Session A36: Colloids: Interactions, Structure, Statistics

Simultaneous three-dimensional imaging and manipulation of grain boundaries in colloidal crystals

Characterizing the properties of grains and grain boundaries is critical for understanding and controlling material properties. We investigate the dynamics of grain boundaries in crystalline materials using concentrated colloidal suspensions of microspheres. The micron-sized particles are suspended in a mixture of solvents whose refractive index and density nearly match those of the particles, enabling three-dimensional visualization and negating gravitational effects. Throughout the sample we disperse specially designed core-shell particles whose cores have a higher refractive index that can be optically trapped. Via optical tweezing, these core-shell particles enable us to directly interact with and probe grain boundaries in 3D within the colloidal crystal. We use a uniquely developed optical microscopy system that combines confocal imaging with holographic trapping, enabling quantitative imaging and precise manipulation simultaneously in three dimensions\footnote{A. Curran, S. Tuohy, D. G. A. L. Aarts, M. J. Booth, T. Wilson, and R. P. A. Dullens, "Decoupled and simultaneous 3D imaging and optical manipulation through a single objective" \textit{Optica} \textbf{1}, 223 (2014)}. Our experiments provide direct insight into the properties of grain boundaries in crystals.   

Capturing "glasslites": structures and dynamics of colloidal liquids under spherical confinement

Recent theories have predicted that when a supercooled liquid approaches the glass transition, "glasslites"-amorphously-ordered particle clusters-nucleate within the liquid, which lead to static correlations dictating the dramatic slowdown of liquid relaxation. The prediction, however, has yet to be verified in 3D experiments. Here, we design a 3D colloidal system, where particles are confined inside spherical cavities with an amorphous layer of particles pinned at boundary. Using this novel system, we capture the glasslites proposed in theories and demonstrate the development of a static correlation. Moreover, by investigating the dynamics of spherically confined samples, we reveal a profound and unexpected influence of the static correlation on the underlying colloidal glass transition. These measurements provide crucial information on how the configurational entropy of a confined supercooled liquid varies when approaching the glass transition.   

Tunable Time-Dependent Colloidal Interactions

Self-assembly of colloidal particles can be driven by changes in temperature, density, or the concentration of solutes, and it is even possible to program the thermal response and equilibrium phase transitions of such systems [1]. It is still difficult, however, to tune how the self-assembly process varies in time. We demonstrate control over the time-dependence of colloidal interactions, using DNA-functionalized colloidal particles with binding energies that are set by the concentration of a free linker strand in solution. We control the rate at which this free strand is consumed using a catalytic DNA reaction [2], whose rate is governed by the concentration of a catalyst strand. Varying the concentration of the linker, its competitor, and the catalyst at a fixed temperature, we can tune the rate and degree of the formation of colloidal aggregates and their following disassembly. Close to the colloidal melting point, the timescales of these out-of-equilibrium assembly and disassembly processes are determined by the rate of the catalytic reaction. Far below the colloidal melting point, however, the effects from varying our linker and competitor concentrations dominate. [1] Rogers and Manoharan, \textit{Science} \textbf{347} (6222): 639-642 (2015). [2] Zhang, Turberfield, Yurke and Winfree, \textit{Science} \textbf{318} (5853): 1121-1125 (2007).   

Transitions in colloidal crystals induced by changes in interparticle interactions

We experimentally study the phase diagram of two-dimensional colloidal crystals as the interparticle interactions transition from weakly attractive to strongly attractive. Simulations have shown that crystals transition from a crystal phase into fluid-crystal coexistence at high attraction strengths. To control the interaction between colloids, we use temperature sensitive, rod-like surfactant micelles as depletants. As the temperature of the system increases, the rod length of the micelles grows, leading to an increase in both the range and strength of interparticle attractions. As the attraction strength increases we observe a decrease in the lattice constant of the crystal, and the creation of “tears” in the crystal structure. These tears allow a colloidal fluid to form, thus yielding the fluid-crystal coexistence phase predicted by previous simulations. These tears and their corresponding phase separation occur simultaneously with a peak in the susceptibility of the orientational order parameter. By creating colloidal systems with various packing fractions and slowly increasing the temperature, which increases the attraction strength between colloids, we attempt to accurately map out the phase diagram of two-dimensional colloidal crystals with attractive interactions.   

Probing Dynamical Heterogeneity in Dense Colloidal Suspensions with Depletion Attraction

We directly observe the particle dynamics in dense colloidal suspensions. Using depletion attraction, we vary inter particle potential to study the reentrant glass transition. Confocal microscopy and particle tracking allow us to follow particle trajectories over time. By varying inter particle~attraction strength~for a fixed volume fraction of colloidal suspensions, we observe three qualitatively different states. Mean square displacement and long time diffusion constant vary with the depletant concentration and indicate a glass state for low attraction strengths, ergodic liquid state for moderate attraction strengths, and attractive arrested state for the highest attraction~strengths.~ Variance in the self overlap function gives the four point susceptibility, a measure of dynamical heterogeneity over a range of~length scales and lag times.~Results show that the lag times corresponding to the most heterogeneous dynamics are longer for arrested states than for fluid states.~The~length scale that maximizes four point susceptibility across a range of attraction strengths exhibits a reentrant glass behavior similar to that of the long time diffusion constant.   

