Continuum Theory Of Liquid Crystals Research Articles

Dynamic and Equilibrium Contribution of Nematic Order in Wetting and Contact Angles

A model for the dynamic contact angles and the spreading kinetics of nematic liquid crystals on a solid surface is presented for the first time using the continuum theory of liquid crystals. The equations of motion for this system are integrated for a wedge or a drop that is thin and moves slowly. The dynamic contact angle is found to depend on the capillary number that represents the importance of viscocapillarity and on the elasticity number that is the ratio between the elastic and surface forces. The model provides an explanation for the extra volume dependence that is reported in experiments, as well as one case of recoil, and for the observation that very small drops were reported to be immobile. For the first time, these previous experimental observations are shown to be due to elastic effects.

Diffraction characteristics of a non-mechanical beam steering system with liquid crystal polarization gratings.

The non-mechanical beam steering system is composed of multiple liquid crystal polarization gratings (LCPGs) cascaded by binary or ternary technologies. However, cascading multiple LCPGs cause the beam from one LCPG to obliquely enter the subsequent LCPGs, changing their diffraction efficiency and working voltage at different steering angles. This paper uses the elastic continuum theory of liquid crystals to simulate the tilt angle of liquid crystal molecules under different voltages. The transmission process of the beam in the system at oblique incidence is described with an extended Jones matrix, and the highest diffraction efficiency and working voltage of each LCPG at different steering angles are calculated using vector diffraction theory. It is convenient to calibrate the LCPGs' working voltage and analyze the system's diffraction characteristics. In addition, we used an improved binary cascade technology to design a LCPG non-mechanical beam steering system with a steering angle of ±10° and an angular resolution of 0.67°. Compared with binary cascade, this technology can effectively reduce the number of cascaded devices and increase the system throughput under the same maximum beam steering angle and angular resolution.

Topological Point Defects of Liquid Crystals in Quasi-Two-Dimensional Geometries

We review the interactions and dynamics of topological defects in liquid crystals (LCs) in quasi-twodimensional (2D) geometries. Such spatial restrictions can be realized in thin freely suspended smectic C films, in thin sandwich cells filled with nematic LCs, and under specific boundary conditions in LC shells embedded in aqueous solutions. Random defect patterns can be created by thermal quenching of the samples from lower ordered into higher ordered phases. On the other hand, well defined isolated defect configurations for the study of elementary interaction steps can be prepared by simple mechanical techniques. Observation by polarizing microscopy is straightforward. Spatial dimensions of the experimental systems as well as time scales are convenient for observation. The continuum theory of LCs is well developed so that in addition to the experimental characterization, an analytical or numerical description is feasible. From interactions and dynamic features observed in these LC systems, general conclusions on defect dynamics can be drawn.

Cascade “Melting” of a Linear Disclination in Chiral Nematic Droplets

A new structure of the elastic field of a chiral nematic liquid crystal in a cylindrical capillary with a singularity on the axis of the capillary in the form of a “melted” helical disclination has been obtained experimentally. It has been shown theoretically that the number of cylindrical surfaces, cascades at which a jump of the direction of the director orientation field n by π occurs, can be arbitrary. The particular number of cascades depends on the radius R of the cylinder and boundary conditions. An expression for the free energy of the elastic field has been obtained in the one-constant approximation of the continuum theory of liquid crystals.

Design, fabrication, characterisation of optical imaging cylindrical micro-lens array based on liquid crystal

The electrical adjustment of the optical performance of liquid crystal cylindrical micro-lens array of 128×128, which is based on the field controlling effect of liquid crystal dielectric behaviour, is realised through constructing smart liquid crystal electro-optic structure, and orderly modulating the refractive index of liquid crystal material and its spatial distribution. According to the elastic continuum theory of liquid crystal, it is firstly described on the formation of specific refractive index spatial distribution of liquid crystal molecules, which is driven by applied electric-field. Furthermore, the white-light focusing, the far-field white-light interference and the monochromatic laser interference are all measured extensively and discussed in details.

