Macroscopic behavior of non-polar tetrahedratic nematic liquid crystals

We discuss the symmetry properties and the macroscopic behavior of a nematic liquid crystal phase with D_2d symmetry. Such a phase is a prime candidate for nematic phases made from banana-shaped molecules where the usual quadrupolar order coexists with octupolar (tetrahedratic) order. The resulting nematic phase is nonpolar. While this phase could resemble the classic D _∞h nematic in the polarizing microscope, it has many static as well as reversible and irreversible properties unknown to nonpolar nematics without octupolar order. In particular, there is a linear gradient term in the free energy that selects parity leading to ambidextrously helical ground states when the molecules are achiral. In addition, there are static and irreversible coupling terms of a type only met otherwise in macroscopically chiral liquid crystals, e.g. the ambidextrous analogues of Lehmann-type effects known from cholesteric liquid crystals. We also discuss the role of hydrodynamic rotations about the nematic director. For example, we show how strong external fields could alter the D_2d symmetry, and describe the non-hydrodynamic aspects of the dynamics, if the two order structures, the nematic and the tetrahedratic one, rotate relative to each other. Finally, we discuss certain nonlinear aspects of the dynamics related to the non-commutativity of three-dimensional finite rotations as well as other structural nonlinear hydrodynamic effects.     

Polar nano-rods under shear: From equilibrium to chaos

The orientational dynamics of rod-like particles with permanent (electric or magnetic) dipole moments in a plane Couette shear flow is investigated using mesoscopic relaxation equations combined with a generalized Landau free energy. The free energy contribution due to the coupling between average alignment and dipole orientation is derived on a microscopic basis. Numerical results of the resulting eight-dimensional dynamical system are presented for the case of longitudinal dipoles and thermodynamic conditions where the equilibrium state is a (polar or non-polar) nematic. Solution diagrams reveal presence of a large variety of periodic, transient chaotic, and chaotic dynamic states of the average alignment and dipole moment, respectively, appearing as a function of Deborah number and tumbling parameter. Compared to rods without dipoles we observe a significant preference of out-of-plane kayaking-tumbling states and, generally, a higher sensitivity to the initial conditions including bistability. We also demonstrate that the average (electric) dipole moment characterizing most of the observed states yields electrodynamic (magnetic) fields of measurable strength.     

On the Possibility of the Precise Test of Interatomic Interaction Potentials Using the Effect of Anomalous Light-Induced Drift

The dynamics of the orientational structure of chiral nematic (CN) droplets in an isotropic medium in dc and ac electric fields is investigated by the polarized light microscopy technique. It is shown theoretically that the dynamics of rotational processes in these kinds of systems is determined by electroconvective processes developing due to the flexoelectric polarization associated with the initial configuration of the director field in droplets. It is established experimentally that the linear and quadratic regions of dependence of the rotational velocity of droplets on the electric field strength are explained by the above-mentioned mechanisms. Numerical simulation on the basis of the approach developed gives good agreement with experimental data.     

Representation of pair correlations in nematics

A complete expansion of equilibrium pair correlation functions for a uniaxial nematic phase composed of axially symmetric, non-polar and chiral molecules is proposed. Full advantage is taken of the symmetry of the nematic state and of the molecules. The explicit analysis and classification of the terms involving spherical harmonics with indices not exceeding 4 is given and illustrated using computer simulations for the nematic phase of a Gay-Berne mesogen. The theory is contrasted with the commonly used approach employing invariants that describe orientational correlations in molecular fluids. The role of the new representation in obtaining a correct understanding of a variety of observables, like the elastic constants, is demonstrated. In particular, the long-standing puzzle concerning the splay-bend degeneracy is resolved. Received 11 April 2000 and Received in final form 19 July 2000     

Effect of a strong electric field on a nematogen: evidence for polar short range order

We present experimental studies on the effect of strong electric fields on the nematogen p-cyanophenyl p-n-heptyl benzoate which has the strongly polar cyano end group and a large positive dielectric anisotropy. We use a local temperature measurement to take into account heating effects and an electrical impedance analysis to determine both the dielectric constant () and the resistance (R) of the sample. We also measure the higher harmonic responses of the medium. The new results obtained in this study are: (i) a detailed temperature dependence of the terms which describe (a) the quenching of macroscopic thermal fluctuations of the nematic director and (b) the enhancement of the orientational order parameter due to Kerr effect, (ii) clear evidence for the critical divergence of susceptibility as reflected in the third harmonic signal, (iii) an unusual enhancement of the conductivity which shows a large peak just below the critical point , (iv) a significant peak in the second harmonic signal at and (v) evidence for a field induced nematic-nematic transition well inside the nematic range. We argue that the results (iii)-(v) indicate the presence of polar short range order in the medium and hence support a molecular model in which such an order has been proposed. Received: 15 July 1997 / Received in final form: 24 September 1997 / Accepted: 29 October 1997     

