Splay Deformation Research Articles

A novel model for smectic liquid crystals: Elastic anisotropy and response to a steady-state flow.

By means of a combination of equilibrium Monte Carlo and molecular dynamics simulations and nonequilibrium molecular dynamics we investigate the ordered, uniaxial phases (i.e., nematic and smectic A) of a model liquid crystal. We characterize equilibrium behavior through their diffusive behavior and elastic properties. As one approaches the equilibrium isotropic-nematic phase transition, diffusion becomes anisotropic in that self-diffusion D⊥ in the direction orthogonal to a molecule's long axis is more hindered than self-diffusion D∥ in the direction parallel to that axis. Close to nematic-smectic A phase transition the opposite is true, D∥ < D⊥. The Frank elastic constants K1, K2, and K3 for the respective splay, twist, and bend deformations of the director field n̂ are no longer equal and exhibit a temperature dependence observed experimentally for cyanobiphenyls. Under nonequilibrium conditions, a pressure gradient applied to the smectic A phase generates Poiseuille-like or plug flow depending on whether the convective velocity is parallel or orthogonal to the plane of smectic layers. We find that in Poiseuille-like flow the viscosity of the smectic A phase is higher than in plug flow. This can be rationalized via the velocity-field component in the direction of the flow. In a sufficiently strong flow these smectic layers are not destroyed but significantly bent.

Flexoelectric effect in an in-plane switching (IPS) liquid crystal cell for low-power consumption display devices.

Technology of displaying static images in portable displays, advertising panels and price tags pursues significant reduction in power consumption and in product cost. Driving at a low-frequency electric field in fringe-field switching (FFS) mode can be one of the efficient ways to save powers of the recent portable devices, but a serious drop of image-quality, so-called image-flickering, has been found in terms of the coupling of elastic deformation to not only quadratic dielectric effect but linear flexoelectric effect. Despite of the urgent requirement of solving the issue, understanding of such a phenomenon is yet vague. Here, we thoroughly analyze and firstly report the flexoelectric effect in in-plane switching (IPS) liquid crystal cell. The effect takes place on the area above electrodes due to splay and bend deformations of nematic liquid crystal along oblique electric fields, so that the obvious spatial shift of the optical transmittance is experimentally observed and is clearly demonstrated based on the relation between direction of flexoelectric polarization and electric field polarity. In addition, we report that the IPS mode has inherent characteristics to solve the image-flickering issue in the low-power consumption display in terms of the physical property of liquid crystal material and the electrode structure.

23-3: Splay and Bend of Liquid Crystal in Vertical Alignment Mode

The process of liquid crystal alignment in Polymer Stabilized Alignment Mode (PSA) is demonstrated in this work. The splay and bend deformation of liquid crystal in PSA was analyzed, and the principle to control the sequence of splay and bend deformation was discovered.

P-129: Investigation on the Variation of Flicker Shift by Changing the Pixel Electrode Structure in ADS Mode LCD

When the ratio of W/S in ADS mode LCD is tuned, V-T Curve symmetry is altered by splay deformations in areas above the pixel electrode and slit, and flicker shift and DC image sticking are changed by bend deformations in area above the border of the pixel electrode and slit.

Entropy-driven formation of chiral nematic phases by computer simulations.

Predicting the macroscopic chiral behaviour of liquid crystals from the microscopic chirality of the particles is highly non-trivial, even when the chiral interactions are purely entropic in nature. Here we introduce a novel chiral hard-particle model, namely particles with a twisted polyhedral shape and obtain a stable fully entropy-driven cholesteric phase by computer simulations. By slightly modifying the triangular base of the particle, we are able to switch from a left-handed prolate (calamitic) to a right-handed oblate (discotic) cholesteric phase using the same right-handed twisted particle model. Furthermore, we show that not only prolate and oblate chiral nematic phases, but also other novel entropy-driven phases, namely chiral blue phases, chiral nematic phases featuring both twist and splay deformations, chiral biaxial nematic phases with one of the axes twisted, can be obtained by varying particle biaxiality and chirality. Our results allow to identify general guidelines for the stabilization of these phases.

Density functional theory of nematic elasticity: softening from the polar order.

