Nematic Elastomers Research Articles

Nonlinear elasticity, fluctuations and heterogeneity of nematic elastomers

Liquid crystal elastomers realize a fascinating new form of soft matter that is a composite of a conventional crosslinked polymer gel (rubber) and a liquid crystal. These solid liquid crystal amalgams, quite similarly to their (conventional, fluid) liquid crystal counterparts, can spontaneously partially break translational and/or orientational symmetries, accompanied by novel soft Goldstone modes. As a consequence, these materials can exhibit unconventional elasticity characterized by symmetry-enforced vanishing of some elastic moduli. Thus, a proper description of such solids requires an essential modification of the classical elasticity theory. In this work, we develop a rotationally invariant, nonlinear theory of elasticity for the nematic phase of ideal liquid crystal elastomers. We show that it is characterized by soft modes, corresponding to a combination of long wavelength shear deformations of the solid network and rotations of the nematic director field. We study thermal fluctuations of these soft modes in the presence of network heterogeneities and show that they lead to a large variety of anomalous elastic properties, such as singular length-scale dependent shear elastic moduli, a divergent elastic constant for splay distortion of the nematic director, long-scale incompressibility, universal Poisson ratios and a nonlinear stress–strain relation for arbitrary small strains. These long-scale elastic properties are universal, controlled by a nontrivial zero-temperature fixed point and constitute a qualitative breakdown of the classical elasticity theory in nematic elastomers. Thus, nematic elastomers realize a stable “critical phase”, characterized by universal power-law correlations, akin to a critical point of a continuous phase transition, but extending over an entire phase.

Loading effect on swelling of nematic elastomers

Externally imposed loading has substantially different effects on the swelling of nematic elastomers in the high-temperature isotropic and low-temperature nematic states. In the isotropic state, the stretching drives a considerably large degree of further swelling, whereas the stretching-induced volume change in the nematic state is significantly suppressed. In the isotropic phase that favors the less anisotropic state, the further swelling occurs to reduce the shape anisotropy caused by the imposed elongation. In the nematic phase, no significant swelling is induced because further swelling decreases the nematic order enhanced by the applied stretching. These different loading effects in the isotropic and nematic states observed in the experiments are qualitatively described by a mean field theory.

The diverse world of liquid crystals

Orientationally ordered soft matter is exceptionally responsive to a variety of excitations. That’s the basis for its great range of applications.

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.

Surface deformation of nematic elastomers under striped illumination

Nematic elastomers containing azobenzene chromophores are activated upon photoabsorption. We study the surface deformation of such elastomers under striped illumination. For an arbitrary orientation of the nematic axis, we obtain an analytical solution to the problem via a phenomenological continuum model. Numerical computations indicate that the profile of the deformed surface depends not only on the stripe width but also on the orientation of the nematic axis. The result may provide a mechanism to manipulate the surface topography of elastomers.

Semisoft Nematic Elastomers and Nematics in Crossed Electric and Magnetic Fields

Nematic elastomers with a locked-in anisotropy direction exhibit semisoft elastic response characterized by a plateau in the stress-strain curve in which stress does not change with strain. We calculate the global phase diagram for a minimal model, which is equivalent to one describing a nematic in crossed electric and magnetic fields, and show that semisoft behavior is associated with a broken symmetry biaxial phase and that it persists well into the supercritical regime. We also consider generalizations beyond the minimal model and find similar results.

Thermally Reversible Distortion Observed for Monodomain Nematic Elastomer of Cross-Linked Main-Chain Polyester

Thermoelastic response of a cross-linked main-chain polyester was examined in the nematic temperature region from 80°C to 150°C. The monodomain nematic elastomer decreased its length in the orientation direction by 45% on heating from 80°C to 150°C and recovered it on cooling to 80°C without change in the degree of orientational ordering. This reversible distortion of the nematic elastomer is well explained by the configurational change of the polymer chain including hairpin folding, the probability of which is proportional to the Boltzmann factor of hairpin energy.

Reflection of homogeneous elastic waves from free surface of nematic elastomer half-space

An application of the linear viscoelastic theory of nematic elastomers in the low-frequency (hydrodynamic) limit is considered. The boundary conditions at a free surface of a nematic elastomer half-space are satisfied to obtain the reflection of acoustic waves (qP or qSV). The expressions for reflection coefficients are obtained for each incident wave. The reflection coefficients are found to depend on various elastic constants, angle of incidence, frequency of incident wave, relaxation times and angle α between a wavevector and a nematic director. The reflection coefficients are plotted against the angle of incidence for suitable values of angle α, frequency and relaxation times. These coefficients are also plotted against non-dimensional frequency.

