Anomalous viscoelastic response of nematic elastomers

Directional Adhesion of Monodomain Liquid Crystalline Elastomers

Pressure-sensitive adhesives (PSAs) are widely employed in consumer goods, health care, and commercial industry. Anisotropic adhesion of PSAs is often desirable to enable high force capacity coupled with facile release and has typically been realized through the introduction of complex surface and/or bulk microstructures while also maintaining high surface conformability. Although effective, microstructure fabrication can add cost and complexity to adhesive fabrication. Here, we explore aligned liquid crystalline elastomers (LCEs) as directional adhesives. Aligned LCEs exhibit direction-dependent stiffness, dissipation, and nonlinear deformation under load. By varying the cross-link content, we study how the bulk mechanical properties of LCEs correlate to their peel strength and peel anisotropy. We demonstrate up to a 9-fold difference in peel force measured when the LCE is peeled parallel vs perpendicular to the alignment axis. Opportunities to spatially localize adhesion are presented in a monolithic LCE patterned with different director orientations.

Momentum transfer on impact damping by liquid crystalline elastomers

The effect of elastomeric damping pads, softening the collision of hard objects, is investigated comparing the reference silicone elastomer and the polydomain nematic liquid crystalline elastomer, which has a far superior internal dissipation mechanism. We specifically focus not just on the energy dissipation, but also on the momentum conservation and transfer during the collision, because the latter determines the force exerted on the target and/or the impactor-and it is the force that does the damage during the short time of an impact, while the energy might be dissipated on a much longer time scale. To better assess the momentum transfer, we compare the collision with a very heavy object and the collision with a comparable mass, when some of the impact momentum is retained in the target receding away from the collision. We also propose a method to estimate the optimal thickness of an elastomer damping pad for minimising the energy in impactor rebound. It has been found that thicker pads introduce a large elastic rebound and the optimal thickness is therefore the thinnest possible pad that does not suffer from mechanical failure. We find good agreement between our estimate of the minimal thickness of the elastomer before the puncture through occurs and the experimental observations.

Soft elasticity optimises dissipation in 3D-printed liquid crystal elastomers

Soft-elasticity in monodomain liquid crystal elastomers (LCEs) is promising for impact-absorbing applications where strain energy is ideally absorbed at constant stress. Conventionally, compressive and impact studies on LCEs have not been performed given the notorious difficulty synthesizing sufficiently large monodomain devices. Here, we use direct-ink writing 3D printing to fabricate bulk (>cm³) monodomain LCE devices and study their compressive soft-elasticity over 8 decades of strain rate. At quasi-static rates, the monodomain soft-elastic LCE dissipated 45% of strain energy while comparator materials dissipated less than 20%. At strain rates up to 3000 s^-1, our soft-elastic monodomain LCE consistently performed closest to an ideal-impact absorber. Drop testing reveals soft-elasticity as a likely mechanism for effectively reducing the severity of impacts - with soft elastic LCEs offering a Gadd Severity Index 40% lower than a comparable isotropic elastomer. Lastly, we demonstrate tailoring deformation and buckling behavior in monodomain LCEs via the printed director orientation.

Nematic liquid crystalline elastomers are aeolotropic materials

Continuum models describing ideal nematic solids are widely used in theoretical studies of liquid crystal elastomers. However, experiments on nematic elastomers show a type of anisotropic response that is not predicted by the ideal models. Therefore, their description requires an additional term coupling elastic and nematic responses, to account for aeolotropic effects. In order to better understand the observed elastic response of liquid crystal elastomers, we analyse theoretically and computationally different stretch and shear deformations. We then compare the elastic moduli in the infinitesimal elastic strain limit obtained from the molecular dynamics simulations with the ones derived theoretically, and show that they are better explained by including nematic order effects within the continuum framework.

Internal constraints and arrested relaxation in main-chain nematic elastomers

Nematic liquid crystal elastomers (N-LCE) exhibit intriguing mechanical properties, such as reversible actuation and soft elasticity, which manifests as a wide plateau of low nearly-constant stress upon stretching. N-LCE also have a characteristically slow stress relaxation, which sometimes prevents their shape recovery. To understand how the inherent nematic order retards and arrests the equilibration, here we examine hysteretic stress-strain characteristics in a series of specifically designed main-chain N-LCE, investigating both macroscopic mechanical properties and the microscopic nematic director distribution under applied strains. The hysteretic features are attributed to the dynamics of thermodynamically unfavoured hairpins, the sharp folds on anisotropic polymer strands, the creation and transition of which are restricted by the nematic order. These findings provide a new avenue for tuning the hysteretic nature of N-LCE at both macro- and microscopic levels via different designs of polymer networks, toward materials with highly nonlinear mechanical properties and shape-memory applications.

