Structural investigations on smectic blue phases

Smectic blue phases ( BP(Sm)) are thermotropic liquid crystalline phases which exhibit both three-dimensional orientational order, such as classical blue phases, and smectic positional order. BP(Sm) appear as the three-dimensional counterpart of twist grain boundary phases. X-ray scattering and optical polarizing microscopy provide information on the hexagonal and cubic symmetries of these new phases.     

Exploration of Induced Blue Phases and Orthogonal Smectic Batonnets in Hydrogen-Bonded Ferroelectric Nanoliquid Crystalline Complexes for Optoelectronic Devices

A novel blue phase hydrogen-bonded ferroelectric liquid crystal (HBFLC) series has been synthesized from cholesteryl stearate (CHS) and p-n-alkyloxybenzoic acid (nOBA, where n?=?2 to12). Blue phase (BP) liquid crystalline complex is a high potent material for next-generation optoelectronic devices. The structural, optical, and thermal properties of present HBFLC complexes have been characterized by X-ray diffraction techniques (XRD), Fourier transform infrared spectroscopy (FT-IR), nuclear magnetic resonance spectroscopy (NMR), polarizing optical microscope (POM), and differential scanning calorimetry (DSC) techniques. The band gap energy of the present HBFLC complex (4.6 eV) is estimated by UV-Visible spectrometer. X-ray diffraction and scanning electron microscope (SEM) studies which confirm the monoclinic nature and morphology of the present complex. Phase diagram of the present CHS + nOBA is constructed from DSC data and the same is discussed. The lower homologous of CHS + nOBA HBFLC (n?=?2 to 6) complex shows BP_sm1, BP_sm2, BP_sm3 while higher homologous (n?=?7 to 12) exhibiting orthogonal smectic A* (SmA*) character with blue phases. A noteworthy observation is that the identification of extended thermal span of smectic blue phases and induced SmA* phase in the present HBFLCs. Another important observation is that the widest BP range is reported in the present hydrogen-bonded ferroelectric nanoliquid crystalline (HBFNLC) complex which is more suitable for photonic devices. In addition, LC parameters such as, phase width, thermal stability factor, phase transition temperature with enthalpy value, and the origination of orthogonal phases in CHS + nOBA HBFLC complex is also reported.     

Hexatic ordering in freely suspended liquid crystal films

In this paper, we report results from synchrotron X-ray scattering studies of thefluid/hexactic/solid phases and phase transitions in both very thick and very thin, freely suspended films of tilted hexatic liquid crystals. Contrary to the thick film case, the higher Fourier coefficients describing the bond orientational order are suppressed in very thin films. This suppression is consistent with a two-dimensional bond orientational order parameter, ₆, rather than the three-dimensional bond orientational order parameter found in very thick films. For a film containing twently-three (23) smectic layers we find that ₆ is two-dimensional whereas the positional order in the crystallineS _J phase is three-dimensional. We present an analysis of the thick film data in terms of the three-dimensionalXY-model and a new mean field theory model which incorporates explicitly the quasi two-dimensional nature of bulk smectic phases.     

Ferrielectric smectic phase with a layer-by-layer change of the two-component order parameter

One of the most remarkable properties of smectics is the wide variety of possible equilibrium structures. In this paper, based on the Landau theory of the phase transitions, the transitions between ferroelectric and antiferroelectric phases and the structure formed by smectic layers with different azimuthal and polar orientations of the molecules were calculated. This unique structure has been predicted [P.V. Dolganov et al., JETP Lett. 76, 498 (2002)] using the minimization of the free energy with respect to the phase and modulus of the two-component order parameter, but never before detected. Recently, a nonresonant Bragg reflection, consistent with the predictions of the model, was found [P. Fernandes et al., Eur. Phys. J. E 20, 81 (2006)] in the ferrielectric smectic C* _FI1(SmC* _FI1) phase. In the three-layer ferrielectric structure with a macroscopic helical pitch, the modulus of the order parameter is larger in anticlinic-like layers and smaller in layers with mixed ordering. The values of the interlayer interactions were determined for smectic liquid-crystalline materials forming different polar structures. The text was submitted by the authors in English.     

