When liquid-crystal elastomers are prepared without any alignment, disordered polydomain structures emerge as the materials are cooled into the nematic phase. These polydomain structures have been attributed to quenched disorder in the cross-linked polymer network. As an alternative explanation, we develop a theory for the dynamics of the isotropic-nematic transition in liquid-crystal elastomers, and show that the dynamics can induce a polydomain structure with a characteristic length scale, through a mechanism analogous to the Cahn-Hilliard equation for phase separation.
We model polydomain liquid-crystal elastomers by extending the neo-classical soft and semi-soft free energies used successfully to describe monodomain samples. We show that there is a significant difference between polydomains cross-linked in homogeneous high symmetry states then cooled to low symmetry polydomain states and those cross-linked directly in the low symmetry polydomain state. For example, elastomers cross-linked in the isotropic state then cooled to a nematic polydomain will, in the ideal limit, be perfectly soft, and with the introduction of non-ideality, will deform at very low …
We address the physics of nematic liquid crystalline elastomers randomly crosslinked in the isotropic state. To do this, we construct a phenomenological effective replica Hamiltonian in terms of two order-parameter fields: one for the vulcanization, the other for nematic alignment. Using a Gaussian variational approach, we analyze both thermal and quenched fluctuations of the local nematic order, and find that, even for low temperatures, the macroscopically isotropic polydomain state is stabilized by the network heterogeneity. For sufficiently strong disorder and low enough temperature, our th…
Structural studies by synchrotron x-ray diffraction on two main-chain smectic-C elastomers reveal the presence of two different relaxation mechanisms in these systems at low and high strains. At low strains, the smectic layers are reoriented with layer-normals distributed in a plane perpendicular to the stretch direction. The system relaxes relatively slowly (time-constant ~ 45 minutes) which is attributed to the flow properties of the LC layers embedded in the elastomer network. At high strains, the equilibration time (~ 4 - 8 minutes) conforms to a faster relaxation and appears to have its o…
We studied the dynamics of isotropic-nematic transitions in liquid crystalline polymers by integrating time-dependent Ginzburg-Landau equations. In a concentrated solution of rodlike polymers, the rotational diffusion constant Dr of the polymer is severely suppressed by the geometrical constraints of the surrounding polymers, so that the rodlike molecules diffuse only along their rod directions. In the early stage of phase transition, the rodlike polymers with nearly parallel orientations assemble to form a nematic polydomain. This polydomain pattern with characteristic length l, grows with se…
In liquid crystal elastomers, the orientational order of liquid crystals is coupled with elastic distortions of crosslinked polymer networks. Previous theoretical research has described these materials through two different approaches: a neoclassical theory based on the liquid crystal director and the deformation tensor, and a geometric elasticity theory based on the difference between the actual metric tensor and a reference metric. Here, we connect those two approaches using a formalism based on differential geometry. Through this connection, we determine how both the director and the geomet…
Wrinkles commonly develop in a thin film deposited on a soft elastomer substrate when the film is subject to compression. Motivated by recent experiments [Agrawal et al., Soft Matter 8, 7138 (2012)] that show how wrinkle morphology can be controlled by using a nematic elastomer substrate, we develop the theory of small-amplitude wrinkles of an isotropic film atop a nematic elastomer. The directors of the nematic elastomer are assumed to lie in a plane parallel to the plane of the undeformed film. For uniaxial compression of the film along the direction perpendicular to the elastomer directors,…
Instabilities in thin elastic sheets, such as wrinkles, are of broad interest both from a fundamental viewpoint and also because of their potential for engineering applications. Nematic liquid crystal elastomers offer a new form of control of these instabilities through direct coupling between microscopic degrees of freedom, resulting from orientational ordering of rod-like molecules, and macroscopic strain. By a standard method of dimensional reduction, we construct a plate theory for thin sheets of nematic elastomer. We then apply this theory to the study of the formation of wrinkles due to …
In this work we will derive an anisotropic generalisation of the finitely extensible chain model, due to Kuhn and Grün, which is well known in rubber elasticity. This provides a chain energy that couples elastic behaviour to a probability distribution describing the orientations of liquid crystal monomers within a main chain elastomer. The key point is to invoke a maximum relative entropy assumption on the distribution of bond angles in an observed chain. The chain energy's fourth order Taylor expansion is also given, which couples to the second and fourth moments of the nematic distribution f…
Stability is an important and fruitful avenue of research for liquid crystal elastomers. At constant temperature, upon stretching, the homogeneous state of a nematic body becomes unstable, and alternating shear stripes develop at very low stress. Moreover, these materials can experience classical mechanical effects, such as necking, void nucleation and cavitation, and inflation instability, which are inherited from their polymeric network. We investigate the following two problems: First, how do instabilities in nematic bodies change from those found in purely elastic solids? Second, how are t…
Materials exhibiting a large caloric effect could lead to the development of new generation of heat-management technologies that will have better energy efficiency and be potentially more environmentally friendly. The focus of caloric materials investigations has shifted recently from solid-state materials toward soft materials, such as liquid crystals and liquid crystalline elastomers. It has been shown recently that a large electrocaloric effect exceeding 7 K can be observed in smectic liquid crystals. Here, we report on a significant elastocaloric response observed by direct elastocaloric m…