The effect of alignment on the rate-dependent behavior of a main-chain liquid crystal elastomer

This study investigated the effect of alignment on the rate-dependent behavior of a main-chain liquid crystal elastomer (LCE). Polydomain nematic LCE networks were synthesized from a thiol-acrylate Michael addition reaction in the isotropic state. The polydomain networks were stretched to different strain levels to induce alignment then crosslinked in a second stage photopolymerization process. The LCE networks were subjected to dynamic mechanical tests to measure the temperature-dependent storage modulus and uniaxial tension load-unload tests to measure the rate-dependence of the Young's modulus, mechanical dissipation, and characteristics of the soft stress response. Three-dimensional (3D) digital image correlation (DIC) was used to characterize the effect of domain/mesogen relaxation on the strain fields. All LCE networks exhibited a highly rate-dependent stress response with significant inelastic strains after unloading. The Young's modulus of the loading curve and hysteresis of the load-unload curves showed a power-law dependence on the strain rate. The Young's modulus increased with alignment and larger anisotropy and a smaller power-law exponent was measured for the Young's modulus and hysteresis for the highly aligned monodomains. The polydomain and pre-stretched networks loaded perpendicular to the alignment direction exhibited a soft stress response that featured a rate-dependent peak stress, strain-softening, and strain-stiffening. The 3D-DIC strain fields for the polydomain network and programmed networks stretched in the perpendicular direction were highly heterogeneous, showing regions of alternating higher and lower strains. The strain variations increased initially with loading, peaked during the strain softening part of the stress response, then decreased during the strain stiffening part of the stress response. Greater variability was measured for lower strain rates. These observations suggest that local domain/mesogen relaxation led to the development of the heterogeneous strain patterns and strain softening in stress response. These findings improved understanding of the kinetics of mesogen relaxation and its contributions to the rate-dependent stress response and mechanical dissipation.

Light-Driven Dynamic Adhesion on Photosensitized Nematic Liquid Crystalline Elastomers

In liquid crystal elastomers (LCEs), the internal mechanical loss increases around the nematic-isotropic phase transition and remains high all through the nematic phase, originating from the internal orientational relaxation related to the so-called "soft elasticity". Because the viscoelastic dissipation of the materials affects their adhesion properties, the nematic-isotropic phase transition can cause dramatic changes in the adhesion strength. Although the phase transitions can generally be induced by heat, here, we demonstrate the light-driven transition in dynamic adhesion in dye-doped nematic LCE. The special dye is chosen to efficiently generate local heat on light absorption. The adhesion strength is lowered with fine tunability depending on the light power, which governs the effective local temperature and through that the viscoelastic damping of the system. We demonstrate the light-assisted dynamic control of adhesion in a 90°-peel test and in pick-and-release of objects, which may lead to the development of stimuli-responsive adhesive systems with fine spatio-temporal controls.

Toward Programmed Complex Stress-Induced Mechanical Deformations of Liquid Crystal Elastomers

We prepare a liquid crystal elastomer (LCE) with a spatially patterned liquid crystal director field from an all-acrylate LCE. Mechanical deformations of this material lead to a complex and spatially varying deformation with localised body rotations, shears and extensions. Together, these dictate the evolved shape of the deformed film. Using polarising microscopy, we map the local rotation of the liquid crystal director in Eulerian and Lagrangian frames and use these to determine rules for programming complex, stress-induced mechanical shape deformations of LCEs. Moreover, by applying a recently developed empirical model for the mechanical behaviour of our LCE, we predict the non-uniform stress distributions in our material. These results show the promise of empirical approaches to modelling the anisotropic and nonlinear mechanical responses of LCEs which will be important as the community moves toward realising real-world, LCE-based devices.

Enhanced Dynamic Adhesion in Nematic Liquid Crystal Elastomers

Smart adhesives that undergo reversible detachment in response to external stimuli enable a wide range of applications in household products, medical devices, or manufacturing. Here, a new model system for the design of smart soft adhesives that dynamically respond to their environment is presented. By exploiting the effect of dynamic soft elasticity in nematic liquid crystal elastomers (LCE), the temperature-dependent control of adhesion to a solid glass surface is demonstrated. The adhesion strength of LCE is more than double in the nematic phase, in comparison to the isotropic phase, further increasing at higher detachment rates. The static work of adhesion, related to the interfacial energy of adhesive contact, is shown to change very little within the explored temperature range. Accordingly, the observed enhanced adhesion in the nematic phase is primarily attributable to the increased internal energy dissipation during the detachment process. This adhesion effect is correlated with the inherent bulk dynamic-mechanical response in the nematic LCE. The reported enhanced dynamic adhesion can lead to the development of a new class of stimuli-responsive adhesives.

