Spectroscopic manifestations of the difference of the local symmetry of calamitic and discoidal nematics

It is shown that the difference in the local symmetry of nematics consisting of rod-shaped and disk-shaped molecules is manifested as an observable qualitative difference in their spectroscopic characteristics. The well-known controversial experimental data are explained. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 12, 805–810 (25 December 1997)     

Quasi-long-range order in nematics confined in random porous media

We study the effect of random porous matrices on the ordering in nematic liquid crystals. The randomness destroys orientational long-range order and drives the liquid crystal into a glass state. We predict two glass phases, one of which possesses quasi-long-range order. In this state the correlation length is infinite and the correlation function of the order parameter obeys a power dependence on the distance. The small-angle light-scattering amplitude diverges but slower than in the bulk nematic. In the uniaxially strained porous matrices two new phases emerge. One type of strain induces an anisotropic quasi-long-range-ordered state while the other stabilizes nematic long-range order.     

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.     

Reorientation dynamics of nematics encapsulated in microscopic volumes in a strong electric field

We theoretically describe a new regime of reorientation of the director field \(\widehat n\) and velocity v of a nematic liquid crystal (LC) encapsulated in a rectangular cell under the action of strong electric field E directed at angle α (~π/2) to the horizontal surfaces bounding the LC cell. The numerical calculations in the framework of nonlinear generalization of the classical Eriksen–Leslie theory showed that at certain relations between the torques and momenta affecting the unit LC volume and E ? E_th, transition periodic structures can arise during reorientation of \(\widehat n\), if the corresponding distortion mode has the fastest response and, thus, suppresses all the rest of the modes, including uniform ones. The position of sites of these periodic structures is affected by the value of field E, angle α, and the character of anchoring of LC molecules to the bounding surfaces. The calculations performed for the nematic formed by 4-n-penthyl-4’-cyanobiphenyl showed that several vortexes can form in an LC cell under the action of reorientation of the nematic field; the boundaries of these vortexes are determined by the positions of periodic structure sites.     

Interface in nematics

Summary The structures of the interface between an isotropic liquid and a nematic liquid crystal and also between different uniaxial nematic phases are studied. It is shown that, at a planar orientation in the case of the nematic-isotropic liquid interface and also at a mutually orthogonal orientation of the director in the case of two nematic phases, the interface has the structure of a biaxial nematic liquid crystal. Work presented at the second USSR-Italy Bilateral Meeting on Liquid Crystals held in Moscow, September 15–21, 1988.     

Breatherlike defects and their dynamics in the one-dimensional roll structure of twisted nematics

The dynamics of the nonsingular defects in the periodic structures of the rolls that appear in π/2-twisted nematic liquid crystals during electroconvection is studied experimentally and theoretically. The roll structures in twisted nematics are characterized by the presence of an axial component of the hydrodynamic flow velocity with opposite directions in neighboring rolls. The critical oscillation frequency of structural defects is quantitatively estimated using a nonlinear equation of motion for roll displacements. It is found that a pair of edge dislocations with topological charges of +1 and–1 nucleates and annihilates periodically during the oscillations of a defect with a nonsingular core. Oscillating defects with a zero topological charge is shown to correspond to the solution of the sine-Gordon equation in the form of standing breathers. Asymmetry is detected in the full oscillation cycle of a breather defect, and it is related to the twist symmetry of a twist nematic. This asymmetry is taken into account as effective anisotropic friction. The behavior of a breather on a trap, namely, a classical defect (dislocation), is investigated. Dislocation motion is shown to be anisotropic in the oscillation cycle: in one direction, a dislocation moves regularly; in the second phase, the transition into the initial state proceeds via the decay of the breather into a dipole pair of dislocations of opposite signs followed by their annihilation.     

Kinetics of the origin of orientational-state nuclei in nematics with metastable surface states

Summary The dynamics of metastable orientational states formed by weak boundary conditions is investigated. The relative stability of these states, the relaxation of nonstable state, the possible control of the kinetics of the process and the critical conditions for such orientational transformation are discussed. Work presented at the second USSR-Italy Bilateral Meeting on Liquid Crystals held in Moscow, September 15–21, 1988.     

Mecanochromatic effect in nematics

We consider a nematic slab, with homeotropic boundary orientations (easy axis z) subjected to two simultaneous perturbations = a uniform shear flow along x and a magnetic field H oriented at 45° in the xz-plane. We find that, in a certain range of H-values, the orientation of the molecules in the mid plane of a thick slab does not correspond to a fixed angle = in this region the director rotates by many turns between the walls and the mid plane. In suitable cases, the periodicity may became comparable to an optical wavelength and the sample may become colored.     