Phase Behavior of Bow-Shaped Hard Particles in Two Dimensions

The phase behavior of a two-dimensional hard-particle model is studied via Monte Carlo simulations using the grand canonical, the isobaric and the canonical ensembles. This model consists of a three-segmented line whose geometry resembles a bow shape. The model reduces to some limiting cases: hard needles and bent-core particles. Manipulating the molecular parameters, a variety of molecular shapes were generated. As a result, several liquid crystalline structures like nematic and tetratic were obtained. Additionally, there are some other regions where the molecules form curvilinear paths. As the density increases, the formation of clusters of two or more particles is observed, producing assemblies with different shapes depending on the particular values of the molecular parameters. One interesting example is when the clusters have chiral features despite the particles are achiral. The two-dimensional tetratic, nematic and polar order parameters as well as the orientational correlation functions g ₂(r ^?) and g ₄(r ^?) and the distribution functions g _∥ and g _⊥ were calculated to describe the resulting mesophases. Besides this, the Gibbs ensemble was used to investigate some cases where indications of first-order phase transitions appeared. The mesophases diagrams are also reported.     

Fluctuations of orientational order in a uniaxial nematic liquid crystal with biaxial molecules and its response to an external field

Homogeneous thermal fluctuations of the orientational order parameters S and G of biaxial molecules in a uniaxial nematic liquid crystal are investigated in the framework of the molecular-statistical theory. It is demonstrated that the molecular biaxiality significantly affects the order parameters S and G, their temperature dependences in the nematic phase, the amplitude and the temperature dependence of the order parameter fluctuations in the nematic and isotropic phases, and the character of the transition from the nematic phase to the isotropic liquid phase. It is established that the fluctuations of the parameters S and G in the nematic phase are related to the temperature dependences of S and G and the susceptibilities χ_S and χ_G of the nematic liquid crystal to external fields, which leads to a change in the parameters S and G at a fixed director orientation. Explanations are offered for the known experimental data on the orientational ordering of biaxial molecules under the action of external fields in the isotropic phase of nematic liquid crystals.     

Simple model for active nematics: quasi-long-range order and giant fluctuations

We propose a simple microscopic model for active nematic particles similar in spirit to the Vicsek model for self-propelled polar particles. In two dimensions, we show that this model exhibits a Kosterlitz-Thouless-like transition to quasi-long-range orientational order and that in this nonequilibrium context, the ordered phase is characterized by giant density fluctuations, in agreement with the predictions of Ramaswamy et al.     

Orientational order parameter studies in two symmetric dimeric liquid crystals – an optical study

The optical technique developed by [W. Kuczynski, B. Zywucki, and J. Malecki, Determination of orientational order parameter in various liquid-crystalline phases, Mol. Cryst. Liq. Cryst. 381 (2002), pp. 1–19; B.J. Zywucki and W. Kuczynski, IEEE transactions on optical phenomena – The orientational order in nematic liquid crystals from birefringence measurements, Dielectr. Electr. Insul. 8 (2001), pp. 512–515] is fabricated and used to determine the orientational order parameter in two dimeric liquid crystalline compounds nematic and SmA phases of α,ω-bis(4-alkylanilinebenzylidene-4′-oxy)alkane (m.OnO.m) homologous series. The compounds studied are 5.O8O.5 and 5.O10O.5 which exhibit nematic and SmA, and nematic phases, respectively. The orientational order parameter in both the phases of nematic and SmA phases of the compound one and the nematic phase of the compound two are obtained using the principle of Newton's rings which gives directly the birefringence, δn of the liquid crystal dimer. The merits of the technique used are presented over the conventional techniques for the determination of orientational order parameter. The results for the two compounds are compared with those values estimated from n _e, n _o and density using the two internal field models due to Vuks and Neugebauer applicable to nematic phase.     