External stimulus driven variable-step grating in a nematic elastomer

We report on the creation of micro-patterns in an oriented nematic elastomer (an artificial muscle material) by photopolymerization of surface aligned nematic liquid crystal monomers. We demonstrate that microscopic techniques are able to create accurate patterns in rubber-like liquid crystal materials. Two approaches, based on one and two-photon excitations respectively, are implemented using a microscope-based setup. Due to its high spatial selectivity, the two-photon excitation mode yields finer patterns. Benefitting from the intrinsic, thermally-induced, contractile properties of the material, gratings with variable steps in response to temperature changes were fabricated.

Ideally soft nematic elastomers

The paper examines a class of energies $W$ of nematic elastomers that exhibit ideally soft behavior. These are generalizations of the neo-classical energy function proposed by Bladon, Terentjev & Warner [7]. The effective energy (quasiconvexification) of $W$ is calculated for a large subclass of considered energies. Within the subclass, the rank 1 convex, quasiconvex, and polyconvex envelopes coincide and reduce to the largest function below $W$ that satisfies the Baker–Ericksen inequalities. Compressible cases are included. The effective energy displays three regimes: one fluid-like, one partially fluid-like and one hard, as established by DeSimone & Dolzmann [20] for the energy function of Bladon, Terentjev & Warner. Ideally soft deformation modes are shown to arise.

Nonlocal model for nematic liquid-crystal elastomers

We have developed a fully nonlocal model to describe the dynamic behavior of nematic liquid-crystal 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 long-wavelength and small-amplitude 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.

Nematic-isotropic transition with quenched disorder

Nematic elastomers do not show the discontinuous, first-order, phase transition that the Landau-De Gennes mean field theory predicts for a quadrupolar ordering in three dimensions. We attribute this behavior to the presence of network crosslinks, which act as sources of quenched orientational disorder. We show that the addition of weak random anisotropy results in a singular renormalization of the Landau-De Gennes expression, adding an energy term proportional to the inverse quartic power of order parameter Q. This reduces the first-order discontinuity in Q. For sufficiently high disorder strength the jump disappears altogether and the phase transition becomes continuous, in some ways resembling the supercritical transitions in external field.

Swelling and Shrinking Dynamics of Nematic Elastomers Having Global Director Orientation

We reveal that the swelling and shrinking of monodomain nematic elastomers in solvents exhibit unusual kinetics owing to the presence of shape and volume variation modes with markedly different rates. A change in the degree of nematic order caused by temperature (T) jumps drives a spontaneous macroscopic deformation along the director as well as a change in the chemical potential of the solvent inside the gel. The former yields an almost instantaneous shape variation, whereas the latter induces a slow volume variation governed by the diffusion of polymer networks, such as the swelling of isotropic gels. The markedly different rates of these two modes yield unique kinetics of swelling and shrinking: (1) a pronounced over- or undershoot of the gel dimensions is observed in the direction where the effect of shape variation on the dimensions counters that of the volume variation, and (2) a large dimensional change (more than 50% of the total change) occurs immediately after the T-jumps in the direction along which the effects of the two modes on the dimensions harmonize.

Slow dynamics of shape recovery of disordered nematic elastomers

A loosely cross-linked liquid crystal elastomer (LCE) having a disordered director alignment (polydomain texture) slowly recovers to their original shape from the deformed state in the order of 10(3) s after the imposed field is removed. The mesogen alignment at the cross-linking stage greatly affects the shape recovery dynamics of polydomain LCEs, whereas it has no appreciable influence on the equilibrium characteristics such as the nematic-isotropic transition temperature, degree of swelling, and field-induced strain. The shape recovery of a LCE formed in the polydomain nematic state is considerably faster than that originally prepared in the isotropic state because of the memory effect of the initial director distribution at the cross-linking stage. The relaxation time rapidly increases as the temperature approaches the transition temperatures; this is independent of the initial mesogen alignment during cross linking.

Disclinations in a homogenously deformed nematic elastomer

We consider a nematic elastomer which has been cross-linked in an isotropic state. As an application, we consider the time-independent, isochoric, homogeneous deformation of a right circular cylinder wherein each circular cross section of the specimen is deformed into an ellipse. We explore the possibility of the existence of disclinations when the molecular conformation is uniaxial. Numerical solution of the governing boundary-value problem indicates the presence of an isotropic core (the disclination core) of material surrounding the cylinder axis in which the polymeric chains are shaped as spherical coils. The isotropic core is bounded by a narrow transition layer across which the molecular conformation changes from spherical to uniaxial. The material thereby becomes anisotropic away from the disclination. The anisotropic regions show a markedly different distribution for the free energy. This distribution of energy determines the radius of the core to be on the order of 10−2 μm. This work is a first step toward gaining an understanding of the existence of defective states in homogenous deformed nematic elastomers.

