Smectic-A elastomers with weak director anchoring

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.

Flexoelectric Polarization in Liquid Crystalline Elastomers Prepared by Cross-Linking under Horseshoe-Shaped Deformation

Flexoelectric polarization, which is caused by symmetry breaking in a distortion of material, was investigated in liquid crystalline elastomers composed of wedge-shaped mesogens prepared by cross-linking under horseshoe-shaped deformation. X-ray diffractometry suggested that splay distortion along the depth direction was induced in the pseudo-isotropic phase. While almost no electric charge was observed in the smectic A phase, an electric charge caused by polarization due to the flexoelectric effect appeared and reached −1367 pC/mm2 in the pseudo-isotropic phase. We tentatively conclude that the macroscopic polarization due to the flexoelectric effect emerged and was fixed in the liquid crystalline elastomers by cross-linking under horseshoe-shaped deformation.

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.

Electroclinic effect in chiral smectic-A liquid crystal elastomers

Chiral smectic-A liquid crystal elastomers are rubbery materials composed of a lamellar arrangement of liquid crystalline mesogens. It has been shown experimentally that these materials shear when subjected to an electric field due to the electrically induced tilt of the director. Experiments have also shown that shearing a chiral smectic-A elastomer gives rise to a polarization. Roughly, the shear force tilts the directors which, in turn, induce electric dipoles. This paper builds on previous works and models the electromechanical response of smectic-A elastomers using free energy contributions that are associated with the lamellar structure, the relative tilt between the director and the layer normal, and the coupling between the director and the electric field. To illustrate the merit of the proposed model, two cases are considered-a deformation induced polarization and an electrically induced deformation. The predictions according to these two models qualitatively agree with experimental findings. Finally, a cylinder composed of helical smectic layers is also considered. It is shown that the electromechanical response varies as a function of the helix angle.

Temperature-memory polymer actuators

Reading out the temperature-memory of polymers, which is their ability to remember the temperature where they were deformed recently, is thus far unavoidably linked to erasing this memory effect. Here temperature-memory polymer actuators (TMPAs) based on cross-linked copolymer networks exhibiting a broad melting temperature range (ΔT(m)) are presented, which are capable of a long-term temperature-memory enabling more than 250 cyclic thermally controlled actuations with almost constant performance. The characteristic actuation temperatures T(act)s of TMPAs can be adjusted by a purely physical process, guiding a directed crystallization in a temperature range of up to 40 °C by variation of the parameter T(sep) in a nearly linear correlation. The temperature T(sep) divides ΔT(m) into an upper T(m) range (T > T(sep)) forming a reshapeable actuation geometry that determines the skeleton and a lower T(m) range (T < T(sep)) that enables the temperature-controlled bidirectional actuation by crystallization-induced elongation and melting-induced contraction. The macroscopic bidirectional shape changes in TMPAs could be correlated with changes in the nanostructure of the crystallizable domains as a result of in situ X-ray investigations. Potential applications of TMPAs include heat engines with adjustable rotation rate and active building facades with self-regulating sun protectors.

Numerical study of stretched smectic-A elastomer sheets

We present a numerical study of stretching monodomain smectic-A elastomer sheets, computed using the finite element method. When stretched parallel to their smectic layer normal the smectic layers are unstable to a transition to a buckled state. We model macroscopic deformations by replacing the microscopic energy with a coarse grained effective free energy that accounts for the fine-scale layer buckling. We augment this model with a term to describe the energy of deforming buckled layers, which is necessary to reproduce the experimentally observed Poisson ratios postbuckling. We examine the spatial distribution of the microstructure phases for various stretching angles relative to the layer normal and for different length-to-width aspect ratios. When stretching parallel to the layer normal the majority of the sample forms a bidirectionally buckled microstructure, except at the clamps where a unidirectionally buckled microstructure is predicted. When stretching at small inclinations to the layer normal the phase of the sample is sensitive to the aspect ratio of the sample, with the bidirectionally buckled phase persistent to large angles only for small aspect ratios. We relate these theoretical results to experiments on smectic-A elastomers.

Negative Poisson's ratio and semisoft elasticity of smectic-C liquid-crystal elastomers

Models of smectic-C liquid-crystal elastomers predict that they 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 investigate the effect of a simple model of these imperfections on the soft modes in monodomain smectic-C elastomers in a variety of geometries. When stretching parallel to the layer normal (with imposed strain) the elastomer has a negative stiffness once the director starts to rotate. We show that this is a result of the negative Poisson's ratio in this geometry through a simple scalar model.

Acoustic waves in compressible planar layered smectic liquid crystals

A dynamic theory for compressible smectic C (SmC) liquid crystals is postulated following previous work by Leslie et al (1991 Mol. Cryst. Liq. Cryst. 198 443-54), Nakagawa (1996 J. Phys. Soc. Japan 65 100-6; 2004 J. Non-Newtonian Fluid Mech. 119 123-9) and de Gennes and Prost (1993 The Physics of Liquid Crystals 2nd edn (Oxford: Oxford University Press)). This theory is then implemented with a constructed bulk elastic energy and asymmetric stress tensor to describe a system of planar layered SmC liquid crystals undergoing various modes of undulation. We show that previous work on smectic A (SmA) liquid crystals by de Gennes and Prost (1993 The Physics of Liquid Crystals 2nd edn (Oxford: Oxford University Press)) can be expanded for SmC and consolidated. Novel and confirming estimates for SmC material parameter values are produced by considering the dependence of the system on these parameters.