Magnetic-field-driven director configuration transitions in radial nematic liquid crystal droplets.

We study the director configurations of nematic liquid crystal (NLC) droplets with homeotropic anchoring in a magnetic field and report observation of a magnetic-field-driven transition from a deformed radial to an axial-with-defect configuration. Magnetic-field-induced transitions in NLC droplets differ fundamentally from the traditional planar Freedericksz transition due to the spherical droplet geometry and resulting topological defect. This transition has been studied theoretically, but the director configurations and mechanism of defect evolution in an applied magnetic field have yet to be observed experimentally. To this end, we combine polarized optical microscopy with a variable electromagnet (≤1 T) for continuous observation of droplet director fields, and we employ Landau-de Gennes numerical simulations to elucidate the director configurations and first-order nature of the transition. We report a configuration transition from point defect to ring defect at a critical field, which varies inversely with droplet radius and is relatively independent of surfactant type and concentration. We also estimate anchoring strengths of commonly used surfactants at the NLC-aqueous interface.

Direction-dependent dynamics of colloidal particle pairs and the Stokes-Einstein relation in quasi-two-dimensional fluids.

Hydrodynamic interactions are important for diverse fluids, especially those with low Reynolds number such as microbial and particle-laden suspensions, and proteins diffusing in membranes. Unfortunately, while far-field (asymptotic) hydrodynamic interactions are fully understood in two- and three-dimensions, near-field interactions are not, and thus our understanding of motions in dense fluid suspensions is still lacking. In this contribution, we experimentally explore the hydrodynamic correlations between particles in quasi-two-dimensional colloidal fluids in the near-field. Surprisingly, the measured displacement and relaxation of particle pairs in the body frame exhibit direction-dependent dynamics that can be connected quantitatively to the measured near-field hydrodynamic interactions. These findings, in turn, suggest a mechanism for how and when hydrodynamics can lead to a breakdown of the ubiquitous Stokes-Einstein relation (SER). We observe this breakdown, and we show that the direction-dependent breakdown of the SER is ameliorated along directions where hydrodynamic correlations are smallest. In total, the work uncovers significant ramifications of near-field hydrodynamics on transport and dynamic restructuring of fluids in two-dimensions.

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.

Ratchetlike motion of helical bilayers induced by boundary constraints.

We show that application of boundary constraints generates unusual folding behaviors in responsive (swellable) helical bilayer strips. Unlike the smooth folding trajectories typical of free helical bilayers, the boundary-constrained bilayers exhibit intermittent folding behaviors characterized by rapid, steplike movements. We experimentally study bilayer strips as they swell and fold, and we propose a simple model to explain the emergence of ratchetlike behavior. Experiments and model predictions are then compared to simulations, which enable calculation of elastic energy during swelling. We investigate the dependence of this steplike behavior as a function of elastic boundary condition strength, strip length, and strip shape; interestingly, "V-shape" strips with the same boundary conditions fold smoothly.

Giant director fluctuations in liquid crystal drops.

We report the discovery and elucidation of giant spatiotemporal orientational fluctuations in nematic liquid crystal drops with radial orientation of the nematic anisotropy axis producing a central "hedgehog" defect. We study the spatial and temporal properties of the fluctuations experimentally using polarized optical microscopy, and theoretically, by calculating the eigenspectrum of the Frank elastic free energy of a nematic drop of radius R_{2}, containing a spherical central core of radius R_{1} and constrained by perpendicular boundary conditions on all surfaces. We find that the hedgehog defect with radial orientation has a complex excitation spectrum with a single critical mode whose energy vanishes at a critical value µ_{c} of the ratio µ=R_{2}/R_{1}. When µ<µ_{c}, the mode has positive energy, indicating that the radial hedgehog state is stable; when µ>µ_{c}, it has negative energy indicating that the radial state is unstable to the formation of a lower-energy state. This mode gives rise to the large-amplitude director fluctuations we observe near the core, for µ near µ_{c}. A collapse of the experimental data corroborates model predictions for µ<µ_{c} and provides an estimate of the defect core size.

Theory of director fluctuations about a hedgehog defect in a nematic drop.

