Author Correction: Molecular heterogeneity drives reconfigurable nematic liquid crystal drops.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Molecular heterogeneity drives reconfigurable nematic liquid crystal drops.

With few exceptions1-3, polydispersity or molecular heterogeneity in matter tends to impede self-assembly and state transformation. For example, shape transformations of liquid droplets with monodisperse ingredients have been reported in equilibrium4-7 and non-equilibrium studies8,9, and these transition phenomena were understood on the basis of homogeneous material responses. Here, by contrast, we study equilibrium suspensions of drops composed of polydisperse nematic liquid crystal oligomers (NLCOs). Surprisingly, molecular heterogeneity in the polydisperse drops promotes reversible shape transitions to a rich variety of non-spherical morphologies with unique internal structure. We find that variation of oligomer chain length distribution, temperature, and surfactant concentration alters the balance between NLCO elastic energy and interfacial energy, and drives formation of nematic structures that range from roughened spheres to 'flower' shapes to branched filamentous networks with controllable diameters. The branched structures with confined liquid crystal director fields can be produced reversibly over areas of at least one square centimetre and can be converted into liquid crystal elastomers by ultraviolet curing. Observations and modelling reveal that chain length polydispersity plays a crucial role in driving these morphogenic phenomena, via spatial segregation. This insight suggests new routes for encoding network structure and function in soft materials.

Depletion-driven antiferromagnetic, paramagnetic, and ferromagnetic behavior in quasi-two-dimensional buckled colloidal solids.

We investigate quasi-two-dimensional buckled colloidal monolayers on a triangular lattice with tunable depletion interactions. Without depletion attraction, the experimental system provides a colloidal analog of the well-known geometrically frustrated Ising antiferromagnet [Y. Han et al., Nature 456, 898-903 (2008)]. In this contribution, we show that the added depletion attraction can influence both the magnitude and sign of an Ising spin coupling constant. As a result, the nearest-neighbor Ising "spin" interactions can be made to vary from antiferromagnetic to para- and ferromagnetic. Using a simple theory, we compute an effective Ising nearest-neighbor coupling constant, and we show how competition between entropic effects permits for the modification of the coupling constant. We then experimentally demonstrate depletion-induced modification of the coupling constant, including its sign, and other behaviors. Depletion interactions are induced by rod-like surfactant micelles that change length with temperature and thus offer means for tuning the depletion attraction in situ. Buckled colloidal suspensions exhibit a crossover from an Ising antiferromagnetic to paramagnetic phase as a function of increasing depletion attraction. Additional dynamical experiments reveal structural arrest in various regimes of the coupling-constant, driven by different mechanisms. In total, this work introduces novel colloidal matter with "magnetic" features and complex dynamics rarely observed in traditional spin systems.

Shear-assisted grain coarsening in colloidal polycrystals.

Grain growth under shear annealing is crucial for controlling the properties of polycrystalline materials. However, their microscopic kinetics are not well understood because individual atomic trajectories are difficult to track. Here, we study grain growth with single-particle kinetics in colloidal polycrystals using video microscopy. Rich grain-growth phenomena are revealed in three shear regimes, including the normal grain growth (NGG) in weak shear melting-recrystallization process in strong shear. For intermediate shear, early stage NGG is arrested by built-up stress and eventually gives way to dynamic abnormal grain growth (DAGG). We find that DAGG occurs via a melting-recrystallization process, which naturally explains the puzzling stress drop at the onset of DAGG in metals. Moreover, we visualize that grain boundary (GB) migration is coupled with shear via disconnection gliding. The disconnection-gliding dynamics and the collective motions of ambient particles are resolved. We also observed that grain rotation can violate the conventional relation [Formula: see text] (R is the grain radius, and θ is the misorientation angle between two grains) by emission and annihilation of dislocations across the grain, resulting in a step-by-step rotation. Besides grain growth, we discover a result in shear-induced melting: The melting volume fraction varies sinusoidally on the angle mismatch between the triangular lattice orientation of the grain and the shear direction. These discoveries hold potential to inform microstructure engineering of polycrystalline materials.

Focal conic flowers, dislocation rings, and undulation textures in smectic liquid crystal Janus droplets.

