Phase Diagram of Active Brownian Spheres: Crystallization and the Metastability of Motility-Induced Phase Separation

TL;DR

This paper investigates the phase behavior of active Brownian particles, revealing that motility-induced phase separation is metastable in three dimensions and often transitions to active crystallization at high activity levels.

Contribution

It uncovers the metastability of MIPS in 3D active particles and characterizes the active crystallization process and conditions leading to phase transitions.

Findings

MIPS is metastable and decays via active crystallization.

Active crystallization occurs at high activity and near maximal packing.

Liquid-gas coexistence lifetime decreases with increasing activity.

Abstract

Motility-induced phase separation (MIPS), the phenomenon in which purely repulsive active particles undergo a liquid-gas phase separation, is among the simplest and most widely studied examples of a nonequilibrium phase transition. Here, we show that states of MIPS coexistence are in fact only metastable for three-dimensional active Brownian particles over a very broad range of conditions, decaying at long times through an ordering transition we call active crystallization. At an activity just above the MIPS critical point, the liquid-gas binodal is superseded by the crystal-fluid coexistence curve, with solid, liquid, and gas all coexisting at the triple point where the two curves intersect. Nucleating an active crystal from a disordered fluid, however, requires a rare fluctuation that exhibits the nearly close-packed density of the solid phase. The corresponding barrier to crystallization is surmountable on a feasible timescale only at high activity, and only at fluid densities near maximal packing. The glassiness expected for such dense liquids at equilibrium is strongly mitigated by active forces, so that the lifetime of liquid-gas coexistence declines steadily with increasing activity, manifesting in simulations as a facile spontaneous crystallization at extremely high activity.