboim-Zanelli black holes. It allowed us to compare our solution of the Einsteinlinear axions theory with that of systems without translational invariance from another method.After the computation on the sound velocity, we calculate the quasinormal modes of scalar-type fluctuations in the Einstein-Maxwell-dilaton-axion theory. The results show that a dynamical instability is observed under the condition that the null energy condition is violated.
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