Experimental investigations of a new TGBC mesophase

We report on optical and structural X-ray studies on a smectic C twist grain boundary phase (TGB) of a pure liquid crystalline material. It is shown that this TGB phase, which exists over a large range of temperature, is definitely different from previously reported and predicted TGB phases. The two main experimental features are: (i) the observation in planar geometry of an optical texture exhibiting a square grid pattern, and (ii) the detection of a broad Bragg ring in reciprocal space instead of one (TGB) or two (TGB) sharp rings. We suggest a few possible tracks that can be explored to understand the complex structure of this new phase. Received 25 January 1999     

Observation of a reentrant twist grain boundary phase

We report the occurrence of a reentrant twist grain boundary phase, which we designate as Re- TGB(A). Microscopic observations on a nonsymmetric dimer showed the phase sequence Iso- N*- TGB(A)-Sm- A-Re- TGB(A)- TGB(C*). Here N* and Sm- A stand for the chiral nematic and smectic- A phases, TGB(A) is the twist grain boundary phase with smectic- A blocks, and TGB(C*) that with smectic- C* blocks and exhibiting features of both the smectic- C* and TGB phases. The reentrance of the TGB(A) phase is unambiguously demonstrated using x-ray diffraction, selective reflection, and optical rotation data.     

Structural and optical investigations of TGBA and TGBC mesophases exhibiting cylindrical and cone-like domain textures

The characterization by optical microscopy, X-ray diffraction and differential scanning calorimetry of two new liquid crystalline compounds is presented. The compounds under consideration incorporate in their molecules two chiral centres (one asymmetric carbon and one asymmetric sulphur of a sulphinate group). While the carbon chirality is fixed in the R configuration the sulphur chirality may be either in the S or in the R configuration. A mesophase in a large temperature domain is evidenced for one of the two diastereomers, while both and mesophases are observed in a similar temperature domain for the other one. For both diastereomers and in both mesophases it is possible to observe the coexistence of two different types of optical textures, namely planar cholesteric textures and developable domains. The latter are coiled in a different way than proposed in an earlier publication. More precisely, they form cylindrical or cone-like domains with double-twist properties as observed in the blue phases. The pitch of the helix in the TGB mesophases is evaluated by means of optical reflection observations in samples exhibiting the planar cholesteric textures. For both diastereomers it is also possible to evaluate structural parameters related to the organization within the mesophases. Finally, the induced phase transition - is studied by the application of an AC electric field. Received: 16 June 1997 / Revised: 17 October 1997 / Accepted: 20 November 1997     

Nuclear magnetic resonance study of the smectic-cholesteric phase transition in a dimesogenic liquid crystal

Nuclear magnetic resonance (NMR) spectroscopy has provided a unique opportunity to study the characteristic smectic-A to chiral nematic phase transition in a dimesogenic liquid crystal (“KI-5S”). The order parameters in the liquid crystalline phases were obtained from the ²H NMR quadrupole splitting and ¹³C NMR chemical shift measurements, manifesting a first-order smectic-nematic phase transition.     

Transition from smectic-A to crystalline phase in the mean field approximation

We present here a smectic-A to crystalline phase transition curve for liquid crystals, in addition to the phase diagram previously reported which includes the isotropic, nematic, and smectic-A phases calculated in the mean field approximation.     

Twisted-grain-boundary (TGB) phases: nanostructured liquid-crystal analogue of Abrikosov vortex lattices

Twisted-grain-boundary (TGB) phases shown by some liquid-crystalline materials have properties common to those of both smectic and cholesteric phases. Following analogy between liquid crystals and super conductors proposed by de Gennes [Solid State Commun., 10, 753 (1972)], Renn and Lubensky [Phys. Rev. A, 38, 2132 (1988)] theoretically predicted a chiral analog of the smectic A (SmA*) phase, which is now known as TGBA phase. The TGBA phase was experimentally observed for the first time by Goodby et al. [Nature, 337, 449 (1989)] in the chiral homologous series of ferroelectric liquid-crystal material R- and S-1-methylheptyl 4′-[(4′′-n-alkoxyphenyl)propionoyloxy]-biphenyl-4-carboxylates (nP₁M₇), with n?=?13,14,15. Since then, more than a hundred pure and mixed systems showing TGBA phase have been found. Later, Renn derived a mean-field phase diagram based on the chiral Chen-Lubensky model, and predicted two more TGB phases, namely TGBC and TGBC?. These two phases have also been experimentally observed in many systems, and in a few, the phase diagram is similar to that predicted by Renn. Unlike the TGBA phase, several theoretical models have been proposed for TGBC and TGBC? phases, and it remains to be ascertained whether all the types of proposed TGBC/TGBC? structures experimentally exist. A review of the theoretically predicted and experimentally observed TGB phases is given in the present article. Some recently observed novel optical textures of the TGB phases are also reported.     

