Dynamics Of Nematic Liquid Crystals Research Articles

A Two-Fluid Model for the Macroscopic Behavior of Nematic Fluids and Gels in a Chiral Solvent

We present the macroscopic dynamics of nematic liquid crystals in a two-fluid context. We investigate the case of a nematic in a chiral solvent as well as of a cholesteric in a non-chiral solvent. In addition, we analyze how the incorporation of a strain field for nematic gels and elastomers in a chiral solvent modifies the macroscopic dynamics. It turns out that the relative velocity between the nematic subsystem and the chiral solvent gives rise to a number of cross-coupling terms, reversible as well as irreversible, unknown from other two-fluid systems considered so far. Possible experiments to study those novel dynamic cross-coupling terms are suggested. As examples we just mention that gradients of the relative velocity lead, in cholesterics to heat currents. We also find that in cholesterics shear flows give rise to a temporal variation in the velocity difference perpendicular to the shear plane, and in cholesteric gels uniaxial stresses or strains generate temporal variations of the velocity difference. Finally, the exotic chiral Q phase of tetragonal (D_4) symmetry is analyzed for an isotropic non-chiral solvent in a two-fluid scenario.

Diamagnetic anisotropy and rotational viscosity of 6CHBT nematic liquid crystal

Nematic liquid crystal with polar terminal NCS group was studied by using acoustic and electro-optical methods. Experimental results on rotational viscosity have been obtained by two methods. The anisotropy of diamagnetic susceptibility of the studied LC with temperature variation was determined based on the comparison of these methods. The present results may be useful for testing physical models of the orientation dynamics of nematic liquid crystals in alternating electric and magnetic fields.

Phase-field model of topological charge interaction force in nematic liquid crystals

ABSTRACT Nematic liquid crystals (LCs) normally contain both integer and half-integer topological charges. In this work, we investigate topological charge evolution dynamics in nematic LCs by the phase-field model. We observe the annihilation of the topological charge, and the total number of charges decreases to two cores with time evolution in a disk. A significant decrease in charges is observed during the initial evolution. The positive topological charge and negative topological charge annihilate depending on the distance between two charges, which can be treated as the interaction force. The form of interaction force is similar to Coulomb’s law, but the force is inversely the distance of defects instead of the square of the distance in Coulomb’s law. Therefore, the present study contributes to the understanding of topological charge evolution dynamics and provides guidance for experiments to design in nematic LCs.

Multiwall carbon nanotube-nematic liquid crystal composite system: preparation and characterization

The present study reveals the efficacious change in carbon nanotube (CNT) doped nematic liquid crystals (NLC). Herein, the optical and dielectric properties have been measured and a notable change in CNT doped systems is observed in compare to pristine NLC. Modification in different parameters of pristine LC material has shown its strong dependence on the concentration of CNTs. For optical study the photoluminescence, UV-absorbance, and Fourier transform infrared spectroscopy (FTIR) has been performed. An enhancement in photoluminescence without any shift in peak value is observed for both composite systems. In UV-absorbance study, it is noticed that absorbance has been increased after doping the CNTs in NLC system. The constructive combination of emerging waves might be the reason behind such enhancement. FTIR study confirms the influence of CNTs on the molecular dynamics of NLC. Dielectric measurement shows the enhanced value to dielectric permittivity and reduction in dielectric loss at lower frequency region. Conductivity changes its value up to double unit, since the CNTs are highly conducting along the long axis. A shift in relaxation frequency for both composites has been observed in tan delta study.

