Andrew B. Schofield

Gelation of particles with short-range attraction

Nanoscale or colloidal particles are important in many realms of science and technology. They can dramatically change the properties of materials, imparting solid-like behaviour to a wide variety of complex fluids. This behaviour arises when particles aggregate to form mesoscopic clusters and networks. The essential component leading to aggregation is an interparticle attraction, which can be generated by many physical and chemical mechanisms. In the limit of irreversible aggregation, infinitely strong interparticle bonds lead to diffusion-limited cluster aggregation (DLCA). This is understood as a purely kinetic phenomenon that can form solid-like gels at arbitrarily low particle volume fraction. Far more important technologically are systems with weaker attractions, where gel formation requires higher volume fractions. Numerous scenarios for gelation have been proposed, including DLCA, kinetic or dynamic arrest, phase separation, percolation and jamming. No consensus has emerged and, despite its ubiquity and significance, gelation is far from understood—even the location of the gelation phase boundary is not agreed on. Here we report experiments showing that gelation of spherical particles with isotropic, short-range attractions is initiated by spinodal decomposition; this thermodynamic instability triggers the formation of density fluctuations, leading to spanning clusters that dynamically arrest to create a gel. This simple picture of gelation does not depend on microscopic system-specific details, and should thus apply broadly to any particle system with short-range attractions. Our results suggest that gelation—often considered a purely kinetic phenomenon—is in fact a direct consequence of equilibrium liquid–gas phase separation. Without exception, we observe gelation in all of our samples predicted by theory and simulation to phase-separate; this suggests that it is phase separation, not percolation, that corresponds to gelation in models for attractive spheres.

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.

Synthesis and Directed Self-Assembly of Patterned Anisometric Polymeric Particles

A simple and versatile method for making chemically patterned anisotropic colloidal particles is proposed and demonstrated for two different types of patterning. Using a combination of thermo/mechanical stretching followed by a wet chemical treatment of a sterically stabilized latex, both patchy ellipsoidal particles with sticky interactions near the tips as well as particles with tunable fluorescent patterns could be easily produced. The potential of such model colloidal particles is demonstrated, specifically for the case of directed self-assembly.

A self-quenched defect glass in a colloid-nematic liquid crystal composite.

A high concentration of colloidal particles stabilizes a defect network in a liquid crystal and creates a gel-like material. Colloidal particles immersed in liquid crystals frustrate orientational order. This generates defect lines known as disclinations. At the core of these defects, the orientational order drops sharply. We have discovered a class of soft solids, with shear moduli up to 104 pascals, containing high concentrations of colloidal particles (volume fraction ϕ>∼20%) directly dispersed into a nematic liquid crystal. Confocal microscopy and computer simulations show that the mechanical strength derives from a percolated network of defect lines entangled with the particles in three dimensions. Such a “self-quenched glass” of defect lines and particles can be considered a self-organized analog of the “vortex glass” state in type II superconductors.

Structure, dynamics, and rheology of colloid-polymer mixtures: From liquids to gels

We investigate the structural, dynamical, and viscoelastic properties of colloid-polymer mixtures at intermediate colloid volume fraction and varying polymer concentrations, thereby tuning the attractive interactions. Within the examined range of polymer concentrations, the samples varied from fluids to gels. In the liquid phase, an increasing correlation length of the density fluctuations when approaching the gelation boundary was observed by static light scattering and microscopy, indicating clustering and formation of space-spanning networks. Simultaneously, the correlation function determined by dynamic light scattering decays completely, indicating the absence of dynamical arrest. Clustering and formation of transient networks when approaching the gelation boundary is supported by significant changes in the viscoelastic properties of the samples. Upon increasing the polymer concentration beyond the gelation boundary, the rheological properties changed qualitatively again, now they are consistent with the formation of colloidal gels. Our experimental results, namely, the location of the gelation boundary as well as the elastic (storage) and viscous (loss) moduli, are compared to different theoretical models. These include consideration of the escape time as well as predictions for the viscoelastic moduli based on scaling relations and mode coupling theories.

Dynamics of drying in 3D porous media.

