A new mesogenic fluorene derivative: 2,7-bis(4-pentylphenyl)-9,9-diethyl-9H-fluorene

The title compound, 2,7-bis(4-pentylphenyl)-9,9-diethyl-9H-fluorene, is a new mesogenic compound containing the fluorene moiety. It exhibits a monotropic nematic liquid crystalline behaviour, with isotropisation temperature of 53°C. The compound is also polymorphic in the solid state, with one crystal phase melting at 103°C and another one melting at 71°C. The crystal and molecular structure of the high melting solid phase have been determined from single crystal X-ray diffraction analysis. Crystals are monoclinic, with cell dimensions a = 16.649(6) Å, b = 8.305(3) Å, c = 24.598(7) Å, β = 111.60(2)?, space group P2₁/c and four molecules in the unit cell. Refinement leads to R = 0.0558. The two terminal alkyl chains and one phenyl ring are disordered over two split positions. The imbricated molecular packing observed in the solid state seems to resemble that of the nematic phase that is formed upon cooling the melt.     

Crystal structure and mesogenic behaviour of a new fluorene derivative: 9,9‐dimethyl‐2,7‐bis(4‐pentylphenyl)‐9H‐fluorene

The title compound, C₃₇H₄₂, is a new mesogenic compound containing the fluorene moiety. It exhibits enantiotropic nematic liquid crystalline behaviour with melting at 125 °C and isotropization at 175 °C. The crystallographically independent unit contains two molecules oriented face‐to‐edge with respect to each other. The two molecules have nearly the same conformation of the bis‐phenyl fluorene moiety. The molecular packing in the crystal phase is nematic‐like.     

Periodic motion around libration points in the Elliptic Restricted Three-Body Problem

Periodicity of motion around the collinear libration point associated with the Elliptic Restricted Three-Body Problem is studied. A survey of periodic solutions in the Circular Restricted Three-Body Problem is presented considering both Sun–Earth and Earth–Moon systems. Halo, Lyapunov and Vertical families around L1, L2 and L3 points are investigated, and their orbital period ranges through the entire family are reported. Resonant motions within the orbit families in the circular problem are identified and selected as suitable initial guess to find periodic orbits in the elliptic problem, which are targeted using a differential correction algorithm. Periodic solutions found are cataloged depending on the number of revolutions around libration points. Geometry, dynamical behavior and stability properties of single-revolution orbits are shown, as well as double-, triple- and quadruple-revolution solutions.     

Growth and characterization of REBa2Cu3O7−δ superconductor single crystals obtained from xenotime mineral

Single crystals of REBa₂Cu₃O_7−δ (RE=natural mixture of Y and heavy lanthanides in the single crystals) superconductor were successfully grown using rare-earth oxides extracted from xenotime mineral, allowing an alternative and simple route for superconductor single-crystal production. The methodology to extract the rare-earth mixed oxides from the xenotime mineral has three main steps: alkaline fusion, acid lixiviation and oxalic precipitation. Large single crystals with a typical 5×5×0.03 mm³ size were obtained by using a CuO-BaO self-flux and were characterized by scanning electron microscopy (SEM), energy-dispersive electron spectroscopy, X-ray diffraction, magnetic measurements and nanoindentation. The composition of the rare-earth elements of the crystal was different from the starting mixture, possibly due to the different solubilities of the elements in the melt. The final crystal stoichiometry was RE:Ba:Cu=1:2:3. X-ray diffraction analysis showed highly oriented c-axis (c=11.716±0.002 Å). The critical temperature was determined to be around T_C≅88-89 K after the crystals have been submitted to oxygen annealing. Hardness and elastic modulus for ab- and b(a)c-planes were 8.5±0.5 and 160±20 GPa, respectively.     