Study the coupling effect of shear and electric field on rheological behaviors of liquid crystals

The rheological behaviors of 5CB liquid crystal under the coupling effect of shear and electric field are investigated by theoretical and experimental study. Establish calculating equation of the system Gibbs free energy by adopting the continuum theory of liquid crystals which contains anchoring energy, elastic free energy, dielectric free energy and flow energy. Then the molecular orientation angle distribution and apparent viscosity of liquid crystal under the coupling effect are obtained by minimizing the Gibbs free energy, revealing the microscopic mechanism of rheological behaviors and influence rules of coupling effect from the molecular model. Meanwhile the calculated results are verified by rheological test. Comparative Analysis of the errors and reasons of theoretical and experimental results, which demonstrates that anchoring effect plays an important role in the molecular orientation and viscosity of liquid crystal. Both the theoretical and experimental results indicate that liquid crystals have electroviscous effect and behavior like non-Newtonian liquids under electric field. The viscosities of liquid crystals are determined by the coupling and competition action of shear and electric field, which can reach 4 times of its original value under electric field. This property of controllable viscosity is important in tribology, which can self-adaptively satisfy the requirement of viscosities for different working conditions as a "smart lubrication" under certain condition.

Gel formation in a mixture of a block copolymer and a nematic liquid crystal

The viscoelastic properties of a binary mixture of a mesogenic side-chain block copolymer in a low molecular weight nematic liquid crystal are studied for mass concentrations ranging from the diluted regime up to a liquid crystalline gel state at about 3%. In the gel state, the system does not flow, exhibits a polydomain structure on a microscopic level, and strongly scatters light. Below the gelation point, the system is homogeneous and behaves like a usual nematic, so the continuum theory of liquid crystals can be applied for interpreting the experimental data. Using the dynamic Fréedericksz transition technique, the dependence of the splay elastic constant and the rotational viscosity on the polymer concentration have been obtained. Comparing the dynamic behavior of block copolymer solutions with the respective homopolymer solutions reveals that, above a mass concentration of 1%, self-assembling of the block copolymer chain segments in clusters occurred, resulting in a gel state at higher concentrations. The effective cluster size is estimated as a function of the concentration, and a scaling-law behavior near the sol-gel transition is confirmed. This technique may serve as an alternative method for determining the gelation point.

Uniqueness in the Freedericksz transition with weak anchoring

In this paper we consider a boundary value problem for a quasi-linear pendulum equation with non-linear boundary conditions that arises in a classical liquid crystals setup, the Freedericksz transition, which is the simplest opto-electronic switch, the result of competition between reorienting effects of an applied electric field and the anchoring to the bounding surfaces. A change of variables transforms the problem into the equation x τ τ = − f ( x ) for τ ∈ ( − T , T ) , with boundary conditions x τ = ± β T f ( x ) at τ = ∓ T , for a convex non-linearity f. By analysing an associated inviscid Burgers' equation, we prove uniqueness of monotone solutions in the original non-linear boundary value problem. This result has been for many years conjectured in the liquid crystals literature, e.g. in [E.G. Virga, Variational Theories for Liquid Crystals, Appl. Math. Math. Comput., vol. 8, Chapman & Hall, London, 1994] and in [I.W. Stewart, The Static and Dynamic Continuum Theory of Liquid Crystals: A Mathematical Introduction, Taylor & Francis, London, 2003].

P‐95: Electro‐Optical Analysis of Super‐IPS LCDs by Using 3‐D Molecular Director Simulation of TFT‐LCDs

AbstractIn this study, we performed a three‐dimensional computer simulation for the electro‐optical characteristics of a super in‐plane switching liquid crystal displays(Super IPS‐LCDs) in a unit pixel of TFT‐LCDs, for the first time, and compared the results with experiments. The dynamic equation of continuum theory for liquid crystals is based on a tensorial formulation. As a numerical technique, we used a finite difference method(FDM) suitable for highly nonlinear equations. As a result, we confirmed that the simulation results such as a transmission profile over a pixel and an average transmittance as a function of applied voltage showed good agreement with the experimental results. We also revealed that Super IPS‐LCDs show good wide viewing angle characteristics with contrast ratio of more than 50:1 up to a polar angle of ±90° both in the horizontal and the vertical directions.

