Active Brownian equation of state: metastability and phase coexistence

Abstract

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.

Static structure of active Brownian hard disks

“…As the phase diagram confirms [17], there opens a small window where the system is not yet crystallized and not yet phase-separated. We discuss two packing fractions for this case, η = 0.6 and η = 0.7.…”

“…Note however that for strong self-propulsion and/or fast reorientational diffusion, significantly smaller time steps may be required. The extension to active particles has been used to study glassy dynamics of dense AHS systems [18], and more recently also MIPS [17].…”

“…This phenomenon is called motilityinduced phase separation (MIPS) as it shares a number of qualitative features with the liquid-gas phase separation known from equilibrium fluids. MIPS has been studied in great detail for various spherical ABP models with different interactions between the particles [14,15,16], since recently also including the hard-sphere case (using the same simulation algorithm as ours) [17]. Here we deliberately restrict our attention to the homogeneous fluid state outside the spinodal of MIPS.…”

Quorum-sensing active particles with discontinuous motility

“…It has been shown that the mean-field behavior of active Brownian particles can be mapped onto an effective free energy [31,51] and thus follows the same scenario as passive liquid-gas coexistence, although the non-equilibrium nature manifests itself in phenomena like a negative interfacial tension [52] and "bubbly" phase separation [53]. Neverthe- less, the generic relation with passive liquid-gas coexistence has been corroborated by detailed numerical investigations of the phase behavior [27,52,[54][55][56]. The resulting phase diagram in the v 0 -ρ plane is sketched in Fig.…”

Generalized thermodynamics of motility-induced phase separation: phase equilibria, Laplace pressure, and change of ensembles

“…Second, our general theory disregards higher order gradient terms in equation (1). This probably explains why the hydrodynamic description works best fairly close to the critical point, where interfaces are smoothest and the gradient expansion, equation (38), most accurate. The quantitative limitations of our gradient expansion highlights that gradient terms directly influence the coexisting densities through equation (11), unlike the equilibrium case.…”