Emanuela Zaccarelli

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.

Colloidal gels: equilibrium and non-equilibrium routes

We attempt a classification of different colloidal gels based on colloid‐ colloid interactions. We discriminate primarily between non-equilibrium and equilibrium routes to gelation, the former case being slaved to thermodynamic phase separation while the latter is individuated in the framework of competing interactions and of patchy colloids. Emphasis is put on recent numerical simulations of colloidal gelation and their connection to experiments. Finally, we underline typical signatures of different gel types, to be looked at, in more detail, in experiments. (Some figures in this article are in colour only in the electronic version)

Phase diagram of patchy colloids: towards empty liquids.

We report theoretical and numerical evaluations of the phase diagram for patchy colloidal particles of new generation. We show that the reduction of the number of bonded nearest neighbors offers the possibility of generating liquid states (i.e., states with temperature T lower than the liquid-gas critical temperature) with a vanishing occupied packing fraction (phi), a case which can not be realized with spherically interacting particles. Theoretical results suggest that such reduction is accompanied by an increase of the region of stability of the liquid phase in the (T-phi) plane, possibly favoring the establishment of homogeneous disordered materials at small phi, i.e., stable equilibrium gels.

Equilibrium Cluster Phases and Low-Density Arrested Disordered States: The Role of Short- Range Attraction and Long-Range Repulsion

We study a model in which particles interact with short-ranged attractive and long-ranged repulsive interactions, in an attempt to model the equilibrium cluster phase recently discovered in sterically stabilized colloidal systems in the presence of depletion interactions. At low packing fractions, particles form stable equilibrium clusters which act as building blocks of a cluster fluid. We study the possibility that cluster fluids generate a low-density disordered arrested phase, a gel, via a glass transition driven by the repulsive interaction. In this model the gel formation is formally described with the same physics of the glass formation.

Observation of empty liquids and equilibrium gels in a colloidal clay

The relevance of anisotropic interactions in colloidal systems has recently emerged in the context of the rational design of new soft materials. Patchy colloids of different shapes, patterns and functionalities are considered the new building blocks of a bottom-up approach toward the realization of self-assembled bulk materials with predefined properties. The ability to tune the interaction anisotropy will make it possible to recreate molecular structures at the nano- and micro-scales (a case with tremendous technological applications), as well as to generate new unconventional phases, both ordered and disordered. Recent theoretical studies suggest that the phase diagram of patchy colloids can be significantly altered by limiting the particle coordination number (that is, valence). New concepts such as empty liquids—liquid states with vanishing density—and equilibrium gels—arrested networks of bonded particles, which do not require an underlying phase separation to form—have been formulated. Yet no experimental evidence of these predictions has been provided. Here we report the first observation of empty liquids and equilibrium gels in a complex colloidal clay, and support the experimental findings with numerical simulations.

Higher-order glass-transition singularities in colloidal systems with attractive interactions

The transition from a liquid to a glass in colloidal suspensions of particles interacting through a hard core plus an attractive square-well potential is studied within the mode-coupling-theory framework. When the width of the attractive potential is much shorter than the hard-core diameter, a reentrant behavior of the liquid-glass line and a glass-glass-transition line are found in the temperature-density plane of the model. For small well-width values, the glass-glass-transition line terminates in a third-order bifurcation point, i.e., in a A3 (cusp) singularity. On increasing the square-well width, the glass-glass line disappears, giving rise to a fourth-order A4 (swallow-tail) singularity at a critical well width. Close to the A3 and A4 singularities the decay of the density correlators shows stretching of huge dynamical windows, in particular logarithmic time dependence.

A fresh look at the Laponite phase diagram

By reviewing experimental and theoretical works, we discuss the phase diagram of Laponite suspensions, with the aim of clarifying several issues that have caused a long-time controversy on the system. We claim that, if aging and sample preparation are correctly taken into account, a unifying picture emerges from different experimental studies. Multiple non-ergodic states are identified, including a low concentration equilibrium gel and a high concentration Wigner glass in the absence of salt. These findings are critically discussed also with respect to recent evidence of phase separation at extremely low densities and to existing theoretical and numerical works.

Hard spheres: crystallization and glass formation

Motivated by old experiments on colloidal suspensions, we report molecular dynamics simulations of assemblies of hard spheres, addressing crystallization and glass formation. The simulations cover wide ranges of polydispersity s (standard deviation of the particle size distribution divided by its mean) and particle concentration. No crystallization is observed for s>0.07. For 0.02<s<0.07, we find that increasing the polydispersity at a given concentration slows down crystal nucleation. The main effect here is that polydispersity reduces the supersaturation since it tends to stabilize the fluid but to destabilize the crystal. At a given polydispersity (<0.07), we find three regimes of nucleation: standard nucleation and growth at concentrations in and slightly above the coexistence region; ‘spinodal nucleation’, where the free-energy barrier to nucleation appears to be negligible, at intermediate concentrations; and, at the highest concentrations, a new mechanism, still to be fully understood, which only requires small rearrangement of the particle positions. The cross-over between the second and third regimes occurs at a concentration, approximately 58 per cent by volume, where the colloid experiments show a marked change in the nature of the crystals formed and the particle dynamics indicate an ‘ideal’ glass transition.

Phase equilibria and glass transition in colloidal systems with short-ranged attractive interactions: Application to protein crystallization

We have studied a model of a complex fluid consisting of particles interacting through a hard-core and short-range attractive potential of both Yukawa and square-well form. Using a hybrid method, including a self-consistent and quite accurate approximation for the liquid integral equation in the case of the Yukawa fluid, perturbation theory to evaluate the crystal free energies, and mode-coupling theory of the glass transition, we determine both the equilibrium phase diagram of the system and the lines of equilibrium between the supercooled fluid and the glass phases. For these potentials, we study the phase diagrams for different values of the potential range, the ratio of the range of the interaction to the diameter of the repulsive core being the main control parameter. Our arguments are relevant to a variety of systems, from dense colloidal systems with depletion forces, through particle gels, nanoparticle aggregation, and globular protein crystallization.

Modeling equilibrium clusters in lysozyme solutions

We present a combined experimental and numerical study of the equilibrium cluster formation in globular-protein solutions under no-added salt conditions. We show that a cluster phase emerges as a result of a competition between a long-range screened Coulomb repulsion and a short-range attraction. A simple effective potential, in which electrostatic repulsion is fixed by experimental conditions and attraction is modeled with a generalized Lennard-Jones potential, accounts in a remarkable way for the wavevector dependence of the X-ray scattering structure factor.