We propose an efficient numerical scheme, based on the method of lines, for solving the Landau-de Gennes equations describing the relaxational dynamics of nematic liquid crystals. Our method is computationally easy to implement, balancing requirements of efficiency and accuracy. We benchmark our method through the study of the following problems: the isotropic-nematic interface, growth of nematic droplets in the isotropic phase and the kinetics of coarsening following a quench into the nematic phase. Our results, obtained through solutions of the full coarse-grained equations of motion with no approximations, provide a stringent test of the de Gennes ansatz for the isotropic - nematic interface, illustrate the anisotropic character of droplets in the nucleation regime and validate dynamical scaling in the coarsening regime.
Topological defects are one of the most conspicuous features of liquid crystals. In two dimensional nematics, they have been shown to behave effectively as particles with both, charge and orientation, which dictate their interactions. Here, we study "twisted" defects that have a radially dependent orientation. We find that twist can be partially relaxed through the creation and annihilation of defect pairs. By solving the equations for defect motion and calculating the forces on defects, we identify four distinct elements that govern the relative relaxational motion of interacting topological …
Particle tracking passive microrheology in 8CB liquid crystals is used to redefine the precessional motion of the orientation of nematic director in liquid crystals. Physical origin of tumbling director in presence of presmectic clusters under zero shear conditions is discussed. Different structural properties (pure nematic phase, presmectic(smectic C and smectic A clusters)) were differentiated with characteristic dependence of $G'$ on $ω$ in the nematic phase of 8CB liquid crystals. Also, dynamic viscosity is observed with a cross over between parallel and perpendicular components as the sme…
A nematic liquid crystal in contact with a grating surface possessing an alternating stripe pattern of locally homeotropic and planar anchoring is studied within the Frank--Oseen model. The combination of both chemical and geometrical surface pattern leads to rich phase diagrams, involving a homeotropic, a planar, and a tilted nematic texture. The effect of the groove depth and the anchoring strengths on the location and the order of phase transitions between different nematic textures is studied. A zenithally bistable nematic device is investigated by confining a nematic liquid crystal betwee…
The nonlinear elastic properties of nematic liquid crystals have acquired new interest with the recent experimental observation of bulk modulated nematic phases which are composed by achiral molecules. We extend the Oseen-Zocher-Frank's elastic theory for nematic liquid crystals by including gradients of the nematic strain tensor in the elastic deformation energy. The invariants of the elastic tensor fields, up to the fourth order in the nematic director spatial derivatives, are calculated. An alternative approach that consists in the extension of the linear elastic energy to higher powers of …
Recently Biscari, DiCarlo and Turzi ["Anisotropic wave propagation in nematic liquid crystals", to appear (arXiv:1311.1802)] proposed a theory for nematoacustics which models nematic liquid crystals as nematic elastomers with molecular relaxation. Here, we extend the analysis of this theory to account for the director motion possibly induced by the propagation of a sound wave. We find that the director vibration is related to the - usually small - anisotropy of the molecular distribution, thus providing a justification to the relative high ultrasonic intensities required to observe non-negligi…
We analyze theoretically the influence of backward propagating waves on the primary threshold when a linearly polarized light impinges at normal incidence on a planarly aligned nematic liquid crystal films. We show, that the primary threshold, as a function of the phase delay induced by the nematic layer, exhibits oscillations. The amplitude of oscillations depends strongly on the drop of the refractivity indices of the nematic and outer media at the boundaries.
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.
The improved expansion in width is applied to curved domain walls in uniaxial nematic liquid crystals in external magnetic field. In the present paper we concentrate on the case of equal elastic constants. We obtain approximate form of the director field up to second order in magnetic coherence length.
Many bent-core nematic liquid crystals exhibit unusual physical properties due to the presence of smectic clusters, known as "cybotactic" clusters in the nematic phase. Effect of these clusters on complex shear modulus ($G^*(ω)$) of such liquid crystals hitherto unexplored. Here, we study flow viscosities and complex shear modulus of two asymmetric bent-core liquid crystals using microrheology technique. The results are corroborated with the measurements of curvature elastic constants. Compound with shorter hydrocarbon chain (8OCH$_\text{3}$) exhibit only nematic (N) phase whereas the compound…
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.
