Eduardo Sanz

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 diagram of a tetrahedral patchy particle model for different interaction ranges

We evaluate the phase diagram of the Kern–Frenkel patchy model with four interaction sites for four different values of the radial interaction range (all in the single-bond-per-patch regime) keeping the area of the interaction patches fixed. Four stable crystal phases are investigated, namely diamond cubic (DC), bcc, fcc, and plastic fcc. The DC is favored at low temperatures and pressures, while the bcc is favored at low temperatures and intermediate to high pressures. At low temperatures and very high pressures an ordered fcc phase is found, while—as expected—at high temperatures, the only stable crystal is a plastic fcc phase. We find a rich phase diagram with several re-entrant coexistence lines, which can be brought in the equilibrium phase diagram by a proper choice of the range. We also show that the gas-liquid phase separation becomes metastable as the range narrows, and it takes place in a region of the phase diagram where the low density diamond crystal is the thermodynamically stable phase.

Crystallization of tetrahedral patchy particles in silico.

We investigate the competition between glass formation and crystallization of open tetrahedral structures for particles with tetrahedral patchy interactions. We analyze the outcome of such competition as a function of the potential parameters. Specifically, we focus on the separate roles played by the interaction range and the angular width of the patches, and show that open crystal structures (cubic and hexagonal diamond and their stacking hybrids) spontaneously form when the angular width is smaller than about 30°. Evaluating the temperature and density dependence of the chemical potential of the fluid and of the crystal phases, we find that adjusting the patch width affects the fluid and crystal in different ways. As a result of the different scaling, the driving force for spontaneous self-assembly rapidly grows as the fluid is undercooled for small-width patches, while it only grows slowly for large-width patches, in which case crystallization is pre-empted by dynamic arrest into a network glass.

Dynamic Monte Carlo versus Brownian dynamics: A comparison for self-diffusion and crystallization in colloidal fluids

Here we present a comparative study of dynamic Monte Carlo and Brownian dynamics simulations of colloidal systems with repulsive interactions. We show that if the Monte Carlo time is rescaled with the acceptance probability, the estimates of the self-diffusion coefficient and of the crystallization times are, respectively, in good and fair agreement with the Brownian dynamics simulations. We also analyze the case of a particle in a one-dimensional potential, where we show that the convergence of a Monte Carlo procedure to the Brownian dynamics result is faster when time is rescaled by the acceptance probability, which gives a theoretical basis for this practical recipe.

Crystallization and gelation in colloidal systems with short-ranged attractive interactions

We systematically study the relationship between equilibrium and nonequilibrium phase diagrams of a system of short-ranged attractive colloids. Using Monte Carlo and Brownian dynamics simulations we find a window of enhanced crystallization that is limited at high interaction strength by a slowing down of the dynamics and at low interaction strength by the high nucleation barrier. We find that the crystallization is enhanced by the metastable gas-liquid binodal by means of a two-stage crystallization process. First, the formation of a dense liquid is observed and second the crystal nucleates within the dense fluid. In addition, we find at low colloid packing fractions a fluid of clusters, and at higher colloid packing fractions a percolating network due to an arrested gas-liquid phase separation that we identify with gelation. We find that this arrest is due to crystallization at low interaction energy and it is caused by a slowing down of the dynamics at high interaction strength. Likewise, we observe that the clusters which are formed at low colloid packing fractions are crystalline at low interaction energy, but glassy at high interaction energy. The clusters coalesce upon encounter.

Crystallization mechanism of hard sphere glasses.

In supercooled liquids, vitrification generally suppresses crystallization. Yet some glasses can still crystallize despite the arrest of diffusive motion. This ill-understood process may limit the stability of glasses, but its microscopic mechanism is not yet known. Here we present extensive computer simulations addressing the crystallization of monodisperse hard-sphere glasses at constant volume (as in a colloid experiment). Multiple crystalline patches appear without particles having to diffuse more than one diameter. As these patches grow, the mobility in neighboring areas is enhanced, creating dynamic heterogeneity with positive feedback. The future crystallization pattern cannot be predicted from the coordinates alone: Crystallization proceeds by a sequence of stochastic micronucleation events, correlated in space by emergent dynamic heterogeneity.