Liquid crystalline phases of matter often exhibit visually stunning patterns or textures. Mostly, these liquid crystal (LC) configurations are uniquely determined by bulk LC elasticity, surface anchoring conditions, and confinement geometry. Here, we experimentally explore defect textures of the smectic LC phase in unique confining geometries with variable curvature. We show that a complex range of director configurations can arise from a single system, depending on sample processing procedures. Specifically, we report on LC textures in Janus drops comprised of silicone oil and 8CB in its smectic-A LC phase. The Janus droplets were made in aqueous suspension using solvent-induced phase separation. After drop creation, smectic layers form in the LC compartment, but their self-assembly is frustrated by the need to accommodate both the bowl-shaped cavity geometry and homeotropic (perpendicular) anchoring conditions at boundaries. A variety of stable and metastable smectic textures arise, including focal conic domains, dislocation rings, and undulations. We experimentally characterize their stabilities and follow their spatiotemporal evolution. Overall, a range of fabrication kinetics produce very different intermediate and final states. The observations elucidate assembly mechanisms and suggest new routes for fabrication of complex soft material structures in Janus drops and other confinement geometries.

Rods in a lyotropic chromonic liquid crystal: emergence of chirality, symmetry-breaking alignment, and caged angular diffusion.

In lyotropic chromonic liquid crystals (LCLCs), twist distortion of the nematic director costs much less energy than splay or bend distortion. This feature leads to novel mirror-symmetry breaking director configurations when the LCLCs are confined by interfaces or contain suspended particles. Spherical colloids in an aligned LCLC nematic phase, for example, induce chiral director perturbations ("twisted tails"). The asymmetry of rod-like particles in an aligned LCLC offer a richer set of possibilities due to their aspect ratio (α) and mean orientation angle (〈θ〉) between their long axis and the uniform far-field director. Here we report on the director configuration, equilibrium orientation, and angular diffusion of rod-like particles with planar anchoring suspended in an aligned LCLC. Video microscopy reveals, counterintuitively, that two-thirds of the rods have an angled equilibrium orientation (〈θ〉 ≠ 0) that decreases with increasing α, while only one-third of the rods are aligned (〈θ〉 = 0). Polarized optical video-microscopy and Landau-de Gennes numerical modeling demonstrate that the angled and aligned rods are accompanied by distinct chiral director configurations. Angled rods have a longitudinal mirror plane (LMP) parallel to their long axis and approximately parallel to the substrate walls. Aligned rods have a transverse and longitudinal mirror plane (TLMP), where the transverse mirror plane is perpendicular to the rod's long axis. Effectively, the small twist elastic constant of LCLCs promotes chiral director configurations that modify the natural tendency of rods to orient along the far-field director. Additional diffusion experiments confirm that rods are angularly confined with strength that depends on α.

Structural and short-time vibrational properties of colloidal glasses and supercooled liquids in the vicinity of the re-entrant glass transition.

We investigate the short-time vibrational properties and structure of two-dimensional, bidisperse, colloidal glasses and supercooled liquids in the vicinity of the re-entrant glass transition, as a function of interparticle depletion attraction strength. The long-time spatiotemporal dynamics of the samples are measured to be non-monotonic, confirming that the suspensions evolve from repulsive glass to supercooled liquid to attractive glass with increasing depletion attraction. Here, we search for vibrational signatures of the re-entrant behavior in the short-time spatiotemporal dynamics, i.e., dynamics associated with particle motion inside its nearest-neighbor cage. Interestingly, we observe that the anharmonicity of these in-cage vibrations varies non-monotonically with increasing attraction strength, consistent with the non-monotonic long-time structural relaxation dynamics of the re-entrant glass. We also extract effective spring constants between neighboring particles; we find that spring stiffness involving small particles also varies non-monotonically with increasing attraction strength, while stiffness between large particles increases monotonically. Last, from study of depletion-dependent local structure and vibration participation fractions, we gain microscopic insight into the particle-size-dependent contributions to short-time vibrational modes in the glass and supercooled liquid states.

Heterogeneous Activation, Local Structure, and Softness in Supercooled Colloidal Liquids.

