Eric R. Weeks

The physics of the colloidal glass transition

As one increases the concentration of a colloidal suspension, the system exhibits a dramatic increase in viscosity. Beyond a certain concentration, the system is said to be a colloidal glass; structurally, the system resembles a liquid, yet motions within the suspension are slow enough that it can be considered essentially frozen. For several decades, colloids have served as a valuable model system for understanding the glass transition in molecular systems. The spatial and temporal scales involved allow these systems to be studied by a wide variety of experimental techniques. The focus of this review is the current state of understanding of the colloidal glass transition, with an emphasis on experimental observations. A brief introduction is given to important experimental techniques used to study the glass transition in colloids. We describe features of colloidal systems near and in glassy states, including increases in viscosity and relaxation times, dynamical heterogeneity and ageing, among others. We also compare and contrast the glass transition in colloids to that in molecular liquids. Other glassy systems are briefly discussed, as well as recently developed synthesis techniques that will keep these systems rich with interesting physics for years to come.

Confocal microscopy of colloids

Colloids have increasingly been used to characterize or mimic many aspects of atomic and molecular systems. With confocal microscopy these colloidal particles can be tracked spatially in three dimensions with great precision over large time scales. This review discusses equilibrium phases such as crystals and liquids, and non-equilibrium phases such as glasses and gels. The phases that form depend strongly on the type of particle interaction that dominates. Hard-sphere-like colloids are the simplest, and interactions such as the attractive depletion force and electrostatic repulsion result in more non-trivial phases which can better model molecular materials. Furthermore, shearing or otherwise externally forcing these colloids while under microscopic observation helps connect the microscopic particle dynamics to the macroscopic flow behaviour. Finally, directions of future research in this field are discussed.

Three-dimensional confocal microscopy of colloids

Confocal microscopy is used in the study of colloidal gels, glasses, and binary fluids. We measure the three-dimensional positions of colloidal particles with a precision of approximately 50 nm (a small fraction of each particles radius) and with a time resolution sufficient for tracking the thermal motions of several thousand particles at once. This information allows us to characterize the structure and the dynamics of these materials in qualitatively new ways, for example, by quantifying the topology of chains and clusters of particles as well as by measuring the spatial correlations between particles with high mobilities. We describe our experimental technique and describe measurements that complement the results of light scattering.

Three-Dimensional Imaging of Colloidal Glasses under Steady Shear

Using fast confocal microscopy we image the three-dimensional dynamics of particles in a yielded hard-sphere colloidal glass under steady shear. The structural relaxation, observed in regions with uniform shear, is nearly isotropic but is distinctly different from that of quiescent metastable colloidal fluids. The inverse relaxation time tau(alpha)(-1) and diffusion constant D, as functions of the local shear rate gamma*, show marked shear thinning with tau(alpha)(-1) proportional to D proportional to gamma*(0.8) over more than two decades in gamma*. In contrast, the global rheology of the system displays Herschel-Bulkley behavior. We discuss the possible role of large scale shear localization and other mechanisms in generating this difference.

Particle migration in pressure-driven flow of a Brownian suspension

Shear induced particle migration of 2 µm diameter spherical col- loidal particles flowing through rectangular capillary tubes (50 µm × 500 µm cross section) is studied by confocal microscopy. The confocal microscope allows imaging of the flowing particles far from the walls of the tube, at particle velocities up to 8000 µm s 1 . The particle volume fraction is varied from � = 0.05-0.34, and the flow rate is also varied, which results in a bulk Peclet number (Pe) which varies by two orders of magnitude. Concentration profiles are measured across the narrow dimension of the tube; particles at the larger volume frac- tions migrate toward the centreline, with the migration progressively stronger as Pe increases. The flow has been analyzed using an existing mixture flow model under the assumption of fully-developed flow and a proposed constitu- tive law which describes the suspension normal stresses as a function of bothand Pe, the latter of which is defined as a variable quantity through the local shear rate. Shear thinning and shear thickening are not included. Comparisons made with the experimental data indicate that the dependence of the extent of migration upon Pe is well cap- tured but discrepancies arise, at least in part because the assumption of full development is not valid for these experiments.

