Polydomain Liquid Crystal Elastomers Research Articles

Modelling the Deformation of Polydomain Liquid Crystal Elastomers as a State of Hyperelasticity

AbstractA hyperelasticity modelling approach is employed for capturing various and complex mechanical behaviours exhibited by macroscopically isotropic polydomain liquid crystal elastomers (LCEs). These include the highly non-linear behaviour of nematic-genesis polydomain LCEs, and the soft elasticity plateau in isotropic-genesis polydomain LCEs, under finite multimodal deformations (uniaxial and pure shear) using in-house synthesised acrylate-based LCE samples. Examples of application to capturing continuous softening (i.e., in the primary loading path), discontinuous softening (i.e., in the unloading path) and auxetic behaviours are also demonstrated on using extant datasets. It is shown that our comparatively simple model, which breaks away from the neo-classical theory of liquid crystal elastomers, captures the foregoing behaviours favourably, simply as states of hyperelasticity. Improved modelling results obtained by our approach compared with the existing models are also discussed. Given the success of the considered model in application to these datasets and deformations, the simplicity of its functional form (and thereby its implementation), and comparatively low(er) number of parameters, the presented isotropic hyperelastic strain energy function here is suggested for: (i) modelling the general mechanical behaviour of LCEs, (ii) the backbone in the neo-classical theory, and/or (iii) the basic hyperelastic model in other frameworks where the incorporation of the director, anisotropy, viscoelasticity, temperature, softening etc parameters may be required.

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.

A Dual-Responsive Liquid Crystal Elastomer for Multi-Level Encryption and Transient Information Display.

Information security has gained increasing attention in the past decade, leading to the development of advanced materials for anti-counterfeiting, encryption and instantaneous information display. However, it remains challenging to achieve high information security with simple encryption procedures and low-energy stimuli. Herein, a series of strain/temperature-responsive liquid crystal elastomers (LCEs) are developed to achieve dual-modal, multi-level information encryption and real-time, rewritable transient information display. The as-prepared polydomain LCEs can change from an opaque state to a transparent state under strain or temperature stimuli, with the transition strains or temperatures highly dependent on the concentration of long-chain flexible spacers. Information encrypted by different LCE inks can be decrypted under specific strains or temperatures, leading to multi-level protection of information security. Furthermore, with the combination of the phase transition of polydomain LCEs and the photothermal effect of multi-walled carbon nanotubes (MWCNTs), we achieved a repeatable transient information display by using near-infrared (NIR) light as a pen for writing. This study provides new insight into the development of advanced encryption materials with versatility and high security for broad applications.

A Dual‐Responsive Liquid Crystal Elastomer for Multi‐Level Encryption and Transient Information Display

AbstractInformation security has gained increasing attention in the past decade, leading to the development of advanced materials for anti‐counterfeiting, encryption and instantaneous information display. However, it remains challenging to achieve high information security with simple encryption procedures and low‐energy stimuli. Herein, a series of strain/temperature‐responsive liquid crystal elastomers (LCEs) are developed to achieve dual‐modal, multi‐level information encryption and real‐time, rewritable transient information display. The as‐prepared polydomain LCEs can change from an opaque state to a transparent state under strain or temperature stimuli, with the transition strains or temperatures highly dependent on the concentration of long‐chain flexible spacers. Information encrypted by different LCE inks can be decrypted under specific strains or temperatures, leading to multi‐level protection of information security. Furthermore, with the combination of the phase transition of polydomain LCEs and the photothermal effect of multi‐walled carbon nanotubes (MWCNTs), we achieved a repeatable transient information display by using near‐infrared (NIR) light as a pen for writing. This study provides new insight into the development of advanced encryption materials with versatility and high security for broad applications.

Photocontrollable Elongation Actuation of Liquid Crystal Elastomer Films with Well-Defined Crease Structures.

