单轴拉伸下液晶高弹体力学行为的热力序耦合特性

本文利用液晶高弹体的应力－应变本构方程和力－序耦合方程,研究了沿指向矢单轴拉伸下液晶高弹体力学行为的热力序耦合特性。由于力－序耦合,有序度在拉伸作用下变大,从而影响了液晶高弹体的应力－应变关系,使得应力在相同伸长下变小。不同温度下应力受到有序度变化影响的程度不同.由于有序度随温度升高而减小,当工程应力不变时,伸长随着温度升高而减小;当伸长不变时,应力随着温度升高而增大;伸长随温度的变化关系和应力随温度的变化关系都呈非线性。     

BIAXIAL LOADING OF NEO-CLASSICAL LIQUID CRYSTAL ELASTOMERS:CONSTITUTIVE RELATIONS AND SOFT BEHAVIOR

The thermo-order-mechanical behaviors of liquid crystal elastomers(LCEs) under biaxial loading are studied in this paper.Inverse method for nonlinear elastic problems is utilized by imposing biaxial stretching to thin rectangular samples.Neo-classical elastic energy is used together with the Landau-de Gennes nematic free energy.Under plane stress assumptions,the constitutive equations are derived.Due to the possible reorientations of the liquid crystal molecules induced by the imposed biaxial loading,the in-plane nonlinear stress-strain relations can have different expressions depending on which loading axis will have the largest effective principal strain.And the free energy is a multi-well non-convex potential function.As shown by some typical loading paths,the LCE samples will exhibit an anisotropic nonlinear elastic behavior,as long as the loading has not induced a reorientation of the liquid crystal molecules.When this did occur,jumps of stresses could take place for dead loadings due to the losing of stability.     

Quasi-soft opto-mechanical behavior of photochromic liquid crystal elastomer: Linearized stress–strain relations and finite element simulations

Based on the neo-classical elastic energy of liquid crystal elastomers, the opto-mechanical behavior is modeled by considering the effect of photoisomerization on the nematic-isotropic transition of liquid crystal phase. Linearized stress–strain relation is derived for infinitesimal deformations with a very unusual shear stress that does not vanish identically as in the case of the soft behavior but is proportional to the rotation of directors. In other words, the shear stress depends on both the shear strain and the skew symmetric part of the displacement gradient with the shear modulus induced by the effect of photoisomerization. Finite element implementation for plane stress problems is obtained through a self-defined material subroutine in ABAQUS FEA tool. Numerical simulations show that the light induced deformations of two dimensional specimens consist of contractions, expansions and bending in different directions. The stress distributions indicate that the driving force for the light induced bending is produced by the bending moment of the normal stress along the director, while the other stress components are much smaller for two dimensional beam shaped specimens. However, the shear stress of the soft LCE is generally nonzero under light illumination due to the inhomogeneity of the opto-mechanical effect. It can be concluded from the strain distributions that the transversal plane cross section could remain plane after deformation if the light intensity or the decay distance is not too small and the sample is in the deep nematic phase. However, the shear strain and in plane rotation are of the same order as the other strain components, and thus should not be neglected. This indicates that the classical simple bending assumptions such as the Euler–Bernoulli beam theory should not be directly applied to model the light induced bending of neo-classical liquid crystal elastomers due to the soft behavior of the materials.     

Orientation instability of the layer of a nematic liquid crystal

The origin of periodic structures in a layer of a lyotropic nematic liquid crystal observed in the director (vector, describing the anisotropic properties of the medium) reorientation experiment is studied. Such perturbations with the wavevector perpendicular to the initial orientation can develop in a liquid crystal layer in the unstable equilibrium state when the director is parallel to the walls under the condition that its orthogonality to the boundary corresponds to the minimum anchoring energy. It is shown that the linear dependence of the domain period on the layer thickness observed experimentally can be theoretically described when the Frank orientation elasticity energy is considered in the most general form taking the divergence terms into account and the anchoring energy of orientation is small as compared with the bulk energy. A relation between the coefficient of the divergence terms (saddlesplay elastic constant) and two other coefficients in the Frank energy is obtained.     

Stress-free layers in photoinduced deformations of photoelastomer beams

Nematic liquid crystals combined with long molecular chains to form liquid crystal elastomers are capable of large extension. When such liquid crystal elastomers contain azo dyes to constitute photoelastomers, illumination can trigger large contraction. Beams made from such photoelastomers possess a non-uniform illumination and hence photostrain across their cross-section, resulting in bending and highly non-linear stress distribution. Due to the non-linear stress distribution, there can be more than one stress-free layers within the beam. In this paper, we present a dimensionless parametric study of nematic photoelastomer beams under the combined effects of light and mechanical loads. We show how the number of stress-free layers depends on three dimensionless parameters. The paths traced out by the system in the space of dimensionless parameters by varying the different real parameters are investigated, showing how the number of stress-free layers changes when e.g. the thickness or the mechanical load of the elastomer beam is varied. These results are important if the strain induced director rotation is not negligible.     

