Inertial effects on crystallization of active particles

Abstract

The phase behavior of inertial active particles in two dimensions is investigated numerically by using structural and dynamical freezing criteria, and melting criterion with a modified Lindemann parameter. It is found that inertial active particles can crystallize at sufficiently high densities. Comparing to the overdamped active particles, the inertia hinders crystallization of inertial active particles. For a given damping coefficient, structural and dynamical freezing criteria are different, and do not coincide for any self-propelling force due to the competition of dissipation and the inertial effect. Because the increasing inertia suppresses the effect of self-propulsion force, the transition region between liquid and solid becomes wider and the position of this region shifts downward to small coupling strength with damping coefficient. There is no structural difference between two suspensions with different inertia in the liquid phase because diffusion dominates the dynamics. Whereas the suspension for large damping coefficient is more structured on the whole but there exist well-separated liquid-like bubbles in the transition region. In addition, it is very difficult to crystallize into the perfect hexagonal crystal for small damping coefficient, which needs very large coupling strength due to the inertial effect.

Introduction

Active colloidal particles is a rapidly developing and exciting research arena within the soft matter realm [1], [2], [3], [4], which comprises artificial microswimmers as well as their biological counterparts, including swimming microorganisms such as bacteria, actin filaments [5], active nematics [6], living tissues [7], the so-called motor-proteins [8], spermatozoa and protozoa [9], [10]. These particles can move actively by gaining kinetic energy from the environment. Various internal self-propulsion mechanisms have been proposed and realized, including laser illumination [11], [12], [13], [14], [15] or concentration gradients (diffusophoresis) [16].

In particular, the collective dynamics of active particles have attracted considerable attention [17], [18], [19], [20], [21], [22], which exhibit fascinating non-equilibrium states in the form of disorder–order transition, such as motility-induced clustering [22], [23], [24], [25], [26], [27], vortex formation [28], [29] and swarming [30], [31]. A. Deblais and coworkers [23] demonstrated that clusters and other interesting collective behaviors can be formed in assemblies of rodlike robots by controlling boundaries. Ivo Buttinoni and coworkers [22] showed there exist phase separation of large clusters and a dilute gas phase in dense active particles while small clusters are stabilized by self-propulsion. I. H. Riedel et al. [28] found spermatozoa at planar surfaces self-organized into dynamic vortices which formed an array with local hexagonal order. The role of shape in swarming and swirling motion of active polar granular rods is studied numerically and experimentally [30]. A. Manacorda and coworkers [31] presented the relation between the active swarming phase and granular shear instability in the system of active particles moving on a lattice.

However, the crystallization or melting has received little attention [32], [33], [34], [35], [36], [37], [38]. G. Briand and O. Dauchot [32] experimentally studied the crystallization of a monolayer of vibrated discs with a built-in polar asymmetry. They found the quasicontinuous crystallization reported for isotropic discs is replaced by a transition, or a crossover, towards a ‘self-melting’ crystal by increasing the packing fraction. P. Digregorio and coworkers [33] established the complete phase diagram of self-propelled hard disks and found the emergence of hexatic and solid order is shifted towards higher densities with activity. J. U. Klamser and coworkers [34] showed thermodynamic phases of active particles with inverse-power-law repulsions moving without alignment. L. F. Cugliandolo et al. [35] investigated phase coexistence in active dumbbell systems with repulsive power-law interactions in two dimensions. Different crystalline states and their defects of active crystals on a sphere are studied theoretically by S. Praetorius and coworkers [36]. Ran Ni et al. [37] founded that doping the system with some active particles can facilitate the crystallization of hard-sphere glasses drastically.

Most of the results reported above were obtained in the limit of overdamped dynamics (at the low Reynolds number regime). In these systems the dynamics is dominated by dissipation and the inertial effect are neglected. However, the overdamped approximation is not justified in many situations (e.g. at the high Reynolds number regime) [39] such as self-propelling microdiodes [40], Janus particles (microparticles) moving through a dusty plasm [41] (air, or even a vacuum), colloidal particles in air, granular matter in dilute systems, and so on. In these systems, energy dissipation is small, the damping is significantly reduced so that inertial effects can play an important role. The coupling of inertia to self-propulsion may play a pivotal role in generating new self-organization effects. We are motivated by one of the previous results describing crystallization of active particles [38]. The researchers found a dense suspension of active particles can crystallize in two dimensions. They applied structural and dynamical freezing criteria, which coincide for small self-propulsion. The active system exhibits a transition region between liquid and solid by employing a melting criterion, which becomes larger with self-propulsion. They found this region is characterized by structural inhomogenities, where the system is globally ordered but unordered liquidlike ‘bubbles’ still persist. However, the results they reported is in the overdamped case, crystallization of inertial active particles has not been considered yet. In the present work, we extend their investigations to the underdamped case, and explore the phase behavior of inertial active particles at sufficiently high densities. We focus on finding how the inertia influences the crystallization. We found that the inertia hinders crystallization of inertial active particles comparing to the overdamped case. Because the increasing inertia suppresses the effect of self-propulsion force, the transition region between liquid and solid becomes wider and the position of this region shifts downward to small coupling strength with damping coefficient. There is no structural difference between two suspensions with different inertia in the liquid phase because diffusion dominates the dynamics. Whereas the suspension for large damping coefficient is more ordered on the whole but there exist well-separated liquid-like ‘bubbles’ in the transition region. Our results suggest a new route to understand active matter and pave the way for emerging applications.