Clustering of self-propelled particles

Many experimental realizations of self-propelled particles exhibit a strong tendency to aggregate and form clusters,[1][2][3][4][5] whose dynamics are much richer than those of passive colloids. These aggregates of particles form for a variety of reasons, from chemical gradients to magnetic and ultrasonic fields.[6] Self-propelled enzyme motors synthetic nanomotors also exhibit clustering effects in the form of chemotaxis. Chemotaxis is a form of collective motion of biological or non-biological particles toward a fuel source or away from a threat, as observed experimentally in enzyme diffusion[7][8] and also synthetic chemotaxis[9][10][11] or phototaxis.[11] In addition to irreversible schooling, self-propelled particles also display reversible collective motion, such as predator–prey behavior and oscillatory clustering and dispersion.[12][13][14]

Phenomenology

This clustering behaviour has been observed for self-propelled Janus particles, either platinum-coated gold particles[1] or carbon-coated sillica beads,[2] and magnetically or ultrasonically powered particles,[5][6] as well as for colloidal particles with an embedded hematite cube[3] and composed of slowly-diffusing metal ions,[4][12][13][14] and for enzyme molecule diffusion.[7][8] 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][4][12][13][14]

Mechanism for synthetic systems

The precise mechanism leading to the appearance of clusters is not completely elucidated and is a current field of research.[15] Three 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;[16] 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.[17] This phase separation can however be arrested by chemically-mediated inter-particle torques[18] or hydrodynamic interactions,[19][20] 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,[21][22] 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. Diffusiophoresis is also a commonly cited mechanism for clustering and collective behavior, involving the attraction of particles to each other and in response to ion gradients.[4][12][13][14] Diffusiophoresis is a process involving the gradients of electrolyte or non-electrolyte concentrations interacting with charged or neutral particles in solution and with the double layer of any walls or surfaces.[14]

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][4][12][13][14]

Reviews

Clustering behavior in self-propelled particles and enzyme motors is discussed in great detail in sections on Collective Behavior, Chemotaxis, and/or Diffusiophoresis within several reviews by leading researchers in the self-propelled particles and nanomotors fields.[23][24][25][26][27]