Although liquid crystal elastomers (LCEs) have demonstrated various applications in artificial muscles and soft robotics, their inherent flexibility and orientation-dependent forces limit their functions. For instance, LCEs can sustain a high actuation force when they contract but cannot elongate to drive loads with large displacements. In this study, it is demonstrated that photocontrollable elongation actuation with a large strain can be achieved in polydomain LCEs by programming the crease structures in a well-defined order to couple the actuation forces. Efficient photoactuation without overheating-induced damage to the materials is favored, based on the well-designed photosensitive molecular switch crosslinker via the synergy of photochemical and photothermal effects. The LCE actuator can jack up heavy loads, elongate freely, and contract back to manipulate distant objects. Theoretical analysis based on a finite element simulation of the deformation energy during the actuation process reveals a trade-off between the abilities of jacking-up and withstanding load. More importantly, this study simplifies the design of a single material with functions inherent only in other soft robotic devices based on the assembly of multiplemodules, thus providing a design strategy for surpassing instinctive properties of conventional soft materials to expand the functions of soft robotics.

A macroscopic constitutive relation for isotropic-genesis, polydomain liquid crystal elastomers

Liquid crystal elastomers (LCEs) are rubber-like solids that incorporate nematic mesogens (stiff rod-like molecules) as a part of their polymer chains. In recent years, isotropic-genesis, polydomain liquid crystal elastomers (I-PLCEs) has been a topic of both scientific and technological interest due to their intriguing properties such as soft behavior, ability to dissipate energy and stimuli response, as well as the ease with which they can be synthesized. We present a macroscopic or engineering scale constitutive model of the behavior of I-PLCEs. The model implicitly accounts for the complex evolution of the domain patterns and is able to faithfully capture the experimentally observed complex response to multi-axial loading. We describe a multiscale framework that motivates the model, explore various aspects of the model, validate it against experiments, and finally verify and demonstrate a numerical implementation.

Programmable Complex Shape Changing of Polysiloxane Main-Chain Liquid Crystalline Elastomers.

Liquid crystal elastomers (LCEs) are shape-morphing materials whose large and reversible shape transformations are caused by the coupling between the mobile anisotropic properties of liquid crystal (LC) units and the rubber elastic of polymer networks. Their shape-changing behaviors under certain stimuli are largely directed by the LC orientation; therefore, various strategies have been developed to spatially modulate the LC alignments. However, most of these methods are limited as they require complex fabrication technologies or have intrinsic limitations in applicability. To address this issue, programmable complex shape changes in some LCE types, such as polysiloxane side-chain LCEs, thiol-acrylate main-chain LCEs, etc., were achieved by using a mechanical alignment programming process coupled with two-step crosslinking. Here, we report a polysiloxane main-chain LCE with programmable 2- and 3D shape-changing abilities that were created by mechanically programming the polydomain LCE with two crosslinking steps. The resulting LCEs exhibited a reversible thermal-induced shape transformation between the initial and programmed shapes due to the two-way memory between the first and second network structures. Our findings expand on the applications of LCE materials in actuators, soft robotics, and smart structures where arbitrary and easily programmed shape morphing is needed.

A constitutive model of liquid crystal elastomers with loading-history dependence

Liquid crystal elastomers (LCEs) are a class of active polymers of increasing interest, because of their excellent actuation performances. To quantify the actuation performances and understand the thermomechanical behavior, many theoretical models were developed, mainly based on the free energy framework with uniaxial order tensor, which, however, cannot well capture the biaxial liquid crystal alignment under biaxial stretching or shearing. The LCE with the shape memory cycle effect exhibits an evident loading-history dependence of the thermomechanical process, which cannot be described without introducing the evolution condition of the alignment. In this work, a constitutive model of LCE is established by introducing a triaxial order tensor to describe the complex alignment under uniaxial/biaxial loading conditions. Inspired by the classical theory of plasticity, an equivalent order parameter is proposed to characterize the order degree of the alignment, and its evolution condition is introduced to specify the condition of the alignment evolution. Experiments of LCE under a variety of thermomechanical loading conditions were carried out to validate the developed model, showing the capability of the model in capturing complex thermomechanical responses of the polydomain LCE with shape memory cycle effect under uniaxial/biaxial stretching. Furthermore, the constitutive model can be extended to predict nonlinear stress-strain curves and actuation performances of LCE lattices, which hold promising potential for applications in soft actuators and flexible robots.

