Pathways to self-organization: Crystallization via nucleation and growth

Abstract

Crystallization, a prototypical self-organization process during which a disordered state spontaneously transforms into a crystal characterized by a regular arrangement of its building blocks, usually proceeds by nucleation and growth. In the initial stages of the transformation, a localized nucleus of the new phase forms in the old one due to a random fluctuation. Most of these nuclei disappear after a short time, but rarely a crystalline embryo may reach a critical size after which further growth becomes thermodynamically favorable and the entire system is converted into the new phase. In this article, we will discuss several theoretical concepts and computational methods to study crystallization. More specifically, we will address the rare event problem arising in the simulation of nucleation processes and explain how to calculate nucleation rates accurately. Particular attention is directed towards discussing statistical tools to analyze crystallization trajectories and identify the transition mechanism.

The Gibbs free energy of homogeneous nucleation: From atomistic nuclei to the planar limit

“…After dropping the higher order correction terms, we obtain (11), which has the same mathematical form as the Tolman correction, has two components: the δn s Φ,V term stems from the difference between the Φ-based dividing surface and the equimolar surface, while the other term is determined from the Tolman length and has a value that is independent of the choice of the dividing surface. Hereafter, we will use CNT(Φ)+Tol to denote the expression in Eqn.…”

“…Hereafter, we will use CNT(Φ)+Tol to denote the expression in Eqn. (11) in order to highlight its dependence on the chosen extensive quantity. An awareness of this dependence on the choice of Φ is crucial when comparing studies performed with different protocols.…”

“…The red symbols indicate the values of the estimates for the fitting parameters γ Φ ∞ Ω that are obtained from the CNT(Φ)+Tol model divided by the estimated Ω at each temperature. In the bottom panel, the red symbols indicate the Tolman correction constant ζ in the CNT(Φ)+Tol fits, while the black symbols indicate the estimate for ζ that is obtained when the planar interface results for µ sl and γ Φ ∞ are used in Eqn (11)…”

Evaporating laminar microjets for studies of rapidly evolving structural transformations in supercooled liquids

“…The fate of a supercooled liquid ultimately depends on the interplay between cooling rate and nucleation time [1]. Usually, a liquid-to-solid first-order phase transition occurs, the dynamics of which is governed by homogeneous crystal nucleation [2,3] followed by crystal growth [4][5][6]. If crystallization can be avoided by cooling the liquid at sufficiently high rates, an amorphous solid (a glass) may form [7][8][9].…”

Theoretische Chemie 2016: Multiskalensimulation von Bio- und Biomaterialsystemen

“…Dazu sind Enhanced-sampling-Methoden nötig. 7,8) Hierbei ist die Nichtgleichgewichtssituation der übersättigten Lösung eine methodische Herausforderung.…”