Thermomechanical modeling of the thermo-order-mechanical coupling behaviors in liquid crystal elastomers

Liquid crystal elastomer is a kind of anisotropic polymeric material, with complicated micro-structures and thermo-order-mechanical coupling behaviors. In this paper, we propose a method to systematically model these coupling behaviors. We derive the constitutive model in full tensor structure according to the Clausius-Duhem inequality. Two of the constitutive equations represent the mechanical equilibrium and the other two represent the phase equilibrium. Choosing the total free energy as the combination of the neo-classical free energy and the Landau-de Gennes nematic free energy, we obtain the Cauchy stress-deformation gradient relation and the order-mechanical coupling equations. We find the analytical homogeneous solutions of the deformation for the typical mechanical loadings, such as uniaxial stretch, and simple shear in any directions. We also compare the compression behavior of prolate liquid crystal elastomers with the stretch behavior of oblate liquid crystal elastomers. As a result, the stress, strain, temperature, order parameter, biaxiality and the direction of the director of liquid crystal elastomers couple with each other. When the prolate liquid crystal elastomer sample is stretched in the direction parallel to its director, the deviatoric stress makes the mesogens more order and increase the transition temperature. When the sample is sheared or stretched in the direction non-parallel to the director, the director of the liquid crystal elastomer will rotate, and the biaxiality will be induced. Because of the order-mechanical coupling, under infinitesimal deformation, liquid crystal elastomer has anisotropic Young’s modulus and zero shear modulus in the direction parallel or perpendicular to the director. While for the oblate liquid crystal elastomers, the stretch parallel to the director will cause the rotation of the director and induce the biaxiality.     

Sub-stripe pattern formation in liquid crystal elastomers: Experimental observations and numerical simulations

We report on some new experimental observations of pattern formation during stretching experiments of nematic liquid crystal elastomers (LCEs).     

Transient thermo-mechanical analysis for bimorph soft robot based on thermally responsive liquid crystal elastomers

Thermally responsive liquid crystal elastomers(LCEs) hold great promise in applications of soft robots and actuators because of the induced size and shape change with temperature. Experiments have successfully demonstrated that the LCE based bimorphs can be effective soft robots once integrated with soft sensors and thermal actuators. Here, we present an analytical transient thermo-mechanical model for a bimorph structure based soft robot, which consists of a strip of LCE and a thermal inert polymer actuated by an ultra-thin stretchable open-mesh shaped heater to mimic the unique locomotion behaviors of an inchworm. The coupled mechanical and thermal analysis based on the thermo-mechanical theory is carried out to underpin the transient bending behavior, and a systematic understanding is therefore achieved. The key analytical results reveal that the thickness and the modulus ratio of the LCE and the inert polymer layer dominate the transient bending deformation. The analytical results will not only render fundamental understanding of the actuation of bimorph structures, but also facilitate the rational design of soft robotics.     

Elasticity,piezoelectricity and crystal lattice dynamics

A review of some recent developments in the area between the dynamical theory of crystal lattices, in the harmonic approximation, and the classical, linear theories of elasticity and piezoelectricity.

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Résumé Un examen de quelques évolutions récentes dans le champ entre la théorie dynamique des réseaux cristallins (upproximation harmonique) et les théories classiques, linéaires, de l'élasticité et de la piézoélectricité.

     

Viscosity of a liquid crystalline polymer solution with a polydomain or a band texture

The viscosity of a main-chain liquid crystalline polymer (anisotropic aqueous solution of hydroxypropylcellulose) is measured in the case where the liquid crystalline polymer presents a band texture and is compared to the case of a polydomain texture.     

Computational rheooptics of liquid crystal polymers

A computational rheooptical model based on the integration of liquid crystal polymer flow equations and two well-known polarized light transmission methods is formulated and applied to the ubiquitous periodic banded textures observed in sheared lyotropic nematic polymers. The selected optical methods are the matrix-type Berreman method and the finite-difference time-domain (FDTD) direct numerical simulation method. The optical response of a single unit cell of the periodic banded texture of sheared lyotropic nematic polymers to polarized light propagation under cross-polars is analyzed and correlated to the shear-induced orientation field previously reported in Han and Rey [W.H. Han, A.D. Rey, Theory and simulation of optical banded textures of nematics polymer during shear flow, Macromolecules 28 (1995) 8401–8405]. The role of orientation gradients on the optical response is elucidated and shown to be source of lack of accuracy of the Berreman matrix method. The findings provide robust guidelines on the applicability and accuracy of matrix and direct numerical simulation optical methods. Computational rheooptics of liquid crystal polymers based on the FDTD method is an additional tool to understand flow-induced texture formation when used in the direct forward mode, and in quantitative assessments of rheological material properties when used in backward mode.     

Equivalent smectic C liquid crystal energies

This article describes the relationships between the alternative formulations of the bulk non-chiral smectic C liquid crystal energies currently available in the literature; the relative equivalence of these energies is discussed and demonstrated.     

Axisymmetric configurations of bipolar liquid crystal droplets

Received July 4, 2001 / Published online April 10, 2002     

An electromechanical liquid crystal model of vesicles

An electromechanical liquid crystal model is developed for characterizing the equilibrium morphology of a lipid vesicle under coupled mechanical and electrical fields. A general equation that governs the vesicle shape is established, which incorporates the effects of elastic bending, osmotic pressure, surface tension, Maxwell pressure, as well as flexoelectric and dielectric properties of the lipid membrane. As an illustration of the model, the problem of an axisymmetric vesicle (e.g., a sphere or a cylinder) in a uniform electric field is considered in some detail, with results in agreement with relevant experimental results. The model provides an efficient tool for studying morphological evolution of dielectric vesicles under mechanical and electrical fields.     

