On some liquid crystalline phases exhibited by compounds made of bent-core molecules and their mixtures with rod-like molecules

In most homologous series of compounds made of bent-core (BC) molecules, the B₂ B₁ and B₆ phases occur as the chain length decreases. We have studied binary mixtures of the compound 1,3-phenylene bis[4-(3-methylbenzoyloxy)]4-n-dodecylbiphenyl 4’-carboxylate (BC12) which exhibits the B₂ phase with the compound 4-biphenylyl 4’-n-undecyloxybenzoate (BO11) made of rod-like (R) molecules. We find the above sequence of occurrence of the B phases with increasing concentration of BOH. In this paper we describe the physical origin for the formation of these phases in both pure compounds and in the mixtures. We have also found the occurrence of the biaxial smectic A phase when the BO11 concentration is increased to 87–95.5 mol%. We also report on another binary system composed of BC12 and 4-n-octyloxy 4’- cyanobiphenyl (8OCB) made of R molecules. This system exhibits the biaxial smectic A phase down to 30°C. Using polarized infrared spectroscopy we find that the mutual orientation of the R and BC molecules in the SmA_db liquid crystal is such that the arrow axes of the BC molecules are along the layer normal of the partial bilayer smectic structure formed by the rods. We also describe unusual growth patterns obtained when the nematic phase transforms to the SmA_db phase in a mixture with 24 mol% of BC12.     

Di-pion emission in heavy quarkonia decays

The dipion spectrum for the ϒ(nS) → ϒ(n′S) transition with n < 4 has the form dw/dq ∼ (phase space) |η − x|², with x = q ² − 4m _π² / (ΔM)² − 4m _π² < q ² ≡ M _ππ², and ΔM = M(nS) − M(n′S). The parameter η is calculated and the spectrum is shown to reproduce the experimental data for all three types of decays: 3 → 1, 2 → 1, and 3 → 2 with η ≈ 0.5, 0, and −3, respectively. The text was submitted by the author in English.     

Anisotropy of rotation of nitroxide probes in nematogenic liquid crystals

An electron paramagnetic resonance (EPR) line shape simulation for nitroxide spin probes in the motional narrowing region was carried out assuming axially symmetricg andA tensors and with different anisotropies of rotationN (=R _∥/R _⊥) whereR _∥ andR _⊥ are, respectively, elements of the diffusion tensor along and perpendicular to its principal axisz′. In addition, it was assumed that the principal axes of the diffusion tensor coincide with the molecular axes. Each of three casesz′=x,z′=y andz′=z, which result from cyclic permutations of the molecular axesx, y andz with thez′,y′ andx′ axes of the diffusion tensor, yields its typical EPR spectrum characterized by the relative intensities of the low-, center- and high-field lines. The parameter δ defined by and calculable from the intensities of the three lines was found to vary linearly withN for thez′=x andz′=y cases and, as anticipated, to be practically constant at a value of 1 for thez′=z case. This suggested a method for estimatingN for a probe from its EPR spectrum. Experimental spectra over a narrow temperature range (1°C) in the vicinity of the nematic-to-isotropic transition (about 34.6°C) ofN-(4-n-butylbenzilidene)-4-amino-2,2,6,6-tetramethylpiperidine-1-oxide at a mole fraction of 1·10⁻³ in 4-n-pentyl-4′-cyanobiphenyl showed a pattern of peak heights characteristic of thez′=x case with δ values that gave, neglecting effects of the mean field, higher and lowerN values in the nematic and isotropic regions, respectively. Analysis of other similar systems in the literature gave similar results.     

Dielectric relaxation behaviour of liquid crystals with opposite orientation of -COO ester group in molecular core

Dielectric measurements were performed for two smectogens, being structurally analogous with the opposite space orientation of the-COO ester group in the molecular core, using a HP4192A impedance analyser. Gold coated electrode cells of different thicknesses were used. Temperature dependences of the relaxation frequency fR and the inverse of the dielectric strength Δε′_┴ ⁻¹ obtained by fitting experimental values of perpendicular components, i.e., the real ε′_┴ and the imaginary ε″_┴ parts of the complex dielectric permittivity to the Cole-Cole equation as well as the investigation of modification of relaxation processes under bias were determined for the SmC_*, SmA_*, and N_* phases of studied compounds. One can conclude, on the basis of the above results, that dielectric relaxation processes observed by us in the studied compounds are similar to those of the soft and Goldstone mode typically observed by others in the SmC_*, SmA_*, and N_* phases. It is concluded from acomparison of their properties with other related compounds that the link between the biphenyl moiety and-COO ester group is closely related to the stability of smectic phases.     

