We review and compare recent work on the properties of fluctuating interfaces between nematic and isotropic liquid-crystalline phases. Molecular dynamics and Monte Carlo simulations have been carried out for systems of ellipsoids and hard rods with aspect ratio 15:1, and the fluctuation spectrum of interface positions (the capillary wave spectrum) has been analyzed. In addition, the capillary wave spectrum has been calculated analytically within the Landau-de Gennes theory. The theory predicts that the interfacial fluctuations can be described in terms of a wave vector dependent interfacial tension, which is anisotropic at small wavelengths (stiff director regime) and becomes isotropic at large wavelengths (flexible director regime). After determining the elastic constants in the nematic phase, theory and simulation can be compared quantitatively. We obtain good agreement for the stiff director regime. The crossover to the flexible director regime is expected at wavelengths of the order of several thousand particle diameters, which was not accessible to our simulations.
We investigate liquid layers adsorbed at spherical and corrugated cylindrical substrates. The effective Hamiltonians for the liquid-gas interfaces fluctuating in the presence of such curved substrates are derived via the mean-field density functional theory. Their structure is compared with the Helfrich Hamiltonian which is parametrized by the bending and Gaussian rigidity coefficients. For long-ranged interparticle interactions of van der Waals type these coefficients turn out to be non-universal functions of interfacial curvatures; their form varies from one interface to another. We discuss …
We solve numerically the equations of nonlinear fluctuating hydrodynamics (NFH) for the supercooled liquid. The time correlation of the density fluctuations in equilibrium obtained here shows quantitative agreement with molecular dynamics(MD) simulation data. We demonstrate numerically that the 1/rho nonlinearity in the NFH equations of motion is essential in restoring the ergodic behavior in the liquid. Under nonequilibrium conditions the time correlation functions relax in a manner similar to that observed in the molecular dynamics simulations in binary mixtures. The waiting time t_w depende…
This theoretical paper is to advance a phenomenological, quasi thermodynamic approach to the dynamics of classical liquids which uses the Levy distribution of probability theory. Doubts from the chemical physics community about the application of its unusual properties to this field are tried to be removed. In particular, to understand the preponderant component of the Levy sum for Glarum Levy defects and Fischer speckles, the classical mathematical proof [D. A. Darling, Trans. Amer. Math. Soc. 73, 95 (1952)] for the existence and the influence of this component is accompanied by addition of p…
The presence of fluctuating local relaxation times, $τ_r(t)$ has been used for some time as a conceptual tool to describe dynamical heterogeneities in glass-forming systems. However, until now no general method is known to extract the full space and time dependent $τ_r(t)$ from experimental or numerical data. Here we report on a new method for determining the local phase field, $ϕ_r(t) = \int^{t} dt'/τ_r(t')$ from snapshots $\{r(t_i)\}_{i=1...M}$ of the positions of the particles in a system, and we apply it to extract $ϕ_r(t)$ and $τ_r(t)$ from numerical simulations. By studying how the phase…
We measure the defect density as a function of time at different temperatures in simulations of a two dimensional system of interacting particles. Just above the solid to liquid transition temperature, the power spectrum of the defect fluctuations shows a 1/f signature, which crosses over to a white noise signature at higher temperatures. When 1/f noise is present, the 5-7 defects predominately form string like structures, and the particle trajectories show a 1D correlated motion that follows the defect strings. At higher temperatures this heterogeneous motion is lost. We demonstrate this hete…
In this paper, we propose a new derivation for the Green-Kubo relationship for the liquid-solid friction coefficient, characterizing hydrodynamic slippage at a wall. It is based on a general Langevin approach for the fluctuating wall velocity, involving a non-markovian memory kernel with vanishing time integral. The calculation highlights some subtleties of the wall-liquid dynamics, leading to superdiffusive motion of the fluctuating wall position.
