Effective Equilibrium, Power Functional, and Interface Structure for Phase-Separating Active Brownian Particles

Abstract

In this thesis we approach the physics of active Brownian particles (ABP) and particularly the emergence of motility induced-phase separation (MIPS) by (i) an effective equilibrium description for small activities [1], (ii) a formally exact power functional theory [2, 3], and (iii) a computer simulation study of the free interface between coexisting phases [4]. Active Brownian particles are modeled as spherical particles that obey Brownian motion described by an overdamped Langevin equation of motion. Activity is thereby induced by a self-propulsion force. This force acts along the built-in orientation of each individual particle, and the time dependence of the orientation is given by an additional Langevin equation that describes free rotational diffusion. This intrinsic out-of-equilibrium system shows a wide variety of phenomena, where phase separation in absence of explicit interparticle attraction between the particles is one of the most spectacular open problems. In the effective equilibrium approach the active system is mapped onto a system of passive Brownian particles that interact via a modified effective interparticle interaction [1]. This is achieved by integrating out the orientations. The resulting Langevin equation contains colored noise. From this equation of motion an approximated Fokker-Planck equation is constructed. In this Fokker-Planck equation an activity-dependent effective interaction force between the particles is identified. In the case of pairwise interaction, the effective interaction can be represented as an activity-dependent effective pair interaction potential. For purely repulsive interaction potentials, an attractive tail develops above an activity threshold. The strength of this attraction increases even further with increasing activity, eventually leading to bulk phase separation. Furthermore, passively attractive interactions are considered, namely the Lennard-Jones potential. In this case, the attractive minimum of the potential weakens at first when activity is increased and suppression of phase separation is observed. Increasing the activity further, the attractive minimum deepens again and a reentrance of phase separation emerges. As the activity determines only the form of the effective interaction and the many-body dynamics resemble the passive dynamics, common methods of liquid state theory can be applied to active systems. We use them for instance to calculate spinodals and the pair correlation function for the active system. An important part of the work is the validation via computer simulations, where the orientations are not integrated out, i.e., the full many-body problem of ABP is considered. The result is that in all situations presented we find a good match between theory and the simulation. Despite the success of the effective equilibrium description in many situations, possible applications are rather limited to low activity cases due to the approximations made in the construction of the Fokker-Planck equation. In order to overcome these limitations we…