Reacting polymers with highly correlated initial conditions

We propose and theoretically study an experiment designed to measure short-time polymer reaction kinetics in melts or dilute solutions. The photolysis of groups centrally located along chain backbones, one group per chain, creates pairs of spatially highly correlated macroradicals. We calculate time-dependent rate coefficients κ(t) governing their first-order recombination kinetics, which are novel on account of the far-from-equilibrium initial conditions. In dilute solutions (good solvents) reaction kinetics are intrinsically weak, despite the highly reactive radical groups involved. This leads to a generalised mean-field kinetics in which the rate of radical density decay - ∼S(t), where S(t) ∼t ^{- (1 + g/3)} is the equilibrium return probability for 2 reactive groups, given initial contact. Here g≈ 0.27 is the correlation hole exponent for self-avoiding chain ends. For times beyond the longest coil relaxation time τ, - ∼S(t) remains true, but center of gravity coil diffusion takes over with rms displacement of reactive groups x(t) ∼t ^1/2 and S(t) ∼ 1/x ³(t). At the shortest times ( t 10^-6s), recombination is inhibited due to spin selection rules and we find ∼tS(t). In melts, kinetics are intrinsically diffusion-controlled, leading to entirely different rate laws. During the regime limited by spin selection rules, the density of radicals decays linearly, n(0) - n(t) ∼t. At longer times the standard result - ∼d ³(t)/d (for randomly distributed ends) is replaced by ∼d2x ³(t)/d ² for these correlated initial conditions. The long-time behavior, t > τ, has the same scaling form in time as for dilute solutions. Received 18 May 2000     

Critical Hardy–Lieb–Thirring Inequalities for Fourth-Order Operators in Low Dimensions

This paper considers Hardy–Lieb–Thirring inequalities for higher order differential operators. A result for general fourth-order operators on the half-line is developed, and the trace inequality

Super-Diffusivity in a Shear Flow Model¶from Perpetual Homogenization

This paper is concerned with the asymptotic behavior solutions of stochastic differential equations dy _t =dω _t −∇Γ(y _t ) dt, y ₀=0 and d=2. Γ is a 2 &\times; 2 skew-symmetric matrix associated to a shear flow characterized by an infinite number of spatial scales Γ₁₂=−Γ₂₁=h(x ₁), with h(x ₁)=∑ _{n =0} ^∞γ _n h ⁿ (x ₁/R _n ), where h ⁿ are smooth functions of period 1, h ⁿ (0)=0, γ _n and R _n grow exponentially fast with n. We can show that y ^t has an anomalous fast behavior (?[|y ^t |²]∼t ^1+ν with ν > 0) and obtain quantitative estimates on the anomaly using and developing the tools of homogenization. Received: 1 June 2001 / Accepted: 11 January 2002     

Dispersion of the Voigt effect in the magnetic semiconductors Cd1−x MnxTe

Spectral measurements of the Voigt birefringence Δn were performed for the cubic magnetic semiconductor Cd_1−x Mn _x Te (0≤x≤0.52) in order to investigate how the exchange interaction of Mn²⁺ ions with itinerant electrons depends on the electron wave vector. It was determined that Δn/x ² is independent of x and the magnetic field direction, i.e., the effect is due to the Mn²⁺ ions and is isotropic. Below the band gap edge the dispersion of the birefringence Δn can be described well in all samples by the unusual dependence Δn∼(E _g −ℏω) ^−3.5. This can be explained by a decrease of the exchange interaction of Mn²⁺ ions with itinerant electrons with increasing distance from the center of the Brillouin zone. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 8, 569–573 (25 April 1998)     