Soft elastic bending response of a nematic elastomer described by a microstructurally relaxed free energy

We consider the bending of a nematic elastomer slab using the material model of DeSimone and Dolzmann. This model supplies a coarse description for the mechanical response associated with three distinct microstructural phases: a solid phase, a smectic phase and a liquid phase. The liquid and smectic phases permit soft modes, in which a variety of deformations are consistent with the same external tractions. Multiple-phase solutions are constructed making use of a standard analytical procedure associated with the fact that the deformation is universal in isotropic, incompressible, hyperelasticity. This requires an exhaustive accounting of the possible phase combinations consistent with the bending deformation. It is shown how an original soft mode response at low flexure angle, wherein the slab is completely in the smectic phase, can give way to conventional (non-soft) response at a threshold flexure angle associated with the nucleation of solid phase at the external boundary. Two separate phase interface fronts then travel through the slab as the flexure angle increases further, quasi-statically transforming smectic phase to solid phase.

Soft elasticity is not necessary for striping in nematic elastomers

The neoclassical model for nematic elastomers, which displays soft elasticity, predicts striping in stretched sheets. Thus the experimental observation of striped domains has been suggested as evidence for soft elasticity. Here we show that the postulated director rotations and shears in the domain regions are also predicted by more general constitutive models that do not involve any notion of softness. Striping in nematic elastomers may therefore be a more general phenomenon that is not necessarily an indication of soft elasticity. Furthermore, constitutive models more general than the neoclassical model may also explain the behavior of some nematic elastomers that do not appear to exhibit striping.

Null Lagrangians for nematic elastomers

In this paper, we calculate all possible null Lagrangians (null energies) for the mechanics of a distinguished class of continua, the nematic elastomers. The calculation is done in order to help to relate different physically equivalent theories of nematic elastomers. We discuss both local and global (hence topological) aspects of the problem.

Shear mechanical anisotropy of side chain liquid-crystal elastomers: Influence of sample preparation

We study the mechanical anisotropy of a series of uniaxial side chain nematic elastomers prepared with the same chemical composition but with different preparation protocols. For all the compounds, the experiments performed as a function of temperature show no discontinuity in both G' (//) and G' ( perpendicular) (the labels // and perpendicular stand for the director parallel, respectively perpendicular to the shear displacement) around the nematic-isotropic (N-I) phase transition temperature determined by DSC. They also all show a small decrease in G' (//) starting at temperatures well above this temperature (from approximately 4( degrees ) C to approximately 20( degrees ) C depending on the compound studied) and leading to a small hydrodynamic value of the G' ( perpendicular)/G' (//) ratio. The measurements taken as a function of frequency show that the second plateau in G' (//) and the associated dip in G (//)" expected from dynamic semi-soft elasticity are not observed. These results can be described by the de Gennes model, which predicts small elastic anisotropy in the hydrodynamic and linear regimes. They correspond to the behavior expected for compounds beyond the mechanical critical point, which is consistent with the NMR and specific heat measurements taken on similar compounds. We also show that a reduction in the cross-linking density does not change the non-soft character of the mechanical response. From the measurements taken as a function of frequency at several temperatures we deduce that the time-temperature superposition method does not apply. From these measurements, we also determine the temperature dependence of the longest relaxation time tau(E) of the network for the situations where the director is either parallel or perpendicular to the shear velocity. Finally, we discuss the influence on the measurements of the mechanical constraint associated with the fact that the samples cannot change their shape around the pseudo phase transition, because of their strong adherence on the sample-bearing glass slides.

Stacking nematic elastomers for artificial muscle applications

Nematic liquid crystal elastomers are thermally actuated to produce macroscopic, anisotropic shape changes. Uniaxial contraction and extension of liquid crystal elastomers can be achieved by cycling the temperature of the material through the nematic to isotropic phase transition. In this report, a new approach is introduced by layering liquid crystal elastomer films to create thermally actuated stacks. A heating element and thermally conductive grease embedded between elastomer films provide a means for rapid internal heat application and distribution when a current is passed through the heating element, thus providing contractile force production in a minimal amount of time. Upon voltage application, stacks composed of two 100 μm-thick films and a single heating element produce 18% strain between contracted and relaxed states. In addition, the stacked elastomer films are capable of producing 10% contraction within 1 s and the blocked stress of the thermally actuated stacked films is calculated to be 130 kPa. The stacking approach provides new opportunities to use liquid crystal elastomers in applications requiring forces greater than those capable of being produced by single elastomer films.