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

The Effect of Polymer-Solvent Interaction on the Swelling of Polymer Matrix Tablets: A Magnetic Resonance Microscopy Study Complemented by Bond Fluctuation Model Simulations

Polymer matrix tablets are an important drug-delivery system widely used for oral drug administration. Understanding the tablet hydration process, both experimentally and theoretically, is, thus, very important for the development of drug delivery systems that exhibit high drug loading capacity and controlled release potential. In this study, we used magnetic resonance microscopy (MRM) to nondestructively and dynamically analyze the water hydration process of xanthan-based tablets. The swelling process was characterized by well-resolved fronts of erosion, swelling, and penetration. The experimental results were complemented by numerical simulations of the polymer matrix hydration process. In the simulations, the polymer tablet matrix was modeled as an assembly of interacting chains with embedded drug particles, while its hydration process was mediated by interaction with solvent particles. The swelling dynamics were modeled within a Monte Carlo-based bond fluctuation model (BFM) that elegantly accounted for steric and nearest-neighbor interactions. This study provides an efficient experimental-theoretical approach for the study of polymer matrix swelling processes.

On the Effects of Different trans and cis Populations in Azobenzene Liquid Crystal Elastomers: A Monte Carlo Investigation

We investigate main-chain liquid crystal elastomers (LCEs) formed by photoresponsive azobenzene units with different populations of trans and cis conformers (from fully trans to fully cis). We study their macroscopic properties as well as their molecular organization using extensive Monte Carlo simulations of a simple coarse-grained model where the trans and cis conformers are represented by soft-core biaxial Gay-Berne particles with size and interaction energy parameters obtained by fitting a bare bone azobenzene moiety represented at atomistic level. We find that increasing the fraction of cis conformers, as could be obtained by near-UV irradiation, shifts the nematic-isotropic transition to a lower temperature, consistently with experiment, while generating internal stress in a clamped sample. An analysis of pair distributions shows that the immediate surroundings of a bent cis molecule are slightly less dense and more orientationally disordered in comparison with that of a trans conformer. Comparing nematic and smectic LCEs, actuation in the smectic phase proved less effective, disrupting the smectic layers to some extent but preserving orientational order of the azobenzene moieties.

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.

Regression analysis for predicting the elasticity of liquid crystal elastomers

It is highly desirable but difficult to understand how microscopic molecular details influence the macroscopic material properties, especially for soft materials with complex molecular architectures. In this study we focus on liquid crystal elastomers (LCEs) and aim at identifying the design variables of their molecular architectures that govern their macroscopic deformations. We apply the regression analysis using machine learning (ML) to a database containing the results of coarse grained molecular dynamics simulations of LCEs with various molecular architectures. The predictive performance of a surrogate model generated by the regression analysis is also tested. The database contains design variables for LCE molecular architectures, system and simulation conditions, and stress-strain curves for each LCE molecular system. Regression analysis is applied using the stress-strain curves as objective variables and the other factors as explanatory variables. The results reveal several descriptors governing the stress-strain curves. To test the predictive performance of the surrogate model, stress-strain curves are predicted for LCE molecular architectures that were not used in the ML scheme. The predicted curves capture the characteristics of the results obtained from molecular dynamics simulations. Therefore, the ML scheme has great potential to accelerate LCE material exploration by detecting the key design variables in the molecular architecture and predicting the LCE deformations.

Liquid Crystal-Based Organosilicone Elastomers with Supreme Mechanical Adaptability

