Pathways of Cluster Growth and Kinetic Slowing Down in a Model of Short-Range Attractive Colloids

Abstract

We present the results of an extensive 3D Brownian dynamics simulation of the self-assembly of colloidal particles for a short-range attractive model that is quenched below its metastable critical point. In particular, results are obtained in the small-volume-fraction, low-temperature region in which we find so-called sticky beads that diffuse around the system, without reaching a final large cluster on the timescale of our simulation. For larger volume fractions in this low-temperature regime, a gel forms as the result of kinetically slowed down spinodal decomposition, as shown earlier for other short-range attractive models (Foffi, G.; De Michele, C.; Sciortino, F.; Tartaglia, P. Phys. Rev. Lett. 2005, 94, 078301. Zaccarelli, E. J. Phys.: Condens. Matter 2007, 19, 323101). We also show that for quenches below the critical point but above the intersection of the binodal with the glass line, two-step crystallization takes place. For sufficiently small volume fractions, the first step is the nucleation of dense fluid drops, followed by the second step of crystallization within these drops, as first proposed for a model of protein crystallization for quenches just above the metastable critical point (ten Wolde, P. R.; Frenkel, D. Science 1997, 277, 1975). For larger values of the volume fraction, the initial step is spinodal decomposition that leads to the formation of an interconnected network of low- and high-density fluids. The second step is crystallization that takes place within the dense fluid phase.

Collective translational and rotational Monte Carlo moves for attractive particles

“…It is shown in Appendix A that although these sets are not the same under the restriction (1c) of this section, nothing changes in the algorithm if we assume that the sets are identical, and we can thus use the simple form of the acceptance cluster probability (27) for the free cluster selection. Since generally F (μ) = F (ν) and B (μ) = B (ν) , we say that the realization of the cluster has asymmetric core and symmetric boundary.…”

“…We again use the SDB condition (22) to express the acceptance probability as in Eq. (27). Equation (27) can then be further simplified by considering relations (13) and (29) which imply…”

“…(27). Equation (27) can then be further simplified by considering relations (13) and (29) which imply…”

“…Note that, if the cluster is not restricted by N C or other conditions, then B * = B, B † = ∅, and the acceptance probability reduces to Eqs. (27). Also, in the derivation of the acceptance probability, we assumed that C was selected by free cluster selection, proposing links to all pairs satisfying (1a) and (1b).…”

“…By using a reasoning analogous to that in Sec. IV, and by using relations (39) and (40), the explicit SDB condition (42) can be simplified into the form (25), and further into the form (27). We note that auxiliary conditions in the SDB condition were originally defined such that {b} should also include the probability of generating S (μ) R .…”