Calculation of critical nucleation rates by the persistent embryo method: application to quasi hard sphere models

Abstract

We study crystal nucleation of the Weeks-Chandler-Andersen (WCA) model, using the recently introduced Persistent Embryo Method (PEM). The method provides detailed characterization of pre-critical, critical and post-critical nuclei, as well as nucleation rates that compare favorably with those obtained using other methods (umbrella sampling, forward flux sampling or seeding). We further map our results to a hard sphere model allowing to compare with other existing predictions. Implications for experiments are also discussed.* Email: yangsun@ameslab.gov (Y.S.) or fzhang@ameslab.gov (F.Z.) 11 . Experimental nucleation rates, however, remain in significant disagreement with most existing theoretical predictions using these simple models 4,12 .Recently, we have introduced the Persistent Embryo Method (PEM) 13 and applied it to the investigation of the nucleation of pure Ni and binary CuZr by all atom MD simulations. In this paper, we demonstrate that PEM is an efficient method by applying it to the Weeks-Chandler-Andersen (WCA) model 14 , assuming the validity of CNT. As we describe further below, PEM can measure the nucleation rate in the low-density regime and does not make any geometrical assumption on the shape of nucleus. Moreover, PEM can obtain the unbiased configuration of the critical nucleus. We expect that PEM will become the method of choice as the optimal implementation of CNT for certain problems. Furthermore, given the current disagreements between nucleation rates as measured in experiments or calculated by theory, new techniques are crucial, in that they provide additional insights on the origins of such discrepancies. This paper is organized as follows: in Sec. 2 we present the WCA model, including the description of Brownian dynamics and order parameter. In Sec. 3 we show the method and discuss the calculation of other necessary quantities, such as the chemical potential. Sec. 4 describes the persistent-embryo method (PEM) and Sec. 5 describes the determination of attachment rate. In Sec. 6, we derive the rate equation and present our predictions. In Sec. 7, we discuss our results and compare them with existing estimates obtained by other methods. A comparison with experimental results is also included. The conclusions are left for Sec. 8. WCA model and simulation details

Analysis of Self-Assembly Pathways with Unsupervised Machine Learning Algorithms

“…Our simulation and analysis of the WCA system confirms observations made previously by Auer and Frenkel, 52 Kawasaki and Tanaka, 4 and recently by Ren et al, 2 that fluctuations of 2) compared to all other environments, with the HCP-like environment (0) between the fluid and FCC (3 and 4) (a). The Steinhardt order parameter Q l , here evaluated for l = 4, 6, 8, and 10, shows narrow distributions of Q 6 for both HCP (0) and FCC (3 and 4).…”

“…The self-assembly of colloidal hard spheres was simulated with the WCA model which approximates the interaction of physical hard spheres via a purely repulsive and short-ranged energy function. The self-assembly behavior of WCA spheres has been studied extensively ,, and was recently analyzed with a similar unsupervised ML approach by Boattini et al The system represents a suitable benchmark for the validation of novel colloidal crystallization pathway analysis methods. We sampled the system with Molecular Dynamics in the NPT ensemble with a constant system size N , pressure P , and temperature T .…”

“…The remaining discrepancy between predicted nucleation and growth rates and those measured in experiment suggests that our models of the crystallization process are still insufficient in capturing all relevant effects. 1,2 One particular ambiguity in studying crystallization is the identification of local motifs that particles participate in as they transform from fluid to solid. The advent of machine learning (ML) in the field of chemical physics provides an avenue to reduce such ambiguities and autonomously identify relevant particle environments, as we will show in this paper.…”

Studying rare events using forward-flux sampling: Recent breakthroughs and future outlook

“…As such, nucleation rate estimates for WCA colloids have been made via direct BD, 57 MD, 79,80 umbrella sampling, 57 the seeding method, 80 and the persistent embryo method. 234 FFS was first used by Filion et al, 57 along with direct BD and umbrella sampling, to calculate nucleation rates for the WCA model with β = 40. The rate estimates obtained from all three methods agreed well with each other and the dependence of the obtained rate on the effective packing fraction, φ eff , was similar to that of hard spheres.…”

Competitive B2 and B33 Nucleation during Solidification of Ni50Zr50 Alloy: Molecular Dynamics Simulation and Classical Nucleation Theory

“…The nucleation process can be efficiently sampled in the PEM by preventing a small crystal embryo consisting of N 0 atoms (N 0 ≪ N*) from melting using external spring forces. 27,28,39 Very long ineffective simulations, in which the system is very far away from forming the critical nucleus, are avoided in this method. As the embryo grows, the harmonic potential is gradually weakened and is completely removed when the cluster size reaches a subcritical threshold, N sc (N 0 < N sc < N*).…”