Elastomers with supreme mechanical adaptability where the increasing stress under continuous deformation is significantly inhibited within a large deformation zone, are highly desired in many areas, such as artificial muscles, flexible and wearable electronics, and soft artificial-intelligence robots. Such system comprises the advantages of recoverable elasticity and internal compensation to external mechanical work. To obtain elastomer with supreme mechanical adaptability, a novel liquid crystal-based organosilicon elastomer (LCMQ) is developed in this work, which takes the advantages of reversible strain-induced phase transition of liquid crystal units in polymer matrix and the recoverable nano-sized fillers. The former is responsible for the inhibition of stress increasing during deformation, where the external work is mostly compensated by internal phase transition, and the latter provides tunable and sufficient high tensile strength. Such LCMQs were synthesized with 4-methoxyphenyl 4-(but-3-en-1-yloxy)benzoate (MBB) grafted thiol silicone oil (crosslinker-g-MBB) as crosslinking agent, vinyl terminated polydimethylsiloxane as base adhesive, and fumed silica as reinforcing filler by two-step thiol-ene “click” reaction. The obtained tensile strength and the elongation at break are better than previously reported values. Moreover, the resulting liquid crystal elastomers exhibit different mechanical behavior from conventional silicone rubbers. When the liquid crystal content increases from 1% (w/w) to 4% (w/w), the stress plateau for mechanical adaptability becomes clearer. Moreover, the liquid crystal elastomer has no obvious deformation from 25 °C to 120 °C and is expected to be used in industrial applications. It also provides a new template for the modification of organosilicon elastomers.

Nematic liquid crystalline elastomers are aeolotropic materials

Continuum models describing ideal nematic solids are widely used in theoretical studies of liquid crystal elastomers. However, experiments on nematic elastomers show a type of anisotropic response that is not predicted by the ideal models. Therefore, their description requires an additional term coupling elastic and nematic responses, to account for aeolotropic effects. In order to better understand the observed elastic response of liquid crystal elastomers, we analyse theoretically and computationally different stretch and shear deformations. We then compare the elastic moduli in the infinitesimal elastic strain limit obtained from the molecular dynamics simulations with the ones derived theoretically, and show that they are better explained by including nematic order effects within the continuum framework.

The nematic-isotropic transition of the Lebwohl-Lasher model revisited

We revisited the nematic-isotropic (NI) transition of the Lebwohl-Lasher lattice model with a detailed investigation of samples containing 200 × 200 × 200 particles. The large-scale Monte Carlo (MC) simulations involved were carried out following the standard Metropolis, as well as the cluster MC Wolff algorithms. A notable free-energy barrier was observed between the isotropic and nematic phase, leading to long-lived metastable states and hysteresis. We provide an improved estimate of the nematic-isotropic transition temperature T_NI, of the supercooling and superheating temperatures, of the temperature of divergence of pretransitional effects [Formula: see text] as well as an analysis of the size distribution of the ordered domains above T_NI, contributing to a better understanding of this transition of key importance for liquid crystals. This article is part of the theme issue 'Topics in mathematical design of complex materials'.

Probing the in-plane liquid-like behavior of liquid crystal elastomers

When isotropic solids are unequally stretched in two orthogonal directions, the true stress (force per actual cross-sectional area) in the larger strain direction is typically higher than that in the smaller one. We show that thiol-acrylate liquid crystal elastomers with polydomain texture exhibit an unusual tendency: The true stresses in the two directions are always identical and governed only by the area change in the loading plane, independently of the combination of imposed strains in the two directions. This feature proves a previously unidentified state of matter that can vary its shape freely with no extra mechanical energy like liquids when deformed in the plane. The theory and simulation that explain the unique behavior are also provided. The in-plane liquid-like behavior opens doors for manifold applications, including wrinkle-free membranes and adaptable materials.

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.

Effect of stretching angle on the stress plateau behavior of main-chain liquid crystal elastomers