Dynamic rheology of the immiscible blends of liquid crystalline polymers and flexible chain polymers

Immiscible blends containing liquid crystalline polymers (LCP) as dispersed phases show different dynamic rheological properties than those composed of flexible polymers. The widely used Palierne’s model was shown by many authors to be insufficient to describe the frequency dependence of dynamic modulus of such blends. A new model was presented to describe the dynamic rheology of the immiscible blend containing LCP as a dispersed phase. The flexible chain polymer matrix was assumed to be a linear viscoelastic material under small amplitude oscillatory shear flow, and the LCP was assumed to be an Ericksen’s transversely isotropic fluid. The Rapini-Papoular equation of anisotropic interfacial energy was used to account for the effect of nematic orientation on the interfacial tension. It was found that the orientation of the director and the anchoring energy greatly influenced the storage modulus at the “shoulder” regime. The overall dynamic modulus of the blend can be well described by the model with suitable choice of the orientation of the director and anchoring energy of LCP.     

A gradient model of light-induced bending in photochromic liquid crystal elastomer and its nonlinear behaviors

Photochromic liquid crystal elastomer was recently reported to be able to deform largely and bend under illumination. In this paper, considering the opto-chemical process and the nematic-isotropic phase transition, we introduce the light and temperature into the constitutive relation of the liquid crystal elastomers, and propose a model for the light-induced bending. The dynamic deflection curve equation of the light-induced bending is derived based on the Hamilton principle. In the equation, the effect of light is introduced as an effective optical bending moment, which is caused by the inhomogeneous light-induced strain and Young's modulus. Several simulation examples are given to show the light-induced bending under different boundary conditions and various illumination or temperature controlling. Under the condition of deep nematic phase and weak enough illumination, the approximate analytical expression of the effective moment and the stress distribution can be obtained. Rich nonlinear behaviors are found in this model. The effective moment is a non-monotonic function of time, thickness ratio, and light intensity when the thickness ratio is not very large. The stress distribution through the thickness is nonlinear with two or three zero-stress planes.     

Continuum Electromechanical Theory for Nematic Continua with Application to Freedericksz Instability

Of interest in this work are nematic continua that exhibit electromechanical coupling. The first part of this paper presents a novel variational formulation with a potential energy depending on four independent variables (the displacement, director, specific polarization and electric displacement perturbation). Variations of the potential energy with respect to each one of these variables lead to the governing mechanical equilibrium and constitutive relations plus Maxwell’s equations.The proposed variational formulation is next applied to the study of bifurcation of an infinite layer of a nematic liquid crystal confined between two parallel plates and subjected to a uniform electric field perpendicular to these plates under full anchoring boundary conditions. As the electric field exceeds a critical value, the nematic directors which are initially parallel to the plates, rotate and tend to align with the electric field orientation. This phenomenon, termed in the literature as Freedericksz transition, is treated here as a bifurcation problem using a fully 2D formulation. It is shown that the solution corresponding to the lowest applied electric field, also termed the critical load, is uniform in the direction parallel to the plates and that the corresponding bifurcated path is stable near this critical load. This result holds for arbitrary positive constants of the Frank-Oseen energy (and values of electric susceptibility constants that allow bifurcation) and justifies the 1D treatment of the Freedericksz transition in 2D settings that is widely adopted in the liquid crystal literature. An asymptotic analysis of the supercritical, stable bifurcated equilibrium path about the critical load is also presented and compared with the exact bifurcated solution.     

介电弹性材料的机电耦合性能研究

作为一种新型的电活性聚合物,介电弹性材料可被用作柔性致动器。其中材料的介电性能和机械性能是影响其机电耦合致动性能的关键因素。通过实验方法研究了一种典型的介电弹性材料VHB4910在不同温度和频率下的介电常数和弹性模量,基于实验结果分析了该材料的机电耦合性能。结果表明:依赖于频率和温度的弹性模量是影响该介电弹性材料致动变形的主要因素,对致动性能的影响最大可达4个数量级,材料的介电常数对其致动性能的影响相对较小。     

Transitions in Poiseuille flow of nematic liquid crystal

Recent experiments by Sengupta et al. (Phys. Rev. Lett. 2013) [9] revealed interesting transitions that can occur in flow of nematic liquid crystal under carefully controlled conditions within a long microfluidic channel of width much larger than height, and homeotropic anchoring at the walls. At low flow rates the director field of the nematic adopts a configuration that is dominated by the surface anchoring, being nearly parallel to the channel height direction over most of the cross-section; but at high flow rates there is a transition to a flow-dominated state, where the director configuration at the channel centerline is aligned with the flow (perpendicular to the channel height direction). We analyze simple channel-flow solutions to the Leslie–Ericksen model for nematics. We demonstrate that two solutions exist, at all flow rates, but that there is a transition between the elastic free energies of these solutions: the anchoring-dominated solution has the lowest energy at low flow rates, and the flow-dominated solution has lowest energy at high flow rates.