Effects of network structure of main-chain liquid crystal elastomer on its thermal actuation performance

The effect of the network structure on the thermal actuation of the main-chain liquid crystal elastomers (LCEs) was studied by controlling the strand length and crosslinking density of the network. The LCEs were prepared with the thiol-terminated oligomers synthesized via a thiol-acrylate Michael addition reaction between dithiol and diacrylate monomers. The LCE network structure was formed by crosslinking the oligomers using the pentaerythritol tetraacylate crosslinkers and coupling between the thiol end groups in the oligomer to form disulfide linkages. The monodomain LCE (MLCE) films were fixed by the dynamic exchange reaction between disulfide linkages through ultraviolet irradiation after drawing the polydomain LCE films. The maximum degree of actuation was obtained when 50% of the available thiol groups were crosslinked with the acrylate groups of the crosslinkers. The degree of actuation increased with the oligomer length for sufficiently high crosslinking density. However, the degree of actuation decreased with the oligomer length after reaching the maximum especially for low crosslinker density because crosslinking with long oligomers did not provide enough crosslinking sites and disulfide linkages. Thus, the oligomer length and crosslinking density of the MLCE are important control factors during LCE preparation to obtain the best actuation performance of the MLCE film.

Accelerated computational micromechanics and its application to polydomain liquid crystal elastomers

We present an approach to solving problems in computational micromechanics that is amenable to massively parallel calculations through the use of graphical processing units (GPUs) and other accelerators. We apply it to study microstructure evolution in polydomain liquid crystal elastomers (LCEs). LCEs are rubber-like solids where rod-like nematic molecules are incorporated into the main or a side polymer chain. They undergo isotropic to nematic phase transition accompanied by spontaneous deformation which can be exploited for actuation. Further, they display a soft behavior at low temperatures due to the reorientation of the nematic directors. The problem of understanding nematic reorientation in the presence of realistic defects (non-ideality) is computationally expensive, and we address this by efficiently exploiting GPUs. The approach is broadly applicable to various phenomena including crystal plasticity and phase transitions that are described by internal variable theories. We verify the approach against previous calculations and establish its performance by studying long wavelength instability of finite elasticity. Our numerical studies of LCEs provide insights into the director distribution and reorientation in polydomain specimens, and how these lead to soft behavior under multiaxial loading. The results show good agreement with experimental observations.

Microscopy of Diffuse Nematic–Isotropic Transition in Main-Chain Nematic Liquid-Crystal Elastomers

Nematic–isotropic phase transition in liquid-crystal elastomers (LCEs), which drastically alters the macroscopic properties of the material, is attractive for both fundamental physics and applications. Herein, we introduce new experimental methods based on polarized and fluorescence optical microscopy to characterize the phase transition of polydomain LCEs, monitoring the order parameter and the nematic domain structure. It is demonstrated that polydomain main-chain nematic LCEs exhibit an ordering transition very different from the classical first-order one, having a diffuse continuous nature. Unexpectedly, the characteristic correlation length of the fading polydomain structure remains unchanged across the transition.

Supersoft elasticity and slow dynamics of isotropic-genesis polydomain liquid crystal elastomers investigated by loading- and strain-rate-controlled tests.

The supersoft elasticity and slow dynamics of isotropic-genesis polydomain nematic elastomers are investigated by loading- and strain-rate-controlled tests. Loading-controlled tests reveal the stretching-driven polydomain-to-monodomain (PM) transition under true equilibrium condition without viscoelastic (time) effect. The equilibrium PM transition is observed as a discontinuous dimensional change at a threshold stress with extremely small magnitude (σ_{PM}^{∞}≈1kPa). The mechanical work required for 80% elongation of the elastomer accompanying the PM transition is only 2% of that required in the high-temperature isotropic state, reflecting the supersoft elasticity effect. The dimensional growth rate (R) under constant loading becomes low as the imposed stress (σ_{0}) approaches σ_{PM}^{∞}. The dependency of the dimension on the reduced time (Rt) is, however, independent of σ_{0}. In the strain-rate (ɛ[over ̇]) controlled tests, the stress-stretch curves show a plateau region characteristic of the PM transition in a finite range of stretch, which is equivalent to the discontinuous stretch in the loading-controlled tests. The plateau stress σ_{pl} significantly decreases with decreasing ɛ[over ̇], whereas the σ_{pl} at the practically accessible low strain rate (on the order of 10^{-4}s^{-1} ) is still significantly higher than σ_{PM}^{∞}. The dependency of σ_{pl} on ɛ[over ̇] is almost similar to the dependency of σ_{0} on R in the loading-controlled tests. This similarity signifies that the two types of tests with different controlled stimuli are governed by the same dynamics of the local director.