Nematic liquid crystals at rough and fluctuating interfaces are analyzed within the Frank elastic theory and the Landau-de Gennes theory. We study specifically interfaces that locally favor planar anchoring. In the first part we reconsider the phenomenon of Berreman anchoring on fixed rough surfaces, and derive new simple expressions for the corresponding azimuthal anchoring energy. Surprisingly, we find that for strongly aligning surfaces, it depends only on the geometrical surface anisotropy and the bulk elastic constants, and not on the precise values of the chemical surface parameters. In …
We consider the tilted-hexatic Hamiltonian on the fluctuating membranes. A renormalization-group analysis leads us to find two critical regions; one corresponds to the strong coupling regime of the gradient cross coupling, the other to the weak coupling regime. In the strong coupling regime, we find the locked tilted-hexatic to liquid phase transition when disclinations and vortices unbind simultaneously. On the other hand, in the weak coupling regime we find four phases; the unlocked tilted-hexatic phase, the hexatic phase, the tilted phase, and liquid phase. Disclinations and vortices unbind…
Using computer simulations, we establish that the structure of a supercooled binary atomic liquid mixture consists of common neighbour structures similar to those found in the equilibrium crystal phase, a Laves structure. Despite the large accumulation of crystal-like structure, we establish that the supercooled liquid represents a true metastable liquid and that liquid can borrow crystal structure without being destabilized. We consider whether this feature might be the origin of all instances of liquids of a strongly favoured local structure.
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.
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 elucidate the polymer dynamics of a liquid crystal elastomer based on the time-dependent response of the pendent liquid crystal mesogens. The molecular tilt and switching time of mesogens are analyzed as a function of temperature and cross-linking density upon application of an electric field. We observe an unexpected maximum in the switching time of the liquid crystal mesogens at intermediate field strength. Analysis of the molecular tilt over multiple time regimes correlates the maximum response time with a transition to entangled polymer dynamics at a critical field strength.
Novel liquid crystalline (LC) compositions are suggested and studied as elements of LC-nose. This allows for optical detection of several volatile organic compounds (VOCs). Ethanol, toluene, pyridine and acetic acid were detected by means of colorimetric and spectroscopic techniques during their diffusion inside chiral elements of LC-nose. Selectivity to different VOCs is enhanced by means of components of liquid crystal matrix with different viscosity, affinities to the solvents, and abilities to form hydrogen bonding.
We study the effect of fluctuations in opening angle of bent-core molecules on stability of the nematic phases. The molecules are built out of two Gay-Berne centers of $κ= 4$, $κ' = 5$, $μ= 1$ and $ν= 2$, each corresponding to one of the molecular arms. Constant-pressure Monte Carlo (MC NPT) simulations are carried out for two versions of the model, with fixed- and fluctuating opening angle, where fluctuations are taken harmonic about the angle of 140o. The systems studied are first cooled down from the isotropic liquid to a highly ordered crystalline smectic phase and then heated up all the w…
We formulate a lattice Boltzmann algorithm which solves the hydrodynamic equations of motion for nematic liquid crystals. The applicability of the approach is demonstrated by presenting results for two liquid crystal devices where flow has an important role to play in the switching.
The correlations of the fluctuating stress tensor are calculated in an equilibrium molecular-dynamics simulation of a Lennard--Jones liquid. We define a coarse-grained local stress tensor which can be calculated numerically and which allows for the first time to determine the stress correlation function both in time and in space. Our findings corroborate the assumptions made in fluctuating hydrodynamics as long as the liquid is isotropic, that is in bulk. In the vicinity of a rigid plate, however, the isotropy is restricted, and major modifications must be done with respect to the usual theory…
We propose a geometrical characterization of amorphous liquid structures that suppress crystallization by competing locally with crystalline order. We introduce for this purpose the crystal affinity of a liquid, a simple measure of its propensity to accumulate local crystalline structures on cooling. This quantity is explicitly related to the high temperature structural covariance between local fluctuations in crystal order and that of competing liquid structures: favouring a structure that, due to poor overlap properties, anticorrelates with crystalline order reduces the affinity of the liqui…
A new method is presented for mesoscopic simulations of particle dispersions in nematic liquid crystal solvents. It allows efficient first-principle simulations of the dispersions involving many particles with many-body interactions mediated by the solvents. A simple demonstration is shown for the aggregation process of a two dimentional dispersion.
