Detection of phase biaxiality in liquid crystals by use of the quadrupole shift in 131Xe NMR spectra

An experimental method to unambiguously distinguish between uniaxial and biaxial liquid crystal phases is introduced. The method is based on the second order quadrupole shift (SOQS) observable in 131Xe NMR spectra of xenon dissolved in liquid crystals. It is shown that besides revealing the biaxiality, the 131Xe SOQS offers a novel method to determine the tilt angle in smectic C phases. As an example, the 131Xe SOQS in a ferroelectric liquid crystal is reported. It yields up a biaxial phase in between isotropic and smectic C phases.     

Evidence for triclinic symmetry in smectic liquid crystals of bent-shape molecules.

The first experimental evidence for triclinic symmetry of bulk smectic liquid-crystal samples of achiral banana-shaped molecules is presented. This phase corresponds to the so-called Sm-CG phase consisting of biaxial molecules and characterized by two tilt directions with respect to the layer normal: tilt of the molecular plane (clinic) and tilt of the molecular kink direction (leaning). Each smectic layer has a polarization component normal to the smectic layers (C1 symmetry). The observations suggest that the phase tentatively labeled as B7 is identical with the Sm-CG phase.     

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.     

Induced anticlinic ordering and nanophase segregation of bow-shaped molecules in a smectic solvent

Recent experiments indicate that doping low concentrations of bent-core molecules into calamitic smectic solvents can induce anticlinic and biaxial smectic phases. We have carried out Monte Carlo simulations of mixtures of rodlike molecules (hard spherocylinders with length/breadth ratio L(rod)/D = 5) and bow-shaped molecules (hard spherocylinder dimers with length/breadth ratio L(ban)/D = 5 or 2.5 and opening angle psi). We find that a low concentration ( 3%) of L(ban)/D = 5 dimers induces anticlinic ( SmC(A)) ordering in an untilted smectic ( SmA) phase for 100 < or = psi < 150. For L(ban)/D = 2.5, no tilted phases are induced. However, with decreasing psi we observe a sharp transition from intralamellar nanophase segregation (bow-shaped molecules segregated within smectic layers) to interlamellar nanophase segregation (bow-shaped molecules concentrated between smectic layers) near psi = 130.     

Hunting for smectic C in calamitic azobenzene ionic liquid crystals with different cationic head groups

The tilted smectic C phase is a rather uncommon phase in ionic liquid crystals (ILCs), whereas the orthogonal smectic A phase is the most common phase in ILCs. We now present 2 new groups of mesogens with an azobenzene core that exhibit smectic C as well as smectic A phases. Their phase sequences and tilt angles were studied by polarizing microscopy, and their temperature‐dependent layer spacings and orientational order parameters were investigated by X‐ray diffraction. We present 1 new amidinium azobenzene mesogen that forms enantiotropic smectic C and A phases and another amidinium as well as 2 new guanidinium azobenzene mesogens that exhibit monotropic smectic C and enantiotropic smectic A phases. With this study, we show that azobenzene is indeed an SmC‐promoting group in ILCs. Comparing these results with our earlier results on azobenzenes with an N‐methylimidazolium head group (N Kapernaum et al, ChemPhysChem 2016, 17, 4116‐4123), we show that the aromaticity of the imidazolium head group plays an important role in the formation of smectic C phases.     

Field-temperature phase diagrams in chiral tilted smectics,evidencing ferroelectric and ferrielectric phases

Usual ferroelectric compounds undergo a paraelectric-to-ferroelectric phase transition when the susceptibility of the electric polarization density changes its sign. The temperature is the only thermodynamic field that governs the phase transition. Chiral tilted smectics may also present an improper ferroelectricity when there is a tilt angle between the average long axis direction and the layer normal. The tilt angle is the order parameter of the phase transition which is governed by the temperature. Although the electric susceptibility remains positive, a polarization proportional to the tilt appears due to their linear coupling allowed by the chiral symmetry. Further complications come in when the chirality increases, as new phases are encountered with the same tilt inside the layers but a distribution of the azimuthal direction which is periodic with a unit cell of two (SmC(A)*, three (SmC(Fi1)*, four (SmC(Fi2)* or more (SmC(alpha)* layers. In most of these phases, the layer normal is a symmetry axis so there is no macroscopic polarization except for the SmC(Fi1)* in which the average long axis is tilted so the phase is ferrielectric. By studying a particular compound with only a SmC(Fi2)* and a SmC(alpha)* phase, we show that we recover the uniformly tilted ferroelectric SmC* when applying an electric field. We are thus led to build field-temperature phase diagrams for this class of compounds by combining different experimental techniques described here.     

Phase diagram of transitions from an isotropic phase to nematic and smectic (uniaxial,biaxial) phases in liquid crystals with achiral molecules

The phase diagrams of transitions from an isotropic phase to nematic and smectic phases are investigated within a simple phenomenological model of the Landau thermodynamic potential. The conditions of the isomorphic phase transition between two uniaxial smectic phases and the direct transition from the isotropic phase to the uniaxial and biaxial smectic phases are determined. The behavior of the order parameters is described along different thermodynamic paths. The theoretical results are discussed using the example of liquid-crystal phases in compounds with banana-shaped achiral molecules.     

