Negative viscosity of liquid crystals in the presence of turbulence: Conductivity dependence, phase diagram, and self-oscillation.

Recently, we reported the discovery of enormous negative viscosity of a nematic liquid crystal in the presence of turbulence induced by ac electric fields, which enabled us to observe unique phenomena related to the negative viscosity, such as spontaneous shear flow, hysteresis in flow curves, and self-oscillation [Orihara et al., Phys. Rev. E 99, 012701 (2019)10.1103/PhysRevE.99.012701]. In the present paper, we report the rheological properties of another nematic liquid crystal, which is a homologue of the previous one. The properties of the present liquid crystal are strongly dependent on electrical conductivity. Three samples with different conductivities were prepared by changing the amount of an ionic dopant. It was found that the lowest-conductivity sample without dopant shows no negative viscosity whereas the other ion-doped samples exhibit negative viscosity with strong dependence on the frequency of the ac electric field, consistent with microscopic observations. Phase diagrams of the negative- and positive-viscosity states in the amplitude and frequency plane are constructed to show the conductivity effect. Furthermore, we propose a model to reproduce another type of self-oscillation found in the present study.

Observation of stochastic resonance in a liquid-crystal light valve with optical feedback induced by colored noise in the driving voltage.

Stochastic resonance is a noise phenomenon that benefits applications such as pattern formation, neural systems, microelectromechanical systems, and image processing. This study experimentally clarifies that the orientation of the liquid crystal molecules was switched between two stable positions when stochastic resonance was induced by colored noises in a liquid crystal light valve with optical feedback. Ornstein-Uhlenbeck and dichotomous noises were used for colored noise, and the noise was applied to the drive voltage of the liquid crystal light valve. The signal-to-noise ratio was measured with respect to changes in the noise type, noise intensity, and autocorrelation time of the noise. It was found that typical stochastic resonance was observed with a noise autocorrelation time of approximately 20 ms or more for both noise types, and dichotomous noise further enhanced the stochastic resonance compared to the Ornstein-Uhlenbeck noise. This suggests that it is possible to maximize stochastic resonance in a liquid crystal light valve by optimizing the conditions of colored noise.

Three-dimensional observation of Brownian particles under steady shear flow by stereo microscopy.

Three-dimensional observation of Brownian particles under shear flow is performed with a stereo microscope to examine the nature of the Brownian motion that occurs in the presence of shear flow. From the three-dimensional trajectories of the particles, we clearly demonstrate the occurrence of anomalous diffusion in the flow direction and the coupling of the displacements in the flow and velocity gradient directions. Furthermore, we experimentally obtain the probability distribution function and current density, which also exhibit characteristic features, and compare the obtained results with theoretical results derived using the Fokker-Planck equation.

Negative viscosity of a liquid crystal in the presence of turbulence.

We report on the discovery of enormous negative viscosity in a nematic liquid crystal in the presence of turbulence induced by electric fields. As the negative viscosity in this system is so large, we are able to observe several phenomena originating from it. For example, we observe a spontaneous shear flow that rotates the upper disk of a rheometer, as well as the reversal of the rotational direction upon applying an external torque in the opposite direction. Hysteresis loops are also observed in the shear-stress-shear-rate curves, which is reminiscent of those seen for ferromagnetic and ferroelectric materials. The similarities between the phenomena observed for our system and ferroic materials are comprehensively demonstrated, although the two systems are fundamentally different in that the former is out of equilibrium. We elucidate the origin of the negative viscosity and propose a simple model that reproduces the phenomena observed in this active fluid.

Tunable two-dimensional polarization grating using a self-organized micropixelated liquid crystal structure.

Utilization of the self-organizing nature of soft materials is promising for fabricating micro- and nano-structures, which can be applied for optics. Because of the high birefringence, liquid crystals are especially suitable for optoelectronic applications such as beam steering and polarization conversion. On the other hand, most self-organized patterns in liquid crystals are one-dimensional and there are only a few examples of two dimensional systems. Here we study the light diffraction from a micro-pixelated pattern of a nematic liquid crystal which is formed by self-organization of topological defects. We demonstrate that the system works as a tunable two dimensional optical grating, which splits the incident laser beam and changes the polarization property. The intensity can be controlled by electrical voltages, which cause extinction of the zeroth-order beam. The polarization properties depend on the location of spots. The numerical calculation and the theoretical analysis not only support the experimental results but also unveil the uniqueness of the pixelated structure.

Polymer-Stabilized Micropixelated Liquid Crystals with Tunable Optical Properties Fabricated by Double Templating.

