As a result of the competition between self-propulsion and excluded volume interactions, purely repulsive self-propelled spherical particles undergo a motility-induced phase separation (MIPS). We carry out a systematic computational study, considering several interaction potentials, systems confined by hard walls or with periodic boundary conditions, and different initial conditions. This approach allows us to identify that, despite its non-equilibrium nature, the equations of state of Active Brownian Particles (ABP) across MIPS verify the characteristic properties of first-order liquid-gas phase transitions, meaning, equality of pressure of the coexisting phases once a nucleation barrier has been overcome and, in the opposite case, hysteresis around the transition as long as the system remains in the metastable region. Our results show that the equations of state of ABPs account for their phase behaviour, providing a firm basis to describe MIPS as an equilibrium-like phase transition.

SignificanceCollections of polar active particles have been unable to form stable and long-living structures due to the presence of self-propulsion. We solve this timely issue by introducing the concept of “active doping” and show that a few light-activated apolar, i.e., non–self-propelling, units can be used to rapidly trigger the formation of solid clusters and gels composed of passive colloidal particles. Our active doping can be used to assemble disparate microscopic objects, including synthetic or biological ones, paving the way toward the extension of fundamental concepts of gel and glass formation to active out-of-equilibrium systems.

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