The structure of the smectic phases of terephthal-bis-(butylaniline) studied by electron spin resonance spectroscopy

Electron spin resonance (E.S.R.) measurements at X-band (3·3 kG) of the spin probe 17β-hydroxy-4,4′-dimethylspiro[5α-androstane-3,2′-oxazolidin]-3′-yloxyl dissolved in the smectic phases (A, C and B) of the mesogen 4,4′-terephthal-bis(butylaniline) (TBBA) are reported. Two types of samples were studied in the dependence on temperature, sample orientation and strength of the magnetic field: (i) glass plate sandwiches with less than 0·1 mm of the mesogen, and (ii) 4 mm i.d. cylindrical glass tube. The sandwich samples were prepared as monodomains with the smectic layers parallel to the glass plates. In these samples the orientation of the layers and of the director is fixed and cannot be reoriented even in a magnetic field of 21 kG. From the angular dependence of the spectrum, the tilt angle, the order parameter and their temperature dependence were determined.

In the cylindrical samples the original orientation of the smectic layers is preserved, and up to about 3 kG the director's orientation with respect to the sample is almost unaffected in all smectic phases. On subjecting the sample to higher fields (～ 20 kG) the director in the smectic C phase will re-align so as to minimize the magnetic energy, subject to the fixed tilt angle. The new alignment is preserved when the strength of the magnetic field is reduced. No such re-alignment is observed in the smectic B phase even after subjecting the sample to a field of 21 kG, in contrast to previous deuterium N.M.R. measurements at 14 kG. It is suggested that in this phase the director is pulled by strong fields but relaxes to its original direction when the magnetic field is brought back to 3·3 kG.     

Molecular models for ferroelectric liquid crystals with conventional and anomalously weak layer contraction

A molecular theory of the ferroelectric smectic C* phase has been developed using the simple model of a chiral molecule composed of a uniaxial core and a pair of off-center nonparallel dipoles which determine molecular chirality and polarity. The interaction between uniaxial cores is modeled by a rather general effective potential which can be used to describe smectic materials with both conventional and anomalously weak layer contraction in the smectic C* phase. Spontaneous polarization, tilt, and layer spacing are calculated numerically as functions of temperature, and it is shown that the variation of the polarization generally deviates from that of the tilt angle. It is shown that this deviation is more pronounced in smectic materials tilting with low layer contraction which corresponds to existing experimental data. The model has been used to reproduce qualitatively the experimental data for polarization, tilt and layer spacing for two similar mixtures exhibiting conventional and anomalously weak layer contraction. The polarization and the tilt are also calculated in the case when the smectic A-smectic C* transition is characterized by the biaxial primary order parameter.     

A molecular theory of smectic C liquid crystals made of rod-like molecules

Organic compounds exhibiting the smectic C phase are made of rod-like molecules that have dipolar groups with lateral components. We argue that the off-axis character of the lateral dipolar groups can account for tilt in layered smectics (SmC, SmC*, SmI etc.). We develop a mean-field theory of the smectic C phase based on a single-particle potential of the form U _C ∝ sin(2θ)cosφ, consistent with the biaxial nature of the phase, where θ and φ are the polar and azimuthal angles, respectively. The hard-rod interactions that favour the smectic A phase with zero tilt angle are also included. The theoretical phase diagrams compare favourably with experimental trends. Our theory also leads to the following results: i) a first-order smectic C to smectic A transition above some value of the McMillan parameter α, leading to a tricritical point on the smectic C to smectic A transition line and ii) a first-order smectic C to smectic C transition over a very small range of values of the model parameters. We have also extended the theory to include the next higher-order term in the tilting potential and to include the effect of different tilt angles for the molecular core and the chain in the SmC phase. Received 3 August 2002 RID="a" ID="a"Present address: Department of Physics, Vijaya College, R. V. Road, Bangalore - 560 004, India. RID="b" ID="b"e-mail: nvmadhu@rri.res.in     

Unusual thickness-dependent thermal behavior and anticlinic coupling in chiral smectic free-standing liquid-crystal films

We observe, in free-standing films of a chiral smectic liquid crystal, a series of discrete transitions in the relative orientation of the tilt of the interior and surface layers. These transitions include a remarkable reentrant synclinic-anticlinic-synclinic ordering sequence of the film surfaces in the presence of an electric field upon cooling. The profiles of the associated heat-capacity anomalies are found to be strongly thickness dependent and exhibit a novel crossover behavior in reduced dimensions. We measure the anticlinic coupling between tilted surface layers in the smectic- A phase.     

Theory of the non-planar surface phase in tilted smectic films under electric field

We present a phenomenological theory of the non-planar tilted surface phase recently observed in freely suspended smectic films. We show that the three phases —Synclinic, Anticlinic, and non-planar (Axial)— stable in non-chiral systems, merge into a single phase in chiral systems. We discuss some experimental consequences of this specific chiral feature. We predict the effects of electric field application parallel to the smectic layers on the stability of the various zero-field surface phases, and determine the conditions for the observation of field-induced chiral Anticlinic/Synclinic crossovers. In thin films they depend only on the ratio between the bulk electroclinic coupling energy and the surface electric-field-tilt coupling.     