Particle dynamics and vibrational properties of disordered colloidal packings with varying interparticle attraction strength

We experimentally study dynamical and vibrational properties of disordered colloidal packings as a function of the strength of the interparticle attraction. ~Specifically, we probe the structural and dynamical changes in disordered colloidal glasses as the interparticle interaction between constituent particles evolves from nearly hard-sphere repulsive to attractive. ~This increase of the interparticle attraction is achieved through use of temperature-tunable surfactant micelle depletants. The depletion-driven entropic attraction between particles in suspension grows with increasing temperature. ~Increasing temperature changes particle interactions in a dense colloidal packing from repulsive (weakly attractive) to strongly attractive, and accompanying variations in structure and dynamics is investigated. ~Preliminary experiments on these disordered systems show a continuous change in particle dynamics as attraction strength increases. ~Interestingly, vibrational properties show a more sudden change reflected in the behavior of the vibrational density of states.   

On Determination of the Equation of State of Colloidal Suspensions

Colloidal suspensions are the main ingredients for a variety of materials in our daily life, e.g., milk, salad dressing, skin lotions and paint for wall coatings. Material properties of these systems require an understanding of the equation of state of these materials. Our project aims to experimentally determine the equation of state of colloidal suspensions by microfluidics, dielectrophoresis (DEP) and optical imaging. We use fluorescent polystyrene latexes as a model system for this study. Placing semi-permeable membranes between microfluidics channels, which made from PDMS, we control the particle concentration and ionic strengths of the suspension. We use osmotic equilibrium equation to analyze the particle concentration distribution in a potential force field created by DEP. We use confocal optical imaging to measure the spatial distribution of the particle concentration. We compare the results of our experimental study with data obtained by computer simulation of osmotic equilibrium of interacting colloids.   

Non-equilibrium steady-state distributions of colloids in a tilted periodic potential

A two-layer colloidal system is constructed to study the effects of the external force $F$ on the non-equilibrium steady-state (NESS) dynamics of the diffusing particles over a tilted periodic potential, in which detailed balance is broken due to the presence of a steady particle flux. The periodic potential is provided by the bottom layer colloidal spheres forming a fixed crystalline pattern on a glass substrate. The corrugated surface of the bottom colloidal crystal provides a gravitational potential field for the top layer diffusing particles. By tilting the sample with respect to gravity, a tangential component $F$ is applied to the diffusing particles. The measured NESS probability density function $P_{ss}(x,y)$ of the particles is found to deviate from the equilibrium distribution depending on the driving or distance from equilibrium. The experimental results are compared with the exact solution of the 1D Smoluchowski equation and the numerical results of the 2D Smoluchowski equation. Moreover, from the obtained exact 1D solution, we develop an analytical method to accurately extract the 1D potential $U_0(x)$ from the measured $P_{ss}(x)$.   

Diffusing colloids in the vicinity of a surface: Anomalous yet Brownian diffusion?

Anomalous yet Brownian diffusion refers to a process with a linear mean-square displacement coexisting with a non-Gaussian Displacement Distribution (DispD) [1]. Chubynsky and Slater [2] proposed a model of this phenomenon in which the diffusion coefficient varies randomly in time ("diffusing diffusivity"). Recently, Bechhoefer's group has showed experimentally that diffusion of colloids near a wall exhibits non-Gaussian DispD with exponential tails. Due to hydrodynamic interactions, the diffusivity $D(r)$ is space-dependent and therefore varies in time as the particle moves in space. Qualitatively, the experimental results agree with the predictions of the diffusing diffusivity model. However, the two situations differ in details. First, space-dependent diffusivity implies the possibility of different interpretations of the stochastic term in the overdamped Langevin equation (i.e. the “Ito-Stratonovich dilemma”). Second, in the system of Bechhoefer et al, there is an external potential due to gravity and the electrostatic repulsion from the wall. Using Lattice Monte Carlo simulations, we explore the role of these effects. [1] B. Wang et al., PNAS 106, 15160 (2009), [2] M. V. Chubynsky and G. W. Slater, PRL 113, 098302 (2014)   

Non-Gaussian yet normal diffusion of a bead near a wall

Brownian motion of microscopic particles in a simple fluid exhibits two key properties: the mean-squared displacement (MSD) increases linearly with time ($\langle \Delta x^2 \rangle = 2D\Delta t$, where $D$ is the diffusivity) and the displacement distribution is Gaussian. Although linear MSD ("normal diffusion") was initially assumed to always imply Gaussian displacements, recent experiments by Granick et al. show that this is not so. Chubynsky et al. [PRL $\textbf{113}$, 098302, 2014] have argued that such behavior arises when $D$ has temporal and/or spatial fluctuations that are convoluted together and form a non-Gaussian distribution. Experiments to date have been in complex settings where direct measurements of $D(x,t)$ have not been possible. Here, we report experiments on a simple system where $D(x,t)$ is known: the Brownian motion of a colloidal sphere near a wall. By choosing the particle size carefully, we ensure that the bead explores a wide range of $D$. We observe a linear MSD curve and non-Gaussian displacements for vertical motion and directly confirm the proposed mechanism of Chubynsky et al. for such "diffusing diffusivity."   

