Clustering of self-propelled particles

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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 and 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][9] and also synthetic chemotaxis[10][11][12] or phototaxis.[12] In addition to irreversible schooling, self-propelled particles also display reversible collective motion, such as predator–prey behavior and oscillatory clustering and dispersion.[13][14][15][16][17]

Phenomenology

This clustering behavior has been observed for self-propelled Janus particles, either platinum-coated gold particles[1] or carbon-coated silica beads,[2] and for magnetically or ultrasonically powered particles.[5][6] Clustering has also been observed for colloidal particles composed of either an embedded hematite cube[3] or slowly-diffusing metal ions.[4][13][14][15][16] Autonomous aggregation has also been observed in anatase TiO2 (titanium dioxide) particles.[18] Clustering also occurs in enzyme molecule diffusion.[7][8][9][19] Recently, enzymes such as hexokinase and alkaline phosphatase were found to aggregate in the presence of their substrates.[20] In all these experiments, the motion of particles takes place on a two-dimensional surface and clustering is seen for area fractions as low as 10%. For such low area fractions, the clusters have a finite mean size[1] while at larger area fractions (30% or higher), 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 "living clusters".[3][4][13][14][15][16]

Mechanism for synthetic systems

The precise mechanism leading to the appearance of clusters is not completely elucidated and is a current field of research for many systems.[21] A few different mechanisms have been proposed, which could be at play in different experimental setups.

Self-propelled particles can accumulate in a region of space where they move with a decreased velocity.[22] After accumulation, in regions of high particle density, the particles move more slowly because of steric hindrance. A feedback between these two mechanisms can lead to the so-called motility induced phase separation.[23] This phase separation can, however, be arrested by chemically-mediated inter-particle torques[24] or hydrodynamic interactions,[25][26] 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, as in equilibrium suspensions. Active forces would then oppose this phase separation by pulling apart the particles in the cluster,[27][28] following two main processes. First, single particles can exist independently if their propulsion forces are sufficient to escape from the cluster. Secondly, a large cluster can break into smaller pieces due to the build-up of internal stress: as more and more particles 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 or repulsion of particles to each other in response to ion gradients.[4][13][14][15][16] Diffusiophoresis is a process involving the gradients of electrolyte or non-electrolyte concentrations interacting with charged (electrophoretic interactions) or neutral (chemophoretic interactions) particles in solution and with the double layer of any walls or surfaces (electroosmotic interactions).[15][16]

In experiments, arguments have been put forward in favor of any of the above mechanisms. For carbon-coated silica beads, attractive interactions are seemingly negligible and phase-separation is indeed seen at large densities.[2] For other experimental systems, however, attractive forces often play a larger role.[1][3][15][16]

