Systems involving nematic liquid crystals subjected to magnetic fields or electric fields are modeled using the Oseen-Frank macroscopic continuum theory, and general criteria are developed to assess the local stability of equilibrium solutions. The criteria take into account the inhomogeneity of the electric field and the mutual influence of the electric field and the liquid-crystal director field on each other. The criteria show that formulas for the instability thresholds of electric-field Freedericksz transitions cannot in all cases be obtained from those for the analogous magnetic-field transitions by simply replacing the magnetic parameters by the corresponding electric parameters, contrary to claims in standard references. This finding is consistent with [Arakelyan, Karayan, Chilingaryan, Sov. Phys. Dokl., 29 (1984) 202-204]. A simple analytical test is provided to determine when an electric-field-induced instability can differ qualitatively from the analogous magnetic field-induced instability. For the systems we study, it is found that taking into account the full coupling between the electric field and the director field can either elevate or leave unchanged an instability threshold (never lower it), compared to the threshold provided by the magnetic-field analogy. The physical mechanism that underlies the effect of elevating an instability threshold is the added free energy associated with a first-order change in the ground-state electric field caused by a perturbation of the ground-state director field. Examples are given that involve classical Freedericksz transitions and also periodic instabilities. The inclusion of flexoelectric terms in the theory is studied, and it is found that these terms are not capable of altering the instability thresholds of any of the classical Freedericksz transitions, consistent with known results for splay transitions.
We consider a phenomenological continuum theory for an extensile, overdamped active nematic liquid crystal, applicable in the dense regime. Constructed from general principles, the theory is universal, with parameters independent of any particular microscopic realization. We show that it exhibits a bend instability similar to that seen in active suspensions, that leads to the proliferation of defects. We find three distinct nonequilibrium steady states: a defect-ordered nematic in which $+\frac{1}{2}$ disclinations develop polar ordering, an undulating nematic state with no defects, and a turb…
We analyse the homogeneous instabilities in a nematic liquid crystal subjected to plane steady Couette or Poiseuille flow in the case when the director is pre-aligned perpendicular to the flow plane taking into account weak anchoring at the confining surfaces. The critical shear rate decreases for decreasing anchoring strength and goes to zero in the limit of torque-free boundary conditions. For Poiseuille flow one has two types of instability depending on the values of the azimuthal ($W_a$) and polar ($W_p$) surface anchoring strengths. The critical line in $(W_a,W_p)$ space which separates t…
We consider the orientational instabilities, both homogeneous and spatially periodic, developing in a nematic liquid crystal under rectilinear oscillatory Couette flow for director alignment perpendicular to the flow plane. Using numerical and analytical approaches we determine the critical amplitude of oscillatory flow instabilities, the critical wave number and the symmetry of the destabilizing mode. It was found, that by varying of the oscillatory flow frequency the instability changes its temporal symmetry. The mechanism of this transition is coupled with the inertia of the nematic fluid. …
Stability is an important and fruitful avenue of research for liquid crystal elastomers. At constant temperature, upon stretching, the homogeneous state of a nematic body becomes unstable, and alternating shear stripes develop at very low stress. Moreover, these materials can experience classical mechanical effects, such as necking, void nucleation and cavitation, and inflation instability, which are inherited from their polymeric network. We investigate the following two problems: First, how do instabilities in nematic bodies change from those found in purely elastic solids? Second, how are t…
Partially wetting nematic liquid crystal (NLC) films on substrates are unstable to dewetting-type instabilities due to destablizing solid/NLC interaction forces. These instabilities are modified by the nematic nature of the films, which influences the effective solid/NLC interaction. In this work, we focus on the influence of imposed substrate anchoring on the instability development. The analysis is carried out within a long-wave formulation based on the Leslie-Ericksen description of NLC films. Linear stability analysis of the resulting equations shows that some features of the instability, …
We study a continuum model of an extensile active nematic to show that mesoscale turbulence develops in two stages: (i) ordered regions undergo an intrinsic hydrodynamic instability generating walls, lines of stong bend deformations, (ii) the walls relax by forming oppositely charged pairs of defects. Both creation and annihilation of defect pairs reinstate nematic regions which undergo further instabilities, leading to a dynamic steady state. We compare this with the development of active turbulence in a contractile active nematic.