Structure of blue phase III of cholesteric liquid crystals

We report large scale simulations of the blue phases of cholesteric liquid crystals. Our results suggest a structure for blue phase III, the blue fog, which has been the subject of a long debate in liquid crystal physics. We propose that blue phase III is an amorphous network of disclination lines, which is thermodynamically and kinetically stabilized over crystalline blue phases at intermediate chiralities. This amorphous network becomes ordered under an applied electric field, as seen in experiments.     

Effect of the chiral chain length on structural and phase properties of ferroelectric liquid crystals

Studies of structural and phase properties obtained on several ferroelectric liquid crystalline materials with 2-alkoxypropionate group used as a chiral centre and without any lateral substitution are presented. In dependence on the chiral chain length these compounds exhibit the cholesteric N* phase, the ferroelectric smectic C* and a low-temperature SmX phase. Values of the spontaneous polarization and spontaneous tilt angle have been determined within the whole range of the SmC* phase. A low-temperature SmX phase has been identified as the orthogonal hexatic SmB* phase. The molecular parameters, namely the layer spacing in the SmC* and SmB* phases and the average intermolecular distances (D) between neighbouring parallel molecules in all investigated phases have been determined using the results of the X-ray diffraction obtained on non-oriented samples. The effect of the chiral chain length on mesomorphic, structural and physical properties of the studied ferroelectric liquid crystalline materials is discussed.     

Twisted Grain Boundary Phases in the Binary Mixtures of 3ß-Chloro-5-Cholestene and 4-N-Decyloxybenzoic Acid

From the thermodynamical, optical texture and dielectric studies of the binary mixtures of 3β-chloro-5-cholestene (ChCl) and 4-n-decyloxybenzoic acid (DOBA), the phase diagram has been drawn. It has been observed that low concentrations of ChCl (1 to 7 mol%) in DOBA induce various types of twisted grain boundary (TGB) submesophases, whereas higher concentrations induce a smectic A (SmA) mesophase. Various optical textures of the TGB phases under different conditions of molecular anchoring have been observed. Weak transitions related with TGB phases have been detected from the temperature dependence of dielectric permittivity. The observed phase diagram of ChCl-DOBA binary system is in complete conformity with the theoretically predicted mean-field phase diagram derived by Renn within the framework of the chiral Chen-Lubenski model     

胆甾相和蓝相液晶的透射和反射特性

针对蓝相液晶显示器中的暗态漏光特性, 采用时域有限差分方法模拟计算了胆甾相液晶的平面态和焦锥态以及蓝相II态液晶的透射和反射特性, 得到了它们在正交和平行偏振片之间的漏光, 并提出了计算等效旋光能力的公式以比较它们的旋光能力. 通过对比焦锥态和蓝相液晶的旋光能力和漏光特性发现, 采用焦锥态替代蓝相液晶而得到良好的暗态特性是一种可行的方法. 通过研究它们的布拉格反射特性, 得知蓝相液晶的布拉格反射与平面态相似, 但反射强度小, 焦锥态无明显的布拉格反射特性.     

Optical and thermal studies on viscous lamellar smectic phases in binary mixture of DTAC and ortho-phosphoric acid

The binary mixture of two non-mesogenic compounds, namely, dodecyl trimethylammonium chloride (DTAC) and ortho-phosphoric acid (H₃PO₄) exhibits very interesting liquid crystalline smectic phases at large range of concentrations and temperature. The mixture with lower and higher concentrations of DTAC exhibits SmA, SmD, SmB and SmE phases, sequentially when the specimen is cooled from its isotropic phase. Different liquid crystalline phases observed in the mixture were studied using optical microscopic techniques. The temperature variations of optical anisotropy and electrical conductivity have also been discussed. Helfrich potential and elastic moduli have also been estimated in the smectic phase using the Helfrich model.     

