Induced ferrielectricity in antiferroelectric liquid crystals

The behaviour of the antiferroelectric SmC_A liquid crystal phase under applied electric field is discussed theoretically. The phase diagram involving the SmA, SmC_A and SmC _A ^* phases is worked out and shown to exhibit a Lifshitz critical point. The deformation of the bilayer structures induced by the field transforms the SmC_A phases into a ferrielectric phase whose specific configuration is described. Received: 23 October 1997 / Revised: 8 April 1998 / Accepted: 14 July 1998     

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.     

Orientational phase transition and the solvation force in a nematic liquid crystal confined between inhomogeneous substrates

A nematic liquid crystal confined between two identical flat solid substrates, with an alternating stripe pattern of planar and homeotropic anchoring, is studied in the framework of the Frank-Oseen theory. By means of numerical minimization of the free energy functional we study the effect of the sample thickness D on the location of the phase transition between a uniform alignment, either planar or homeotropic, and a distorted nematic texture. The solvation force f due to distortions of the nematic director is also studied. It is found that f is always attractive, and for D small compared to the periodicity of the surface structure it exhibits two distinct asymptotic behaviors: f ∼ - D ^-1/2 or f ∼ - D ^-1, depending on the relation between D and the extrapolation lengths. Received 12 November 2002 Published online: 16 April 2003     

Rectangular to hexagonal columnar phase transition exhibited by a biforked mesogen

We present the structural study of a biforked compound exhibiting a Col_r-Col_h phase transition. This study was performed by means of DSC, optical microscopy, X-ray diffraction, dilatometry and molecular modelling. The molecular packing within the two columnar mesophases of this compound is discussed. For the first time, it is shown that the clusters of adjacent molecules which form the elementary section of a column are tilted with respect to the columnar axis in the rectangular mesophase. From the whole set of experimental data, the number of molecules in a columnar section is found to be about 5 in the rectangular mesophase, and 4 in the hexagonal one. The transition between the two columnar mesophases is discussed with respect to its slow kinetics. Received 1st October 2002 Published online: 16 April 2003 RID="a" ID="a"e-mail: ribeiro@cii.fc.ul.pt RID="b" ID="b"UMR 7504     

Effect of aerosil dispersions on the nematic-to-isotropic interface

The effect of silica aerosils on the kinetics of the first-order nematic-isotropic (NI) phase transition is phenomenologically described in the framework of the time-dependent Landau-Ginzburg equation. A steady-state solution to the equation is presented such that the NI interface may propagate with a solitary-like wave profile under constant quenching. The results provide a plausible basis for the interpretation of the dynamical effects of quenched disorder in the liquid-crystal systems, caused by randomly interconnected porous media, such as aerosils. In the low silica aerosil ρ_s ( ≤0.1 g/cm^3) regime, the calculated values of the interface velocity v(T,ρ_s), the interface thickness κ(T,ρ_s), and the critical radius of a spherical nucleus of new nematic phase in a bulk isotropic environment, composed of polar molecules, such as 4-n-octyl- 4^′- cyanobiphenyl and 4-n-heptyl- 4^′- cyanobiphenyl shows that the effect of silica aerosils on the kinetics is reflected in a shifting of the set of temperature-dependent curves to lower temperature values.-1     

Probing the material properties and phase transitions of ferroelectric liquid crystals by determination of the Landau potential

The full Landau potential of several, widely varying ferroelectric liquid-crystalline materials has been experimentally determined. Tilt angle and polarisation data is analysed across the SmA to SmC transition for varying applied electric-field amplitudes, allowing the determination of all the coefficients of the generalised Landau model of ferroelectric liquid crystals. The materials investigated encompass different materials, including low-polarisation mixtures to high-polarisation single-component materials. The materials also possess a variation in the order of the SmA to SmC phase transition from strongly first order to strongly second order. The effects of both the polarisation and order of phase transition of the system are discussed with respect to the various terms of the generalised Landau model. Further, the mechanisms behind the difference between a first- and second-order phase transition are discussed with respect to the Landau potential and the second Landau coefficient b .     

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.     

Elastic energies for nematic elastomers

We discuss several elastic energies for nematic elastomers and their small strain expansions both in the regime of large director rotations, and in the case that director changes are small. We propose two fully non-linear model anisotropic energies and compare the behavior they predict with the currently available experimental evidence.     

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.     

Reentrant isotropic-calamitic nematic phase transition in potassium laurate-decanol- D<Subscript>2</Subscript>O mixtures

The phase diagram is an interesting field of research, particularly in lyotropic liquid crystals (LLC). In this way, one of the most important phase diagrams of this LLC system was reported by Yu and Saupe. Two uniaxial (calamitic--N(C) and discotic--N(D)) and one biaxial nematic (N(B)) phases were determined by these authors. Furthermore, in this phase diagram the classical isotropic phase (I was observed at high temperature as well as a reentrant isotropic phase (I(RE)) which takes place at lower temperature. Later, this phase diagram was also studied by several authors and in all cases the I(RE)-N(C)-I phase transitions were not observed. In this work, we present a study of this phase diagram through digital image processing and refractometry optical techniques. The occurrence of these phase transitions is investigated and characterized. In addition, the order parameter is obtained based on the Vuks hypothesis from a particular point, in the range of the N(C) phase, where the absolute value of the optical birefringence (Deltan is maximum.     

