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Clustering of self-propelled particles

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Many experimental realisations of self-propelled particles exhibit a strong tendency to aggregate and form clusters [1][2][3] whose dynamics are much richer than those of passive colloids.

Phenomenology

This clustering behaviour has been observed for self-propelled Janus particles, either platinum-coated gold particles[1] or carbon-coated sillica beads,[2] as well as for colloidal particles with an embedded hematite cube.[3] In all these experiments, the motion of particles takes place on a two-dimensional surface and clustering is seen for area fraction as low as 10%. For such low area fractions, the clusters have a finite mean size[1] while at larger area fractions, larger than 30%, a complete phase separation has been reported.[2] The dynamics of the finite-size clusters are very rich, exhibiting either crystalline order or amorphous packing. The finite size of the clusters comes from a balance between attachment of new particles to pre-existing clusters and breakdown of large clusters into smaller ones, which has led to the term of "living clusters".[3]

Mechanism at play

The precise mechanism leading to the appearance of clusters is not completely elucidated and is a current field of research.[4] Two different mechanisms have been proposed, which could be at play in different experimental setups.

First, self-propelled particles have a tendency to accumulate in region of space where they go slower;[5] then, self-propelled particles tend to go slower where they are denser, because of steric hindrance. A feedback between these two mechanisms can lead to the so-called motility induced phase separation.[6] This phase separation can however be arrested by chemically-mediated inter-particle torques[7] or hydrodynamic interactions,[8][9] which could explain the formation of finite-size clusters.

Alternatively, clustering and phase-separation could be due to the presence of inter-particle attractive forces, much as in equilibrium suspensions. Active forces would then oppose this phase separation by pulling apart the particles in the cluster,[10][11] following two main processes. First, single particles can evaporate if their propulsion forces are sufficient to escape from the cluster. Then, a large cluster can break into smaller ones due to the build-up of its internal stress: as more and more particle enter the cluster, their propulsive forces add up until they break down its cohesion.

In experiments, arguments have been put forward in favour of both mechanisms. For carbon-coated sillica beads, attractive interactions are supposed to be negligible and phase-separation is indeed seen at large densities.[2] For other experimental systems, attractive forces could however play a larger role.[1][3]

References

  1. ^ a b c d Theurkauff, I.; Cottin-Bizonne, C.; Palacci, J.; Ybert, C.; Bocquet, L. (2012-06-26). "Dynamic Clustering in Active Colloidal Suspensions with Chemical Signaling". Physical Review Letters. 108 (26): 268303. doi:10.1103/PhysRevLett.108.268303.
  2. ^ a b c d Buttinoni, Ivo; Bialké, Julian; Kümmel, Felix; Löwen, Hartmut; Bechinger, Clemens; Speck, Thomas (2013-06-05). "Dynamical Clustering and Phase Separation in Suspensions of Self-Propelled Colloidal Particles". Physical Review Letters. 110 (23): 238301. doi:10.1103/PhysRevLett.110.238301.
  3. ^ a b c d Palacci, Jeremie; Sacanna, Stefano; Steinberg, Asher Preska; Pine, David J.; Chaikin, Paul M. (2013-01-31). "Living Crystals of Light-Activated Colloidal Surfers". Science: 1230020. doi:10.1126/science.1230020. ISSN 0036-8075. PMID 23371555.
  4. ^ "Focus: Particle Clustering Phenomena Inspire Multiple Explanations". Retrieved 2015-09-22.
  5. ^ Schnitzer, Mark J. (1993-10-01). "Theory of continuum random walks and application to chemotaxis". Physical Review E. 48 (4): 2553–2568. doi:10.1103/PhysRevE.48.2553.
  6. ^ Cates, Michael E.; Tailleur, Julien (2015-01-01). "Motility-Induced Phase Separation". Annual Review of Condensed Matter Physics. 6 (1): 219–244. doi:10.1146/annurev-conmatphys-031214-014710.
  7. ^ Pohl, Oliver; Stark, Holger (2014-06-10). "Dynamic Clustering and Chemotactic Collapse of Self-Phoretic Active Particles". Physical Review Letters. 112 (23): 238303. doi:10.1103/PhysRevLett.112.238303.
  8. ^ Matas-Navarro, Ricard; Golestanian, Ramin; Liverpool, Tanniemola B.; Fielding, Suzanne M. (2014-09-18). "Hydrodynamic suppression of phase separation in active suspensions". Physical Review E. 90 (3): 032304. doi:10.1103/PhysRevE.90.032304.
  9. ^ Zöttl, Andreas; Stark, Holger (2014-03-18). "Hydrodynamics Determines Collective Motion and Phase Behavior of Active Colloids in Quasi-Two-Dimensional Confinement". Physical Review Letters. 112 (11): 118101. doi:10.1103/PhysRevLett.112.118101.
  10. ^ Redner, Gabriel S.; Baskaran, Aparna; Hagan, Michael F. (2013-07-26). "Reentrant phase behavior in active colloids with attraction". Physical Review E. 88 (1): 012305. doi:10.1103/PhysRevE.88.012305.
  11. ^ Mognetti, B. M.; Šarić, A.; Angioletti-Uberti, S.; Cacciuto, A.; Valeriani, C.; Frenkel, D. (2013-12-11). "Living Clusters and Crystals from Low-Density Suspensions of Active Colloids". Physical Review Letters. 111 (24): 245702. doi:10.1103/PhysRevLett.111.245702.
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