Dynamic soft elasticity in monodomain nematic elastomers

We study the linear dynamic-mechanical response of monodomain nematic liquid crystalline elastomers under shear in the geometry that allows the director rotation. The aspects of time-temperature superposition are discussed at some length and Master Curves are obtained between the glassy state and the nematic transition temperature Tni. However, the time-temperature superposition did not work through the clearing point Tni, due to the transition from the "soft-elasticity" nematic regime to the ordinary isotropic rubber response. We focus on the low-frequency region of the Master Curves and establish the power law dependence of the modulus G' alpha w(a). This law agrees very well with the results of the static stress relaxation, where each relaxation curve obeys the analogous power law G' alpha t(-a) in the corresponding region of long times and temperatures.     

Linear hydrodynamics and viscoelasticity of nematic elastomers

We develop a continuum theory of linear viscoelastic response in oriented monodomain nematic elastomers. The expression for the dissipation function is analogous to the Leslie-Ericksen version of anisotropic nematic viscosity; we propose the relations between the anisotropic rubber moduli and new viscous coefficients. A new dimensionless number is introduced, which describes the relative magnitude of viscous and rubber-elastic torques. In an elastic medium with an independently mobile internal degree of freedom, the nematic director with its own relaxation dynamics, the model shows a dramatic decrease in the dynamic modulus in certain deformation geometries. The degree to which the storage modulus does not altogether drop to zero is shown to be both dependent on frequency and to be proportional to the semi-softness, the non-ideality of a nematic network. We consider the most interesting geometry for the implementation of the theory, calculating the dynamic response to an imposed simple shear and making predictions for effective moduli and (exceptionally high) loss factors. Received 16 October 2000 and Received in final form 10 December 2000     

The elastic anisotropy of nematic elastomers

We examine the robustness of order in nematic elastomers under mechanical strains imposed along and perpendicularly to the director when director rotation is prohibited. In contrast to electric and magnetic fields applied to conventional nematics, mechanical fields are shown theoretically and experimentally to greatly affect the degree of nematic order and related quantities. Unlike in liquid nematics, one can impose fields perpendicular to the director, thereby inducing biaxial order which should be susceptible to experimental detection. Nematic elastomers with unchanging director and degree of order should theoretically have the same elastic moduli for longitudinal and transverse extensions. This is violated when nematic order is permitted to relax in response to strains. Near the transition we predict the longitudinal modulus to be smaller than the transverse modulus; at lower temperatures the converse is true, with a crossover a few degrees below the transition. The differences are ascribed to the different temperature dependence of the stiffness of uniaxial and biaxial order. We synthesised side chain single-crystal nematic polymer networks, performed DSC, X-ray, birefringence, and thermo-mechanical characterisations, and then obtained linear moduli from stress-strain measurements. Received 29 September 2000     

Deformation of cholesteric elastomers by uniaxial stress along the helix axis

The deformation of cholesteric elastomers by mechanical stress applied parallel to the helix axis is studied by calculation of the free-energy density. The Frank-elasticity contribution is taken into account. A chiral solvent, present at cross-linking time, is in general considered to be replaced after cross-linking by a solvent with different chirality. Two special cases considered are zero and unchanged solvent chirality, the first known as that of imprinted cholesteric elastomers, the latter equivalent to intrinsic cholesteric elastomers with chemically attached chiral groups. Depending on material parameters and imposed strain, the director can show a tilt towards the helix axis up to the maximum tilt, corresponding to a nematic state. In case of intrinsic elastomers with low conformation anisotropy, direct transitions from untilted to nematic states can be induced by straining. The helix structure of the director field is coarsened with an average wave number different to that of the information inscribed in the network at cross-linking time, if this lowers the average free-energy density. Switching between different states can be achieved with electric fields of reasonable values applied parallel to the helix axis. Spectra of the reflection of polarized light are calculated.     