The molecular dynamics of nematic liquid crystal confined in porous membranes treated by different surfactants

The molecular dynamics of the well-known nematic liquid crystal 4-n-pentyl-4′-cyanobiphenyl geometrically restricted in Anopore and Synpor porous membranes with various pore structure and treated by different surfactants (namely decanoic acid and lecithin) is compared. In the Anopore membrane the chosen surfactants induce the homeotropic orientation of the molecules on the walls of the cylindrical pores and observed corresponding relaxation processes (librational modes) are practically the same. The dielectric measurements of lecithin treated Synpor membranes reveals the reorientation of the molecules from planar to homeotropic on the complex multilayer structure present in their volume. The dielectric strengths of the observed two molecular processes (δ-process and librational mode) are inversed in the ratio compared to the untreated membranes. The observed differences in molecular dynamics results from the orientation of the liquid crystal molecules in untreated and treated membranes and the structure of the membranes themselves.

Multiparticle collision dynamics for tensorial nematodynamics.

Liquid crystals establish a nearly unique combination of thermodynamic, hydrodynamic, and topological behavior. This poses a challenge to their theoretical understanding and modeling. The arena where these effects come together is the mesoscopic (micron) scale. It is then important to develop models aimed at capturing this variety of dynamics. We have generalized the particle-based multiparticle collision dynamics (MPCD) method to model the dynamics of nematic liquid crystals. Following the Qian-Sheng theory [Phys. Rev. E 58, 7475 (1998)1063-651X10.1103/PhysRevE.58.7475] of nematics, the spatial and temporal variations of the nematic director field and order parameter are described by a tensor order parameter. The key idea is to assign tensorial degrees of freedom to each MPCD particle, whose mesoscopic average is the tensor order parameter. This nematic MPCD method includes backflow effect, velocity-orientation coupling, and thermal fluctuations. We validate the applicability of this method by testing (i) the nematic-isotropic phase transition, (ii) the flow alignment of the director in shear and Poiseuille flows, and (iii) the annihilation dynamics of a pair of line defects. We find excellent agreement with existing literature. We also investigate the flow field around a force dipole in a nematic liquid crystal, which represents the leading-order flow field around a force-free microswimmer. The anisotropy of the medium not only affects the magnitude of velocity field around the force dipole, but can also induce hydrodynamic torques depending on the orientation of dipole axis relative to director field. A force dipole experiences a hydrodynamic torque when the dipole axis is tilted with respect to the far-field director. The direction of hydrodynamic torque is such that the pusher- (or puller-) type force dipole tends to orient along (or perpendicular to) the director field. Our nematic MPCD method can have far-reaching implications not only in modeling of nematic flows, but also to study the motion of colloids and microswimmers immersed in an anisotropic medium.

The small Deborah number limit of the Doi–Onsager equation without hydrodynamics

We study the small Deborah number limit of the Doi–Onsager equation in the case when hydrodynamic effects are neglected. This is a Smoluchowski-type equation that describes the dynamics of nematic liquid crystals at a molecular level, by characterizing the evolution of a number density function, depending upon both particle position x∈Rd(d=2,3) and orientation vector m∈S2 (the unit sphere). We prove that, when the Deborah number tends to zero, the family of solutions with rough initial data near local equilibria will converge strongly to a local equilibrium distribution prescribed by a weak solution of the harmonic map heat flow into S2. This flow is a special case of the gradient flow of the well known Oseen–Frank energy functional for nematic liquid crystals. The key ingredient is to show the strong compactness of the family of number density functions. The proof relies on the strong compactness of the corresponding Q-tensor (namely the second moment), a detailed analysis of the linearized operator near the limit local equilibrium distribution, and an energy dissipation estimate.

Temporal dynamics of light-written waveguides in unbiased liquid crystals

The control of light by light is one of the main aims in modern photonics. In this context, a fundamental cornerstone is the realization of light-written waveguides in real time, resulting in all-optical reconfigurability of communication networks. Light-written waveguides are often associated with spatial solitons, that is, non-diffracting waves due to a nonlinear self-focusing effect in the harmonic regime. From an applicative point of view, it is important to establish the temporal dynamics for the formation of such light-written guides. Here we investigate theoretically the temporal dynamics in nematic liquid crystals, a material where spatial solitons can be induced using continuous wave (CW) lasers with few milliWatts power. We fully address the role of the spatial walk-off and the longitudinal nonlocality in the waveguide formation. We show that, for powers large enough to induce light self-steering, the beam undergoes several fluctuations before reaching the stationary regime, in turn leading to a much longer formation time for the light-written waveguide.

