Modeling and simulation of liquid-crystal elastomers

Recent Trends in Continuum Modeling of Liquid Crystal Networks: A Mini-Review

This work aims to provide a comprehensive review of the continuum models of the phase behaviors of liquid crystal networks (LCNs), novel materials with various engineering applications thanks to their unique composition of polymer and liquid crystal. Two distinct behaviors are primarily considered: soft elasticity and spontaneous deformation found in the material. First, we revisit these characteristic phase behaviors, followed by an introduction of various constitutive models with diverse techniques and fidelities in describing the phase behaviors. We also present finite element models that predict these behaviors, emphasizing the importance of such models in predicting the material's behavior. By disseminating various models essential to understanding the underlying physics of the behavior, we hope to help researchers and engineers harness the material's full potential. Finally, we discuss future research directions necessary to advance our understanding of LCNs further and enable more sophisticated and precise control of their properties. Overall, this review provides a comprehensive understanding of the state-of-the-art techniques and models used to analyze the behavior of LCNs and their potential for various engineering applications.

Modeling and Control Strategies for Liquid Crystal Elastomer-Based Soft Robot Actuator

Liquid crystal elastomer is a type of soft material with unique physical and chemical properties that offer a variety of possibilities in the growing field of soft robot actuators. This type of material is able to exhibit large, revertible deformation under various external stimuli, including heat, electric or magnetic fields, light, etc., which may lead to a wide range of different applications such as bio-sensors, artificial muscles, optical devices, solar cell plants, etc. With these possibilities, it is important to establish modeling and control strategies for liquid crystal elastomer-based actuators, to obtain the accurate prediction and description of its physical dynamics. However, so far, existing studies on this type of the actuators mainly focus on material properties and fabrication, the state of art on the modeling and control of such actuators is still preliminary. To gain a better understanding on current studies of the topic from the control perspective, this review provides a brief collection on recent studies on the modeling and control of the liquid crystal elastomer-based soft robot actuator. The review will introduce the deformation mechanism of the actuator, as well as basic concepts. Existing studies on the modeling and control for the liquid crystal elastomer-based actuator will be organized and introduced to provide an overview in this field as well as future insights.

Numerical Methods in Studies of Liquid Crystal Elastomers

Liquid crystal elastomers (LCEs) are a type of material with specific features of polymers and of liquid crystals. They exhibit interesting behaviors, i.e., they are able to change their physical properties when met with external stimuli, including heat, light, electric, and magnetic fields. This behavior makes LCEs a suitable candidate for a variety of applications, including, but not limited to, artificial muscles, optical devices, microscopy and imaging systems, biosensor devices, and optimization of solar energy collectors. Due to the wide range of applicability, numerical models are needed not only to further our understanding of the underlining mechanics governing LCE behavior, but also to enable the predictive modeling of their behavior under different circumstances for different applications. Given that several mainstream methods are used for LCE modeling, viz. finite element method, Monte Carlo and molecular dynamics, and the growing interest and reliance on computer modeling for predicting the opto-mechanical behavior of complex structures in real world applications, there is a need to gain a better understanding regarding their strengths and weaknesses so that the best method can be utilized for the specific application at hand. Therefore, this investigation aims to not only to present a multitude of examples on numerical studies conducted on LCEs, but also attempts at offering a concise categorization of different methods based on the desired application to act as a guide for current and future research in this field.

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.

Bending of Thin Liquid Crystal Elastomer under Irradiation of Visible Light: Finsler Geometry Modeling

In this paper, we show that the 3D Finsler geometry (FG) modeling technique successfully explains a reported experimental result: a thin liquid crystal elastomer (LCE) disk floating on the water surface deforms under light irradiation. In the reported experiment, the upper surface is illuminated by a light spot, and the nematic ordering of directors is influenced, but the nematic ordering remains unchanged on the lower surface contacting the water. This inhomogeneity of the director orientation on/inside the LCE is considered as the origin of the shape change that drives the disk on the water in the direction opposite the movement of the light spot. However, the mechanism of the shape change is still insufficiently understood because to date, the positional variable for the polymer has not been directly included in the interaction energy of the models for this system. We find that this shape change of the disk can be reproduced using the FG model. In this FG model, the interaction between σ, which represents the director field corresponding to the directional degrees of LC, and the polymer position is introduced via the Finsler metric. This interaction, which is a direct consequence of the geometry deformation, provides a good description of the shape deformation of the LCE disk under light irradiation.

Uniaxial and biaxial structures in the elastic Maier-Saupe model

We perform statistical mechanics calculations to analyze the global phase diagram of a fully connected version of a Maier-Saupe-Zwanzig lattice model with the inclusion of couplings to an elastic strain field. We point out the presence of uniaxial and biaxial nematic structures, depending on temperature T and on the applied stress σ. Under uniaxial extensive tension, applied stress favors uniaxial orientation, and we obtain a first-order boundary along which there is a coexistence of two uniaxial paranematic phases, and which ends at a simple critical point. Under uniaxial compressive tension, stress favors biaxial orientation; for small values of the coupling parameters, the first-order boundary ends at a tricritical point, beyond which there is a continuous transition between a paranematic and a biaxially ordered structure. For some representative choices of the model parameters, we obtain a number of analytic results, including the location of critical and tricritical points and the line of stability of the biaxial phase.

Nematoelastic crawlers

A propagating "beam" triggering a local phase transition in a nematic elastomer sets it into a crawling motion, which may morph due to buckling. We consider the motion of the various configurations of slender rods and thin stripes with both uniform and splayed nematic order in cross-section and detect the dependence of the gait and speed on flexural rigidity and substrate friction.