Main-chain liquid-crystal elastomers versus side-chain liquid-crystal elastomers: similarities and differences in their mechanical properties

After a general introduction on the main aspects of the mechanical properties of main-chain liquid-crystal elastomers (MCLCEs) and side-chain liquid-crystal elastomers (SCLCEs), new results will be presented dealing with several MCLCEs with a cross-linker density C = 8%, 6% and 4% and with a SCLCE with C = 10%, all prepared by the two-step cross-linking process. A non-SCLCE with bulky side-groups similar in shape to the mesogens was also synthesized for comparison with the SCLCE. Most of the experiments were performed with a piezorheometer allowing the determination of the shear anisotropy of the samples by applying shear in a direction parallel or perpendicular to the director, and with a thermo-elastic device for the E measurements. The main results concern: (a) the influence of the supercritical nature of SCLCE and the subcritical nature of MCLCEs on the mechanical properties of these elastomers, as well as that of SmC domains present in MCLCEs; (b) the relationship between the degrees of elongation and of anisotropy deduced from the variations of and during the poly-domain to mono-domain transition of the 10% SCLCE and the 8% MCLCE; (c) the determination of the Poisson's ratio showing that it is isotropic for the non-SCLCE, with a crossover between 0.5 (classical value for rubbers) for small strains and 0.38 for high strains, and anisotropic for the 10% SCLCE and 8% MCLCE, with values <0.5. The particular behaviors of the Poisson's ratios can be explained by confinement effects occurring when stretching increases.

Effects of thermo-order-mechanical coupling on band structures in liquid crystal nematic elastomer porous phononic crystals

Liquid crystal nematic elastomers are one kind of smart anisotropic and viscoelastic solids simultaneously combing the properties of rubber and liquid crystals, which is thermal sensitivity. In this paper, the wave dispersion in a liquid crystal nematic elastomer porous phononic crystal subjected to an external thermal stimulus is theoretically investigated. Firstly, an energy function is proposed to determine thermo-induced deformation in NE periodic structures. Based on this function, thermo-induced band variation in liquid crystal nematic elastomer porous phononic crystals is investigated in detail. The results show that when liquid crystal elastomer changes from nematic state to isotropic state due to the variation of the temperature, the absolute band gaps at different bands are opened or closed. There exists a threshold temperature above which the absolute band gaps are opened or closed. Larger porosity benefits the opening of the absolute band gaps. The deviation of director from the structural symmetry axis is advantageous for the absolute band gap opening in nematic state whist constrains the absolute band gap opening in isotropic state. The combination effect of temperature and director orientation provides an added degree of freedom in the intelligent tuning of the absolute band gaps in phononic crystals.

A readily programmable, fully reversible shape-switching material

Liquid crystalline (LC) elastomers (LCEs) enable large-scale reversible shape changes in polymeric materials; however, they require intensive, irreversible programming approaches in order to facilitate controllable actuation. We have implemented photoinduced dynamic covalent chemistry (DCC) that chemically anneals the LCE toward an applied equilibrium only when and where the light-activated DCC is on. By using light as the stimulus that enables programming, the dynamic bond exchange is orthogonal to LC phase behavior, enabling the LCE to be annealed in any LC phase or in the isotropic phase with various manifestations of this capability explored here. In a photopolymerizable LCE network, we report the synthesis, characterization, and exploitation of readily shape-programmable DCC-functional LCEs to create predictable, complex, and fully reversible shape changes, thus enabling the literal square peg to fit into a round hole.

Shape instability on swelling of a stretched nematic elastomer filament

Liquid crystalline elastomers combine the ordering properties of liquid crystals with elasticity of crosslinked polymer networks. In monodomain (permanently aligned) elastomers, altering the orientational (nematic) order causes changes in the equilibrium sample length, which is the basis of the famous effect of large-amplitude reversible mechanical actuation. The stimulus for this effect could be a change in temperature, or illumination by light in photosensitized elastomers, but equally the nematic order changes by mixing with a solvent. This work theoretically investigates a competition between the spontaneous contraction on swelling of a monodomain nematic elastomer and the externally imposed stretching. We find that this competition leads to bistability in the system and allows a two-phase separation between a nematic state with lower swelling and an isotropic state with higher solvent concentration. We calculated the conditions in which the instability occurs as well as the mechanical and geometric parameters of equilibrium states. Being able to predict how this instability arises will provide opportunities for exploiting nematic elastomer filaments.

