Dynamic response of the spherical pendulum subjected to horizontal Lissajous excitation

Nonlinear Dynamics - This paper examines the oscillations of a spherical pendulum with horizontal Lissajous excitation. The pendulum has two degrees of freedom: a rotational angle defined in the...     

On the Adams–Riemann–Roch theorem in positive characteristic

Let p > 0 be a prime number. We give a short proof of the Adams–Riemann–Roch theorem for the p-th Adams operation, when the involved schemes live in characteristic p. We also answer a question of B. Köck.     

Non-symmetric chiral isoflavone dimers: synthesis,characterisation and mesomorphic behaviour

A new series of non-symmetric chiral isoflavone-based liquid crystalline dimers, α-(2-methylbutyl-4′-(4″-phenyloxy)benzoate)-ω-(3-(4′-decyloxyphenyl)-4H-1-benzopyran-4-one-7-oxy)alkanes, with 3–12 carbon atoms in the alkyloxy spacer, have been synthesised. A pronounced odd–even effect for the phase transition temperatures upon varying the spacer length was observed. The short dimers exhibited monolayer smectic A (SmA) and smectic C (SmC*) phases while for longer homologues a chiral nematic (N*) phase was found. The temperature range of the nematic phase was broadened with elongation of the alkyl spacer. Stabilisation of the nematic phase resulted from competition between the monolayer and intercalated smectic structures. The SmA–SmC* phase transition was second order for all studied compounds with a cross over to the de Vries type behaviour for the shortest homologue.     

Sulfur-linked cyanobiphenyl-based liquid crystal dimers and the twist-bend nematic phase

ABSTRACT

The synthesis and characterisation of two series of cyanobiphenyl-based liquid crystal dimers containing sulfur links between the spacer and mesogenic units, the 4?-[1,ω-alkanediylbis(thio)]bis-[1,1?-biphenyl]-4-carbonitriles (CBSnSCB), and 4?-({ω-[(4?-cyano[1,1?-biphenyl]-4-yl)oxy]alkyl}thio)[1,1?-biphenyl]-4-carbonitriles (CBSnOCB) are described. The odd members of both series show twist-bend nematic and nematic phases, whereas the even members exhibit only the nematic phase. An analogous cyanoterphenyl-based dimer, 3⁴-{6-[(4?-cyano[1,1?-biphenyl]-4-yl)thio]-hexyl}[1¹,2¹:2⁴,3¹-terphenyl]-1⁴-carbonitrile (CT6SCB), is also reported and shows enantiotropic N_TB and N phases. The transitional properties of these dimers are discussed in terms of molecular curvature, flexibility and biaxiality. The same molecular factors also influence the birefringence of nematic phases. Resonant X-ray scattering studies of the twist-bend nematic phase at both the carbon and sulfur absorption edges were performed, which allowed for the determination of critical behaviour of the helical pitch at the transition to the nematic phase, the behaviour was found to be independent of molecular structure. It was also observed that despite the different molecular bending angle and flexibility, in all compounds the helical pitch length far from the N-N_TB transition corresponds to 4 longitudinal molecular distances.     

Nanocomposite of CeVO4/BiVO4 Loaded on Reduced Graphene Oxide for the Photocatalytic Degradation of Methyl Orange

A facile procedure, involving one-pot synthesis of CeVO₄/BiVO₄ and in-situ reduction of graphene oxide (GO), has been used to prepare CeVO₄/BiVO₄/rGO nanocomposites. Different ratios of the CeVO₄–BiVO₄ were prepared to afford composites represented as CBVG3, CBVG5, and CBVG7. The ternary nanocomposite materials were characterized by using powder X-ray diffractometer (XRD), scanning electron microscopy (SEM), transmission electron microscope (TEM), photoluminescence and UV–vis spectroscopic techniques. Photocatalytic efficiency of the as-prepared ternary nanocomposites was investigated through the photo degradation of methyl orange under a visible light irradiation at 470 nm. The photocatalytic performance was enhanced by loading the CeVO₄/BiVO₄ nanoparticles on reduced graphene oxide (rGO), given MO degradation rate of 57, 65, 80, and 90% for BVG, CBVG3, CBVG5, and CBVG7, respectively after exposure to visible light for 120 min. Effects of experimental process parameters including initial dye concentration, catalysts loading and effect of different modification regimes were studied using CBVG7, which exhibited the highest efficiency. The improvement in the photocatalytic efficiency may be attributed to increased surface area of the nanocomposites, enhanced light absorption capacity and improved charge separation. The study showed a one-pot synthesis route to prepare promising CeVO₄/BiVO₄/GO nanocomposites for the photo-enhanced degradation of dye contaminants.

     

Single versus poly-crystalline layered oxide cathode materials for solid-state battery applications - a short review article

The recent developments in the application of single-crystalline (SC) cathode materials in solid-state batteries are discussed in this mini-review. The characteristics of SC and poly-crystalline (PC) cathode materials are explored, with emphasis on the kinetic and mechanical properties. The critical factors influencing their performance in liquid electrolyte and solid-state battery cells are investigated. Finally, the advantages and disadvantages of both morphologies are discussed and considerations to ensure a fair comparison between SC and PC cathodes in different systems are raised.     

Twist-Bend Nematic Glasses: The Synthesis and Characterisation of Pyrene-based Nonsymmetric Dimers

A selection of pyrene-based liquid crystal dimers have been prepared, containing either methylene-ether or diether linked spacers of varying length and parity. All the diether linked materials, CBOnO.Py (n=5, 6, 11, 12), exhibit conventional nematic and smectic A phases, with the exception of CBO11O.Py which is exclusively nematic. The methylene-ether linked dimer, CBnO.Py, with an even-membered spacer (n=5) was solely nematogenic, but odd-members (n=6, 8, 10) exhibited both nematic and twist-bend nematic phases. Replacement of the cyanobiphenyl fragment by cyanoterphenyl giving CT6O.Py, gave elevated melting and nematic-isotropic transition temperatures, and SmA and SmC_A phases were observed on cooling the nematic phase. Intermolecular face-to-face associations of the pyrene moieties drive glass formation, and all these materials have a glass transition temperature at or above room temperature. The stability of the glassy twist-bend nematic phase allowed for its study using AFM, and the helical pitch length, P_TB, was measured as 6.3 and 6.7 nm for CB6O.Py and CB8O.Py, respectively. These values are comparable to the shortest pitch of a twist-bend nematic phase measured to date.     

Enzymatic Desymmetrising Redox Reactions for the Asymmetric Synthesis of Biaryl Atropisomers

Atropisomeric biaryls carrying ortho‐hydroxymethyl and formyl groups were made enantioselectively by desymmetrisation of dialdehyde or diol substrates. The oxidation of the symmetrical diol substrates was achieved using a variant of galactose oxidase (GOase), and the reduction of the dialdehydes using a panel of ketoreductases. Either M or P enantiomers of the products could be formed, with absolute configurations assigned by time‐dependent DFT calculations of circular dichroism spectra. The differing selectivities observed with different biaryl structures offer an insight into the detailed structure of the active site of the GOase enzyme.