Self-organized nano- and microstructures of soft materials are attracting considerable attention because most of them are stimuli-responsive due to their soft nature. In this regard, topological defects in liquid crystals (LCs) are promising not only for self-assembling colloids and molecules but also for electro-optical applications such as optical vortex generation. However, there are currently few bottom-up methods for patterning a large number of defects periodically over a large area. It would be highly desirable to develop more effective techniques for high-throughput and low-cost fabrication. Here, a micropixelated LC structure consisting of a square array of topological defects is stabilized by photopolymerization. A polymer network is formed on the structure of a self-organized template of a nematic liquid crystal (NLC), and this in turn imprints other nonpolymerizable NLC molecules, which maintains their responses to electric field and temperature. Photocuring of specific local regions is used to create a designable template for the reproducible self-organization of defects. Moreover, a highly diluted polymer network (≈0.1 wt% monomer) exhibits instant on-off switching of the patterns. Beyond the mere stabilization of patterns, these results demonstrate that the incorporation of self-organized NLC patterns offers some unique and unconventional applications for anisotropic polymer networks.

Direct observation of coupling between orientation and flow fluctuations in a nematic liquid crystal at equilibrium.

To demonstrate coupling between orientation and flow fluctuations in a nematic liquid crystal at equilibrium, we simultaneously observe the intensity change due to director fluctuations under a polarizing microscope and the Brownian motion of a fluorescent particle trapped weakly by optical tweezers. The calculated cross-correlation function of the particle position and the spatial gradient of the intensity is nonzero, clearly indicating the existence of coupling.

Large-scale self-organization of reconfigurable topological defect networks in nematic liquid crystals.

Topological defects in nematic liquid crystals are ubiquitous. The defects are important in understanding the fundamental properties of the systems, as well as in practical applications, such as colloidal self-assembly, optical vortex generation and templates for molecular self-assembly. Usually, spatially and temporally stable defects require geometrical frustration imposed by surfaces; otherwise, the system relaxes because of the high cost of the elastic energy. So far, multiple defects are kept in bulk nematic liquid crystals by top-down lithographic techniques. In this work, we stabilize a large number of umbilical defects by doping with an ionic impurity. This method does not require pre-patterned surfaces. We demonstrate that molecular reorientation controlled by an AC voltage induces periodic density modulation of ions accumulated at an electrically insulating polymer interface, resulting in self-organization of a two-dimensional square array of umbilical defects that is reconfigurable and tunable.

Electric-field-induced flow-aligning state in a nematic liquid crystal.

The response of shear stress to a weak ac electric field as a probe is measured in a nematic liquid crystal under shear flow and dc electric fields. Two states with different responses are clearly observed when the dc electric field is changed at a constant shear rate: the flow aligning and non-flow aligning states. The director lies in the shear plane in the flow aligning state and out of the plane in the non-flow aligning state. Through application of dc electric field, the non-flow aligning state can be changed to the flow aligning state. In the transition from the flow aligning state to the non-flow aligning state, it is found that the response increases and the relaxation time becomes longer. Here, the experimental results in the flow aligning state are discussed on the basis of the Ericksen-Leslie theory.

Direct visualization of spatiotemporal structure of self-assembled colloidal particles in electrohydrodynamic flow of a nematic liquid crystal.

Characterization of spatiotemporal dynamics is of vital importance to soft matter systems far from equilibrium. Using a confocal laser scanning microscopy, we directly reveal three-dimensional motion of surface-modified particles in the electrohydrodynamic convection of a nematic liquid crystal. Particularly, visualizing a caterpillar-like motion of a self-assembled colloidal chain demonstrates the mechanism of the persistent transport enabled by the elastic, electric, and hydrodynamic contributions. We also precisely show how the particles' trajectory is spatially modified by simply changing the surface boundary condition.

Stepwise heat-capacity change at an orientation transition in liquid crystals.

During a phase transition in a bulk material, heat is exchanged with matter to balance the changes in the internal energy and the entropy of the system. Here we report on the thermal detection of a surface-mediated anchoring transition, a spontaneous and discontinuous orientation change between planar (P) and homeotropic (H) alignments within a single nematic phase by changing temperature. In this case a stepwise change in the heat flow, similar to a glass transition, is observed by means of high-resolution differential scanning calorimetry. We found that the jump in the specific heat does not depend on the sample volume, although the contribution of molecules in the vicinity of surfaces, which trigger the transition, becomes less with increasing the sample volume. This means that different molecular orientations, H and P, with respect to surfaces have different thermodynamic free energies. We also address why the anchoring transition occurs by means of grazing-incidence x-ray diffraction measurements, which clearly reveal the formation of quasismectic layers parallel to surfaces in the nematic phase.

Nonequilibrium steady-state response of a nematic liquid crystal under simple shear flow and electric fields.

The effect of a dc electric field on the response of a nematic liquid crystal under shear flow has been investigated by measuring the shear stress response to an ac electric field used as a probe. It was found that both the first- and second-order responses do not vanish at high frequencies, but have constant nonzero values. The experimental results are in good agreement with calculations based on the Ericksen-Leslie theory. The role of the Parodi relation (which is derived from the Onsager reciprocal relation) in the stress response is discussed.

Colloidal caterpillars for cargo transportation.

Tunable transport of tiny objects in fluid systems is demanding in diverse fields of science such as drug delivery, active matter far from equilibrium, and lab-on-a-chip applications. Here, we report the directed motion of colloidal particles and self-assembled colloidal chains in a nematic liquid crystal matrix using electrohydrodynamic convection (EHC) rolls. The asymmetric distortion of the molecular orientation around the particles results - for single particles - in a hopping motion from one EHC roll to the next and - for colloidal chains - in a caterpillar-like motion in the direction perpendicular to the roll axes. We demonstrate the use of colloidal chains as microtraction engines for the transport of various types of microcargo.

