Session J8: Colloids: Crystals and Other Phases

Transitions from hard-sphere colloidal crystals to colloidal crystals with strong attractive interactions

Recently, colloid experiments have probed and found interesting differences in the properties of disordered glassy media as a function of the sign of the interparticle interaction [1-3]. Here, we report a similar kind of experiment, this time involving colloidal crystals wherein the interparticle interaction between constituent particles evolves from hard-sphere repulsive to attractive. This change in sign of the interparticle interaction is achieved through use of temperature-tunable depletants assembled from surfactants. The depletion-driven entropic attraction between particles in suspension grows with increasing temperature. Increasing temperature changes particle interactions in a dense crystal from repulsive to attractive, and accompanying variations in structure and dynamics of the crystal can be tracked. The increase in attractive interaction can also be turned on slowly and rapidly. Preliminary experiments on polycrystalline hard-sphere samples show accompanying decreases the lattice constant and a fluid-crystal coexistence phase consisting of small, dense ``attractive'' crystalline domains separated by ``voids'' filled with dilute colloidal fluid. These voids appear to originate at grain boundaries and near lattice defects in the original hard-sphere polycrystal. Further work explores the dense parts of the colloidal phase diagram with depletion interactions. [1] Eckert \textit{et al}., PRL \textbf{89}, 125701 (2002). [2] Pham \textit{et al}., Science \textbf{296}, 5565 (2002). [3] Kaufman \textit{et al}., J. Chem. Phys. \textbf{125}, 074716 (2006).   

Melting of colloidal crystals in small cavities

We studied the melting behaviors of small colloidal crystals in different sized and shaped small cavities by video microscopy. The crystals were composed of temperature-sensitive N-isopropyl acrylamide (NIPA) microgel spheres. The cavity shape and defects can dramatically alter the melting kinetics and the vibration modes. The melting point can increase or decrease with size of colloid crystal, depending on the shape of the cavity. Single defect- free crystals melt from edges via nucleation mechanism in large hexagonal cavities, but melt catastrophically without nucleation when the cavity is smaller than a threshold. The smaller-angled cavity better promotes the melting.   

Born melting of three dimensional crystals

While the microscopic nature of melting in 1 and 2 dimensions has been elucidated both theoretically and experimentally, this has proven elusive for three-dimensional crystalline solids. Max Born hypothesized that melting can be described as a rigidity catastrophe where the crystal's shear elastic constant vanishes at melting. Here we show experimental evidence, using three-dimensional imaging of soft colloidal crystals, for such a mechanical instability underlying melting. Our results reveal how non-affine fluctuations govern the mechanical instability which precipitates melting; modification of Born's theory to take non-affinity into account accurately describes our experimental data. Moreover, we show how the continuous weakening of the crystal's resistance to shear leads to the emergence of collective fluctuations who's size diverges at the melting point.   

Grain Boundary Roughening in Colloidal Crystals

We studied the grain-boundary roughening transition inside the bulk of thermal-sensitive thin-film colloidal crystals by video microscopy and phase-field simulations. As the volume fraction of the microgel colloidal polycrystals decrease, we observed that the large-angle grain boundaries become rough with the strongest shape fluctuations at the roughening transition point below the premelting point. The roughening transition exhibits critical behaviors. We discovered the structural change responsible to the exotic decrease of the shape fluctuation and the mobility change of the grain boundary as approaching the premelting point. Small-angle grain boundaries do not have the roughening transition and exhibit different melting behaviors.   

Exploring melting transition with soft colloids

A comparative study has been made to explore melting transition for two different types of soft colloids: sterically stabilized aqueous core-shell (CS) microgels and charge stabilized PMMA particles. The shell component made of polymer network stabilize the CS suspension whereas the PMMA particle suspension is stabilized by the surface charge on each particle. Both types of particles form stable three dimensional crystal structures at higher volume fractions. We locate individual particles to construct 3D pair-correlation function and mean-square-displacements (MSD). We explore the melting transition in equilibrium for both the systems by changing the inter-particle separation i.e by changing volume fraction. Different melting criterions have been used to identify melting point. The result shows that melting transition for sterically stabilized CS microgel is fundamentally different from that of charge stabilized PMMA particles.   

