Nematic Liquid Crystal Elastomers Research Articles

Overdamping of vibration resonances by liquid crystal elastomers

This work aims to compare the capability of vibration attenuation by standard elastomeric polymers, and by the new anomalously damping nematic liquid crystal elastomer. We use the most mainstream materials in both categories, and design two testing platforms: the ASTM-standard constrained layer plate resonance geometry, and the attenuation of resonances in a commercial device (electric drill) where the damping polymers were inserted into the casing. In the standard plate resonance testing, we find that LCE outperforms all standard damping materials, moreover, it brings the vibrating plate into the overdamped condition, which is unique for a non-fluid dissipative system. In the attenuation of high-frequency vibrations of a device, we also found LCE dissipates these vibrations much better, although we did not find the optimal insertion configuration for the damping polymer, and did not reach overdamping.

Effects of carbon nanotubes on the isotropic to nematic phase transition in nematic liquid crystal elastomer

The isotropic to nematic phase transition on nematic liquid crystal elastomer - carbon nanotubes composites has been studied theoretically. The model free energy density has been constructed using Flory Huggins theory of isotropic mixing and Landau-de Gennes theory. The effects of carbon nanotubes and external mechanical stress on the isotropic to nematic phase transition of the nematic liquid crystal elastomer-carbon nanotubes composites have been discussed. The volume fraction of carbon nanotubes dependence of the isotropic to nematic transition temperature, mechanical strain and strain birefringence has been calculated. The weak first-order character of the isotropic to nematic phase transition on nematic liquid crystal elastomer-carbon nanotubes composites has been predicted.

A hyperelastic beam model for the photo-induced response of nematic liquid crystal elastomers

Liquid crystal elastomers (LCEs) are a novel class of materials created by combining polymeric solids with stiff, rod-like molecules known as nematic mesogens. These materials exhibit large, reversible deformations under mechanical, thermal, and optical stimuli. In this work, we develop a nonlinear beam formulation for analyzing the finite elastic deformation of beam-like structures made of LCEs under photo-actuation. This formulation applies to ideal, non-ideal, isotropic genesis, and nematic genesis LCEs. We establish the variational form of the problem based on the principle of virtual work. To solve numerical examples, we also develop a nonlinear finite element formulation based on B-spline functions. Several numerical examples are presented to demonstrate the applicability of the proposed formulation.

Theoretical and experimental study of elastocaloric responses in liquid crystalline elastomers

We carry out systematic experimental and theoretical study of elastocaloric (eC) response in nematic liquid crystal elastomers (LCEs), which possess the elastic properties of elastomers combined with the orientational order of liquid crystals. The chemical linking of mesogens to the polymer backbone enables thermomechanical response yielding a large spontaneous change in the LCE geometry on varying the temperature. In LCEs, a relatively large eC effect could be obtained upon adiabatic application or removal of a stress field in the isotropic state near phase transformation to the more ordered state. In these cases a change in the isothermal entropy or adiabatic temperature is compensated with the temperature change of liquid crystal elastomers. This effect could be exploited towards soft condensed state cooling technologies that gain increasing interest due to environmental issues, low-cost and low stimuli field. In the present study we measure directly the elastocaloric temperature change. Experimental measurements are interpreted using a modified Landau-de Gennes mesoscopic model taking into account both internal and external stress fields. Our systematic study identifies conditions yielding responsivity of a few K/MPa, which is two orders of magnitude larger than in the shape memory alloys, the most intensively studied materials for this effect.

Mesogen Organizations in Nematic Liquid Crystal Elastomers Under Different Deformation Conditions.

Liquid crystal elastomers (LCEs) exhibit unique mechanical properties of soft elasticity and reversible shape-changing behaviors, and so serve as potentially transformative materials for various protective and actuation applications. This study contributes to filling a critical knowledge gap in the field by investigating the microscale mesogen organization of nematic LCEs with diverse macroscopic deformation. A polarized Fourier transform infrared light spectroscopy (FTIR) tester is utilized to examine the mesogen organizations, including both the nematic director and mesogen order parameter. Three types of material deformation are analyzed: uniaxial tension, simple shear, and bi-axial tension, which are all commonly encountered in practical designs of LCEs. By integrating customized loading fixtures into the FTIR tester, mesogen organizations are examined across varying magnitudes of strain levels for each deformation mode. Their relationships with macroscopic stress responses are revealed and compared with predictions from existing theories. Furthermore, this study reveals unique features of mesogen organizations that have not been previously reported, such as simultaneous evolutions of the mesogen order parameter and nematic director in simple shear and bi-axial loading conditions. Overall, the findings presented in this study offer significant new insights for future rational designs, modeling, and applications of LCE materials.

