In their paper, using the principle of energy conservation, F. Castles, S. M. Morris, and H. J. Coles [AIP Advances 1, 032120 (2011)] establish inequalities involving the elastic and dielectric constants and flexoelectric coefficients of liquid crystals. They then argue that recently measured values of flexoelectric coefficients by Harden et al. do not obey these inequalities, hence they violate the principle of energy conservation. In this comment, we point out that in their calculation, Castles et al. use an inappropriate value for an elastic constant, hence their conclusions, predicated on the outcome of this calculation, are not justified. Copyright 2013 Author(s). This article is distributed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4774285]

Mirage Mirror on the Wall12/15/2000We discuss mirages formed near a sunheated wall, and consider the underlying physics. The temperature and refractive index variations in air near the wall are estimated, and a simple approximate picture of ray propagation is presented. Estimates of the thermal decay length and ray curvature are compared with experimental observations. 
The Single Particle Potential in MeanField Theory04/15/2002The problem of determining the single particle energy in a meanfield description of interacting particles is considered. It is shown that the single particle energy must satisfy two consistency conditions, and a general procedure for obtaining the single particle energy from the pair energy is proposed. Interacting dipolar systems are examined, current approaches in the literature are discussed, and the usefulness of the proposed method is demonstrated. 
ThreeDimensional Dye Distribution in PhotoOriented LiquidCrystal Alignment Layers04/15/2002The threedimensional optical anisotropy of photobuffed dyedoped polymer films and the resulting orientation imparted to a liquid crystal in contact are probed using total internal reflection. Although the linearly polarized writing light generates a uniaxial distribution of dye molecules, the polymer films are biaxial, a result of symmetry breaking by the film surface. 
Experimental Studies of the Mechanisms of Photomechanical Effects in a Nematic Liquid Crystal Elastomer08/01/2011Azodyedoped liquid crystal elastomers (LCEs) are known to show a strong photomechanical response. We report on experiments that suggest that photothermal heating is the underlying mechanism in surfaceconstrained geometry. In particular, we use optical interferometry to probe the length change of the material and direct temperature measurements to determine heating. LCEs with various dopants and optical density were used to study the individual mechanisms. In the high dyedoped limit, most of the light is absorbed near the entry surface, which causes a local strain from photothermal heating and a nonlocal strain from thermal diffusion. The results of our research on the microscopic mechanisms of the photomechanical response can be applied to designing photomechanical materials for actuating/sensing devices, the potential basis of smart structures. (C) 2011 Optical Society of America 
ThermalLens Model Compared with the SheikBahae Formalism in Interpreting ZScan Experiments on Lyotropic Liquid Crystals06/01/2002We carried out Zscan measurements on lyotropic liquid crystals and on lyotropic liquid crystals doped with ferrofluid. In these experiments, the sample is translated through the focal region of a focused Gaussian laser beam. The dependence of the farfield intensity on sample position due to intensitydependent optical nonlinearities has been analyzed on the basis of the thermallens model of Gordon et al. and the Gaussian decomposition analysis of SheikBahae et al. The thermallens model is nonlocal in space and time, whereas the Gaussian decomposition is predicated on a strictly local response. We compare the goodness of fit of the predictions of these models to experimental data, and we discuss limitations of these models in describing Zscan experiments on systems with nonlocal response. (C) 2002 Optical Society of America. 
Ultraviolet Lasing in Cholesteric Liquid Crystals06/01/2001We report the observation of stimulated emission and mirrorless lasing in pure cholesteric liquid crystals. The lasing action is attributed to the combination of the fluorescence and the distributed feedback that are due to the inherent periodic structure of the liquid crystal. If the reflection band matches the intrinsic emission of the cholesteric liquid crystal, the crystal becomes a natural laser material, which will selflase, without any optical elements or the addition of dyes, under picosecond excitation at 355 nm. Samples have been made to lase at different wavelengths in the near UV by shifting of the edge of the reflection band in the range of 385405 nm. Typical linewidths observed are of the order of 0.5 nm. (C) 2001 Optical Society of America. 