Strongly anisotropic elastic moduli of nematic elastomers: Analytical expressions and nonlinear temperature dependence

Exact formulae for the elastic moduli of the nematic elastomers are obtained by the implicit function method based on somewhat general energy functions. The formulae indicate that both the moduli parallel and perpendicular to the director of the nematic elastomers are smaller than the modulus of the classical elastomers because of the mechanical-nematic coupling. Moreover, the moduli are generally anisotropic due to the biaxiality induced by stretching the nematic elastomers perpendicular to the director. Then we get the explicit analytical expressions of the parallel and perpendicular moduli by making use of the Landau-de Gennes free energy and the neo-classical elastic energy. Very different from the classical elastomers, they are both strongly nonlinear functions of the temperature in the nematic phase. Furthermore, their ratio, the degree of anisotropy, changes with the temperature as well. The results agree qualitatively with some experiments. Better quantitative agreement is obtained by some modifications of the constitutive relation of the elastic energy.     

Elastic effects in disordered nematic networks

Elastic effects in a model of disordered nematic elastomers are numerically investigated in two dimensions. Networks crosslinked in the isotropic phase exhibit an unusual soft mechanical response against stretching. It arises from a gradual alignment of orientationally correlated regions that are elongated along the director. A sharp crossover to a macroscopically aligned state is obtained on further stretching. The effect of random internal stress is also discussed.     

Role of polarization and alignment in photoactuation of nematic elastomers

Changing the orientational order in liquid-crystal elastomers leads to internal stresses and changes of the sample shape. When this effect is induced by light, due to photoisomerization of constituent molecular moieties, the photomechanical actuation results. We investigate quantitatively how the intensity and the polarization of light affect photoactuation. By studying dissolved, as well as covalently bonded azo-dyes, we determine the changes in absorption and the response kinetics. For the first time we compare the response of aligned monodomain, and randomly disordered polydomain nematic elastomers, and demonstrate that both have a comparable photoresponse, strongly dependent on the polarization of light. Polarization-dependent photoactuation in polydomain elastomers gives an unambiguous proof of its mechanism since it is the only experiment that distinguishes from the associated thermal effects.     

Elastic energies for nematic elastomers

We discuss several elastic energies for nematic elastomers and their small strain expansions both in the regime of large director rotations, and in the case that director changes are small. We propose two fully non-linear model anisotropic energies and compare the behavior they predict with the currently available experimental evidence.     

Thermal diffusion and bending kinetics in nematic elastomer cantilever

Vertically aligned monodomain nematic liquid-crystal elastomers contract when heated. If a temperature gradient is applied across the width of such a cantilever, inhomogeneous strain distribution leads to bending motion. We modelled the kinetics of thermally induced bending in the limit of a long thin strip and the predicted time variation of curvature agreed quantitatively with experimental data from samples with a range of critical indices and nematic-isotropic transition temperatures. We also deduced a value for the thermal diffusion coefficient of the elastomer.     

Response of prestretched nematic elastomers to external fields

We investigate the response of prestretched nematic side-chain liquid single-crystal elastomers to superimposed external shear, electric, and magnetic fields of small amplitude. The prestretching direction is oriented perpendicular to the initial nematic director orientation, which enforces director reorientation. Furthermore, the shear plane contains the direction of prestretch. In this case, we obtain a strongly decreased effective shear modulus in the vicinity of the onset and the completion of the enforced director rotation. For the same regions, we find that it becomes comparatively easy to reorient the director by external electric and magnetic fields. These results were derived using conventional elasticity theory and its coupling to relative director-network rotations.     

Hairpin rubber elasticity

We model the elastic properties of main chain liquid crystalline elastomers, formed by cross linking chains in a strongly nematic state, when they have hairpin defects. We study the response of the elastomer to imposed uniaxial extension along the nematic direction, and employ a microscopic model of how the deformation is distributed non-affinely amongst the hairpin and straight chain populations. The rubber shows a plateau in the stress as a function of the elongation imposed along the director. It is a consequence of the depletion of the actively stretching population of hairpin chains and should not be confused with soft elasticity effects associated with director rotation.     