Nematic fluctuations and semisoft elasticity in liquid-crystal elastomers

We give a detailed theory of nematic fluctuations in liquid-crystal elastomers (LCEs) and calculate relaxation rates as obtained by dynamic light scattering (DLS). In ideal LCEs, a nematic state is formed by a spontaneous orientational symmetry breaking of an isotropic state, manifesting itself in an existence of a coupled director-shear soft mode (Goldstone mode). The relaxation rate of the soft mode (a pure bend and a pure splay mode) goes to zero in a long-wavelength limit. In a real, nonideal sample with a locked-in anisotropy, on the other hand, the relaxation rates of these modes become finite. Nonideal elastomers are characterized by a plateau in the stress-strain curve, and the soft mode can be detected only upon stretching to the point of elastic instability at which the director starts to rotate. We use the semisoft model of Gaussian elasticity to derive relaxation rates as a function of deformation for different scattering geometries. We show that the bend-mode relaxation rate goes to zero at the threshold strain, so it is the soft mode. The splay mode, on the other hand, is not soft because the relaxation rate is finite at the threshold strain. We provide experimental evidence and compare DLS measurements of splay and bend modes of two side-chain LCE samples differing in crosslinking densities. Results of both samples are in complete agreement with the predictions of the semisoft model, which indicates that director relaxation properties are not influenced much by the crosslinking conditions.

Mechanical properties of monodomain nematic side-chain liquid-crystalline elastomers with homeotropic and in-plane orientation of the director

We present the first study of the shear mechanical properties of monodomain nematic side-chain liquid-crystal elastomers (SCLCEs) prepared by cross-linking with UV irradiation a nematic side-chain liquid-crystal polymer oriented with an electric or a magnetic field. Their elastic behavior was studied in the dry, swollen and stretched states, in order to check the various theoretical descriptions of these systems. The shear measurements taken on the dry samples show that the shear anisotropy is much smaller than that of the usual twice cross-linked samples oriented by a mechanical stretching of the network formed after the first cross-linking step, demonstrating that the elasticity of the networks strongly depends on the preparation procedure used. The shear experiments performed on the swollen state of these two different types of elastomers reveal that the elasticity of the network is Gaussian for the elastomers oriented with the electric or the magnetic field, and non-Gaussian for the elastomers oriented with the usual stretching procedure. The analysis of the stress-strain curves of both types of elastomers with the neoclassical model based on Gaussian rubber elasticity confirms the Gaussian and non-Gaussian nature of their elasticity. The shear experiments performed as a function of the elongation of the homeotropically oriented elastomer when the shear is applied in a direction parallel to the elongation, do not show the decrease of the associated shear modulus, which is theoretically expected when the strain approaches the threshold value marking the beginning of the elastic plateau. However, the observation of this effect could be prevented by possible small misalignments of the director, as suggested by a calculation presented in one of the theories describing this effect.

Modeling and simulation of liquid-crystal elastomers

We 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 implicit-explicit 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.

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.

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.

Mechanical manipulation of molecular lattice parameters in smectic elastomers

Smectic liquid crystalline elastomers (SLCE) represent unique materials that combine a 1-D molecular lattice arrangement and orientational order with rubber-elasticity mediated by a polymer network. Such materials may exhibit large thermo-mechanical, opto-mechanical and electro-mechanical effects, due to the coupling of macroscopic sample geometry and microscopic structural features. It is shown that the molecular layer dimensions in the smectic phases can be influenced reversibly by macroscopic strain of the material. We present a microscopic model on the basis of experimental results obtained by mechanical dilatation measurements, optical interferometry, X-ray scattering, (13)C NMR, FTIR and polarizing microscopy data. The model gives an explanation of the controversial results obtained in different types of smectic elastomers.

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 lambda < or = lambda(c) = 1.3 (10 mol% crosslinker density), respectively lambda < or = lambda(c) = 1.6 (5 mol% crosslinker density) no change of the mean orientation and the molecular order parameters is observed, while for lambda > or = lambda(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 lambda(c).

