Equilibrium route to colloidal gelation: mixtures of hard-sphere-like colloids

Gelation and Re-entrance in Mixtures of Soft Colloids and Linear Polymers of Equal Size

Liquid mixtures composed of colloidal particles and much smaller non-adsorbing linear homopolymers can undergo a gelation transition due to polymer-mediated depletion forces. We now show that the addition of linear polymers to suspensions of soft colloids having the same hydrodynamic size yields a liquid-to-gel-to-re-entrant liquid transition. In particular, the dynamic state diagram of 1,4-polybutadiene star-linear polymer mixtures was determined with the help of linear viscoelastic and small-angle X-ray scattering experiments. While keeping the star polymers below their nominal overlap concentration, a gel was formed upon increasing the linear polymer content. Further addition of linear chains yielded a re-entrant liquid. This unexpected behavior was rationalized by the interplay of three possible phenomena: (i) depletion interactions, driven by the size disparity between the stars and the polymer length scale which is the mesh size of its entanglement network; (ii) colloidal deswelling due to the increased osmotic pressure exerted onto the stars; and (iii) a concomitant progressive suppression of the depletion efficiency on increasing the polymer concentration due to reduced mesh size, hence a smaller range of attraction. Our results unveil an exciting new way to tailor the flow of soft colloids and highlight a largely unexplored path to engineer soft colloidal mixtures.

Glass transition and reversible gelation in asymmetric binary mixtures: A study by mode coupling theory and molecular dynamics

The glass transition and the binodals of asymmetric binary mixtures are investigated from the effective fluid approach in the mode coupling theory and by molecular dynamics. Motivated by previous theoretical predictions, the hard-sphere mixture and the Asakura-Oosawa models are used to analyze experimental results from the literature, relative to polystyrene spheres mixed either with linear polymers or with dense microgel particles. In agreement with the experimental observations, the specificity of the depletant particles is shown to favor lower density gels. It further favors equilibrium gelation by reducing also the tendency of the system to phase separate. These results are confirmed by a phenomenological modification of the mode coupling theory in which the vertex functions are computed at an effective density lower than the actual one. A model effective potential in asymmetric mixtures of hard particles is used to further check this phenomenological modification against molecular dynamics simulation.

α-relaxation, shear viscosity, and elastic moduli of hard-particle fluids from a mode-coupling theory with a retarded vertex

The recently proposed modification of the mode-coupling theory (MCT) in which the static structure used in the vertex is computed at a lower density than the actual one is tested on several dynamics-related properties. The predictions from this modified version of MCT calibrated on the one-component hard-sphere fluid are found in very good agreement with simulation data for one-component and binary hard-sphere fluids. They are also relevant for the stress moduli for models with attractive tails beyond the hard core. The clear improvement observed on several properties should give a new impetus to the use of MCT as a quantitative tool.

Different scenarios of dynamic coupling in glassy colloidal mixtures

The composition of mixtures determines the mechanism of glass formation and dynamic coupling of different species.

Glass transition in hard-core fluids and beyond, using an effective static structure in the mode coupling theory

The dynamical arrest in classical fluids is studied using a simple modification of the mode coupling theory (MCT) aimed at correcting its overestimation of the tendency to glass formation while preserving its overall structure. As in previous attempts, the modification is based on the idea of tempering the static pair correlations used as input. It is implemented in this work by computing the static structure at a different state point than the one used to solve the MCT equation for the intermediate scattering function, using the pure hard-sphere glass for calibration. The location of the glass transition predicted from this modification is found to agree with simulations data for a variety of systems --pure fluids and mixtures with either purely repulsive interaction potentials or ones with attractive contributions. Besides improving the predictions in the long-time limit, and so reducing the non-ergodicity domain, the same modification works as well for the time-dependent correlators.

Different mechanisms for dynamical arrest in largely asymmetric binary mixtures

Using confocal microscopy we investigate binary colloidal mixtures with large size asymmetry, in particular the formation of dynamically arrested states of the large spheres. The volume fraction of the system is kept constant, and as the concentration of small spheres is increased we observe a series of transitions of the large spheres to different arrested states: an attractive glass, a gel, and an asymmetric glass. These states are distinguished by the degree of dynamical arrest and the amount of structural and dynamical heterogeneity. The transitions between two different arrested states occur through melting and the formation of a fluid state. While a space-spanning network of bonded particles is found in both arrested and fluid states, only arrested states are characterized by the presence of a space-spanning network of dynamically arrested particles.