Structural relaxation of vapour-deposited colloidal glass

Freshly made glasses by vapor deposition exhibit ultra-stability similar to fully aged glasses formed by quenching liquids. It has been suggested that the mobile surface layers in vapor deposition accelerates the aging process, but its mechanism is unclear. Here we study the vapor deposition process of colloidal glass by video microscopy and MD simulation with single-particle dynamics. We found that the structural relaxation near the surface, characterized by cooperative-rearrangement regions (CRRs), is much stronger during the deposition process than after deposition due to the perturbation of newly attached particles. Near the surface, a thermal-induced vacancy can triggered a large CRR which propagates from the vacancy to the surface. Deep inside the bulk, CRRs are rare, smaller and cannot propagate to the surface. By measuring the evolution of free-volume entropy , we found that the strong structural relaxation is accompanied by local free energy decreasing.   

Assembly of colloidal strings in a simple fluid flow

Colloidal particles self-assemble into ordered structures ranging from face- and body-centered cubic crystals to binary ionic crystals and to kagome lattices. Such diverse micron-scale structures are of practical importance for creating photonic materials and also of fundamental interest for probing equilibrium and non-equilibrium statistical mechanics. As a particularly interesting example, 1D colloidal strings provide a unique system for investigating non-equilibrium dynamics of crystal lattices. Here, we report a simple experimental method for constructing 1D colloidal crystals, where colloidal particles self-assemble into flow-aligned string structures near solid boundary under unidirectional flows. Using fast confocal microscopy, we explore the degree of particle alignment as functions of flow rate, particle concentrations, wetting properties of solid boundary and ionic strength of solvent. Through our systematic experiments, we show that these colloidal strings arise from hydrodynamic coupling, facilitated by electrostatic attractions between particles and the boundary. Compared with previous methods, our work provides a much simpler experimental procedure for assembling a large number of colloidal strings.   

Hiding in plain view: Colloidal self-assembly from polydisperse populations

We report small-angle x-ray scattering (SAXS) experiments on aqueous dispersions of colloidal silica with a broad monomodal size distribution (polydispersity 14\%, size $a = 8$ nm). This distribution of sizes was expected to destroy any long-range order of the particles. However, we found ordered states when the particles repelled each other with soft ionic potentials of range $\sim a$. Over a range of volume fractions the particles segregated to build first one, then two distinct sets of colloidal crystals. These dispersions thus demonstrate fractional crystallization and multiple-phase (bcc, Laves AB$_2$, liquid) coexistence. Their remarkable ability to build complex crystal structures from a polydisperse population originates from the intermediate-range nature of interparticle forces, and suggests routes for designing self-assembling colloidal crystals from the bottom-up.   

Controlling Chirality of Entropic Crystals

Colloidal crystal structures with complexity and diversity rivaling atomic and molecular crystals have been predicted and obtained for hard particles by entropy maximization. However, thus far homochiral colloidal crystals, which are candidates for photonic metamaterials, are absent. Using Monte~Carlo simulations we show that chiral polyhedra exhibiting weak directional entropic forces self-assemble either an achiral crystal or a chiral crystal with limited control over the crystal handedness. Building blocks with stronger faceting exhibit higher selectivity and assemble a chiral crystal with handedness uniquely determined by the particle chirality. Tuning the strength of directional entropic forces by means of particle rounding or the use of depletants allows for reconfiguration between achiral and homochiral crystals. We rationalize our findings by quantifying the chirality strength of each particle, both from particle geometry and potential of mean force and torque diagrams.   

Realization of atomistic transitions with colloidal nanoparticles using an ultrafast laser

We report on realization of rapid atomistic transitions with colloidal nanoparticles in a setting that constitutes a dissipative far-from-equilibrium system subject to stochastic forces. Large colloidal crystals (comprising hundreds of particles) can be formed and transitions between solid-liquid-gas phases can be observed effortlessly and within seconds. Furthermore, this system allows us to form and dynamically arrest metastable phases such as glassy structures and to controllably transform a crystal pattern from square to hexagonal lattices and vice versa as well as to observe formation and propagation of crystal defects (i.e. line defects, point defects, planar defects). The mechanism largely relies on an interplay between convective forces induced by femtosecond pulses and strong Brownian motion; the former drags the colloids to form and reinforce the crystal and the latter is analogous to lattice vibrations, which makes it possible to observe phase transitions, defect formation and propagation and lattice transformation. This unique system can help us get insight into the mechanisms underlying various solid state phenomena that were previously studied under slowly evolving (within hours/days), near-equilibrium colloidal systems.