Topological order and conformal quantum critical points

We discuss a certain class of two-dimensional quantum systems which exhibit conventional order and topological order, as well as quantum critical points separating these phases. All of the ground-state equal-time correlators of these theories are equal to correlation functions of a local two-dimensional classical model. The critical points therefore exhibit a time-independent form of conformal invariance. These theories characterize the universality classes of two-dimensional quantum dimer models and of quantum generalizations of the eight-vertex model, as well as and non-abelian gauge theories. The conformal quantum critical points are relatives of the Lifshitz points of three-dimensional anisotropic classical systems such as smectic liquid crystals. In particular, the ground-state wave functional of these quantum Lifshitz points is just the statistical (Gibbs) weight of the ordinary two-dimensional free boson, the two-dimensional Gaussian model. The full phase diagram for the quantum eight-vertex model exhibits quantum critical lines with continuously varying critical exponents separating phases with long-range order from a deconfined topologically ordered liquid phase. We show how similar ideas also apply to a well-known field theory with non-Abelian symmetry, the strong-coupling limit of 2+1-dimensional Yang–Mills gauge theory with a Chern–Simons term. The ground state of this theory is relevant for recent theories of topological quantum computation.     

Polar smectic subphases: Phase diagrams, structures and X-ray scattering

We analyze a discrete phenomenological model accounting for phase transitions and structures of polar Smectic-C* liquid-crystalline phases. The model predicts a sequence of phases observed in experiment: antiferroelectric SmC _A ^* –ferrielectric SmC _FI1 ^* –antiferroelectric SmC _FI2 ^* (three-and four-layer periodic, respectively)–incommensurate SmC _α ^* –SmA. We find that, in the three-layer SmC _FI1 ^* structure, both the phase and the module of the order parameter (tilt angle) differ in smectic layers. This modulation of the tilt angle (and therefore of the layer spacing d) must lead to X-ray diffraction at the wave vectors Q _s =2πs/d(s=n±1/3) even for the nonresonant scattering.     

Studies on the microstructure of phase transitions in two kinds of liquid crystals by PAT and DSC

The positron lifetime and DSC measerments for EBBA and DOBAMBC have been made with heating and cooling clycles. The experimental results show that a shorter lifetime (₁) is essentially independent of temperature while the longer lifetime (₂) and the intensity (I ₂) change abruptly double or triple with temperature. Consequently, the EBBA has only nematic phases while the DOBAMBC has two liquid-crystalline phases (smectic C* and smectic A) with transition temperatures as follows: for EBBA, solid nematic (304.5 K), nematic isotropic (356.5 K), isotropic nematic (356.5 K), nematic solid (301 K); and for DOBAMBC, solid smectic C* (346 K), smectic C* smectic A (357.5 K), smectic A isotropic (389 K). These critical temperatures are in accordance with the transition temperatures measured by DSC. In addition, the difference in the solid-nematic transition temperature in the heating and cooling cycles was also observed. A discussion about the correlation of the observed changes in lifetime (₂) with the changes in molecular orientational order (S) and dielectric anisotropy () is presented.     

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     

Specific heat of Sm0.55Sr0.45MnO3 manganite in magnetic fields up to 15 T: An anomalous critical behavior of the ferromagnet in magnetic field and the observation of a tricritical point

The specific heat of Sm_0.55Sr_0.45MnO₃ manganite is measured in the vicinity of the ferromagnetic phase transition in strong magnetic fields up to 15 T. An anomalous critical behavior of the Sm_0.55Sr_0.45MnO₃ ferromagnet in magnetic field is predicted and experimentally observed. The anomalous behavior manifests itself in that, in magnetic fields up to 4 T, the field favors fluctuations and the specific-heat anomaly increases with the field and sharpens, becoming λ-shaped. In fields above 4 T, the behavior becomes classical: the field suppresses the fluctuations and the specific-heat peak is smeared out. The hysteresis of the transition temperature measured in the heating and cooling runs is about 15 K in zero magnetic field. As the field increases, it narrows gradually and vanishes completely when the field reaches 4 T. The results of the experiments are explained in terms of the competition between the hysteresis and the fluctuations of the magnetic order parameter. The H-T phase diagram of Sm_0.55Sr_0.45MnO₃ certainly indicates that, at 4 T, Sm_0.55Sr_0.45MnO₃ has a tricritical point, at which the ferromagnetic and paramagnetic phases of Sm_0.55Sr_0.45MnO₃ are leveled.     