Bond lifetime and diffusion coefficient in colloids with short-range interactions

We use molecular dynamics simulations to study the influence of short-range structures in the interaction potential between hard-sphere-like colloidal particles. Starting from model potentials and effective potentials in binary mixtures computed from the Ornstein-Zernike equations, we investigate the influence of the range and strength of a possible tail beyond the usual core repulsion or the presence of repulsive barriers. The diffusion coefficient and mean "bond" lifetimes are used as indicators of the effect of this structure on the dynamics. The existence of correlations between the variations of these quantities with the physical parameters is discussed to assess the interpretation of dynamics slowing down in terms of long-lived bonds. We also discuss the question of a universal behaviour determined by the second virial coefficient B ((2)) and the interplay of attraction and repulsion. While the diffusion coefficient follows the B ((2)) law for purely attractive tails, this is no longer true in the presence of repulsive barriers. Furthermore, the bond lifetime shows a dependence on the physical parameters that differs from that of the diffusion coefficient. This raises the question of the precise role of bonds on the dynamics slowing down in colloidal gels.

Depletion potentials in highly size-asymmetric binary hard-sphere mixtures: comparison of simulation results with theory

We report a detailed study, using state-of-the-art simulation and theoretical methods, of the effective (depletion) potential between a pair of big hard spheres immersed in a reservoir of much smaller hard spheres, the size disparity being measured by the ratio of diameters q ≡ σ(s)/σ(b). Small particles are treated grand canonically, their influence being parameterized in terms of their packing fraction in the reservoir η(s)(r). Two Monte Carlo simulation schemes--the geometrical cluster algorithm, and staged particle insertion--are deployed to obtain accurate depletion potentials for a number of combinations of q ≤ 0.1 and η(s)(r). After applying corrections for simulation finite-size effects, the depletion potentials are compared with the prediction of new density functional theory (DFT) calculations based on the insertion trick using the Rosenfeld functional and several subsequent modifications. While agreement between the DFT and simulation is generally good, significant discrepancies are evident at the largest reservoir packing fraction accessible to our simulation methods, namely, η(s)(r) = 0.35. These discrepancies are, however, small compared to those between simulation and the much poorer predictions of the Derjaguin approximation at this η(s)(r). The recently proposed morphometric approximation performs better than Derjaguin but is somewhat poorer than DFT for the size ratios and small-sphere packing fractions that we consider. The effective potentials from simulation, DFT, and the morphometric approximation were used to compute the second virial coefficient B(2) as a function of η(s)(r). Comparison of the results enables an assessment of the extent to which DFT can be expected to correctly predict the propensity toward fluid-fluid phase separation in additive binary hard-sphere mixtures with q ≤ 0.1. In all, the new simulation results provide a fully quantitative benchmark for assessing the relative accuracy of theoretical approaches for calculating depletion potentials in highly size-asymmetric mixtures.

Gelation and phase coexistence in colloidal suspensions with short-range forces: generic behavior versus specificity

The interplay between physical gelation and equilibrium phase transitions in asymmetric binary mixtures is analyzed from the effective fluid approach, in which the big particles interact via a short-range effective attraction beyond the core due to the depletion mechanism. The question of the universality of the scenario for dynamical arrest is then addressed. The comparison of the phase diagrams of the hard-sphere mixture and the Asakura-Oosawa models at various size ratios shows that strong specificity is observed for nonideal depletants. In particular, equilibrium gelation, without the competition with fluid-fluid transition is possible in mixtures of hard-sphere colloids. This is interpreted from the specificities of the effective potential, such as its oscillatory behavior and its complex variation with the physical parameters. The consequences on the dynamical arrest and the fluid-fluid transition are then investigated by considering in particular the role of the well at contact and the first repulsive barrier. This is done for the actual effective potential in the hard-sphere mixture and for a square well and shoulder model, which allows a separate discussion of the role of the different parameters, in particular on the localization length and the escape time. This study is next extended to mixtures of "hard-sphere-like" colloids with residual interactions. It confirms the trends relative to equilibrium gelation and illustrates a diversity of the phase behavior well beyond the scenarios expected from simple models.

Hard-sphere fluids in annular wedges: density distributions and depletion potentials

We analyze the density distribution and the adsorption of solvent hard spheres in an annular slit formed by two large solute spheres or a large solute and a wall at close distances by means of fundamental measure density-functional theory, anisotropic integral equations, and simulations. We find that the main features of the density distribution in the slit are described by an effective two-dimensional system of disks in the vicinity of a central obstacle. This has an immediate consequence for the depletion force between the solutes (or the wall and the solute) since the latter receives a strong line-tension contribution due to the adsorption of the effective disks at the circumference of the central obstacle. For large solute-solvent size ratios, the resulting depletion force has a straightforward geometrical interpretation which gives a precise "colloidal" limit for the depletion interaction. For intermediate size ratios of 5-10 and high solvent packing fractions larger than 0.4, the explicit density-functional results show a deep attractive well for the depletion potential at solute contact, possibly indicating demixing in a binary mixture at low solute and high solvent packing fraction besides the occurrence of gelation and freezing.