Three-dimensional Liquid Crystal Research Articles

New quasiperiodic structures in nematic liquid crystals.

Liquid crystal molecules tend to align with each other, often forming regions of opposite alignment that meet at a boundary-topological defects. These often offer information on configuration of the liquid crystal molecules with competing constraints on their order. Here, we experimentally demonstrate a mechanism to generate topological defects in the form of spatially oscillatory domain walls in nematic liquid crystals. We initially orient the molecules perpendicular to the substrate (i.e. homeotropic alignment) and when a horizontal electric field is applied, domain walls that change their shape with time emerge. These walls form at low frequencies of the applied electric field and remain stable as the frequency increases. If the initial biasing field is at larger frequencies (kHz regime), the domain walls still form, but are not oscillatory. We develop a general theory to predict the three-dimensional liquid crystal director evolution in any two-dimensional varying field. This theory gives the time dependence for the domain walls and confirms that both the oscillatory and straight walls are stable.

Three-dimensional liquid crystal polymer actuators assembled by athermal photo-welding.

Photodeformable liquid crystal polymers (LCPs) exhibit shape changes of different modes like bending, twisting, and oscillation, which depend on the orientation of liquid crystals. However, it is challenging to create a three-dimensional (3D) actuator with distinct actuation modes due to the difficulty of local orientation in a complex bulk architecture. Here we propose a strategy based on athermal photo-welding to integrate different orientations into a single flexible actuator by the photofluidization of azobenzene-containing linear LCPs. Stretch-induced uniaxial films are cut in different directions and subsequently welded via local photofluidization, during which the LCP transitions from a high-modulus glassy state to a rubbery state upon photoisomerization of azobenzene at room temperature. As a consequence, a cucumber vine-like structure with the opposite handedness and a lifting gripper are constructed by such a cut-and-weld process, demonstrating diverse deformation modes of winding, unwinding, and curling. This strategy provides an athermal process for the fabrication of seamless 3D flexible actuators without structural defects, which have potential applications in micromechanical systems, soft robotics, and artificial muscles.

Short-Chain Mono-Alkyl β-D-Glucoside Crystals-Do They Form a Cubic Crystal Structure?

Three-dimensional liquid crystal (LC) phases, cubic LC phases, have been extensively studied as fascinating molecular assembled systems formed by amphiphilic compounds. However, similar structures have only been seen in rare instances in lipid crystal states in glycolipid crystal studies. In this study, we prepared short-chain n-alkyl β-D-glucosides (CnG) with an alkyl chain length n ranging from 4 to 6 and investigated their crystal structures. First, differential thermal analysis (DTA) and thermogravimetric analysis (TG) measurements showed the formation of hydrated crystals for C4G and C5G, respectively. Second, the crystal structures of CnG (n = 4, 5, 6) in both anhydrous and hydrated states were examined using a temperature-controlled powder X-ray diffraction (PXRD) measurement. Both hydrate and anhydrous crystals of C4G and C5G with critical packing parameters (CPPs) less than 0.33 formed cubic crystal phases. Bilayer lengths, calculated from the main diffraction peaks in each PXRD profile, depended on crystalline moisture for C5G, but no significant change was confirmed for C4G, indicating that the properties of each hydrophilic layer differ. However, C6G with a CPP of 0.42 formed a crystal structure with a modulated lamellar structure similar to C7G and C8G with similar CPP values. Thus, a glycolipid motif concept with a cubic crystal structure was demonstrated.

Tunable polarization volume gratings based on blue phase liquid crystals.

A large-angle polarization volume grating (PVG) with circular-polarization selectivity is demonstrated using a three-dimensional chiral liquid crystal with simple cubic symmetry - the blue phase (BP) II. We confirm defect-free alignment of the BP crystal on a periodically patterned substrate down to a period of 700 nm, with Kossel diagrams and far-field diffraction patterns suggesting that the lattice becomes slanted within the cell to accommodate to the imprinted pattern. We further demonstrate a tunable PVG by exploiting the external field-responsivity of BPs, making this PVG attractive for a wide range of applications from tunable photonics to augmented reality.

Three-dimensional thermochromic liquid crystal elastomer structures with reversible shape-morphing and color-changing capabilities for soft robotics.