Pattern formation at the traveling liquid-crystal twist grain boundary-smectic a interface

Summary Pattern formation at phase boundaries moving in a temperature gradient is one of the major areas of nonequilibrium physics attracting considerable attention. While most of the early work concentrated on the moving solid-liquid interface, now the focus has changed to phase transitions characterized by broken continuous symmetry. Most recently we investigated consequences to interfacial patterns of a chirality-induced equilibrium length. Here we study patterns at another chiral interface where one of the phases has a chirality-induced defect lattice, the twist grain boundary (TGB) phase. The TGB state is analogous to the vortex lattice in Type-II superconductors predicted by the Gennes’ analogy between the nematic (N)-smectic A (A) transition and the normal-superconducting transition. In this analogy, a cholesteric A transition is analogous to the normal-superconducting transition in an external magnetic field and a theory has been developed for its analogous vortex lattice, the TGB phase, when this transition is Type II. We study patterns formed at the traveling TGB-A phase boundary. Different patterns are observed depending on whether TGB grows into A or A into TGB. Indeed, this maybe the first time a steady-state pattern is observed in directional melting (i.e. TGB growing into A). As these patterns have a broad band of wavelengths, they are difficult to characterize physically. Thus, we introduced a novel analysis (most simply but not rigorously described as) measuring the fractal dimension of the patterns at these traveling interfaces. Two lengths emerged from this analysis: a longer one set by sample thickness and a shorter one set by the smallest TGB unit that can grow into an oriented smectic A phase. We invoke our old dynamic arguments to account for why TGB cannot propagate at a second-order TGB-cholesteric phase transition so it is eventually squeezed out leaving behind a direct cholesteric-A transition. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Quantum phase transition of cold atoms trapped in optical lattices

We review our recent theoretical advances in phase transition of cold atoms in optical lattices, such as triangular lattice, honeycomb lattice, and Kagomé lattice. By employing the new developed numerical methods called dynamical cluster approximation and cellular dynamical mean-field theory, the properties in different phases of cold atoms in optical lattices are studied, such as density of states, Fermi surface and double occupancy. On triangular lattice, a reentrant behavior of phase translation line between Fermi liquid state and pseudogap state is found due to the Kondo effect. We find the system undergoes a second order Mott transition from a metallic state into a Mott insulator state on honeycomb lattice and triangular Kagomé lattice. The stability of quantum spin Hall phase towards interaction on honeycomb lattice with spin-orbital coupling is systematically discussed. And we investigate the transition from quantum spin Hall insulator to normal insulator in Kagomé lattice which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian. In addition, we propose the experimental protocols to observe these phase transition of cold atoms in optical lattices.     

Cholesteric–nematic transitions induced by a shear flow and a magnetic field

The untwisting of the helical structure of a cholesteric liquid crystal under the action of a magnetic field and a shear flow has been studied theoretically. Both factors can induce the cholesteric–nematic transition independently; however, the difference in the orienting actions of the magnetic field and the shear flow leads to competition between magnetic and hydrodynamic mechanisms of influence on the cholesteric liquid crystal. We have analyzed different orientations of the magnetic field relative to the direction of the flow in the shear plane. In a number of limiting cases, the analytic dependences are obtained for the pitch of the cholesteric helix deformed by the shear flow. The phase diagrams of the cholesteric–nematic transitions and the pitch of the cholesteric helix are calculated for different values of the magnetic field strength and the angle of orientation, the flow velocity gradient, and the reactive parameter. It is shown that the magnetic field stabilizes the orientation of the director in the shear flow and expands the boundaries of orientability of cholesterics. It has been established that the shear flow shifts the critical magnetic field strength of the transition. It is shown that a sequence of reentrant orientational cholesteric–nematic–cholesteric transitions can be induced by rotating the magnetic field in certain intervals of its strength and shear flow velocity gradients.     

On the helical domain structure of the liquid ferroelectrics

The case when a nematic liquid crystalline phase is ferroelectric is considered. Such “liquid ferroelectric” is, surely, instable and transforms into a helical cholesteric-type structure which for this case is a variety of the ferroeltric domain structure. One can think that some cholesteric phases are liquid ferroelectrics with the helical domain structure.     