EPR studies of Cu2+ and V4+ ions in phosphate glasses

Two lead-phosphate glass systems doped with both copper and vanadium ions in different ratios were studied by EPR (electron paramagnetic resonance) method. EPR spectra and parameters (g_‖ = 2.44, g_⊥ = 2.08 andA _‖ = 117.6 · 10⁻⁴ cm⁻¹) obtained for x(CuO · V₂O₅)(l−x)[2P₂O₅ · PbO] glasses withx ≤ 10 mol% suggest a tetrahedral (Td) coordination of Cu²⁺ ions and not a tetragonally elongated octahedron as has been assumed in previous works. The ground state of the paramagnetic electron is thed _xy copper orbital with a 4p_z contribution of 6%. For 20 ≤x ≤ 40 mol% a broad line (ΔB = 307 G) characteristic for clustered ions appears atg = 2.18. The V⁴⁺ ions are evidenced only in the spectra of x(CuO · 2V₂O₅)(1 −x)[2P₂O₅ · PbO] glasses and the resonance parameters suggest a pentacoordinated C_4v local symmetry for these ions. The hyperfine structures characteristic for Cu²⁺ and V⁴⁺ ions disappear for 10 ≤x ≤ 40 mol% due to the mixed exchange Cu²⁺−V⁴⁺ pair formation in these glasses.     

The effect of bias field on the value and temperature dependence of the piezoelectric coefficient d 31 in (1 ? x )Pb(Mg1/3Nb2/3)O3? x PbTiO3 ( x = 0.06, 0.13) single crystals

It is established that, as a result of application of even a small (∼0.5 kV cm⁻¹) bias field E, the maximum of the piezoelectric coefficient d ₃₁ in (1 − x)Pb(Mg_1/3Nb_2/3)O₃ − xPbTiO₃(x = 0.06, 0.13) crystals shifts from the Vogel-Fulcher temperature to the critical point in the E-T phase diagram of a given composition. The field dependence of the d ₃₁(T) peak magnitude has a maximum near the E values corresponding to the critical point. Original Russian Text ? A.S. Emelyanov, S.I. Raevskaya, F.I. Savenko, I.P. Raevski, M.A. Malitskaya, E.I. Sitalo, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 1, pp. 132–133.     

Valence instability of uranium in U(Al1−x Gex)3

The electronic structure of U and Ge in the solid solutions U(Al_1−x Ge_x)₃ is investigated by measuring x-ray line shifts. It is shown that uranium has the mixed valence U³⁺ [Rn](5f ³)-U⁴⁺ [Rn](5f ²) over the entire composition range (0⩽x⩽1) and that the population of the uranium 5f shell increases by ∼0.28 5f electrons/U atom from UAl₃ (x=0) to UGe₃ (x=1). The electronic structure of Ge is close to the electronic structure of Ge metal over the entire composition range 0<x⩽1. No variation of the population of the Ge 4p shell is detected to within the experimental error (∼0.1 4p electrons/Ge atom) as the composition varies from x=0.2 to 1. It is established that the delocalization of a U 5f electron occurs as a result of its transition to the s or d band of the same uranium atom. Fiz. Tverd. Tela (St. Petersburg) 39, 1505–1508 (September 1997)     

A Measurement of the ψ′ to J/ψ production ratio in 920?GeV proton-nucleus interactions

Ratios of the ψ^′ over the J/ψ production cross sections in the dilepton channel for C, Ti and W targets have been measured in 920 GeV proton-nucleus interactions with the HERA-B detector at the HERA storage ring. The ψ^′ and J/ψ states were reconstructed in both the μ⁺μ^- and the e⁺e^- decay modes. The measurements covered the kinematic range -0.35≤x_F≤0.1 with transverse momentum p_T≤4.5 GeV/c. The angular dependence of the ratio has been used to measure the difference of the ψ^′ and J/ψ polarization. All results for the muon and electron decay channels are in good agreement: their ratio, averaged over all events, is R_ψ′(μ)/R_ψ′(e)=1.00±0.08±0.04. This result constitutes a new, direct experimental constraint on the double ratio of branching fractions, (B^′(μ)B(e))/(B(μ)B^′(e)), of ψ^′ and J/ψ in the two channels. The ψ^′ to J/ψ production ratio is almost constant in the covered x_F range and shows a slow increase with p_T.     

