Disjoining pressure in free-standing smectic-A films and its influence on their reflectivity

This paper reports the results of calculating the disjoining pressure and average thickness of smectic layers in free-standing liquid-crystal films heated above the temperature of breakdown of the smectic order in the bulk of the mesogens. The effect of the disjoining pressure on the reflectivity of free-standing smectic-A films with different numbers of smectic layers has been studied. The results of the calculations agree with the experimental study of the reflectivity of free-standing smectic-A films in the optical wavelength range.     

Phase transition studies in polymesomorphic compounds(v): Density studies in N-(p-n-Octyloxy benzylidene)-p-n-butyl aniline

The density, ρ, of N-(p-n-octyloxy benzylidene) p-n-butyl aniline (OBBA) is measured as a function of temperature from the isotropic liquid to the smectic-G phase. The compound is trimorphic, exhibiting three smectic phases, smectic-G, crystal smectic-B, and smectic-A phase. The changes in density across the phase transformations and the calculated thermal expansion coefficients confirm the order of the transitions as first order. Particular importance of the smectic-A to crystal smectic-B transformation, which is of first order, is apparent from the density jump across the transition.     

Thermal fluctuations in smectic-<Emphasis Type="Italic">A</Emphasis> films on the surface of solid substrates

The static and dynamic characteristics of layer displacement fluctuations in smectic-A films supported on the surface of a solid substrate are calculated with due regard for the profiles of the flexural and tensile (compressive) moduli of smectic layers. The difference in the surfaces bounding the film and the asymmetry of the profiles of the elastic moduli with respect to the central layer of the film are taken into account. The profiles of fluctuations of smectic-layer displacements and the correlations between these fluctuations are determined for the films formed by liquid-crystal compounds that can undergo a bulk smectic-A-nematic phase transition. The dynamic correlation functions derived for these fluctuations are used for calculating the correlations between the intensities of x-ray scattering by a film at different instants of time. It is demonstrated that, in smectic-A films supported on the surface of a solid substrate, unlike free-standing smectic-A films, the effect of temperature on the dynamics of layer displacement fluctuations can be observed in experiments on dynamic x-ray scattering from films that are not very thick (the number of layers N ～ 20) and at considerably smaller recoilmomentum components in the film plane.     

Experimental indication of macroscopic polarization parallel to the tilt plane in free-standing films of ferroelectric liquid crystals 8SI* and DOBAMBC

Optical reflectivity and x-ray studies have been conducted on free-standing films and bulk samples of ferroelectric liquid crystals near the smectic-A-smectic-C ^* transition. A tilt plane rotation with respect to the direction of an applied electric field is found in the ferroelectric films above the bulk transition temperature. Whereas the macroscopic polarization is perpendicular to the tilt plane at low temperature, it is parallel to the tilt plane at elevated temperature. The temperature dependence of the average tilt angle is measured. Zh. éksp. Teor. Fiz. 116, 1329–1334 (October 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Nonchiral ferroelectric smectic-C films

Free-standing films of nonchiral liquid crystal compound are studied by optical reflectivity measurements. The existence of macroscopic ferroelectric properties and orientation of the tilt plane parallel to an electric field in the temperature range above the smectic-C-smectic-A bulk transition is demonstrated. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 10, 808–813 (25 May 1998)     

Temperature-and field-induced transitions in free-standing films of an antiferroelectric liquid crystal

Thin free-standing films of a compound with the smectic-C _A ^* and smectic-C _α ^* phases were investigated by means of depolarized microscopy and optical reflectivity. In thin films, the smectic phase sequence C _A ^* ?C_α/*?A is replaced by a series of temperature-and field-induced transitions into states with the coplanar orientation of molecular tilt planes. Transitions are accompanied by a change in the direction of the electric polarization with respect to the tilt plane of molecules. The coplanar structure of these states is consistent with the Ising model.     

Surface ordering near the smectic-A-smectic-C transition in thin, free-standing, liquid-crystal films

Optical reflectivity measurements have been conducted near the smectic-A-smectic-C phase transition in free-standing films with thickness between two and eleven molecular layers. The temperature dependence of the reflectivity in thin film differs significantly from that in thick films. The optical thickness per layer increases in films with two to five layers as a result of cooling, in contrast with thick films. The average layer spacing was found to decrease with decreasing film thickness. Zh. éksp. Teor. Fiz. 111, 949–953 (March 1997) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Discrete thinning of free-standing smectic films in the de Gennes “pre-smectic liquid” model

