Slow Director Research Articles

Lattice Boltzmann scheme for modeling liquid-crystal dynamics: Zenithal bistable device in the presence of defect motion

A lattice Boltzmann scheme is presented which recovers the dynamics of nematic and chiral liquid crystals; the method essentially gives solutions to the Qian-Sheng [Phys. Rev. E 58, 7475 (1998)] equations for the evolution of the velocity and tensor order-parameter fields. The resulting algorithm is able to include five independent Leslie viscosities, a Landau-deGennes free energy which introduces three or more elastic constants, a temperature dependent order parameter, surface anchoring and viscosity coefficients, flexoelectric and order electricity, and chirality. When combined with a solver for the Maxwell equations associated with the electric field, the algorithm is able to provide a full "device solver" for a liquid crystal display. Coupled lattice Boltzmann schemes are used to capture the evolution of the fast momentum and slow director motions in a computationally efficient way. The method is shown to give results in close agreement with analytical results for a number of validating examples. The use of the method is illustrated through the simulation of the motion of defects in a zenithal bistable liquid crystal device.

Theory of director precession and nonlinear waves in nematic liquid crystals under elliptical shear

We study theoretically the slow director precession and nonlinear waves observed in homeotropically oriented nematic liquid crystals subjected to circular or elliptical Couette and Poiseuille flow and an electric field. From a linear analysis of the nematodynamic equations it is found that in the presence of the flow the electric bend Fréedericksz transition is transformed into a Hopf-type bifurcation. In the framework of an approximate weakly nonlinear analysis we have calculated the coefficients of the modified complex Ginzburg-Landau equation, which slightly above onset describes nonlinear waves with strong nonlinear dispersion. We also derive the equation describing the precession and waves well above the Fréedericksz transition and for small flow amplitudes. Then the nonlinear waves are of diffusive nature. The results are compared with full numerical simulations and with experimental data.

Transverse Nuclear Spin Relaxation Due to Director Fluctuations in Liquid Crystals A Slow-Motional Theory

Transverse nuclear spin relaxation measurements, employing the Carr−Purcell−Meiboom−Gill sequence, can provide detailed information on the dynamics of director fluctuations in liquid crystals. In principle, a full characterization of the rate dispersion of the director modes can be derived from such measurements. However, the rigorous analysis of these experiments is generally hampered by the lack of a time-scale separation between the slow director fluctuations and the transverse magnetization decay. Under these conditions, the use of a fast-motion theory (i.e., Redfield theory) is no longer justified and one should resort to a slow-motional approach based on the stochastic Liouville equation for the simultaneous evolution of the stochastic variables (i.e., the director field) and the spin degrees of freedom. In this paper, explicit expressions for transverse deuteron spin relaxation times are derived without invoking any time-scale separation, on condition that (i) the stochastic variables are described as a multidimensional Gaussian process and that (ii) the spin Hamiltonian linearly depends on the stochastic variables. These are precisely the conditions usually adopted for the modeling of director fluctuations and their relaxation effects in the harmonic approximation. Thus, the present theory allows for a rather general analysis of the transverse magnetization decay in different kinds of experiments. In particular, analytical expressions are derived for the transverse relaxation times in Carr−Purcell−Meiboom−Gill sequences and evaluated as a function of the pulse spacing and the number of cycles in the sequence. It is shown that in the limit of an infinite number of pulses, one can interpret the measured asymptotic relaxation time as a superposition of independent contributions evaluated according to the Luz−Meiboom equation (Luz, Z.; Meiboom, S. J. Chem. Phys. 1963, 39, 366), originally derived within the Redfield limit.

Nematic liquid crystals under oscillatory shear flow

This contribution deals with three types of orientational phenomena generated by oscillatory flow in nematic liquid crystals: (1) Uniform orientational instabilities in the geometry where the director is initially oriented within the flow plane. The instability occurs under rectilinear Poiseuille flow and not under Couette flow. (2) The first instability under rectilinear Couette flow is a bifurcation to a stationary roll pattern with the roll axis perpendicular to the flow direction. The threshold amplitude has been measured for homeotropic alignment and calculated by linear stability analysis. (3) An interesting slow director precession and nonlinear waves which arise in homeotropically aligned nematics exposed to an elliptical shear flow in the bend Fréedericksz distorted state. The experimental data are compared with a theoretical analysis. The precession can also be generated by oscillatory compression.

