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     

Fluctuations at the domain edges of nematic liquid crystals in two dimensions

Capillary waves and director fluctuations reduce the surface tension of a non-anchoring unbound nematic surface by comparable amounts. These are relatively small effects in three dimensions, but in two dimensions they become more significant. We examine the conditions in two dimensions under which they dominate explicitly within the framework of a model of the Maier-Saupe type. We find that for reasonable physical parameters of the model the onset of the fluctuation dominated regime generally preempts the nematic-isotropic transition. We conclude that processes which are sensitive to line tension, such as Ostwald ripening during two-dimensional liquid-gas phase separation, are much more strongly coupled to anisotropic molecular interactions and associated nematic ordering than in three dimensions. Received 10 February 1999 and Received in final form 29 March 1999     

Polymorphism and chevron layer structure of an antiferroelectric liquid crystal studied by X-ray diffraction

We report X-ray diffraction experiments performed on an antiferroelectric compound exhibiting a very rich polymorphism (). The structural study of the unknown phases only allows us to exclude some phenomenological models. The use of oriented planar samples prepared between solid glass plates generate by cooling from the phase a chevron structure of tilted layers already well characterized for the phase. The extensive analysis of the evolution of the chevron structure through the numerous smectic-smectic phase transitions provides some original information in three distinct areas: fundamental data on the important physical parameters in the chevron structure formation, detection of the smectic-smectic phases transition by small change of the chevron structure, and information on the local molecular order induced by the alignment layer (interaction with a rubbed polymer). Received: 13 November 1996 / Received in final form: 19 January 1997 / Accepted: 30 January 1998     

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     

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     

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     

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     

Structure and elastic properties of a nematic liquid crystal: A theoretical treatment and molecular dynamics simulation

The Frank elasticity constants which describe splay (K ₁), twist (K ₂), and bend (K ₃) distortion modes are investigated for 4-n-pentyl-4'-cyanobiphenyl (5CB) in the nematic liquid crystal. The calculations rest on statistical-mechanical approaches where the absolute values of K _i (i=1,2,3) are dependent on the direct correlation function (DCF) of the corresponding nematic state. The DCF was determined using the pair correlation function by solving the Ornstein-Zernike equation. The pair correlation function, in turn, was obtained from molecular dynamics (MD) trajectory. Three different approaches for calculations of the elasticity constants were employed based on different level of approximation about the orientational order and molecular correlations. The best agreement with experimental values of elasticity constants was obtained in a model where the full orientational distribution function was used. In addition we have investigated the approximation about spherical distribution of the intermolecular vectors in the nematic phase, often used in derivation of various mean-field theories and employed here for the construction of the DCF. We found that this assumption is not strictly valid, in particular a strong deviation from the isotropic distribution is observed for short intermolecular distances. Received 22 March 2000 and Received in final form 9 June 2000     

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     

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     

Free energy of semiflexible polymers and structure of interfaces

The free energy of semiflexible polymers is calculated as a functional of the compositional scalar order parameter and the orientational order parameter of second-rank tensor S_ij on the basis of a microscopic model of wormlike chains with variable segment lengths. We use a density functional theory and a gradient expansion to evaluate the entropic part of the free energy, which is given in a power series of .The interaction term of the free energy is derived with a random phase approximation. For the rigid rod limit, the nematic-isotropic transition point is given by , N and w being the degree of polymerization and the anisotropic interaction parameter, respectively, and the degree of ordering at the transition point is 0.33448. We also find that the contour length of polymer chains becomes larger in a nematic phase than in an isotropic phase. Interface profiles are obtained numerically for some typical cases. In the neighborhood of isotropic-isotropic interfaces, polymer chains tend to align parallel to the interface on the polymer-rich side and perpendicular on the poor side. When an isotropic region and a nematic region coexist, orientational order parallel to the interface is preferred in the nematic region. Received: 28 May 1998 / Revised: 12 August 1998 / Accepted: 8 September 1998     

Effect of surface electric field on the anchoring of nematic liquid crystals

We analyse the influence of adsorbed ions and the resulting surface electric field and its gradient on the anchoring properties of nematics with ionic conductivity. We take into account two physical mechanisms for the coupling of the nematic director with the surface electric field: (i) the dielectric anisotropy and (ii) the coupling of the quadrupolar component of the flexoelectric coefficient with the field gradient. It is shown that for sufficiently large fields near saturated coverage of the adsorbed ions, there can be a spontaneous curvature distortion in the cell even when the anchoring energy is infinitely strong. We also discuss the director distortion when the anchoring energy of the surface is finite. Received: 29 September 1997 / Received in final from: 10 November 1997 / Accepted: 18 November 1997     

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 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.     