Shear flow dynamics in the Beris-Edwards model of nematic liquid crystals.

We consider the Beris-Edwards model describing nematic liquid crystal dynamics and restrict it to a shear flow and spatially homogeneous situation. We analyse the dynamics focusing on the effect of the flow. We show that in the co-rotational case one has gradient dynamics, up to a periodic eigenframe rotation, while in the non-co-rotational case we identify the short- and long-time regimes of the dynamics. We express these in terms of the physical variables and compare with the predictions of other models of liquid crystal dynamics.

Insensitivity of active nematic liquid crystal dynamics to topological constraints.

Confining a liquid crystal imposes topological constraints on the orientational order, allowing global control of equilibrium systems by manipulation of anchoring boundary conditions. In this article, we investigate whether a similar strategy allows control of active liquid crystals. We study a hydrodynamic model of an extensile active nematic confined in containers, with different anchoring conditions that impose different net topological charges on the nematic director. We show that the dynamics are controlled by a complex interplay between topological defects in the director and their induced vortical flows. We find three distinct states by varying confinement and the strength of the active stress: A topologically minimal state, a circulating defect state, and a turbulent state. In contrast to equilibrium systems, we find that anchoring conditions are screened by the active flow, preserving system behavior across different topological constraints. This observation identifies a fundamental difference between active and equilibrium materials.

Impact of ferroelectric and superparaelectric nanoparticles on phase transitions and dynamics in nematic liquid crystals.

Results of broadband dielectric spectroscopy (BDS) studies of pure liquid crystalline (4-pentyloxy-4-biphenylcarbonitryle) 5OCB and its nanocolloids with BaTiO_{3} nanoparticles (NPs) under varying pressure and temperature are presented. The notable impact of NPs on phase transitions and dynamics was found. Particularly strong impact on pretransitional behavior was observed for relatively low concentrations of NPs, which can be related to the NPs-induced disorder. There are also notable differences between pressure and temperature paths of studies for nanocomposites, absent for the pure LC compound. For instance, tests focused on the translational orientational decoupling via the fractional Debye-Stokes-Einstein relation yielded S=0.71 and S=0.3 for the temperature and pressure paths, respectively: S=1 is for the complete coupling. The possible theoretical frame of observed phenomena is also proposed.

Global solvability of the inhomogeneous Ericksen–Leslie system with only bounded density

The most established theory for modeling the dynamics of nematic liquid crystals is the celebrated Ericksen–Leslie system, which presents some major analytical challenges. We study a simplified version of the system, which still exhibits the major difficulties. We consider the density-dependent case and study the Cauchy problem in the whole space. We establish the global existence of solutions for small initial data by assuming only that the initial density is bounded and kept away far from vacuum, while the initial velocity and the gradient of the initial director field belong to certain critical Besov spaces. Under slightly more assumptions on the initial velocity and the director field, we also prove that the solutions are unique.

Generalization of the Ericksen-Leslie theory.

We generalize the Ericksen-Leslie theory for the dynamics of nematic liquid crystals by including the director-density coupling energy [Formula: see text]. It corresponds to the cost in energy due to the interaction of spatially varying mass density [Formula: see text] and the liquid crystal director [Formula: see text]. A striking confirmation of the theory is achieved by confronting it with experimental data on acoustical Fréedericksz transition.

A note on the stochastic Ericksen-Leslie equations for nematic liquid crystals

In this note we prove the existence and uniqueness of local maximal smooth solution of the stochastic simplified Ericksen-Leslie systems modelling the dynamics of nematic liquid crystals under stochastic perturbations.

