Dynamic Clustering and Chemotactic Collapse of Self-Phoretic Active Particles

Abstract

Recent experiments with self-phoretic particles at low concentrations show a pronounced dynamic clustering [I. Theurkauff et al., Phys. Rev. Lett. 108, 268303 (2012)]. We model this situation by taking into account the translational and rotational diffusiophoretic motion, which the active particles perform in their self-generated chemical field. Our Brownian dynamics simulations show pronounced dynamic clustering only when these two phoretic contributions give rise to competing attractive and repulsive interactions, respectively. We identify two dynamic clustering states and characterize them by power-law-exponential distributions. In case of mere attraction a chemotactic collaps occurs directly from the gas-like into the collapsed state, which we also predict by mapping our Langevin dynamics on the Keller-Segel model for bacterial chemotaxis.The collective motion of self-propelling objects is a most fascinating subject which has been studied in a variety of systems [1,2]. At the macroscale, collective patterns occur, for example, in flocks of birds or fish schooles [3][4][5] while at the microscopic scale bacterical cells in an aqueous environment generate intricate motional patterns [6][7][8]. To understand basic features of structure formation in non-equilibrium, systems with spherical or circular microswimmers are investigated. A number of theoretical and experimental studies have demonstrated that activity of microswimmers alone can result in clustering and phase separation [9-17] due to reduced motility in dense aggregates [9,15]. However, the colloidal density has to be large enough that the characteristic time for a particle to join a cluster becomes comparable to its rotational diffusion time needed to dissolve from it [13]. Other investigations explore the influence of hydrodynamics on collective motion [18][19][20][21][22][23][24].In experiments with dilute suspensions of self-phoretic active Janus colloids, dynamic clustering has been observed [25,26]. In this novel non-equilibrium phenomenon, particles constantly join and leave clusters which exhibit a very dynamic shape. [7,29,30,32].Recent theoretical and experimental studies included short-range attraction between active colloids and observed clustering at low colloidal densities [26,[33][34][35].Ref.[36] implements diffusiophoresis for concrete surface properties of self-phoretic colloids and indentifies various states such as clumping and asters.The work presented here has very much been inspired by the experiments of the Lyon group [25]. The diffusiophoretic interaction has a translational and orientational contribution. Using Brownian dynamics simulations, we demonstrate that pronounced dynamic clustering occurs only when these two contributions give rise to competing attractive and repulsive interactions, respectively. We identify two dynamic clustering states and characterize them. Otherwise, in case of mere attraction a chemotactic collaps occurs directly from the gas-like state before pronounced clusters are able to form. We support this...

Clustering and Pattern Formation in Chemorepulsive Active Colloids

“…This agrees with recent experimental observations [5,6,16] and may shed light on the still mysterious mechanism underlying their appearance. (Competing explanations based on the chemoattractive KS instability either predict macrophase separation [26] or clusters shrinking with increasing v 0 [15].) Although we mainly report regular patterns in our figures, our model suggests that irregular cluster arrangements, more akin to patterns found in experiments with active colloids, can also be found depending on location in parameter space and boundary conditions (Videos 3-5, Supplemental Material [22]).…”

“…This mapping, which assumed that active colloids swim up chemical gradients (the "chemoattractive" case), can explain clustering, but leads to complete phase separation, rather than a self-limiting cluster size. A combination of a passive drift up the chemical gradient and self-propulsion down it ("chemorepulsion") might lead to finite size clusters [15]; however, at variance with experiments [5,16], these should shrink as the self-propulsion speed increases [15]. A more general study of chemoresponsive active colloids in the limit of fast chemical dynamics suggests a far larger potential for pattern formation than is predicted by the KS model [10].…”

Chemically Propelled Motors Navigate Chemical Patterns

“…For example, if a motor tends to move toward high product concentrations, it will tend to move toward other motors that produce product leading to clustering in many‐motor systems. The collective dynamics of self‐diffusiophoretic motors present new features 55, 56, 57. Microscopic simulations of the collective behavior of Janus motors have shown that both chemical gradients and hydrodynamic effects are important in determining the nature of the observed inhomogeneous states 58.…”

Swimming in external fields

“…Their emergent collective dynamics is a most fascinating topic. Interacting microswimmers may show turbulence at low Reynolds number [4] and exhibit dynamic clustering due to phoretic interactions [5][6][7] or motility-induced phase separation [8][9][10][11][12][13]. Their collective motion drives macroscopic fluid flow as in bioconvection [15] or vortex formation [16].…”