On a flow to untangle elastic knots

In this paper we present a method to untangle smooth knots by a gradient flow for a suitable energy. We show that the flow of smooth initial knots remains smooth for all time and approaches asymptotically an “optimal embedding” in its isotopy type. The method is to set up a gradient flow for the total energy of knots, which consists of bending energy and the Möbius energy of knots.     

Charge-changing cross sections of the neutron-rich isotopes8,9,11Li

Total charge-changing cross sections have been measured for⁸Li on C and Pb targets, for⁹Li on C, Al, Cu, Sn and Pb targets, as well as for¹¹Li on C, Sn and Pb targets at about 80 MeV/nucleon. These data are compared to measured total reaction cross sections and Glauber-type calculations using Hartree-Fock density distributions. These comparisons allow to draw conclusions on the proton density distribution of the neutronrich lithium isotopes. The results show that even for the most exotic nucleus¹¹Li the proton distribution is only very weakly influenced by the long tail in the neutron density distribution already established in several experiments.     

Systematic study of muon transfer to sulphur dioxide

In a systematic study of the transfer process to sulphur dioxide, in seven different H₂ + SO₂ gas mixtures, the time spectra of the muonic sulphur X-rays yield muon transfer rates to the SO₂ molecule, deduced from the lifetimes of the p atoms, which agree all well with each other. The muonic oxygen time spectra show an additional structure as if p atoms of another kind were present. Reduced transfer rates_O are reproducible if one uses the model of ephemeral p atoms. The intensity ratios between the different kinds of p atoms are also discussed in the framework of this model and the one of black and white p atoms.     

Acetic Anhydride as an Oxygen Donor in the Non-Hydrolytic Sol–Gel Synthesis of Mesoporous TiO2 with High Electrochemical Lithium Storage Performances

An original, halide-free non-hydrolytic sol–gel route to mesoporous anatase TiO₂ with hierarchical porosity and high specific surface area is reported. This route is based on the reaction at 200 °C of titanium(IV) isopropoxide with acetic anhydride, in the absence of a catalyst or solvent. NMR spectroscopic studies indicate that this method provides an efficient, truly non-hydrolytic and aprotic route to TiO₂. Formation of the oxide involves successive acetoxylation and condensation reactions, both with ester elimination. The resulting TiO₂ materials were nanocrystalline, even before calcination. Small (about 10 nm) anatase nanocrystals spontaneously aggregated to form mesoporous micron-sized particles with high specific surface area (240 m² g⁻¹ before calcination). Evaluation of the lithium storage performances shows a high reversible specific capacity, particularly for the non-calcined sample with the highest specific surface area favouring pseudo-capacitive storage: 253 mAh g⁻¹ at 0.1 C and 218 mAh g⁻¹ at 1 C (C=336 mA g⁻¹). This sample also shows good cyclability (92 % retention after 200 cycles at 336 mA g⁻¹) with a high coulombic efficiency (99.8 %). Synthesis in the presence of a solvent (toluene or squalane) offers the possibility to tune the morphology and texture of the TiO₂ nanomaterials.     

A New Class of Lanthanide Complexes with Three Ligand Centered Radicals: NMR Evaluation of Ligand Field Energy Splitting and Magnetic Coupling

Combination of three radical anionic Ph-BIAN ligands (Ph-BIAN=bis-(phenylimino)-acenaphthenequinone) with lanthanoid ions leads to a series of homoleptic, six-coordinate complexes of the type Ln(Ph-BIAN)₃. Magnetic coupling data were measured by paramagnetic solution NMR spectroscopy. Combining ¹H NMR with ²H NMR of partially deuterated compounds allowed a detailed study of the magnetic susceptibility anisotropies over a large temperature range. The observed chemical shifts were separated into ligand- and metal-centered contributions by comparison with the Y analogue (diamagnetic at the metal). The metal-centered contributions of the complexes with the paramagnetic ions could then be separated into pseudocontact and Fermi contact shifts. The latter is large within the Ph-BIAN scaffold, which shows that magnetic coupling is significant between the lanthanide ion and the radical ligand. Pseudocontact shifts were further correlated to structural data obtained from X-ray diffraction experiments. Ligand-field parameters were determined by fitting the temperature dependence of the observed magnetic susceptibility anisotropies. The electronic structure determined by this approach shows, that the Er and Tm analogues are candidates for single molecule magnets (SMM). These results demonstrate the possibilities for the application of NMR spectroscopy in investigations of paramagnetic systems in general and single molecule magnets in particular.     

1,2,5,6-Tetrakis(guanidino)-Naphthalenes: Electron Donors,Fluorescent Probes and Redox-Active Ligands

New redox-active 1,2,5,6-tetrakis(guanidino)-naphthalene compounds, isolable and storable in the neutral and deep-green dicationic redox states and oxidisable further in two one-electron steps to the tetracations, are reported. Protonation switches on blue fluorescence, with the fluorescence intensity (quantum yield) increasing with the degree of protonation. Reactions with N-halogenosuccinimides or N-halogenophthalimides led to a series of new redox-active halogeno- and succinimido-/phthalimido-substituted derivatives. These highly selective reactions are proposed to proceed via the tri- or tetracationic state as the intermediate. The derivatives are oxidised reversibly at slightly higher potentials than that of the unsubstituted compounds to dications and further to tri- and tetracations. The integration of redox-active ligands in the transition-metal complexes shifts the redox potentials to higher values and also allows reversible oxidation in two potentially separated one-electron steps.