Functional structures with reversible shape-morphing and color-changing capabilities are promising for applications including soft robotics and biomimetic camouflage devices. Despite extensive studies, there are few reports on achieving both reversible shape-switching and color-changing capabilities within one structure. Here, we report a facile and versatile strategy to realize such capabilities via spatially programmed liquid crystal elastomer (LCE) structures incorporated with thermochromic dyes. By coupling the shape-changing behavior of LCEs resulting from the nematic-to-isotropic transition of liquid crystals with the color-changing thermochromic dyes, 3D thermochromic LCE structures change their shapes and colors simultaneously, which are controlled by the nematic-isotropic transition temperature of LCEs and the critical color-changing temperature of dyes, respectively. Demonstrations, including the simulated blooming process of a resembled flower, the camouflage behavior of a "butterfly"/"chameleon" robot in response to environmental changes, and the underwater camouflage of an "octopus" robot, highlight the reliability of this strategy. Furthermore, integrating micro-ferromagnetic particles into the "octopus" thermochromic LCE robot allows it to respond to thermal-magnetic dual stimuli for "adaptive" motion and diverse biomimetic motion modes, including swimming, rolling, rotating, and crawling, accompanied by color-changing behaviors for camouflage. The reversibly reconfigurable and color-changing thermochromic LCE structures are promising for applications including soft camouflage robots and multifunctional biomimetic devices.

Topological fine structure of smectic grain boundaries and tetratic disclination lines within three-dimensional smectic liquid crystals.

Observing and characterizing the complex ordering phenomena of liquid crystals subjected to external constraints constitutes an ongoing challenge for chemists and physicists alike. To elucidate the delicate balance appearing when the intrinsic positional order of smectic liquid crystals comes into play, we perform Monte-Carlo simulations of rod-like particles in a range of cavities with a cylindrical symmetry. Based on recent insights into the topology of smectic orientational grain boundaries in two dimensions, we analyze the emerging three-dimensional defect structures from the perspective of tetratic symmetry. Using an appropriate three-dimensional tetratic order parameter constructed from the Steinhardt order parameters, we show that those grain boundaries can be interpreted as a pair of tetratic disclination lines that are located on the edges of the nematic domain boundary. Thereby, we shed light on the fine structure of grain boundaries in three-dimensional confined smectics.

Bioinspired Color-Changing Photonic Polymer Coatings Based on Three-Dimensional Blue Phase Liquid Crystal Networks.

Photonic polymer coatings that can adaptively respond to the constant changes of surrounding environments are of profound significance for diverse applications such as optical sensors, information encryption, and adaptive camouflage. Here, we report the fabrication of humidity-driven color-changing photonic polymer coatings on the basis of judiciously designed hydrogen-bonded three-dimensional (3D) blue phase liquid crystal networks. Thanks to the inherent self-assembled 3D photonic nanostructures and tough covalent bonding between the polymers and substrate surfaces, the resulting polymer coatings are found to exhibit vivid structural colors, and humidity-driven reversible color changes across the visible spectrum of light can be achieved upon breaking the hydrogen bonds and subsequent conversion into a hygroscopic polymer coating. As the proof-of-concept applications, we demonstrate the information encryption, inkjet-printable photonic patterns, bioinspired adaptive camouflage, and colorimetric humidity sensor with such promising humidity-driven color-changing photonic polymer coatings. The results disclosed herein are expected to provide new insights into the development of stimuli-responsive advanced functional materials with tailorable 3D photonic nanostructures toward technological applications ranging from sensing, display, anticounterfeiting, and biomimetic camouflage.

Intrinsic geometry and director reconstruction for three-dimensional liquid crystals

We give a description of the intrinsic geometry of elastic distortions in three-dimensional nematic liquid crystals and establish necessary and sufficient conditions for a set of functions to represent these distortions by describing how they couple to the curvature tensor. We demonstrate that, in contrast to the situation in two dimensions, the first-order gradients of the director alone are not sufficient for full reconstruction of the director field from its intrinsic geometry: it is necessary to provide additional information about the second-order director gradients. We describe several different methods by which the director field may be reconstructed from its intrinsic geometry. Finally, we discuss the coupling between individual distortions and curvature from the perspective of Lie algebras and groups and describe homogeneous spaces on which pure modes of distortion can be realised.