Recent experiments have evidenced some unconventional features in the elasticity of nematics, which cannot be explained by standard microscopic theories. Here, in the framework of a second-virial density functional theory, we have developed a general approach, relaxing the usual assumption that the angular distribution of particles with respect to their local director is unaffected by the deformation. We show that, for particles with polar symmetry, a new contribution to the splay and bend deformation free energy arises, associated with the onset of polar order. Calculations for conical and bent-shaped particles reveal dramatic softening of the splay and the bend mode, respectively, which eventually may lead to spontaneous deformation.

Elastic deformations of bolalipid membranes.

Archaeal membranes have unique mechanical properties that enable these organisms to survive under extremely aggressive environmental conditions. The so-called bolalipids contribute to this exceptional stability. They have two polar heads joined by two hydrocarbon chains. The two headgroups can face different sides of the membrane (O-shape conformation) or the same side (U-shape conformation). We have developed an elasticity theory for bolalipid membranes and show that the energetic contributions of (i) tilt deformations, (ii) area compression/stretching deformations, (iii) as well as those of Gaussian splay from the two membrane surfaces are additive, while splay deformations yield a cross-term. The presence of a small fraction of U-shaped molecules resulted in spontaneous membrane curvature. We estimated the tilt modulus to be approximately equal to that of membranes in eukaryotic cells. In contrast to conventional lipids, the bolalipid membrane possesses two splay moduli, one of which is estimated to be an order of magnitude larger than that of conventional lipids. The projected values of elastic moduli act to hamper pore formation and to decelerate membrane fusion and fission.

Hydrodynamics of Turning Flocks.

We present a hydrodynamic model of flocking that generalizes the familiar Toner-Tu equations to incorporate turning inertia of well-polarized flocks. The continuum equations controlled by only two dimensionless parameters, orientational inertia and alignment strength, are derived by coarse-graining the inertial spin model recently proposed by Cavagna etal. The interplay between orientational inertia and bend elasticity of the flock yields anisotropic spin waves that mediate the propagation of turning information throughout the flock. The coupling between spin-current density to the local vorticity field through a nonlinear friction gives rise to a hydrodynamic mode with angular-dependent propagation speed at long wavelengths. This mode becomes unstable as a result of the growth of bend and splay deformations augmented by the spin wave, signaling the transition to complex spatiotemporal patterns of continuously turning and swirling flocks.

Impact of Doping CdSe/ZnS Quantum Dots on the Elasticity Coefficients of Nematic

C-V dependencies of pure NLC cells and suspensions with semiconductor CdSe/ZnS QDs were simulated. Comparison method of fitting theoretical capacity-voltage dependencies with experimental data of homogeneously aligned by polyimide layers LC cells was applied to estimate elasticity coefficients for splay and bend director deformation and parallel and perpendicular components of NLC cell dielectric constant. Increase of these parameters for QDs-NLC suspension compared to pure NLC was observed when the QDs concentrations were 0.5–1 mg/ml. The calculations were performed excluding the screening effect associated with QDs doping which can increases Frederick's threshold voltage.

Chiral structures from achiral liquid crystals in cylindrical capillaries

We study chiral symmetry-broken configurations of nematic liquid crystals (LCs) confined to cylindrical capillaries with homeotropic anchoring on the cylinder walls (i.e., perpendicular surface alignment). Interestingly, achiral nematic LCs with comparatively small twist elastic moduli relieve bend and splay deformations by introducing twist deformations. In the resulting twisted and escaped radial (TER) configuration, LC directors are parallel to the cylindrical axis near the center, but to attain radial orientation near the capillary wall, they escape along the radius through bend and twist distortions. Chiral symmetry-breaking experiments in polymer-coated capillaries are carried out using Sunset Yellow FCF, a lyotropic chromonic LC with a small twist elastic constant. Its director configurations are investigated by polarized optical microscopy and explained theoretically with numerical calculations. A rich phenomenology of defects also arises from the degenerate bend/twist deformations of the TER configuration, including a nonsingular domain wall separating domains of opposite twist handedness but the same escape direction and singular point defects (hedgehogs) separating domains of opposite escape direction. We show the energetic preference for singular defects separating domains of opposite twist handedness compared with those of the same handedness, and we report remarkable chiral configurations with a double helix of disclination lines along the cylindrical axis. These findings show archetypally how simple boundary conditions and elastic anisotropy of confined materials lead to multiple symmetry breaking and how these broken symmetries combine to create a variety of defects.