Nematic liquid crystals exhibit configurations in which the underlying ordering changes markedly on macroscopic length scales. Such structures include topological defects in the nematic phase and tactoids within nematic-isotropic coexistence. We discuss a computational study of inhomogeneous configurations that is based on a field theory extension of the Maier-Saupe molecular model of a uniaxial, nematic liquid crystal. A tensor order parameter is defined as the second moment of an orientational probability distribution, leading to a free energy that is not convex within the isotropic-nematic …
Phase behavior of liquid crystals is of long-standing interest due to numerous applications, with one of the key issues being how the presence of impurities affects the liquid crystalline order. Here we study the orientational order of 4-cyano-4$^{'}$-pentylbiphenyl (5CB) and 4-cyano-4$^{'}$-hexylbiphenyl (6CB) nematic liquid crystals in the presence of varying concentrations of water and n-hexane molecules serving as impurities, by carrying out both fully atomistic simulations and experiments. Our results reveal that mixing of the impurities (in case of hexane) with the host liquid crystals c…
The influence of controlable parameters like temperature and wavelength on the trajectories of light in a nematic liquid crystal with topological defects is studied through a geometric model. The model incorporates phenomenological details as how the refractive indices depend on such parameters. The deflection of light by the topological defect is then shown to be greater at lower temperatures and shorter wavelengths.
We present a Monte Carlo simulation of a polymer nematic for varying volume fractions, concentrating on the structure function of the sample. We achieve nematic ordering with stiff polymers made of spherical monomers that would otherwise not form a nematic state. Our results are in good qualitative agreement with theoretical and experimental predictions, most notably the bowtie pattern in the static structure function.
The paper analyses kinematics and dynamics of internal rotations with spin and their effects on the constitutive relations for uniaxial (nematic) liquids and for weakly elastic nematic solids. It is shown that neglecting the internal rotational inertia terms and effects of director gradient made the stress symmetric. This not only highly simplifies the theories but also allows calculating all the kinematic variables of internal rotations without any additional constants, other than those presented in the simplified theory with symmetric stress.
We put forward a hydrodynamic theory of nematic liquid crystals that includes both anisotropic elasticity and dynamic relaxation. Liquid remodeling is encompassed through a continuous update of the shear-stress free configuration. The low-frequency limit of the dynamical theory reproduces the classical Ericksen-Leslie theory, but it predicts two independent identities between the six Leslie viscosity coefficients. One replicates Parodi's relation, while the other-which involves five Leslie viscosities in a nonlinear way-is new. We discuss its significance, and we test its validity against evid…
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 introduce a new mesoscopic model for nematic liquid crystals (LCs). We extend the particle-based stochastic rotation dynamics method, which reproduces the Navier-Stokes equation, to anisotropic fluids by including a simplified Ericksen-Leslie formulation of nematodynamics. We verify the applicability of this hybrid model by studying the equilibrium isotropic-nematic phase transition and nonequilibrium problems, such as the dynamics of topological defects, and the rheology of sheared LCs. Our simulation results show that this hybrid model captures many essential aspects of LC physics at the …
We present a Monte Carlo study of external surface anchoring in nematic cells with partially disordered solid substrates, as well as of intrinsic anchoring at free nematic interfaces. The simulations are based on the simple hexagonal lattice model with a spatially anisotropic intermolecular potential. We estimate the corresponding extrapolation length $b$ by imposing an elastic deformation in a hybrid cell-like nematic sample. Our estimates for $b$ increase with increasing surface disorder and are essentially temperature--independent. Experimental values of $b$ are approached only when both th…
We study transformations of self-organized defect arrays at the nematic-smectic A liquid crystal phase transition, and show that these defect configurations are correlated, or "remembered", across the phase transition. A thin film of thermotropic liquid crystal is subjected to hybrid anchoring by an air interface and a water substrate, and viewed under polarized optical microscopy. Upon heating from smectic-A to nematic, a packing of focal conic domains melts into a dense array of boojums---nematic surface defects---which then coarsens by pair-annihilation. With the aid of Landau-de Gennes num…
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.