Influence of pressure on the electric-field-induced phase transitions in liquid crystals

Within the framework of Landau-de-Gennes formulation, we analyse the effect of pressure on electric-field-induced phase transitions in a liquid crystal which shows spontaneously an isotropic-smectic A transition. Inferring from the experimental pressure dependences on the layer spacing in smectic A phase, as well as the nematic-smectic A metastable temperature T^*_AN, we incorporated the pressure dependence in the free energy through (the surface energy term) and the coupling between the quadrupolar nematic ordering Q_ij and the smectic order parameter ψ. From the S-T phase diagram, we found that the stability of field-induced nematic phase increases with pressure, whereas the discontinuity of the transition decreases. Also, the region where paranematic phase transits directly to smectic A phase increases with pressure.     

Refractive index and orientational order parameter of a polar–polar binary system showing induced smectic Ad and re-entrant nematic phases

Refractive index measurements have been done on a polar–polar binary system, 4-cyanophenyl [4′(4″-n-heptylphenyl)] benzoate (7CPB)?+?4-cyanophenyl-4-nonylbenzoate (9.CN), exhibiting nematic–smectic A_d–re-entrant nematic phase sequence using thin prism technique. From refractive index as well as density data, the polarizability anisotropy in the mesomorphic state has been calculated from the standard Vuks model and the orientational order parameter (?P ₂?) values have been determined. By measuring the refractive indices and density in the solid phase, the validity of the Haller's extrapolation method for systems having higher order phases has been verified. The temperature variation of the density, birefringence, and ?P ₂? values at the nematic–smectic A_d and smectic A_d–re-entrant nematic transitions for all the mixtures are found to be continuous. The experimental ?P ₂? values have been compared with our previous X-ray data and also those calculated from the Luckhurst and Timimi model.     

Phase transitions and structural studies ofp-n-alkoxybenzyliden-p’-fluoro-anilines

Summary The transition temperatures and phase diagrams of five fluorinated benzylidenaniline derivatives have been studied by TM and X-ray diffraction techniques. A smectic polimorphism appears in all compounds. The structure of smecticB phases has been deeply studied in order to evidence a possible utilization of such phases as solvents able to exert stereochemical effects on polimerization reactions. The parameters of theS _B hexagonal lattice area=b=4.29 ? in all the studied compounds, whilstc varies from 18.9? to 24? as a function of the C atom number of the alkyl chain; its averaged increase is 1.265? for each CH₂ group. In any case, the distance between the smectic planes is equal to the molecular length so that interdigitated structures are to be excluded. Work presented at the First USSR-Italy Bilateral Meeting on Liquid Crystals held in Portonovo, Ancona (Italy), September 30-October 2, 1987.     

Macroscopic properties of smectic liquid crystals

We discuss the macroscopic behavior of smectic C_G liquid crystals. Smectic C_G is the most general tilted smectic phase that is fluid in the layers. It is characterized by global C₁ symmetry. Consequently, it is ferroelectric, pyroelectric and piezoelectric, opening up a number of possible applications for such a phase. As smectic C_G-phase has a macroscopic hand due to its structure, it is a natural candidate to explain the recent experimental observations of left and right-handed helices in a system composed of achiral molecules. We also discuss critically to what extent smectic C_G could be important for liquid crystalline phases formed by banana-shaped molecules. Phase transitions involving a smectic C_G phase and defects of its in-plane director are briefly discussed. Received: 25 March 1998 / Revised: 15 June 1998 / Accepted: 15 July 1998     

Phase polymorphism and electro-optical properties of a ferroelectric liquid crystal containing the biphenyl system

ABSTRACT

In this article we present results concerning phase transitions and physical properties of the ferroelectric phase of the compound (S)-4-(1-methylheptyloxy)biphenyl–4'-(heptyloxy phenyl)-4-carboxylate (MHOBOPO7). The compound has the following phases: smectic ferroelectric C (SmC*), chiral nematic N*, and two defected phases, TGB_C and blue phase. The mesomorphic properties were investigated by means of three complementary methods: differential scanning calorimetry, polarizing light optical microscopy, and transmitted light intensity. The electro-optical measurements were carried out on an ordered sample in a middle electric field during very slow cooling from the nematic phase to the ferroelectric phase.     

Dielectric investigations in the nematic and hexatic smectic B phases of 4-hexyl-4′-[2-(4-isothiocyanatophenyl)ethyl]-1,1′-biphenyl

Temperature-dependent dielectric characterization of 4-hexyl-4′-[2-(4-isothiocyanatophenyl)ethyl]-1,1′-biphenyl (HIEB), which exhibits smectic B and nematic phases, has been carried out over the frequency range of 1 Hz to 10 MHz for homeotropic and planar alignment of sample molecules. This compound shows positive dielectric anisotropy (Δε = ε _∥ ? ε _⊥ > 0) in the nematic (N) phase. One mode of dielectric relaxation showing Arrhenius behaviour has been detected in the hexatic smectic B (SmB) phase. Various electrical parameters, namely, dielectric anisotropy, relaxation frequency and activation energy, have been determined in the N and SmB phases.     