Shear-flow-induced transition in nematics

The distortion, induced by a shear flow in a nematic (MBBA) layer having its director initially normal to the velocity and to the velocity gradient, has been observed by a conoscopic technique. At low velocity, the sample retains an ideal planar texture. Above a certain velocity threshold v_c, a distortion is observed. The threshold is inversely proportional to the sample thickness, and can also be modified by a magnetic field. These results are in agreement with a simple calculation based on the Leslie equations.     

Universal nuclear spin relaxation and long-range order in nematics strongly confined in mass fractal silica gels

We show how the low-frequency dependence of the proton spin-lattice relaxation time T1(nu) of octylcyanobiphenyl liquid crystals confined in high-density silica gels evidences a long-range order nematic phase in spite of the strong confinement and random disorder of the gels. The universal value and frequency dependence observed, T1(nu) proportional, variant nu(2/3), is interpreted within a relaxation model due to director fluctuations in nematic liquid crystals confined to mass fractal porous media. The model provides a relation T1(nu) proportional, variant nu(2-d/2), giving a reliable value of the structural fractal dimension d(f)=2.67 for all the host silica gels.     

Fluid dynamics in higher order gravity

We examine the kinematic and dynamic properties of fluid spacetimes in higher order gravity. In particular we extend the general equations of Ehlers and Ellis governing relativistic fluid dynamics from general relativity to the higher order theory. We find exact results for the evolution of shear in Bianchi spacetimes with isotropic surfaces, thus generalising the general relativity results. Furthermore we show that the vanishing of vorticity, shear and acceleration does not imply FRW geometry inR + R ² gravity without the further assumption of a barotropic equation of state,p = p(p), p(p) 0. In particular, this result means that the Ehlers-Geren-Sachs theorem on cosmic background radiation also holds in the higher order theory.     

Colloidal interactions in two-dimensional nematics

The interaction between two disks immersed in a 2D nematic is investigated i) analytically using the tensor order parameter formalism for the nematic configuration around isolated disks and ii) numerically using finite-element methods with adaptive meshing to minimize the corresponding Landau-de Gennes free energy. For strong homeotropic anchoring, each disk generates a pair of defects with one-half topological charge responsible for the 2D quadrupolar interaction between the disks at large distances. At short distance, the position of the defects may change, leading to unexpected complex interactions with the quadrupolar repulsive interactions becoming attractive. This short-range attraction in all directions is still anisotropic. As the distance between the disks decreases, their preferred relative orientation with respect to the far-field nematic director changes from oblique to perpendicular. Received 1 October 2002 and Received in final form 12 November 2002 RID="a" ID="a"e-mail: miko@cii.fc.ul.pt     

Active turbulence in active nematics

Dense, active systems show active turbulence, a state characterised by flow fields that are chaotic, with continually changing velocity jets and swirls. Here we review our current understanding of active turbulence. The development is primarily based on the theory and simulations of active liquid crystals, but with accompanying summaries of related literature.     

Temperature-induced orientational transition of nematics on the surface of a ferroelectric crystal

A temperature-induced orientational transition is investigated in a mixture of nematic liquid crystals on the surface of a cleavage of a ferroelectric triglycine sulfate crystal. The transition has been observed by the variation of the polarized absorbance components of a dye introduced into the nematic matrix with increasing temperature. The reorientation of molecules in the liquid crystal volume confined by solid walls is due to competition between dispersion and polar forces at the surface and the decrease in the electric field of the substrate up to its complete disappearance at the ferroelectric Curie point.     

Excitable patterns in active nematics

We analyze a model of mutually propelled filaments suspended in a two-dimensional solvent. The system undergoes a mean-field isotropic-nematic transition for large enough filament concentrations, and the nematic order parameter is allowed to vary in space and time. We show that the interplay between nonuniform nematic order, activity, and flow results in spatially modulated relaxation oscillations, similar to those seen in excitable media. In this regime the dynamics consists of nearly stationary periods separated by "bursts" of activity in which the system is elastically distorted and solvent is pumped throughout. At even higher activity, the dynamics becomes chaotic.     

Topological defects in spherical nematics

We study the organization of topological defects in a system of nematogens confined to the two-dimensional sphere (S2). We first perform Monte Carlo simulations of a fluid system of hard rods (spherocylinders) living in the tangent plane of S2. The sphere is adiabatically compressed until we reach a jammed nematic state with maximum packing density. The nematic state exhibits four +1/2 disclinations arrayed on a great circle. This arises from the high elastic anisotropy of the system in which splay (K1) is far softer than bending (K3). We also introduce and study a lattice nematic model on S2 with tunable elastic constants and map out the preferred defect locations as a function of elastic anisotropy. We find a one-parameter family of degenerate ground states in the extreme splay-dominated limit K_{3}/K_{1}-->infinity. Thus the global defect geometry is controllable by tuning the relative splay to bend modulus.