Commentary on "Mechanical properties of monodomain side chain nematic elastomers" by P. Martinoty et al

We discuss the rheology experiments on nematic elastomers by Martinoty et al. in the light of theoretical models for the long-wavelength low-frequency dynamics of these materials. We review these theories and discuss how they can be modified to provide a phenomenological description of the non-hydrodynamic frequency regime probed in the experiments. Moreover, we review the concepts of soft and semi-soft elasticity and comment on their implications for the experiments.

Commentary on "Mechanical properties of monodomain side-chain nematic elastomers" by P. Martinoty, P. Stein, H. Finkelmann, H. Pleiner and H.R. Brand

We discuss the background to static and dynamic soft elasticity. The evidence in the static case and the symmetry basis for soft and semi-soft elasticity is well understood. By contrast the dynamic analogy is less clear. Lack of clean time scale separation clouds the interpretation of director relaxation keeping up, or not, with imposed strains. However, the reduction in modulus between geometries obtaining at low frequencies and being lost at high frequencies confirms that director reaction indeed determines dynamical semi-softness.

Mechanical properties of mono-domain side chain nematic elastomers

We investigate the behavior of the shear rigidity modulus G = G' + iG" of three mono-domain side chain liquid-crystalline elastomers composed of side chain polysiloxanes cross-linked by either flexible or rigid cross-linkers. The measurements were taken in a frequency domain ranging from approximately 0.02 Hz to approximately 10(4) Hz applying the shear in a plane perpendicular to or containing the director. The measurements as a function of temperature show an anisotropy of G' which appears around T(NI), when decreasing the temperature, and which is due to the expected lowering of G'(//) coming from the coupling between the shear and the director. The measurements as a function of frequency show that G has two components for both geometries, in both the isotropic phase and in the nematic phase around the phase transition. One reflects the network behavior in its hydrodynamic regime ( G' is constant and G'' is approximately f, where f is the frequency), the other which appears at higher frequencies is characterized by a scaling law behavior (G' is approximately G" is approximately f(0.5)) of the Rouse type. We discuss the results in the framework of available theories and show that the three elastomers present a non-soft behavior, even for the elastomer for which the contrary was claimed, and that there is no separation of time scales between the director and the network. We also present data on a poly-domain sample and a non-mesomorphic one which complement these results.

Dynamics of nematic elastomers

We study the low-frequency, long-wavelength dynamics of soft and semisoft nematic elastomers using two different but related dynamic theories. Our first formulation describes the pure hydrodynamic behavior of nematic elastomers in which the nematic director has relaxed to its equilibrium value in the presence of strain. We find that the sound-mode structure for soft elastomers is identical to that of columnar liquid crystals. Our second formulation generalizes the derivation of the equations of nematohydrodynamics by Forster et al. to nematic elastomers. It treats the director explicitly and describes slow modes beyond the hydrodynamic limit.

Fast liquid-crystal elastomer swims into the dark

Liquid-crystal elastomers (LCEs) are rubbers whose constituent molecules are orientationally ordered. Their salient feature is strong coupling between the orientational order and mechanical strain. For example, changing the orientational order gives rise to internal stresses, which lead to strains and change the shape of a sample. Orientational order can be affected by changes in externally applied stimuli such as light. We demonstrate here that by dissolving-rather than covalently bonding-azo dyes into an LCE sample, its mechanical deformation in response to non-uniform illumination by visible light becomes very large (more than 60 degrees bending) and is more than two orders of magnitude faster than previously reported. Rapid light-induced deformations allow LCEs to interact with their environment in new and unexpected ways. When light from above is shone on a dye-doped LCE sample floating on water, the LCE 'swims' away from the light, with an action resembling that of flatfish such as skates or rays. We analyse the propulsion mechanism in terms of momentum transfer.

Liquid crystalline elastomers: dynamics and relaxation of microstructure

The equilibrium mechanical response of nematic elastomers can be soft or hard depending on the relation between the imposed strains and the nematic director, in particular, if the local nematic director is able to respond by rotating. The dynamical response proves to be equally unusual. We examine the linear dynamic mechanical response of monodomain nematic elastomers under shear and the aspects of time-temperature superposition of the dynamical data across phase-transition regions. In the low-frequency region of the master curves, one finds a dramatic reduction of rubber plateau modulus and the rise in internal dissipation: in the shear geometries compatible with dynamic soft elasticity. Power-law variation of the storage modulus with frequency G' proportional, variant omega(a) agrees very well with the results of static stress relaxation, where each relaxation curve obeys the analogous power law G' proportional, variant t(-a) in the corresponding region of long times and temperatures.