On the effect of strain rate during the cyclic compressive loading of liquid crystal elastomers and their 3D printed lattices

Nematic liquid crystal elastomers (LCEs) are a unique class of network polymers with the potential for enhanced mechanical energy absorption and dissipation capacity over conventional network polymers because they exhibit both conventional viscoelastic behavior and soft-elastic behavior (nematic director changes under shear loading). This additional inelastic mechanism makes them appealing as candidate damping materials in a variety of applications from vibration to impact. The lattice structures made from the LCEs provide further mechanical energy absorption and dissipation capacity associated with packing out the porosity under compressive loading.Understanding the extent of mechanical energy absorption, which is the work per unit mass (or volume) absorbed during loading, versus dissipation, which is the work per unit mass (or volume) dissipated during a loading cycle, requires measurement of both loading and unloading response. In this study, a bench-top linear actuator was employed to characterize the loading-unloading compressive response of polydomain and monodomain LCE polymers and polydomain LCE lattice structures with two different porosities (nominally, 62% and 85%) at both low and intermediate strain rates at room temperature. As a reference material, a bisphenol-A (BPA) polymer with a similar glass transition temperature (9 °C) as the nematic LCE (4 °C) was also characterized at the same conditions for comparing to the LCE polymers. Based on the loading-unloading stress-strain curves, the energy absorption and dissipation for each material at different strain rates (0.001, 0.1, 1, 10 and 90 s-1) were calculated with considerations of maximum stress and material mass/density. The strain-rate effect on the mechanical response and energy absorption and dissipation behaviors was determined. The energy dissipation ratio was also calculated from the resultant loading and unloading stress-strain curves. All five materials showed significant but different strain rate effects on energy dissipation ratio. The solid LCE and BPA materials showed greater energy dissipation capabilities at both low (0.001 s−1) and high (above 1 s−1) strain rates, but not at the strain rates in between. The polydomain LCE lattice structure showed superior energy dissipation performance compared with the solid polymers especially at high strain rates.

Generalized continuum theory for nematic elastomers: Non-affine motion and characteristic behavior

We develop a physically-motivated mechanical theory for predicting the behavior of nematic elastomers — a subset of liquid crystal elastomers (LCEs). We begin with a statistical description of network geometry that naturally incorporates independent descriptors for the mesogens, which create the nematic phase, and the polymer chains, which are assumed to not deform affinely with global deformations. From here, we develop thermodynamically consistent constitutive laws based on classical continuum mechanics principles and ultimately provide simple governing equations with transparent physical interpretation. We found that our framework converges identically to two previously developed mechanical theories, including the well-known neo-classical theory, when considering the extreme ends of our parametric space. We then explore the new predictive capabilities of our model inside these two extremes and illustrate its unique predictions at finite strains, which are distinct in form from other theories. We validate our model using published experimental data from four monodomain nematic liquid crystal elastomers.

Toward Monodomain Nematic Liquid Crystal Elastomers of Arbitrary Thickness through PET-RAFT Polymerization.

Liquid crystal elastomers (LCEs) are polymeric materials that are proposed for a range of applications. However, to reach their full potential, it is desirable to have as much flexibility as possible in terms of the sample dimensions, while maintaining well-defined alignment. In this work, photoinduced electron/energy transfer reversible addition-fragmentation chain transfer (PET-RAFT) polymerization is applied to the synthesis of LCEs for the first time. An initial LCE layer (∼100 μm thickness) is partially cured before a second layer of the precursor mixture is added. The curing reaction is then resumed and is observed by FTIR to complete within 15 min of irradiation, yielding samples of increased thickness. Monodomain samples that exhibit an auxetic response and are of thickness 250-300 μm are consistently achieved. All samples are characterized thermally, mechanically, and in terms of their order parameters. The LCEs have physical properties comparable to those of analogous LCEs produced via free-radical polymerization.

