Do Lehmann cholesteric droplets subjected to a temperature gradient rotate as rigid bodies?

Fluorescence Recovery after Photobleaching in Colloidal Science: Introduction and Application

FRAP (fluorescence recovery after photo bleaching) is a method for determining diffusion in material science. In industrial applications such as medications, foods, Medtech, hygiene, and textiles, the diffusion process has a substantial influence on the overall qualities of goods. All these complex and heterogeneous systems have diffusion-based processes at the local level. FRAP is a fluorescence-based approach for detecting diffusion; in this method, a high-intensity laser is made for a brief period and then applied to the samples, bleaching the fluorescent chemical inside the region, which is subsequently filled up by natural diffusion. This brief Review will focus on the existing research on employing FRAP to measure colloidal system heterogeneity and explore diffusion into complicated structures. This description of FRAP will be followed by a discussion of how FRAP is intended to be used in colloidal science. When constructing the current Review, the most recent publications were reviewed for this assessment. Because of the large number of FRAP articles in colloidal research, there is currently a dearth of knowledge regarding the growth of FRAP's significance to colloidal science. Colloids make up only 2% of FRAP papers, according to ISI Web of Knowledge.

Steady rigid-body rotation of cholesteric droplets and their dumbbell-shaped aggregates driven by heat flux along the helical axes

We investigated the steady unidirectional rotation of cholesteric (Ch) droplets driven by a heat flux. The droplets coexisted with the isotropic (Iso) phase and possessed a helical molecular arrangement. When a heat flux was transported along the helical axis, the droplets and their dumbbell-shaped aggregates exhibited steady rigid rotation. Our results are in contrast with those of previous reports in which Ch droplets in the same geometry exhibited pure director rotation. The fact that Ch droplets and their aggregates prefer rigid rotation can be ascribed to the orientational elasticity combined with the anchoring force at the Ch-Iso interface, which locks the director to the rotational flow in the droplets.

Observation of Backflow during the Anihilation of Topologocal Defects in Freely Suspended Smectic Films

Freely suspended films in the smectic C phase are excellent templates for the study of topological defect dynamics. It is well known that, during the annihilation of a pair of disclinations with strengths +/−1, the +1 defect moves faster because it is carried towards its opponent by backflow, whereas the flow in the vicinity of the −1 defect is negligibly small. This backflow pattern is created by the defect motion itself. An experimental confirmation of this theoretical prediction and its quantitative characterization is achieved here by fluorescence labeling. Film regions near the defect positions are labeled and their displacements are tracked optically.

Differential rotation in cholesteric pillars under a temperature gradient

Steady rotation is induced in cholesteric droplets dispersed in a specific liquid solvent under a temperature gradient. In this phenomenon, two rotational modes have been considered: (1) collective rotation of the local director field and (2) rigid-body rotation of the whole droplet structure. However, here we present another rotational mode induced in a pillar-shaped cholesteric droplet confined between substrates under a temperature gradient, that is, a differential rotation where the angular velocity varies as a function of the radial coordinate in the pillar. A detailed flow field analysis revealed that every pillar under a temperature gradient involves a double convection roll. These results suggested that the differential rotation in the cholesteric pillars was driven by the inhomogeneous material flow induced by a temperature gradient. The present experimental study indicates that the coupling between the flow and the director motion plays a key role in the rotation of the cholesteric droplets under the temperature gradient.

Heat-Driven Rigid-Body Rotation of a Mixture of Cholesteric Liquid Crystal Droplets and Colloids

We show that cholesteric (Ch) liquid crystal droplets with cylindrically symmetric orientation dispersing in an isotropic (Iso) phase exhibited unidirectional rotation under a heat flux along the symmetry axis. By introducing colloidal particle adhesive to the Ch droplet surface, we traced the translational motion of the colloids and found that the colloids rotated unidirectionally around the center of each Ch droplet. The director configuration of the droplets was not distorted either spatially or temporally, while the colloids rotated constantly. The results suggest that the Ch droplets under the heat flux should rotate as a rigid body. Using this heat-driven rotation of the Ch droplets, we designed new geometries of various composites of Ch droplets and colloids and succeeded in driving intriguing complex dynamics.