Local discontinuous Galerkin schemes for a nonlinear variational wave equation modelling liquid crystals

We consider a nonlinear variational wave equation that models the dynamics of nematic liquid crystals. Discontinuous Galerkin schemes that either conserve or dissipate a discrete version of the energy associated with these equations are designed. Numerical experiments illustrating the stability and efficiency of the schemes are presented. An interesting feature of these schemes is their ability to approximate two distinct weak solutions of the underlying system.

Elastic constants and dynamics in nematic liquid crystals

In this paper, we present molecular dynamics calculations of the Frank elastic constants, and associated time correlation functions, in nematic liquid crystals. We study two variants of the Gay–Berne potential, and use system sizes of half a million molecules, significantly larger than in previous studies of elastic behaviour. Equilibrium orientational fluctuations in reciprocal (k-) space were calculated, to determine the elastic constants by fitting at low |k|; our results indicate that small system size may be a source of inaccuracy in previous work. Furthermore, the dynamics of the Gay–Berne nematic were studied by calculating time correlation functions of components of the order tensor, together with associated components of the velocity field, for a set of wave vectors k. Confirming our earlier work, we found exponential decay for splay and twist correlations, and oscillatory exponential decay for the bend correlation. In this work, we confirm similar behaviour for the corresponding velocity components. In all cases, the decay rates, and oscillation frequencies, were found to be accurately proportional to k2 for small k, as predicted by the equations of nematodynamics. However, the observation of oscillatory bend fluctuations, and corresponding oscillatory shear flow decay, is in contradiction to the usual assumptions appearing in the literature, and in standard texts. We discuss the advantages and drawbacks of using large systems in these calculations.

Stick-slip motion of surface point defects prompted by magnetically controlled colloidal-particle dynamics in nematic liquid crystals

We explore the dynamics of topological point defects on surfaces of magnetically responsive colloidal microspheres in a uniformly aligned nematic liquid crystal host. We show that pinning of the liquid crystal director to a particle surface with random nanostructured morphology results in unexpected translational dynamics of both particles and topological point defects on their surfaces when subjected to rotating magnetic fields. We characterize and quantify the "stick-slip" motion of defects as a function of field rotation rates as well as temperature, demonstrating the roles played by the competition of elastic forces, surface anchoring, and magnetic torques on the sphere as well as random-surface-mediated pinning of the easy axis of the nematic director on colloidal microspheres. We analyze our findings through their comparison to similar dynamic processes in other branches of science.

Equivalent Theories of Liquid Crystal Dynamics

There are two competing descriptions of nematic liquid crystal dynamics: the Ericksen-Leslie director theory and the Eringen micropolar approach. Up to this day, these two descriptions have remained distinct in spite of several attempts to show that the micropolar theory comprises the director theory. In this paper we show that this is the case by using symmetry reduction techniques and introducing a new system that is equivalent to the Ericksen-Leslie equations and includes disclination dynamics. The resulting equations of motion are verified to be completely equivalent, although one of the two different reductions offers the possibility of accounting for orientational defects. After applying these two approaches to the ordered micropolar theory of Lhuiller and Rey, all the results are eventually extended to flowing complex fluids, such as nematic liquid crystals.

Modelling spreading dynamics of nematic liquid crystals in three spatial dimensions

AbstractWe study spreading dynamics of nematic liquid crystal droplets within the framework of the long-wave approximation. A fourth-order nonlinear parabolic partial differential equation governing the free surface evolution is derived. The influence of elastic distortion energy and of imposed anchoring variations at the substrate are explored through linear stability analysis and scaling arguments, which yield useful insight and predictions for the behaviour of spreading droplets. This behaviour is captured by fully nonlinear time-dependent simulations of three-dimensional droplets spreading in the presence of anchoring variations that model simple defects in the nematic orientation at the substrate.

Homogenization of the equations of dynamics of nematic liquid crystals with inhomogeneous density

Homogenization of the equations of dynamics of nematic liquid crystals with inhomogeneous density