These lecture notes discuss classical models of liquid crystals, and the different ways in which defects are described according to the different models.
We calculate the degree to which the final structure of the local groundstate in a liquid is a function of the strength of a perturbing potential applied during energy minimization. This structural susceptibility is shown to correlate well with the observed tendency of liquid adjacent to a crystal interface to exhibit a crystalline groundstate, a feature that has been strongly linked to the observation of ultra-fast crystal growth in pure metals and ionic melts. It is shown that the structural susceptibility increases dramatically as the interaction potential between atoms is softened.
This review introduces the elasticity theory of two-dimensional crystals and nematic liquid crystals on curved surfaces, the energetics of topological defects (disclinations, dislocations and pleats) in these ordered phases, and the interaction of defects with the underlying curvature. This chapter concludes with two cases of three-dimensional nematic phases confined to spaces with curved boundaries, namely a torus and a spherical shell.
The motion of topological defects is an important feature of the dynamics of all liquid crystals, and is especially conspicuous in active liquid crystals. Understanding defect motion is a challenging theoretical problem, because the dynamics of orientational order is coupled with backflow of the fluid, and because a liquid crystal has several distinct viscosity coefficients. Here, we suggest a coarse-grained, variational approach, which describes the motion of defects as effective `particles.' For passive liquid crystals, the theory shows how the drag depends on defect orientation, and shows t…
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…
Based on static and dynamical density functional theory, a phase-field-crystal model is derived which involves both the translational density and the orientational degree of ordering as well as a local director field. The model exhibits stable isotropic, nematic, smectic A, columnar, plastic crystalline and orientationally ordered crystalline phases. As far as the dynamics is concerned, the translational density is a conserved order parameter while the orientational ordering is non-conserved. The derived phase-field-crystal model can serve for efficient numerical investigations of various none…
The research herein studies the Langevin dynamics allowing for an exchange of energy between liquid crystals and the thermal environment. This dynamics leads to fluctuation and dissipation behaviors in the motions of liquid crystals, and therefore drives the system toward non-equilibrium evolutional processes. In particular, for the operations of liquid-crystal metastable systems, the fluctuation could allow an excitation (non-equilibrium) transition against energy barriers to the globally-stable state. Implemented with an actual case of liquid crystal pi configuration, this work statistically…
Using a generalized order parameter gradient expansion within density functional theory, we derive a phase-field-crystal model for liquid crystals composed by apolar particles in three spatial dimensions. Both the translational density and the orientational direction and ordering are included as order parameters. Different terms involving gradients in the order parameters in the resulting free energy functional are compared to the macroscopic Ginzburg-Landau approach as well as to the hydrodynamic description for liquid crystals. Our approach provides microscopic expressions for all prefactors…
We investigate theoretically the wetting properties of cholesteric liquid crystals at a planar substrate. If the properties of substrate and of the interface are such that the cholesteric layers are not distorted the wetting properties are similar to those of a nematic liquid crystal. If, on the other hand, the anchoring conditions force the distortion of the liquid crystal layers the wetting properties are altered, the free cholesteric-isotropic interface is non-planar and there is a layer of topological defects close to the substrate. These deformations can either promote or hinder the wetti…
In this article is proposed the general approach to determination the character of the interaction between colloidal particles in a different liquid crystals. The main idea of this approach are in the presentation of the colloidal particle as sours of the possible deformation of the ground state of the director field. The ground state of liquid crystal imposes restrictions on the possible deformations and as result determine the character of the interaction between the colloidal particles. Based on this approach the Coulomb like interaction between dipole particles in a cholesteric liquid crys…
Colloidal particles trapped at an interface between two fluids can form a wide range of different structures. Replacing one of the fluid with a liquid crystal increases the complexity of interactions and results in a greater range of possible structures. New behaviour emerges when colloidal particles interact with defects in the liquid crystal phases. Here we discuss the templating of colloids at a cholesteric isotropic interface.