Director Dynamics in LiquidCrystal Physical Gels05/30/2007Nematic liquid crystal (LC) elastomers and gels have a rubbery polymer network coupled to the nematic director. While LC elastomers show a single, non hydrodynamic relaxation mode, dynamic light scattering studies of self assembled liquid crystal gels reveal orientational fluctuations that relax over a broad time scale. At short times, the relaxation dynamics exhibit hydrodynamic behavior. In contrast, the relaxation dynamics at long times are nonhydrodynamic, highly anisotropic, and increase in amplitude at small scattering angles. We argue that the slower dynamics arise from coupling between the director and the physically associated network, which prevents director orientational fluctuations from decaying completely at short times. At long enough times the network restructures, allowing the orientational fluctuations to fully decay. Director dynamics in the self assembled gels are thus quite distinct from those observed in LC elastomers in two respects: they display soft orientational fluctuations at short times, and they exhibit at least two qualitatively distinct relaxation processes. 
A Dunking Bird of the Second Kind06/01/2004
The conventional dunking bird is a heat engine that relies on the temperature difference between the head and the tail of the bird for its operation. We describe a new type of dunking bird that is not a heat engine, but one that directly uses the chemical potential difference between liquid water and its vapor. (C) 2004 American Association of Physics Teachers.

Optically Induced Periodic Structures in SmecticC Liquid Crystals01/01/2001
We explore periodic structures of smecticC (SmC) liquid crystals, induced optically by a polarization grating. The studied cells contain a passive surface of rubbed polyimide and an active photosensitive substrate of atedye doped polyimide. In a nematic phase the director field can be periodic independent of the angle between the grating vector and the rubbing direction. In the SmA phase periodic structure can be induced only by layer undulations. The SmC behaves similarly to the nematic phase, but the director can rotate only on a cone, which results in a more complex geometry. The periodic pattern is superimposed with four different director and layer structures. In spite of the coexistence of the nonuniform structures the diffraction efficiency is better in the SmC, than in the nematic phase.

BentCore Liquid Crystal Elastomers01/01/2010Liquid crystal (LC) elastomers with bentcore sidegroups incorporate the properties of bentcore liquid crystals in a flexible and selfsupporting polymer network. Bentcore liquid crystal elastomers (BCEs) with uniform alignment were prepared by attaching a reactive bentcore LC to poly(hydrogenmethylsiloxane) and crosslinking with a divinyl crosslinker. Phase behavior studies indicate a nematic phase over a wide temperature range that approaches room temperature, and thermoelastic measurements show that these BCEs can reversibly change their length by more than a factor of two upon heating and cooling. Smallangle Xray scattering studies reveal multiple, broad lowangle peaks consistent with shortrange smectic C order of the bentcore side groups. A comparison of these patterns with predictions of a Landau model for shortrange smectic C order shows that the length scale for smectic ordering in BCEs is similar to that seen in pure bentcore LCs. The combination of rubber elasticity and smectic ordering of the bentcore side groups suggests that BCEs may be promising materials for sensing, actuating, and other advanced applications. 
Distance of Closest Approach of Two Arbitrary Hard Ellipsoids06/01/2007The distance of closest approach of hard particles is a key parameter of their interaction and plays an important role in the resulting phase behavior. For nonspherical particles, the distance of closest approach depends on orientation, and its calculation is surprisingly difficult. Although overlap criteria have been developed for use in computer simulations [ VieillardBaron J. Chem. Phys. 56 4729 (1972); Perram and Wertheim J. Comput. Phys. 58 409 (1985)], no analytic solutions have been obtained for the distance of closest approach of ellipsoids in three dimensions, or, until now, for ellipses in two dimensions. We have derived an analytic expression for the distance of closest approach of the centers of two arbitrary hard ellipses as a function of their orientation relative to the line joining their centers. We describe our method for solving this problem, illustrate our result, and discuss its usefulness in modeling and simulating systems of anisometric particles such as liquid crystals. 
