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Register a new userGeneralized thermodynamics of Motility-Induced Phase Separation: Phase equilibria, Laplace pressure, and change of ensembles
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Motility-induced phase separation (MIPS) leads to cohesive active matter in the absence of cohesive forces. We present, extend and illustrate a recent generalized thermodynamic formalism which accounts for its binodal curve. Using this formalism, we identify both a generalized surface tension, that controls finite-size corrections to coexisting densities, and generalized forces, that can be used to construct new thermodynamic ensembles. Our framework is based on a nonequilibrium generalization of the Cahn-Hilliard equation and we discuss its application to active particles interacting either via quorum-sensing interactions or directly through pairwise forces.
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We establish the complete phase diagram of self-propelled hard disks in two spatial dimensions from the analysis of the equation of state and the statistics of local order parameters. The equilibrium melting scenario is maintained at small activities, with coexistence between active liquid and hexatic order, followed by a proper hexatic phase and a further transition to an active solid. As activity increases, the emergence of hexatic and solid order is shifted towards higher densities. Above a critical activity and for a certain range of packing fractions, the system undergoes MIPS and demixes into low and high density phases; the latter can be either disordered (liquid) or ordered (hexatic or solid) depending on activity.
Active Brownian particles (ABPs, such as self-phoretic colloids) swim at fixed speed $v$ along a body-axis ${bf u}$ that rotates by slow angular diffusion. Run-and-tumble particles (RTPs, such as motile bacteria) swim with constant $u$ until a random tumble event suddenly decorrelates the orientation. We show that when the motility parameters depend on density $rho$ but not on ${bf u}$, the coarse-grained fluctuating hydrodynamics of interacting ABPs and RTPs can be mapped onto each other and are thus strictly equivalent. In both cases, a steeply enough decreasing $v(rho)$ causes phase separation in dimensions $d=2,3$, even when no attractive forces act between the particles. This points to a generic role for motility-induced phase separation in active matter. However, we show that the ABP/RTP equivalence does not automatically extend to the more general case of $u$-dependent motilities.
A collection of self-propelled particles with volume exclusion interactions can exhibit the phenomenology of gas-liquid phase separation, known as motility-induced phase separation (MIPS). The non-equilibrium nature of the system is fundamental to the phase transition, however, it is unclear whether MIPS at criticality contributes a novel universality class to non-equilibrium physics. We demonstrate here that this is not the case by showing that a generic critical MIPS belongs to the Ising universality class with conservative dynamics.
We review understanding of kinetics of fluid phase separation in various space dimensions. Morphological differences, percolating or disconnected, based on overall composition in a binary liquid or density in a vapor-liquid system, have been pointed out. Depending upon the morphology, various possible mechanisms and corresponding theoretical predictions for domain growth are discussed. On computational front, useful models and simulation methodologies have been presented. Theoretically predicted growth laws have been tested via molecular dynamics simulations of vapor-liquid transitions. In case of disconnected structure, the mechanism has been confirmed directly. This is a brief review on the topic for a special issue on coarsening dynamics, expected to appear in Comptes Rendus Physique.
Using computer simulations and dynamic mean-field theory, we demonstrate that fast enough rotation of circle active Brownian particles in two dimensions generates a dynamical clustering state interrupting the conventional motility induced phase separation (MIPS). Multiple clusters arise from the combination of the conventional MIPS cohesion, and the circulating current caused disintegration. The non-vanishing current in non-equilibrium steady states microscopically originates from the motility ``relieved by automatic rotation, which breaks the detailed balance at the continuum level. This mechanism sheds light on the understanding of dynamic clusters formation observed in a variety of active matter systems, and may help examine the generalization of effective thermodynamic concepts developed in the context of MIPS.
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