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

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 At an activity just above the MIPS critical point, the liquid-gas binodal is superseded by the crystal-fluid coexistence curve, with solid, liquid, and gas all coexisting at the triple point where the two curves intersect.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.

Disordered collective motion in dense assemblies of persistent particles

“…Hence, our results (for example Fig. 1) parallel the similar programme that was recently completed for monodisperse particles, which display ordered phases at large density [26][27][28].…”

Wetting Transition of Active Brownian Particles on a Thin Membrane

“…Following previous studies [15,30], we take the number density ρ ¼ N=V and the Péclet number Pe ¼ v 0 =σD r as control parameters, where N is the number of particles, V the total volume in units of σ d (with σ the particle diameter), v 0 is the swimming speed, and D r is the rotational diffusion constant, coupled to the translational diffusivity by D r ¼ 3D t =σ 2 , which defines an intrinsic persistent-motion timescale τ R ¼ 1=D R . This standard setting gives rise to liquid-gas MIPS both in 2D and 3D, with the difference that in the latter case this is metastable with respect to crystal-gas phase separation [15,31].…”

Noether's Theorem in Statistical Mechanics

“…This would allow to investigate whether Triezenberg and Zwanzig's concept that they originally developed for the free gas-liquid interface applies to the also self-sustained density inhomogeneity in a solid. Furthermore, addressing further cases of self motility [42][43][44], including active freezing [99,100], as well as further types of time evolution, such as molecular dynamics or quantum mechanics should be interesting. This is feasible, as the Noether considerations are not restricted to overdamped classical systems, as (formal) power functional generators exist for quantum [101] and classical Hamiltonian [102] many-body systems.…”