Nonlinear photomechanics of nematic networks: upscaling microscopic behaviour to macroscopic deformation

A liquid crystal network whose chromophores are functionalized by photochromic dye exhibits light-induced mechanical behaviour. As a result, the micro-scaled thermotropic traits of the network and the macroscopic phase behaviour are both influenced as light alternates the shape of the dyes. In this paper, we present an analysis of this photomechanical behaviour based on the proposed multiscale framework, which incorporates the molecular details of microstate evolution into a continuum-based understanding. The effects of trans-to-cis photoisomerization driven by actinic light irradiation are first examined using molecular dynamics simulations, and are compared against the predictions of the classical dilution model; this reveals certain characteristics of mesogenic interaction upon isomerization, followed by changes in the polymeric structure. We then upscale the thermotropic phase-related information with the aid of a nonlinear finite element analysis; macroscopic deflection with respect to the wide ranges of temperature and actinic light intensity are thereby examined, which reveals that the classical model underestimates the true deformation. This work therefore provides measures for analysing photomechanics in general by bridging the gap between the micro- and macro-scales.

Light and thermal responses of liquid-crystal-network films: A finite element study

As a polymeric system incorporating rigid molecules within its structure, the liquid-crystal network (LCN) has been envisaged as a novel heterogeneous material. Under the influence of external stimuli, the orientational order of the liquid-crystalline phase becomes dilute and overall anisotropy is hence decreased; the actinic light absorbed by photochromic molecules, for example, induces the geometric isomerization and subsequently yields internal stress within the local network. In this study we investigate light- and temperature-induced spontaneous deformations of the LCN structure via a three-dimensional finite element model that incorporates geometric nonlinearity with a photomechanical constitutive model. We first examine the bending behavior and its nonlinearity and then parametrically study the various behaviors that stem from different origins ranging from the microscale to the macroscale: (i) the geometry of the LCN film, (ii) the macroscopic global order, (iii) the distorted mesogenic orientation due to the Fredericks distortion, and (iv) defect-induced instability. These interrelated behaviors demonstrate both the simulation capability and the necessity of the presenting framework. By employing a nonlinear consideration along with a microscopic shape parameter r the present approach facilitates further understanding of photomechanical physics such as the deconvolution of various stimuli and the deformed shape obtained due to snap-through instability. Furthermore, this study may offer insight into the design of light-sensitive actuation systems by deepening our knowledge and providing an efficient measure.

Photomobile polymer materials with crosslinked liquid-crystalline structures: molecular design, fabrication, and functions

Crosslinked liquid-crystalline polymer materials that macroscopically deform when irradiated with light have been extensively studied in the past decade because of their potential in various applications, such as microactuators and microfluidic devices. The basic motions of these materials are contraction-expansion and bending-unbending, which are observed mainly in polysiloxanes and polyacrylates that contain photochromic moieties. Other sophisticated motions such as twisting, oscillation, rotation, and translational motion have also been achieved. In recent years, efforts have been made to improve the photoresponsive and mechanical properties of this novel class of materials through the modification of molecular structures, development of new fabrication methods, and construction of composite structures. Herein, we review structures, functions, and working mechanisms of photomobile materials and recent advances in this field.

Tricritical behavior of soft nematic elastomers

We propose a lattice statistical model to investigate the phase diagrams and the soft responses of nematic liquid-crystal elastomers. Using suitably scaled infinite-range interactions, we obtain exact self-consistent equations for the tensor components of the nematic order parameter in terms of temperature, the distortion and stress tensors, and the initial nematic order. These equations are amenable to simple numerical calculations, which are used to characterize the low-temperature soft regime. We find a peculiar phase diagram, in terms of temperature and the diagonal component of the distortion tensor along the stretching direction, with first- and second-order transitions to the soft phase, and the prediction of tricritical points. This behavior is not qualitatively changed if we use different values of the initial nematic order parameter.

Phase separation and disorder in doped nematic elastomers

We formulate and analyse a model describing the combined effect of mechanical deformation, dynamics of the nematic order parameter, and concentration inhomogeneities in an elastomeric mixture of a mesogenic and an isotropic component. The uniform nematic state may exhibit a long-wave instability corresponding to nematic-isotropic demixing. Numerical simulations starting from either a perfectly ordered nematic state or a quenched isotropic state show that coupling between the mesogen concentration and the nematic order parameter influences the shape and orientation of the domains formed during the demixing process.

Contributions to membrane-embedded-protein diffusion beyond hydrodynamic theories

The diffusion coefficients of proteins embedded in a lipid membrane are traditionally described by the hydrodynamic Saffman-Delbrück theory, which predicts a weak dependence of the diffusion coefficient on protein radius, D∼lnR. Recent experiments have observed a stronger dependence, D∼1/R. This has led to speculation that the primary sources of drag on the protein are not hydrodynamic, but originate in coupling to other fields, such as lipid chain stretching or tilt. We discuss a generic model of a protein coupled to a nonconserved scalar order parameter (e.g., chain stretching), and show that earlier results may not be as universal as previously believed. In particular, we note that the drag depends on the way the protein-order parameter coupling is imposed. In this model, D∼1/R can be obtained if the protein is much larger than the order parameter correlation length. However, if we modify the model to include advection of the order parameter, which is a more appropriate assumption for a fluid membrane, we find that the entrainment of the order parameter by the protein's motion significantly changes the scaling of the diffusion coefficient. For parameters appropriate to protein diffusion, the Saffman-Delbrück-like scaling is restored, but with an effective radius for the protein that depends on the order parameter's correlation length. This qualitative difference suggests that hydrodynamic effects cannot be neglected in the computation of drag on a protein interacting with the membrane.