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.

Control of active turbulence through addressable soft interfaces.

We present an experimental study of a kinesin/tubulin active nematic formed at different oil interfaces. By tuning the interfacial rheology of the contacting oil, we have been able to condition and control the seemingly chaotic motion that characterizes the self-sustained active flows in our preparations. The active nematic is inherently unstable and spontaneously develops defects from an initial homogeneous state. We show that the steady state and, in particular, the density and dynamics of the defects strongly depends on the rheology of the contacting oil. Using a smectic-A thermotropic liquid crystal as the oil phase, we pattern the interface thanks to the anisotropy of the shear viscosity in this material. The geometry of the active nematic adapts to the boundary conditions at the interface by changing from the so-called active turbulent regime to laminar flows along the easy flow directions. The latter can be either a lattice of self-assembled circular paths or reconfigurable homogeneous orientations that can be addressed by means of an external magnetic field. We show that, under all confinement conditions, the spatiotemporal modes exhibited by the active liquid are consistent with a single intrinsic length scale, which can be tuned by the material parameters, and obey basic topological requirements imposed on the defects that drive the active flows. Future control strategies, including a tunable depleting agent, are discussed.

Taming active turbulence with patterned soft interfaces.

Active matter embraces systems that self-organize at different length and time scales, often exhibiting turbulent flows apparently deprived of spatiotemporal coherence. Here, we use a layer of a tubulin-based active gel to demonstrate that the geometry of active flows is determined by a single length scale, which we reveal in the exponential distribution of vortex sizes of active turbulence. Our experiments demonstrate that the same length scale reemerges as a cutoff for a scale-free power law distribution of swirling laminar flows when the material evolves in contact with a lattice of circular domains. The observed prevalence of this active length scale can be understood by considering the role of the topological defects that form during the spontaneous folding of microtubule bundles. These results demonstrate an unexpected strategy for active systems to adapt to external stimuli, and provide with a handle to probe the existence of intrinsic length and time scales.Active nematics consist of self-driven components that develop orientational order and turbulent flow. Here Guillamat et al. investigate an active nematic constrained in a quasi-2D geometrical setup and show that there exists an intrinsic length scale that determines the geometry in all forcing regimes.

Helical sense selective domains and enantiomeric superhelices generated by Langmuir-Schaefer deposition of an axially racemic chiral helical polymer.

The chiral polymer poly-(R)-1 behaves in solution, despite its chiral pendants, as a dynamic axially racemic (i.e., 1 : 1) mixture of left- and right-handed helices, but its deposition on graphite by a Langmuir-Schaefer (LS) technique leads to a helical sense-selective packing that forms separate enantiomeric domains of left- and right-handed helical chains observed by high resolution atomic force microscopy (AFM). The polymer structure within these domains is very uniform, seldom altered by the presence of reversals, grouped always in contiguous pairs maintaining a single helical sense along the polymer chain. The LS deposition technique has been shown to be crucial to obtain good quality monolayers from poly-(R)-1 and other poly(phenylacetylene)s (PPAs: poly-2, poly-3 and poly-4) with short pendants, where spin coating, drop casting and Langmuir-Blodgett (LB) failed, and suggests that this technique could be the method of choice for the preparation of 2D monolayers for high resolution AFM studies of PPAs with short pendants. Key helical parameters (i.e., sense, pitch, packing angle) are easily measured in this way.

Thermodynamics and mesoscopic organisation in Langmuir monolayers of an azobenzene derivative.

We have carried out the analysis of liquid crystalline Langmuir monolayers at the air-water interface composed of the amphiphilic azobenzene derivative 8Az5COOH. By varying the temperature and the isomeric (trans-cis) composition, the monolayer behaviour has been studied in comparison with a shorter homologue, 8Az3COOH, by measuring the surface pressure-area isotherms along with Brewster angle microscopy (BAM). Our data with the pure trans isomer enable a posterior thermodynamic analysis, which was not feasible with the shorter homologue. For the mixed trans-cis monolayers, BAM observations reveal a phase segregation with trans enriched domains surrounded by a cis enriched matrix. Line tension between the two phases is lower than in the shorter homologue. The organisation of the rodlike molecules inside the trans domains results in highly symmetric textures that make the quantitative analysis of the BAM images possible, and a better understanding of the microscopic structure of the monolayer can be achieved.

Dynamics of point defects and stripe textures in Smectic-C Langmuir monolayers.

Langmuir monolayers of an azobenzene fatty acid derivative have been studied experimentally in a regime where confined domains with Smectic-C order form spontaneously. Coalescence of domains results in a dynamics of formation and annihilation of point defects and string-like distortions of the molecular field amenable to semi-quantitative analysis. Absence of backflow and layer thickness effects enables us to extract values for material parameters from the analysis of defect dynamics.

Travelling waves in two-dimensional smectic-C domains.

Continued irradiation of smectic-C-like domains of photosensitive Langmuir monolayers from azobenzene derivatives induces the nucleation and propagation of orientational travelling waves as observed with Brewster angle microscopy (BAM). BAM image analysis has allowed to identify different dynamical behaviors involving the generation and propagation of such waves. A model based on the coupling between an orientational and a composition field proposes a scenario for dynamic self-assembly that accounts for most of the observed phenomena, and allows to pinpoint the relevance of boundary defects in wave-emitting structures.-1.

Orientational structures in confined smectic-C domains in Langmuir monolayers.