Molecular-statistical approach to a behavior of ferroelectric,antiferroelectric and ferrielectric smectic phases in the electric field

The fundamental theoretical approach derived in A.V. Emelyanenko et al., Phys. Rev. E 74, 011705 (2006) is complemented by a consideration of the influence of the homogeneous electric field on Sm- C _A ^* , biaxial intermediate phases, and Sm-C ^* . The crucial role of the induced polarization is investigated for the first time. The evolution of any tilted smectic phase in the electric field is found to meet the two thresholds. The first threshold corresponds to the unwinding process, and the second one corresponds to the phase transition into the bi-domain structure of Sm-C ^* , where the tilt plane has some contribution either along or against the electric field, while the average direction may still be perpendicular to the electric field. The tilt plane in the monodomain (conventional) structure preceding the second threshold is the same in every unwound phase, and is perpendicular to the electric field. No 3D distortion in Sm- C _A ^* is predicted on application of the electric field. The entire electric-field-temperature phase diagrams including the possibility of existence of the maximal number of tilted smectic phases are plotted and compared with the experimental ones. The numerical calculations in the framework of this fundamental study are done with help of AFLC Phase Diagram Plotter software developed by the author and available at his web page.     

Effect of shape anisotropy on the phase diagram of the Gay-Berne fluid

We have used the density functional theory to study the effect of molecular elongation on the isotropic-nematic, isotropic-smectic A and nematic-smectic A phase transitions of a fluid of molecules interacting via the Gay-Berne intermolecular potential. We have considered a range of length-to-width parameter 3.0 ⩽ x₀ ⩽ 4.0 in steps of 0.2 at different densities and temperatures. Pair correlation functions needed as input information in density functional theory are calculated using the Percus-Yevick integral equation theory. Within the small range of elongation, the phase diagram shows significant changes. The fluid at low temperature is found to freeze directly from isotropic to smectic A phase for all the values of x₀ considered by us on increasing the density while the nematic phase stabilizes in between isotropic and smectic A phases only at high temperatures and densities. Both isotropic-nematic and nematic-smectic A transition density and pressure are found to decrease as we increase x₀. The phase diagram obtained is compared with computer simulation result of the same model potential and is found to be in good qualitative agreement.     

Density studies across the smectic G-nematic and nematic-lsotropic transitions

The densities of N(p-n-pentyloxy benzylidene) p-ethylaniline and N(p-n-hexyloxy benzylidene) p-ethylaniline are measured as a function of temperature from the isotropic liquid to the smectic G phase. Both the compounds exhibit enantiotropic smectic G and nematic liquid crystalline phases. The changes in density across the phase transformations and the thermal expansion coefficient confirm the order of the transitions as of first order. The particular importance of the smectic G to nematic transformation is apparent from the density jump across the transition. An estimate of the pressure dependence of the isotropic-nematic transition temperature is found to be in reasonable accord with the literature data.     

Insights on some chiral smectic phases

Combining layered positional order as smectic order and chirality can generate complex architectures since twist parallel to the layers is not allowed. This paper will review some new experimental results on different phases resulting from the competition between smectic positional order and twist orientational order. It concerns the TGB_A and the NL^*, that is the liquid line phase as well as the SmQ phase. Chiral effects in the isotropic phase will also be discussed.     

Universal non-monotonic smectic fluctuations of liquid crystal films in a magnetic field

Free-standing liquid crystal films with positive diamagnetic susceptibility can have the smectic ordering enhanced by an external field applied perpendicular to the plane layers. Within a quadratic functional integral approach, we investigate the interplay between the smectic order induced by an external field H and that due to the surface tension γ between the film and the surrounding gas. We find that the average smectic fluctuation is a non-monotonic function of film thickness, with a characteristic thickness scale ξ _H delimiting the predominance of surface tension and magnetic field effects. This characteristic thickness obeys simple asymptotic power-law relations as a function of the ordering terms which allows us to represent the average smectic fluctuations in a universal scaling form. Received 7 January 2003 Published online 1st April 2003 RID="a" ID="a"e-mail: marcelo@ising.fis.ufal.br