Distance of Closest Approach of Two Arbitrary Hard Ellipses in Two Dimensions06/01/2007The distance of closest approach of hard particles is a key parameter of their interaction and plays an important role in the resulting phase behavior. For nonspherical particles, the distance of closest approach depends on orientation, and its calculation is surprisingly difficult. Although overlap criteria have been developed for use in computer simulations [ VieillardBaron J. Chem. Phys. 56 4729 (1972); Perram and Wertheim J. Comput. Phys. 58 409 (1985)], no analytic solutions have been obtained for the distance of closest approach of ellipsoids in three dimensions, or, until now, for ellipses in two dimensions. We have derived an analytic expression for the distance of closest approach of the centers of two arbitrary hard ellipses as a function of their orientation relative to the line joining their centers. We describe our method for solving this problem, illustrate our result, and discuss its usefulness in modeling and simulating systems of anisometric particles such as liquid crystals. 
One Order Parameter Tensor Mean Field Theory for Biaxial Liquid Crystals03/15/2011In this paper, we present a simple one tensor mean field model of biaxial nematic liquid crystals. The salient feature of our approach is that material parameters appear explicitly in the order parameter tensor. We construct the free energy from a mean field potential based on anisotropic dispersion interactions, identify the order parameter tensor and its elements, and obtain selfconsistent equations, which are then solved numerically. The results are illustrated in a 3D ternary phase diagram. The phase behavior can be simply related to molecular parameters. The results may be useful for designing molecules that show a thermotropic biaxial phase. 
Solar to Electrical Conversion via Liquid Crystal Elastomers06/15/2011We have constructed a hypothetical charge pump which converts solar energy into DC electricity. The output is generated by cyclic changes in the capacitance of a circuit, which transfers charge from a low to a high voltage. The electric field across the capacitor must be of the order of 10(8)Vm(1) to compete with efficiencies of photovoltaics. We have modeled the output using a liquid crystal elastomer as the working substance. Efficiencies of 1  4% are obtained, and are enhanced by careful choices in the capacitor geometries and the operating voltages of the charge pump. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3581134] 
Domain Size in the Presence of Random Fields01/01/1998We consider the size of domains formed in ordered systems in the presence of quenched random fields. We argue that below the critical dimension, the, domain size shows a nonmonotonic dependence on the correlation length of the random field. If the random field is slowly varying in space, the order parameter follows the field, and the domain size is comparable to the correlation length. If the field is rapidly varying, the domain size becomes larger than the correlation length, and diverges as the correlation length of the random field goes to zero. 
Nonlinear Schrodinger Equation in Nematic Liquid Crystals01/01/1998We derive the amplitude equation, in the weakly nonlinear regime, for an optical wave packet that propagates in an initially undistorted nematic liquid crystal. By using the dyad representation Q(ij), we find the retarded and nonlocal equation for the nematic configuration and solve it in Fourier space. This allows us to calculate the amplitude dependent dispersion relation for a nematic liquid crystal in a given initial undistorted stationary state. We consider a linearly polarized wave packet that travels along the principal axis of the nematic dielectric tensor. We find a nonlinear Schrodinger equation for the amplitude, which includes an additional quadratic term with dissipation. [S1063651X(98)093106]. 
Control of Viscous Fingering Patterns in a Radial HeleShaw Cell01/01/2009We study numerically and experimentally the dynamics and control of viscous fingering patterns in a circular HeleShaw cell. The nonlocality and nonlinearity of the system, especially interactions among developing fingers, make the emergent pattern difficult to predict and control. By controlling the injection rate of the less viscous fluid, we can precisely suppress the evolving interfacial instabilities. There exist denumerable attractive, selfsimilarly evolving symmetric, universal shapes. Experiments confirm the feasibility of the control strategy, which is summarized in a morphology diagram. 
A Cellulose Liquid Crystal Motor: A Steam Engine of the Second Kind01/04/2013The salient feature of liquid crystal elastomers and networks is strong coupling between orientational order and mechanical strain. Orientational order can be changed by a wide variety of stimuli, including the presence of moisture. Changes in the orientation of constituents give rise to stresses and strains, which result in changes in sample shape. We have utilized this effect to build soft cellulosebased motor driven by humidity. The motor consists of a circular loop of cellulose film, which passes over two wheels. When humid air is present near one of the wheels on one side of the film, with drier air elsewhere, rotation of the wheels results. As the wheels rotate, the humid film dries. The motor runs so long as the difference in humidity is maintained. Our cellulose liquid crystal motor thus extracts mechanical work from a difference in humidity. 