Determination of the Maier-Saupe strength parameter from dielectric relaxation experiments: a molecular dynamics simulation study

Molecular dynamics simulations have been performed to investigate the rotational motion in the nematic and isotropic phases of a model mesogenic system in which the interactions between the molecules are represented by the Gay-Berne potential. First-rank end-over-end rotational relaxation times, analogous to those measured using dielectric relaxation spectroscopy for real mesogens with a longitudinal electric dipole, have been determined as a function of temperature and density. The relaxation times at temperatures throughout the nematic region are found to be larger than the values extrapolated from the isotropic phase to the same temperature. The simulation results are compared with the extended Debye theory for dielectric relaxation in the nematic phase. This relates the reduction in the relaxation rate to the retardation factor which depends on the Maier-Saupe strength parameter, and in turn is defined uniquely by the second-rank orientational order parameter. The simulations indicate that the retardation factor at constant strength parameter is density dependent, a feature neglected in the relaxation theory. We compare the simulation results where possible with experiment.     

Crossover from dilute to majority spin freezing in two leg ladder system Sr(Cu,Zn)2O3

The two-dimensional electron gas (2DEG) in moderate magnetic fields in ultraclean AlAs-GaAs heterojunctions exhibits transport anomalies suggestive of a compressible anisotropic metallic state. Using scaling arguments and Monte Carlo simulations, we develop an order parameter theory of an electron nematic phase. The observed temperature dependence of the resistivity anisotropy behaves like the orientational order parameter if the transition to the nematic state occurs at a finite temperature T(c) approximately 65 mK, and is slightly rounded by a small background microscopic anisotropy. We propose a light scattering experiment to measure the critical susceptibility.     

Threshold effects in homeotropically oriented nematic liquid crystals in an external electric field

The electric field-induced orientational transition in a homeotropically oriented nematic liquid crystal cell is investigated. The interaction with the field as a result of anisotropy of the permittivity and flexoelectric polarization is taken into account. For an arbitrary energy of interaction of the nematic with the substrate simple relations are derived for determining the threshold characteristics of the phase transition. It is shown that, in contrast with planar orientation, in fields above a critical value a periodic structure can occur only by virtue of the flexoelectric effect. The resulting dependences for the threshold parameters in the given geometry are exceptionally useful for determining experimentally the surface energy and the difference in the flexoelectric coefficients. Zh. éksp. Teor. Fiz. 116, 543–550 (August 1999)     

Influence of dipole-dipole correlations on the stability of the biaxial nematic phase in the model bent-core liquid crystal

A molecular theory of biaxial nematic ordering in the system of bent-core molecules has been developed in the two-particle cluster approximation which enables one to take into account short-range polar correlations determined by both electrostatic dipole-dipole interaction and polar molecular shape. All orientational order parameters and short-range correlation functions are calculated numerically as functions of temperature in the uniaxial and in the biaxial nematic phases, and the results are compared with the ones obtained in the mean-field approximation and in the cluster approximation but without taking into consideration the dipole-dipole interaction. It is shown that short-range polar correlations and, in particular, the dipole-dipole correlations dramatically increase the temperature of the transition into the biaxial nematic phase and enhancing its stability range. The results are also very sensitive to the value of the opening angle of a model bent-core molecule.     

Effect of high electric fields on the nematic to isotropic transition in a material exhibiting large negative dielectric anisotropy

We report the experimental high electric field phase diagram of a nematic liquid crystal which exhibits a large negative dielectric anisotropy. We measure simultaneously the birefringence (Δn) and the dielectric constant (epsilon_⊥) at various applied fields as functions of the local temperature of an aligned sample. We also measure the higher harmonics of the electrical response of the medium. The following experimental results are noted: (i) enhancement of orientational order parameter S in the nematic phase due to both the Kerr effect and quenching of director fluctuations; (ii) enhancement in the paranematic to nematic transition temperature (T_PN) with field; (iii) divergence of the order parameter susceptibility beyond the tricritical point as measured by third harmonic electrical signal; (iv) a small second harmonic electrical signal which also diverges near T_PN, indicating the presence of polarised domains. Our measurements show that ΔT_PN(= T_PN(E)-T_NI(0)) varies linearly with |E| whereas the Landau de Gennes theory predicts a dependence on E². It is argued that the quenching of director fluctuations by the field makes the dominant contribution to all the observations, including the thermodynamics of the transition.     

The McMillan parameter as an effective field variable for the nematic–smectic tricritical point in NO.M compounds

The dependence of the coupling of orientational and translational order parameters on the nematic-smectic A tricritical point (TCP), observed through birefringence experiments in the pure compounds and in the binary mixtures in the homologous series of N(p-n-alkyloxybenzylidene)p-n-alkylanilines, results in a mean field tricritical exponent. The McMillan parameter, M = T _NA/T _NI (where T _NA and T _NI are the smectic A—nematic (AN) and the nematic—isotropic (NI) phase transition temperatures respectively), is used as an effective and relevant field variable in analysing the TCP. The observed linear dependence of the jump in the orientational order parameter with new density variables in the tricritical region is found to be consistent with the results obtained from both the Landau mean field and the decoupled mean field models. The width of the mean field tricritical region is discussed in terms of the McMillan parameter. Further, the McMillan parameter is observed to be characteristic of chemical composition at the NA tricritical point.     