Dynamic large strain formulation for nematic liquid crystal elastomers

Liquid crystal elastomers (LCEs) are a class of materials which exhibit an anisotropic behavior in their nematic state due to the main orientation of their rod-like molecules called mesogens. The reorientation of mesogens leads to the well-known actuation properties of LCEs, i.e. exceptionally large deformations as a consequence of particular external stimuli, such as temperature increase. Another key feature of nematic LCEs is the capability to undergo deformation by constant stresses while being stretched in a direction perpendicular to the orientation of mesogens. During this plateau stage, the mesogens rotate towards the stretching direction. Such characteristic is defined as semisoft elastic response of nematic LCEs. We aim at modeling the semisoft behavior in a dynamic finite element method based on a variational-based mixed finite element formulation. The reorientation process of the rigid mesogens relative to the continuum rotation is introduced by micropolar drilling degrees of freedom. Responsible for the above-mentioned characteristics is an appropriate free energy function. Starting from an isothermal free energy function based on the small strain theory, we aim to widen it into the framework of large strains by identifying tensor invariants. In this work, we analyze the isothermal influence of the tensor invariants on the mechanical response of the finite element formulation and show that its space-time discretization preserves mechanical balance laws in the discrete setting.

Coupling between viscoelasticity and soft elasticity in main-chain nematic Liquid Crystal Elastomers

Liquid crystal elastomers (LCEs) are a class of smart elastomers exhibiting unusual mechanical behavior, including large energy dissipation and soft elasticity under uniaxial tensile loading. LCEs are composed of liquid crystal molecules, called mesogens, linked by a network of polymer chains. During deformation, the mesogens orient in the direction of the loading, leading to soft elasticity, which is an increase in strain at constant stress. The combination of mesogen rotation and intrinsic polymer viscoelasticity leads to a nonlinear viscoelastic soft elastic behavior. The aim of this paper is to investigate the coupling between the viscoelastic mechanisms and soft elasticity in main chain LCEs. We propose a rheological model in which the mesogen rotation during deformation is represented by a reversible slider while viscoelastic relaxation mechanisms are modeled as series of Maxwell elements coupled or decoupled with mesogen rotation. Fitting this model to experimental data demonstrate that the coupling between polymer chain viscoelasticity and mesogen rotation is partial, i.e. the long-time relaxation mechanisms are coupled and the short-time relaxation mechanisms are decoupled from mesogen rotation. Furthermore, we show that the viscosity of mesogen rotation is not necessary to properly predict the elastic modulus during the soft elasticity but it is needed to properly predict the initiation of the phenomenon.

Revealing the unusual rate-dependent mechanical behaviors of nematic liquid crystal elastomers

Liquid crystal elastomers (LCEs) exhibit unique mechanical properties of soft elasticity and enhanced energy dissipation with rate dependency. They are potentially transformative materials for applications in mechanical impact mitigation and vibration isolation. However, previous studies have primarily focused on the mechanics of LCEs under equilibrium and quasistatic loading conditions. Critical knowledge gaps exist in understanding their rate-dependent behaviors, which are a complex mixture of traditional network viscoelasticity and the soft elastic behaviors with changes in the mesogen orientation and order parameter. Together, these inelastic mechanisms lead to unusual rate-dependent energy absorption responses of LCEs. In this work, we developed a viscoelastic constitutive theory for monodomain nematic LCEs to investigate how multiple underlying sources of inelasticity manifest in the rate-dependent and dissipative behaviors of monodomain LCEs. The theoretical modeling framework combines the neo-classical network theory with evolution rules for the mesogen orientation and order parameter with conventional viscoelasticity. The model is calibrated with uniaxial tension and compression data spanning six decades of strain rates. The established 3D constitutive model enables general loading predictions taking the initial mesogen orientation and order parameter as inputs. Additionally, parametric studies were performed to further understand the rate dependence of monodomain LCEs in relation to their energy absorption characteristics. Based on the parametric studies, particularly loading scenarios are identified as conditions where LCEs outperform conventional elastomers regarding energy absorption.

Modeling nematic phase main-chain liquid crystal elastomer synthesis, mechanics, and thermal actuation via coarse-grained molecular dynamics.