Calculation of the structure and vibrational states for anionic forms of Co-, Ni-, and Cu-porphines

The structure and vibrations of neutral porphine metal complexes (Me-P, Me = Co, Ni, Cu) and their d-anionic forms with an additional electron localized in vacant d_x² -_y² - d_x^2 -_y^2 - and d_z² d_z^2 -orbitals are compared based on calculations by a DFT method. It is shown that such electron population causes a significant increase of the electronic charge on the macrocycle rather than on the Me atom and is accompanied by a considerable redistribution of π- and σ-electron densities (ρ_π ρ_σ). A predominant gain of ρ_π (0.49e) is found for the monoanion of Co-P (Co-P^–, d_z² d_z^2 -monoanion); of ρ_σ (0.6e), for Ni-P^–( d_x² -_y² - d_x^2 -_y^2 - monoanion). These features are reflected in both the structure of the anions and the behavior of their vibrational frequencies. The greatest frequency shifts among IR active modes when populating the d_z² d_z^2 - and d_x² -_y² - d_x^2 -_y^2 - orbitals occur for out-of-plane vibrations (>30 cm^–1) and in-plane modes (34–46 cm^–1) involving MeN- and C_αC_m-bonds, respectively. Abnormally large frequency lowering is found for B_1g-type modes (active in the resonance Raman spectrum) involving mainly C_αC_m-, C_βC_β-, C_αC_β-, and MeN-bonds. This is related to a change in the d_π-e_g interaction strength during such vibrations that contributes to a decrease in the corresponding force constants.     

Electronic structure of thin film iron-tetracyanoethylene: Fe(TCNE)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>

Thin film iron-tetracyanoethylene Fe(TCNE) _x , x∼2, as determined by photoelectron spectroscopy, was grown in situ under ultra-high vacuum conditions using a recently developed physical vapor deposition-based technique for fabrication of oxygen- and precursor-free organic-based molecular magnets. Photoelectron spectroscopy results show no spurious trace elements in the films, and the iron is of Fe²⁺ valency. The highest occupied molecular orbital of Fe(TCNE) _x is located at ∼1.7 eV vs. Fermi level and is derived mainly from the TCNE⁻ singly occupied molecular orbital according to photoelectron spectroscopy and resonant photoelectron spectroscopy results. The Fe(3d)-derived states appear at higher binding energy, ∼4.5 eV, which is in contrast to V(TCNE)₂ where the highest occupied molecular orbital is mainly derived from V(3d) states. Fitting ligand field multiplet and charge transfer multiplet calculations to the Fe L-edge near edge X-ray absorption fine structure spectrum yields a high-spin Fe²⁺ (3d⁶) configuration with a crystal field parameter 10Dq∼0.6 eV for the Fe(TCNE) _x system. We propose that the significantly weaker Fe-TCNE ligand interaction as compared to the room temperature magnet V(TCNE)₂ (10Dq∼2.3 eV) is a strongly contributing factor to the substantially lower magnetic ordering temperature (T _C ) seen for Fe(TCNE) _x -type magnets.     

Simulation of diffusion instability of a mercury atomic distribution in the cadmium-mercury-tellurium alloy

The formation of inhomogeneities in Cd_xHg_1-x Te alloys upon post-growth cooling or upon low-temperature annealing is simulated numerically. The mechanism of the formation of inhomogeneities is based on the diffusion instability in a system involving mercury atoms located at lattice sites, interstitial mercury atoms, and cation vacancies. It is revealed that, upon prolonged annealing of the Cd_xHg_1-x Te alloys with a cadmium content x = 0.2 at a temperature of ∼200°C, the concentrations of mercury atoms at lattice sites, interstitial mercury atoms, and vacancies are characterized by an inhomogeneous nearly periodical distribution arising from a small fluctuation when the initial equilibrium concentration of interstitial mercury atoms exceeds a threshold value (∼3 × 10¹⁷ cm⁻³). The spatial and time scales of the concentration distribution are determined primarily by the equilibrium concentration of vacancies and do not depend on the type of fluctuation involved. The spatial period of the concentration distribution increases linearly from 0.01 to 3.00 μm as the equilibrium concentration of vacancies changes from 10¹⁹ to 10¹⁴ cm⁻³. At lower concentrations of vacancies, the periodic structure is formed for a considerably longer time.     