Nematic elastomers are rubbery solids which have liquid crystals incorporated into their polymer chains. These materials display many unusual mechanical properties, one such being the ability to form fine-scale microstructure. In this work, we explore the response of taut and appreciably stressed sheets made of nematic elastomer. Such sheets feature two potential instabilities -- the formation of fine-scale material microstructure and the formation of fine-scale wrinkles. We develop a theoretical framework to study these sheets that accounts for both instabilities, and we implement this framew…
Liquid crystal elastomers are cross-linked polymer networks covalently bonded with liquid crystal mesogens. In the nematic phase, due to strong coupling between mechanical strain and orientational order, these materials display strain-induced instabilities associated with formation and evolution of orientational domains. Using a 3-d finite element elastodynamics simulation, we investigate one such instability, the onset of stripe formation in a monodomain film stretched along an axis perpendicular to the nematic director. In our simulation we observe the formation of striped domains with alter…
Many lyotropic liquid crystals are composed of mesogens that display a considerable spread in size or shape affecting their material properties and thermodynamics via various demixing and multi-phase coexistence scenarios. Starting from a generalized Onsager theory we formulate a generic framework that enables locating spinodal polydispersities as well as identifying the nature of incipient size fractionation for arbitrary model potentials and size distributions. We apply our theory to nematic phases of both hard rods and disks whose main particle dimension is described by a unimodal log-norma…
Growing tissue and bacterial colonies are active matter systems where cell divisions and cellular motion generate active stress. Although they operate in the non-equilibrium regime, these biological systems can form large-scale ordered structures such as nematically aligned cells, topological defects, and fingerings. Mechanical instabilities also play an essential role during growth by generating large structural folding. How active matter dynamics and mechanical instabilities together develop large-scale order in growing tissue is not well understood. Here, we use chain forming Bacillus subti…
Nematic elastomers with a locked-in anisotropy direction exhibit semi-soft elastic response characterized by a plateau in the stress-strain curve in which stress does not change with strain. We calculate the global phase diagram for a minimal model, which is equivalent to one describing a nematic in crossed electric and magnetic fields, and show that semi-soft behavior is associated with a broken symmetry biaxial phase and that it persists well into the supercritical regime. We also consider generalizations beyond the minimal model and find similar results.
Instabilities in thin elastic sheets, such as wrinkles, are of broad interest both from a fundamental viewpoint and also because of their potential for engineering applications. Nematic liquid crystal elastomers offer a new form of control of these instabilities through direct coupling between microscopic degrees of freedom, resulting from orientational ordering of rod-like molecules, and macroscopic strain. By a standard method of dimensional reduction, we construct a plate theory for thin sheets of nematic elastomer. We then apply this theory to the study of the formation of wrinkles due to …
A computational study of morphological instabilities of a two-dimensional nematic front under directional growth was performed using a Landau-de Gennes type quadrupolar tensor order parameter model for the first-order isotropic/nematic transition of 5CB (pentyl-cyanobiphenyl). A previously derived energy balance, taking anisotropy into account, was utilized to account for latent heat and an imposed morphological gradient in the time-dependent model. Simulations were performed using an initially homeotropic isotropic/nematic interface. Thermal instabilities in both the linear and non-linear reg…
Morphodynamic equations governing the behaviour of active nematic fluids on deformable curved surfaces are constructed in the large deformation limit. Emphasis is placed on the formulation of objective rates that account for normal deformations whilst ensuring that tangential flows are Eulerian, and the use of the surface derivative (rather than the covariant derivative) in the nematic free energy, which elastically couples local order to out-of-plane bending of the surface. Focusing on surface geometry and its dynamical interplay with the hydrodynamics, several illustrative instabilities are …
We study theoretically the instabilities induced by a linearly polarized ordinary light wave incident at a small oblique angle on a thin layer of homeotropically oriented nematic liquid crystal with special emphasis on the dye-doped case. The spatially periodic Hopf bifurcation that occurs as the secondary instability after the stationary Freedericksz transition is analyzed.