This paper presents a coarse-grained molecular dynamics simulation study of the synthesis, mechanics, and thermal actuation of nematic phase main-chain liquid crystal elastomers (LCEs), a type of soft, temperature-responsive, polymeric actuating material. The simulations herein model the crosslinking, mechanical stretching, and additional crosslinking synthesis process, following which, the simulated LCE exhibits a direction-dependent thermal actuation and mechanical response. The thermal actuation response shows good qualitative agreement with experimental results, including the variation of a global order parameter that describes the orientation of the mesogen domains comprising the LCE. The mechanical response due to applied deformation shows less agreement, but manifests the key features observed in experiments on LCEs, namely soft strain and hyperelasticity that is present when loaded perpendicularly and in-line, respectively, to the mesogen alignment direction. We also present a topological analysis of the simulated LCEs, which, in conjunction with the simulated thermomechanical responses, allows us to infer the relative contribution of entanglements and chemical crosslinks on those responses. We suggest that the model proposed herein will help enable improved LCE formulations via mechanistic insights that can be gained via the use of such a relatively computationally inexpensive coarse-grained molecular dynamics model, which may be of further value to application areas including soft robotics, bio-mimicking devices, artificial muscles, and adaptive materials.

Modeling the thermo-responsive behaviors of polydomain and monodomain nematic liquid crystal elastomers

Liquid crystal elastomers (LCEs) are polymeric materials that combine liquid crystal orientation and rubber elasticity. The mechanical responses of LCEs strongly depend on the nematic order and temperature. Developing a thermo-order-mechanical coupling model is important for the engineering applications of LCEs. In this work, we first synthesize both polydomain and monodomain LCEs. The shape change with temperature under a certain stress level is further characterized. In the theoretical part, the Landau–de Gennes model and neo-classical model are combined to construct the free energy density of LCEs. A linear term accounting for the effect of interior stress on nematic–isotropic transition is incorporated into the Landau–de Gennes free energy density, while a macro-order parameter is defined to describe the polydomain–monodomain transition for polydomain LCEs induced by the external force. Comparison between the model predictions and experimental results shows acceptably consistency for both polydomain and monodomain LCEs. Therefore, this work provides an efficient approach to predict the shape change of LCEs in various scenarios.

Anti-Hertz bulging of actuated liquid crystal elastomers

We consider the ‘anti-Hertz’ elastic problem of inverse indentation, which happens when the surface of an elastic material is pressed down with a plate with a round hole to form a bulge. This classical problem takes on a new life when a polydomain nematic liquid crystal elastomer is used. In this case, the nematic director aligns with the leading principal direction of local stress distribution created by bulging. When the deformed material is crosslinked a second time, this alignment pattern and the resulting permanent protrusion are preserved as pressure is removed, creating a bulge that can be reversibly actuated from a flat surface upon cooling. Experimentally, we also observe a dimple ring around the bulge and a punt (indentation) underneath it at the bottom. Theoretically, we model the deformation by coupling linear elastic and anelastic deformations using non-monotonic nematic elasticity and the singular stress-order relation of the polydomain-monodomain transition. The theory is in excellent agreement with the experiments, and predicts the emergence of all observed features.

Mechanism of Pressure-Sensitive Adhesion in Nematic Elastomers.

Nematic liquid crystal elastomers (LCEs) have anomalously high vibration damping, and it has been assumed that this is the cause of their anomalously high-pressure-sensitive adhesion (PSA). Here, we investigate the mechanism behind this enhanced PSA by first preparing thin adhesive tapes with LCE of varying cross-linking densities, characterizing their material and surface properties, and then studying the adhesion characteristics with a standard set of 90° peel, lap shear, and probe tack tests. The study confirms that the enhanced PSA is only present in (and due to) the nematic phase of the elastomer, and the strength of bonding takes over 24 h to fully reach its maximum value. Such a long saturation time is caused by the slow relaxation of local stress and director orientation in the nematic domains after pressing against the surface. We confirm this mechanism by showing that freshly pressed and annealed tape reaches the same maximum bonding strength on cooling, when the returning nematic order is forming in its optimal configuration in the pressed film.

A theoretical liquid crystal elastomer model that mimics the elasticity of cat skin

A mathematical model for nematic liquid crystal elastomers is proposed that mimics the elastic response of cat skin where reorientation of dermal fibres produces an increase in the thickness direction under tensile stretch. To capture this unusual effect, the uniaxial order parameter in the nematic elastomer model is allowed to decrease then increase again, and the critical stretch at which this change of monotonicity occurs and where the director also rotates suddenly is predicted. In addition, the model parameters are described by probability density functions and their uncertainty is propagated numerically to the predicted mechanical results.