We experimentally characterize heterogeneous nonexponential relaxation in bidisperse supercooled colloidal liquids utilizing a recent concept called "softness" [Phys. Rev. Lett. 114, 108001 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.108001]. Particle trajectory and structure data enable classification of particles into subgroups with different local environments and propensities to hop. We determine residence times t_{R} between particle hops and show that t_{R} derived from particles in the same softness subgroup are exponentially distributed. Using the mean residence time t[over ¯]_{R} for each softness subgroup, and a Kramers' reaction rate model, we estimate the activation energy barriers E_{b} for particle hops, and show that both t[over ¯]_{R} and E_{b} are monotonic functions of softness. Finally, we derive information about the combinations of large and small particle neighbors that determine particle softness, and we explicitly show that multiple exponential relaxation channels in the supercooled liquid give rise to its nonexponential behavior.

Excess entropy and long-time diffusion in colloidal fluids with short-range interparticle attraction.

Liquid structure and dynamics are experimentally investigated in colloidal suspensions with short-range depletion attraction. The colloidal fluid samples consist of hard-sphere colloidal particles suspended along with rodlike depletants based on surfactant micelles. The spheres have a range of surface chemistries, diameters, and packing fractions, and the rodlike micelle length depends on the temperature. Thus, the combination of hard-spheres and depletants generates a sample wherein short-range interparticle attraction can be temperature-tuned in situ. Video optical microscopy and particle tracking techniques are employed to measure particle trajectories from which structural and dynamical quantities are derived, including the particle pair correlation function [g(r)], mean square displacement, long-time diffusion coefficient, and the sample two-body excess entropy (S2). The samples with stronger short-range attractions exhibit more order, as characterized by g(r) and S2. The stronger short-range attractions are also observed to lead to slower long-time diffusion and more heterogeneous dynamics at intermediate time scales. Finally, the excess entropy scaling law prediction, i.e., the exponential relationship between two-body excess entropy and long-time diffusivity, is observed across the full range of samples.

Brownian Dynamics of Particles "Dressed" by Chiral Director Configurations in Lyotropic Chromonic Liquid Crystals.

We study Brownian dynamics of colloidal spheres, with planar anchoring conditions, suspended in the nematic phase of the lyotropic chromonic liquid crystal disodium chromoglycate (DSCG). Unlike typical liquid crystals, the unusually small twist elastic modulus of DSCG permits two energetically distinct helical distortions (twisted tails) of the nematic director to "dress" the suspended spheres. Video microscopy is used to characterize the helical distortions versus particle size and to measure particle mean-square displacements. Diffusion coefficients parallel and perpendicular to the far-field director, and their anisotropy ratio, are different for the two twisted tail configurations. Moreover, the crossover from subdiffusive to diffusive behavior is anomalously slow for motion perpendicular to the director (>100 s). Simple arguments using Miesowicz viscosities and ideas about twist relaxation are suggested to understand the mean-square displacement observations.

Interaction anisotropy and the KPZ to KPZQ transition in particle deposition at the edges of drying drops.

The deposition process at the edge of evaporating colloidal drops varies with the shape of suspended particles. Experiments with prolate ellipsoidal particles suggest that the spatiotemporal properties of the deposit depend strongly on particle aspect ratio. As the aspect ratio increases, the particles form less densely-packed deposits and the statistical behavior of the deposit interface crosses over from the Kardar-Parisi-Zhang (KPZ) universality class to another universality class which was suggested to be consistent with the KPZ plus quenched disorder. Here, we numerically study the effect of particle interaction anisotropy on deposit growth. In essence, we model the ellipsoids, at the interface, as disk-like particles with two types of interaction patches that correspond to specific features at the poles and equator of the ellipsoid. The numerical results corroborate experimental observations and further suggest that the deposition transition can stem from interparticle interaction anisotropy. Possible extensions of our model to other systems are also discussed.

Chiral structures from achiral liquid crystals in cylindrical capillaries.

We study chiral symmetry-broken configurations of nematic liquid crystals (LCs) confined to cylindrical capillaries with homeotropic anchoring on the cylinder walls (i.e., perpendicular surface alignment). Interestingly, achiral nematic LCs with comparatively small twist elastic moduli relieve bend and splay deformations by introducing twist deformations. In the resulting twisted and escaped radial (TER) configuration, LC directors are parallel to the cylindrical axis near the center, but to attain radial orientation near the capillary wall, they escape along the radius through bend and twist distortions. Chiral symmetry-breaking experiments in polymer-coated capillaries are carried out using Sunset Yellow FCF, a lyotropic chromonic LC with a small twist elastic constant. Its director configurations are investigated by polarized optical microscopy and explained theoretically with numerical calculations. A rich phenomenology of defects also arises from the degenerate bend/twist deformations of the TER configuration, including a nonsingular domain wall separating domains of opposite twist handedness but the same escape direction and singular point defects (hedgehogs) separating domains of opposite escape direction. We show the energetic preference for singular defects separating domains of opposite twist handedness compared with those of the same handedness, and we report remarkable chiral configurations with a double helix of disclination lines along the cylindrical axis. These findings show archetypally how simple boundary conditions and elastic anisotropy of confined materials lead to multiple symmetry breaking and how these broken symmetries combine to create a variety of defects.