The equilibrium nonlinear stress-stretch relationships for a monodomain main-chain nematic elastomer (MNE) are investigated by varying the angle between the stretching and initial director axes (θ₀). Angle θ₀ has pronounced effects on the ultimate elongation as well as on the width of the low stress plateau regime (Λ_p) during director rotation, whereas θ₀ has no appreciable effect on the plateau stress (σ_p). In the stretching normal to the initial director (θ₀ = 90°), the plateau end exceeds 200% strain. At oblique angles of 90° > θ₀≥ 35°, Λ_p decreases with decreasing θ₀, whereas the definite plateau regime vanishes at θ₀ < 24°. Wide-angle X-ray scattering and polarized optical microscopy measurements reveal that the director rotates uniformly in the biased direction for the MNE of θ₀°≪ 90°, whereas directors rotating clockwise and counterclockwise are coexistent for θ₀ = 90°. Over the entire plateau regime, the MNEs exhibit pure shear deformation characterized by a Poisson's ratio of zero in the direction of the rotation axis. The Λ_p for the corresponding polydomain NE (PNE) undergoing a transition to the monodomain alignment is smaller than that of the MNE of θ₀ = 90°, while the σ_p values for both NEs are almost similar. The semi-soft elasticity concept satisfactorily explains the effects of θ₀ on Λ_p, and the Λ_p value of the PNE, using a single anisotropy parameter which is evaluated from the degree of thermally induced deformation of MNEs.

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.

3D Printable and Reconfigurable Liquid Crystal Elastomers with Light-Induced Shape Memory via Dynamic Bond Exchange

3D printable and reconfigurable liquid crystal elastomers (LCEs) that reversibly shape-morph when cycled above and below their nematic-to-isotropic transition temperature (T_NI ) are created, whose actuated shape can be locked-in via high-temperature UV exposure. By synthesizing LCE-based inks with light-triggerable dynamic bonds, printing can be harnessed to locally program their director alignment and UV light can be used to enable controlled network reconfiguration without requiring an imposed mechanical field. Using this integrated approach, 3D LCEs are constructed in both monolithic and heterogenous layouts that exhibit complex shape changes, and whose transformed shapes could be locked-in on demand.

Machine learning-aided analysis for complex local structure of liquid crystal polymers

Elucidation of mesoscopic structures of molecular systems is of considerable scientific and technological interest for the development and optimization of advanced materials. Molecular dynamics simulations are a promising means of revealing macroscopic physical properties of materials from a microscopic viewpoint, but analysis of the resulting complex mesoscopic structures from microscopic information is a non-trivial and challenging task. In this study, a Machine Learning-aided Local Structure Analyzer (ML-LSA) is developed to classify the complex local mesoscopic structures of molecules that have not only simple atomistic group units but also rigid anisotropic functional groups such as mesogens. The proposed ML-LSA is applied to classifying the local structures of liquid crystal polymer (LCP) systems, which are of considerable scientific and technological interest because of their potential for sensors and soft actuators. A machine learning (ML) model is constructed from small, and thus computationally less costly, monodomain LCP trajectories. The ML model can distinguish nematic- and smectic-like monodomain structures with high accuracy. The ML-LSA is applied to large, complex quenched LCP structures, and the complex local structures are successfully classified as either nematic- or smectic-like. Furthermore, the results of the ML-LSA suggest the best order parameter for distinguishing the two mesogenic structures. Our ML model enables automatic and systematic analysis of the mesogenic structures without prior knowledge, and thus can overcome the difficulty of manually determining the specific order parameter required for the classification of complex structures.

Molecular organizations of conical mesogenic fullerenes

We have studied liquid crystal phases formed by fullerenes functionalized with mesogenic groups yielding a cone-shaped molecular structure. We have modelled these shuttlecock-like molecules with a set of Gay-Berne particles grafted with flexible springs to a spherical core and we have studied, using Monte Carlo simulations, their phase organization, also with a view to examining their possible use as candidate organic photovoltaic materials. We have found that, upon cooling from the isotropic phase, the system forms a columnar phase, like in the experimental work of Kato and coworkers [T. Kato et al., Nature, 2002, 419, 702]. However the phase is made of polar stacks extending not more than about ten molecules, which could limit their usefulness in enhancing and directing charge transport for possible photovoltaic applications.

