Gd3N@C2n (n = 40, 42, and 44): remarkably low HOMO-LUMO gap and unusual electrochemical reversibility of Gd3N@C88

High-performance liquid chromatography was used to isolate two new trimetallic nitride endohedral fullerenes, Gd3N@C2n (n = 42 and 44), and they were characterized by MALDI-TOF mass spectrometry, UV-vis-NIR, and cyclic voltammetry. It was found that their electronic HOMO-LUMO gaps depend pronouncedly on the size of the cage, from a large band gap for Gd3N@C80 (2.02 V) to a small band gap for Gd3N@C88 (1.49 V). The electrochemical properties also change dramatically with the size of the cage, going from irreversible for the C80 cage to reversible for Gd3N@C88. The latter is the largest trimetallic cluster inside C88 isolated and characterized to date. Gd3N@C88 has one of the lowest electrochemical energy gaps for a nonderivatized metallofullerene.     

Direct identification and decongestion of Fermi resonances by control of pulse time ordering in two-dimensional IR spectroscopy

We show that it is possible to both directly measure and directly calculate Fermi resonance couplings in benzene. The measurement method used was a particular form of two-dimensional infrared spectroscopy (2D-IR) known as doubly vibrationally enhanced four wave mixing. By using different pulse orderings, vibrational cross peaks could be measured either purely at the frequencies of the base vibrational states or split by the coupling energy. This capability is a feature currently unique to this particular form of 2D-IR and can be helpful in the decongestion of complex spectra. Five cross peaks of the ring breathing mode nu13 with a range of combination bands were observed spanning a region of 1500-4550 cm(-1). The coupling energy was measured for two dominant states of the nu13+nu16 Fermi resonance tetrad. Dephasing rates were measured in the time domain for nu13 and the two (nu13+nu16) Fermi resonance states. The electronic and mechanical vibrational anharmonic coefficients were calculated to second and third orders, respectively, giving information on relative intensities of the cross peaks and enabling the Fermi resonance states of the combination band nu13+nu16 at 3050-3100 cm(-1) to be calculated. The excellent agreement between calculated and measured spectral intensities and line shapes suggests that assignment of spectral features from ab initio calculations is both viable and practicable for this form of spectroscopy.     

Synthesis and characterization of a new monophosphate (C<Subscript>6</Subscript>H<Subscript>16</Subscript>N<Subscript>2</Subscript>)(H<Subscript>2</Subscript>PO<Subscript>4</Subscript>)<Subscript>2</Subscript>

Chemical preparation, crystal structure, and NMR spectroscopy of a new trans-2,5-dimethylpiperazinium monophosphate are given. This new compound crystallizes in the triclinic system, with the space group P-1 and the following parameters: a = 6.5033(3), b = 7.6942(4), c = 8.1473(5) Å, α = 114.997(3), β = 92.341(3), γ = 113.136(3), V = 329.14(3) ų, Z = 1, and D_x = 1.565 g cm^?3. The crystal structure has been determined and refined to R = 0.030 and R _w(F ²) = 0.032 using 1558 independent reflections. The structure can be described as infinite [H₂PO₄] _n ^n? chains with (C₆H₁₆N₂)²⁺ organic cations anchored between adjacent polyanions to form columns of anions and cations running along the b axis. This compound has also been investigated by IR, thermal, and solid-state, ¹³C and ³¹P MAS NMR spectroscopies and Ab initio calculations.     

Poincaré’s Equations for Cosserat Media: Application to Shells

In 1901, Henri Poincaré discovered a new set of equations for mechanics. These equations are a generalization of Lagrange’s equations for a system whose configuration space is a Lie group which is not necessarily commutative. Since then, this result has been extensively refined through the Lagrangian reduction theory. In the present contribution, we apply an extended version of these equations to continuous Cosserat media, i.e. media in which the usual point particles are replaced by small rigid bodies, called microstructures. In particular, we will see how the shell balance equations used in nonlinear structural dynamics can be easily deduced from this extension of the Poincaré’s result. In future, these results will be used as foundations for the study of squid locomotion, which is an emerging topic relevant to soft robotics.     

Random walks on free products of cyclic groups

Let G be a free product of a finite family of finite groups,with the set of generators being formed by the union of thefinite groups. We consider a transient nearest-neighbour randomwalk on G. We give a new proof of the fact that the harmonicmeasure is a special Markovian measure entirely determined bya finite set of polynomial equations. We show that in severalsimple cases of interest, the polynomial equations can be explicitlysolved to get closed form formulae for the drift. The examplesconsidered are /2 /3, /3 /3, /k /k and the Hecke groups /2 /k.We also use these various examples to study Vershik's notionof extremal generators, which is based on the relation betweenthe drift, the entropy and the growth of the group.     

Comparison of the thermal performances of two nanofluids at low temperature in a plate heat exchanger

The objective of this study is to compare experimentally the thermal performances of two types of commercial nanofluids. The first is composed of oxides of alumina (γAl₂O₃) dispersed in water and the second one is aqueous suspensions of nanotubes of carbons (CNTs). The viscosity of the nanofluids is measured as a function of the temperature between 2 and 10 °C. An experimental device, containing three thermal buckles controlled in temperature and greatly instrumented permits to study the thermal convective transfers. The evolution of the convective coefficient permits to study the convective thermal transfers. The evolution of the convective coefficient is presented according to the Reynolds number, at low temperature from 0 to 10 °C and for the two aforementioned nanofluids. An assessment of the pressure drops in the circuit as well as of the powers of the circulator and outputs is dealt with.     

Non-linear dynamics of the photodissociation of nitrous oxide: equilibrium points, periodic orbits, and transition states

The diffuse vibrational bands, observed in the ultraviolet photodissociation spectrum of nitrous oxide by exciting the molecule in the first (1)A' state, have recently been attributed to resonances localized mainly in the NN stretch and bend degrees of freedom. To further investigate the origin of this localization, fundamental families of periodic orbits emanating from several stationary points of the (1)A' potential energy surface and bifurcations of them are computed. We demonstrate that center-saddle bifurcations of periodic orbits are the main mechanism for creating stable regions in phase space that can support the partial trapping of the wave packet, and thus they explain the observed spectra. A non-linear mechanical methodology, which involves the calculation of equilibria, periodic orbits, and transition states in normal form coordinates, is applied for an in detail exploration of phase space. The fingerprints of the phase space structures in the quantum world are identified by solving the time dependent Schro?dinger equation and calculating autocorrelation functions. This demonstrates that different reaction channels could be controlled if exact knowledge of the phase space structure is available to guide the initial excitation of the molecule.     

Evaluation of a multiarray system for pharmaceutical analysis by microemulsion electrokinetic chromatography

A multiplexed capillary electrophoresis (CE) system equipped with 96 channels was evaluated for high-throughput screening in drug discovery by microemulsion electrokinetic chromatography (MEEKC). Method transfer from a single channel to a multichannel CE system is described. Loss of efficiency and reduced migration times could be elucidated to the poor efficacy in Joule heat dissipation by forced air cooling in the multiarray system compared to liquid cooling in the single channel instrument. On the other hand, only 48 channels could actually be used because of the maximum total current of 3 mA. Precision data remained below 8% and 9% for migration times and peak areas, respectively. Some UV-detector cross-talk interference between neighboring capillary channels was noted. Impurities at 0.5% compared to the main peak (100%) could be detected with the multiplexed system which is 10 times lower compared to the single capillary system. Higher efficiency and improved figures of merit (absolute sensitivity and no cross-talk interferences) were obtained by using an array of only 24 capillaries.