Limit of validity of Ostwald's rule of stages in a statistical mechanical model of crystallization

TL;DR

This paper investigates the limitations of Ostwald's rule of stages in predicting crystallization pathways using a statistical mechanical model of patchy particles, revealing richer behaviors and microscopic controls.

Contribution

It provides a detailed analysis combining simulation and theory to understand when Ostwald's rule applies or fails in a model of crystallization.

Findings

Crystallization pathways are more diverse than Ostwald's rule predicts.

Microscopic parameters influence pathway selection.

Strategies for controlling self-assembly are proposed.

Abstract

We have only rules of thumb with which to predict how a material will crystallize, chief among which is Ostwald's rule of stages. It states that the first phase to appear upon transformation of a parent phase is the one closest to it in free energy. Although sometimes upheld, the rule is without theoretical foundation and is not universally obeyed, highlighting the need for microscopic understanding of crystallization controls. Here we study in detail the crystallization pathways of a prototypical model of patchy particles. The range of crystallization pathways it exhibits is richer than can be predicted by Ostwald's rule, but a combination of simulation and analytic theory reveals clearly how these pathways are selected by microscopic parameters. Our results suggest strategies for controlling self-assembly pathways in simulation and experiment.