References

  1. 1 2 3 4 Theurkauff, I.; Cottin-Bizonne, C.; Palacci, J.; Ybert, C.; Bocquet, L. (26 June 2012). "Dynamic Clustering in Active Colloidal Suspensions with Chemical Signaling". Physical Review Letters. 108 (26): 268303. Bibcode:2012PhRvL.108z8303T. doi:10.1103/PhysRevLett.108.268303.
  2. 1 2 3 4 Buttinoni, Ivo; Bialké, Julian; Kümmel, Felix; Löwen, Hartmut; Bechinger, Clemens; Speck, Thomas (5 June 2013). "Dynamical Clustering and Phase Separation in Suspensions of Self-Propelled Colloidal Particles". Physical Review Letters. 110 (23): 238301. Bibcode:2013PhRvL.110w8301B. doi:10.1103/PhysRevLett.110.238301.
  3. 1 2 3 4 Palacci, Jeremie; Sacanna, Stefano; Steinberg, Asher Preska; Pine, David J.; Chaikin, Paul M. (31 January 2013). "Living Crystals of Light-Activated Colloidal Surfers". Science. 339: 1230020. doi:10.1126/science.1230020. ISSN 0036-8075. PMID 23371555.
  4. 1 2 3 4 5 Ibele, Michael; Mallouk, Thomas E.; Sen, Ayusman (20 April 2009). "Schooling Behavior of Light-Powered Autonomous Micromotors in Water". Angewandte Chemie. 121 (18): 3358–3362. doi:10.1002/ange.200804704. ISSN 1521-3757.
  5. 1 2 Kagan, Daniel; Balasubramanian, Shankar; Wang, Joseph (10 January 2011). "Chemically Triggered Swarming of Gold Microparticles". Angewandte Chemie International Edition. 50 (2): 503–506. doi:10.1002/anie.201005078. ISSN 1521-3773.
  6. 1 2 Wang, Wei; Castro, Luz Angelica; Hoyos, Mauricio; Mallouk, Thomas E. (24 July 2012). "Autonomous Motion of Metallic Microrods Propelled by Ultrasound". ACS Nano. 6 (7): 6122–6132. doi:10.1021/nn301312z. ISSN 1936-0851.
  7. 1 2 Muddana, Hari S.; Sengupta, Samudra; Mallouk, Thomas E.; Sen, Ayusman; Butler, Peter J. (24 February 2010). "Substrate Catalysis Enhances Single-Enzyme Diffusion". Journal of the American Chemical Society. 132 (7): 2110–2111. doi:10.1021/ja908773a. ISSN 0002-7863. PMC 2832858Freely accessible. PMID 20108965.
  8. 1 2 Sengupta, Samudra; Dey, Krishna K.; Muddana, Hari S.; Tabouillot, Tristan; Ibele, Michael E.; Butler, Peter J.; Sen, Ayusman (30 January 2013). "Enzyme Molecules as Nanomotors". Journal of the American Chemical Society. 135 (4): 1406–1414. doi:10.1021/ja3091615. ISSN 0002-7863.
  9. ↑ Pavlick, Ryan A.; Sengupta, Samudra; McFadden, Timothy; Zhang, Hua; Sen, Ayusman (26 September 2011). "A Polymerization-Powered Motor". Angewandte Chemie International Edition. 50 (40): 9374–9377. doi:10.1002/anie.201103565. ISSN 1521-3773.
  10. ↑ Hong, Yiying; Blackman, Nicole M. K.; Kopp, Nathaniel D.; Sen, Ayusman; Velegol, Darrell (26 October 2007). "Chemotaxis of Nonbiological Colloidal Rods". Physical Review Letters. 99 (17): 178103. Bibcode:2007PhRvL..99q8103H. doi:10.1103/PhysRevLett.99.178103.
  11. 1 2 Chaturvedi, Neetu; Hong, Yiying; Sen, Ayusman; Velegol, Darrell (4 May 2010). "Magnetic Enhancement of Phototaxing Catalytic Motors". Langmuir. 26 (9): 6308–6313. doi:10.1021/la904133a. ISSN 0743-7463.
  12. 1 2 3 4 5 Hong, Yiying; Diaz, Misael; Córdova-Figueroa, Ubaldo M.; Sen, Ayusman (25 May 2010). "Light-Driven Titanium-Dioxide-Based Reversible Microfireworks and Micromotor/Micropump Systems". Advanced Functional Materials. 20 (10): 1568–1576. doi:10.1002/adfm.201000063. ISSN 1616-3028.
  13. 1 2 3 4 5 Ibele, Michael E.; Lammert, Paul E.; Crespi, Vincent H.; Sen, Ayusman (24 August 2010). "Emergent, Collective Oscillations of Self-Mobile Particles and Patterned Surfaces under Redox Conditions". ACS Nano. 4 (8): 4845–4851. doi:10.1021/nn101289p. ISSN 1936-0851.
  14. 1 2 3 4 5 6 Duan, Wentao; Liu, Ran; Sen, Ayusman (30 January 2013). "Transition between Collective Behaviors of Micromotors in Response to Different Stimuli". Journal of the American Chemical Society. 135 (4): 1280–1283. doi:10.1021/ja3120357. ISSN 0002-7863.
  15. ↑ "Focus: Particle Clustering Phenomena Inspire Multiple Explanations". Retrieved 2015-09-22.
  16. ↑ Schnitzer, Mark J. (1 October 1993). "Theory of continuum random walks and application to chemotaxis". Physical Review E. 48 (4): 2553–2568. doi:10.1103/PhysRevE.48.2553.
  17. ↑ Cates, Michael E.; Tailleur, Julien (1 January 2015). "Motility-Induced Phase Separation". Annual Review of Condensed Matter Physics. 6 (1): 219–244. doi:10.1146/annurev-conmatphys-031214-014710.
  18. ↑ Pohl, Oliver; Stark, Holger (10 June 2014). "Dynamic Clustering and Chemotactic Collapse of Self-Phoretic Active Particles". Physical Review Letters. 112 (23): 238303. Bibcode:2014PhRvL.112w8303P. doi:10.1103/PhysRevLett.112.238303.
  19. ↑ Matas-Navarro, Ricard; Golestanian, Ramin; Liverpool, Tanniemola B.; Fielding, Suzanne M. (18 September 2014). "Hydrodynamic suppression of phase separation in active suspensions". Physical Review E. 90 (3): 032304. doi:10.1103/PhysRevE.90.032304.
  20. ↑ Zöttl, Andreas; Stark, Holger (18 March 2014). "Hydrodynamics Determines Collective Motion and Phase Behavior of Active Colloids in Quasi-Two-Dimensional Confinement". Physical Review Letters. 112 (11): 118101. Bibcode:2014PhRvL.112k8101Z. doi:10.1103/PhysRevLett.112.118101.
  21. ↑ Redner, Gabriel S.; Baskaran, Aparna; Hagan, Michael F. (26 July 2013). "Reentrant phase behavior in active colloids with attraction". Physical Review E. 88 (1): 012305. doi:10.1103/PhysRevE.88.012305.
  22. ↑ Mognetti, B. M.; Šarić, A.; Angioletti-Uberti, S.; Cacciuto, A.; Valeriani, C.; Frenkel, D. (11 December 2013). "Living Clusters and Crystals from Low-Density Suspensions of Active Colloids". Physical Review Letters. 111 (24): 245702. Bibcode:2013PhRvL.111x5702M. doi:10.1103/PhysRevLett.111.245702.
  23. ↑ Sánchez, Samuel; Soler, Lluís; Katuri, Jaideep (26 January 2015). "Chemically Powered Micro- and Nanomotors". Angewandte Chemie International Edition. 54 (5): 1414–1444. doi:10.1002/anie.201406096. ISSN 1521-3773.
  24. ↑ Sengupta, Samudra; Ibele, Michael E.; Sen, Ayusman (20 August 2012). "Fantastic Voyage: Designing Self-Powered Nanorobots". Angewandte Chemie International Edition. 51 (34): 8434–8445. doi:10.1002/anie.201202044. ISSN 1521-3773.
  25. ↑ Duan, Wentao; Wang, Wei; Das, Sambeeta; Yadav, Vinita; Mallouk, Thomas E.; Sen, Ayusman (1 January 2015). "Synthetic Nano- and Micromachines in Analytical Chemistry: Sensing, Migration, Capture, Delivery, and Separation". Annual Review of Analytical Chemistry. 8 (1): 311–333. doi:10.1146/annurev-anchem-071114-040125. PMID 26132348.
  26. ↑ Wang, Wei; Duan, Wentao; Ahmed, Suzanne; Mallouk, Thomas E.; Sen, Ayusman (1 October 2013). "Small power: Autonomous nano- and micromotors propelled by self-generated gradients". Nano Today. 8 (5): 531–554. doi:10.1016/j.nantod.2013.08.009.
  27. ↑ Yadav, Vinita; Duan, Wentao; Butler, Peter J.; Sen, Ayusman (1 January 2015). "Anatomy of Nanoscale Propulsion". Annual Review of Biophysics. 44 (1): 77–100. doi:10.1146/annurev-biophys-060414-034216. PMID 26098511.
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