It is shown that the successive discrete thinning of free-standing smectic films (FSSFs), which is observed when the films are heated above the temperature of the smectic A-nematic bulk phase transition, has a natural explanation in terms of the de Gennes “pre-smectic liquid” model, provided that a sufficiently large external compressive force is applied to the free surfaces of the FSSF. In a real situation this force stems from the curvature of the surrounding miniscus, which plays the role of a volume reservoir. In this model a superheated FSSF is stabilized by balancing the external compressive and elastic forces. When heating takes place the bulk modulus of the pre-smectic lattice decreases, and when the superheating reaches a critical value, the FSSF is subject to a long-wavelength instability in thickness beause the external compressive and elastic forces can no longer be balanced for a fixed number of smectic layers. If a superheated FSSF possesses adequate stability against disruption, the balance of forces, which was disrupted, and hence the stability of the FSSF can be restored as a result of spontaneous thinning of the film to a thickness corresponding to a smaller number of smectic layers. In general, heating of a superheated FSSF is accompanied by a series of such thinning transitions. Near the critical points where the balance of the forces breaks down, the dislocation mechanism of spontaneous thinning, which could be responsible for the stratified nature of the progressive discrete thinning of real FSSFs, can become dangerous. Zh. éksp. Teor. Fiz. 115, 61–69 (January 1999)     

The effect of spontaneous polarization on two-dimensional elasticity of smectic liquid crystals

The influence of polarity on orientational elasticity and on structures formed in the director field is studied in free-standing smectic films. Periodic stripe patterns and 2π-walls in a magnetic field are investigated. Measurements are performed on a nonpolar racemic mixture, on an optically pure ferroelectric compound, and in mixtures with different concentrations of the chiral isomers of opposite signs. The structure of periodic stripes changes drastically with the polarity of the film. The ratio of the bend K _B and splay K _S elastic constants for smectic films is determined as a function of polarization from the structure of periodic stripe patterns and 2π-walls. We find that the elastic anisotropy K _B /K _S increases essentially with increasing the polarity of the film. Changes of the elasticity and the structure of periodic stripes are explained by polarization charge effects.     

Dielectric investigation on some binary mixtures of hockey-stick-shaped liquid crystal and octyloxy-cyanobiphenyl

We report the measurement of temperature-dependent dielectric parameters in some binary liquid crystal mixtures comprising of a hockey-stick-shaped mesogen 4-(3-decyloxyphenyliminomethyl) phenyl-4-decyloxycinnamate (SF7) and calamitic compound 4′-octyloxy-4-cyanobiphenyl (8OCB). All the investigated mixtures possess a large positive dielectric anisotropy (Δε), although a noticeable reduction has been found by increasing the diverse-shaped dopant concentration. Investigation on the pretransitional behavior in the vicinity of isotropic to nematic (I–N) phase transition suggesting a tricritical character for all the studied mixtures. Parameterization of dielectric permittivity close to the nematic to smectic-A (N–Sm-A) phase transition exhibits non-universal values of the critical exponents describing a second-order nature of the transition. Systematic variation of critical exponents against dopant concentration and McMillan ratio reveals a well consistency with those obtained from the high-resolution optical birefringence measurements.     

Temperature dependence of the exchange interaction constant in iron garnet films

The spin-wave resonance method is used to investigate the temperature dependence of the exchange interaction constant A in iron garnet films. The experimental results are compared with theoretical results based on the theory of second-order phase transitions. It is shown that the temperature dependence A(T) for films of pure yttrium iron garnet is different from A(T) for films exhibiting a point of compensation of the magnetic moment. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 7, 528–532 (10 April 1996)     

Effect of carbon nanotubes on the isotropic to nematic and the nematic to smectic- A phase transitions in liquid crystal and carbon nanotubes composites

A high-resolution ac-calorimetric study on the weakly first-order isotropic to nematic (I -N and the continuous nematic to smectic-A (N -SmA phase transitions of the liquid crystal octyl-cyanobiphenyl (8CB) doped with well-dispersed multiwall carbon nanotubes (CNTs) as a function of CNT concentrations is reported. Thermal scans were performed for all samples having CNT weight fraction from f_w \phi_{{w}}^{} = 0.0005 to 0.0060 over a wide temperature range well above and below the two transitions in pure 8CB. Both the I -N and the N -SmA transitions evolve in character and have their transition temperatures qualitatively offset by ∼ 1.10 K lower as compared to that in pure 8CB for all 8CB+CNTs samples. The enthalpy change associated with each phase transition is essentially the same as that of pure 8CB and remains unchanged with increasing f_w \phi_{{w}}^{} . However, there is an evidence that the thermal transport properties of the composites differ from the pure LC upon cooling below a f_w \phi_{{w}}^{} -dependent temperature within the nematic phase. In addition, a new C_p feature is resolved for intermediate f_w \phi_{{w}}^{} samples that appears to be correlated to this onset temperature.     

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.     

Director dynamics near the nematic-smectic-A phase transition

The Landau-de Gennes model for the free energy of a nematic liquid crystal near the phase transition to the smectic A-phase is used to determine the frequency dependence of the fluctuation corrections to the Frank elastic constants. It is shown that the interaction of the fluctuations of the smectic order parameter and the director results in corrections to all the Frank elastic constants. In the low-frequency limit (ω→0), the corrections to the Frank elastic constants K ₂₂ and K ₃₃ are the largest, and decrease to zero in the infinite-frequency limit. The correction to K ₁₁ is negative, and vanishes in both limits. The absolute value of the correction to K ₁₁ is the largest at frequencies in the megahertz range. It is shown that in oriented nematics the interaction of the smectic fluctuations and the director limits deviations of the director from the direction of preferred orientation, as a result of which relaxation of both inhomogeneous and homogeneous distortions of the director field can be observed. It is also shown that this gives rise to a frequency interval in the megahertz range in which shear waves begin to propagate in the nematic. The propagation speed of these waves is roughly a hundred times smaller than that of sound and strongly depends on the direction of propagation. Zh. éksp. Teor. Fiz. 114, 2022–2033 (December 1998)     

