Collective behaviour of Self-Propelled Particles: Non-equilibrium phase coexistence in active systems

Abstract

Self-propelled colloids are microscopic entities of typical size between a few nanometers to a few micrometers that exhibit persistent random motion in a medium such as oil or water, due to a continuous intake of energy from its surroundings. Such non-equilibrium systems are also termed as Active matter. A large collection of these constituents (or agents) shows extremely interesting phenomena like clustering, condensation and phase separation which otherwise are not observable for ‘passive’ systems and are highly desirable technologically in applications involving drug delivery, cleaning pollutants from water, oil recovery etc. The out-of-equilibrium nature of these systems makes it difficult to predict their behaviour. Hence, there is a significant interest in exploring an extended thermodynamical description of these systems. In this thesis, we study the collective behaviour of such systems using the active Brownian particle (ABP) model and the tools of statistical physics and computer simulations. We explore some of the principles which govern their emergent behaviour such as phase separation and the effects at the interface by systematically investigating the effect of increasing drive/activity in pushing the system away from equilibrium and whether certain known physical quantities can be extended to account for these effects. In the first two chapters, Chapter 2 and 3, we study the effect of slowly increasing the activity on, respectively, the density of coexisting states and the interfacial tension in systems of ABPs while comparing with the passive system of an Lennard-Jones (LJ) fluid. We study the shift in the binodals and investigate the temperature-scaling of the order-parameters describing the densities of coexisting states and numerically establish an exponential dependence. We further explore the local mechanical equilibrium and the interfacial tension and obtain similar scaling with respect to the degree of activity as we increase the temperature. In Chapter 4 we investigate the phase separation from a microscopic approach and propose a chemical-potential like quantity for active systems, which includes an additional contribution due to the activity of particles. We study mechanical and diffusive equilibrium in systems at low and high activity to identify the coexisting densities from the conditions of having equal bulk pressure and bulk chemical potential as found in equilibrium systems. We continue this investigation further in Chapter 5 where we explicitly perturb the interface by applying an external potential. We find that the densities of the two bulk states, in the regions arbitrarily far away, on either side of the external potential depend significantly on the parameters of the potential itself. In Chapter 6 we focus on connecting the phase transitions in two-dimensional equilibrium systems of repulsive disks to the phase separation induced due to the motility of active systems. We establish that the two-step melting scenario is similar to passive systems upto a low degree of activity but differs for highly active systems. We particularly investigate the hexatic-solid transition further and the role of topological defects on the elastic constants and find interesting hexatic states devoid of defects not typically observed in equilibrium systems.