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Clustering of self-propelled particles

clustering of self-propelled particles meaning, clustering of self-propelled particles of matter
Many experimental realizations of self-propelled particles exhibit a strong tendency to aggregate and form clusters, 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 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 and also synthetic chemotaxis or phototaxis In addition to irreversible schooling, self-propelled particles also display reversible collective motion, such as predator–prey behavior and oscillatory clustering and dispersion


  • 1 Phenomenology
  • 2 Mechanism for synthetic systems
  • 3 Reviews
  • 4 References


This clustering behaviour has been observed for self-propelled Janus particles, either platinum-coated gold particles or carbon-coated sillica beads, and magnetically or ultrasonically powered particles, as well as for colloidal particles with an embedded hematite cube and composed of slowly-diffusing metal ions, and for enzyme molecule diffusion 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 while at larger area fractions, larger than 30%, a complete phase separation has been reported 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"

Mechanism for synthetic systems

The precise mechanism leading to the appearance of clusters is not completely elucidated and is a current field of research 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; 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 This phase separation can however be arrested by chemically-mediated inter-particle torques or hydrodynamic interactions, 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, 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 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

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 For other experimental systems, attractive forces could however play a larger role


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


  1. ^ a b c d 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:2012PhRvL108z8303T doi:101103/PhysRevLett108268303 
  2. ^ a b c d 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:2013PhRvL110w8301B doi:101103/PhysRevLett110238301 
  3. ^ a b c d 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:101126/science1230020 ISSN 0036-8075 PMID 23371555 
  4. ^ a b c d e 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:101002/ange200804704 ISSN 1521-3757 
  5. ^ a b Kagan, Daniel; Balasubramanian, Shankar; Wang, Joseph 10 January 2011 "Chemically Triggered Swarming of Gold Microparticles" Angewandte Chemie International Edition 50 2: 503–506 doi:101002/anie201005078 ISSN 1521-3773 
  6. ^ a b 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:101021/nn301312z ISSN 1936-0851 
  7. ^ a b 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:101021/ja908773a ISSN 0002-7863 PMC 2832858 PMID 20108965 
  8. ^ a b 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:101021/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:101002/anie201103565 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:2007PhRvL99q8103H doi:101103/PhysRevLett99178103 
  11. ^ a b Chaturvedi, Neetu; Hong, Yiying; Sen, Ayusman; Velegol, Darrell 4 May 2010 "Magnetic Enhancement of Phototaxing Catalytic Motors" Langmuir 26 9: 6308–6313 doi:101021/la904133a ISSN 0743-7463 
  12. ^ a b c d e 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:101002/adfm201000063 ISSN 1616-3028 
  13. ^ a b c d e 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:101021/nn101289p ISSN 1936-0851 
  14. ^ a b c d e f 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:101021/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:101103/PhysRevE482553 
  17. ^ Cates, Michael E; Tailleur, Julien 1 January 2015 "Motility-Induced Phase Separation" Annual Review of Condensed Matter Physics 6 1: 219–244 doi:101146/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:2014PhRvL112w8303P doi:101103/PhysRevLett112238303 
  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:101103/PhysRevE90032304 
  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:2014PhRvL112k8101Z doi:101103/PhysRevLett112118101 
  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:101103/PhysRevE88012305 
  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:2013PhRvL111x5702M doi:101103/PhysRevLett111245702 
  23. ^ Sánchez, Samuel; Soler, Lluís; Katuri, Jaideep 26 January 2015 "Chemically Powered Micro- and Nanomotors" Angewandte Chemie International Edition 54 5: 1414–1444 doi:101002/anie201406096 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:101002/anie201202044 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:101146/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:101016/jnantod201308009 
  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:101146/annurev-biophys-060414-034216 PMID 26098511 

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