The dielectric dispersion in the uniaxial nematic liquid crystals affects the switching dynamics of the director, as the dielectric torque is determined by not only the present values of the electric field and director but also by their past values. We demonstrate that this dielectric memory leads to an unusual contribution to the dielectric torque that is linear in the present field and thus polarity-sensitive. This torque can be used to accelerate the switch-off phase of director dynamics.
Fluctuation-induced interactions between anisotropic objects immersed in a nematic liquid crystal are shown to depend on the relative orientation of these objects. The resulting long-range ``Casimir'' torques are explicitely calculated for a simple geometry where elastic effects are absent. Our study generalizes previous discussions restricted to the case of isotropic walls, and leads to new proposals for experimental tests of Casimir forces and torques in nematics.
An elastic membrane with embedded nematic molecules is considered as a model of anisotropic fluid membrane with internal ordering. By considering the geometric coupling between director field and membrane curvature, the nematic texture is shown to induce anisotropic stresses additional to Canham-Helfrich elasticity. Building upon differential geometry, analytical expressions are found for the membrane stress and torque induced by splaying, twisting and bending of the nematic director as described by the Frank energy of liquid crystals. The forces induced by prototypical nematic textures are vi…
We show that the elastic charge of colloids in a nematic liquid crystal can be generated by the vector of external torque. The torque components play the role of two component charge (dyad) and give rise to the Coulomb-like potential, while their conservation law plays the role similar to that of Gauss' theorem in the electrostatics. The theory is applied to the colloid-surface interaction. A wall with homeotropic or planar director is shown to induce a repulsive 1/r^4 force on the elastic dipole. The external torque, however, induces the elastic charge in this colloid and triggers switching t…
How epithelial cells coordinate their polarity to form functional tissues is an open question in cell biology. Here, we characterize a unique type of polarity found in liver tissue, nematic cell polarity, which is different from vectorial cell polarity in simple, sheet-like epithelia. We propose a conceptual and algorithmic framework to characterize complex patterns of polarity proteins on the surface of a cell in terms of a multipole expansion. To rigorously quantify previously observed tissue-level patterns of nematic cell polarity (Morales-Navarette et al., eLife 8:e44860, 2019), we introdu…
Up to now it is commonly believed that a colloidal particle suspended in a nematic liquid crystal never produces elastic monopoles because this violates the mechanical equilibrium condition. And the only way to obtain deformations of director field falling off with distance as r^{-1} is to exert an external torque Γ_{ext} on the colloid \cite{de_Gennes}. In this paper we demonstrate that this statement is not quite correct and elastic monopoles, as well as dipoles and quadrupoles, can be induced without any external influence just by the particle itself. A behavior of a spherical colloidal par…
Non-equilibrium dynamics of topological defects can be used as a fundamental propulsion mechanism in microscopic active matter. Here, we demonstrate swimming of topological defect-propelled colloidal particles in (passive) nematic fluids through experiments and numerical simulations. Dynamic swim strokes of the topological defects are driven by colloidal rotation in an external magnetic field, causing periodic defect rearrangement which propels the particles. The swimming velocity is determined by the colloid's angular velocity, sense of rotation and defect polarity. By controlling them we can…
The mechanics of a flexible membrane decorated with a nematic liquid-crystal texture is considered in a variational framework. The variations on the splay, twist and the bend energy of the nematics are obtained from the local deformations leading to changes in the shape membrane. The Euler-Lagrange derivatives and the Noether charges are identified from the variational equations. The nematic stress tensor is obtained as a consequence of translational invariance. Likewise, the rotational invariance implies the torque nematic tensor. The corresponding boundary conditions are obtained for free ed…
Combining molecular dynamics and Monte Carlo simulation we study defect structures around an elongated colloidal particle embedded in a nematic liquid crystal host. By studying nematic ordering near the particle and the disclination core region we are able to examine the defect core structure and the difference between two simulation techniques. In addition, we also study the torque on a particle tilted with respect to the director, and modification of this torque when the particle is close to the cell wall.
Spherical microparticles dispersed in nematic liquid crystals have been extensively investigated in the past years. Here, we report experimental studies on the elastic deformation, colloidal interaction and self-assembly of hematite microcubes with homeotropic surface anchoring in a nematic liquid crystal. We demonstrate that the colloidal interaction and self-assembly of cubic colloids are orientation dependent. In a notable departure from the conventional microspheres, the microcubes stabilise diverse structures, such as bent chains, branches, kinks and closed-loops. The microcubes reorient …
We study the immersion of a ferromagnetic nanowire within a nematic liquid crystal using a lattice Boltzmann algorithm to solve the full three-dimensional equations of hydrodynamics. We present an algorithm for including a moving boundary, to simulate a nanowire, in a lattice Boltzmann simulation. The nematic imposes a torque on a wire that increases linearly with the angle between the wire and the equilibrium direction of the director field. By rotation of these nanowires, one can determine the elastic constants of the nematic.