We consider a nematic liquid crystal, in coexistence with its isotropic phase, in contact with a substrate patterned with rectangular grooves. In such a system, the nematic phase may fill the grooves without the occurrence of complete wetting. There may exist multiple (meta)stable filled states, each characterised by the type of distortion (bend or splay) in each corner of the groove and by the shape of the nematic-isotropic interface, and additionally the plateaux that separate the grooves may be either dry or wet with a thin layer of nematic. Using numerical simulations, we analyse the dynam…
In this review, we report recent developments on the shear-induced transitions and instabilities found in surfactant wormlike micelles. The survey focuses on the non-linear shear rheology and covers a broad range of surfactant concentrations, from the dilute to the liquid-crystalline states and including the semi-dilute and concentrated regimes. Based on a systematic analysis of many surfactant systems, the present approach aims to identify the essential features of the transitions. It is suggested that these features define classes of behaviors. The review describes three types of transitions…
We report hybrid lattice Boltzmann (HLB) simulations of the hydrodynamics of an active nematic liquid crystal sandwiched between confining walls with various anchoring conditions. We confirm the existence of a transition between a passive phase and an active phase, in which there is spontaneous flow in the steady state. This transition is attained for sufficiently ``extensile'' rods, in the case of flow-aligning liquid crystals, and for sufficiently ``contractile'' ones for flow-tumbling materials. In a quasi-1D geometry, deep in the active phase of flow-aligning materials, our simulations giv…
In a sharp contrast to the response of silica particles we show that the metal-dielectric Janus particles with boojum defects in a nematic liquid crystal are self-propelled under the action of an electric field applied perpendicular to the director. The particles can be transported along any direction in the plane of the sample by selecting the appropriate orientation of the Janus vector with respect to the director. The direction of motion of the particles is controllable by varying the field amplitude and frequency. The command demonstrated on the motility of the particles is promising for t…
The Green function method developed in Ref.[S. B. Chernyshuk and B. I. Lev, Phys. Rev. E \textbf{81}, 041707 (2010)] is used to describe elastic interactions between axially symmetric colloidal particles in the nematic cell in the presence of the external electric or magnetic field. General formulas for dipole-dipole, dipole-quadrupole and quadrupole-quadrupole interactions in the homeotropic and planar nematic cells with parallel and perpendicular field orientations are obtained. A set of new results has been predicted: 1) \textit{Deconfinement effect} for dipole particles in the homeotropic …
Realignment of ferroelectric nematic by photoinduced electric field
Kent State University（肯特州立大学）；Institute of Physics, National Academy of Sciences of Ukraine（乌克兰国家科学院物理研究所）；Institute of Physical Chemistry, Polish Academy of Sciences（波兰国家科学院物理化学研究所）
The occurrence of new textures of liquid crystals is an important factor in tuning their optical and photonics properties. Here, we show, both experimentally and by numerical computation, that under an electric field chitin tactoids (i.e. nematic droplets) can stretch to aspect ratios of more than 15, leading to a transition from a spindle-like to a cigar-like shape. We argue that the large extensions occur because the elastic contribution to the free energy is dominated by the anchoring. We demonstrate that the elongation involves hydrodynamic flow and is reversible, the tactoids return to th…
Direct visualization of local electric fields in a layer of a ferroelectric nematic liquid
Jožef Stefan Institute（约瑟夫·斯特凡研究所）；Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学与物理学院）；School of Chemistry, University of Leeds（利兹大学化学学院）；School of Physics and Astronomy, University of Leeds（利兹大学物理与天文学学院）
One objective of active matter science is to unveil principles by which chaotic microscale dynamics could be transformed into useful work. A nematic liquid crystal environment offers a number of possibilities, one of which is a directional motion of an active droplet filled with an aqueous dispersion of swimming bacteria. In this work, using the responsiveness of the nematic to the electric field and light, we demonstrate how to control the direction and speed of active droplets. The dielectric response of nematic to the electric field causes two effects: (i) reorientation of the overall direc…
Chiral domains of opposite chirality are observed surprisingly in a nematic phase of an achiral rod-like liquid crystalline mesogen that shows ferroelectric nematic and antiferroelectric smectic phases. The observations of chiral domains of opposite chirality are enabled by application of a weak electric field across a planar-aligned cell. However once domains of opposite chirality are created, these stay permanently even if the field is removed. The observed phenomenon is due to the symmetry breaking of achiral mesogens of rod-shaped molecules. These domains are similarly observed in the Nx p…