Spontaneous thermal expansion of nematic elastomers

We study the monodomain (single-crystal) nematic elastomer materials, all side-chain siloxane polymers with the same mesogenic groups and crosslinking density, but differing in the type of crosslinking. Increasing the proportion of long di-functional segments of main-chain nematic polymer, acting as network crosslinking, results in dramatic changes in the uniaxial equilibrium thermal expansion on cooling from the isotropic phase. At higher concentration of main chains their behaviour dominates the elastomer properties. At low concentration of main-chain material, we detect two distinct transitions at different temperatures, one attributed to the main-chain, the other to the side-chain component. The effective uniaxial anisotropy of nematic rubber, r(T) = / proportional to the effective nematic order parameter Q(T), is given by an average of the two components and thus reflects the two-transition nature of thermal expansion. The experimental data is compared with the theoretical model of ideal nematic elastomers; applications in high-amplitude thermal actuators are discussed in the end. Received 25 June 2001 and Received in final form 29 September 2001     

Rotational reorientation of the director in twisted nematic liquid-crystal cells

The orientational relaxation of the director to its equilibrium orientation under electric, elastic, and viscous torques arising in twisted nematic liquid-crystal cells is investigated. It is shown that the relaxation time of the director depends strongly on the external electric field strength and weakly on the energy of anchoring of liquid-crystal molecules to the surfaces of the cell. The relaxation time of the director anomalously increases in electric fields close to the Fréedericksz threshold. It is established that, at specific strengths of the external electric field, the relaxation can occur in the form of traveling waves propagating from one edge to the other edge of the twisted nematic liquid-crystal cell. The calculations of the relaxation processes in the vicinity of the nematic-smectic A phase transition temperature demonstrate that the distortion of the director field is uniform over the entire cross section of the liquid-crystal cell and does not depend on the strength of anchoring of the liquid-crystal molecules to the surfaces of the cell.     

Untwisting of a cholesteric elastomer by a mechanical field

A mechanical strain field applied to a monodomain cholesteric elastomer will unwind the helical director distribution. There are similarities with the classical problem of an electric field applied to a cholesteric liquid crystal but also differences. Frank elasticity is of minor importance unless the gel is very weak. The interplay is between the director being helically anchored to the rubber elastic matrix and the external mechanical field. Stretching perpendicular to the helix axis induces the uniform unwound state via the elimination of sharp, pinned twist walls above a critical strain. Unwinding through conical director states occurs when the elastomer is stretched along the helical axis.     

Strain-induced reorientation and mobility in nematic liquid-crystalline elastomers as studied by time-resolved FTIR spectroscopy

Polarized Fourier transform infrared (FTIR) spectroscopy is employed to study the segmental orientation and mobility of liquid-crystalline elastomers (LCEs) with a monodomain structure in response to external mechanical fields parallel and perpendicular to the initial nematic director. The mean orientation and the molecular order parameter of the different molecular moieties referring to the mesogen, the spacer and the network are analyzed in detail. Parallel stretch leaves the mean orientation of the different molecular moieties and its molecular order parameter nearly uninfluenced. Perpendicular stretch results in a threshold-like dependence: for elongation ratios λ ⩽ λ_c = 1.3 (10 mol% crosslinker density), respectively λ ⩽ λ_c = 1.6 (5 mol% crosslinker density) no change of the mean orientation and the molecular order parameters is observed, while for λ ≥ λ_c all molecular units reorient and their molecular order parameters are strongly decreased. The present studies give no indications that the reorientational dynamics of the network and the mesogens differ as long as the elongation ratio is smaller than λ_c.     

Relaxation of the director field in the form of a traveling wave in twisted nematic cells

The orientational relaxation of the director field toward its equilibrium orientation in the form of a traveling wave is investigated. It is shown that the nonlinear relaxation can occur in the form of a traveling wave in a twisted nematic cell under specific conditions for the external electric field and material parameters characterizing the nematic liquid crystal. The calculations of the relaxation processes in the form of traveling waves have demonstrated that these nonlinear processes in the twisted nematic cell proceed more easily when the initial perturbation of the director is induced in the vicinity of one of the bounding cell surfaces.     

Nonlinear photoresponse of disordered elastomers

We model the polarization-dependent photocontractions of polydomain nematic elastomers. Contraction initially arises by light-induced director rotation. At higher light intensity, strain recovers because the local order parameter diminishes. Thus we predict photostrains to be nonmonotonic with light intensity and predict the induction of a negative global order parameter for the system of polydomains. Nonmonotonic strains would give curvature reversal in thick samples. Our model also predicts an elongational strain response to nonpolarized light.