Optical studies of phase transitions in oxyfluoride (NH4)2NbOF5

Polarization-optical studies and measurements of the birefringence Δn and the angle of rotation of the optical indicatrix for the (NH₄)₂NbOF₅ crystal have been carried out in the temperature range 100–350 K. Two anomalies of the birefringence have been revealed at the temperatures T ₀₁ = 258 K and T ₀₂ ≈ 219 K. According to the twinning pattern, the crystal undergoes successive changes in symmetry: orthorhombic ↔ monoclinic 1 ↔ monoclinic 2. The twofold axis of the monoclinic phases (or the normal to the plane) is directed along [001]_or. The effect of the uniaxial compression along [011]_or and the electric field E ≈ 25 kV/cm along [100]_or on the twin structure has been studied. The ferroelastic phase transition at T ₀₁ is due to the appearance of the shear deformation x ₄(T) and is accompanied by significant anomalies of the birefringence. Strong pretransition phenomena mask the jumps in the birefringence Δn(T) and in the angle of rotation of the indicatrix φ(T) at T ₀₁.     

Smectic-A edge dislocations in a very thin cell

We study stable “bookshelf” smectic-A structures within a very thin plane-parallel cell of thickness L in which the mismatch between surface preferred (d _s) and intrinsic (d₀) smectic layer thicknesses occurs. The Landau-Ginzburg approach based on a complex smectic order parameter is used. For a weak enough smectic positional anchoring strength W smectic layers adopt the modified bookshelf profile. In a thick enough cell with increasing W a lattice of edge dislocations is continuously formed at the confining surfaces and then depinned from them. The structure with dislocations is formed when the condition d ₀/( d ₀/d _s - 1) ∼ 2 is fulfilled, where is the positional surface anchoring extrapolation length. If the cell is thin enough the dislocations formed at opposite cell plates annihilate and consequently the smectic layers adopt a locked bookshelf structure. This transition is discontinuous and takes place when d ₀/(L d ₀/d _s - 1) ∼ 5 is realized. To observe these transitions in a cell of thickness L∼ 1μm the conditions W∼ 10^-6 J/m ² and d ₀/d _s - 1∼ 5 ^. 10^-4 have to be fulfilled. All the three qualitatively different structures coexist at the triple point. Received 21 February 2002     

Excess 1/f noise in systems with an exponentially wide spectrum of resistances and dual universality of the percolation-like noise exponent

The excess 1/f noise in a random lattice with bond resistances r∼exp(−λx), where x is a random variable and λ≪1, is studied theoretically. It is shown that if the correlation function {δr ²}∼r r ^θ+2, then the relative spectral density of the noise in the system is expressed as C _e∼λ^m exp(−λ(1−p _c)), where p _c is the percolation threshold and m=νd (ν is the critical exponent of the correlation length and d is the dimensionality of the problem). It is hypothesized that the exponent m possesses a dual universality: It is independent of 1) the geometry of the lattice and 2) the θ-mechanism responsible for the generation of the local noise. Numerical modeling in a three-dimensional lattice gives m=52.3 for θ=1 and θ=0, in agreement with the hypothesis. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 8, 614–618 (25 April 1996)     

Orientation ordering of N<Subscript>2</Subscript> molecules in vertically aligned CN<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> nanotubes

Arrays of vertically aligned nitrogen-doped carbon (CN _x ) nanotubes have been synthesized by decomposition of aerosol mixture of acetonitrile and ferrocene at 850°C. Nitrogen concentration in the outer shells of the CN _x nanotubes was found from X-ray photoelectron spectroscopy (XPS) data to reach ∼6%. The XPS N 1s spectra and N 1s near-edge X-ray absorption fine structure (NEXAFS) spectra identified three chemical forms of nitrogen in the CN _x nanotube arrays: pyridine-like, graphitic, and molecular nitrogen. The π ^* resonance of molecular nitrogen showed clear polarization dependence that indicates predominant orientation of N₂ molecules along the nanotubes axis. The estimated range of the polar angle distribution of the N₂ molecules orientation in the CN _x nanotube array amounts to 15°.     

Hitting Time and Dimension in Axiom A Systems, Generic Interval Exchanges and an Application to Birkoff Sums

In this note we prove that for equilibrium states of axiom A systems having positive dimension the time τ _B (x) needed for a typical point x to enter for the first time in a typical ball B with radius r behaves for small r as τ _B (x)∼ r ^−d where d is the local dimension of the invariant measure at the center of the ball. A similar relation is proved for a full measure set of interval exchanges. Some applications to Birkoff averages of unbounded (and not L ¹) functions are shown.