Principle of virtual power and drilling degrees of freedom for dynamic modeling of the behavior of liquid crystal elastomer films

In this work, we aim to model the reorientation process of mesogens in nematic liquid crystal elastomers within the context of dynamics. We consider a continuum model with separate mappings for the deformation of the monolithic material and the orientation of the nematic director, where the latter describes the inclination of the mesogens. We achieve the inextensibility of the nematic director through the introduction of drilling degrees of freedom. We combine this approach with the application of the principle of virtual power and a mixed finite element formulation, in order to formulate distinct momentum and angular momentum balance laws for the two separate mappings. Furthermore, we include in our continuum model a volume load and a surface load associated only with the orientation mapping. We show in the presented three numerical examples that our formulation enables the fulfillment of all momentum and angular momentum balance laws.

Equilibrium and transient response of photo-actuated Liquid Crystal Elastomer beams

Light actuation is one of the preferred and advantageous approaches to remotely induce and control deformations in soft materials such as photoactive Liquid Crystal Elastomers (LCEs). Various experimental and numerical works have been carried out in the literature to study the actuation of photoactive LCE sheets under illumination. In this study, we have developed a reduced multi-physics model to predict the equilibrium and dynamic response of photoactive LCE beams under illumination. We test our model against an experiment in which a double-clamped thin nematic LCE beam is subjected to UV light, and the stress is generated in the beam due to induced contraction under illumination. Our numerical results demonstrate reasonable agreement with the experiment regarding stress evolution trend and saturation time. We also investigate the bending response of a photoactive LCE beam subjected to UV light. Based on our parameters, we observe that the nematic beam bends towards the light only due to the photochemical strain gradient along the thickness. Finally, to test our model in a dynamic situation, we perform the simulation for the self-oscillations of an LCE beam under illumination. We show that the alternate activation of the top and bottom surfaces of the LCE beam by uniform steady illumination can pump energy into the system, resulting in the phenomenon of self-oscillations.

A nonlinear bending theory for nematic LCE plates

In this paper, we study an elastic bilayer plate composed of a nematic liquid crystal elastomer in the top layer and a nonlinearly elastic material in the bottom layer. While the bottom layer is assumed to be stress-free in the flat reference configuration, the top layer features an eigenstrain that depends on the local liquid crystal orientation. As a consequence, the plate shows non-flat deformations in equilibrium with a geometry that non-trivially depends on the relative thickness and shape of the plate, material parameters, boundary conditions for the deformation, and anchorings of the liquid crystal orientation. We focus on thin plates in the bending regime and derive a two-dimensional bending model that combines a nonlinear bending energy for the deformation, with a surface Oseen–Frank energy for the director field that describes the local orientation of the liquid crystal elastomer. Both energies are nonlinearly coupled by means of a spontaneous curvature term that effectively describes the nematic-elastic coupling. We rigorously derive this model as a [Formula: see text]-limit from three-dimensional, nonlinear elasticity. We also devise a new numerical algorithm to compute stationary points of the two-dimensional model. We conduct numerical experiments and present simulation results that illustrate the practical properties of the proposed scheme as well as the rich mechanical behavior of the system.

Shape memory behaviors of 3D printed liquid crystal elastomers

As soft active materials, shape-memory polymers (SMPs) and liquid crystal elastomers (LCEs) have attracted considerable research interest due to their potential applications in various areas. SMPs refer to polymeric materials that can return to their permanent shape in response to external stimuli, such as heat, light, and solvent. In this sense, LCEs can exhibit intrinsic shape-memory behaviors since LCEs can switch between two shapes with temperature change due to the order-disorder transition of liquid crystals. In this work, we fabricate both the polydomain and monodomain nematic LCEs through direct ink writing 3D printing. With increasing the temperature of the substrates, the printed LCEs change from the monodomain state to the polydomain state. For polydomain LCEs, a reversible shape change can occur upon constant loading, while the monodomain can switch the shape with temperature in the stress-free state. This two-way shape-memory behavior is caused by the nematic-isotropic phase transition. We further show that the printed LCEs exhibit a good one-way shape-memory effect due to glass transition. The shape recovery region increases with the programming temperature, which is a typical temperature memory effect. Finally, it is demonstrated that complex shape-memory performance can be designed by combining one-way and two-way shape-memory effects. Specifically, for the monodomain LCEs, with increasing temperature, the programmed shape first recovers, and a second shape change can further occur due to the nematic-isotropic transition.