Flutelike porous hematite nanorods and branched nanostructures: synthesis, characterisation and application for gas-sensing

Flute-like porous alpha-Fe2O3 nanorods and branched nanostructures such as pentapods and hexapods were prepared through dehydration and recrystallisation of hydrothermally synthesised beta-FeOOH precursor. Transmission electron microscopy (TEM), high-resolution TEM and selected area electron diffraction analyses reveal that the nanorods, which grow along the [110] direction, have nearly hollow cavities and porous walls with a pore size of 20-50 nm. The hexapods have six symmetric arms with a diameter of 60-80 nm and length of 400-900 nm. The growth direction of the arms in the hexapod-like nanostructure is also along the [110] direction, and there is a dihedral angle of 69.5 degrees between adjacent arms. These unique iron oxide nanostructures offer the first opportunity to investigate their magnetic and gas sensing properties. The nanostructures exhibited unusual magnetic behaviour, with two different Morin temperatures under field-cooled and zero-field-cooled conditions, owing to their shape anisotropy and magnetocrystalline anisotropy. Furthermore, the alpha-Fe2O3 nanostructures show much better sensing performance towards ethanol than that of the previously reported polycrystalline nanotubes. In addition, the alpha-Fe2O3 nanostructure based sensor can selectively detect formaldehyde and acetic acid among other toxic, corrosive and irritant vapours at a low working temperature with rapid response, high sensitivity and good stability.     

An Integrated approach (thermodynamic, structural, and computational) to the study of complexation of alkali-metal cations by a lower-rim calix[4]arene amide derivative in acetonitrile

The calix[4]arene secondary-amide derivative L was synthesized, and its complexation with alkali-metal cations in acetonitrile (MeCN) was studied by means of spectrophotometric, NMR, conductometric, and microcalorimetric titrations at 25 °C. The stability constants of the 1:1 (metal/ligand) complexes determined by different methods were in excellent agreement. For the complexation of M(+) (M = Li, Na, K) with L, both enthalpic and entropic contributions were favorable, with their values and mutual relations being quite strongly dependent on the cation. The enthalpic and overall stability was the largest in the case of the sodium complex. Molecular and crystal structures of free L, its methanol and MeCN solvates, the sodium complex, and its MeCN solvate were determined by single-crystal X-ray diffraction. The inclusion of a MeCN molecule in the calixarene hydrophobic cavity was observed both in solution and in the solid state. This specific interaction was found to be stronger in the case of metal complexes compared to the free ligand because of the better preorganization of the hydrophobic cone to accept the solvent molecule. Density functional theory calculations showed that the flattened cone conformation (C(2) point group) of L was generally more favorable than the square cone conformation (C(4) point group). In the complex with Na(+), L was in square cone conformation, whereas in its adduct with MeCN, the conformation was slightly distorted from the full symmetry. These conformations were in agreement with those observed in the solid state. The classical molecular dynamics simulations indicated that the MeCN molecule enters the L hydrophobic cavity of both the free ligand and its alkali-metal complexes. The inclusion of MeCN in the cone of free L was accompanied by the conformational change from C(2) to C(4) symmetry. As in solution studies, in the case of ML(+) complexes, an allosteric effect was observed: the ligand was already in the appropriate square cone conformation to bind the solvent molecule, allowing it to more easily and faster enter the calixarene cavity.     

Isomorphism Checking of I-graphs

We consider the class of I-graphs, which is a generalization of the class of the generalized Petersen graphs. We show that two I-graphs I(n, j, k) and I(n, j ₁, k ₁) are isomorphic if and only if there exists an integer a relatively prime to n such that either {j ₁, k ₁} =? {a j mod n, a k mod n } or {j ₁, k ₁} =? {a j mod n, ? a k mod n }. This result has an application in the enumeration of non-isomorphic I-graphs and unit-distance representations of generalized Petersen graphs.     

Bisimulations and bisimulation games between Verbrugge models

Interpretability logic is a modal formalization of relative interpretability between first-order arithmetical theories. Verbrugge semantics is a generalization of Veltman semantics, the basic semantics for interpretability logic. Bisimulation is the basic equivalence between models for modal logic. We study various notions of bisimulation between Verbrugge models and develop a new one, which we call w-bisimulation. We show that the new notion, while keeping the basic property that bisimilarity implies modal equivalence, is weak enough to allow the converse to hold in the finitary case. To do this, we develop and use an appropriate notion of bisimulation games between Verbrugge models.