Renormalisation of q-Regularised Multiple Zeta Values

We consider a particular one-parameter family of q-analogues of multiple zeta values. The intrinsic q-regularisation permits an extension of these q-multiple zeta values to negative integers. Renormalised multiple zeta values satisfying the quasi-shuffle product are obtained using an Hopf-algebraic Birkhoff factorisation together with minimal subtraction.     

Nanoscale deformation of a liquid surface

We study the interaction between a solid particle and a liquid interface. A semianalytical solution of the nonlinear equation that describes the interface deformation points out the existence of a bifurcation behavior for the apex deformation as a function of the distance. We show that the apex curvature obeys a simple power-law dependency on the deformation. Relationships between physical parameters disclose the threshold distance at which the particle can approach the liquid before capillarity provokes a "jump to contact." A prediction of the interface original position before deformation takes place, as well as the attraction force measured by an approaching probe, are produced. The results of our analysis agree with the force curves obtained from atomic force microscopy experiments over a liquid puddle.     

Strain hardening and fracture of heat-set fractal globular protein gels

Non-linear mechanical behavior at large shear deformation was been investigated for heat-set beta-lactoglobulin gels at pH 7 and 0.1 M NaCl using both oscillatory shear and shear flow. These gels have a self-similar structure at length scales smaller than the correlation length of the gel with fractal dimension d(f)=2. Strain hardening is observed that can be well described using the model proposed by Gisler et al. [T.C. Gisler, R.C. Ball, D.A. Weitz, Phys. Rev. Let. 82 (1999) 1064] for fractal colloidal gels. The increase of the shear modulus normalized by the low strain value (G(0)) is independent of G(0). For weak gels the elasticity increases up to a factor of ten, while for strong gels the increase is very small. At higher deformation irreversible fracture occurs, which leads eventually to macroscopic failure of the gel. For weak gels formed at low concentrations the deformation at failure is about 2, independent of the shear modulus. For strong gels fracture occurs at approximately constant stress (2 x 10(3) Pa).     

Photoinduced magnetization in copper octacyanomolybdate

This article describes the studies of a photomagnetic cyanide-bridged Cu-Mo bimetallic assembly, Cu(II)(2)[Mo(IV)(CN)(8)].8H(2)O (Cu(II), S = (1)/(2); Mo(IV), S = 0) (1), which has an intervalence transfer (IT) band from Mo(IV)-CN-Cu(II) to Mo(V)-CN-Cu(I) around 480 nm. Wide-angle X-ray scattering and X-ray spectroscopic studies provide precise information about the 3D connectivity and the local environment of the transition metal ions. Irradiating with blue light causes solid 1 to exhibit a spontaneous magnetization (Curie temperature = 25 K). The thermal reversibility is carefully studied and shows the long-time stability of the photoinduced state up to 100 K. Photoreversibility is also observed; i.e., the magnetization is induced by irradiation with light below 520 nm, while the magnetization is reduced by irradiation with light above 520 nm. The UV-vis absorption spectrum after irradiation shows a decrease of the IT band and the appearance of the reverse-IT band in the region of 600-900 nm (lambda(max) = 710 nm). This UV-vis absorption spectrum is recovered to the original spectrum by irradiation with 658-, 785-, and 840-nm light. In this photomagnetic effect, the excitation of the IT band causes an electron transfer from Mo(IV) to Cu(II), producing a ferromagnetic mixed-valence isomer of Cu(I)Cu(II)[Mo(V)(CN)(8)].8H(2)O (Cu(I), S = 0; Cu(II), S = (1)/(2); Mo(V), S = (1)/(2)) (1'). 1' returns to 1 by irradiation of the reverse-IT band, which obeys the scheme for the potential energy surface in mixed-valence class II compounds.     

Photomagnetic properties of an iron(II) low-spin complex with an unusually long-lived metastable LIESST state

A comprehensive study of the photomagnetic behavior of the [Fe(L222N5)(CN)2].H2O complex has been carried out. This complex is characterized by a low-spin (LS) iron(II)-metal center up to 400 K and exhibits at 10 K the well-known Light-Induced Excited Spin State Trapping (LIESST) effect. The critical LIESST temperature (T(LIESST)) has been measured to be 105 K. The kinetics of the transition from the metastable high-spin (HS) state to the low-spin state have been determined and used for reproducing the experimental T(LIESST) curve. This study represents a second example of a fully low-spin iron(II)-metal complex up to 400 K, which can be photoexcited at low temperature with an atypical long-lived metastable HS state. This underlines the preponderant role of the inner coordination sphere for stabilizing the lifetime of the photoinduced HS state.     

