Theory of Nonequilibrium Crystallization and the Phase Diagram of Active Brownian Spheres

TL;DR

This paper develops a statistical mechanical framework to understand how activity influences crystallization in active Brownian spheres, revealing shifts in phase transitions and constructing a comprehensive phase diagram.

Contribution

It introduces a novel theoretical approach for active crystallization, extending thermodynamic concepts to active matter and accurately predicting phase behavior.

Findings

Crystallization shifts to higher packing fractions with increased activity.

The phase diagram includes solid-fluid and liquid-gas coexistence curves.

The theory quantitatively matches simulation results for phase boundaries.

Abstract

The crystallization of hard spheres at equilibrium is perhaps the most familiar example of an entropically-driven phase transition. In recent years, it has become clear that activity can dramatically alter this order-disorder transition in unexpected ways. The theoretical description of active crystallization has remained elusive as the traditional thermodynamic arguments that shape our understanding of passive freezing are inapplicable to active systems. Here, we develop a statistical mechanical description of the one-body density field and a nonconserved order parameter field that represents local crystalline order. We develop equations of state, guided by computer simulations, describing the crystallinity field which result in shifting the order-disorder transition to higher packing fractions with increasing activity. We then leverage our recent dynamical theory of coexistence to construct the full phase diagram of active Brownian spheres, quantitatively recapitulating both the solid-fluid and liquid-gas coexistence curves and the solid-liquid-gas triple point.