Ferroelectric ordering in liquids is a fundamental question of physics. Here, we show that ferroelectric ordering of the molecules causes formation of recently reported splay nematic liquid-crystalline phase. As shown by dielectric spectroscopy, the transition between the uniaxial and the splay nematic phase has the characteristics of a ferroelectric phase transition, which drives an orientational ferroelastic transition via flexoelectric coupling. The polarity of the splay phase was proven by second harmonic generation (SHG) imaging, which additionally allowed for determination of the splay m…
We demonstrate, for the first time, the large electromechanical response in nematic liquid crystalline elastomers filled with a very low (~0.01%) concentration of carbon nanotubes, aligned along the nematic director at preparation. The nanotubes create a very large effective dielectric anisotropy of the composite. Their local field-induced torque is transmitted to the rubber-elastic network and is registered as the exerted uniaxial stress of order ~1kPa in response to a constant field of order ~1MV/m. We investigate the dependence of the effect on field strength, nanotube concentration and rep…
We investigate the emergence of orientational order among +1/2 disclinations in active nematic liquid crystals. Using a combination of theoretical and experimental methods, we show that +1/2 disclinations have short-range antiferromagnetic alignment, as a consequence of the elastic torques originating from their polar structure. The presence of intermediate -1/2 disclinations, however, turns this interaction from anti-aligning to aligning at scales that are smaller than the typical distance between like-sign defects. No long-range orientational order is observed. Strikingly, these effects are …
We study DC and AC electrophoresis of silica micro and nanorods in a thin film of a nematic liquid crystal. These particles induce virtual topological defects and also demonstrate nontrivial electrophoresis in a nematic liquid crystal. We measure several nonlinear electrophoretic mobility coefficients and compare with those calculated theoretically. We demonstrate a competing effect of the elastic and electrostatic torques that arises due to tilting of the rods with respect to the liquid crystal director. A basic theory describing this effect allows us to measure the effective polarizability o…
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…
Surface interactions are responsible for many properties of condensed matter, ranging from crystal faceting to the kinetics of phase transitions. Usually, these interactions are polar along the normal to the interface and apolar within the interface. Here, we demonstrate that polar in-plane surface interactions of a ferroelectric nematic NF produce polar monodomains in micron-thin planar cells and stripes of an alternating electric polarization, separated by 180 degree domain walls, in thicker slabs. The surface polarity binds together pairs of these walls, yielding a total polarization rotati…
We derive a mathematical model of a nematic electrolyte based on the Leslie-Ericksen theory of liquid crystal flow. Our goal is to investigate the nonlinear electrokinetic effects that occur because the nematic matrix is anisotropic, in particular, transport of ions in a direction perpendicular to the electric field as well as quadratic dependence of the induced flow velocity on the electric field. The latter effect makes it possible to generate sustained flows in the nematic electrolyte that do not reverse their direction when the polarity of the applied electric field is reversed. From a pra…
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…
We investigate the effect of an anisotropic substrate on the turbulent dynamics of a simulated two dimensional active nematic. This is introduced as an anisotropic friction and an effective anisotropic viscosity, with the orientation of the anisotropy being defined by the substrate. In this system we observe the emergence of global nematic order of topological defects that is controlled by the degree of anisotropy in the viscosity and the magnitude of the active stress. No global defect alignment is seen in passive liquid crystals with anisotropic viscosity or friction confirming that ordering…
We develop a lattice model for the splay flexoelectric effect in nematic liquid crystals. In this model, each lattice site has a spin representing the local molecular orientation, and the interaction between neighboring spins represents pear-shaped molecules with shape polarity. We perform Monte Carlo simulations and mean-field calculations to find the behavior as a function of interaction parameters, temperature, and applied electric field. The resulting phase diagram has three phases: isotropic, nematic, and polar. In the nematic phase, there is a large splay flexoelectric effect, which dive…
We model a cholesteric liquid crystal as a planar uniaxial multilayer system, where the orientation of each layer differs slightly from that of the adjacent one. This allows us to analytically simplify the otherwise acutely complicated calculation of the Casimir-Lifshitz torque. Numerical results differ appreciably from the case of nematic liquid crystals, which can be treated like bloc birefringent media. In particular, we find that the torque deviates considerably from its usual sinusoidal behavior as a function of the misalignment angle. In the case of a birefringent crystal faced with a ch…
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…
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 of nematics, the spatial and temporal variations of the nematic director field and or…
Dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in areas such as the transformation of stored or environmental energy into systematic motion, micro-robotics, and transport of matter at the microscale. This overview presents an approach to command microscale dynamics by replacing an isotropic medium such as water with an anisotropic fluid, a nematic liquid crystal. Orientational or…
