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     

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     

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.     

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     

Competition between ferroelectric and flexoelectric polarization in freely suspended smectic films

We report a detailed ellipsometric study of freely suspended films of chiral liquid-crystal compounds possessing smectic-A and smectic-C phases. In the temperature region between the smectic-A - smectic-C bulk and surface transitions, a discontinuous reconstruction of the tilt profile across the film is observed in the presence of a constant d.c. electric field. Comparison of the measured ellipsometric quantities with values calculated from model tilt profiles reveals a competition between a structure possessing a homogeneous tilt direction and large ferroelectric polarization and a structure with opposite tilt direction in the two film halfs and large flexoelectric polarization. Received 21 October 1998     

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.     

Memory of silica aggregates dispersed in smectic liquid crystals: Effect of the interface properties

Previous studies on nematic liquid crystals containing silica particles indicated memory effects that might be due to hydrogen bonds between the individual silica particles. We made smectic liquid crystal dispersions containing silica particles with various surface properties. Using a neutron scattering technique we studied the interfacial surface effects on the structure of the silica aggregates, and on the smectic layer alignment. Our observations indicate that the stability of the memory correlates to the number of OH groups on the silica surfaces. The observations imply that, with fine-tuning of the OH content of the silica surfaces, various types of memory devices can be designed. We considered three different effects that can memorise the alignment of the liquid crystal. Measurements on tilted SmC phases indicate that surface effects become important only after repeated heating-cooling cycles, as the average size of the aggregates decrease. Received 31 July 1998 and Received in final form 17 December 1998     

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     

Depletion effects in smectic phases of hard-rod-hard-sphere mixtures

It is known that when hard spheres are added to a pure system of hard rods the stability of the smectic phase may be greatly enhanced, and that this effect can be rationalised in terms of depletion forces. In the present paper we first study the effect of orientational order on depletion forces in this particular binary system, comparing our results with those obtained adopting the usual approximation of considering the rods parallel and their orientations frozen. We consider mixtures with rods of different aspect ratios and spheres of different diameters, and we treat them within Onsager theory. Our results indicate that depletion effects, and consequently smectic stability, decrease significantly as a result of orientational disorder in the smectic phase when compared with corresponding data based on the frozen-orientation approximation. These results are discussed in terms of the τ parameter, which has been proposed as a convenient measure of depletion strength. We present closed expressions for τ, and show that it is intimately connected with the depletion potential. We then analyse the effect of particle geometry by comparing results pertaining to systems of parallel rods of different shapes (spherocylinders, cylinders and parallelepipeds). We finally provide results based on the Zwanzig approximation of a fundamental-measure density-functional theory applied to mixtures of parallelepipeds and cubes of different sizes. In this case, we show that the τ parameter exhibits a linear asymptotic behaviour in the limit of large values of the hard-rod aspect ratio, in conformity with Onsager theory, as well as in the limit of large values of the ratio of rod breadth to cube side length, d, in contrast to Onsager approximation, which predicts τ ∼ d ³. Based on both this result and the Percus-Yevick approximation for the direct correlation function for a hard-sphere binary mixture in the same limit of infinite asymmetry, we speculate that, for spherocylinders and spheres, the τ parameter should be of order unity as d tends to infinity.     

Helically modulated electroclinical effects in twist grain boundary liquid crystals

We report the first observation of an electroclinical effect at the TGB-TGB transition induced by an external DC electric field applied perpendicular to the pitch direction. Upon increasing the field, the smectic layers rather than the director field tilt over relative to the helical axis, allowing to detect the effect by X-ray scattering from well aligned samples. The observations are qualitatively interpreted in the frame of a mean field phenomenological model of a helically modulated electroclinical effect. Received: 24 April 1998 / Revised: 22 June 1998 / Accepted: 31 July 1998     

Field-induced phase transitions and reversible field-induced inversion of chirality in tilted smectic phases of bent-core mesogens

Three homologous achiral five-ring bent-core mesogens are presented where 4-chlororesorcinol is the central core and the aromatic rings are linked by ester groups. These compounds form smectic phases with a tilted arrangement of the molecules (tilt angle ≈ 45^°). On cooling the isotropic liquid this phase adopts a fan-like texture which shows for two homologues at relatively high electric fields ( 25-35V μm^-1) an antiferroelectric electro-optical response based on the collective rotation of the molecules around their long axes. At lower temperature the application of a sufficiently high electric field leads to a continuous transition into a non-birefringent texture which exhibits randomly distributed domains of opposite handedness. These domains can be reversibly switched into a state of opposite chirality by reversal of the field polarity. This switching is bistable and shows a current response typical for a ferroelectric ground state. The possible mechanism of the field-induced phase transition, of the ferroelectric switching and of the field-induced inversion of the chirality is discussed on the base of XRD, ¹³C- and ¹H-NMR investigations, dielectric and electro-optical measurements.     