We study azimuthal gliding of the easy axis that occurs in nematic liquid crystals brought in contact with the photoaligned azo-dye film under the action of reorienting UV light combined with an in-plane electric field. For irradiation with the linearly polarized light, dynamics of easy axis reorientation is found to be faster as compared to the case of non-polarized light. In addition, it slows down with the initial irradiation dose used to prepare the azo-dye film. This effect is interpreted by using the previously suggested phenomenological model. We present the theoretical results computed…
Tactoids are spindle shaped-droplets of a uniaxial nematic phase suspended in the co-existing isotropic phase. They are found in dispersions of a wide variety of elongated colloidal particles, including actin, fd virus, carbon nanotubes, vanadium peroxide and chitin nanocrystals. Recent experiments on tactoids of chitin nanocrystals in water show that electric fields can very strongly elongate tactoids even though the dielectric properties of the co-existing isotropic and nematic phases differ only subtly. We develop a model for partially bipolar tactoids, where the degree of bipolarness of th…
Janus particles are special types of nano or micro particles possessing at least two surfaces with distinct physical or chemical properties. The most studied Janus particles are the metal-dielectric particles, in which half surface of dielectric particles is coated with a very thin layer of metals. The external electric field induces dipole moment, and consequently the particles exhibit self-assembled dynamic structures in concentrated aqueous suspensions. Here, we study metal-dielectric Janus particles in a nematic liquid crystal under AC electric field and demonstrate a novel method for meas…
The electroviscous effect deals with the change in the viscosity of fluids due to an external electric field. Here, we report experimental studies on the electroviscous effects in a ferroelectric nematic liquid crystal. It was synthesised accomplishing a new synthetic route which provides higher yield than conventional one. We measure electric field-dependent viscosity under a steady shear at different temperatures. In the low field range, the increase in viscosity ($Δη=η(E)-η_0$) is proportional to $E^2$ and the corresponding viscoelectric coefficient ($f\approx10^{-9}$m\textsuperscript{2}/V\…
We consider a mathematical model that describes the flow of a Nematic Liquid Crystal (NLC) film placed on a flat substrate, across which a spatially-varying electric potential is applied. Due to their polar nature, NLC molecules interact with the (nonuniform) electric field generated, leading to instability of a flat film. Implementation of the long wave scaling leads to a partial differential equation that predicts the subsequent time evolution of the thin film. This equation is coupled to a boundary value problem that describes the interaction between the local molecular orientation of the N…
The nematic-nematic transitions in a nematic compound DIO are studied in homogeneously planar and homeotropic aligned cells using dielectric spectroscopy in the frequency range 0.1 Hz to 10 MHz over a wide range of temperatures. Three relaxation processes are identified in this material. All the three relaxation processes show large jumps in the dielectric strength and discontinuity in frequency at the NX to NF transition, indicative of it being a first order phase transition. Unlike a conventional nematic liquid crystalline material that usually shows molecular relaxation processes at higher …
We have carried out a spectroscopic study on a prototype ferroelectric nematic material (RM7343) doped with a non-polar chiral compound. The mixture presents two chiral nematic phases, one conventional (N*) and the other polar (NF*), whose behaviours under electric fields E are totally different. On the one hand, the N* phase shows a single reflection band if E is not very high, while fields perpendicular to the helix of a few V/mm are already sufficient to produce multiple bands in the NF* phase. On the other hand, the pitch of the NF* phase grows notably on increasing fields, however remaini…
Percolation of carbon nanotubes (CNTs) in liquid crystals (LCs) opens way for a unique class of anisotropic hybrid materials with a complex dielectric constant widely controlled by CNT concentration. Percolation in such systems is commonly described as a one-step process starting at a very low loading of CNTs. In the present study the two-step percolation was observed in the samples of thickness 250 $μ$m obtained by pressing the suspension between two substrates. The percolation concentrations for the first and second percolation processes were $C_n^{p_1}\approx 0.0002$ wt. \% and $C_n^{p_2}\a…
Instabilities are discussed which take place when a nematic liquid crystal (LC) layer, enclosed between a planar reference plate and a photosensitive substrate, is illuminated with polarized light from the reference side ({\it reverse} geometry). The dependence of the observed effects on the wavelength, polarization direction of the light, and on the thickness of the LC layer is explained by a model based on photoinduced surface torque. The application possibilities of the phenomena are also explored.