Topography-guided buckling of swollen polymer bilayer films into three-dimensional structures.

Thin films that exhibit spatially heterogeneous swelling often buckle into the third dimension to minimize stress. These effects, in turn, offer a promising strategy to fabricate complex three-dimensional structures from two-dimensional sheets. Here we employ surface topography as a new means to guide buckling of swollen polymer bilayer films and thereby control the morphology of resulting three-dimensional objects. Topographic patterns are created on poly(dimethylsiloxane) (PDMS) films selectively coated with a thin layer of non-swelling parylene on different sides of the patterned films. After swelling in an organic solvent, various structures are formed, including half-pipes, helical tubules, and ribbons. We demonstrate these effects and introduce a simple geometric model that qualitatively captures the relationship between surface topography and the resulting swollen film morphologies. The model's limitations are also examined.

Suppression of the coffee-ring effect by shape-dependent capillary interactions.

When a drop of liquid dries on a solid surface, its suspended particulate matter is deposited in ring-like fashion. This phenomenon, known as the coffee-ring effect, is familiar to anyone who has observed a drop of coffee dry. During the drying process, drop edges become pinned to the substrate, and capillary flow outward from the centre of the drop brings suspended particles to the edge as evaporation proceeds. After evaporation, suspended particles are left highly concentrated along the original drop edge. The coffee-ring effect is manifested in systems with diverse constituents, ranging from large colloids to nanoparticles and individual molecules. In fact--despite the many practical applications for uniform coatings in printing, biology and complex assembly-the ubiquitous nature of the effect has made it difficult to avoid. Here we show experimentally that the shape of the suspended particles is important and can be used to eliminate the coffee-ring effect: ellipsoidal particles are deposited uniformly during evaporation. The anisotropic shape of the particles significantly deforms interfaces, producing strong interparticle capillary interactions. Thus, after the ellipsoids are carried to the air-water interface by the same outward flow that causes the coffee-ring effect for spheres, strong long-ranged interparticle attractions between ellipsoids lead to the formation of loosely packed or arrested structures on the air-water interface. These structures prevent the suspended particles from reaching the drop edge and ensure uniform deposition. Interestingly, under appropriate conditions, suspensions of spheres mixed with a small number of ellipsoids also produce uniform deposition. Thus, particle shape provides a convenient parameter to control the deposition of particles, without modification of particle or solvent chemistry.

Chiral symmetry breaking and surface faceting in chromonic liquid crystal droplets with giant elastic anisotropy.

Confined liquid crystals (LC) provide a unique platform for technological applications and for the study of LC properties, such as bulk elasticity, surface anchoring, and topological defects. In this work, lyotropic chromonic liquid crystals (LCLCs) are confined in spherical droplets, and their director configurations are investigated as a function of mesogen concentration using bright-field and polarized optical microscopy. Because of the unusually small twist elastic modulus of the nematic phase of LCLCs, droplets of this phase exhibit a twisted bipolar configuration with remarkably large chiral symmetry breaking. Further, the hexagonal ordering of columns and the resultant strong suppression of twist and splay but not bend deformation in the columnar phase, cause droplets of this phase to adopt a concentric director configuration around a central bend disclination line and, at sufficiently high mesogen concentration, to exhibit surface faceting. Observations of director configurations are consistent with Jones matrix calculations and are understood theoretically to be a result of the giant elastic anisotropy of LCLCs.

Dynamics of ordered colloidal particle monolayers at nematic liquid crystal interfaces.