Ericksen's Bar and Modeling of the Smectic ANematic Phase Transition03/21/2000We consider free energy functionals to model equilibrium smectic A liquid crystal configurations in the neighborhood of the nematic phase transition. We begin with the functional proposed by de Gennes based on the Ginzburg Landau model for superconductivity and consider its covariant formulations. Exploring qualitative analogies with the nonlinear elastic bar of Ericksen, we motivate a revision of the liquid crystal energy so as to include a nonconvex constraint. We study boundaryvalue problems corresponding to Neumann and Dirichlet boundary conditions for smectic A liquid crystals conned between two parallel plates. We show that the nonconvex term of the free energy density causes the presence in the solutions of nematic defects known to occur near the phase transition from smectic A to nematic. The latter are reminiscent of the dislocations occurring in higher dimensional configurations. We also determine parameter values that give rise to nucleation of nematic defects for boundary conditions consistent with externally imposed winding of the smectic phase field. The resulting energy also allows us to sort out liquidlike and solidlike behaviors, respectively. 
MaierSaupe Theory in Four Dimensions04/06/2011MaierSaupe theory is the canonical mean field description of thermotropic nematic liquid crystals. In this paper, we examine the predictions of the theory in four spatial dimensions. Representations of the order parameter tensor and the existence of new phases are discussed. The phase diagram, based on numerical solution of the selfconsistent equations and Landau theory, is presented. Orientational order decreases as the number of spatial dimensions is increased. 
Modeling the Mechanisms of the Photomechanical Response of a Nematic Liquid Crystal Elastomer09/01/2011Recent studies of azodyedoped liquid crystal elastomers show a strong photomechanical response. We report on models that predict experimental results that suggest photothermal heating is the dominant mechanism in a planar constrained geometry. We compare our models with experiments to determine key material parameters, which are used to predict the dynamical response as a function of intensity. We show that a local strain from photothermal heating and a nonlocal strain from thermal diffusion is responsible for the observed length changes over time. This work both elucidates the fundamental mechanisms and provides input for the design of photomechanical optical devices, which have been shown to have the appropriate properties for making smart materials. 
Analytical Solution of Maxwell's Equations in Lossy and Optically Active Crystals03/01/2000Analytical solution of Maxwell's equations is obtained for general linear optical materials: lossy and optically active crystals. Explicit expressions are obtained for the dispersion relation and the propagating eigenmodes. In general, four rather than two distinct modes are present. The results are useful in describing light propagation in optically complex media. 
Surface Wrinkling in Liquid Crystal Elastomers01/01/2012Structured surfaces give rise to novel and potentially useful properties such as controllable wettability and structural colour. Here, we demonstrate structured surfaces via reversible surface wrinkling in liquid crystal elastomers (LCEs). A thin polymer film deposited on top of a shaperesponsive LCE exhibits a reversible, periodic surface wrinkling pattern in response to temperature changes. The orientation of the wrinkles depends on the orientation of the nematic director and the temperature at which the bilayer is prepared, and the wrinkles can be reoriented in a single sample by heating or cooling the sample above or below the preparation temperature. We show that this bilayer system can be used to measure the modulus of nanoscale thin poly(styrene) films deposited on the LCE. Additionally, when a micronthick polymer film is deposited on top of an LCE, the bilayer exhibits reversible curling with temperature. This system provides a simple method for measuring the mechanical properties of thin polymer films without the need for clamping and mechanical stretching and provides a new approach to generate reversible, microstructured surfaces. 
Nonphotochemical LaserInduced Nucleation of Nematic Phase and Alignment of Nematic Director from a Supercooled Thermotropic Liquid Crystal02/01/2009A nonphotochemical laserinduced phase transition was studied in a supercooled 4′‐npentyl4cyanobiphenyl (5CB, also referred to as PCB and K15) liquid crystal, using linearly polarized 45 ps light pulses at a wavelength of 532 nm. The laser induced nucleation from the metastable supercooled isotropic phase to the nematic phase during slow cooling (0.001 °C∕min) and high light intensity (3.9 MW∕cm2). The resulting nematic director tended to be aligned along the direction of the plane of polarization of the light. At the intensities used, there is no observable laserinduced realignment of the director once the sample is in the nematic phase, nor any permanent laserinduced ordering when the sample is illuminated only in the stable isotropic phase during slow cooling. These experimental results are consistent with a mechanism based on optical Kerr alignment. 