Quantifying Stress Fields of Defects in 3D Colloidal Crystals

We introduce the ``Stress Assessment from Local Structural Anisotropy'' (SALSA) method and use it to directly measure the local stress fields of defects including vacancies, dislocations, and polycrystals in 3D colloidal suspensions. In this technique, we extract a time-series of particle positions from confocal images from which we determine stresses on the particle scale. In the case of the vacancy, we find a nonlinear pressure ring which is well described by linear elastic theory with a geometric nonlinearity. We next measure the stress fields in a polycrystal before and after cyclic shear. We find that the normal stresses in the grain boundaries are about 10\%-20\% lower than in the grains. This provides a more detailed, particle level measurement of polycrystalline stresses that is consistent with analogous X-ray experiments as well as previous simulations.   

Stripe Systems with Competing Interactions on Quasi-One Dimensional Periodic Substrates

We numerically examine the two-dimensional ordering of a stripe forming system of particles with competing long-range repulsion and short-range attraction in the presence of a quasi-one-dimensional corrugated substrate. As a function of increasing substrate strength or the ratio of the number of particles to the number of substrate minima we show that a remarkable variety of distinct orderings can be realized, including modulated stripes, prolate clump phases, two dimensional ordered kink structures, crystalline void phases, and smectic phases. Additionally in some cases the stripes align perpendicular to the substrate troughs. Our results suggest that a new route to self assembly for systems with competing interactions can be achieved through the addition of a simple periodic modulated substrate.   

Conformal Crystals

Interacting particles which would otherwise form a perfect crystal arrange into fascinating structures when immersed in spatially varying potentials. Using colloidal experiments and molecular dynamics simulations, we explore the two dimensional ordering of repulsive particles confined by external potentials. By relating the resulting inhomogenous structures to a lattice frustrated by Gaussian curvature, we investigate the role of topological defects in organizing the conformal crystal-like ground states.   

Self-Healing Colloidal Crystals: Why Soft Particles Feel the Squeeze

Point defects in crystalline materials disturb the crystal structure and often prevent crystallization. In particular, this is the case for too big particles that are put into a crystal. In metal melts, a size mismatch of 15\% of the atoms in the melt suppresses crystallization. Furthermore, hard spheres with a polydispersity greater than 12\% do not form crystals, and the polydispersity in the crystal state does not exceed 5.7\%, as local segregation occurs. These restrictions do not necessarily apply for soft microgels. Lyon et al. (A. St. J. Iyer and L. A. Lyon, \emph{Angew. Chem. Int. Ed.}, 48, 2009) find bigger microgels to shrink and fit into the lattice formed by smaller ones. We find that charged groups in the microgel and their counter-ions are the key to explain this remarkable spontaneous deswelling of microgels. Using small-angle neutron and X-ray scattering, we directly observe the deswelling of bigger particles with increasing volume fraction and the effect of the bigger particles on the phase behavior of the suspension. Furthermore, we determine the osmotic pressure using osmometry and present a model for the selective deswelling of the big particles.   

Self-Assembly of an Icosahedral Quasicrystal Network

Icosahedral quasicrystals (IQCs) are a form of matter that is ordered but not periodic in any direction. IQCs have the highest symmetry of all crystals and therefore exhibit orientationally highly uniform properties. This makes them candidates for materials with a complete photonic bandgap or as specialized alloys. Unlike axially-symmetric quasicrystals, which have been reported experimentally in micellar or nanoparticle systems and suggested in bi-layer water, silicon, and mesoporous silica, IQCs have not been observed in the context of non-intermetallic systems. Here, we demonstrate the self-assembly of an IQC by means of molecular dynamics simulations. The IQC is a predominantly tetrahedral, body-centered-icosahedral network and is structurally related to clathrates and other tetrahedrally coordinated crystalline networks. The IQC self-assembles rapidly and reproducibly from a fluid phase in a one-component system of particles. We provide a crystallographic structure model and show the presence of a diffusion mechanism not available in periodically ordered solids. [1] M. Engel, P.F. Damasceno, P.L. Phillips, S.C. Glotzer, Nature Materials, in press (2014).   

