Vapour-Liquid Coexistence of an Active Lennard-Jones fluid

We study a three-dimensional system of self-propelled Lennard-Jones particles using Brownian Dynamics simulations. Using recent theoretical results for active matter, we calculate the pressure and report equations of state for the system. Additionally, we chart the vapour-liquid coexistence and show that the coexistence densities can be well described using simple power laws. Lastly, we demonstrate that our out-of-equilibrium system shows deviations from both the law of rectilinear diameters and the law of corresponding states.Comment: 8 pages, 8 figure

The role of topological defects in the two-stage melting and elastic behavior of active Brownian particles

We find that crystalline states of repulsive active Brownian particles at high activity melt into a hexatic state but this transition is not driven by an unbinding of bound dislocation pairs as suggested by the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory. Upon reducing the density, the crystalline state melts into a high-density hexatic state devoid of any defects. Decreasing the density further, the dislocations proliferate and introduce plasticity in the system, nevertheless maintaining the hexatic state, but eventually melting into a fluid state. Remarkably, the elastic constants of active solids are equal to those of their passive counterparts, as the swim contribution to the stress tensor is negligible in the solid state. The sole effect of activity is that the stable solid regime shifts to higher densities. Furthermore, discontinuities in the elastic constants as a function of density correspond to changes in the defect concentrations rather than to the solid-hexatic transition

Chemical potential in active systems: predicting phase equilibrium from bulk equations of state?

We derive a microscopic expression for a quantity $\mu$ that plays the role of chemical potential of Active Brownian Particles (ABPs) in a steady state in the absence of vortices. We show that $\mu$ consists of (i) an intrinsic chemical potential similar to passive systems, which depends on density and self-propulsion speed, but not on the external potential, (ii) the external potential, and (iii) a newly derived one-body swim potential due to the activity of the particles. Our simulations on active Brownian particles show good agreement with our Fokker-Planck calculations, and confirm that $\mu(z)$ is spatially constant for several inhomogeneous active fluids in their steady states in a planar geometry. Finally, we show that phase coexistence of ABPs with a planar interface satisfies not only mechanical but also diffusive equilibrium. The coexistence can be well-described by equating the bulk chemical potential and bulk pressure obtained from bulk simulations for systems with low activity but requires explicit evaluation of the interfacial contributions at high activity.Comment: Added new results in Section 3.4 and updated Discussion and Conclusio

Ratchet-induced variations in bulk states of an active ideal gas

We study the distribution of active, noninteracting particles over two bulk states separated by a ratchet potential. By solving the steady-state Smoluchowski equations in a flux-free setting, we show that the ratchet potential affects the distribution of particles over the bulks, and thus exerts an influence of infinitely long range. As we show, crucial for having such a long-range influence is an external potential that is nonlinear. We characterize how the difference in bulk densities depends on activity and on the ratchet potential, and we identify power law dependencies on system parameters in several limiting cases. While weakly active systems are often understood in terms of an effective temperature, we present an analytical solution that explicitly shows that this is not possible in the current setting. Instead, we rationalize our results by a simple transition state model, that presumes particles to cross the potential barrier by Arrhenius rates modified for activity. While this model does not quantitatively describe the difference in bulk densities for feasible parameter values, it does reproduce - in its regime of applicability - the complete power law behavior correctly.Comment: 11 pages, 6 figure

Non-Equilibrium Surface Tension of the Vapour-Liquid Interface of Active Lennard-Jones Particles

We study a three-dimensional system of self-propelled Brownian particles interacting via the Lennard-Jones potential. Using Brownian Dynamics simulations in an elongated simulation box, we investigate the steady states of vapour-liquid phase coexistence of active Lennard-Jones particles with planar interfaces. We measure the normal and tangential components of the pressure tensor along the direction perpendicular to the interface and verify mechanical equilibrium of the two coexisting phases. In addition, we determine the non-equilibrium interfacial tension by integrating the difference of the normal and tangential component of the pressure tensor, and show that the surface tension as a function of strength of particle attractions is well-fitted by simple power laws. Finally, we measure the interfacial stiffness using capillary wave theory and the equipartition theorem, and find a simple linear relation between surface tension and interfacial stiffness with a proportionality constant characterized by an effective temperature.Comment: 12 pages, 5 figures (Corrected typos and References

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

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

Role of topological defects in the two-stage melting and elastic behavior of active Brownian particles

We find that crystalline states of repulsive active Brownian particles at high activity melt into a hexatic phase, but this transition is not driven by an unbinding of bound dislocation pairs as suggested by the Kosterlitz-Thouless-Halperin-Nelson-Young theory. Upon reducing the density, the crystalline state melts into a high-density hexatic state devoid of any defects. Decreasing the density further, the dislocations proliferate and introduce plasticity in the system, nevertheless maintaining the hexatic state, but eventually melting into a fluid state. Remarkably, the elastic constants of active solids are equal to those of their passive counterparts, as the swim contribution to the stress tensor is negligible in the solid state. The sole effect of activity is that the stable solid regime shifts to higher densities. Furthermore, discontinuities in the elastic constants as a function of density correspond to changes in the defect concentrations rather than to the solid-hexatic transition

Subcorneal pustular dermatosis occuring in association with pyoderma gangrenosum and rheumatoid arthritis: A triple whammy!

Neutrophilic dermatoses are a wide group of disorders encompassing indolent to severely disabling conditions. A co-existence of two such conditions, pyoderma gangrenosum (PG) and subcorneal pustular dermatosis, necessitates a thorough investigation for IgA dysglobulinemia. We report a middle-aged woman who developed PG following 18 years of (undiagnosed) subcorneal pustular dermatosis, along with rheumatoid arthritis, a known association of PG

Role of topological defects in the two-stage melting and elastic behavior of active Brownian particles

We find that crystalline states of repulsive active Brownian particles at high activity melt into a hexatic phase, but this transition is not driven by an unbinding of bound dislocation pairs as suggested by the Kosterlitz-Thouless-Halperin-Nelson-Young theory. Upon reducing the density, the crystalline state melts into a high-density hexatic state devoid of any defects. Decreasing the density further, the dislocations proliferate and introduce plasticity in the system, nevertheless maintaining the hexatic state, but eventually melting into a fluid state. Remarkably, the elastic constants of active solids are equal to those of their passive counterparts, as the swim contribution to the stress tensor is negligible in the solid state. The sole effect of activity is that the stable solid regime shifts to higher densities. Furthermore, discontinuities in the elastic constants as a function of density correspond to changes in the defect concentrations rather than to the solid-hexatic transition