Droplet smectic-C domains in films of surfactant molecules exhibit different orientational textures. For these systems we formulate a kinetic model based on a free energy functional containing bulk (elastic) and surface interactions. Numerical simulations for the corresponding relaxational equation show the existence of two different equilibrium configurations with a centered defect. In particular, when the elastic terms dominate, bend-shaped textures appear, whereas for strong boundary effects mixed bend/splay conformations are displayed. A variational analysis for the free energy functional confirms the validity of the above numerical results. The stability of textures with centered defects with respect to the formation of periferic defects (boojums) is also discussed qualitatively. The above theoretical predictions are compared with experimental results from Brewster angle microscopy imaging of azobenzene Langmuir monolayers.

Controlled nucleation of point defects on a disclination line near a free surface during smectic-A-to-nematic directional melting.

A disclination line populated with point defects that break the translational symmetry forms near a free nematic (N) interface in a confined geometry. The disclination line is, however, absent in the smectic-A phase (SmA). We use this fact to control the formation of point defect distributions on a disclination line by directional melting of the SmA phase in a temperature gradient. A threshold velocity ( v(th)) exists below which a defect-free disclination line is formed. The frequency of nucleation of point defects increases steadily for v > v(th) and exhibits a remarkable regularity. We derive an empirical scaling for v(th) in terms of the experimental tuning parameters. We propose a simple model that allows to understand the formation of the point defects.

Formation and distribution of point defects on a disclination line near a free nematic interface.

Point defects of opposite signs can alternately nucleate on the -1/2 disclination line that forms near the free surface of a confined nematic liquid crystal. We show the existence of metastable configurations consisting of periodic repetitions of such defects. These configurations are characterized by a minimal interdefect spacing that is seen to depend on sample thickness and on an applied electric field. The time evolution of the defect distribution suggests that the defects attract at small distances and repel at large distances.

Shear-induced molecular precession in a hexatic Langmuir monolayer.

Liquid crystalline behaviour is generally limited to a select group of specially designed bulk substances. By contrast, it is a common feature of simple molecular monolayers and other quasi-two-dimensional systems, which often possess a type of in-plane ordering that results from unbinding of dislocations-a 'hexatic' liquid crystalline phase. The flow of monolayers is closely related to molecular transport in biological membranes, affects foam and emulsion stability and is relevant to microfluidics research. For liquid crystalline phases, it is important to understand the coupling of the molecular orientation to the flow. Orientationally ordered (nematic) phases in bulk liquid crystals exhibit 'shear aligning' or 'tumbling' behaviour under shear, and are described quantitatively by Leslie-Ericksen theory. For hexatic monolayers, the effects of flow have been inferred from textures of Langmuir-Blodgett films and directly observed at the macroscopic level. However, there is no accepted model of hexatic flow at the molecular level. Here we report observations of a hexatic Langmuir monolayer that reveal continuous, shear-induced molecular precession, interrupted by occasional jump discontinuities. Although superficially similar to tumbling in a bulk nematic phase, the kinematic details are quite different and provide a possible mechanism for domain coarsening and eventual molecular alignment in monolayers. We explain the precession and jumps within a quantitative framework that involves coupling of molecular orientation to the local molecular hexatic 'lattice', which is continuously deformed by shear.

Growth and melting of the nematic phase: sample thickness dependence of the mullins-sekerka instability

In this article we report our systematic studies of the dependence on the sample thickness of the onset parameters of the instability of the nematic-isotropic interface during directional growth and melting, in homeotropic or planar anchoring.

Alignment of hexatic langmuir monolayers under shear.

We have studied the structural changes that fatty acid monolayers in the Ov phase undergo when a simple shear flow is imposed. A strong coupling is revealed by the changes in domain structure that are observable using Brewster angle microscopy, suggesting the possibility of shear alignment. The dependence of the alignment on the molecular polar tilt proves that the mechanism is different than in nematic liquid crystals. We argue that the degenerate lattice symmetry lines of the underlying pseudohexagonal lattice align in the flow direction, and we explain the observed alignment angle using geometrical arguments.

Effect of lattice defects on Hele-Shaw flow over an etched lattice.

We examine the patterns formed by injecting nitrogen gas into the center of a horizontal, radial Hele-Shaw cell filled with paraffin oil. We use smooth plates and etched plates with lattices having different amounts of defects (0-10 %). In all cases, a quantitative measure of the pattern ramification shows a regular trend with injection rate and cell gap, such that the dimensionless perimeter scales with the dimensionless time. By adding defects to the lattice, we observe increased branching in the pattern morphologies. However, even in this case, the scaling behavior persists. Only the prefactor of the scaling function shows a dependence on the defect density. For different lattice defect densities, we examine the nature of the different morphology phases.

Velocity-jump instabilities in Hele-Shaw flow of associating polymer solutions.

We study fracturelike flow instabilities that arise when water is injected into a Hele-Shaw cell filled with aqueous solutions of associating polymers. We explore various polymer architectures, molecular weights, and solution concentrations. Simultaneous measurements of the finger tip velocity and of the pressure at the injection point allow us to describe the dynamics of the finger in terms of the "finger mobility," which relates the velocity to the pressure gradient. The flow discontinuities, characterized by jumps in the finger tip velocity, which are observed in experiments with some of the polymer solutions, can be modeled by using a nonmonotonic dependence between a characteristic shear stress and the shear rate at the tip of the finger. A simple model, which is based on a viscosity function containing both a Newtonian and a non-Newtonian component, and which predicts nonmonotonic regions when the non-Newtonian component of the viscosity dominates, is shown to agree with the experimental data.