Correlation of the molecular structure of discotic nematic liquid crystals with their orientational order and specific features of the nematic-isotropic phase transition

The orientational order parameter S of molecules in high-temperature discotic nematic liquid-crystal phases of triphenylene derivatives is investigated as a function of the length of side flexible molecular chains at different temperatures. It is established that the orientational order parameters S in the range of the transition from the nematic phase to the isotropic liquid phase (the N _D -I transition) are smaller than those predicted from the molecular-statistical theory and computer simulation. It is shown that the N _D -I transition is close to both the isolated Landau point and the tricritical point (regardless of the chemical structure of the molecules and the anisotropy of dispersion intermolecular interactions). Consistent explanations are offered for a number of experimental findings, such as the anomalously small changes in the enthalpy and entropy upon the N _D -I transition (as compared to those revealed upon the N-I transition in calamitic nematic liquid crystals), the anomalously strong response of the isotropic phase of discotic nematic liquid crystals to external fields (thermodynamically conjugate to the order parameter S) and the long relaxation times of this response, and the formation of cybotactic discotic molecular clusters in the isotropic phase in the vicinity of the N _D -I transition.     

Phase transition behavior of hydrogen bonded liquid crystal (6BA)<Subscript>2</Subscript>-(BPy)<Subscript><Emphasis Type="Bold">x</Emphasis></Subscript> as studied by <Superscript>2</Superscript>H NMR

The thermal properties and the orientational order of hydrogen-bonded liquid crystals (6BA)₂-(BPy)_0.4 and (6BA)₂-(BPy)_0.3 (6BA: 4-n-hexylbenzoicacid, BPy: 4,4’-bipyridine) were investigated by DSC and ²H NMR. On cooling, isotropic liquid - liquid crystal phase transition temperatures were T _C= 409 and 405 K for (6BA)₂-(BPy)_0.4 and (6BA)₂-(BPy)_0.3, respectively. Thermal anomalies in the liquid crystal phase were observed at T _LC1= 402 and T _LC2= 375 K for (6BA)₂-(BPy)_0.4 and at T _LC1= 398 and T _LC2= 375 K for (6BA)₂-(BPy)_0.3. For (6BA)₂-(BPy)_0.4, only the smectic component was created above T _LC1. In addition, the nematic component was created below T _LC1. The nematic component gradually changed to the smectic component with decreasing temperature and only the smectic component was observed below T _LC2. For (6BA)₂-(BPy)_0.3, only the nematic component was created above T _LC2. The phase transition from the nematic phase to the smectic phase took place at around T _LC2.     

Rapid viscous flow of a nematic liquid crystal in the vicinity of the nematic-smectic <Emphasis Type="Italic">A</Emphasis> transition

The resistance to shear flow is investigated theoretically for polar liquid crystals, such as 4-n-octyl-4′-and 4-n-octyloxy-4′-cyanobiphenyls. It is established that the lowest resistance to shear flow at temperatures in the vicinity of the nematic-smectic A phase transition point T _NA is observed when the nematic director is oriented perpendicular to both the flow velocity vector and the flow velocity gradient. The three Miesowicz shear viscosity coefficients η_i (i=1–3) at temperatures close to the phase transition temperature (tens of millikelvins from T _NA ) and far from this transition are calculated in the framework of the Ericksen-Leslie theory. The decrease in the viscosity coefficients in the order η₂>η₁>η ₃ is explained by the fact that fluctuations of the local smectic order in the nematic phase lead to a singular behavior of the viscosity coefficient η₂, whereas the other two viscosity coefficients η₁ and η₃ are not affected by order parameter fluctuations.     

Limits on the scalar-leptoquark and scalar-gluon masses from the parameters <Emphasis Type="Italic">S</Emphasis>, <Emphasis Type="Italic">T</Emphasis>, and <Emphasis Type="Italic">U</Emphasis> in the minimal model based on four-color symmetry

The contributions to the parameters S, T, and U of radiative corrections from the doublets of scalar leptoquarks and scalar gluons are analyzed within the minimal model based on four-color symmetry of the Pati-Salam type. It is shown that current experimental data on the parameters S, T, and U admit the existence of relatively light scalar leptoquarks and scalar gluons (of mass lower than 1 TeV), the best fit to experimental data being attained at mass values not greater than 400 GeV. In particular, the existence of scalar leptoquarks of mass below 300 GeV is found to be compatible with data on the parameters S, T, and U at χ² < 3.1 (3.2) for m_H = 115 (300) GeV as against χ _SM ² = 3.5 (5.0) in the Standard Model. The mass of the lightest scalar gluon is then predicted to be less than 850 (720) GeV. It is emphasized that the aforementioned doublets of scalar leptoquarks and scalar gluons can play a significant role in processes involving a t quark at LHC.     