The phenomenological torque balance model previously introduced to describe the electrically assisted light-induced gliding is generalized to study the reorientation dynamics of the nematic liquid crystal easy axis at photoaligned azo-dye films under the combined action of in-plane electric field and reorienting UV light linearly polarized at varying polarization azimuth, $φ_p$. We systematically examine the general properties of the torque balance model by performing analysis of the bifurcations of equilibria at different values of the polarization azimuth and apply the model to interpret the…
We have developed a molecular theory for the enantiotopic discrimination in prochiral solutes dissolved in chiral nematic solvents by means of NMR spectroscopy. The leading rank tensor contributions to the proposed potential of mean torque include symmetric as well as antisymmetric terms with respect to spatial inversion, these lead to a consistent determination of all the prochiral solute symmetries for which enantiotopes are distinguishable by NMR and also to excellent quantitative agreement when tested against the available experimental data for the rigid solute acenaphthene and for the mod…
The viscoelastic behavior of composites consisting of spindle-shaped hematite particles in poly-N-isopropylacrylamide hydrogels is investigated both, by means of rheological oscillatory shear experiments, and the field-induced alignment of these mesoscale, anisotropic particles in external magnetic fields. Due to their magnetic moment and magnetic anisotropy hematite spindles align with their long axis perpendicular to the direction of an external magnetic field. The field induced torque acting on the magnetic particles leads to an elastic deformation of the hydrogel matrix. Thus, the field-de…
We develop a continuum theory of linear viscoelastic response in oriented monodomain nematic elastomers. The expression for dissipation function is analogous to the Leslie-Ericksen version of anisotropic nematic viscosity; we propose the relations between the anisotropic rubber moduli and new viscous coefficients. A new dimensionless number is introduced, which describes the relative magnitude of viscous and rubber-elastic torques. In an elastic medium with an independently mobile internal degree of freedom, the nematic director with its own relaxation dynamics, the model shows a dramatic decr…
Nematic shells are colloidal particles coated with nematic liquid crystal molecules which may freely glide and rotate on the colloid's surface while keeping their long axis on the local tangent plane. We describe the nematic order on a shell by a unit director field on an orientable surface. Equilibrium fields can then be found by minimising the elastic energy, which in general is a function of the surface gradient of the director field. We learn how to extract systematically out of this energy a fossil component, related only to the surface and its curvatures, which expresses a curvature pote…
We study mutual alignment and interactions between colloidal particles of dissimilar shapes and dimensions when dispersed in a nematic host fluid. Convex pentagonal and concave starfruit-shaped nanoprisms and microspheres induce dipolar or quadrupolar director structures. The ensuing elastic pair interactions between microspheres and nanoprisms are highly dependent on the nanoparticle shape being omnidirectionally attractive for convex prisms but strongly anisotropic for concave prisms. Elastic deformations due to spherical particles cause well-defined alignment of complex-shaped nanoparticles…
Colloidal particles dispersed in a partially ordered medium, such as a liquid crystal (LC) phase, disturb its alignment and are subject to elastic forces. These forces are long-ranged, anisotropic and tunable through temperature or external fields, making them a valuable asset to control colloidal assembly. The latter is very sensitive to the particle geometry since it alters the interactions between the colloids. We here present a detailed numerical analysis of the energetics of elongated objects, namely prolate ellipsoids, immersed in a nematic host. The results, complemented with qualitativ…
We formulate the statistical dynamics of topological defects in the active nematic phase, formed in two dimensions by a collection of self-driven particles on a substrate. An important consequence of the non-equilibrium drive is the spontaneous motility of strength +1/2 disclinations. Starting from the hydrodynamic equations of active nematics, we derive an interacting particle description of defects that includes active torques. We show that activity, within perturbation theory, lowers the defect-unbinding transition temperature, determining a critical line in the temperature-activity plane t…
Microtubules and motor proteins self organize into biologically important assemblies including the mitotic spindle and the centrosomal microtubule array. Outside of cells, microtubule-motor mixtures can form novel active liquid-crystalline materials driven out of equilibrium by ATP-consuming motor proteins. Microscopic motor activity causes polarity-dependent interactions between motor proteins and microtubules, but how these interactions yield such larger-scale dynamical behavior such as complex flows and defect dynamics is not well understood. We develop a multiscale theory for microtubule-m…
Microbullet particles, cylinders with one blunt and one spherical end, offer a novel platform to study the effects of anisotropy and curvature on colloidal assembly in complex fluids. Here, we disperse microbullets in 4-cyano-4'-pentylbiphenyl (5CB) nematic liquid crystal (NLC) cells and form oriented elastic dipoles with a nematic point defect located near the curved end. This feature allows us to study particle interactions as a function of dipole alignment. By careful control of the surface anchoring at the particle surface and the confining boundaries, we study the interactions and assembl…
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.
Monopole-like electrostatic interactions are ubiquitous in biology and condensed matter, but they are often screened by counter-ions and cannot be switched from attractive to repulsive. In colloidal science, where the prime goal is to develop colloidal particles that mimic and exceed the diversity and length-scales of atomic and molecular assembly, electrostatically charged particles cannot change the sign of their surface charge or transform from monopoles to higher-order multipoles. In liquid-crystal colloids, elastic interactions between particles arise to minimize the free energy associate…
