&Bullet; physics 14, 70

Under the right conditions, simulations show that self-propelled particles move together from a state of liquid gas coexistence to a state in which the particles can crystallize.

Self-propelled particles, whose directions of movement change continuously and randomly, begin in a state of liquid gas coexistence (green, which means more disorder), but eventually crystallize (purple, means more order).

Assemblies of small particles can imitate atoms by forming the equivalents of solids, liquids and gases according to the rules of thermodynamics. However, these rules do not apply to many systems in the natural world because they are out of balance. Of particular interest are systems such as agile bacteria, which use energy to drive the movement of individual particles, which often leads to self-organizing behavior. Now Phillip Geissler of the University of California at Berkeley and his colleagues have used computer simulations to map the full phase diagram of what is perhaps the simplest model of self-propelled particles, and found a surprise: a known state of particles in which areas of liquid and gas coexist, are not completely stable, but eventually crystallize into a solid under the right conditions [1] .

The team studied active Brownian particles (ABPs), which are spheres whose propulsion is continuous but whose direction changes continuously and randomly. They studied the behavior of the particles when two parameters were varied: the strength of the drive and the density of the particles. The resulting 2D phase diagram contained a large area of ​​liquefied gas coexistence known from previous work as motility-induced phase separation (MIPS).

In equilibrium systems, a liquefied gas coexistence phase (the equivalent of the MIPS state) can crystallize when conditions change. However, it is not clear whether there is a solid phase near the MIPS state in the phase diagram for non-equilibrium systems. Geissler and his colleagues found that almost the entire MIPS range of the phase diagram was metastable – not stable for a long time – and that the particles in this state actually transition to a coexistence of solid and liquid or solid and gas. Since a preference for the coexistence of solid gas is already known for most equilibrium systems, the new observations suggest that the behavior of both particle types could ultimately be explained with some kind of unified theory, says Ahmad Omar, member of the Berkeley team.

Bullets unimpressed. Wait long enough and the self-propelled bullets in the simulation above (see video) will switch from a liquefied gas coexistence phase to a solid-liquid coexistence phase. This picture shows a close-up of a solid-liquid interface.

David Ehrenstein

David Ehrenstein is Senior Editor for Physics.


  1. AK Omar et al., “Phase diagram of active Brownian spheres: Crystallization and metastability of the motility-induced phase separation” Phys. Rev. Lett.126188002 (2021).

Subject areas

Soft MatterCondensed Matter Physics

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