Polar Order,Mirror Symmetry Breaking,and Photoswitching of Chirality and Polarity in Functional Bent-Core Mesogens

In recent years, liquid crystals (LCs) responding to light or electrical fields have gained significant importance as multifunctional materials. Herein, two new series of photoswitchable bent-core liquid crystals (BCLCs) derived from 4-cyanoresorcinol as the central core connected to an azobenzene based wing and a phenyl benzoate wing are reported. The self-assembly of these molecules was characterized by differential scanning calorimetry (DSC), polarizing light microscopy (POM), electro-optical, dielectric, second harmonic generation (SHG) studies, and XRD. Depending on the direction of the COO group in the phenyl benzoate wing, core-fluorination, temperature, and the terminal alkyl chain length, cybotactic nematic and lamellar (smectic) LC phases were observed. The coherence length of the ferroelectric fluctuations increases continuously with decreasing temperature and adopts antipolar correlation upon the condensation into superparaelectric states of the paraelectric smectic phases. Finally, long-range polar order develops at distinct phase transitions; first leading to polarization modulated and then to nonmodulated antiferroelectric smectic phases. Conglomerates of chiral domains were observed in the high permittivity ranges of the synclinic tilted paraelectric smectic phases of these achiral molecules, indicating mirror symmetry breaking. Fine-tuning of the molecular structure leads to photoresponsive bent-core (BC)LCs exhibiting a fast and reversible photoinduced change of the mode of the switching between ferroelectric- and antiferroelectric-like as well as a light-induced switching between an achiral and a spontaneous mirror-symmetry-broken LC phase.     

Synthesis,structure and magnetism of a novel Cu4^ⅡTi5^Ⅳ heterometallic cluster

A nonanuclear Cu4^ⅡTi5^Ⅳheterometallic cluster,[Ti5 Cu4 O6(ba)(16)](1,Hba=benzoic acid)was synthesized in one-pot reaction under the solvothermal condition.The metallic skeleton 1 contains a Ti5 core constructed from two vertex-shared Ti3 triangles and four separated Cu atoms outside which are connected together byμ3-O^2- ions.Total 16 ba ligands adoptμ2-η^1:η^1 coordination mode to protect the overall hetero metallic co re.Due to the unique d-d transitions of Cu^Ⅱion,the reflectance spectrum of 1 displays broad and strong absorption towards visible light extending to the near-infrared region.Moreover,1 shows almost purely paramagnetic behavior with the presence of weak antiferromagnetic interactions at low temperatures.     

Solvophobically Driven Complexation of Adamantyl Mannoside with β-Cyclodextrin in Water and Structured Organic Solvents

The effects of solvent and temperature on the complexation of adamantyl mannoside with β-cyclodextrin and 6-O-monotosyl-6-deoxy-β-cyclodextrin were explored experimentally and by means of molecular dynamics simulations. Efficient binding was observed only in hydrogen-bonded solvents, which indicated solvophobically driven complexation. The stability of the inclusion complex was considerably higher in aqueous media. A pronounced temperature dependence of Δ_rH^○ and Δ_rS^○, resulting in perfect enthalpy–entropy compensation, was observed in water. The complexation thermodynamics was in line with classical rationale for the hydrophobic effect at lower temperatures and the nonclassical explanation at higher temperatures. This finding linked cyclodextrin complexation thermodynamics with insights regarding the effect of temperature on the hydration water structure. The complexation enthalpies and entropies were weakly dependent on temperature in organic media. The signs of Δ_rH^○ and Δ_rS^○ were in accordance with the nonclassical hydrophobic (solvophobic) effect. The structures of the optimized product corresponded to those deduced spectroscopically, and the calculated and experimentally obtained values of Δ_rG^○ were in very good agreement. This investigation clearly demonstrated that solvophobically driven formation of cyclodextrin complexes could be anticipated in structured solvents in general. However, unlike in water, adamantane and the host cavity behaved solely as structure breakers in the organic media explored so far.     