Change in the polarizability of MBBA molecules upon the nematic-isotropic liquid transition and physical consequences

The Lorentz tensor components L _j and the polarizability tensor components γ _j of 4-methoxyben-zylidene-4′-butylaniline (MBBA) liquid crystal molecules in nematic and isotropic phases have been determined experimentally. The quadratic dependences of the mean value $\bar \gamma $ (S) and anisotropy Δγ(S) of the polarizability in the nematic phase on the orientational order parameter S of molecules have been established. Within the phenomenological approach, the dependences $\bar \gamma $ (S) and Δγ(S) have been derived, and their features for MBBA and other known objects have been interpreted. The relation of the dependences $\bar \gamma $ (S) and Δγ(S) to the features of the nematic-isotropic liquid phase transition has been found.     

Phase diagram and transport properties of Sb-doped Ca0.88La0.12Fe2As2 single crystals

The effects of isovalent Sb substitution on the superconducting properties of the Ca_0.88La_0.12Fe₂(As_1-ySb_y)₂ system have been studied through electrical resistivity measurements. It is seen that the antiferromagnetic or structural transition is suppressed with Sb content, and a high-T_c superconducting phase, accompanied by a low-T_c phase, emerges at 0.02 ≤ y ≤ 0.06. In this intermediate-doping regime, normal-state transport shows non-Fermi-liquid-like behaviors with nearly T-linear resistivity above the high-T_c phase. With further Sb doping, this high-T_c phase abruptly vanishes for y > 0.06 and the conventional Fermi liquid is restored, while the low-T_c phase remains robust against Sb impurities. The coincidence of the high-T_c phase and non-Fermi liquid transport behaviors in the intermediate Sb-doping regime suggests that AFM fluctuations play an important role in the observed non-Fermi liquid behaviors, which may be intimately related to the unusual nonbulk high-T_c phase in this system.     

Effect of Hall current and chemical reaction on MHD flow along a fluctuating porous flat plate with internal heat absorption/generation

Effect of Hall current on the unsteady free convection flow of a viscous incompressible and electrically conducting fluid past a fluctuating porous flat plate with internal heat absorption/generation in the presence of foreign gasses (such as H₂, CO₂, H₂O, NH₃) was investigated. The results are discussed with the effect of the parameters m, the Hall current, Mt, the hydromagnetic parameter, G _r the Grashoff number for heat transfer, G _c , the Grashoff number for mass transfer, S, the internal heat absorption/generation parameter, α, the transpiration parameter, S _c , the Schmidt parameter, and K _c the chemical reaction parameter for Prandtl number P _r = 0.71, which represents air. Further, the present study accounts for the 1st order chemical reaction affecting the flow characteristics. The governing equations are solved in closed form applying Hh _n (x) function. The effects of pertinent parameters characterizing the flow field are discussed with the help of graphs and tables. The important observation of the present study is that heat generation/absorption modifies the flow of current simultaneously to a magnetic force and thermal bouncy force. Heat generation combined with blowing leads to a sharp fall of temperature.     

Influence of the probe sizes on the parameters of the surface morphology of hemispherical-grain polysilicon films: Estimation via atomic-force microscopy

The influence of probe sizes on the basic surface-morphology parameters of hemispherical-grain polysilicon films which possess substantial surface roughness and non-Gaussian height distribution functions with appreciable negative skewness is studied. The dependences between the basic surface morphology parameters S _dr , S _q , S _al , S _z , S _v , S _p , and S _sk defined by the ISO 25178-2:2012 standard and the probe width-to-tip height (W/L) ratio are determined. It is ascertained that the relative increase S _dr in the surface area is most sensitive to the “degree of sharpness” (W/L ratio) and, on the contrary, the autocorrelation length S _al is least sensitive. Hemispherical-grain silicon films with considerable parameter S _dr can be employed as test samples in estimating the degree of sharpness of a probe.     