Models of smectic-C liquid crystal elastomers predict that it can display soft elasticity, in which the shape of the elastomer changes at no energy cost. The amplitude of the soft mode and the accompanying shears are dependent on the orientation of the layer normal and the director with respect to the stretch axis. We demonstrate that in some geometries the director is forced to rotate perpendicular to the stretch axis, causing lateral expansion of the sample; a negative Poisson's ratio. Current models do not include the effect of imperfections that must be present in the physical sample. We i…
Macroscale robotic systems have demonstrated great capabilities of high speed, precise, and agile functions. However, the ability of soft robots to perform complex tasks, especially in centimeter and millimeter scale, remains limited due to the unavailability of fast, energy-efficient soft actuators that can programmably change shape. Here, we combine desirable characteristics from two distinct active materials: fast and efficient actuation from dielectric elastomers and facile shape programmability from liquid crystal elastomers into a single shape changing electrical actuator. Uniaxially ali…
The shape of liquid crystalline elastomers (LCEs) with spatial variation in the director orientation can be transformed by exposure to a stimulus. Here, informed by previously reported analytical treatments, we prepare complex spiral patterns imprinted into LCEs and quantify the resulting shape transformation. Quantification of the stimuli-induced shapes reveals good agreement between predicted and experimentally observed curvatures. We conclude this communication by reporting a design strategy to allow LCE films to be anchored at their external boundaries onto rigid substrates without incurri…
This paper presents the derivation of the homogenized equations that describe the macroscopic mechanical response of elastomers filled with liquid inclusions in the setting of small quasistatic deformations. The derivation is carried out for materials with periodic microstructure by means of a two-scale asymptotic analysis. The focus is on the non-dissipative case when the elastomer is an elastic solid, the liquid making up the inclusions is an elastic fluid, the interfaces separating the solid elastomer from the liquid inclusions are elastic interfaces featuring an initial surface tension, an…
We introduce a simple mean-field lattice model to describe the behavior of nematic elastomers. This model combines the Maier-Saupe-Zwanzig approach to liquid crystals and an extension to lattice systems of the Warner-Terentjev theory of elasticity, with the addition of quenched random fields. We use standard techniques of statistical mechanics to obtain analytic solutions for the full range of parameters. Among other results, we show the existence of a stress-strain coexistence curve below a freezing temperature, analogous to the P-V diagram of a simple fluid, with the disorder strength playin…
In this paper, we speculate on a possible application of Liquid Crystal Elastomers to the field of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a flat solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change). The presence of frictional forces that are sensitive to the direction of sliding transforms reciprocal, 'breathing-li…
In this paper, the two-dimensional pure bending of a hyperelastic substrate coated by a nematic liquid crystal elastomer (abbreviated as NLCE) is studied within the framework of nonlinear elasticity. The governing system, arising from the deformational momentum balance, the orientational momentum balance and the mechanical constraint, is formulated, and the corresponding exact solution is derived for a given constitutive model. It is found that there exist two different bending solutions. In order to determine which the preferred one is, we compare the total potential energy for both solutions…
The mechanical properties of liquid crystal elastomers (LCEs) make them suitable candidates for pressure-sensitive adhesives (PSAs). Using the nematic dumbbell constitutive model, and the block model of PSAs, we study their tack energy and the debonding process as could be measured experimentally in the probe-tack test. To investigate their performance as switchable PSAs we compare the tack energy for the director aligned parallel, and perpendicular to the substrate normal, and for the isotropic state. We find that the tack energy is larger in the parallel alignment than the isotropic case by …
Photoactive liquid crystal elastomers are polymer networks of liquid crystal mesogens embedded with chromophores like azobenzene. They undergo large deformation when illuminated by light of a certain wavelength through photochemical reaction, inspiring exciting new applications. However, despite the recent progresses in both the experiment and theory of these materials, the fundamental understanding of the temperature effect on their photomechanical actuation through various molecular-to-mesoscale processes have remained largely unexplored. This paper constructs a theoretical model to investig…
This paper explores different photo-bending shapes in polydomain nematic glass. The motivation is to explain the phenomenon in experiment [1] under polarized light in which a nematic film curls into an circular arc, like part of a cylindrical surface. Polarized light triggers photo-isomerization and therefore makes liquid crystals (LCs) contract along their directors. We apply the Sachs limit to homogenize the deformation of polydomain LC glass. Photo-strain can be either contraction or expansion through the material. Bending shapes can be anticlastic, bowl-shaped and cylindrical affected by P…
Liquid crystal elastomers represent a novel class of programmable shape-transforming materials whose shape change trajectory is encoded in the material's nematic director field. Using three-dimensional nonlinear finite element elastodynamics simulation, we model a variety of different actuation geometries and device designs: thin films containing topological defects, patterns that induce formation of folds and twists, and a bas-relief structure. The inclusion of finite bending energy in the simulation model reveals features of actuation trajectory that may be absent when bending energy is negl…
