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.

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.

Long-wavelength fluctuations and anomalous dynamics in 2-dimensional liquids.

In 2-dimensional systems at finite temperature, long-wavelength Mermin-Wagner fluctuations prevent the existence of translational long-range order. Their dynamical signature, which is the divergence of the vibrational amplitude with the system size, also affects disordered solids, and it washes out the transient solid-like response generally exhibited by liquids cooled below their melting temperatures. Through a combined numerical and experimental investigation, here we show that long-wavelength fluctuations are also relevant at high temperature, where the liquid dynamics do not reveal a transient solid-like response. In this regime, these fluctuations induce an unusual but ubiquitous decoupling between long-time diffusion coefficient D and structural relaxation time τ, where [Formula: see text], with [Formula: see text] Long-wavelength fluctuations have a negligible influence on the relaxation dynamics only at extremely high temperatures in molecular liquids or at extremely low densities in colloidal systems.

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.

Site-specific colloidal crystal nucleation by template-enhanced particle transport.

The monomer surface mobility is the single most important parameter that decides the nucleation density and morphology of islands during thin-film growth. During template-assisted surface growth in particular, low surface mobilities can prevent monomers from reaching target sites and this results in a partial to complete loss of nucleation control. Whereas in atomic systems a broad range of surface mobilities can be readily accessed, for colloids, owing to their large size, this window is substantially narrow and therefore imposes severe restrictions in extending template-assisted growth techniques to steer their self-assembly. Here, we circumvented this fundamental limitation by designing templates with spatially varying feature sizes, in this case moiré patterns, which in the presence of short-range depletion attraction presented surface energy gradients for the diffusing colloids. The templates serve a dual purpose: first, directing the particles to target sites by enhancing their surface mean-free paths and second, dictating the size and symmetry of the growing crystallites. Using optical microscopy, we directly followed the nucleation and growth kinetics of colloidal islands on these surfaces at the single-particle level. We demonstrate nucleation control, with high fidelity, in a regime that has remained unaccessed in theoretical, numerical, and experimental studies on atoms and molecules as well. Our findings pave the way for fabricating nontrivial surface architectures composed of complex colloids and nanoparticles as well.

Dynamical facilitation governs glassy dynamics in suspensions of colloidal ellipsoids.

One of the greatest challenges in contemporary condensed matter physics is to ascertain whether the formation of glasses from liquids is fundamentally thermodynamic or dynamic in origin. Although the thermodynamic paradigm has dominated theoretical research for decades, the purely kinetic perspective of the dynamical facilitation (DF) theory has attained prominence in recent times. In particular, recent experiments and simulations have highlighted the importance of facilitation using simple model systems composed of spherical particles. However, an overwhelming majority of liquids possess anisotropy in particle shape and interactions, and it is therefore imperative to examine facilitation in complex glass formers. Here, we apply the DF theory to systems with orientational degrees of freedom as well as anisotropic attractive interactions. By analyzing data from experiments on colloidal ellipsoids, we show that facilitation plays a pivotal role in translational as well as orientational relaxation. Furthermore, we demonstrate that the introduction of attractive interactions leads to spatial decoupling of translational and rotational facilitation, which subsequently results in the decoupling of dynamical heterogeneities. Most strikingly, the DF theory can predict the existence of reentrant glass transitions based on the statistics of localized dynamical events, called excitations, whose duration is substantially smaller than the structural relaxation time. Our findings pave the way for systematically testing the DF approach in complex glass formers and also establish the significance of facilitation in governing structural relaxation in supercooled liquids.

Shape of dynamical heterogeneities and fractional Stokes-Einstein and Stokes-Einstein-Debye relations in quasi-two-dimensional suspensions of colloidal ellipsoids.

We examine the influence of the shape of dynamical heterogeneities on the Stokes-Einstein (SE) and Stokes-Einstein-Debye (SED) relations in quasi-two-dimensional suspensions of colloidal ellipsoids. For ellipsoids with repulsive interactions, both SE and SED relations are violated at all area fractions. On approaching the glass transition, however, the extent to which this violation occurs changes beyond a crossover area fraction. Quite remarkably, we find that it is not just the presence of dynamical heterogeneities but their change in the shape from stringlike to compact that coincides with this crossover. On introducing a suitable short-range depletion attraction between the ellipsoids, associated with the lack of morphological evolution of dynamical heterogeneities, the extent to which the SE and SED relations are violated remains unchanged even for deep supercooling.

Two-step glass transition induced by attractive interactions in quasi-two-dimensional suspensions of ellipsoidal particles.

We study experimentally the glass transition dynamics in quasi-two-dimensional suspensions of colloidal ellipsoids, aspect ratio α=2.1, with repulsive as well as attractive interactions. For the purely repulsive case, we find that the orientational and translational glass transitions occur at the same area fraction. Strikingly, for intermediate depletion attraction strengths, we find that the orientational glass transition precedes the translational one. By quantifying structure and dynamics, we show that quasi-long-range ordering is promoted at these attraction strengths, which subsequently results in a two-step glass transition. Most interestingly, within experimental certainty, we observe reentrant glass dynamics only in the translational degrees of freedom.

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.

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.

Cooperative particle rearrangements facilitate the self-organized growth of colloidal crystal arrays on strain-relief patterns.

Strain-relief pattern formation in heteroepitaxy is well understood for particles with long-range attraction and is a routinely exploited organizational principle for atoms and molecules. However, for particles with short-range attraction such as colloids and nanoparticles, which form brittle assemblies, the mechanism(s) of strain-relief is not known. Here, we found that for colloids with short-range attraction, monolayer films on substrates with square symmetry could accommodate large compressive misfit strains through locally dewetted hexagonally ordered stripes. Unexpectedly, over a window of compressive strains, cooperative particle rearrangements first resulted in a periodic strain-relief pattern, which then guided the growth of laterally ordered defect-free colloidal crystals. Particle-resolved imaging of monomer dynamics on strained substrates also helped uncover cooperative kinetic pathways for surface transport. These processes, which substantially influenced the film morphology, have remained unobserved in atomic heteroepitaxy studies hitherto. Leaning on our findings, we developed a heteroepitaxy approach for fabricating hierarchically ordered surface structures.

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.

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.