Angular effects on thermochromic liquid crystal thermography

This paper directly discusses the effects of lighting and viewing angles on liquid crystal thermography. This is because although thermochromic liquid crystals (TLCs) are a widely-used and accepted tool in heat transfer research, little effort has been directed to analytically describing these effects. Such insight is invaluable for the development of effective mitigation strategies. Using analytical relationships that describe the perceived color shift, a systematic manner of improving the performance of a TLC system is presented. This is particularly relevant for applications where significant variations in lighting and/or viewing angles are expected (such as a highly curved surface). This discussion includes an examination of the importance of the definition of the hue angle used to calibrate the color of a TLC-painted surface. The theoretical basis of the validated high-accuracy calibration approach reported by Kodzwa et al. (Exp Fluids s00348-007-0310-6, 2007) is presented. This work was funded by the General Electric Aircraft Engines University Strategic Alliance Program.     

Shear orientation of a lamellar lyotropic liquid crystal

Shear orientation of a lyotropic lamellar liquid crystalline phase of tetra ethyleneglycol mono dodecylether, C₁₂A₄ in water was studied by combined rheo-small-angle light scattering. Shear thinning was observed with a sample of 500 m thickness. The scattering patterns showed that domains were aligned and stretched in flow direction. Shear thinning was also observed with a thinner sample, but caused a strong change in light-scattering pattern. A maximum of scattering intensity was observed at finite scattering vector and shifted to a higher scattering vector with increasing shear stress. This observation can be explained by a fragmentation of domains at high shear stress and is supported by a mosaic texture observed in optical microscopy.     

Flow visualization of a recirculating flow by rheoscopic liquid and liquid crystal techniques

Experiments were conducted in a three-dimensional lid-driven cavity flow to study the behavior of longitudinal Taylor-Görtler-like vortices. Flow visualization was accomplished by use of a rheoscopic liquid and of liquid crystals, together with laser-light and white-light sheets, respectively. Photographs of the lighted planes in the flow confirmed the existence of the vortices for a wide range of Reynolds numbers and for stable, neutrally-buoyant and buoyant global flow conditions. As usual the flow visualization revealed flow patterns not deducible by in situ measurements; the liquid crystal photographs give both flow pathlines and temperature distribution on any lighted plane.     

Dynamics of shear aligning of nematic liquid crystal monodomains

The equations of linear and angular momentum for nematic liquid crystals have been described with Ericksen's transversely isotropic fluid [TIF] model and solved for start-up of shear flow at constant rate and varying initial alignment conditions. An analytical solution for the rotation provides predictions of the nematic director which closely agree with experimental results of Boudreau et al. (1999), supporting the validity of Ericksen's TIF model. The solution is limited to flows where the effects of director gradients are negligible. Received: 13 September 1999/Accepted: 24 January 2000     

A rheological theory for liquid crystal thin films

A macroscopic rheological theory for compressible isothermal nematic liquid crystal films is developed and used to characterize the interfacial elastic, viscous, and viscoelastic material properties. The derived expression for the film stress tensor includes elastic and viscous components. The asymmetric film viscous stress tensor takes into account the nematic ordering and is given in terms of the film rate of deformation and the surface Jaumann derivative. The material function that describes the anisotropic viscoelasticity is the dynamic film tension, which includes the film tension and dilational viscosities. Viscous dissipation due to film compressibility is described by the anisotropic dilational viscosity. Three characteristic film shear viscosities are defined according to whether the nematic orientation is along the velocity direction, the velocity gradient, or the unit normal. In addition the dependence of the rheological functions on curvature and film thickness has been identified. The rheological theory provides a theoretical framework to future studies of thin liquid crystal film stability and hydrodynamics, and liquid crystal foam rheology. Received: 9 October 2000 Accepted: 6 April 2001     

Shear viscosity of polybutyleneterephthalate/liquid crystal polymer blends

Viscosity measurements have been carried out on blends of polybuty-leneterephthalate (PBT) and a liquid crystalline copolyesteramide (LCP). The flow curves of the blends with LCP content larger than 20%, show a behavior similar to that of the pure LCP, with a rapid rise of the viscosity at low shear rates. The viscosity-composition curves exhibit a deep minimum at low LCP content which may be mainly attributed to the lack of interactions between the two phases.     

Light-powered self-excited motion of a liquid crystal elastomer rotator

Nonlinear Dynamics - Self-excited motions have the advantages of directly harvesting energy from the environment, autonomy, and portability of the equipment, and consequently, the development of a...     

Multiple solutions in twisted nematic liquid crystal layers

A twisted nematic layer is modelled using a continuum theory which allows for the presence of phase changes and biaxiality within liquid crystals. Under certain approximations analytical solutions are found and used to validate numerical solutions of the full problem. Using a numerical continuation package (AUTO) it is possible to find regions where multiple solutions for the director configuration and hysterisis can occur. Changes in temperature, amount of twist and gap width are investigated in d etail and subsequently the relevance of these results to display technology is discussed.     

Orientational instability of a lyotropic nematic liquid crystal layer

The problem of periodic domain initiation in a thin lyotropic nematic liquid crystal layer is studied. This layer has a planar director initial orientation, but the anchoring energy is minimized by the homeotropic one. The periodic structures whose wave vector is perpendicular to the director exist during the director reorientation process from the planar orientation to the homeotropic one when the reorientation wave front appears. It is shown that the divergent terms of the Prank orientation elasticity energy plays an important role in this effect. The saddle-splay Prank constant and the anisotropic anchoring energy coefficient are estimated.