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

A Molecular Rheology Dynamics Study on 3D Printing of Liquid Crystal Elastomers

This work presents a rheological study of a biocompatible and biodegradable liquid crystal elastomer (LCE) ink for three dimensional (3D) printing. These materials have shown that their structural variations have an effect on morphology, mechanical properties, alignment, and their impact on cell response. Within the last decade LCEs are extensively studied as potential printing materials for soft robotics applications, due to the actuation properties that are produced when liquid crystal (LC) moieties are induced through external stimuli. This report utilizes experiments and coarse-grained molecular dynamics to study the macroscopic rheology of LCEs in nonlinear shear flow. Results from the shear flow simulations are in line with the outcomes of these experimental investigations. This work believes the insights from these results can be used to design and print new material with desirable properties necessary for targeted applications.

On the origin of elasticity and heat conduction anisotropy of liquid crystal elastomers at gigahertz frequencies

Liquid crystal elastomers that offer exceptional load-deformation response at low frequencies often require consideration of the mechanical anisotropy only along the two symmetry directions. However, emerging applications operating at high frequencies require all five true elastic constants. Here, we utilize Brillouin light spectroscopy to obtain the engineering moduli and probe the strain dependence of the elasticity anisotropy at gigahertz frequencies. The Young's modulus anisotropy, E_||/E_⊥~2.6, is unexpectedly lower than that measured by tensile testing, suggesting disparity between the local mesogenic orientation and the larger scale orientation of the network strands. Unprecedented is the robustness of E_||/E_⊥ to uniaxial load that it does not comply with continuously transformable director orientation observed in the tensile testing. Likewise, the heat conductivity is directional, κ_||/κ_⊥~3.0 with κ_⊥ = 0.16 Wm^-1K^-1. Conceptually, this work reveals the different length scales involved in the thermoelastic anisotropy and provides insights for programming liquid crystal elastomers on-demand for high-frequency applications.

Influence of Liquid Crystallinity and Mechanical Deformation on the Molecular Relaxations of an Auxetic Liquid Crystal Elastomer

Liquid Crystal Elastomers (LCEs) combine the anisotropic ordering of liquid crystals with the elastic properties of elastomers, providing unique physical properties, such as stimuli responsiveness and a recently discovered molecular auxetic response. Here, we determine how the molecular relaxation dynamics in an acrylate LCE are affected by its phase using broadband dielectric relaxation spectroscopy, calorimetry and rheology. Our LCE is an excellent model system since it exhibits a molecular auxetic response in its nematic state, and chemically identical nematic or isotropic samples can be prepared by cross-linking. We find that the glass transition temperatures (Tg) and dynamic fragilities are similar in both phases, and the T-dependence of the α relaxation shows a crossover at the same T* for both phases. However, for T>T*, the behavior becomes Arrhenius for the nematic LCE, but only more Arrhenius-like for the isotropic sample. We provide evidence that the latter behavior is related to the existence of pre-transitional nematic fluctuations in the isotropic LCE, which are locked in by polymerization. The role of applied strain on the relaxation dynamics and mechanical response of the LCE is investigated; this is particularly important since the molecular auxetic response is linked to a mechanical Fréedericksz transition that is not fully understood. We demonstrate that the complex Young's modulus and the α relaxation time remain relatively unchanged for small deformations, whereas for strains for which the auxetic response is achieved, significant increases are observed. We suggest that the observed molecular auxetic response is coupled to the strain-induced out-of-plane rotation of the mesogen units, in turn driven by the increasing constraints on polymer configurations, as reflected in increasing elastic moduli and α relaxation times; this is consistent with our recent results showing that the auxetic response coincides with the emergence of biaxial order.

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.

Light-induced spontaneous bending of a simply supported liquid crystal elastomer rectangular plate

Designing the director alignment of a liquid crystal elastomer (LCE) is a key tuning approach for LCE based smart devices. In this paper, the spontaneous strain of the LCE with arbitrary three-dimensional director orientation is derived, and the governing equation for a simply supported LCE rectangular plate is established. By using the finite difference method, the bending configurations are obtained. Different from the freestanding case, three bending modes, that is, unimodal, bimodal, and trimodal modes, are observed for the simply supported rectangular LCE plate. The relation between the bending modes and the director orientation is established. This paper enhances the understanding and facilitates the design of LCE based intelligent light driven devices.

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.

Influence of the degree of polymerisation and of the architecture on the elastic properties of new polyurea elastomers

The elastic properties of new polyurea elastomers have been studied by varying the segmental molecular weight and the chemical nature of the polymer end groups showing up to two plateaus.

On the nonlinear behaviour of nematic single crystal elastomers under biaxial mechanic and electrical force fields

A slab of nematic-side-chain-liquid-single-crystal elastomer (NSCLSCE), with the director initially oriented in the z -direction, is subjected to a pair of equal mechanical loads and electrical force fields in the x , y directions. The electric fields tend to make easier the rotation of the director after the application of the mechanical force field. A nonlinear expression for the free energy density is used to obtain the interval of stretching for which the system becomes unstable. However, the elastic energy of the network is assumed to be linear. The stress-strain curves predicted by the model show an unstable zone between two linearly increasing segments. The possibility of bifurcation phenomena has been examined.

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.