Edge Structure of through Pore in Lipid Membrane

Theoretical model of edge structure of through pore in lipid membrane was developed. We assumed that membrane monolayers are not necessary in close contact with each other everywhere; instead, hydrophobic void can appear between monolayers of the membrane near the pore edge. If formed, the void is supposed to be filled by organic solvent or low-polarity impurities, which are usually present in artificial and cell membranes. The monolayer of pore edge was divided to three regions: almost vertical monolayer, almost horizontal monolayer, and horizontal monolayer of bilayer part of the membrane. All three regions were assumed continuously conjugated. Pore line tension was calculated in the framework of theory of elasticity of liquid crystals adapted to lipid membranes, by taking into account splay and tilt deformations. Line tension depends on the value of surface tension at the boundary of lipid tails with the void. For sufficiently high surface tension the void collapses. Calculated values of pore edge line tension are in good agreement with available experimental data both for membranes containing and lacking organic solvent or low-polarity impurities.

Manifold configurations of the director field formed by topological defects in free and confined geometry in smectic films.

We study the topology of the c-director field near topological defects with point core and with a droplet in the core of the defect in nonpolar smectic-C and ferroelectric smectic-C* freestanding films using polarized optical microscopy. Free and confined geometry of topological defects and droplets with strong outer boundary condition are compared. The c-director field can be remarkably different around a point defect and a droplet with the same topological charge S=+1. In ferroelectric films, splay deformation of the c-director transforms into bend deformation after droplet nucleation. Heating a ferroelectric film with an S=+1 droplet leads to a dramatic change of the c-director topology from bend to splay. In confined geometry we found spiral structures in which the c-director has opposite direction of rotation along the inner and outer boundaries of the island. Our observations are discussed on the basis of theories taking into account both the influence of polarity and of confined geometry on elasticity and topology of the c-director field.

24.2: Investigation of Flexoelectric Effect in Vertically‐Aligned In‐Plane‐Switching Mode by Low Frequency Driving

AbstractDue to the inhomogeneous electric field, liquid crystal molecules reveal splay deformation in vertically‐aligned in‐plane‐switching mode. The flexoelectric effect from the splay is confirmed by fast CCD images. We introduce a model to explain the mechanism of such phenomenon and to determine the sign of flexoelectric coefficient.

How the electric-field parameters affect the optical response of a nematic liquid crystal

This paper discusses the dynamics of the optical response of a nematic liquid crystal with positive dielectric anisotropy for splay deformation of the layer and how it is affected by the shape of the electric-field oscillations. The efficiency of the action of sinusoidal, bipolar, and unipolar meanders with different frequencies and polarities is compared. It is shown that using a unipolar meander promotes a substantial acceleration of the liquid crystal’s optical response when the electrical signal is simultaneously reduced.

On the problem of transient hydrodynamic instability of nematics in magnetic field: I. Instability at splay deformation

A dependence of the square of dimensionless magnetic-field (MF) strength on the square of dimensionless wave vector of the domain structure, \(h^2 \left( {\tilde q^2 } \right)\), is analytically derived for the transient hydrodynamic instability arising at splay deformation under a MF. The domain formation is related to the fold catastrophe; the square of the critical field of domain formation, h D 2 , is determined from the condition \({{\partial \left[ {h^2 \left( {\tilde q^2 } \right)} \right]} \mathord{\left/ {\vphantom {{\partial \left[ {h^2 \left( {\tilde q^2 } \right)} \right]} \partial }} \right. \kern-\nulldelimiterspace} \partial }\left( {\tilde q^2 } \right) = 0\). In the general case, the function \(h^2 \left( {\tilde q^2 } \right)\) is a ratio of two polynomials whose coefficients for calamitics are determined by combinations of four dimensionless viscosities ν2/ν1, ν6/ν1, ν7/ν1, and ν8/ν1. Under some assumptions, the quotient of the polynomials at large \(\tilde q^2\) is a quadratic function which allows one to experimentally determine the dimensionless viscosities ν2/ν1, ν6/ν1, ν7/ν1, and α2/ν1.

Thermotropic orientational order of discotic liquid crystals in nanochannels: an optical polarimetry study and a Landau-de Gennes analysis.