Sample preparation affects the nematic-isotropic transition in liquid crystal elastomers: insights from molecular simulation

The features of nematic-isotropic transition in liquid crystal elastomers are important for the potential applications of these materials as sensors and actuators. In this paper, we use molecular simulations to obtain insights into the nature of this transition, focusing on the role of sample preparation leading to different polymer network architectures, as well as on the role of swelling. We perform a series of isostress Monte Carlo simulations in a swollen crosslinked system consisting of soft-core Gay-Berne ellipsoids, finding that the smoothness of the nematic-isotropic transition in irregular samples can be attributed to quenched disorder resulting in a distribution of local transition temperatures, and in the strongly swollen samples to a polymer network-swelling monomers phase separation.

Liquid-crystal order during synthesis affects main-chain liquid-crystal elastomer behavior

This study presents the first direct comparison of the influence of liquid-crystal order during synthesis on the thermo-mechanical behaviors of main-chain liquid-crystal elastomers (LCEs) in thiol-acrylate networks. Six polydomain nematic elastomer (PNE) chemistries were compared directly by synthesizing with the mesogens in either an isotropic state (i-PNE) or a nematic state (n-PNE). The i-PNE networks were created in the presence of solvent, which disrupted any liquid-crystal order during network formation. Conversely, the n-PNE networks were created without the presence of solvent below the isotropic transition (T_NI). Differential scanning calorimetry (DSC) was first performed, and it showed that i-PNE networks experienced a clearly defined nematic-to-isotropic transition upon heating, whereas the transition in n-PNE networks was unable to be identified, which may be the result of a nematic-to-paranematic phase transition. Dynamic mechanical analysis (DMA) tests revealed that while both networks maintained elevated loss tangent in the nematic region, only i-PNE networks prominently displayed dynamic soft elasticity behavior. The two-way shape switching behaviors of LCE networks were examined using actuation tests under a 100 kPa bias stress. It showed that the strain amplitude strongly depends on synthesis history; it ranges from 66% to 126% in i-PNE samples and 3% to 61% in n-PNE samples. To help interpret the different actuation strain behaviors between i-PNEs and n-PNEs, wide-angle X-ray scattering (WAXS) was then performed where the LCE samples were strained to 40%. The results showed that order parameter (S) in n-PNE samples (ranging from 0.37 to 0.50) is lower than that in i-PNE samples (0.54 for all cases), and the parameter decreased as the cross-linking density increased. The stress-strain behaviors of the LCE networks measured from uniaxial tension tests revealed that all i-PNE samples had a lower soft-elasticity plateau during loading compared to the n-PNE samples. Finally, free-standing strain recovery of LCE samples after being strained to 100% was investigated. Immediately after removing stress on the samples, i-PNE and n-PNE samples recovered 14% to 38% and 27% to 73% of strain, respectively. We discuss the advantages and disadvantages of the different synthetic histories on LCE design.

Pseudo-Casimir stresses and elasticity of a confined elastomer film

Investigations of the elastic behavior of bulk elastomers have traditionally proceeded on the basis of classical rubber elasticity, which regards chains as thermally fluctuating but disregards the thermal fluctuations of the cross-links. Herein, we consider an incompressible and flat elastomer film of an axisymmetric shape confined between two large hard co-planar substrates, with the axis of the film perpendicular to the substrates. We address the impact that thermal fluctuations of the cross-links have on the free energy of elastic deformation of the system, subject to the requirement that the fluctuating elastomer cannot detach from the substrates. We examine the behavior of the deformation free energy for one case where a rigid pinning boundary condition is applied to a class of elastic fluctuations at the confining surfaces, and another case where the same elastic fluctuations are subjected to soft "gluing" potentials. We find that there can be significant departures (both quantitative and qualitative) from the prediction of classical rubber elasticity theory when elastic fluctuations are included. Finally, we compare the character of the attractive part of the elastic fluctuation-induced, or pseudo-Casimir, stress with the standard thermal Casimir stress in confined but non-elastomeric systems, finding the same power law decay behavior when a rigid pinning boundary condition is applied; for the case of the gluing potential, we find that the leading order correction to the attractive part of the fluctuation stress decays inversely with the inter-substrate separation.