Orientational transitions in antiferromagnetic liquid crystals

The orientational phases in an antiferromagnetic liquid crystal (ferronematic) based on the nematic liquid crystal with the negative anisotropy of diamagnetic susceptibility are studied in the framework of the continuum theory. The ferronematic was assumed to be compensated; i.e., in zero field, impurity ferroparticles with the magnetic moments directed parallel and antiparallel to the director are equiprobably distributed in it. It is established that under the action of a magnetic field the ferronematic undergoes orientational transitions compensated (antiferromagnetic) phase–non-uniform phase–saturation (ferrimagnetic) phase. The analytical expressions for threshold fields of the transitions as functions of material parameters are obtained. It is shown that with increasing magnetic impurity segregation parameter, the threshold fields of the transitions significantly decrease. The bifurcation diagram of the ferronematic orientational phases is built in terms of the energy of anchoring of magnetic particles with the liquid-crystal matrix and magnetic field. It is established that the Freedericksz transition is the second-order phase transition, while the transition to the saturation state can be second- or first-order. In the latter case, the suspension exhibits orientational bistability. The orientational and magnetooptical properties of the ferronematic in different applied magnetic fields are studied.     

Rotational reorientation of the director in twisted nematic liquid-crystal cells

The orientational relaxation of the director to its equilibrium orientation under electric, elastic, and viscous torques arising in twisted nematic liquid-crystal cells is investigated. It is shown that the relaxation time of the director depends strongly on the external electric field strength and weakly on the energy of anchoring of liquid-crystal molecules to the surfaces of the cell. The relaxation time of the director anomalously increases in electric fields close to the Fréedericksz threshold. It is established that, at specific strengths of the external electric field, the relaxation can occur in the form of traveling waves propagating from one edge to the other edge of the twisted nematic liquid-crystal cell. The calculations of the relaxation processes in the vicinity of the nematic-smectic A phase transition temperature demonstrate that the distortion of the director field is uniform over the entire cross section of the liquid-crystal cell and does not depend on the strength of anchoring of the liquid-crystal molecules to the surfaces of the cell.     

Refractive index and orientational order parameter of a polar–polar binary system showing induced smectic Ad and re-entrant nematic phases

Refractive index measurements have been done on a polar–polar binary system, 4-cyanophenyl [4′(4″-n-heptylphenyl)] benzoate (7CPB)?+?4-cyanophenyl-4-nonylbenzoate (9.CN), exhibiting nematic–smectic A_d–re-entrant nematic phase sequence using thin prism technique. From refractive index as well as density data, the polarizability anisotropy in the mesomorphic state has been calculated from the standard Vuks model and the orientational order parameter (?P ₂?) values have been determined. By measuring the refractive indices and density in the solid phase, the validity of the Haller's extrapolation method for systems having higher order phases has been verified. The temperature variation of the density, birefringence, and ?P ₂? values at the nematic–smectic A_d and smectic A_d–re-entrant nematic transitions for all the mixtures are found to be continuous. The experimental ?P ₂? values have been compared with our previous X-ray data and also those calculated from the Luckhurst and Timimi model.     

Optically switchable, polarization-independent holographic polymer dispersed liquid crystal (H-PDLC) gratings

An optically switchable, polarization-independent holographic polymer dispersed liquid crystal (H-PDLC) transmission grating is demonstrated by adding azobenzene-LC and chiral molecules into the H-PDLC formulation. The optical switchable mechanism is from the trans-cis photoisomerization of the doped azobenzene-LC, which modulates the refractive index of the LC rich area. The dependence of the diffraction efficiency of the H-DPLC grating without chiral molecules on light polarization suggests that the orientation of LC directors within the droplet is ellipsoidal and uniaxial. However, the addition of chiral molecules into the H-PDLC formulation helps the formation of isotropic and non-uniaxial LC directors within the droplets. The polarization properties of the grating are investigated and analyzed by the coupled and modified coupled wave theory with a model of sinusoidal dielectric modulation. The results show that the addition of chiral molecules changes the LC phase from nematic to chiral-nematic, where the grating efficiency, which is modulated by the photoinduced phase transition, is independent of the polarization of incident light. Our findings may help improve optical systems that utilize non-polarized light.