Pattern forming instabilities induced by ultralow frequency sinusoidal voltages were studied in a rod-like nematic liquid crystal by microscopic observations and simultaneous electric current measurements. Two pattern morphologies, electroconvection (EC) and flexodomains (FD), were distinguished; both appearing as time separated flashes within each half period of driving. A correlation was found between the time instants of the EC flashes and that of the nonlinear current response. The voltage dependence of the pattern contrast C(U) for EC has a different character than that for the FD. The fl…
Motivated by the experimentally observed shear-induced destabilization and reorientation of smectic A like systems, we consider an extended formulation of smectic A hydrodynamics. We include both, the smectic layering (via the layer displacement u and the layer normal p) and the director n of the underlying nematic order in our macroscopic hydrodynamic description and allow both directions to differ in non equilibrium situations. In an homeotropically aligned sample the nematic director does couple to an applied simple shear, whereas the smectic layering stays unchanged. This difference leads …
We present a general theory of liquid crystals under inhomogeneous electric field in a Ginzburg-Landau scheme. The molecular orientation can be deformed by electric field when the dielectric tensor is orientation-dependent. We then investigate the influence of a charged particle on the orientation order in a nematic state. The director is aligned either along or perpendicular to the local electric field around the charge, depending on the sign of the dielectric anisotropy. The deformation becomes stronger with increasing the ratio $Ze/R$, where $Ze$ is the charge and $R$ is the radius of the p…
We investigate similarities in the micro-structural dynamics between externally driven and actively driven nematics. Walls, lines of strong deformations in the director field, and topological defects are characteristic features of an active nematic. Similar structures form in driven passive nematics when there are inhomogeneities in imposed velocity gradients due to non-linear flow fields or geometrical constraints. Specifically, pressure driven flow of a tumbling passive nematic in an expanding-contracting channel produces walls and defects similar to those seen in active nematics. We also st…
In this paper we investigate the dynamics of liquid crystal textures in a two-dimensional nematic under applied electric fields, using numerical simulations performed using a publicly available LIquid CRystal Algorithm (LICRA) developed by the authors. We consider both positive and negative dielectric anisotropies and two different possibilities for the orientation of the electric field (parallel and perpendicular to the two-dimensional lattice). We determine the effect of an applied electric field pulse on the evolution of the characteristic length scale and other properties of the liquid cry…
We study the effect of the rotation of an external electric field on the dynamics of half-integer disclination networks in two dimensional nematic liquid crystals with a negative dielectric anisotropy using LICRA, a LIquid CRystal Algorithm developed by the authors. We show that a rotation of $π$ of the electric field around an axis of the liquid crystal plane continuously transforms all half-integer disclinations of the network into disclinations of opposite sign via twist disclinations. We also determine the evolution of the characteristic length scale, thus quantifying the impact of the ext…
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 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, flexo-electric and order electricity and chirality. When combined with a solver for the Maxwell equations asso…