We present calculations of eigenmode energies and wave functions of both azimuthal and polar distortions of the nematic director relative to a radial hedgehog trapped in a spherical drop with a smaller concentric spherical droplet at its core. All surfaces interior to the drop have perpendicular (homeotropic) boundary conditions. We also calculate director correlation functions and their relaxation times. Of particular interest is a critical mode whose energy, with fixed Frank constants, vanishes as the ratio µ=R_{2}/R_{1} increases toward a critical value µ_{c}, where R_{2} is the radius of the drop and R_{1} that of the inner droplet, and then becomes negative for µ>µ_{c}. Our calculations form a basis for interpreting experimental measurements of director fluctuations relative to a radial hedgehog state in a spherical drop. We compare results with those obtained by previous investigations, which use a calculational approach different from ours, and with our experimental observations.

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.

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.

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.

Highly conductive and transparent coatings from flow-aligned silver nanowires with large electrical and optical anisotropy.

Conductive and transparent coatings consisting of silver nanowires (AgNWs) are promising candidates for emerging flexible electronics applications. Coatings of aligned AgNWs offer unusual electronic and optical anisotropies, with potential for use in micro-circuits, antennas, and polarization sensors. Here we explore a microfluidics setup and flow-induced alignment mechanisms to create centimeter-scale highly conductive coatings of aligned AgNWs with order parameters reaching 0.84, leading to large electrical and optical anisotropies. By varying flow rates, we establish the relationship between the shear rate and the alignment and investigate possible alignment mechanisms. The angle-dependent sheet resistance of the aligned AgNW networks exhibits an electronic transport anisotropy of ∼10× while maintaining low resistivity (<50 Ω sq-1) in all directions. When illuminated, the aligned AgNW coatings exhibit angle- and polarization-dependent colors, and the polarized reflection anisotropy can be as large as 25. This large optical anisotropy is due to a combination of alignment, polarization response, and angle-dependent scattering of the aligned AgNWs.

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.

Correlations between short- and long-time relaxation in colloidal supercooled liquids and glasses.

Spatiotemporal dynamics of short- and long-time structural relaxation are measured experimentally as a function of packing fraction, ϕ, in quasi-two-dimensional colloidal supercooled liquids and glasses. The relaxation times associated with long-time dynamic heterogeneity and short-time intracage motion are found to be strongly correlated and to grow by orders of magnitude with increasing ϕ toward dynamic arrest. We find that clusters of fast particles on the two timescales often overlap, and, interestingly, the distribution of minimum-spatial-separation between closest nonoverlapping clusters across the two timescales is revealed to be exponential with a decay length that increases with ϕ. In total, the experimental observations suggest short-time relaxation events are very often precursors to heterogeneous relaxation at longer timescales in glassy materials.

Dynamic Heterogeneities in Colloidal Supercooled Liquids: Experimental Tests of Inhomogeneous Mode Coupling Theory.

The dynamics in supercooled liquids slow enormously upon approaching the glass transition, albeit without significant change of liquid structure. This empirical observation has stimulated development of many theoretical models which attempt to elucidate microscopic mechanisms in glasses and glass precursors. Here, quasi-two-dimensional colloidal supercooled liquids and glasses are employed to experimentally test predictions of widely used models: mode coupling theory (MCT) and its important extension, inhomogeneous MCT (IMCT). We measure two-point dynamic correlation functions in the glass forming liquids to determine structural relaxation times, τα, and mode coupling exponents, a, b, and γ; these parameters are then used to extract the mode coupling dynamic crossover packing area-fraction, ϕ c. This information, along with our measurements of supercooled liquid spatiotemporal dynamics, permits characterization of dynamic heterogeneities in the samples and facilitates direct experimental tests of the scaling predictions of IMCT. The time scales at which dynamic heterogeneities are largest, and their spatial sizes, exhibit power law growth on approaching ϕ c. Within experimental error, the exponents of the measured power laws are close to the predictions of IMCT.

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.

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.

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.

Structure-property relationships from universal signatures of plasticity in disordered solids.

When deformed beyond their elastic limits, crystalline solids flow plastically via particle rearrangements localized around structural defects. Disordered solids also flow, but without obvious structural defects. We link structure to plasticity in disordered solids via a microscopic structural quantity, "softness," designed by machine learning to be maximally predictive of rearrangements. Experimental results and computations enabled us to measure the spatial correlations and strain response of softness, as well as two measures of plasticity: the size of rearrangements and the yield strain. All four quantities maintained remarkable commonality in their values for disordered packings of objects ranging from atoms to grains, spanning seven orders of magnitude in diameter and 13 orders of magnitude in elastic modulus. These commonalities link the spatial correlations and strain response of softness to rearrangement size and yield strain, respectively.