Semisoft elasticity and director reorientation in stretched sheets of nematic elastomers

A two-dimensional effective model for the semisoft elastic behavior of nematic elastomers is derived in the thin film limit. The model is used to investigate numerically the force-stretch curves and the deformed shape, and to resolve the local patterns in the director orientation in a stretching experiment. From the force-stretch curves we recover the two critical stretches which mark the transition from hard to soft and back to hard response. We present an analytical model for their dependence on the aspect ratio of the sample, and compare it with numerical results.

Isotropic-nematic transition in liquid-crystalline elastomers

In liquid-crystalline elastomers, the nematic order parameter and the induced strain vary smoothly across the isotropic-nematic transition, without the expected first-order discontinuity. To investigate this smooth variation, we measure the strain as a function of temperature over a range of applied stress, for elastomers cross-linked in the nematic and isotropic phases, and analyze the results using a variation on Landau theory. This analysis shows that the smooth variation arises from quenched disorder in the elastomer, combined with the effects of applied stress and internal stress.

Propagation of acoustic waves in nematic elastomers

We develop a theory of elastic waves in oriented monodomain nematic elastomers. The effect of soft elasticity, combined with the Leslie-Ericksen version of dissipation function, results in an unusual dispersion and anomalous anisotropy of shear acoustic waves. A characteristic time scale of nematic rotation determines the crossover frequency, below which waves of some polarizations have a very strong attenuation while others experience no dissipation at all. We study the anisotropy of low-frequency Poynting vectors and wave fronts, and discuss a "squeeze" effect of energy transfer nonparallel to the wave vector. Based on these theoretical results, an application, the acoustic polarizer, is proposed.

Symmetries and elasticity of nematic gels

A nematic liquid-crystal gel is a macroscopically homogeneous elastic medium with the rotational symmetry of a nematic liquid crystal. In this paper, we develop a general approach to the study of these gels that incorporates all underlying symmetries. After reviewing traditional elasticity and clarifying the role of broken rotational symmetries in both the reference space of points in the undistorted medium and the target space into which these points are mapped, we explore the unusual properties of nematic gels from a number of perspectives. We show how symmetries of nematic gels formed via spontaneous symmetry breaking from an isotropic gel enforce soft elastic response characterized by the vanishing of a shear modulus and the vanishing of stress up to a critical value of strain along certain directions. We also study the phase transition from isotropic to nematic gels. In addition to being fully consistent with approaches to nematic gels based on rubber elasticity, our description has the important advantages of being independent of a microscopic model, of emphasizing and clarifying the role of broken symmetries in determining elastic response, and of permitting easy incorporation of spatial variations, thermal fluctuations, and gel heterogeneity, thereby allowing a full statistical-mechanical treatment of these materials.

Structure and elastic properties of smectic liquid crystalline elastomer films

Mechanical measurements, x-ray investigations, and optical microscopy are employed to characterize the interplay of chemical composition, network topology, and elastic response of smectic liquid crystalline elastomers (LCEs) in various mesophases. Macroscopically ordered elastomer films of submicrometer thicknesses were prepared by cross linking freely suspended smectic polymer films. The cross-linked material preserves the mesomorphism and phase transitions of the precursor polymer. The elastic response of the smectic LCE is entropic, and the corresponding elastic moduli are of the order of MPa. In the tilted ferroelectric smectic-C* phase, the network structure plays an important role. Due to the coupling of elastic network deformations to the orientation of the mesogenic groups in interlayer cross-linked materials (mesogenic cross-linker units), the stress-strain characteristics is found to differ qualitatively from that in the other phases.

Effect of cross-linker geometry on dynamic mechanical properties of nematic elastomers

We study three monodomain (single-crystal) nematic elastomer materials, all side-chain siloxane polymers with the same mesogenic groups but with different types of cross linking: (i) short flexible siloxane linkage affine to the network backbone, (ii) short flexible aliphatic cross links miscible with mesogenic side-chain groups, and (iii) long segments of main-chain nematic polymer. The dynamic mechanical response of these three systems shows a characteristically universal decrease of storage modulus and a corresponding increase of loss factor. This effect of "dynamic soft elasticity" is strongly anisotropic, depending on the nematic director orientation. We examine the important role of the average backbone chain anisotropy r(T)=l(parallel)/l(perpendicular), which is affected by the cross-linking geometry and contributes to the magnitude and frequency dependence of the dynamic anomaly, and discuss possible applications in mechanical damping and polarized acoustic technology.