The drying dynamics in three dimensional porous media are studied with confocal microscopy. We observe abrupt air invasions in size from single particle to hundreds of particles. We show that these result from the strong flow from menisci in large pores to menisci in small pores during drying. This flow causes air invasions to start in large menisci and subsequently spread throughout the entire system. We measure the size and structure of the air invasions and show that they are in accord with invasion percolation. By varying the particle size and contact angle we unambiguously demonstrate that capillary pressure dominates the drying process.

Passive and active microrheology of hard-sphere colloids.

We performed passive and active microrheology using probe particles in a bath of well-characterized, model hard-sphere colloids in the fluid state over the whole range of volume fractions below the glass transition. The probe and bath particles have nearly the same size. Passive tracking of probe particles yields short-time self-diffusion coefficients. Comparison with literature data demonstrates that the interaction between probe and bath particles is hard-sphere-like. The short-time diffusivities yield one set of microviscosities as a function of volume fraction, which agrees with previous macrorheological measurements of the high-frequency viscosity of hard-sphere colloids. Using optical tweezers, we measure the force on a trapped probe particle as the rest of the sample is translated at constant velocity. This yields a second set of microviscosities at high Péclet numbers. These agree with previous macrorheological measurements of the high-shear viscosity of similar colloids, at shear-rates below the onset of shear-thickening.

Effects of shear induced crystallization on the rheology and ageing of hard sphere glasses

The rheological properties of highly concentrated suspensions of hard sphere particles are studied with particular reference to the rheological response of shear induced crystals. Using practically monodisperse hard spheres, we prepare shear induced crystals under oscillatory shear and examine their linear and non-linear mechanical responses in comparison with their glassy counterparts at the same volume fraction. It is evident, that shear induced crystallization causes a significant drop in the elastic and viscous moduli due to structural rearrangements that ease flow. For the same reason the critical (peak of G″) and crossover (overlap of G′ and G″) strain are smaller in the crystal compared to the glass at the same volume fraction. However, when the distance from the maximum packing in each state is taken into account the elastic modulus of the crystal is found to be larger than the glass at the same free volume, suggesting a strengthened material due to long range order. Finally, shear induced crystals counter-intuitively exhibit similar rheological ageing to the glass (with a logarithmic increase of G′), indicating that the shear induced structure is not at thermodynamic equilibrium.

Arrested fluid-fluid phase separation in depletion systems: Implications of the characteristic length on gel formation and rheology

We investigate the structural, dynamical, and rheological properties of colloid-polymer mixtures in a volume fraction range of ϕ=0.15–0.35. Our systems are density-matched, residual charges are screened, and the polymer-colloid size ratio is ∼0.37. For these systems, the transition to kinetically arrested states, including disconnected clusters and gels, coincides with the fluid-fluid phase separation boundary. Structural investigations reveal that the characteristic length, L, of the networks is a strong function of the quench depth: for shallow quenches, L is significantly larger than that obtained for deep quenches. By contrast, L is for a given quench depth almost independent of ϕ; this indicates that the strand thickness increases with ϕ. The strand thickness determines the linear rheology: the final relaxation time exhibits a strong dependence on ϕ, whereas the high frequency modulus does not. We present a simple model based on estimates of the strand breaking time and shear modulus that semiquantit...

Transient dynamics in dense colloidal suspensions under shear: shear rate dependence

A combination of confocal microscopy and rheology experiments, Brownian dynamics (BD) and molecular dynamics (MD) simulations and mode coupling theory (MCT) have been applied in order to investigate the effect of shear rate on the transient dynamics and stress-strain relations in supercooled and glassy systems under shear. Immediately after shear is switched on, the microscopic dynamics display super-diffusion and the macroscopic rheology a stress overshoot, which become more pronounced with increasing shear rate. MCT relates both to negative sections of the generalized shear modulus, which grow with increasing shear rate. When the inverse shear rate becomes much smaller than the structural relaxation time of the quiescent system, relaxation through Brownian motion becomes less important. In this regime, larger stresses are accumulated before the system yields and the transition from localization to flow occurs earlier and more abruptly.