Crystal nucleation of hard spheres using molecular dynamics, umbrella sampling, and forward flux sampling: A comparison of simulation techniques

Abstract

Over the last number of years several simulation methods have been introduced to study rare events such as nucleation. In this paper we examine the crystal nucleation rate of hard spheres using three such numerical techniques: molecular dynamics, forward flux sampling, and a Bennett-Chandler-type theory where the nucleation barrier is determined using umbrella sampling simulations. The resulting nucleation rates are compared with the experimental rates of Harland and van Megen [Phys. Rev. E 55, 3054 (1997)], Sinn et al. [Prog. Colloid Polym. Sci. 118, 266 (2001)], Schätzel and Ackerson [Phys. Rev. E 48, 3766 (1993)], and the predicted rates for monodisperse and 5% polydisperse hard spheres of Auer and Frenkel [Nature 409, 1020 (2001)]. When the rates are examined in units of the long-time diffusion coefficient, we find agreement between all the theoretically predicted nucleation rates, however, the experimental results display a markedly different behavior for low supersaturation. Additionally, we examined the precritical nuclei arising in the molecular dynamics, forward flux sampling, and umbrella sampling simulations. The structure of the nuclei appears independent of the simulation method, and in all cases, the nuclei contains on average significantly more face-centered-cubic ordered particles than hexagonal-close-packed ordered particles.

Crystallization in suspensions of hard spheres: a Monte Carlo and molecular dynamics simulation study

“…During the quench we monitored the crystallinity to ensure that no crystal precursors were formed. (As prestructuring during the preparation procedure can have a significant impact on the nucleation behaviour, we cross-checked the quality of our starting configurations; the authors of [10] ran trajectories from our starting configurations using their simulation code. Within the error bars we found no differences in the crystallization process observed.…”

“…The simple interaction potential makes hard spheres a particularly popular model system for computer simulation studies of crystallization and the competing glass transition (see e.g. [2][3][4][5][6][7][8][9][10]). …”

“…However, in the meantime computers have become fast enough to sample crystal nucleation by 'brute force' simulation in simple model systems, such as hard spheres. Hence hard spheres have recently been used to test the predictions of rare event sampling techniques (such as results obtained by Umbrella Sampling [3]) and to compare nucleation pathways directly to experiment [6,10].…”

Crystal nucleation of colloidal hard dumbbells

“…It has been shown recently that the choice of order parameter (r c , d c , and ξ c ) does not affect the resulting nucleation rate if it is not too restrictive. 20,23 To analyze the structure of the critical nuclei, we use the averaged local bond order parameter q l and w l proposed by Lechner and Dellago, 24 which allows us to identify each particle as fcc-like or hcp-like, provided the number of neighboring particles N b (i) ≥ 10:…”

Nonclassical Nucleation in a Solid-Solid Transition of Confined Hard Spheres

“…In order to gain a better fundamental understanding of how to control self-assembly processes in the fabrication of novel structures, many experimental and simulation studies have been devoted to colloidal systems. Experiments [1-4] and computer simulations [5][6][7] on bulk hard-sphere colloids suggested that the metastable fluid crystallizes and superheated crystals melt via a single-step nucleation process that is well described by classical nucleation theory (CNT) [8]. However, Ostwald's step rule suggests that the kinetic pathway to the most stable state can initially proceed through the nucleation of intermediate, metastable phases [9].…”