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…
We report a molecular dynamics simulation demonstrating that a columnar liquid crystal, commonly formed by disc-shaped molecules, can be formed by identical particles interacting via a spherically symmetric potential. Upon isochoric cooling from a low-density isotropic liquid state the simulated system performed a weak first order phase transition which produced a liquid crystal phase composed of parallel particle columns arranged in a hexagonal pattern in the plane perpendicular to the column axis. The particles within columns formed a liquid structure and demonstrated a significant intracolu…
In this paper, we propose a suitable surface energy expression for cholesteric liquid crystals. We show that there exists a symmetry allowed term for chiral nematics that doesn't appear in the traditional Rapini-Papoular surface energy form. We discuss some consequences of this new surface anchoring term.
The metamaterial based on two planar photonic crystals was used on experimental express analysis of liquids. The metamaterial operates at a frequency of about 9.5 GHz, and has a small size. It was shown experimentally that when the liquid in container was placed in the resonance region at the interface of the two photonic crystals the parameters of resonance peak of transmission coefficient were changed. It was shown experimentally that different liquids have a different character of depending of the inverse Q-factor and the resonance frequency of the resonance peak on the distance from the in…
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 collective diffusion effects in system of a colloidal particles in a liquid crystal has been proposed. In this article described peculiarity of collective diffusion colloidal particles in a liquid crystal, which can be observe experimentally. The diffusion coefficient should be crucial dependence from temperature and concentration of particles. In system colloidal particles arise from the elastic distortion of the elastic director field the inter-particle interaction. These interaction can cause nontrivial collective behavior, as the results the non-monotonic dependence collective diffusio…
In liquid crystal elastomers, the orientational order of liquid crystals is coupled with elastic distortions of crosslinked polymer networks. Previous theoretical research has described these materials through two different approaches: a neoclassical theory based on the liquid crystal director and the deformation tensor, and a geometric elasticity theory based on the difference between the actual metric tensor and a reference metric. Here, we connect those two approaches using a formalism based on differential geometry. Through this connection, we determine how both the director and the geomet…
Large scale Molecular Dynamics simulations of sixty-five systems with N=80000 Lennard-Jones particles at two different supercooled liquid state points reveals, that the supercooled states contain spatially heterogeneous distributed subdomains of particles with significant higher bond-order than the mean bond-order in the supercooled liquid. The onset of crystallization starts in such an area with relative high six-ford bond-order for a supercooled state, but low bond-order for a fcc crystal. The critical nucleus of N \approx 70 particles is surrounded by many hundred of particles with relative…
Bulk properties of ionic liquid crystals are investigated using density functional theory. The liquid crystal molecules are represented by ellipsoidal particles with charges located in their center or at their tails. Attractive interactions are taken into account in terms of the Gay-Berne pair potential. Rich phase diagrams involving vapor, isotropic and nematic liquid, as well as smectic phases are found. The dependence of the phase behavior on various parameters such as the length of the particles and the location of charges on the particles is studied.
We demonstrate that one-dimensional photonic crystals with pure nematic liquid-crystal defects can operate as all-optical switching devices based on optical orientational nonlinearities of liquid crystals. We show that such a periodic structure is responsible for a modulated threshold of the optical Fréedericksz transition in the spectral domain, and this leads to all-optical switching and light-induced multistability. This effect has no quasi-statics electric field analogue, and it results from nonlinear coupling between light and a defect mode.