Most, but not all, liquid crystals tend to align when subject to shear flow, while most nematic polymeric liquid crystals undergo a tumbling instability, where the director rotate with the flow. The reasons of this instability remain elusive, as it is possible to find similar molecules exhibiting opposite behaviors. We propose a theory suitable for describing a wide range of material behaviors, ranging form nematic elastomers to nematic polymers and nematic liquid crystals, where the physical origins of tumbling emerge clearly. There are two possible ways to relax the internal stress in a nema…
We present experiments where anisometric colloidal microparticles dispersed in a nematic liquid crystal cell with homeotropic anchoring conditions are dynamically assembled by means of liquid-crystal-enabled electrophoresis (LCEEP) using an AC electric field perpendicular to the confining plates. A nematic host with negative dielectric anisotropy leads to a driving force parallel to the cell plates. We take advantage of the resulting gliding anchoring conditions and the degeneracy in the direction of particle motion to design reconfigurable trajectories using a photosensitive anchoring layer (…
We present the first systematic measurements of the dynamic response of a glassy soft-solid formed on dispersing colloids in a thermotropic nematic liquid crystal. Through applying a simple theoretical model, we reveal that the nematic elasticity dominates at low frequencies (longest timescales) and prevents flow. The Ericksen number $E_R$, determines a critical frequency $ω_c$, above which the viscous component $G'' \propto ω^{1/2}$. We find that the value of tan$δ$ is independent of the colloidal volume fraction ($ϕ$), and is determined by the ratio of lengthscales associated with the defect…
The effect of rough walls on the phase behaviour of a confined liquid crystal (LC) fluid is studied using constant pressure Monte Carlo simulations. The LC is modelled as a fluid of soft ellipsoidal molecules and the rough walls are represented as a hard wall with a number of molecules randomly embedded in them. It is found that the isotropic-nematic (IN) transition is shifted to higher pressures for rougher walls.
We propose a simple theoretical model which explains a formation of dipolar 2D and 3D colloidal structures in nematic liquid crystal. Colloidal particles are treated as effective hard spheres interacting via their elastic dipole, quadrupole and octopole moments. It is shown that octopole moment plays an important role in the formation of 2D and 3D nematic colloidal crystals. We generalize this assumption on the case of the external electric field and theoretically explain a giant electrostriction effect in 3D crystals observed recently [A. Nych et al., Nature Communications \textbf{4}, 1489 (2…
Surface-induced profiles of both nematic and smectic order parameters in a nematic liquid crystal, ranging from an orienting substrate to "infinity", were evaluated numerically on base of an extended Landau theory. In order to obtain a smooth behavior of the solutions at "infinity" a boundary energy functional was derived by linearizing the Landau energy around its equilibrium solutions. We find that the intrinsic wave number of the smectic structure, which plays the role of a coupling between nematic and smectic order, strongly influences the director reorientation. Whereas the smectic order …
We study the pair interaction of charged silica microrods in chiral nematic liquid crystals and show that the microrods with homeotropic surface anchoring form a bound state due to the competing effect of electrostatic (Coulomb) and elastic interactions. The robustness of the bound state is demonstrated by applying external electrical and mechanical forces that perturbs their equilibrium position as well as orientation. In the bound state we have measured the correlated thermal fluctuations of the position, using two-particle cross-correlation spectroscopy that uncovers their hydrodynamic inte…
The influence of the molecular structure of the nematic liquid crystal (NLC) on the photoalignment process at the NLC -- polymer interface has been investigated experimentally. NLCs having exclusively phenyl-, or cyclohexane rings in the rigid core, as well as NLCs containing both phenyl and cyclohexane groups have been considered. Substantial differences have been found in the photoalignment process depending on the molecular structure of the NLC, supporting the assumption that the polymer -- NLC interface should be regarded as a coupled system, where the two components mutually influence eac…
We show by means of continuum theory and simulations that geometric percolation in uniaxial nematics of hard slender particles is fundamentally different from that in isotropic dispersions. In the nematic, percolation depends only very weakly on the density and is, in essence, determined by a distance criterion that defines connectivity. This unexpected finding has its roots in the non-trivial coupling between the density and the degree of orientational order that dictate the mean number of particle contacts. Clusters in the nematic are much longer than wide, suggesting the use of nematics for…
We examine the behavior of spherical silica particles trapped at an air-nematic liquid crystal interface. When a strong normal anchoring is imposed, the beads spontaneously form various structures depending on their area density and the nematic thickness. Using optical tweezers, we determine the pair potential and explain the formation of these patterns. The energy profile is discussed in terms of capillary and elastic interactions. Finally, we detail the mechanisms that control the formation of an hexagonal lattice and analyze the role of gravity for curved interfaces.
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.