On fluid-solid direct coexistence simulations: the pseudo-hard sphere model.

We investigate methodological issues concerning the direct coexistence method, an increasingly popular approach to evaluate the solid-fluid coexistence by means of computer simulations. The first issue is the impact of the simulation ensemble on the results. We compare the NpT ensemble (easy to use but approximate) with the NpzT ensemble (rigorous but more difficult to handle). Our work shows that both ensembles yield similar results for large systems (>5000 particles). Another issue, which is usually disregarded, is the stochastic character of a direct coexistence simulation. Here, we assess the impact of stochasticity in the determination of the coexistence point. We demonstrate that the error generated by stochasticity is much larger than that caused by the use of the NpT ensemble, and can be minimized by simply increasing the system size. To perform this study we use the pseudo hard-sphere model recently proposed by Jover et al. [J. Chem. Phys. 137, 144505 (2012)], and obtain a coexistence pressure of p∗ = 11.65(1), quite similar to that of hard spheres (only about 0.6% higher). Therefore, we conclude that this model can be reliably used to investigate the physics of hard spheres in phenomena like crystal nucleation.

Colloidal gels assembled via a temporary interfacial scaffold.

The liquid-liquid phase separation of a binary solvent can be arrested by colloidal particles trapped at the interface [K. Stratford, Science 309, 2198 (2005)]. We show experimentally that the colloidal network so formed can remain stable after fully remixing the liquids, creating a new type of gel in which colloids in a single-phase solvent have locally planar coordination. We argue that this structure is likely maintained by primary-minimum Derjaguin-Landau-Verweg-Overbeek bonding of our charged colloids, created under strong compression by capillary forces. We present simulation evidence that the combination of a short-ranged attraction with a repulsive barrier can strongly stabilize such locally planar gels.

Role of the Range in the Fluid−Crystal Coexistence for a Patchy Particle Model

We evaluate the phase diagram of the four-site Kern-Frenkel patchy particle model [Kern, N.; Frenkel, D. J. Chem. Phys. 2003, 118, 9882.], a model representative of particles interacting via short-range orientational interactions, for several values of the interaction range. Similar to what has been found for isotropic potentials, the liquid phase disappears as an equilibrium phase for values of the range on the order of 15% of the particle diameter. For smaller ranges, the gas-liquid phase separation becomes metastable with respect to crystallization into a diamond-like structure. Interestingly, and differently from the isotropic case, the supersaturation of the fluid at the critical point does not significantly increase upon going toward the adhesive (vanishing interaction range) limit.

Gel Formation in Suspensions of Oppositely Charged Colloids: Mechanism and Relation to the Equilibrium Phase Diagram

We study gel formation in a mixture of equally-sized oppositely charged colloids both experimentally and by means of computer simulations. Both the experiments and the simulations show that the mechanism by which a gel is formed from a dilute, homogeneous suspension is an interrupted gas-liquid phase separation. Furthermore, we use Brownian dynamics simulations to study the relation between gel formation and the equilibrium phase diagram. We find that, regardless of the interaction range, an interrupted liquid-gas phase separation is observed as the system is quenched into a state point where the gas-liquid separation is metastable. The structure of the gel formed in our experiments compares well with that of a simulated gel, indicating that gravity has only a minor influence on the local structure of this type of gel. This is supported by the experimental evidence that gels squeezed or stretched by gravity have similar structures, as well as by the fact that gels do not collapse as readily as in the case of colloid-polymer mixtures. Finally, we check whether or not crystallites are formed in the gel branches; we find crystalline domains for the longer ranged interactions and for moderate quenches to the metastable gas-liquid spinodal regime.