Particle dynamics in dense colloidal suspensions with short-range attraction

We study single particle dynamics and dynamical heterogeneity in colloidal suspensions with tunable short-range attraction as the sample evolves from a repulsive glass towards an attractive glass. Short-range depletion forces induce the transition. Using confocal microscopy we identify colloidal particles that exhibit substantial motional events. We observe that these particles demonstrate heterogeneous dynamics which is manifested by non-Gaussian distribution of the particle displacements. Maximum dynamical susceptibility is determined systematically over a range of probe length and time scales. Preliminary results show that at volume fractions just above the colloidal glass transition the intensity of spatial heterogeneities decreases as the interparticle attraction strength is increased suggesting the system enters the ergodic fluid state.   

Jamming and Phase Transition in Binary Soft Colloids

We report on jamming, yielding, and flow of binary mixtures of self-suspended silica nanoparticles densely grafted with Polyethylene glycol (PEG)(MW $\sim$ 5000g/mol). The ratio of volume fraction of the larger particles to the total volume fraction of the silica cores, x$_{\mathrm{L}}$, is shown to sensitively affect both the yielding and jamming transitions of these systems. For all the binary systems a two-step yielding is observed in oscillatory shear measurements, which we discuss in terms of the breaking of small and big particle cages. We find that addition of larger particles to a suspension of smaller ones softens the suspensions and, for small values of the particle radius ratio $r=R_{s}/R_{L}$, the larger particles produce complete fluidization of their smaller counterparts. We show that these behaviors coincide with a speeding-up of de-correlation dynamics of all particles in the suspensions using XPCS measurements and are preceded by an abrupt transition in the average inter-particle spacing, similar to behavior predicted for a semi-dilute binary hard sphere suspension model as observed from SAXS experiment.   

Anisotropic stress correlations in 2D liquids

We demonstrate the presence of anisotropic stress correlations in the simulated 2D liquids. Whereas the temporal correlation of macroscopic shear stress is known to contribute to viscosity via the Green-Kubo formula, the general question regarding angular dependence of the spatial correlation among atomic level stresses in liquids without external shear has not been explored. Besides the apparent anisotropicity with well-defined symmetry, we found that the characteristic length of shear stress correlation depends on temperature and follows the power law, suggesting divergence around the glass transition temperature. The anisotropy of the stress correlations can be explained in terms of the inclusion model by Eshelby, based upon which we suggest that the mismatch between the atom and its nearest neighbor cage produces the atomic level stress as well as the long-range stress fields.   

Frustrated packing of monodisperse spheres in a flat container

We study the packing of monodisperse spheres in a flat vertical box with cell gap slightly larger than the particle diameter, and evaluate the statistics of the particle arrangements. After 'gravitational' filling of the container and appropriate agitation, the particles form a nearly regular triangular lattice in the cell plane. The additional freedom of a displacement normal to the cell plane places the particles either at the front or rear cell plate. This leads to a denser arrangement in the cell plane, but at the same time causes frustrated states: Two of three neighboring beads in a local triangle have to occupy the same cell wall. Analogies to order in antiferroelectric Ising spin systems on a triangular lattice and to colloidal assemblies in thin layers are evident. We analyse experimental packings statistically and compare them to the predictions of models and Monte Carlo simulations. When the container is tilted from the vertical, the gravitational field mimics an external force similar to a magnetic field in spin systems. The experiment both offers insights into the influence of geometrical constraints on random packing, and provides a descriptive example of frustrated ordering.