NonNewtonian HeleShaw Flow and the SaffmanTaylor Instability02/16/1998We explore the SaffmanTaylor instability of a gas bubble expanding into a shear thinning liquid in a radial HeleShaw cell. Using Darcy's law generalized for nonNewtonian fluids, we perform simulations of the full dynamical problem. The simulations show that shear thinning significantly influences the developing interfacial patterns. Shear thinning can suppress tip splitting, and produce fingers which oscillate during growth and shed side branches. Emergent length scales show reasonable agreement with a general linear stability analysis. 
Pattern Formation in NonNewtonian HeleShaw Flow01/01/2001We study theoretically the SaffmanTaylor instability of an air bubble expanding into a nonNewtonian fluid in a HeleShaw cell, with the motivation of understanding suppression of tipsplitting and the formation of dendritic structures observed in the flow of complex fluids, such as polymeric liquids or liquid crystals. A standard viscoelastic flow model is simplified in the case of flow in a thin gap, and it is found that there is a distinguished limit where shear thinning and normal stress differences are apparent, but elastic response is negligible. This observation allows formulation of a generalized Darcy's law, where the pressure satisfies a nonlinear elliptic boundary value problem. Numerical simulation shows that shearthinning alone modifies considerably the pattern formation and can produce fingers whose tipsplitting is suppressed, in agreement with experimental results. These fingers grow in an oscillating fashion, shedding "sidebranches" from their tips, closely resembling solidification patterns. A careful analysis of the parametric dependencies of the system provides an understanding of the conditions required to suppress tipsplitting, and an interpretation of experimental observations, such as emerging lengthscales. (C) 2001 American Institute of Physics. 
Nonlocal Model for Nematic LiquidCrystal Elastomers01/01/2006We have developed a fully nonlocal model to describe the dynamic behavior of nematic liquidcrystal elastomers. The free energy, incorporating both elastic and nematic contributions, is a function of the material displacement vector and the orientational order parameter tensor. The free energy cost of spatial variations of these order parameters is taken into account through nonlocal interactions rather than through the use of gradient expansions. We also give an expression for the Rayleigh dissipation function. The equations of motion for displacement and orientational order are obtained from the free energy and the dissipation function by the use of a Lagrangian approach. We examine the free energy and the equations of motion in the limit of longwavelength and smallamplitude variations of the displacement and the orientational order parameter. We compare our results with those in the literature. If the scalar order parameter is held fixed, we recover the usual viscoelastic theory for nematic liquid crystals. 
Modeling and Simulation of LiquidCrystal Elastomers01/01/2011We consider a continuum model describing the dynamic behavior of nematic liquid crystal elastomers (LCEs) and implement a numerical scheme to solve the governing equations. In the model, the Helmholtz free energy and Rayleigh dissipation are used, within a Lagrangian framework, to obtain the equations of motion. The free energy consists of both elastic and liquid crystalline contributions, each of which is a function of the material displacement and the orientational order parameter. The model gives dynamics for the material displacement, the scalar order parameter and the nematic director, the latter two of which correspond to the orientational order parameter tensor. Our simulations are carried out by solving the governing equations using an implicitexplicit scheme and the Chebyshev polynomial method. The simulations show that the model can successfully capture the shape changing dynamics of LCEs that have been observed in experiments, and also track the evolution of the order parameter tensor. 
Cholesteric LiquidCrystal Laser as an Optic FiberBased Temperature Sensor10/04/2004
In this work, we have studied the temperature dependence of a cholesteric liquidcrystal laser coupled to an optical fiber, with a view towards optical fiber sensor applications. To stabilize the laser emission, we developed a procedure to align the liquid crystal placed in the fiber. Unexpected oscillations in the laser emission were observed as the temperature was varied, which can be understood in terms of the competition between bulk and surface anchoring torques. (C) 2004 American Institute of Physics.

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