Chain dynamics in a chiral C phase by deuteron spin relaxation study

Molecular reorientations and internal conformational transitions of an aligned chiral liquid crystal (LC) 10B1M7 are studied by means of deuterium spin-lattice relaxation in its smectic A (SmA) and smectic C* (SmC*) phase. The motional model which is applicable to uniaxial phases of many LCs is found to be adequate even when the phase is a tilted SmC* phase. The deuterium NMR spectrum in this phase cannot discern rotations of the molecular director about the pitch axis. The basic assumption is that the phase biaxiality is practically unobservable. However, the relaxation rates can be accounted for by the tilt angle between the molecular director and the layer normal in the SmC* phase. The tumbling motion appears to show a higher activation energy upon entering from the uniaxial SmA into the SmC* phase.     

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     

Tilted and helical columnar phases for an axially symmetric discoidal system

We report novel phase behavior for a system of disclike ellipsoidal particles interacting via a pair potential. We identify a structural phase transition between two hexagonal columnar phases, both tilted, induced by spatial ordering of the tilt about the columnar axis and positional correlations between neighboring columns upon cooling. The local minima of the potential energy surface support irregular helical arrangements of the discoids about the columnar axis for the high-temperature hexagonal columnar phase, and a tilted arrangement for both phases. Our study demonstrates that dispersion-repulsion forces corresponding to oblate ellipsoids are sufficient to produce a columnar phase that is tilted and helical.     

Helix unwinding in ferroelectric liquid crystals induced by tilted electric field

Helix unwinding in ferroelectric liquid crystals induced by an electric field is theoretically studied on the basis of the continuum theory. By applying a weak electric field tilted to the smectic layers, the contribution of the dielectric interaction energy density to the total free energy density is increased. Approximation methods are used to calculate the free energy for different tilt angles between the electric field and the smectic layers. The obtained results suggest selecting the optimal number of pitches in the film that matches to the minimum of the free energy.     

129Xe diffusion in a ferroelectric liquid crystal

Measurements of ¹²⁹Xe self-diffusion and shielding as a function of temperature were performed to cover the different phases of the ferroelectric liquid crystal FELIX-R&;D. The shielding data prove untwisting of the helical structure in the nematic phase (i.e. non-chiral nematic phase) of FELIX-R&;D. Self-diffusion measurements were carried out in a direction parallel to the main magnetic field of the NMR spectrometer. However, in order to yield the anisotropy of the xenon self-diffusion tensor a few measurements also were performed in the perpendicular direction. A special technique, based on the observation of the second spin echo instead of the conventional first one, was applied to avoid convection problems. The experiments reveal all the phase transitions and a continuous decrease in the self-diffusion constant along the external magnetic field, D‖, when moving from the isotropic to the smectic C? phase. The respective activation energy E‖ appears to vary remarkably, however, being about the same in the isotropic and smectic C? phases. In the smectic mesophases significantly faster xenon self-diffusion was detected in the perpendicular direction than in the parallel direction. The detected self-diffusion constant D ⊥ in the perpendicular direction seems to remain almost constant in the smectic mesophases and close to the value of the self-diffusion constant in the isotropic phase. The results are in agreement with the structural features of smectic phases and indicate redistribution of xenon atoms towards the interlayer space of smectic mesophases.     

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.     

X-ray diffraction micro-imaging of strain in laterally overgrown GaAs layers. Part I: analysis of a single GaAs stripe

Spatially resolved X-ray diffraction (SRXRD) is used for micro-imaging of strain in GaAs:Si layers grown by liquid phase epitaxial lateral overgrowth (ELO) on SiO₂-masked GaAs substrates. We show that laterally overgrown parts of the layers (wings) are tilted towards the underlying mask. By SRXRD mapping local wing tilt is easily distinguished from macroscopic sample curvature. The direction of the tilt and distribution of tilt magnitude across the width of each layer can also be readily determined. This allows measuring of the shape of the lattice planes in individual ELO stripes. Downward wing tilt disappears completely when the mask is removed by selective etching. Then residual strain in ELO layers is exposed. In particular, upward tilt is found in free-standing ELO wings. Numerical simulations show that this phenomenon is caused by different concentrations of silicon dopant in vertically and laterally grown parts of the layer. PACS 61.05.cp; 61.72.Ff; 68.55.ag     

Flexoelectricity and piezoelectricity: the reason for the rich variety of phases in antiferroelectric smectic liquid crystals

The free energy of antiferroelectric smectic liquid crystals which takes into account polar order explicitly is presented. Steric, van der Waals, piezoelectric, and flexoelectric interactions to the nearest layers, and dipolar electrostatic interactions to the nearest and to the next-nearest layers, induce indirect tilt interactions with chiral and achiral properties, which extend to the third- and to the fourth-nearest layers. Although the strength of microscopic interactions changes monotonically with decreasing temperature, the effective interlayer interactions change nonmonotonically and give rise to a nonmonotonic change of the modulation period through various phases. Increased chirality changes the phase sequence.