We perform Dynamic Monte Carlo simulations to investigate the equilibrium dynamics of hard colloidal cuboids in oblate and prolate nematic liquid crystals. In particular, we characterise the particles' diffusion along the nematic director and perpendicularly to it, and observe a structural relaxation decay that strongly depend on the particle anisotropy. To assess the Gaussianity of their dynamics and eventual occurrence of collective motion, we calculate two- and four-point correlation functions that incorporate the instantaneous values of the diffusion coefficients parallel and perpendicular…
We propose an extension of Frank-Oseen's elastic energy for bulk nematic liquid crystals which is based on the hypothesis that the fundamental deformations allowed in nematic liquid crystals are splay, twist and bend. The extended elastic energy is a fourth order form in the fundamental deformations. The existence of bulk spontaneous modulated or deformed nematic liquid crystal ground states is investigated. The analysis is limited to bulk nematic liquid crystals in the absence of limiting surfaces and/or external fields. The non deformed ground state is stable only when Frank-Oseen's elastic …
Within the macroscopic Landau-de Gennes approach, we examine the Gaussian normal mode fluctuations of semi-infinite nematic liquid crystals in a regime of critical wetting. It is argued that surface free-energy potentials that strongly suppress the long-range nematic order favor the appearance of bound biaxial nematic-director fluctuation modes, located in the domain occupied by the thermodynamic phase wetting the wall. Instead, substrates enhancing the orientational order promote the existence of uniaxial nematic-director local excitations. Close to the phase coexistence temperature both type…
The isotropic-to-nematic transition in liquid crystals is studied in d=3 spatial dimensions. A simulation method is proposed to measure the angle dependent interfacial tension g(theta), with theta the anchoring angle of the nematic phase at the interface. In addition, an alternative liquid crystal model is introduced, defined on a lattice. The advantage of the lattice model is that accurate simulations of anchoring effects become possible. For the lattice model, g(theta) depends sensitively on the nearest-neighbor pair interaction, and both stable and metastable anchoring angles can be detecte…
We predict theoretically the existence of a class of colloidal structures in nematic liquid crystal (NLC) cells, which are induced by surface patterns on the plates of the cell (like cells with UV-irradiated polyimide surfaces using micron size masks). These bulk structures arise from non-zero boundary conditions for the director distortions at the confining surfaces. In particular, we demonstrate that quadrupole spherical particles (like spheres with boojums or Saturn-ring director configurations) form a square lattice inside a planar NLC cell, which has checkerboard patterns on both its plat…
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 …
Light traveling through a liquid crystal with disclinations perceives a geometrical background which causes lensing effects similar to the ones predicted for cosmic objects like global monopoles and cosmic strings. In this article we explore the effective geometry as perceived by light in such media. The comparison between both systems suggests that experiments can be done in the laboratory to simulate optical properties, like gravitational lensing, of cosmic objects.
Particle tracking with a 0.98$μ$m silica sphere is used in determining precessional motion of nematic director in nematic phase of 8CB liquid crystals, as it probes those oriented structures which are of the same wavelength as of the sphere size. Velocity auto correlation(VACF) is used in determining those structures in both parallel and perpendicular orientations to the neamatic director. Further, a generic approach by considering the time dependent harmonic oscillator motions is used to analyze the VACF distribution function. This approach leads to observe a transition in the structures of n…
We investigated the effect of a photovoltaic field generated on the surface of iron-doped lithium niobate crystals on droplets of a ferroelectric nematic liquid crystalline and a standard nematic liquid crystalline material deposited on this surface. When such assembly is illuminated with a laser beam, a wide range of dynamic phenomena are initiated. Droplets located outside the laser spot are dragged in the direction of the illuminated area, while droplets located inside the illuminated region tend to bridge each other and rearrange into tendril-like structures. In the ferroelectric nematic p…
A thermal gradient-induced circular motion of particles placed on ferroelectric nematic liquid crystal sessile drops is demonstrated and explained. Unlike hurricanes and tornadoes that are the prime examples for thermal motors and where turbulent flows are apparent, here the texture without tracer particles appears completely steady indicating laminar flow. We provide a simple model showing that the tangential arrangement of the ferroelectric polarization combined with the vertical thermal gradient and the pyroelectricity of the fluid drives the rotation of the tracer particles that become ele…
The critical field of the Freedericksz transition and switching dynamics are investigated for polymer stabilized nematic liquid crystals as a function of polymer concentration. A simple phenomenological model is proposed to describe the observed critical field and dynamic response time behaviors as a function of concentration. In this model the polymer fibrils form director domains, which are bounded by virtual surfaces with a finite anchoring energy. The Freedericksz transition occurs independently within each of these domains.