1H and 19F ultra-fast MAS double-quantum single-quantum NMR correlation experiments using three-spin terms of the dipolar homonuclear Hamiltonian

Measuring internuclear distances through dipolar interaction is a major challenge for solid-state nuclear magnetic resonance (NMR) spectroscopy. Obtaining reliable interatomic distances provides an access to the local structure in ordered or disordered solids. We show that at magic angle spinning (MAS) frequencies larger than ca. 50 kHz, some of the three-spin terms of the homogeneous homonuclear dipolar Hamiltonian can be used to promote the creation of double-quantum coherences between neighbouring (1)H or (19)F spins without using dipolar recoupling pulse sequences in the Dipolar Homonuclear Homogeneous Hamiltonian (DH(3)) double-quantum/single-quantum correlation experiment. This makes it possible to probe inter-nuclear spatial proximity with limited risk of probe or sample damage from radio-frequency (RF) irradiation, and is fully appropriate for fast repetition rate offering sensitivity gains in favourable cases. Experimental demonstrations are supported by multi-spin numerical simulations, which points to new possibilities for the characterization of spin-system geometries.     

Effects of substituted ligands on the mobility of complexed anions

From conductance and viscosities measurements on Pr₄NCl, Et₄NBr, and AgNO₃ in acetonitrile and Et₃NBr in nitrobenzene, the Walden products of the anion at infinite dilution were determined in presence of various concentrations of substituted benzoic acids. From these data it was possible to compute the values of the Walden products of the once complexed anions and to estimate the order of magnitude of the Walden products of twice complexed anions. Stokes' law is not obeyed, and the Walden products are not proportional to the third root of the molar volume of the complexed ions, as a consequence of their lack of sphericity. The assumption that the drag force which acts on the ions is proportional to the volume of the substituents results in a linear expression between the reciprocals of the Walden products and the molar volume of the ligands. The experimental results fit this expression within the limits of the experimental errors, and the slopes of the lines are nearly the same for all the anions and for the two solvents studied here, namely, 2.5×10^–4 ohm-cm^–5 mole-cP^–1.     

Tetrathiafulvalene hydrazone: efficient synthon for the synthesis of novel bidentate redox active ligands

The synthesis and the ability of TTF-hydrazone to act as a versatile precursor for the design of electroactive ligands are reported together with the chelating ability of these ligands through their M(CO)₄ complexes, (M = Mo, W).     

Electronic core levels of hydroxyls at the surface of chromia related to their XPS O 1s signature: A DFT + U study

The Cr 2p and O 1s binding energy (BE) levels have been calculated by first principles methods for different models of hydroxylated (0001)-Cr₂O₃ surfaces. Several surface terminations have been considered. The calculations allow us to reproduce the O 1s shifts between O in oxide and OH groups. It is found that two main effects account for the OH binding energy shifts. On the one hand, the increased covalency of the O–H bond with respect to the Cr–O bond, lowers the electronic O (1s and 2p) energy, and in consequence the BE of the core levels (O 1s) are higher. On the other hand, the lower the OH coordination number, the higher the valence and core levels energy, and the lower the BE. Consequently, mono-coordinated hydroxyls have a binding energy near that of O^2? in the oxide (ΔBE_OH–O = ? 0.2–0.0 eV). Two-fold coordinated hydroxyls have a slightly higher BE (ΔBE_OH–O = + 0.3 eV). Three-fold coordinated OH groups have a higher binding energy (ΔBE_OH–O = + 0.6?0.7 eV), corresponding to that experimentally measured for OH groups. Finally, water adsorbed above OH groups exhibits a still higher BE (ΔBE_HOH–O = + 0.9–1.0 eV). The ΔBE are slightly under-estimated under the initial state approximation, and overestimated under the final state (Z + 1) approximation.     

Revealing Phosphorus Nitrides up to the Megabar Regime: Synthesis of α′-P3N5, δ-P3N5 and PN2

Non-metal nitrides are an exciting field of chemistry, featuring a significant number of compounds that can possess outstanding material properties. These properties mainly rely on maximizing the number of strong covalent bonds, with crosslinked XN₆ octahedra frameworks being particularly attractive. In this study, the phosphorus–nitrogen system was studied up to 137 GPa in laser-heated diamond anvil cells, and three previously unobserved phases were synthesized and characterized by single-crystal X-ray diffraction, Raman spectroscopy measurements and density functional theory calculations. δ-P₃N₅ and PN₂ were found to form at 72 and 134 GPa, respectively, and both feature dense 3D networks of the so far elusive PN₆ units. The two compounds are ultra-incompressible, having a bulk modulus of K₀=322 GPa for δ-P₃N₅ and 339 GPa for PN₂. Upon decompression below 7 GPa, δ-P₃N₅ undergoes a transformation into a novel α′-P₃N₅ solid, stable at ambient conditions, that has a unique structure type based on PN₄ tetrahedra. The formation of α′-P₃N₅ underlines that a phase space otherwise inaccessible can be explored through materials formed under high pressure.