Black Hole Entropy of IR Modified Ho?ava-Lifshitz Gravity in Quantum Statistics Perspective

In this paper we investigate quantum statistical entropy for the Kehagias-Sfetsos black hole in IR modified Hořava-Lifshitz gravity by using t’ Hooft’s brick-wall method and generalized uncertainty principle method. By carefully calculating, we obtain the brick-wall entropy S _BWM =A/4 and the generalized uncertainty principle entropy S _GUP =A/96πγ. It is found if we view from quantum statistics, the brick-wall entropy and generalized uncertainty principle entropy may possibly is proportional to the event horizon area. This type area entropy is also justified by Wang et al. (Phys. Rev. D 81:083006, 2010). The study of the quantum statistical entropy may shed light on the understand of Hořava-Lifshitz gravity.     

Intraexcitonic transitions in two-dimensional systems in a high magnetic field

The internal transitions of two-dimensional (2D) excitons in a high magnetic field B exhibit features due to the coupling of the internal and center-of-mass motions. A study is made of these features, and it is shown that for magnetoexcitons with a center-of-mass momentum K ≠0 the energies of the strong transitions decrease with increasing K, and the absorption spectra show weakly resolved transitions, whose total intensity depends strongly on the exciton statistics (distribution function). Pis’ma Zh. éksp. Teor. Fiz. 66, No. 9, 588–593 (10 November 1997)     

Extensions of Lieb’s Concavity Theorem

The operator function (A,B)→ Trf(A,B)(K ^*)K, defined in pairs of bounded self-adjoint operators in the domain of a function f of two real variables, is convex for every Hilbert Schmidt operator K, if and only if f is operator convex. We obtain, as a special case, a new proof of Lieb’s concavity theorem for the function (A,B)→ TrA ^p K ^* B ^q K, where p and q are non-negative numbers with sum p+q ≤ 1. In addition, we prove concavity of the operator function

Flexible-to-semiflexible chain crossover on the pressure-area isotherm of a lipid bilayer

We find theoretically that competition between ∼K _f q ⁴ and ∼Qq ² terms in the Fourier-transformed conformational energy of a single-lipid chain, in combination with interchain entropic repulsion in the hydrophobic part of the lipid (bi)layer, may cause a crossover on the bilayer pressure-area isotherm P(A)∼(A−A ₀)^−α. The crossover manifests itself in the transition from α = 5/3 to α = 3. Our microscopic model represents a single-lipid molecule as a worm-like chain with a finite irreducible cross-section area A ₀, a flexural rigidity K _f , and a stretching modulus Q in a parabolic potential with the self-consistent curvature B(A) formed by entropic interactions between hydrocarbon chains in the lipid layer. The crossover area A* obeys the relation Q/√K _f B(A*) ≈ 2. We predict a peculiar possibility of deducing the effective elastic moduli K _f and Q of an individual hydrocarbon chain from the analysis of the isotherm with such a crossover. Also calculated is the crossover-related behavior of the area compressibility modulus K _A , the equilibrium area per lipid A _t , and the chain order parameter S(θ). The text was submitted by the authors in English.     

Structure of a time-variable photoresponse from semiconductor sensors

It is found that the conversion of time-variable photoresponse I(t) from a crystal to signature I(t) − dI/dt of the phase plane makes it possible to determine partial contributions from the constituents of the photoresponse and their interrelation. In addition, such a procedure allows one to introduce the integrative indices of stability (B _din) and asymmetry (K _{λ, E} ) of the photoresponse’s structure, which reflect the influence of external and internal factors, respectively.     

Calorimetric study of phase transitions in nanocomposites of quantum dots and a liquid crystal

The complex specific heat is measured over a wide temperature range for the liquid crystal (LC) 4-cyano-4-octylbiphenyl (8CB) and cadmium sulfate quantum dots (QDs) composites as a function of QD concentration. The thermal scans were performed under near-equilibrium conditions for all samples having QDs weight percent (φ_w) from 0 to 3wt% over a wide range of temperature well above and below the two transitions in pure 8CB. Isotropic (I) to nematic (N) and nematic to smectic-A (SmA) phase transitions evolve in character and their transition temperatures offset by (～2.3 to 2.6 K) lower for all composite samples as compared to that in pure 8CB. The enthalpy change associated with I–N phase transitions shows slightly different behavior on heating and cooling and it also shows crossover behavior at lower and higher QD content. The enthalpy change associated with N–SmA phase transitions is independent of QD loading and thermal treatment. Given the homogeneous and random distribution of QD in these nanocomposites, we interpret that these results as arising that the nematic phase imposes self-assembly on QDs to form one-dimensional arrays leading to QDs and induces net local disordering effect in LC media.