2H NMR studies of liquid crystal elastomers: macroscopic vs. molecular properties

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.

Deuteron NMR investigation on orientational order parameter in polymer dispersed liquid crystal elastomers

Polymer-dispersed liquid crystal elastomers have been recently introduced as a thermomechanically active composite material, consisting of magnetically oriented liquid crystal elastomer particles incorporated in a cured polymer matrix. Their thermomechanical properties are largely governed by the degree of imprinted particle alignment, which can be assessed by means of deuterium perturbed 2H-NMR. Spectra of samples with various degrees of imprinted particle alignment were recorded and the results simulated using the discrete reorientational exchange model developed for determining the dispersion of liquid crystal elastomer's domain orientational distribution. We show that the model can be applied to measure the orientational distribution of embedded liquid crystal microparticles and successfully determine the orientational order parameter in the composite system. Thermomechanical measurements correlate well with the obtained results, thus additionally confirming the validity of the applied method.

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.

Nanostructured Composites Based on Liquid-Crystalline Elastomers

Liquid-crystalline elastomers (LCEs) are the object of many research investigations due to their reversible and controllable shape deformations, and their high potential for use in the field of soft robots and artificial muscles. This review focuses on recent studies about polymer composites based on LCEs and nanomaterials having different chemistry and morphology, with the aim of instilling new physical properties into LCEs. The synthesis, physico-chemical characterization, actuation properties, and applications of LCE-based composites reported in the literature are reviewed. Several cases are discussed: (1) the addition of various carbon nanomaterials to LCEs, from carbon black to carbon nanotubes, to the recent attempts to include graphene layers to enhance the thermo-mechanic properties of LCEs; (2) the use of various types of nanoparticles, such as ferroelectric ceramics, gold nanoparticles, conductive molybdenum-oxide nanowires, and magnetic iron-oxide nanoparticles, to induce electro-actuation, magnetic-actuation, or photo-actuation into the LCE-based composites; (3) the deposition on LCE surfaces of thin layers of conductive materials (i.e., conductive polymers and gold nanolayers) to produce bending actuation by applying on/off voltage cycles or surface-wrinkling phenomena in view of tunable optical applications. Some future perspectives of this field of soft materials conclude the review.

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.

Mathematical Modeling and Simulations for Large-Strain J-Shaped Diagrams of Soft Biological Materials

Herein, we study stress⁻strain diagrams of soft biological materials such as animal skin, muscles, and arteries by Finsler geometry (FG) modeling. The stress⁻strain diagram of these biological materials is always J-shaped and is composed of toe, heel, linear, and failure regions. In the toe region, the stress is almost zero, and the length of this zero-stress region becomes very large (≃150%) in, for example, certain arteries. In this paper, we study long-toe diagrams using two-dimensional (2D) and 3D FG modeling techniques and Monte Carlo (MC) simulations. We find that, except for the failure region, large-strain J-shaped diagrams are successfully reproduced by the FG models. This implies that the complex J-shaped curves originate from the interaction between the directional and positional degrees of freedom of polymeric molecules, as implemented in the FG model.

J-shaped stress-strain diagram of collagen fibers: Frame tension of triangulated surfaces with fixed boundaries

We present Monte Carlo data of the stress-strain diagrams obtained using two different triangulated surface models. The first is the canonical surface model of Helfrich and Polyakov (HP), and the second is a Finsler geometry (FG) model. The shape of the experimentally observed stress-strain diagram is called J-shaped. Indeed, the diagram has a plateau for the small strain region and becomes linear in the relatively large strain region. Because of this highly nonlinear behavior, the J-shaped diagram is far beyond the scope of the ordinary theory of elasticity. Therefore, the mechanism behind the J-shaped diagram still remains to be clarified, although it is commonly believed that the collagen degrees of freedom play an essential role. We find that the FG modeling technique provides a coarse-grained picture for the interaction between the collagen and the bulk material. The role of the directional degrees of freedom of collagen molecules or fibers can be understood in the context of FG modeling. We also discuss the reason for why the J-shaped diagram cannot (can) be explained by the HP (FG) model.

Deuteron NMR resolved mesogen vs. crosslinker molecular order and reorientational exchange in liquid single crystal elastomers

²H NMR spectroscopy can resolve differences in orientational order and reorientational dynamics between crosslinker and mesogen molecules in liquid single crystal elastomers.

Brief overview on 2H NMR studies of polysiloxane-based side-chain nematic elastomers

This is a brief overview on recent studies on liquid crystalline elastomers (LCEs) based on polysiloxane chain, in the form of monodomain films, selectively (2)H-labeled in different parts of the LCE samples, i.e. on the crosslinker or mesogenic units. (2)H NMR spectroscopic techniques were used to measure the temperature dependence of the quadrupolar splittings, line widths and relaxation times, T(1) and T(2). From these data, several information about the orientational order parameter, S, of various LCE fragments, thermodynamic features of the isotropic-nematic transition and main motional processes could be generalized for this type of elastomers.

Correlation 2D-NMR experiments involving both 13C and 2H isotopes in oriented media: methodological developments and analytical applications

Correlation 2D-NMR experiments for (13)C and (2)H isotopes turn out to be powerful methods for the assignment of the quadrupolar doublets in the (2)H NMR spectra of isotopically modified (polydeuterated or perdeuterated) or unmodified solutes in homogeneously oriented solvents, such as thermotropic systems or lyotropic liquid crystals. We review here the different pulse sequences, which have been employed, their properties, and their most salient applications. These 2D-NMR sequences have been used for (i) (13)C-(2)H correlation with and without (1)H relay and (ii) (2)H-(2)H correlation with (13)C relay. The (13)C-(2) H correlation experiments without (1)H relay have been achieved for specifically deuterated or non-selectively deuterated analytes, but also more recently for isotopically unmodified ones thanks to the high sensitivity of very high-field NMR spectrometers (21.1 T) equipped with cryogenic probes. The (13)C-(2)H correlation 2D-NMR experiments are especially useful for the assignment of overcrowded deuterium spectra because the (2)H signals are correlated to (13)C signals, which benefit from a much larger dispersion of chemical shifts. In this contribution, particular attention will be paid to the use of correlation 2D-NMR experiments for (2)H and (13)C nuclei in weakly aligning, polypeptide oriented chiral solvents, because these methods are useful and original tools for enantiomeric and enantiotopic analyses.

Effect of co-monomers' relative concentration on self-assembling behaviour of side-chain liquid crystalline elastomers

A new series of liquid single crystal elastomers having a nematic–SmA and a direct isotropic–SmA phase transition.

Optical properties of light-sensitive liquid-crystal elastomers in the vicinity of the nematic-paranematic phase transition

We investigate light-induced patterning of a monodomain side-chain liquid crystal elastomer (SC-LCE) doped with light-sensitive azobenzene moiety in the temperature region close to the nematic-paranematic phase transition. We show that a strongly nonlinear relationship between the concentration of the cis isomers of the azomesogens and the refractive index modification of the material, which is characteristic for the phase transition region, results in nonmonotonous time dependence of the diffraction efficiency of a probe beam. From this effect we determine the sensitivity of the nematic transition temperature on the molar fraction of the cis isomers. The relation between the cis isomer molar fraction and nematic order also provides a possibility for recording hidden holograms, which can be made visible by cooling the sample from the paranematic to the nematic phase.