Computational modeling in processing flows of carbonaceous mesophases

Carbonaceous mesophases are liquid crystalline precursor materials that can be spun into high performance carbon fibers using the melt spinning process, which is a flow sequence consisting of capillary, diverging, porous media, converging, and extensional flows that modifies the precursor molecular orientation structure. Carbon fiber property optimization requires a better understanding of the principles that control the structure development during the fiber formation processes and the rheological processing properties. This paper presents the elastic and continuum theory of liquid crystals and computer simulations of structure formation for pressure-driven capillary flow of carbonaceous mesophase precursors used in the industrial carbon fiber spinning process. The simulation results capture the non-Newtonian rheology of mesophase and the formation of characteristic fiber macro-textures.

Computational modeling in processing flows of carbonaceous mesophases

Carbonaceous mesophases are liquid crystalline precursor materials that can be spun into high performance carbon fibers using the melt spinning process, which is a flow sequence consisting of capillary, diverging, porous media, converging, and extensional flows that modifies the precursor molecular orientation structure. Carbon fiber property optimization requires a better understanding of the principles that control the structure development during the fiber formation processes and the rheological processing properties. This paper presents the elastic and continuum theory of liquid crystals and computer simulations of structure formation for pressure-driven capillary flow of carbonaceous mesophase precursors used in the industrial carbon fiber spinning process. The simulation results capture the non-Newtonian rheology of mesophase and the formation of characteristic fiber macro-textures.

Temperature pitch variations in planar cholesteric layers: The role of fluctuations and surface anchoring

The influence of thermodynamic fluctuations on temperature pitch variations in planar cholesteric samples with a finite surface anchoring energy is theoretically investigated in the framework of the continuum theory of liquid crystals. It is shown that taking fluctuations into account allows explanation of experimental observations, namely, the absence of a temperature pitch jump hysteresis in sufficiently thick samples and its existence in thin ones. A description of fluctuations, including two phenomenological parameters, is proposed. It allows us to predict temperature points at which the pitch jumps in the sample between two configurations, with the numbers of director half-turns differing by one, as a function of the anchoring energy, Frank elastic modulus, sample thickness, and temperature (or fluctuation energy). It is shown that performing precise measurements of the pitch versus the temperature in well-controlled samples should allow determination of the phenomenological constants and then prediction the influence of fluctuations on pitch jump parameters in samples of an arbitrary thickness and/or surface anchoring energy. The corresponding calculations are performed using the Rapini-Papoular anchoring potential. It is shown that the influence of fluctuations on the pitch variation is only negligible in sufficiently thin layers. It is also noted that the results obtained could be useful for investigating pitch jump dynamics in the future.

Rigorous calculation of pixel and inter-electrode capacitances of thin-film transistor liquid crystal displays using three-dimensional simulation

We have rigorously calculated for the first time all the inter-electrode and pixel capacitances of Thin-Film Transistor Liquid Crystal Displays using the electrical energy distribution inside a liquid crystal cell. The energy distribution is obtained from the three-dimensional profiles of potential distribution and molecular director. The dynamic equation of continuum theory for liquid crystals is described in a tensorial form in order to maintain the equivalence of n and n. The effects of lateral fields generated by multiple electrodes of finite sizes are taken into account in the simulation. As a numerical technique, we used a finite difference method which is suitable for the highly non-linear equations. As a result, we confirmed that the pixel capacitance for our pixel structure is about 40% larger than that of the conventional approach. It is also revealed that the gate-common and gate-data inter-electrode capacitances are not negligible.

