Active matter in silico: phase behaviour of attractive, repulsive and anisotropic self-propelled particles

Abstract

In this thesis we study emergent statistical properties of many-particle systems of self-propelled particles using computer simulations. Ensembles of self-propelled particles belong to the class of physical systems labeled active matter, a term that refers to systems whose individual components are able to convert internal energy or energy from their environment into motion. Active matter systems are intrinsically out-of-equilibrium systems due to the constant input of energy and yet, surprisingly, paradigms of equilibrium thermodynamics and statistical physics can be applied to active matter in many cases, suggesting that perhaps an extended thermodynamical description of such systems is possible. The model systems that we consider here are toy models that can be associated with the world of active colloids. Colloids are small particles in the nanometer to micrometer scale, typically immersed in a molecular solvent. Our models take into account three essential components that dictate the movement of particles: the self-propulsion of individual particles, the interactions between them and the implicit forces between colloids and surrounding solvent. The first three research chapters of this thesis are devoted to the study of the same system, namely a system of attractive self-propelled spherical particles. In Chapter 2 we focus on the self-assembly of the system and present its phase diagram along with a description of the structural and dynamical properties of the different phases that we identify. In Chapters 3 and 4 we apply statistical physics and critical phenomena language to study, in the former chapter, the vapour-liquid transition of the system and, in the latter chapter, the vapour-liquid interface. In both chapters we make use of equilibrium statistical physics notions such as the mechanical pressure and the surface tension and determine the extent of their possible application to the system. Chapter 5 can be grouped together with the three previous Chapters 2-4 since it concerns systems with purely isotropic interactions among its constituent particles. In this chapter we study two binary mixtures, one of attractive and one of purely repulsive self-propelled particles that undergo vapour-liquid and motility-induced phase separation respectively. The purpose of this chapter is to demonstrate the existence of two quantities, equivalent to the mechanical pressure and the chemical potential of equilibrium systems, and their application to the construction of phase diagrams for active matter systems. In Chapters 6 and 7 we study systems with anisotropic interactions between particles. Chapter 6 contains a description of the phase behaviour and dynamics of a system of self-propelled squares, where the anisotropic interactions result solely from the anisotropic shape of the particles. We find that certain properties of the phase diagram are in accordance with equilibrium scaling laws, despite the presence of anisotropic interactions. Motivated by this finding, in Chapter 7 we test the machinery of Chapter 5 for a system of purely repulsive self-propelled particles with explicit anti-aligning interactions that can undergo motility-induced phase separation. In this way we examine whether our method to predict phase diagrams of systems with purely isotropic interactions can be extended to active systems in general.