Coexistence of Spin–Lattice Relaxation and Phonon-Bottleneck Processes in GdIII–Phthlocyaninato Triple-Decker Complexes under Highly Diluted Conditions

Gd³⁺ complexes have been shown to undergo unusual slow magnetic relaxation processes similar to those of single-molecule magnets (SMMs), even though Gd³⁺ does not exhibit strong magnetic anisotropy. To reveal the origin of the slow magnetic relaxation of Gd³⁺ complexes, we have investigated the magnetic properties and heat capacities of two Gd³⁺-phthalocyaninato triple-decker complexes, one of which has intramolecular Gd³⁺–Gd³⁺ interactions and the other does not. It was found that the Gd³⁺–Gd³⁺ interactions accelerate the magnetic relaxation processes. In addition, magnetically diluted samples, prepared by doping a small amount of the Gd³⁺ complexes into a large amount of diamagnetic Y³⁺ complexes, underwent dual magnetic relaxation processes. A detailed dynamic magnetic analysis revealed that the coexistence of spin–lattice relaxation and phonon-bottleneck processes is the origin of the dual magnetic relaxation processes.     

The effect of an external magnetic field on the resonant neutralization of negative ions near a solid state surface

The influence of an external magnetic field on the resonant neutralization of negative ions near a solid state surface is considered. It is shown that the magnetic field reduces the neutralization probability considerably.     

Optimal Error Estimate of the Penalty Finite Element Method for the Micropolar Fluid Equations

We present an optimal error estimate of the numerical velocity, pressure, and angular velocity for the fully discrete penalty finite element method of the micropolar equations when the parameters ?, Δ t, and h are sufficiently small. In order to obtain this estimate, we present the time discretization of the penalty micropolar equation that is based on the backward Euler scheme; the spatial discretization of the time discretized penalty micropolar equation is based on a finite elements space pair (X _h , M _h ) that satisfies some approximations properties.     

Dynamical properties of a particle in a wave packet: Scaling invariance and boundary crisis

Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is mixed in the sense that there are regular and chaotic regions coexisting. We use a connection with the standard map in order to find the position of the first invariant spanning curve which borders the chaotic sea. We find that the position of the first invariant spanning curve increases as a power of the control parameter with the exponent 2/3. The standard deviation of the kinetic energy of an ensemble of initial conditions obeys a power law as a function of time, and saturates after some crossover. Scaling formalism is used in order to characterise the chaotic region close to the transition from integrability to nonintegrability and a relationship between the power law exponents is derived. The formalism can be applied in many different systems with mixed phase space. Then, dissipation is introduced into the model and therefore the property of area preservation is broken, and consequently attractors are observed. We show that after a small change of the dissipation, the chaotic attractor as well as its basin of attraction are destroyed, thus leading the system to experience a boundary crisis. The transient after the crisis follows a power law with exponent −2.     

Extensions of the Fill–Fishkind formula and the infimum – parallel sum relation

Recently, in (Arias ML, Corach G, Maestripieri A. Range additivity, shorted operator and the Sherman–Morrison–Woodburry formula, Linear Algebra Appl. 2015;467), authors gave a generalization of a formula by Fill and Fishkind, regarding the Moore–Penrose inverse of the sum of two matrices, in the setting of arbitrary Hilbert spaces. We consider this formula under some weaker assumptions and derive certain conclusions generalizing the mentioned result. We also extend a formula connecting the infimum of two orthogonal projections and their parallel sum to a formula connecting the star-infimum and the parallel sum of operators which need not be positive, using the concept of parallel sum that was introduced in (Antezana J, Corach G, Stojanoff D. Bilateral shorted operators and parallel sums. Linear Algebra Appl. 2006;414).     

Free energy and entropy production in planar Couette flow far from equilibrium

The macroscopic thermodynamic stability of a system of 108 diatomic molecules undergoing planar Couette flow far from equilibrium is reported. The system is perturbed from the steady state using a nondissipative variable colour field which induces a polarization in the system. It is found that the steady state for the system corresponds to an extremum in the generalized free energy and entropy production. However, while the free energy is always a minimum, the entropy production may be either a minimum or a maximum depending upon the direction of the colour field. These results, for a molecular system, are fundamentally different from those for an equivalent atomic system.     

The <Emphasis Type="Italic">D</Emphasis><Superscript>(−)</Superscript>-Center Energy Spectrum in the Quantum Narrowing in the Presence of a Longitudinal Magnetic Field

The dispersion equation for an electron localized at the D⁰-center in the quantum narrowing in the presence of a magnetic field longitudinal with respect to the axis of constriction is analytically derived within the model of zero-radius potential. It is found that a special feature of the electron spectrum in the quantum narrowing manifests itself in the dependence of the D(−)-state binding energy on the effective constriction length. The evolution of the D(−)-state binding energy with changes in the longitudinal magnetic-field strength is investigated and compared with the case of D(−)-states in quantum wires. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 23–27, June, 2005.