Rotationally invariant ring-shaped liquid crystal structures between two substrates with different photoalignment

Planar patterned photoalignment can be used to align liquid crystals (LCs) in any azimuthal orientation. Using different patterns on both substrates, we fabricated and analyzed complex three-dimensional LC structures. We developed four configurations in which planar patterns with rotational symmetry are defined at each substrate. All four configurations generate a ring-shaped region in the bulk of the sample where the LC aligns vertically. The director configurations are calculated using numerical simulations and are verified by comparing the simulated optical transmission to the measured microscopy images. The vertical alignment in the bulk of the cell makes it possible to use this configuration as a waveguide, as demonstrated by a waveguide mode simulation.

Heat-Resistant Polymer Materials Based on Liquid Crystal Compounds

Data on heat-resistant linear and crosslinked polymer materials containing mesogenic groups in their structure have been systematized. Principles of the macromolecular design of thermoplastic liquid-crystal (LC) polymers providing high performance characteristics and their relationship with the supermolecular organization and processing conditions have been discussed. Methods for synthesizing LC precursors with reactive terminal groups cured to form three-dimensional LC networks have been discussed; the effect of the chemical nature of the terminal groups on the thermal stability of the resulting material has been shown.

Symmetric Continuously Tunable Photonic Band Gaps in Blue-Phase Liquid Crystals Switched by an Alternating Current Field.

Symmetric continuously tunable three-dimensional (3D) liquid photonic crystals have been investigated using self-organized blue-phase liquid crystal films. The photonic band gap in the overall visible spectrum can be tuned continuously, reversibly, and rapidly as the applied electric field changes. After driven by the applied field, four-time enhancement of the reflectivity results in more vivid reflection colors. A lasing emission of tuning working wavelength has been demonstrated by using the dye-doped blue-phase liquid crystal film. With the advantages of fast response speed, no alignment layer, large-scale electrically shift of the photonic band gap, and macro optical isotropy, this self-assembled soft material has many potential applications in high-performance reflective full-color display, 3D tunable lasers, and nonlinear optics.

Long-time anomalous swimmer diffusion in smectic liquid crystals.

The dynamics of self-locomotion of active particles in aligned or liquid crystalline fluids strongly deviates from that in simple isotropic media. We explore the long-time dynamics of a swimmer moving in a three-dimensional smectic liquid crystal and find that the mean-square displacement transverse to the director exhibits a distinct logarithmic tail at long times. The scaling is distinctly different from that in an isotropic or nematic fluid and hints at the subtle but important role of the director fluctuation spectrum in governing the long-time motility of active particles. Our findings are based on a generic hydrodynamic theory and Brownian dynamics computer simulation of a three-dimensional soft mesogen model.

Finsler geometry modeling and Monte Carlo study of 3D liquid crystal elastomer

We study a three-dimensional (3D) liquid crystal elastomer (LCE) in the context of Finsler geometry (FG) modeling, where FG is a mathematical framework for describing anisotropic phenomena. The LCE is a 3D rubbery object and has remarkable properties, such as the so-called soft elasticity and elongation, the mechanisms of which are unknown at present. To understand these anisotropic phenomena, we introduce a variable σ, which represents the directional degrees of freedom of a liquid crystal (LC) molecule. This variable σ is used to define the Finsler metric for the interaction between the LC molecules and bulk polymers. Performing Monte Carlo (MC) simulations for a cylindrical body between two parallel plates, we numerically find the soft elasticity in MC data such that the tensile stress and strain are consistent with reported experimental results. Moreover, the elongation is also observed in the results of MC simulations of a spherical body with free boundaries, and the data obtained from the MC simulations are also consistent with existing experimental results.

Nematic phase transition and texture dynamics

ABSTRACTResearch advances over the past decade in the areas of nematic phase transition and texture dynamics are reviewed. Research studies applying theoretical techniques able to resolve the length and time scales inherent to liquid crystal (LC) dynamics are focused on: coarse-grained molecular dynamics and continuum mechanics. The focus on LC dynamics is due to their importance in both fundamental and technological processes involving complex LC textures and texture transitions. Meta-stable textures frequently occur in soft matter systems, thus knowledge of LC textures that result in free energy minima for a specific system is not sufficient to characterise its behaviour. Resolution of dynamics enables researchers to predict with more accuracy observable LC textures and texture transitions. As is reflected in the reviewed research, LC dynamics simulations have enabled both validation of simulations with existing experimental observations and predictive results, which augment direct experimentation. While the outlook is positive as a result of this, several key challenges stymie further progress: (i) the availability of validated open-source software implementing nematic dynamics simulation methods, (ii) development of suitable visualisation and characterisation methods for transient three-dimensional LC textures, and (iii) inclusion of thermal fluctuations in nematic dynamics models.