Phase transitions and soft elasticity of smectic elastomers

Smectic-C elastomers can be prepared by cross-linking, e.g., liquid crystal polymers, in the smectic-A phase followed by a cooling through the smectic-A to smectic-C phase transition. This transition from D(infinityh) to C(2h) symmetry spontaneously breaks rotational symmetry in the smectic plane as does the transition from a smectic-A to a biaxial smectic phase with D(2h) symmetry. We study these transitions and the emergent elasticity of the smectic-C and biaxial phases in three related models and show that these phases exhibit soft elasticity analogous to that of nematic elastomers.     

Phase transitions in ferroelectric liquid crystals

Molecular chirality plays an important role in the science of liquid crystals, leading to cholesteric liquid crystal, blue phases, ferroelectric and antiferroelectric smectic phases and twist grain boundary phases. In all of these mesogens, chirality is an intrinsic property built into the chemical structure of mesogenic molecules. The study of ferroelectric liquid crystals has seen substantial experimental strides. In theoretical aspects, there has been relatively little basic work on this fascinating class of material. This review will try to present a comprehensive overview of the current status of the phase transitions in ferroelectric smectic liquid crystals. The article begins with a brief introduction about the symmetry and structure of ferroelectric mesophases. An attempt is made to identify a range of problems and related questions associated with the study of phase transitions. In the remaining parts of the article the important experimental and theoretical developments are summarized. Finally, some of the future directions have been identified.     

Self-assembling properties of lactic acid derivative with several ester linkages in the molecular core

The effect of several polar ester linkage groups incorporated in the molecular core of a chiral lactic acid derivative on self-assembling properties has been investigated by polarizing optical microscopy, small angle X-ray diffraction, differential scanning calorimetry, optical and electro--optical studies. The compound possesses the paraelectric smectic A* (SmA*) and ferroelectric smectic C* (SmC*) phases over a broad temperature range. Mesomorphic behaviour, spontaneous polarization, birefringence, optical transmission, dielectric anisotropy and structural properties of the self-assembled chiral material have been determined. The obtained results are discussed and compared with that of other liquid crystalline materials. Experimentally determined spontaneous polarization and tilt angle values are also used to elucidate the nature of SmC* to SmA* phase transition. The effect of polar ester linkages in the molecular core has also been discussed.     

High-resolution calorimetric study of the phase transitions of tridecylcyanobiphenyl and tetradecylcyanobiphenyl liquid crystals

A thermal study of the liquid crystals tridecylcyanobiphenyl and tetradecylcyanobiphenyl has been performed by means of adiabatic scanning calorimetry. Both compounds exhibit only the smectic-A mesophase between the normal liquid and the crystalline phase and their phase transitions are strongly first order. A summary of the enthalpies and transition temperatures for all the smectic homologues of the cyanobiphenyl family is given, based on high-resolution measurements of the present work and previous studies.     

The synthesis of the chiral non-mesogenic d-seco estrone derivatives and their influence on the phase transitions of cholesteric liquid crystals

The synthesis of new chiral seco-estrone derivatives is presented, as well as their influence on the phase transition of binary mixtures of cholesteryc liquid crystals. The new chiral derivatives do not posses any liquid crystalline phases and were synthesized in several synthetic steps, starting from estrone. We have studied the mixtures of cholesteryl non-anoate (40%) with cholesteryl myristate (40%) and addition of new chiral derivatives 3 4, or 5 (20%). It was concluded that the addition of chiral derivative 3 to the binary mixture stabilizes smectic A and cholesteric phase and shifts the phase transition temperature with respect to pure binary mixture for about 5°C towards lower temperatures. The extension of the temperature range of the cholesteric phase from 5°C to 15°C was established in the case when the derivatives 3 and 4 are added to the binary mixture of cholesteryl nonanoate with cholesteryl myristate. The phase diagrams of investigated compounds are formed on the basis of data obtained by the optical microscopy. Using X-ray diffraction on the crystalline powder of unoriented samples we have determined the molecular parameters: the thickness of smectic and cholesteric layers and average distance between the long axes of neighboring molecules.