Localizing genesis in polydomain liquid crystal elastomers.

Programming the local orientation of liquid crystal elastomers (LCEs) is a differentiated approach to prepare monolithic material compositions with localized deformation. Our prior efforts prepared LCEs with surface-enforced spatial variations in orientation to localize deformation when the LCEs were subjected to directional load. However, because these surface alignment methods included regions of planar orientation, the deformation of these programmed LCEs is inherently directional. The absence of macroscopic orientation in polydomain LCEs results in uniform, nonlinear deformation in all axes (omnidirectional soft elasticity). Here, we exploit the distinct mechanical response of polydomain LCEs prepared with isotropic or nematic genesis. By localizing the polydomain genesis via masked photopolymerizations conducted at different temperatures, we detail the preparation of main-chain, polydomain LCEs that are homogeneous in composition but exhibit spatially localized programmability in their mechanical response that is uniform in all directions.

Mechanotropic Elastomers.

Liquid crystal elastomers (LCEs) are anisotropic polymeric materials. When subjected to an applied stress, liquid crystalline (LC) mesogens within the elastomeric polymer network (re)orient to the loading direction. The (re)orientation during deformation results in nonlinear stress-strain dependence (referred to as soft elasticity). Here, we uniquely explore mechanotropic phase transitions in elastomers with appreciable mesogenic content and compare these responses to LCEs in the polydomain orientation. The isotropic (amorphous) elastomers undergo significant directional orientation upon loading, evident in strong birefringence and x-ray diffraction. Functionally, the mechanotropic displacement of the elastomers to load is also nonlinear. However, unlike the analogous polydomain LCE compositions examined here, the isotropic elastomers rapidly recover after deformation. The mechanotropic orientation of the mesogens in these materials increase the toughness of these thiol-ene photopolymers by nearly 1300 % relative to a chemically similar elastomer prepared from wholly isotropic precursors.

Finsler geometry modeling and Monte Carlo study of liquid crystal elastomers under electric fields

The shape transformation of liquid crystal elastomers (LCEs) under external electric fields is studied through Monte Carlo simulations of models constructed on the basis of Finsler geometry (FG). For polydomain side-chain-type LCEs, it is well known that the external-field-driven alignment of the director is accompanied by an anisotropic shape deformation. However, the mechanism of this deformation is quantitatively still unclear in some part and should be studied further from the microscopic perspective. In this paper, we evaluate whether this shape deformation is successfully simulated, or in other words, quantitatively understood, by the FG model. The FG assumed inside the material is closely connected to the directional degrees of freedom of LC molecules and plays an essential role in the anisotropic transformation. We find that the existing experimental data on the deformations of polydomain LCEs are in good agreement with the Monte Carlo results. It is also found that experimental diagrams of strain versus external voltage of a monodomain LCE in the nematic phase are well described by the FG model.

Thermomechanical properties of monodomain nematic main-chain liquid crystal elastomers.