We derive a Föppl-von Kármán-type constitutive model for solid liquid crystalline plates where the nematic director may or may not rotate freely relative to the elastic network. To obtain the reduced two-dimensional model, we rely on the deformation decomposition of a nematic solid into an elastic deformation and a natural shape change. The full solution to the resulting equilibrium equations consists of both the deformation displacement and stress fields. The model equations are applicable to a wide range of thin nematic bodies subject to optothermal stimuli and mechanical loads. For illustra…
We derive a multiphysics model that accounts for network elasticity with spontaneous strains, swelling and nematic interactions in liquid crystal gels (LCGs). We discuss the coupling among the various physical mechanisms, with particular reference to the effects of nematic interactions on chemical equilibrium and that of swelling on the nematic-isotropic transition. Building upon this discussion and using numerical simulations, we explore the transient phenomena involving concurrent swelling and phase transition in LCGs subject to a temperature change. Specifically, we demonstrate separation i…
Combining molecular simulation, Onsager theory and the elastic description of nematic liquid crystals, we study the dependence of the nematic liquid crystal elastic constants and the zenithal surface anchoring coefficient on the value of the bulk order parameter.
Inspired by recent experiments that highlight the role of nematic defects in the morphogenesis of epithelial tissues, we develop a minimal framework to study the dynamics of an active curved surface driven by its nematic texture. Allowing the surface to evolve via relaxational dynamics leads to a theory linking nematic defect dynamics, cellular division rates and Gaussian curvature. Regions of large positive (negative) curvature and positive (negative) growth are colocalized with the presence of positive (negative) defects. Applying this framework to the dynamics of cultured murine neural prog…
The article presents a straightforward experiment that directly and illustratively demonstrates double refraction. For this purpose, two liquid crystalline cells were designed, which enable qualitative and quantitative measurements of the extraordinary refractive index direction dependency in a uniaxial nematic liquid crystal.
We consider the effects of polydispersity on isotropic-nematic phase equilibria in thermotropic liquid crystals, using a Maier-Saupe theory with factorized interactions. A sufficient spread (approx. 50%) in the interaction strengths of the particles leads to phase separation into two or more nematic phases, which can in addition coexist with an isotropic phase. The isotropic-nematic coexistence region widens dramatically as polydispersity is increased, leading to re-entrant isotropic-nematic phase separation in some regions of the phase diagram. We show that similar phenomena will occur also f…
We derive a mathematical model of a nematic electrolyte based on a variational formulation of nematodynamics. Extending our previous work, we consider a general setup which incorporates dielectric anisotropy of the liquid-crystalline matrix and the full set of nematic viscosities. We verify the model by comparing its predictions to the results of the experiments on the substrate-controlled liquid-crystal-enabled electrokinetics. In the experiments a nematic liquid crystal confined to a thin planar cell with surface-patterned anchoring conditions exhibit electro-osmotic flows along the "guiding…
We propose electrically tunable hybrid metamaterial consisting of special wire grid immersed into nematic liquid crystal. The plasma-like permittivity of the structure can be substantially varied due to switching of the liquid crystal alignment by external voltages applied to the wires. Depending on the scale of the structure, the effect is available for both microwave and optical frequency ranges.
Recent experiments have reported that ferroelectric nanoparticles have drastic effects on nematic liquid crystals--increasing the isotropic-nematic transition temperature by about 5 K, and greatly increasing the sensitivity to applied electric fields. To understand these effects, we develop a theory for the statistical mechanics of ferroelectric nanoparticles in liquid crystals. This theory predicts the enhancements of liquid-crystal properties, in good agreement with experiments. These predictions apply even when electrostatic interactions are partially screened by moderate concentrations of …
We analyze the interaction with uniform external fields of nematic liquid crystals within a recent generalized free-energy posited by Virga and falling in the class of quartic functionals in the spatial gradients of the nematic director. We review some known interesting solutions, i. e., uniform heliconical structures, which correspond to the so-called twist-bend nematic phase and we also study the transition between this phase and the standard uniform nematic one. Moreover, we find liquid crystal configurations, which closely resemble some novel, experimentally detected, structures called Sky…