Complex Dynamics in a ODE Model Related to Phase Transition

Motivated by some recent studies on the Allen–Cahn phase transition model with a periodic nonautonomous term, we prove the existence of complex dynamics for the second order equation

$$\begin{aligned} -\ddot{x} + \left( 1 + \varepsilon ^{-1} A(t)\right) G'(x) = 0, \end{aligned}$$

where A(t) is a nonnegative T-periodic function and \(\varepsilon > 0\) is sufficiently small. More precisely, we find a full symbolic dynamics made by solutions which oscillate between any two different strict local minima \(x_0\) and \(x_1\) of G(x). Such solutions stay close to \(x_0\) or \(x_1\) in some fixed intervals, according to any prescribed coin tossing sequence. For convenience in the exposition we consider (without loss of generality) the case \(x_0 =0\) and \(x_1 = 1\).

     

The Moments Sliding Vector Field on the Intersection of Two Manifolds

In this work, we consider a special choice of sliding vector field on the intersection of two co-dimension 1 manifolds. The proposed vector field, which belongs to the class of Filippov vector fields, will be called moments vector field and we will call moments trajectory the associated solution trajectory. Our main result is to show that the moments vector field is a well defined, and smoothly varying, Filippov sliding vector field on the intersection \(\Sigma \) of two discontinuity manifolds, under general attractivity conditions of \(\Sigma \). We also examine the behavior of the moments trajectory at first order exit points, and show that it exits smoothly at these points. Numerical experiments illustrate our results and contrast the present choice with other choices of Filippov sliding vector field.     

Copolymers at Selective Interfaces: New Bounds on the Phase Diagram

We investigate the phase diagram of disordered copolymers at the interface between two selective solvents, and in particular its weak-coupling behavior, encoded in the slope m _c of the critical line at the origin. We focus on the directed walk case, which has turned out to be, in spite of the apparent simplicity, extremely challenging. In mathematical terms, the partition function of such a model does not depend on all the details of the Markov chain that models the polymer, but only on the time elapsed between successive returns to zero and on whether the walk is in the upper or lower half plane between such returns. This observation leads to a natural generalization of the model, in terms of arbitrary laws of return times: the most interesting case being the one of return times with power law tails (with exponent 1+α, α=1/2 in the case of the symmetric random walk). The main results we present here are:

Chromatographic NMR in NMR solvents

Recently, it was demonstrated that pseudo-chromatographic NMR experiments could be performed using typical chromatographic solids and solvents. This first setup yielded improved separation of the spectral components of the NMR spectra of mixtures using PFG self-diffusion measurements. The method (dubbed Chromatographic NMR) was successively shown to possess, in favorable cases, superior resolving power on non-functionalized silica, compared to its LC counterpart. To further investigate the applicability of the method, we studied here the feasibility of Chromatographic NMR in common deuterated solvents. Two examples are provided, using deuterated chloroform and water, for homologous compounds soluble in these solvents, namely aromatic molecules and alcohols, respectively.     

Spectral shaping of femtosecond pulses in aperiodic quasi-phase-matched gratings

We analyze the use of cascading second harmonic interactions in quadratic nonlinear crystals to mould the spectral characteristics of broadband near-infrared femtosecond pulses. Using a genetic algorithm, we optimize the design of the aperiodically poled ferroelectric crystal capable of generating the desired femtosecond infrared pulsed radiation.     

Polymer association in poor solvents: from monomolecular micelles to clusters of chains and phase separation

We report some recent results obtained in our laboratory on the poor‐solvent behavior of macromolecules. We first discuss the globular collapse of short chains that, unlike long ones, may form compact ordered states. We then address the collapse of random AB copolymers, which may provide significant clues to understanding biophysical issues such as the protein folding problem or the DNA arrangement in a living cell. Afterwards, we turn to the many‐chain problem of homopolymer aggregation into polymolecular micelles or clusters of chains and eventually phase separation. The unifying feature of our approach consists in the self‐consistent free‐energy minimization with inclusion of intra‐ and inter‐molecular interactions, whenever they are required, that enables us to describe the chain conformation in detail.