Two-stage thiol-acrylate Michael addition reactions have proven useful in programming main-chain liquid crystal elastomers (LCEs). However, the influence of excess acrylate concentration, which is critical to monodomain programming, has not previously been examined with respect to thermomechanical properties in these two-stage LCEs. Previous studies of thiol-acrylate LCEs have focused on polydomain LCEs and/or variation of thiol crosslinking monomers or linear thiol monomers. This study guides the design of monodomain LCE actuators using the two-stage methodology by varying the concentration of mesogenic acrylate monomers from 2 mol% to 45 mol% in stoichiometric excess of thiol. The findings demonstrate a technique to tailor the isotropic transition temperature by 44 °C using identical starting monomers. In contrast to expectations, low amounts of excess acrylate showed excellent fixity (90.4 ± 2.9%), while high amounts of excess acrylate did not hinder actuation strain (87.3 ± 2.3%). Tensile stress-strain properties were influenced by excess acrylate. Linear elastic behavior was observed parallel to the director with modulus increasing from 1.4 to 6.1 MPa. The soft elastic plateau was observed perpendicular to the director with initial modulus and threshold stresses increasing from 0.6 MPa to 2.6 MPa and 14 kPa to 208 kPa, respectively. Overall, this study examines the influence of excess acrylate on mechanical properties of LCE actuators.

Molecular Simulations Shed Light on Supersoft Elasticity in Polydomain Liquid Crystal Elastomers

Liquid crystal elastomers (LCE)—polymer networks constructed with liquid crystal units—are functional materials characterized by a pronounced coupling between elastic strain and liquid crystalline orientational ordering. When prepared by polymerization and cross-linking in the isotropic phase, and then cooled (“isotropic genesis”), a polydomain LCE presents an extraordinary “supersoft” elastic behavior under unidirectional pulling, with a plateau-like low elastic modulus region in the stress–strain curve, before turning into a monodomain LCE where a standard elastic resistance is recovered. The physical mechanism of this behavior is of great interest, but still mysterious. This work investigates its origin, reproducing the experiment and succeeding to observe the plateau-like stress–strain behavior by means of large-scale molecular iso-stress Monte Carlo simulations. The results not only show that the basic molecular mechanism behind supersoft elasticity hinges on local domain rotation and growth but also...

Unusual field-coupled nonlinear continuum mechanics of smart materials

A set of anisotropic constitutive relations is developed using nonlinear continuum mechanics to model chemical and field-coupled material behavior in a relatively broad range of smart materials. A Landau-based free energy function is formulated and numerically implemented to elucidate how finite deformation and crystal anisotropy affect field-coupled deformation and how deformation affects microstructure evolution. Rotationally invariant order parameters are introduced within the Landau energy function to illustrate how field-coupled mechanics occurs without introducing explicit phenomenological parameters. Spontaneous deformation due to scalar, vector, and tensor order parameters is quantified. It is shown that both the scalar and vector order parameters induce hydrostatic deformation, while the second-order tensor order parameter induces a range of different anisotropic spontaneous deformation states. Numerical simulations are given, which illustrate unusual field-coupled microstructure evolution for a select number of active materials in comparison with data in the literature. The materials simulated range from chemically responsive glassy polymer networks, soft polydomain liquid crystal elastomers, to tetragonal phase ferroelectric materials. The results illustrate that finite deformation continuum mechanics can be useful in modeling many unusual field-coupled, anisotropic constitutive relations without introducing explicit coupling parameters.

Supersoft Elasticity in Polydomain Nematic Elastomers

We consider the equilibrium stress-strain behavior of polydomain liquid crystal elastomers (PLCEs). We show that there is a fundamental difference between PLCEs cross-linked in the high temperature isotropic and low temperature aligned states. PLCEs cross-linked in the isotropic state then cooled to an aligned state will exhibit extremely soft elasticity (confirmed by recent experiments) and ordered director patterns characteristic of textured deformations. PLCEs cross-linked in the aligned state will be mechanically much harder and characterized by disclination textures.

Electromechanical and Electrooptical Effects of Liquid Crystal Elastomers Swollen with a Low Molecular Weight Liquid Crystal

We experimentally investigated the electromechanical and electrooptical effects in polydomain liquid crystal elastomers (LCEs) swollen with a well known LMWLC, 4-n-pentyl-4-cyanobiphenyl (5CB). The displacement and optical intensity changes were measured as a function of the voltage. We found that the threshold value for the onset of electromechanical and electrooptical effects is small, V ∼ 1.0 V.