PHYSICAL REVIEW E 101, 012611 (2020) Clusterization of self-propelled particles in a two-component system Shibashis Paul, 1 Debankur Bhattacharyya, 2 , * and Deb Shankar Ray 1 , † 1 Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India 2 Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India (Received 19 June 2019; revised manuscript received 20 November 2019; published 29 January 2020) We consider a mixture of active solute molecules in a suspension of passive solvent particles comprising a thermal bath. The solute molecules are considered to be extended objects with two chemically distinct heads, one head of which having chemical affinity towards the solvent particles. The coupled Langevin equations for the solvent particles along with the equations governing the dynamics of active molecules are numerically simulated to show how the active molecules self-assemble to form clusters which remain in dynamic equilibrium with the free solute molecules. We observe an interesting crossover at an intermediate time in the variation of the order parameter with time when the temperature of the bath is changed signifying the differential behavior of clusterization below and above the crossover time associated with a transition between a thermodynamic and a quasithermodynamic regime. Enthalpy-entropy compensation in the formation of clusters below the crossover is demonstrated. DOI: 10.1103/PhysRevE.101.012611 I. INTRODUCTION An assembly of particles which draw energy at the indi- vidual level from the surroundings to execute self-propelled coordinated motion constitutes what is referred to as active matter [1–11]. The subject encompasses a variety of systems, e.g., bird flocks [12], fish schools [13], insect swarms [14], migrating bacteria [15], molds [16], and pedestrians [17]. Over the years both discrete [1,7,18] as well as contin- uum models based on hydrodynamics [3–5,8,19] have been proposed to investigate the universal features of collective behavior [8], new phase transitions [1,2], structure-forming cytoskeletons of cells [20], controlling liquid crystals swirling on spherical vesicles [21], modeling of tissues and tumors as flowing cells self-organizing through cell-to-cell short range interaction [22,23], homochirality in chemical systems [24], and pattern formation in activator-inhibitor systems [25] to name a few. A key feature of the self-propelled coordinated motion of particles in active matter is that it concerns systems under far- from-equilibrium condition. More specifically, the symmetry- breaking transition between a disordered and an ordered state is affected by external noise on the particles the motion of which is governed by a mean speed and an alignment determined by that of their neighboring particles within a sphere of interaction assisted by small fluctuations [1,7]. As the motion of the particles in discrete time steps follows simple local interaction rules without any specific form of potential, the statistical approach captures many realistic fea- tures in flocking behavior, which has been complemented by the detailed consideration of hydrodynamic approaches. The * Present address: University of Maryland, College Park, MD 20742, USA. † Corresponding author: pcdsr@iacs.res.in focus of the present paper is to explore the collective behavior of active systems undergoing clusterization, in a thermal bath of solvent particles. The active systems are considered to be molecules or extended objects with two heads, one head having chemical affinity towards the solvent particles. Our model of a two-component system is mainly motivated by the experimental and theoretical work on active colloidal suspensions [26–29] pioneered by Wu and Libchaber [30]. Theurkauff et al. [31] have experimentally investigated the collective behavior of a dense active suspension of gold colloids half covered with platinum which are spherical Janus particles [32–38] undergoing self-phoretic motion on con- sumption of hydrogen peroxide to exhibit a novel cluster phase at high densities. At low densities, as observed by Howse et al. [39], colloidal particles use chemical reaction catalyzed on their own surface to achieve directed motion. The nonequilibrium steady state of an active colloidal suspension under gravity has been investigated by Palacci et al. [40] to introduce the concept of an effective temperature of the active system in the light of the fluctuation-dissipation relation- ship. Active hydrodynamics has also been studied by Miño et al. [41] to understand enhanced diffusion at a solid surface. The common feature of all these colloidal suspensions is that they are, in general, two-component systems, composed of an active system and a passive solvent. The activity leading to self-propulsion is affected by chemical or other means. Based on these considerations we introduce a two-component system with an active solute and a passive solvent modeled as a thermal bath. This naturally concerns Brownian noise of the thermal bath and furthermore we consider solvent-induced interaction due to the affinities between one head of the solute molecules towards solvent particles. The dynamics of solvent particles is treated by Langevin equations while the motion of the solute molecules is guided by a scaled mean speed as determined by the Brownian motion. The activity of the solute molecules in this model originates from their 2470-0045/2020/101(1)/012611(9) 012611-1 ©2020 American Physical Society