See also

References

  1. ↑ 1.0 1.1 1.2 1.3 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. doi:10.1103/PhysRevLett.108.268303. PMID 23005020. Bibcode: 2012PhRvL.108z8303T. 
  2. ↑ 2.0 2.1 2.2 2.3 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. doi:10.1103/PhysRevLett.110.238301. PMID 25167534. Bibcode: 2013PhRvL.110w8301B. 
  3. ↑ 3.0 3.1 3.2 3.3 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 (6122): 936–40. doi:10.1126/science.1230020. ISSN 0036-8075. PMID 23371555. Bibcode: 2013Sci...339..936P. 
  4. ↑ 4.0 4.1 4.2 4.3 Ibele, Michael; Mallouk, Thomas E.; Sen, Ayusman (20 April 2009). "Schooling Behavior of Light-Powered Autonomous Micromotors in Water" (in en). Angewandte Chemie 121 (18): 3358–3362. doi:10.1002/ange.200804704. ISSN 1521-3757. Bibcode: 2009AngCh.121.3358I. 
  5. ↑ 5.0 5.1 Kagan, Daniel; Balasubramanian, Shankar; Wang, Joseph (10 January 2011). "Chemically Triggered Swarming of Gold Microparticles" (in en). Angewandte Chemie International Edition 50 (2): 503–506. doi:10.1002/anie.201005078. ISSN 1521-3773. PMID 21140389. 
  6. ↑ 6.0 6.1 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. PMID 22631222. https://figshare.com/articles/Autonomous_Motion_of_Metallic_Microrods_Propelled_by_Ultrasound/2502772. 
  7. ↑ 7.0 7.1 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. PMID 20108965. 
  8. ↑ 8.0 8.1 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. PMID 23308365. 
  9. ↑ 9.0 9.1 Dey, Krishna Kanti; Das, Sambeeta; Poyton, Matthew F.; Sengupta, Samudra; Butler, Peter J.; Cremer, Paul S.; Sen, Ayusman (2014-12-23). "Chemotactic Separation of Enzymes". ACS Nano 8 (12): 11941–11949. doi:10.1021/nn504418u. ISSN 1936-0851. PMID 25243599. 
  10. ↑ Pavlick, Ryan A.; Sengupta, Samudra; McFadden, Timothy; Zhang, Hua; Sen, Ayusman (26 September 2011). "A Polymerization-Powered Motor" (in en). Angewandte Chemie International Edition 50 (40): 9374–9377. doi:10.1002/anie.201103565. ISSN 1521-3773. PMID 21948434. 
  11. ↑ 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. doi:10.1103/PhysRevLett.99.178103. PMID 17995374. Bibcode: 2007PhRvL..99q8103H. 
  12. ↑ 12.0 12.1 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. PMID 20102166. 
  13. ↑ 13.0 13.1 13.2 13.3 Hong, Yiying; Diaz, Misael; Córdova-Figueroa, Ubaldo M.; Sen, Ayusman (25 May 2010). "Light-Driven Titanium-Dioxide-Based Reversible Microfireworks and Micromotor/Micropump Systems" (in en). Advanced Functional Materials 20 (10): 1568–1576. doi:10.1002/adfm.201000063. ISSN 1616-3028. 
  14. ↑ 14.0 14.1 14.2 14.3 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. PMID 20666369. https://figshare.com/articles/Emergent_Collective_Oscillations_of_Self_Mobile_Particles_and_Patterned_Surfaces_under_Redox_Conditions/2740561. 
  15. ↑ 15.0 15.1 15.2 15.3 15.4 15.5 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. PMID 23301622. 
  16. ↑ 16.0 16.1 16.2 16.3 16.4 16.5 Altemose, Alicia; Sánchez-Farrán, Maria A.; Duan, Wentao; Schulz, Steve; Borhan, Ali; Crespi, Vincent H.; Sen, Ayusman (2017). "Chemically-Controlled Spatiotemporal Oscillations of Colloidal Assemblies". Angew. Chem. Int. Ed. 56 (27): 7817–7821. doi:10.1002/anie.201703239. PMID 28493638. 
  17. ↑ Zhang, Jianhua; Laskar, Abhrajit; Song, Jiaqi; Shklyaev, Oleg E.; Mou, Fangzhi; Guan, Jianguo; Balazs, Anna C.; Sen, Ayusman (2023-01-10). "Light-Powered, Fuel-Free Oscillation, Migration, and Reversible Manipulation of Multiple Cargo Types by Micromotor Swarms" (in en). ACS Nano 17 (1): 251–262. doi:10.1021/acsnano.2c07266. ISSN 1936-0851. PMID 36321936. https://pubs.acs.org/doi/10.1021/acsnano.2c07266. 
  18. ↑ Zhang, Jianhua; Song, Jiaqi; Mou, Fangzhi; Guan, Jianguo; Sen, Ayusman (2021-02-26). "Titania-Based Micro/Nanomotors: Design Principles, Biomimetic Collective Behavior, and Applications" (in en). Trends in Chemistry 3 (5): 387–401. doi:10.1016/j.trechm.2021.02.001. ISSN 2589-5974. 
  19. ↑ Zhao, Xi; Palacci, Henri; Yadav, Vinita; Spiering, Michelle M.; Gilson, Michael K.; Butler, Peter J.; Hess, Henry; Benkovic, Stephen J. et al. (2017-12-18). "Substrate-driven chemotactic assembly in an enzyme cascade" (in En). Nature Chemistry 10 (3): 311–317. doi:10.1038/nchem.2905. ISSN 1755-4330. PMID 29461522. Bibcode: 2018NatCh..10..311Z. 
  20. ↑ Gentile, Kayla; Bhide, Ashlesha; Kauffman, Joshua; Ghosh, Subhadip; Maiti, Subhabrata; Adair, James; Lee, Tae-Hee; Sen, Ayusman (2021-09-22). "Enzyme aggregation and fragmentation induced by catalysis relevant species" (in en). Physical Chemistry Chemical Physics 23 (36): 20709–20717. doi:10.1039/D1CP02966E. ISSN 1463-9084. PMID 34516596. Bibcode: 2021PCCP...2320709G. https://pubs.rsc.org/en/content/articlelanding/2021/cp/d1cp02966e. 
  21. ↑ Ball, Philip (2013-12-11). "Focus: Particle Clustering Phenomena Inspire Multiple Explanations". Physics 6: 134. doi:10.1103/physics.6.134. https://physics.aps.org/articles/v6/134. Retrieved 2015-09-22. 
  22. ↑ 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. PMID 9960890. Bibcode: 1993PhRvE..48.2553S. 
  23. ↑ 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. Bibcode: 2015ARCMP...6..219C. 
  24. ↑ Pohl, Oliver; Stark, Holger (10 June 2014). "Dynamic Clustering and Chemotactic Collapse of Self-Phoretic Active Particles". Physical Review Letters 112 (23): 238303. doi:10.1103/PhysRevLett.112.238303. PMID 24972234. Bibcode: 2014PhRvL.112w8303P. 
  25. ↑ 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. PMID 25314443. Bibcode: 2014PhRvE..90c2304M. 
  26. ↑ 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. doi:10.1103/PhysRevLett.112.118101. PMID 24702421. Bibcode: 2014PhRvL.112k8101Z. 
  27. ↑ 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. PMID 23944461. Bibcode: 2013PhRvE..88a2305R. 
  28. ↑ 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. doi:10.1103/PhysRevLett.111.245702. PMID 24483677. Bibcode: 2013PhRvL.111x5702M. 



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