The commensurate and incommensurate TGBC^* liquid crystal phases

We propose complements to the Renn model of the liquid crystal TGBC^* phase. We argue that the rotation angle per helislab is spontaneously in the radian range, not too small to limit the energy cost of the twist grain boundaries between the helislabs, not too large to preserve the double twisting efficiency. Taking the elastic interactions between the helislabs into account, we show that the structure may undergo two different lock-ins, provided that the uncontrolled interactions at the sample surfaces are small enough. First, for appropriate values of the elastic constants, an angular lock-in may fix the rotation angle per helislab at values exactly commensurate to π. Three characteristic lengths of the TGBC^* phase, the TGB period and the thicknesses of both the smectic blocks and of the helislabs are then commensurate to one another, with moreover, integer ratios at the most efficient commensurabilities. The TGBC^* phase could thus exist in several versions, incommensurate and commensurate, according to the steps of a restricted Devil's staircase. A second elastic lock-in should then arise in the commensurate TGBC^* phases, to set the arrays of disclination lines between the helislabs in simple rectangular lattices, arranged in a helical manner. Being placed right behind one another, the disclination lines then coincide when observed along the TGB axis. This could explain the typical textures with square or hexagonal grids, observed in oriented samples. The commensurability of the TGBC^* phases could be analyzed with X-ray scattering experiments in the same manner as already reported for the TGBC phase. Received 30 November 1999 and Received in final form 5 May 2000     

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     

Director field configurations around a spherical particle in a nematic liquid crystal

We study the director field around a spherical particle immersed in a uniformly aligned nematic liquid crystal and assume that the molecules prefer a homeotropic orientation at the surface of the particle. Three structures are possible: a dipole, a Saturn-ring, and a surface-ring configuration, which we investigate by numerically minimizing the Frank free energy supplemented by a magnetic-field and a surface term. In the dipole configuration, which is the absolutely stable structure for micron-size particles and sufficiently strong surface anchoring, a twist transition is found and analyzed. We show that a transition from the dipole to the Saturn ring configuration is induced by either decreasing the particle size or by applying a magnetic field. The effect of metastability and the occurrence of hysteresis in connection with a magnetic field are discussed. The surface-ring configuration appears when the surface-anchoring strength W is reduced. It is also favored by a large saddle-splay constant K₂₄. A comparison with recent experiments [#!itapdb:Poulin1997!#,#!itapdb:Poulin1998!#] gives a lower bound for W, i.e., for the interface of water and pentylcyanobiphenyl (5CB) in the presence of the surfactant sodium dodecyl sulfate. Received 2 November 1998     

Anisotropic surface melting in lyotropic cubic crystals

From experiments with ice or metal crystals, in the vicinity of their crystal/liquid/vapor triple points, it is known that melting of crystals starts on their surfaces and is anisotropic. It is shown here by direct observations under an optical microscope that this anisotropic surface melting phenomenon occurs also in lyotropic systems. In the case of C12EO2/water mixture, it takes place in the vicinity of the peritectic Pn3m/L3/L1 triple point. Above the peritectic triple point, where the Pn3m and L1 phases coexist in the bulk, the surface of a Pn3m-in-L1 crystal is composed of (111)-type facets surrounded by rough surfaces. The angular junction suggests that rough surfaces are wet by a L3-like layer while facets stay “dry”. This is analogous to the pre-melting at rough surfaces in solid crystals. Upon cooling below the peritectic triple point, where L3 and L1 phases coexist in the bulk, a thick layer of the L3 phase grows from the pre-melted, rough Pn3m/L1 interface. Simultaneously, facets stay dry and their radius decreases. In this tri-phasic configuration, stable in a narrow temperature range, the L3/L1 and L3/Pn3m interfaces have shapes of constant mean curvature surfaces having common borders: edges of facets.     

Director configuration and dynamics of a nematic liquid crystal around a two-dimensional spherical particle: Numerical analysis using adaptive grids

We study numerically the director and orientational order parameter configurations in a nematic liquid crystal around a two-dimensional spherical particle on the basis of the tensor order parameter formalism. To properly account for the large length scale difference between the particle and the accompanying orientational defect, we devise an adaptive grid scheme in which the lattice spacing is automatically and locally adjusted in response to the spatial gradient of the orientational order parameter. This adaptive grid scheme is useful in studying dynamical as well as static orientational structures. We present a simulation result which shows how a hedgehog defect of topological charge -1 becomes unstable in two dimensions, and splits into a defect pair of topological charge -1/2, located symmetrically around the particle. Received 14 September 2000 and Received in final form 27 December 2000     

Theoretical investigations of rotational phenomena and dielectric properties in a nematic liquid crystal

The molecular dynamics (MD) simulation, based on a realistic atom-atom interaction potential, was performed on 4-n-pentyl-4'-cyanobiphenyl (5CB) in the nematic phase. The rotational viscosity coefficients (RVCs) γ _i, (i = 1, 2) and the ratio of the RVCs λ = - γ ₂/γ ₁ were investigated. Furthermore, static and frequency-dependent dielectric constants and ε were calculated using parameters obtained from the MD simulation. Time correlation functions were computed and used to determine the rotational diffusion coefficient, D _⊥. The RVCs and λ were evaluated using the existing statistical-mechanical approach (SMA), based on a rotational diffusion model. The SMA rests on a model in which it is assumed that the reorientation of an individual molecule is a stochastic Brownian motion in a certain potential of mean torque. According to the SMA, γ _i are dependent on the orientational order and rotational diffusion coefficients. The former was characterized using: i) orientational distribution function (ODF), and ii) a set of order parameters, both derived from analyses of the MD trajectory. A reasonable agreement between the calculated and experimental values of γ _i and λ was obtained. Received 22 March 2000 and Received in final form 8 October 2000