Investigation of zero-frequency solutions to the pion dispersion equation

The instability of nuclear matter is considered for the case where it is generated by the vanishing of the frequencies of collective excitations belonging to specific types (specifically, excitations that have the pion quantum numbers J ^π = 0^?). The behavior of zero-frequency solutions to the pion dispersion equation is analyzed versus the strength G′ of spin—isospin particle—hole interaction. It is shown that there exists a strength value G′_tr (|G′_tr| ? 1) such that, for G′ < G′_tr, zero-frequency solutions are excitations of the ω _P type, while, for G′ ≥ G′_tr, such solutions are excitations of the ω _c type. Excitations of the ω _P type for G′ < ?1 describe the instability of nuclear matter against small density fluctuations (Pomeranchuk’s instability), while excitations of the ω _c type are responsible for the instability associated with pion condensation at G′ ≈ 2. For stable nuclear matter, the solutions ω _P(κ) and ω _c (κ) lie on unphysical sheets of the complex plane of frequency.     

Thermodynamic and dilatometric properties of the dimerized phase of a C<Subscript>60</Subscript> fullerene

This paper reports on the results of complex investigations into the structural, thermodynamic, and dilatometric properties of the C₆₀ dimerized phase prepared under compression of a C₆₀ fullerite at a pressure up to 8 GPa and a temperature of 290 K. It is demonstrated that the dimerized phase has a face-centered cubic structure with a lattice parameter a=14.02±0.05 Å. The dimeric structure of the studied sample is confirmed by x-ray diffraction analysis. According to the dilatometric data, the volume jump observed in the vicinity of the orientational transition for the dimerized phase is estimated to be approximately 30 times less than that for the C₆₀ fullerite. The temperature dependence of the heat capacity of the (C₆₀)₂ crystalline dimer is examined using precision adiabatic vacuum calorimetry under normal pressure in the temperature range from T → 0 K to 340 K. The results obtained are used in the calculations of thermodynamic functions, namely, the heat capacity C _p ⁰ (T), the enthalpy H⁰(T)-H⁰(0), the entropy S⁰(T), and the Gibbs function G⁰(T)-H⁰(0). The fractal dimension D is determined as a function of the heat capacity. The standard entropy of the formation of the (C₆₀)₂ crystalline dimer from a simple compound (graphite) at T=298.15 K and normal pressure is calculated.     

EPR study of the spin dynamics of the (La<Subscript>1−<Emphasis Type="Italic">y</Emphasis></Subscript>Pr<Subscript>y</Subscript>)<Subscript>0.7</Subscript>Ca<Subscript>0.3</Subscript>MnO<Subscript>3</Subscript> system

The EPR of Mn ions in the (La_1?yPr_y)_0.7Ca_0.3MnO₃ system has been studied within a broad range of temperatures (4<T<600 K) and Pr concentrations (0≤y≤1), as well as under isotope substitution of ¹⁸O for ¹⁶O. All compositions were shown to undergo transitions to a magnetically ordered state with decreasing temperature. Magnetic phase diagrams were constructed for systems with different oxygen isotopes. The diagrams include paramagnetic, ferromagnetic, and antiferromagnetic regions. In the paramagnetic region, at temperatures not too close to the phase transition points, the Mn ion linewidth ΔH _pp (T) is related to the magnetic susceptibility χ(T) through the relation ΔH _pp (T) = [χ₀/χ(T)]ΔH _pp (∞) + ΔH₀, where ΔH _pp (∞) is the width of the exchange-narrowed line in the high-temperature approximation, χ₀ ∝ 1/T is the susceptibility of noninteracting ions, and ΔH₀ is the residual width originating from the sample porosity and resonance-field scatter in unoriented grains of a powder sample. An analysis of the data on ΔH _pp (∞), ΔH₀, and χ(T) made it possible to estimate the symmetric and antisymmetric exchange interaction of Mn ions and of the noncubic crystal-field component of the oxygen ions. These parameters were found to be independent of the oxygen isotope species to within experimental error.     

Magnetic susceptibility of La<Subscript>2</Subscript>NiO<Subscript>4+δ</Subscript> single crystals with δ = 0.095 and 0.105. Ordering of holes and ferromagnetic heisenberg chains

The temperature dependence of the magnetic susceptibility of La₂NiO_4+δ single crystals with δ = 0.095 and 0.105 has been analyzed. The anomalous dependence of χ(T) characteristic of stripe structures previously found in La_1.8Sr_0.2NiO₄ has been found. Investigation of the dependence χ(T) on the impurity and charge disorder degrees makes it possible to separate the contribution associated with the ordering of holes and impurity oxygen. It has been shown that the contribution from the ordering of holes is well described by the model of ferromagnetic Heisenberg chains of spins S = 1/2. The length of the chains and intrachain interaction J _N have been determined from the temperature dependence χ(T).     