We propose the first Skyrmion Spin Ice, realized via confined, interacting liquid crystal skyrmions. Skyrmions in a chiral nematic liquid crystal behave as quasi-particles that can be dynamically confined, bound, and created or annihilated individually with ease and precision. We show that these quasi-particles can be employed to realize binary variables that interact to form ice-rule states. Because of their unique versatility, liquid crystal skyrmions can open entirely novel avenues in the field of frustrated systems. More broadly, our findings also demonstrate the viability of LC skyrmions …
The classic Kob-Andersen (KA) binary Lennard-Jones mixtures which are designed to prevent crystallization has been extensively studied in simulation of slow dynamics. Although crystallization can occur if a liquid system is cooled slowly, so far the KA model has not been crystallized. Here we report using molecular simulation the observation of crystal growth in the supercooled KA liquids. The onset of crystallization is observed occurring at temperature $T_c= 0.55$ which is higher than the glass transition temperature of $T_g=0.40$. We further examine the statistical distribution of single pa…
Liquid-crystal networks consist of weakly crosslinked polymers that are coupled to liquid-crystal molecules. The resultant hybrid system has rich elastic properties. We develop a phase field model to describe mechanical properties of a hexagonal liquid-crystal network. The hexagonal liquid-crystal network is found to have soft shear deformations. The elastic properties are predicted analytically and confirmed with numerical simulations. In addition the model incorporates non-linear elasticity and dislocations or disclinations.
A scattering polarizer is created by subjecting a polymer dispersed liquid crystal (PDLC) film to tensile strain. The optomechanical properties of the film are investigated by simultaneously measuring the stress-strain and polarization dependent optical transmission characteristics. The correlation between transmittances of two orthogonal polarizations and the stress-strain curve reveals that the polymer orientation as well as the droplet shape anisotropy influences the liquid crystal alignment within the droplets. A Monte-Carlo simulation based on the Lebwohl-Lasher model is used to explain t…
Controlling the anchoring of liquid crystal molecules at an interface with a water solution influences the entire organization of the underlying liquid crystal phase, which is crucial for many applications. The simplest way to stabilize such interfaces is by fabricating droplets of liquid crystal in water; however, a greater sensitivity to interfacial effects can be achieved using liquid crystal shells, i.e. spherical films of liquid crystal suspended in water. Anchoring transitions on those systems are traditionally triggered by the adsorption of surfactant molecules onto the interface, which…
We study photopolymerization in a low-molecular weight liquid crystal with non-uniform director gradients. Phase separation results in spatially non-uniform distribution of polymer density controlled by the distorted nematic matrix. Director-gradient-controlled polymerization provides a new and useful technique to assemble micron-scale polymer architectures.
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.
This article re-examines a classic question in liquid-crystal physics: What are the elastic modes of a nematic liquid crystal? The analysis uses a recent mathematical construction, which breaks the director gradient tensor into four distinct types of mathematical objects, representing splay, twist, bend, and a fourth deformation mode. With this construction, the Oseen-Frank free energy can be written as the sum of squares of the four modes, and saddle-splay can be regarded as bulk rather than surface elasticity. This interpretation leads to an alternative way to think about several previous re…
James Lee Fergason (1934 - 2008) focused his research on the liquid crystals. His studies correspond to a relevant part of the history of soft matter science and technology of liquid crystals. Here a discussion of some of his researches.
Liquid crystal is a typical kind of soft matter that is intermediate between crystalline solids and isotropic fluids. The study of liquid crystals has made tremendous progress over the last four decades, which is of great importance on both fundamental scientific researches and widespread applications in industry. In this paper, we review the mathematical models and their connections of liquid crystals, and survey the developments of numerical methods for finding the rich configurations of liquid crystals.
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 present a calculation of the Casimir torque acting on a liquid crystal near a birefringent crystal. In this system, a liquid crystal bulk is uniformly aligned at one surface and is twisted at the other surface by a birefringent crystal, e.g. barium titanate. The liquid crystal is separated from the solid crystal by an isotropic, transparent material such as SiO$_2$. By varying the thickness of the deposited layer, we can observe the effect of retardation on the torque (which differentiates it from the close-range van der Waals torque). We find that a barium titanate slab would cause 5CB (4-…
There are at least three fundamental states of matter, depending upon temperature and pressure: gas, liquid, and solid (crystal). These states are separated by first-order phase transitions between them. In both gas and liquid phases the complete translational and rotational symmetry exist, whereas in a solid phase both symmetries are broken. In intermediate phases between liquid and solid, which include liquid crystal and plastic crystal phases, only one of the two symmetries is preserved. Among the fundamental states of matter, the liquid state is most poorly understood. We argue that it is …
