Activity induced phase separation and the emergence of liquid crystal phases in chiral and achiral systems, and development of an efficient method to compute the entropy of various liquid crystal phases

Abstract

The phase behaviour of shape-anisotropic particles is an emerging field of research that gives rise to various liquid crystal phases. In this thesis, we explore various equilibrium and non-equilibrium properties of shape-anisotropic particles by modelling them as soft repulsive spherocylinders (SRSs) and soft helical rods. In the first part, we introduce the two-temperature model to study the phase behaviour of scalar active SRS and soft helical rods. Most realisations of activity are vectorial in nature due to the force of self-propulsion. Recent studies have shown that many physical and biological processes, like phase separation in colloidal systems, chromatin organisation in the nucleus, are operated by the unequal sharing of energy by the constituents of the system. Such systems are classified as scalar active systems. In the simplest case, these systems can be modelled by connecting half the particles with a thermostat of higher temperature (labelled ‘hot’/‘active’) while maintaining temperature of the rest constant (labelled ‘cold’/‘passive’) at a lower value. The relative temperature difference between the two constituents of the system is a measure of activity. This model is known as two-temperature model that has been found to capture many essential properties of scalar activity. Starting from a homogeneous isotropic phase at a definite temperature, we show that this model leads to phase separation into hot and cold regions and induces liquid-crystal ordering of the cold particles while hot particles remain in the isotropic phase. In particular, we find that activity drives the cold particles through a phase transition to a more ordered state and the hot particles to a state of less order compared to the initial equilibrium state. Hence, the phase boundary of the isotropic-nematic transition shifts towards lower densities for cold particles and higher densities for the hot particles with respect to its equilibrium location. Remarkably, we find liquid crystalline phases for the aspect ratios [length(L)/diameter(D)] as low as L/D = 2, 3 which do not satisfy the minimum shape-anisotropy criteria that Onsager’s theory demands in equilibrium. Similar model we have employed in a system of soft helical particles of various intrinsic chiralities and found different liquid crystal ordering in these cases as well. The following nonequilibrium features emerge from our study: an enhancement of the temperature of half of the particles gives rise to LC ordering in the remaining half of the particles at any density. The hot and cold domains should not be viewed as bulk equilibrium phases with non-equilibrium behaviour only at the interfaces. By calculating the stress anisotropy and heat current, we find that the non-equilibrium behaviour is not restricted to the hot-cold interfaces but pervades the system as a whole, driving various ordering transitions in the cold zone. Thus, our study unravels various aspects of non-equilibrium scalar active rods in the framework of the two-temperature model. In the second part, we discuss the Two-phase thermodynamic (2PT) model for computing entropy, free energy, and other thermodynamic properties of various liquid crystal phases in equilibrium. In the 2PT method, the density of state (DoS) of the LC phases is decomposed into vibrational (solid) and diffusive (gas) components. The thermodynamic quantities are then calculated using harmonic oscillator approximations for the solid component, hard sphere approximations for the gas component, and the rigid rotor approximation for the rotational mode. In the 2PT method, the entropy of a definite state point is calculated from a single MD trajectory, which makes it advantageous for systems for which the analytical form of the equation of state is unknown (such as SRS). Our method can be used to calculate entropy and other thermodynamic quantities of different liquid crystal phases formed by the SRS system.