Optical polarimetry measurements of the orientational order of a discotic liquid crystal based on a pyrene derivative confined in parallelly aligned nanochannels of monolithic, mesoporous alumina, silica, and silicon as a function of temperature, channel radius (3-22 nm) and surface chemistry reveal a competition of radial and axial columnar orders. The evolution of the orientational order parameter of the confined systems is continuous, in contrast to the discontinuous transition in the bulk. For channel radii larger than 10 nm we suggest several, alternative defect structures, which are compatible both with the optical experiments on the collective molecular orientation presented here and with a translational, radial columnar order reported in previous diffraction studies. For smaller channel radii our observations can semi-quantitatively be described by a Landau-de Gennes model with a nematic shell of radially ordered columns (affected by elastic splay deformations) that coexists with an orientationally disordered, isotropic core. For these structures, the cylindrical phase boundaries are predicted to move from the channel walls to the channel centres upon cooling, and vice-versa upon heating, in accord with the pronounced cooling/heating hystereses observed and the scaling behavior of the transition temperatures with the channel diameter. The absence of experimental hints of a paranematic state is consistent with a biquadratic coupling of the splay deformations to the order parameter.

Measuring liquid crystal elastic constants with free energy perturbations.

A first principles method is proposed to calculate the Frank elastic constants of nematic liquid crystals. These include the constants corresponding to standard splay, twist and bend deformations, and an often-ignored surface-like contribution known as saddle-splay. The proposed approach is implemented on the widely studied Gay-Berne (3, 5, 2, 1) model [J. G. Gay and B. J. Berne, J. Chem. Phys., 1981, 74, 3316], and the effects of temperature and system size on the elastic constants are examined in the nematic phase. The results of simulations for splay, twist, and bend elastic constants are consistent with those from previous literature reports. The method is subsequently applied to the saddle-splay elastic constant k24 which is found to exist at the limits of the Ericksen inequalities governing positive definite free energy. Finally, extensions of the method are discussed that present a new paradigm for in silico measurements of elastic constants.

Labyrinthine instability in freely suspended films of a polarization-modulated smectic phase

We report on fingering and labyrinthine instabilities of the layer dislocation lines in freely suspended polar liquid-crystalline films. These polar fingerlike and labyrinth structures reversibly form upon a transition into a modulated phase. External electric fields of several kV/m applied in the film plane can reversibly influence the formation of the finger textures. We show that the labyrinthine pattern is intrinsically related to regular splay deformations of the polarization.

P.101: Investigation on Flexoelectric Effect in the Fringe Field Switching Mode

AbstractOrientation of liquid crystal (LC) in an on state of the fringe field switching (FFS) mode has splay and bend deformation of LC director, which might cause spontaneous polarization by LC layer itself. Existence of flexoelectric effect is confirmed by observing appearance of flickering while the device is driven by ac voltage. We have tested LC mixtures having positive dielectric anisotropy and studied flexoelectric effects dependent on frequency and temperature.

How Cholesterol Tilt Modulates the Mechanical Properties of Saturated and Unsaturated Lipid Membranes

Although there have been great advances in understanding the effect of cholesterol on various properties of lipid membranes, its mechanistic role in determining the elasticity of bilayers at the molecular level is not fully resolved. Indeed, to date the molecular mechanisms that drive the experimentally detected differences in properties of saturated and unsaturated lipid bilayers that contain cholesterol remain unclear. By quantifying the cholesterol orientational degrees of freedom from atomistic molecular dynamics simulations of mixed lipid-cholesterol membranes, we address this question from the perspective of cholesterol tilt and splay. Following the fluctuations in orientations of cholesterol and of lipid molecules in simulations, we have extracted tilt and splay moduli both for cholesterol molecules and hydrocarbon lipid tails. This has further allowed us to estimate the contributions of these modes to the response of membranes to elastic deformations. We find that tilt and splay deformations importantly contribute to the overall elasticity of the mixed lipid membranes, and that they can account for the experimentally established differences between the liquid ordered sphingomyelin (SM)/cholesterol bilayers and fluid dioleoylphosphocholine (DOPC)/cholesterol bilayers. These findings underscore the importance of tilt and splay moduli, derived from simulations with relative computational ease, as useful metrics for quantitatively characterizing the mechanical properties of mixed lipid-cholesterol bilayers.