On the validity of the elastic expansion of the free energy of nematic liquid crystals

The elastic free energy F el of nematic liquid crystals is a truncated power expansion of the free energy F in the gradients of the director field n(r) . In principle, the cut-off distortion length for F el could be estimated from the direct comparison between the elastic terms and the higher order ones. However, in the case of dispersion interactions, the higher order elastic constants diverge and this comparison is not possible. The divergence of the higher order constants poses some doubt about the internal consistency of the elastic expansion itself. In this paper, we use a molecular model of a nematic liquid crystal to calculate the total free energy and its elastic approximation. The two free energies are calculated numerically for some director configurations as a function of the characteristic distortion length L dis. A good agreement between the two free energies is found for slow director fields, and large deviations are observed only if L dis ≈ a, where a is the molecular length. This result demonstrates the validity of the elastic expansion and shows that the higher order terms affect only the behavior at very short length scales.

Molecular dynamics and order of microconfined liquid crystals

A new technique based on the dipolar-correlation effect was applied in combination with field-cycling-relaxometry to study ordering effects and slow director fluctuations in a nematic liquid crystal confined in porous glasses. Both methods demonstrate a strong influence of geometrical confinements on the distribution of director fluctuation modes. The mean-squared fluctuation estimated from the dipolar-correlation effect decreases exponentially with decreasing pore diameter. The critical mean pore size for the onset of bulk behaviour was found to be of the order of 120 nm. Frequency dependences of spin-lattice relaxation times exhibit sudden sharp deviations from the square root law at frequencies below the MHz-range. These changes are assumed to reflect the lack of long wavelength fluctuations in the spectrum of director fluctuation modes due to finite pore sizes.

Fluctuations in Confined Liquid Crystals above Nematic-Isotropic Phase Transition Temperature

The pretransitional fluctuations of tensor order parameter in confined liquid crystals are studied within Landau--de Gennes theory. We show that in the case of homeotropic anchoring and complete wetting of the substrate by the nematic phase, the spectrum of excitations in the paranematic phase is characterized by a soft normal mode, which is associated with fluctuations of thickness of the substrate-aligned boundary layer, and slow director fluctuations in this ordered region.

Characterization of director fluctuations in liquid crystals using the dipolar correlation effect of the stimulated echo

The purpose of this work is to show that the stimulated-echo pulse sequence can be employed for the examination of slow collective motions in ordered systems. In nematics of low molecular weight (4′- n-pentyl-4-cyanobiphenyl) the attenuation of the ratio of the stimulated and primary echo amplitudes was measured as a function of the time delay between the first and the second 90° pulses. The attenuation of the echo quotient as well as the atypical (compared to the isotropic phase) oscillating behavior of the attenuation curves are described by means of stochastically time dependent interactions of dipolar coupled proton pairs. Slow director fluctuations are considered as a mechanism tending to average these interactions. Good agreement with the experimental data was obtained.

Flow-alignment instability and slow director oscillations in nematic liquid crystals under oscillatory flow.

The nonlinear response of a nematic slab subjected to a rectilinear low-frequency oscillatory Couette and Poiseuille flow is investigated theoretically. We find that under Poiseuille flow and with appropriate alignment conditions by surface anchoring and/or magnetic field a state with slow, spontaneous director rotation appears. This may provide a model for the slow director rotations observed in high-frequency Couette flow. \textcopyright{} 1996 The American Physical Society.