Experimental study of de Vries properties in antiferroelectric smectic liquid crystals

Results of the experimental study on different antiferroelectric liquid crystal (AFLC) materials are presented using a number of techniques such as the optical birefringence, electro-optics and the measurements of optical thickness of free-standing films. Despite differences in the molecular structures of the various AFLC materials studied, these are found to exhibit a de Vries type of smecticA^* (SmA ^*) properties in a temperature range higher than SmC ^* . This correlation leads to the conclusion that these two classes of liquid crystals are related to each other. Furthermore, we suggest that these arise from the same physical mechanism, namely the existence of the weak synclinic (or reduced anticlinic) correlations between the neighbouring molecular tilt directions.     

Small inclusions in smectic C* free standing films

The creation and the coalescence of inclusions has recently been observed in smectic C* freely suspended films at the temperature near the smectic C*-cholesteric phase transition. A small finite anchoring energy permits to describe small inclusions by analytical approximate solutions of dipolar or quadrupolar type. Using the proposed solutions our model enables us to discuss the coalescence of smallest inclusions and their observed growth. This work was supported by the research project AV0Z1-010-914 and by Grant No. 202/02/0840 of the Grant Agency of the Czech Republic.     

A chiral axial next nearest neighbour xy-model for antiferroelectric liquid crystals

We describe a chiral axial next nearest neighbour xy-model to account for the various subphases exhibited by antiferroelectric liquid crystals made of chiral rod-like molecules. The assumed form of the interlayer interactions is based on physical processes which are discussed. Using a discrete model, the predicted sequence of transitions is SmA-SmC-SmC-FI_H-FI_I-FI_L-SmC ^* A, where FI stands for a ferriphase, as seen in many compounds. The ferri and SmC phases are characterized by relatively large angles between the c-vectors of successive layers and occur only when the compounds have high optical purity. The calculated field induced structures exhibit a plateau of the apparent tilt angle at , where is the tilt angle of the molecules in the ferriphase. The conoscopic figures in the presence of a field and ellipsometric parameters in the absence of a field have also been generated, which agree extremely well with the experimental results. Recent anomalous X-ray scattering studies prove the xy-character of the configurations, though the commensurate structures that are found in the ferriphase require an extension of the model to include lock-in terms. Received 23 August 1999     

Instabilities in nematic elastomers in external electric and magnetic fields

In this paper we study the macroscopic behavior of nematic side-chain liquid single crystal elastomers exposed to an external electric or magnetic field. For this purpose we use the framework of a continuum model. The geometries investigated comprise the bend and the twist geometry known from the classical Frederiks transition in low molecular weight liquid crystals. For the bend geometry we find a laterally homogeneous and a two-dimensional undulatory instability, which may compete at onset. In the case of the twist geometry three instabilities can occur at onset, two of which are two dimensional and clearly show undulations. As a major result we propose how the values of the twist coefficient K(2) and the values of the material parameters D(1) and D(2) connected to relative rotations between the director field and the polymer network can be determined from experimental observations. In addition, we explain why a twist experiment is probably the most suitable set-up in order to measure the material parameter D(1).     

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     

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     

Tilted smectic layers of a liquid crystal between homeotropically treated plates

We investigated SmC^* films sandwiched between silane coated glass plates and observed formation of textures exhibiting a uniform tilt of the smectic layers with respect to the boundary plates. The layer tilt angle increases from zero to as the sample is cooled from the smectic A phase to room temperature. These films show linear electro-optical effects because the permanent polarization can be aligned so that it has a component parallel to the applied field without changing the layer structure. Our analysis indicates that mainly two effects determine the layer tilt. On the one hand, the surface tension tends to minimise the layer tilt. On the other hand, the surface energy promotes the director to be normal to the boundary plates. Received 17 July 1998     

Field-induced realignment of a smectic nanodroplet in an external magnetic field: A numerical investigation

The field-induced realignment of a smectic-A phase is in principle a complicated process involving the director rotation via the interaction with the field and the layer rotation via the molecular interactions. Time-resolved X-ray scattering experiments have revealed major phenomena concerning the maintenance of the integrity of the smectic-A layer structure during the alignment process. In order to obtain a deeper insight into this process, we have carried out a dissipative particle dynamics study of the realignment kinetics of a nanodroplet of a smectic-A liquid crystal suspended in an isotropic fluid following a switch in the direction of an applied magnetic field. The strength of the mesogen-field interaction is small compared to the inter-molecular interactions. The reaction of the smectic configuration to the field switch was found to depend on the balance between the inter-molecular interactions stabilising the formation of the smectic layering and the interaction of the mesogens with the external field. It is found that the rotational behaviour of the smectic layers under the influence of an external magnetic field arises from a combination of stochastic translational displacements and rotational motions of the centres of mass of the mesogens in the nanodroplets. The simulations indicate that X-ray scattering and NMR experiments monitoring the orientational order are sensitive to different aspects of the realignment process.     

Cubic phases of amphiphilic molecular aggregates

Stability and geometry of the lyotropic periodic cubic mesophases are considered in the framework of a general symmetry based phenomenological approach. A limited number of cubic structural types is shown to be formed by amphiphilic molecular aggregates due to the specific nature of self-organizing units. The related thermodynamic models predict topology of phase diagrams and specific features of transitions between isotropic, lamellar, cubic bicontinuous and cubic micellar phases. Received 25 February 1999 and Received in final form 29 June 1999     

On the deflection of light by topological defects in nematic liquid crystals

The influence of controllable parameters like temperature and wavelength on the trajectories of light in a nematic liquid crystal with topological defects is studied through a geometric model. The model incorporates phenomenological details as how the refractive indices depend on such parameters. The deflection of light by the topological defect is then shown to be greater at lower temperatures and shorter wavelengths.