Biaxially stretched nematic liquid crystalline elastomers

The biaxial stretching of sheets of liquid crystalline neo-Hookean elastomer has been studied in the isotropic case. The results suggest two types of laminate structures in the process of quasiconvexification of the free energy, a fact that implies the appearance of several shear terms in the deformation gradient matrix. More that one decomposition of the deformation gradient is possible, which is consistent with a bifurcation in the undeformed configuration (λ = 1) . This situation is similar to the well-known Rivlin's problem of the triaxial symmetric traction of a neo-Hookean cube. The problem can easily be generalized for an anisotropic material by introducing a semisoft term in the free-energy expression. In this case, the horizontal plateau corresponding to the minimal energy, characteristic of the soft elasticity, disappears, and only an equilibrium condition is obtained.

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.

Elastic response and Ward identities in stressed nematic elastomers

Nematic elastomers exhibit a rich elastic response to external stresses. Of particular interest is the semisoft response of elastomers with an anisotropy direction (z) frozen in by a double cross-linking process. This response is characterized by a stress-strain curve for stresses along x perpendicular to z that rises initially, exhibits a nearly flat plateau between two critical values of strain, and then rises again. This paper explores elastic response in semisoft elastomers as a function of externally applied strain. It derives general Ward identities for elastic moduli and shows that the elastic modulus measuring response to xz shears vanishes at the boundaries of the semisoft plateau whereas moduli measuring response to shears perpendicular to the xz plane do not. It then calculates all relevant moduli in a simple model of elastomers and verifies the general Ward-identity predictions.

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.

Gel-like elasticity in glass-forming side-chain liquid-crystal polymers

We study the complex shear modulus G of two side-chain liquid-crystal polymers (SCLCPs), a methoxy-phenylbenzoate substituted polyacrylate (thereafter called PAOCH3 ), and a cyanobiphenyl substituted polyacrylate supplied by Merck (thereafter called LCP105) using a piezoelectric rheometer. Two methods of filling the cell are used: (a) a capillary method, which can be used only at high temperature because of the low value of the viscosity, and (b) the classical one, thereafter called compression method, which consists in placing the sample between the two slides of the cell and to bring them closer. By filling the cell at high temperature either with the compression or the capillary method, we show that the response of both compounds is liquidlike ( G' approximately f2 and G'' approximately f , where f is the frequency) for temperatures higher than a certain temperature T0 and gel-like (G' approximately const, G'' approximately f) below T0. This change in behavior from the conventional flow response to a gel-like response, when approaching the glass transition, is observed for nonsliding conditions and for very weak-imposed shear strains. It can be explained by a percolation-type mechanism of preglassy elastic clusters, which correspond to long-range and long-lived density fluctuations that are frozen at the time scale of the experiment. The sample response is therefore the sum of two contributions: one is due to the flow response of the polymer melt and the other to the elastic response of the network formed by the preglassy elastic clusters. By filling the cell below T0 with the compression method, both compounds exhibit a gel-type behavior by gently bringing closer the slides of the cell and an anomalous low-frequency behavior characterized by G'=const and G''=const by increasing the pressure used to bring closer the slides of the cell. A compression-assisted aggregation of the preglassy elastic clusters can explain both the increase in the low-frequency elastic plateau when the sample thickness is decreased and the anomalous low-frequency behavior. Further evidence for the existence of these elastic clusters is provided by the following results: (a) the nonlinear response of the samples as a function of the strain amplitude, which can be explained by the Payne effect, and (b) the aggregation effects, which can be mimicked by a polydimethylsiloxane melt filled with silica particles, the silica particles playing the role of the preglassy elastic clusters. All these observations show that PAOCH3 is not a macroscopically solidlike material with an unconventional type of elasticity, as claimed by Mendil [Phys. Rev. Lett. 96, 077801 (2006)]. The gel-type behavior observed here on two SCLCPs ( PAOCH3 and LCP105) and previously on some conventional flexible polymers (atactic polystyrene, poly-n-butylacrylate) seems to be a generic effect of the glass transition. The presence of the preglassy elastic clusters questions the widely accepted hypothesis of ergodicity in the supercooled state.

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.

Semisoft elastic response of nematic elastomers to complex deformations

We consider a relaxed semisoft elastomer with its director oriented along the z axis that is first subjected to a large stretch in the x direction then to a slight x-z shear. We give a general argument that in any theory including director rotation, at the onset and end of the director rotation induced by these large stretches, there will be kinks in the stress-large strain curve (forming a stress-strain plateau) and zeros in the x-z shear modulus (C5) associated with small shears imposed on top of the stretches. We then find the analytical forms of the C5 -strain curves for a particular model of semisoftness (arising from compositional fluctuations) and show that it, together with the known stress-strain curve, provides the basis for a strong test of this theory. Finally, we consider the scope for other semisoft models and show that the compositional fluctuations model in fact yielded a generic form, that is, it is the most general quadratic free energy that does not explicitly include a final state direction other than the director. By introducing such additional directions, a large range of alternative models could be developed.

Nematic elastomers: from a microscopic model to macroscopic elasticity theory

A Landau theory is constructed for the gelation transition in cross-linked polymer systems possessing spontaneous nematic ordering, based on symmetry principles and the concept of an order parameter for the amorphous solid state. This theory is substantiated with help of a simple microscopic model of cross-linked dimers. Minimization of the Landau free energy in the presence of nematic order yields the neoclassical theory of the elasticity of nematic elastomers and, in the isotropic limit, the classical theory of isotropic elasticity. These phenomenological theories of elasticity are thereby derived from a microscopic model, and it is furthermore demonstrated that they are universal mean-field descriptions of the elasticity for all chemical gels and vulcanized media.

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.