Electrically induced deformation in chiral smectic elastomers with different domain structures.

Electrical actuation is investigated in two kinds of chiral smectic liquid-crystal elastomers (LCEs) with different domain structures LCE1 and LCE2: The latter is better than the former in orientational order. Tracking fluorescent beads dispersed on the samples enables us to measure the two-dimensional strain tensors in ferroelectric elastomer films. It turns out that the electric-field-induced strain is polarity dependent and the type of molecular orientation responsible for the strain is specified. In LCE1 the shear strain is dominant, whereas in LCE2 it is comparable to the elongation strain, which is explained by the rotation of the principal axes. The essential differences of the two elastomers are observed in the eigenvalues of the strain tensors. The absolute values for LCE1 are larger than those for LCE2. The difference is discussed on the basis of the domain structures.

Dynamical properties of nematic liquid crystals subjected to shear flow and magnetic fields: tumbling instability and nonequilibrium fluctuations.

We investigate the dynamical properties of monodomain nematic liquid crystals under shear flow and magnetic fields on the basis of the Ericksen-Leslie theory. Stable and unstable states appear depending on the magnetic field and the shear rate. The trajectory of the unstable state shows tumbling motion. The phase diagram of these states is plotted as a function of the three components of the magnetic field at a constant shear rate. The phase diagram changes depending on the viscous properties of different types of nematic liquid crystals. In this nonequilibrium steady state, we calculate the correlation function of director fluctuations and the response function, and discuss the nonequilibrium fluctuations and the modified fluctuation-dissipation relation in connection with nonconservative forces due to shear flow.

Apparent viscosity of p-methoxybenzylidene-p'-n-butylaniline in the presence of electrohydrodynamic convection.

The apparent shear viscosity of p-methoxybenzylidene-p'-n-butylaniline in the presence of electrohydrodynamic convection (EHC) is investigated experimentally. In the absence of an electric field, directors are almost aligned along the flow direction such that the viscosity is close to the minimum of the Miesowicz viscosities. Since EHC disturbs the flow-aligned director configuration, the viscosity increases as the applied voltage is increased in the low-voltage regime. In the high-voltage regime, however, further increasing the voltage leads to a decrease in viscosity. Microscope observations using a rheometer reveal that the decrease in viscosity occurs in the dynamic scattering mode 2 (DSM2) state, whose spatial director distribution is anisotropic due to the shear flow. By adopting the Ericksen-Leslie theory for the shear flow under the electric field, we find that the viscosity decrease can be attributed to the negative contribution of the electric stress caused by the anisotropic director distribution of the DSM2 state.

Persistence of Brownian motion in a shear flow.

The persistence of a Brownian particle in a shear flow is investigated. The persistence probability P(t), which is the probability that the particle does not return to its initial position up to time t, is known to obey a power law P(t)∝t(-θ). Since the displacement of a particle along the flow direction due to convection is much larger than that due to Brownian motion, we define an alternative displacement in which the convection effect is removed. We derive theoretically the two-time correlation function and the persistence exponent θ of this displacement. The exponent has different values at short and long times. The theoretical results are compared with experiment and a good agreement is found.

Influence of shear flow on the linear response of a nematic liquid crystal to external electric fields.

We have investigated the linear response of shear stress to ac electric fields under shear flow in a nematic liquid crystal. The experimental results were compared with the theoretical results derived from the Ericksen-Leslie theory. Although close agreement was obtained at low shear rates, discrepancies were observed at high shear rates. By introducing a two-mode coupling model the experimental results were well reproduced for the entire range of shear rates, and nonconservative forces were found to play an important role in determining the fluctuation dynamics, which is a characteristic of nonequilibrium steady states.

Shear banding in an F-actin solution.

We report herein the first evidence that an F-actin solution shows shear banding, which is characterized by the spontaneous separation of homogeneous shear flow into two macroscopic domains of different definite shear rates. The constant shear stress observed in the F-actin solution is explained by the banded flow with volume fractions that obey the lever rule. Nonhomogenous reversible flows were observed in the F-actin solution with respect to upward and downward changes in the shear rate. This is the first time shear banding has been observed in a simple biomacromolecule. The biological implications and dynamic aspects of shear flow velocity characteristic patterns are discussed.

Measurement of electrically induced shear strain in a chiral smectic liquid-crystal elastomer.

The mechanical response to electrical stimulation was investigated in a chiral smectic elastomer. The two-dimensional strain tensor in an elastomer film was precisely measured by tracking fluorescent beads dispersed on the film. Shear deformation in the film was clearly observed when an electric field was applied perpendicular to the film surface. The temperature dependence of the strain tensor was also investigated, and the origin of the electric-field-induced shear strain in the chiral smectic-C phase was mainly attributed to the Nambu-Goldstone mode.