Subdiffusion and the cage effect studied near the colloidal glass transition

Abstract The dynamics of a glass-forming material slow greatly near the glass transition, and molecular motion becomes inhibited. We use confocal microscopy to investigate the motion of colloidal particles near the colloidal glass transition. As the concentration in a dense colloidal suspension is increased, particles become confined in transient cages formed by their neighbors. This prevents them from diffusing freely throughout the sample. We quantify the properties of these cages by measuring temporal anticorrelations of the particles’ displacements. The local cage properties are related to the subdiffusive rise of the mean square displacement: over a broad range of time scales, the mean square displacement grows slower than linearly in time.

Forced motion of a probe particle near the colloidal glass transition

We use confocal microscopy to study the motion of a magnetic bead in a dense colloidal suspension, near the colloidal glass transition volume fraction g. For dense liquid-like samples near g, below a threshold force the magnetic bead exhibits only localized caged motion. Above this force, the bead is pulled with a fluctuating velocity. The relationship between force and velocity becomes increasingly nonlinear as g is approached. The threshold force and nonlinear drag force vary strongly with the volume fraction, while the velocity fluctuations do not change near the transition.

Chaotic advection in a two-dimensional flow: Le´vy flights and anomalous diffusion

Long-term particle tracking is used to study chaotic transport experimentally in laminar, chaotic, and turbulent flows in an annular tank that rotates sufficiently rapidly to insure two-dimensionality of the flow. For the laminar and chaotic velocity fields, the flow consists of v flow regimes, tracer particles stick for long times to remnants of invariant surfaces around the vortices, then make long excursions (“flights”) in the jet regions. The probability distributions for the flight time durations exhibit power-law rather than exponential decays, indicating that the parrticle trajectories are described mathematically as Levy flights (i.e. the trajectories have infinite mean square displacement per flight). Sticking time probability distributions are also characterized by power laws, as found in previous numerical studies. The mixing of an ensemble of tracer particles is superdiffusive: the variance of the displacement grows with time as tλ with 1<λ<2. The dependence of the diffusion exponent λ and the scaling of the probability distributions are investigated for periodic and chaotic flow regimes, and the results are found to be consistent with theoretical predictions relating Levy flights and anomalous diffusion. For a turbulent flow, the Levy flight description no longer applies, and mixing no longer appears superdiffusive.

Anomalous diffusion in asymmetric random walks with a quasi-geostrophic flow example

We present a model of one-dimensional symmetric and asymmetric random walks. The model is applied to an experiment studying fluid transport in a rapidly rotating annulus. In the model, random walkers alternate between flights (steps of constant velocity) and sticking (pauses between flights). Flight time and sticking time probability distribution functions (PDFs) have power law decays: P(t) ∼ t−μ and t−ν for flights and sticking, respectively. We calculate the dependence of the variance exponent γ (σ2 ∼ tγ) on the PDF exponents μ and ν. For a broad distribution of flight times (μ 3, ν > 3), normal diffusion (γ = 1) is recovered. Predictions of the model are related to experimental observations of transport in a rotating annulus. The Eulerian velocity field is chaotic, yet it is still possible to distinguish between well-defined sticking events (particles trapped in vortices) and flights (particles making long excursions in a jet). The distribution of flight lengths is well described by a power law with a divergent second moment (Levy distribution). The observed transport is strongly asymmetric and is well described by the proposed model.

Colloidal glass transition observed in confinement

We study a colloidal suspension confined between two quasiparallel walls as a model system for glass transitions in confined geometries. The suspension is a mixture of two particle sizes to prevent wall-induced crystallization. We use confocal microscopy to directly observe the motion of colloidal particles. This motion is slower in confinement, thus producing glassy behavior in a sample which is a liquid in an unconfined geometry. For higher volume fraction samples (closer to the glass transition), the onset of confinement effects occurs at larger length scales.