Neutral Particle Motion around a Schwarzschild Black Hole in Modified Gravity

We investigate circular motion of neutral test particles on equatorial plane near a black hole in scalar-tensor-vector gravity. We consider three cases (i) α < G/G_N (ii) α = G/G_N and (iii) α > G/G_N to find the regions where motion can exist. The corresponding effective potential, energy, angular momentum and center of mass energy are evaluated. Further, we define four different cases for α > G/G_N and identify stable and unstable regions of circular orbits. It is found that circular orbits having zero angular momentum exist at r = αGNM due to repulsive gravity effects. We conclude that the structure of stable regions for α < G/G_N as well as α = G/G_N case is completely different from that of α > G/G_N.     

Electronic Structure and Magnetic Phase Transition in Helicoidal Fe<Subscript>1 - <Emphasis Type="Italic">x</Emphasis></Subscript>Co<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Si Ferromagnets

LSDA + U + SO calculations of the electronic structure of helicoidal Fe_{1 - x}Co _x Si ferromagnets within the virtual crystal approximation have been supplemented with the consideration of the Dzyaloshinski-Moriya interaction and ferromagnetic fluctuations of the spin density of collective d electrons with the Hubbard interactions at Fe and Co atoms randomly distributed over sites. The magnetic-state equation in the developed model describes helicoidal ferromagnetism and its disappearance accompanied by the occurrence of a maximum of uniform magnetic susceptibility at temperature T _C and chiral fluctuations of the local magnetization at T > T _C . The reasons why the magnetic contribution to the specific heat at the magnetic phase transition changes monotonically and the volume coefficient of thermal expansion (VCTE) at low temperatures is negative and has a wide minimum near T _C have been investigated. It is shown that the VCTE changes sign when passing to the paramagnetic state (at temperature T _S ).     

Six-Dimensional Nearly Kähler Manifolds of Cohomogeneity One (II)

Let M be a six dimensional manifold, endowed with a cohomogeneity one action of G = SU₂ × SU₂, and \({M_{\rm reg} \subset M}\) its subset of regular points. We show that M _reg admits a smooth, 2-parameter family of G-invariant, non-isometric strict nearly Kähler structures and that a 1-parameter subfamily of such structures smoothly extends over a singular orbit of type S ³. This determines a new class of examples of nearly Kähler structures on T S ³.     

The influence of anchoring energy on the prolate shape of tactoids in lyotropic inorganic liquid crystals

A model was constructed to describe the prolate shape of anisotropic regions, tactoids, coexisting with the isotropic phase in lyotropic inorganic liquid crystals. The elastic energy of the tactoid, the surface energy, and the interaction energy between the director field and the boundary of the tactoid were taken into account. Large-sized tactoids were shown to be prolate because of the competition between the elastic energy of the nematic phase of the tactoid and the surface energy. Small-sized tactoids were prolate because of the competition of the surface energy with the anchoring energy between the director and the boundary of the tactoid. The suggested model was applied to experimental data to determine the ratio of the elastic constants K₃/K₁ and the ratio between the anchoring energy W and the surface tension σ depending on the “time of aging” of vanadium pentoxide sols in water.     

The Rank-One Separable Interaction Kernel for Nucleons with Scalar Propagator

In the paper the covariant kernel of the nucleon-nucleon interaction of particles with scalar propagators is analyzed. The Bethe–Salpeter equation for the T matrix is considered in the rank-one separable kernel. The parameters of the kernel for the specific partial-wave channels explicitly connect with the observables low energy scattering parameters and phase shifts, deuteron binding energy. Covariant separable kernels for the partial-wave channels with total angular momentum J = 0 (¹S₀, ³P₀) and J =1 (³S₁ ? ³D₁, ¹P₁, ³P₁) are constructed.     

Effets des fluctuations longitudinales de l’aimantation sur la résistivité des métaux ferromagnétiques à basse température

Using a simple model which represents a ferromagnetic metal in part as an ensemble of localized magnetic moments ?γ S _n coupled by exchange interactions, and in part as a sea of conduction electrons with spinss _i , coupled to theS _n by a scalar interaction\( - \mathop \sum \limits_{n,i} J(r_i - R_n )s_i \cdot S_n\), we show that the longitudinal fluctuations of theS _n have a negligible effect on the resistivity as compared to the transverse fluctuations.