Lyotropic chromonic liquid crystals (LCLCs) represent aqueous dispersions of organic disk-like molecules that form cylindrical aggregates. Despite the growing interest in these materials, their flow behavior is poorly understood. Here, we explore the effect of shear on dynamic structures of the nematic LCLC, formed by 14wt ${\%}$ water dispersion of disodium cromoglycate (DSCG). We employ in-situ polarizing optical microscopy (POM) and small-angle and wide-angle X-ray scattering (SAXS/WAXS) to obtain independent and complementary information on the director structures over a wide range of shea…
We demonstrate facile optical manipulation of shape of birefringent colloidal microparticles made from liquid crystal elastomers. Using soft lithography and polymerization, we fabricate elastomeric microcylinders with weakly undulating director oriented on average along their long axes. These particles are infiltrated with gold nanospheres acting as heat transducers that allow for an efficient localized transfer of heat from a focused infrared laser beam to a submicrometer region within a microparticle. Photothermal control of ordering in the liquid crystal elastomer using scanned beams allows…
In this article, we construct and analyze models of anisotropic crosslinked polymers employing tools from the theory of liquid crystal elastomers. The anisotropy of these systems stems from the presence of rigid-rod molecular units in the network. We study minimization of the energy for incompressible as well as compressible materials, combining methods of isotropic nonlinear elasticity with the theory of lyotropic liquid crystals. We apply our results to the study of phase transitions in networks of rigid rods, in order to model the behavior of actin filament systems found in the cytoskeleton…
We elucidate the polymer dynamics of a liquid crystal elastomer based on the time-dependent response of the pendent liquid crystal mesogens. The molecular tilt and switching time of mesogens are analyzed as a function of temperature and cross-linking density upon application of an electric field. We observe an unexpected maximum in the switching time of the liquid crystal mesogens at intermediate field strength. Analysis of the molecular tilt over multiple time regimes correlates the maximum response time with a transition to entangled polymer dynamics at a critical field strength.
Liquid crystal elastomers are rubbers with liquid crystal order. They contract along their nematic director when heated or illuminated. The shape changes are large and occur in a relatively narrow temperature interval, or at low illumination, around the nematic-isotropic transition. We present a conceptual design of a mechanical, turbine-based engine using photo-active liquid crystal elastomers to extract mechanical work from light. Its efficiency is estimated to be 40%.
Considerable recent attention has been given to the study of shape formation using modern responsive materials that can be preprogrammed to undergo spatially inhomogeneous local deformations. In particular, nematic liquid crystal polymer networks offer exciting possibilities in this context. In this paper, we discuss the generation of Gaussian curvature in thin nematic sheets using smooth in-plane director fields patterned across the surface. We highlight specific patterns which encode constant Gaussian curvature of prescribed sign and magnitude and present experimental results which appear to…
The blue phases are observed in highly chiral liquid crystalline compositions that nascently organize into a three-dimensional, crystalline nanostructure. The periodicity of the unit cell lattice parameters is on the order of the wavelength of visible light and accordingly, the blue phases exhibit a selective reflection as a photonic crystal. Here, we detail the synthesis of liquid crystalline elastomers (LCEs) that retain blue phase I, blue phase II, and blue phase III. The mechanical properties and deformation of LCEs retaining the blue phases are contrasted to the cholesteric phase in fully…
Liquid crystal elastomers are rubber-like solids with liquid crystalline mesogens (stiff, rod-like molecules) incorporated either into the main chain or as a side chain of the polymer. These solids display a range of unusual thermo-mechanical properties as a result of the coupling between the entropic elasticity of rubber and the orientational phase transitions of liquid crystals. One of these intriguing properties is the soft behavior, where it is able to undergo significant deformations with almost no stress. While the phenomenon is well-known, it has largely been examined in the context of …
Recent studies of azo-dye doped liquid crystal elastomers show a strong photomechanical response. We report on models that predict experimental results that suggest photothermal heating is the dominant mechanism in a planar constrained geometry. We compare our models with experiments to determine key material parameters, which are used to predict the dynamical response as a function of intensity. We show that a local strain from photothermal heating and a nonlocal strain from thermal diffusion is responsible for the observed length changes over time. This work both elucidates the fundamental m…
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, th…
Control of physical behaviors of nematic colloids and colloidal crystals has been demonstrated by tuning particle shape, topology, chirality and surface charging. However, the capability of altering physical behaviors of such soft matter systems by changing particle shape and the ensuing responses to external stimuli has remained elusive. We fabricated genus-one nematic elastomeric colloidal ring-shaped particles and various microstructures using two-photon photopolymerization. Nematic ordering within both the nano-printed particle and the surrounding medium leads to anisotropic responses and …
Elastomers are artificial polymeric materials created for industrial and commercial applications. Depending on their purpose, they are performing in different species and structure modifications. Our studies focus on the systems of elastomers randomly standing-distributed in a smectic $A$ (Sm$A$) liquid crystal. Basing on the suggestion following from the experiment, that at a phase transition from Sm$A$ to nematic phase caused by an increase of a crosslink concentration, such a system survives a percolation transition at low crossilink concentrations, we propose a modeling explaining this phe…