We prepare two-dimensional crystalline packings of colloidal particles on surfaces of the nematic liquid crystal (NLC) 5CB, and we investigate the diffusion and vibrational phonon modes of these particles using video microscopy. Short-time particle diffusion at the air-NLC interface is well described by a Stokes-Einstein model with viscosity similar to that of 5CB. Crystal phonon modes, measured by particle displacement covariance techniques, are demonstrated to depend on the elastic constants of 5CB through interparticle forces produced by LC defects that extend from the interface into the underlying bulk material. The displacement correlations permit characterization of transverse and longitudinal sound velocities of the crystal packings, as well as the particle interactions produced by the LC defects. All behaviors are studied in the nematic phase as a function of increasing temperature up to the nematic-isotropic transition.

Tunable capillary-induced attraction between vertical cylinders.

Deformation of a fluid interface caused by the presence of objects at the interface can lead to large lateral forces between objects. We explore these fluid-mediated attractive force between partially submerged vertical cylinders. Forces are experimentally measured by slowly separating cylinder pairs and cylinder triplets after capillary rise is initially established for cylinders in contact. For cylinder pairs, numerical computations and a theoretical model are found to be in good agreement with measurements. The model provides insight into the relative importance of the contributions to the total force. For small separations, the lateral force is dominated by the fluid pressure acting over the wetted cylinder surfaces. At large separations, the surface tension acting along the contact line dominates the lateral force. A crossover between the two regimes occurs at a separation of around half of a capillary length. The experimentally measured forces between cylinder triplets are also in good agreement with numerical computations, and we show that pairwise contributions account for nearly all of the attractive force between triplets. For cylinders with an equilibrium capillary rise height greater than the height of the cylinder, we find that the attractive force depends on the height of the cylinders above the submersion level, which provides a means to create precisely controlled tunable cohesive forces between objects deforming a fluid interface.

Liquid crystal Janus emulsion droplets: preparation, tumbling, and swimming.

This study introduces liquid crystal (LC) Janus droplets. We describe a process for the preparation of these droplets, which consist of nematic LC and polymer compartments. The process employs solvent-induced phase separation in emulsion droplets generated by microfluidics. The droplet morphology was systematically investigated and demonstrated to be sensitive to the surfactant concentration in the background phase, the compartment volume ratio, and the possible coalescence of multiple Janus droplets. Interestingly, the combination of a polymer and an anisotropic LC introduces new functionalities into Janus droplets, and these properties lead to unusual dynamical behaviors. The different densities and solubilities of the two compartments produce gravity-induced alignment, tumbling, and directional self-propelled motion of Janus droplets. LC Janus droplets with remarkable optical properties and dynamical behaviors thus offer new avenues for applications of Janus colloids and active soft matter.

Physics in ordered and disordered colloidal matter composed of poly(N-isopropylacrylamide) microgel particles.

This review collects and describes experiments that employ colloidal suspensions to probe physics in ordered and disordered solids and related complex fluids. The unifying feature of this body of work is its clever usage of poly(N-isopropylacrylamide) (PNIPAM) microgel particles. These temperature-sensitive colloidal particles provide experimenters with a 'knob' for in situ control of particle size, particle interaction and particle packing fraction that, in turn, influence the structural and dynamical behavior of the complex fluids and solids. A brief summary of PNIPAM particle synthesis and properties is given, followed by a synopsis of current activity in the field. The latter discussion describes a variety of soft matter investigations including those that explore formation and melting of crystals and clusters, and those that probe structure, rearrangement and rheology of disordered (jammed/glassy) and partially ordered matter. The review, therefore, provides a snapshot of a broad range of physics phenomenology which benefits from the unique properties of responsive microgel particles.

Rheology of soft colloids across the onset of rigidity: scaling behavior, thermal, and non-thermal responses.

We study the rheological behavior of colloidal suspensions composed of soft sub-micron-size hydrogel particles across the liquid-solid transition. The measured stress and strain-rate data, when normalized by thermal stress and time scales, suggest our systems reside in a regime wherein thermal effects are important. In a different vein, critical point scaling predictions for the jamming transition, typical in athermal systems, are tested. Near dynamic arrest, the suspensions exhibit scaling exponents similar to those reported in Nordstrom et al., Phys. Rev. Lett., 2010, 105, 175701. The observation suggests that our system exhibits a glass transition near the onset of rigidity, but it also exhibits a jamming-like scaling further from the transition point. These observations are thought-provoking in light of recent theoretical and simulation findings, which show that suspension rheology across the full range of microgel particle experiments can exhibit both thermal and athermal mechanisms.