Well-posedness for the three-dimensional compressible liquid crystal flows

This paper is concerned with the initial-boundary value problem for the three-dimensional compressible liquid crystal flows. The system consists of the Navier-Stokes equations describing the evolution of a compressible viscous fluid coupled with various kinematic transport equations for the heat flow of harmonic maps into $\mathbb{S}^2$. Assuming the initial density has vacuum and the initial data satisfies a natural compatibility condition, the existence and uniqueness is established for the local strong solution with large initial data and also for the global strong solution with initial data being close to an equilibrium state. The existence result is proved via the local well-posedness and uniform estimates for a proper linearized system with convective terms.

Global strong solution to the three-dimensional liquid crystal flows of Q-tensor model

A complex hydrodynamic system that models the fluid of nematic liquid crystals in a bounded domain in R3 is studied. The system is a forced incompressible Navier–Stokes equation coupled with a parabolic type equation of Q-tensors. We invoke the maximal regularity of the Stokes operators and parabolic operators in Besov spaces to obtain the local strong solution if the initial Q-tensor is not too “wild”. In addition, it is showed that such solution can be extended to a global one if the initial data is a sufficiently small perturbation around the trivial equilibrium state. Finally, it is proved that the global strong solution obtained here is identical to those weak solutions obtained in Paicu and Zarnescu [26].

Role of Surfactant during Microemulsion Photopolymerization for the Creation of Three-Dimensional Liquid Crystal Elastomer Microsphere Spatial Cell Scaffolds

Three-dimensional (3D) cell scaffolds based on connected nematic liquid crystal elastomer microsphere architectures support the attachment and proliferation of C2C12 myoblasts, neuroblastomas (SHSY5Y) and human dermal fibroblasts (hDF). The microsphere spatial cell scaffolds were prepared by an oil-in-water microemulsion photopolymerization of reactive nematic mesogens in the presence of various surfactants, and the as-prepared scaffold constructs are composed of smooth surface microspheres with diameter ranging from 10 to 30 μm. We here investigate how the nature and type of surfactant used during the microemulsion photopolymerization impacts both the size and size distribution of the resulting microspheres as well as their surface morphology, i.e. the surface roughness.

Three-dimensionally modulated anisotropic structure for diffractive optical elements created by one-step three-beam polarization holographic photoalignment

A diffractive optical element with a three-dimensional liquid crystal (LC) alignment structure for advanced control of polarized beams was fabricated by a highly efficient one-step photoalignment method. This study is of great significance because different two-dimensional continuous and complex alignment patterns can be produced on two alignment films by simultaneously irradiating an empty glass cell composed of two unaligned photocrosslinkable polymer LC films with three-beam polarized interference beam. The polarization azimuth, ellipticity, and rotation direction of the diffracted beams from the resultant LC grating widely varied depending on the two-dimensional diffracted position and the polarization states of the incident beams. These polarization diffraction properties are well explained by theoretical analysis based on Jones calculus.

Global existence and temporal decay for the nematic liquid crystal flows

This paper is concerned with the Cauchy problem of the three-dimensional nematic liquid crystals. We establish the global well-posedness and time decay rates of the classical solutions with smooth initial data which are of small energy by using Fourier splitting technique and pure energy method.

Modeling microtubule cytoskeleton via an active liquid crystal elastomer model

In this work, a three-dimensional (3D) liquid crystal polymer model is developed to model the microtubule cytoskeleton aggregate and to study its interaction with the extracellular matrix. In the proposed microtubule cytoskeleton model, the cytoskeleton aggregate is treated as a homogenized liquid crystal elastomer medium, with an extra active stress term included to account for the effect of the active process of Guanosine Triphosphate (GTP) hydrolysis. The cell extracellular matrix (ECM) is modeled as a hyperelastic material. The specific and non-specific interactions between the cell and its ECM are modeled by a Coarse-Grained Contact Model. Surface tension effects are incorporated into the simulation, through a Multiscale Dynamic Wetting Model, to account for the interface conditions between the cell and its surrounding environment. The cell model is implemented in a Lagrange type Galerkin formulation. The numerical results show that the cell can sense and move under the gradient of matrix elasticity.