Defects in a TGBA phase: A theoretical approach

Following our experimental observations of disclination lines in freely suspended droplets and free-standing films (Yu.A. Nastishin et al., Eur. Phys. J. E 5 353 (2001)), topological defects of the twist grain boundary (TGBA) phase are considered according to two aspects: topological and energetical. There are two classes of line defects, disclinations (as in the cholesteric (N*) phase and the liquid vortices phase (NL*), relating to the directors tripod symmetries) and dispirations (relating to the translation-rotation symmetries); there are no topological point defects. Differences between N*, NL* and TGBA disclinations are physical, not topological. The absence of focal conic domains in the TGBA phase is an immediate consequence of the materialization of the helical axis (along the χ-director); the same feature, coupled to the trend to parallelism of the smectic layers, accounts for the predominance of λ-lines. Finally, the presence of defects akin to developable domains is explained in the frame of the leastcurvaturemodel, that requires the introduction of a third type of defects: the densitiesofedgedislocations of the smectic layers. Received 20 February 2002     

c-director relaxation around a vortex of strength +1 in free-standing smectic-C films

The relaxation of director fields in freely suspended smectic films is studied experimentally by means of polarizing microscopy, and analyzed by solving the torque balance equation under appropriate initial and boundary conditions. We consider in particular the role of anchoring conditions of the c-director at particles and defects in the film. The structure of regular relaxation patterns allows to determine the elastic anisotropy of smectic materials. The splay elastic constant can exceed the bend constant by a factor of two and more. A remarkable consequence of this anisotropy is the stick-slip-like relaxation around a central defect of topological strength s = + 1.     

Zigzag instability of a χ disclination line in a cholesteric liquid crystal

We studied the formation of χ disclination lines in planar cholesteric samples placed in a temperature gradient near the cholesteric to smectic A phase transition. We observed that the first simple line which forms close to the smectic-cholesteric front zigzags when it is perpendicular to the direction of planar anchoring and is straight for other orientations. This instability is similar to Herring instability for crystalline surfaces. We show numerically that it originates from a strong increase of the elastic anisotropy close to the transition. In addition, we propose a new method to measure the pitch divergence at the smectic to cholesteric phase transition.     

Shearing of planar smectic C chevrons

We have theoretically investigated chevron formation in smectic C materials and the transformation of this chevron structure to a tilted layer structure as the cell is sheared. We find a series of transition temperatures at which the behaviour of the cell critically changes. As the cell is cooled from the smectic A phase past the first critical temperature there is a second order transition which forms two tilted layer states with lower energy than the smectic A bookshelf structure. Although these low energy tilted structures exist the bookshelf structure is the stable state for zero shear. However, upon further cooling this bookshelf structure becomes unstable to the formation of a chevron state. Now when the cell is sheared the chevron structure smoothly transforms into the tilted layer structure. As each further critical temperature is passed an additional multiple chevron solution is formed which although a high energy, unstable state may be observed transiently. For sufficiently low temperatures the transition from chevron to tilted layer becomes first order. This first order transition occurs as the chevron interface merges with the surface alignment region to form the tilted layer structure. Received 28 December 1998 and Received in final form 8 April 1999     

Different mechanisms of nucleation and self-organization of droplets in ferroelectric smectic membranes

New mechanisms of droplet nucleation and self-organization in ferroelectric membranes are described. The droplets may be accompanied by different number of topological defects (zero, one, two) whose location may be on the droplet boundary or in the membrane. Nucleation and self-organization of droplets with total topological charge S = 0 , S = + 1 and S = - 1 were investigated. We found that an S = - 1 topological defect may be the center of both droplet nucleation and chain formation. This mechanism of chaining drastically differs from the droplet self-organization described earlier which is realized by attraction of droplet-defect pairs. Our observations demonstrate new possibilities for manipulating the inclusions and their self-organization in smectic membranes.     

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     

Identification of a TGBA liquid crystal phase via its defects

We have shown that cholesteryl nonanoate, a thermotropic compound which is well known to exhibit pretransitional effects at the smectic A (SmA) cholesteric (N*) transition (W.L. McMillan, Phys. Rev. A 4, 1238 (1971); 6, 936 (1972)), has in fact a TGBA phase in between. Our arguments rely on the observation of new TGBA defects, either in Robinson spherulites cooled from the N* phase or in free-standing films. The same new defects can be obtained in a well-documented TGBA phase of a tolane compound. We analyze qualitatively the TGBA defects in both geometries, in particular their relation to the disclination radius of the N* Robinson spherulites. Received 12 February 2001     

Optical reflectivity study of synclinic and anticlinic structures in thin freely suspended smectic films

Optical reflectivity studies have been conducted on freely suspended films with synclinic and anticlinic structures. For the first time quantitative data were obtained on orientational ordering in films with anticlinic structure. In the same wide temperature range of more than 30 K we observed both transverse and longitudinal ferroelectricity in the films of the same thickness. Equilibrium transition temperatures between structures with transverse and longitudinal polarization were above the bulk transition temperature to the SmC phase. The molecule tilt was determined in superthin films with synclinic and anticlinic ordering. Received 29 October 1999 and Received in final form 17 February 2000     

Water droplets in a spherically confined nematic solvent: A numerical investigation

Recently, it was observed that water droplets suspended in a nematic liquid crystal form linear chains [Poulin et al., Science 275, 1770 (1997)]. The chaining occurs, e.g., in a large nematic drop with homeotropic boundary conditions at all the surfaces. Between each pair of water droplets a point defect in the liquid crystalline order was found in accordance with topological constraints. This point defect causes a repulsion between the water droplets. In our numerical investigation we limit ourselves to a chain of two droplets. For such a complex geometry we use the method of finite elements to minimize the Frank free energy. We confirm an experimental observation that the distance d of the point defect from the surface of a water droplet scales with the radius r of the droplet like .When the water droplets are moved apart, we find that the point defect does not stay in the middle between the droplets, but rather forms a dipole with one of them. This confirms a theoretical model for the chaining. Analogies to a second order phase transition are drawn. We also find the dipole when one water droplet is suspended in a bipolar nematic drop with two boojums, i.e., surface defects at the outer boundary. Finally, we present a configuration where two droplets repel each other without a defect between them. Received 11 December 1998