Stable and Metastable Patterns in Chromonic Nematic Liquid Crystal Droplets Forced with Static and Dynamic Magnetic Fields

Spherical confinement of nematic liquid crystals leads to the formation of equilibrium director field configurations that include point and line defects. Driving these materials with flows or dynamic fields often results in the formation of alternative metastable states. In this article, we study the effect of magnetic field alignment, both under static and dynamic conditions, of nematic gems (nematic droplets in coexistence with the isotropic phase) and emulsified nematic droplets of a lyotropic chromonic liquid crystal. We use a custom polarizing optical microscopy assembly that incorporates a permanent magnet whose strength and orientation can be dynamically changed. By comparing simulated optical patterns with microscopy images, we measure an equilibrium twisted bipolar pattern within nematic gems that is only marginally different from the one reported for emulsified droplets. Both systems evolve to concentric configurations upon application of a static magnetic field, but behave very differently when the field is rotated. While the concentric texture within the emulsified droplets is preserved and only displays asynchronous oscillations for high rotating speeds, the nematic gems transform into a metastable untwisted bipolar configuration that is memorized by the system when the field is removed. Our results demonstrate the importance of boundary conditions in determining the dynamic behavior of confined liquid crystals even for configurations that share similar equilibrium bulk structures.

A thermomechanical coupling in cholesteric liquid crystals: Unidirectional rotation of double-twist cylinders driven by heat flux

We made aggregates of cholesteric liquid crystalline Cylinders with Double-Twist orientational structure (DTC) and investigated their rigid-body rotation under a temperature gradient, focusing on how the rotational speed should depend on the cylinder size. The experimental results showed that the angular velocity of the DTC aggregates linearly increased with the height of the cylinders and was inversely proportional to the base area. With a phenomenological equation, we analyzed the torque caused by the heat flux and its balance with the viscous friction, and found that the simple analysis well explained the size-dependence of the rotation of the DTC aggregates. The coupling constant between the heat flux and the torque to drive the rigid-body rotation was in the same order of magnitude as that for the director rotation.

Hydrodynamic rotlet dipole driven by spinning chiral liquid crystal droplets

Chirality is an essential evolutionary-conserved physical aspect of swimming microorganisms. However, the role of chirality on the hydrodynamics of such microswimmers is still being elucidated. Hydrodynamic theories have so far predicted that, under a torque-free condition satisfied in the system of microswimmers, a rotlet dipole generating a twisting flow is the leading-order singularity of the chiral flow field. Nevertheless, such a chiral flow field has never been experimentally detected. Here we explore a hydrodynamic field generated in a system of a chiral microswimmer, where a droplet of a cholesteric liquid crystal (CLC) exhibits helical and spinning motions in surfactant solutions due to a chiral nonequilibrium cross coupling between the rotation and the Marangoni flow. Combining measurement of the flow field around the spinning CLC droplets and a computational flow modeling, we revealed that the CLC droplets generate a flow field of a rotlet dipole. Remarkably, we found that the chiral component of the flow field decays with distance r as r^{-3}, which is consistent with the theoretical prediction for the flow field produced by a point singularity of a rotlet dipole. Our findings will promote the understanding of roles of chirality on the hydrodynamics in active matter as well as liquid crystals.

Lehmann rotation of cholesteric droplets driven by Marangoni convection

We show experimentally and theoretically that the Lehmann effect recently observed by Yoshioka and Araoka (Nat. Commun., 2018, 9, 432) in emulsified cholesteric liquid crystal droplets under temperature gradients is due to Marangoni flows rather than to the thermomechanical or chemomechanical couplings often invoked to explain the phenomenon. Using colloidal tracers we visualize convection rolls surrounding stationary cholesteric droplets in vertical temperature gradients, while a shift in the position of internal point defects reveals the corresponding inner convection in nematic droplets thermomigrating in a horizontal temperature gradient. We attribute these phenomena to the temperature dependence of the surface tension at the interface between these partially-miscible liquids, and justify their absence in the usual case of purely lyophobic emulsions. We perform a theoretical analysis to help validate this hypothesis, demonstrating the strong dependence of the precession velocity on the configuration of the cholesteric director field.