Phase-conjugate reflection and self-starting optical phase-conjugate oscillation in planar nematic liquid-crystal cells

A theoretical model for phase-conjugate reflection of planar nematic liquid-crystal cells is presented based on the continuum theory of liquid crystals and the optical theory of degenerate four-wave mixing. An analytical solution for the phase-conjugate reflectivity R is derived under the undepleted-pump approximation, and the necessary conditions for self-starting optical phase-conjugate oscillation are obtained. The dependence of these conditions on the related physical parameters is also discussed. The reconstruction phenomenon of phase-conjugate light and the self-starting optical phase-conjugate oscillation have been observed experimentally. The intensities of the phase-conjugate light versus the biased voltages for various incident optical intensities have been measured, and the results agree very well with the prediction of our theoretical model.

Modified continuum theory of liquid crystals based on the differentiable manifolds

In the paper an application of differential geometry to construction of microstructural the-theory is presented. This theory is formulated in spaces tangent to material and microstructural manifolds, which form the bundle space Ω. The fibre space F, or the space of microstructure is isomorphic with the orthogonal group O. This way the modified micropolar theory has been formulated. In the paper the deformation, kinematics, balance equations and constitutive equations for such a medium have been considered. The considerations have been related to the theory of Liquid Crystals in Eringen formulation.

Observation of self-starting phase-conjugate oscillation in a planar nematic liquid-crystal cell

We report the observation of self-starting optical phase-conjugate oscillation in a nematic liquid-crystal cell. A theoretical model based on the continuum theory of liquid crystals and optical theory of degenerate four-wave mixing is developed to explain the observed phenomena.

A unified continuum theory of liquid crystals

A unified continuum theory is proposed governing physical behavior of all liquid crystals whose molecules are modelled with rigid directors. Balance laws and constitutive equations are given and thermodynamic restrictions are obtained. Chiral and nonchiral liquid crystals are shown to differ only in their symmetry groups and smectic liquid crystals in a constraint on twist elasticities. Dynamic constitutive equations include translation and gyration viscosities coupled with heat conduction. The theory is shown to give the director (Oseen-Frank) theory under special conditions valid for that theory.

Experiments and analysis of combined diffraction and self-diffraction effects in a nematic-liquid-crystal cell

The potential for nonlinear optical processes in nematic-liquid-crystal cells is great due to the large phase changes resulting from reorientation of the nematic-liquid-crystal director. Here the combination of diffraction and self-diffraction effects are studied simultaneously by the use of a pair of focused laser beams which are coincident on a homeotropically aligned liquid-crystal cell. The result is a complicated diffraction pattern in the far field. This is analyzed in terms of the continuum theory for liquid crystals, using a one-elastic-constant approximation to solve the reorientation profile. Very good comparison between theory and experiment is obtained. An interesting transient grating, existing due to the viscosity of the liquid-crystal material, is observed in theory and practice for large cell-tilt angles.

A matrix method for modelling liquid crystal textures

Abstract A simple method for modelling the textures of liquid-crystalline phases, recently proposed by Bedford et al., is here rewritten in matrix form. A formal similarity is found between their method and the continuum theory of liquid crystals. Disclination patterns are simulated by solving a modified matrix equation.

A continuum theory for liquid crystals describing different degrees of orientational order

Abstract Starting out with mesoscopic orientational balance equations for each orientational component of a liquid crystal which is described as a formal mixture, a set of independent macroscopic variables, the state space Z, is induced This set includes a second-order tensorial measure of alignment, called the alignment tensor A, and its derivatives. In terms of these state space variables constitutive equations are proposed by exploiting the dissipation inequality due to Coleman and Noll. The constitutive equations around equilibrium are investigated. The results are compared in the case of total alignment to those of Ericksen and Leslie, who described the alignment in a liquid crystal with only a macroscopic unit director field d(x, t) indicating the ‘mean orientation’ of the media. In a recent paper Ericksen introduced beside the macroscopic director an additional scalar order parameter S(x, t) and its derivatives (Maier-Saupe theory) which turns out to be the uniaxial case in the alignment tensor formulation. Also in this case the restrictions on the constitutive equations caused by the dissipation inequality are discussed and compared to Ericksen's results.