A Conspicuous Orientation and Localization of Pyrene in Langmuir Lipid Monolayers

A previous study of pyrene solubilized in Langmuir lipid monolayers of eicosanoic acid (EA) suggests that pyrene is localized close to the water phase (Langmuir 1992, 8, 1366). In this work, we have examined the orientation of pyrene in monolayers of EA and monolayers of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) by means of polarized light spectroscopic methods. At low pyrene concentrations, fluorescence anisotropy experiments reveal that the aromatic plane is preferentially oriented perpendicular to the normal of the monolayer. The deviation from the theoretical value expected for a perfectly planar monolayer is compatible with the existence of slow director fluctuations. The experimental results strongly suggest that the pyrene molecules at low concentrations are located between the monolayer and water, so that the aromatic plane forms an interface. With increasing pyrene concentrations, the orientation of pyrene becomes gradually disordered.

Studies on lipid membranes by two-dimensional Fourier transform ESR: Enhancement of resolution to ordering and dynamics

The first two-dimensional Fourier-transform electron spin resonance (2D-FT-ESR) studies of nitroxide-labeled lipids in membrane vesicles are reported. The considerable enhancement this experiment provides for extracting rotational and translational diffusion rates, as well as orientational ordering parameters by means of ESR spectroscopy, is demonstrated. The 2D spectral analysis is achieved using theoretical simulations that are fit to experiments by an efficient and automated nonlinear least squares approach. These methods are applied to dispersions of 1-palmitoyl-2oleoyl-sn-glycerophosphatidylcholine (POPC) model membranes utilizing spin labels 1-palmitoyl-2-(16-doxyl stearoyl) phosphatidylcholine and the 3-doxyl derivative of cholestan-3-one (CSL). Generally favorable agreement is obtained between the results obtained by 2D-FT-ESR on vesicles with the previous results on similar systems studied by continuous wave (cw) ESR on aligned samples. The precision in determining the dynamic and ordering parameters is significantly better for 2D-FT-ESR, even though the cw ESR spectra from membrane vesicles are resolved more poorly than those from well aligned samples. Some small differences in results by the two methods are discussed in terms of limitations of the methods and/or theoretical models, as well as possible differences between dynamic molecular structure in vesicles versus aligned membranes. An interesting observation with CSL/POPC, that the apparent homogeneous linewidths seem to increase in "real time," is tentatively attributed to the effects of slow director fluctuations in the membrane vesicles.

Probing director fluctuations in liquid crystals. 2H relaxation dispersion of deuterated toluene and p-xylene

Deuterium spin-lattice relaxation rates in toluene-d8 and p-xylene-d10, dissolved in nematic Phase V, have been measured at five different field strengths. The frequency-dependent relaxation behavior can be satisfactorily described by a model in which the molecules undergo small step rotational diffusion in an axially symmetric orienting potential, with contributions from slow director fluctuations. The parameters defining the model are fitted to the relaxation rates of para and methyl deuterons, using a least-squares parameter estimation program. Parameter values obtained are consistent with a physically acceptable set of values of the associated hydrodynamic properties of the solutions, and are in agreement with results obtained previously on 14N relaxation in methylisocyanide. Relaxation rates of ortho and meta deuterons in toluene, and of the ring deuterons in p-xylene lead to a J1/J2 ratio smaller than unity. Moreover, both J1 and J2 are weakly frequency dependent. The former effect may turn up as a consequence of the assumption of axially symmetric diffusion; the frequency dependence of J2 is probably due to second order effects of the director fluctuations.

Linewidth analysis of the proton resonance spectrum of benzene in a nematic solution

A nonaromatic nematic solvent consisting of an equimolar mixture of trans-4- n-butyl and trans-4- n-hexyl-cyclohexane-l-carboxylic acid was used to study the hydrogen NMR spectrum of partially oriented benzene. Variations in linewidths between 0.7 and 2.6 Hz could be observed but there was no strong correlation between splitting frequency and linewidth. The spectrum was analyzed using the Redfield theory considering intramolecular and intermolecular dipolar relaxation separately. Best agreement with the experiment is obtained by combining intermolecular relaxation effects with the zero frequency term of the intramolecular relaxation which gives contributions to the linewidths that are proportional to the square of the splitting frequency. The results indicate that the intermolecular interactions dominate and that intramolecular interactions become of importance only due to relatively slow director fluctuations.