Formation and dynamics of the aggregates of cholesteric double-twist cylinders

We succeeded in driving the unidirectional rigid-body rotation of cholesteric (Ch) double-twist cylinder (DTC) droplets under a heat flux along the cylindrical symmetry axis. To directly observe the rigid-body rotation of DTC droplets, in each of which the center of the rotation and the symmetry axis of the structure correspond, we fabricated DTC aggregates that comprise several DTCs with intact structures. Given a steady heat flux, the DTC aggregates metastabilized by the shape and the surface anchoring show a unidirectional rigid-body rotation with a constant angular velocity. The rotational direction is determined by the molecular chirality and the direction of the heat flux, and the rotational velocity increases with the temperature gradient and decreases with the aggregation number N of the DTCs as 1 + 2/sin2(π/N). The behavior agrees with a simple model based on the linear phenomenological equation.

Topology-dependent self-structure mediation and efficient energy conversion in heat-flux-driven rotors of cholesteric droplets

When heat flux is applied to a chiral liquid crystal, unidirectional rotation is induced around the flux axis, as first discovered by Otto Lehmann in 1900. In recent years, this heat-flux-induced phenomenon has been studied mostly in droplets of cholesteric liquid crystals undergoing phase transition from the isotropic to cholesteric phase, i.e., in the coexistence region, which occurs over a very narrow temperature range. Here, we report that the heat-flux-induced rotation can be stabilised by the use of a dispersion system, in which the cholesteric droplets are dispersed in a viscous and poorly miscible isotropic solvent. Interestingly, the phenomenon is found to be topology dependent. Moreover, the rotation is not only stable but also more efficient than that in the known systems. We describe in detail how the dynamics of the heat-flux-induced rotation are altered in the present dispersion system.

The Lehmann effect describes the spontaneous rotation of cholesteric liquid crystals in response to heat input. Here, the authors stabilise it by dispersing cholesteric droplets into a poorly miscible solvent and show dependences of rotation speed and conversion efficiency on the topological states.

Generalized drift velocity of a cholesteric texture in a temperature gradient

We propose a general method to calculate the drift velocity of cholesteric textures subjected to a temperature gradient when the backflow effects are negligible. The textures may be Translationally Invariant Configurations (TICs) or localized structures such as cholesteric droplets or cholesteric fingers. For the TICs and for the droplets, the drift is rotational while for the fingers, the drift is translational. We show that for the TICs, the drift is only due to the thermomechanical coupling terms of Leslie (classical term) and of Akopyan and Zel'dovich (which are additional texture-dependent terms). For the localized structures, we show that another mechanism involving the temperature variations of the elastic constants and the existence of a transverse temperature gradient can lead to a drift which adds to the one due the classical thermomechanical effects.

Continuous Rotation of Achiral Nematic Liquid Crystal Droplets Driven by Heat Flux

Suspended droplets of cholesteric (chiral nematic) liquid crystals spontaneously rotate in the presence of a heat flux due to a temperature gradient, a phenomenon known as the Lehmann effect. So far, it is not clear whether this effect is due to the chirality of the phase and the molecules or only to the chirality of the director field. Here, we report the continuous rotation in a temperature gradient of nematic droplets of a lyotropic chromonic liquid crystal featuring a twisted bipolar configuration. The achiral nature of the molecular components leads to a random handedness of the spontaneous twist, resulting in the coexistence of droplets rotating in the two senses, with speeds proportional to the temperature gradient and inversely proportional to the droplet radius. This result shows that a macroscopic twist of the director field is sufficient to induce a rotation of the droplets, and that the phase and the molecules do not need to be chiral. This suggests that one can also explain the Lehmann rotation in cholesteric liquid crystals without introducing the Leslie thermomechanical coupling-only present in chiral mesophases. An explanation based on the Akopyan and Zeldovich theory of thermomechanical effects in nematics is proposed and discussed.