- Letter
- Open Access
Collective behavior of active molecules: Dynamic clusters, holes, and active fractalytes
Phys. Rev. Research 5, L032038 – Published 15 September, 2023
DOI: https://doi.org/10.1103/PhysRevResearch.5.L032038
Abstract
Recent experiments have led to active colloidal molecules, which aggregate from nonmotile building blocks and acquire self-propulsion through their nonreciprocal interactions. Here, we model the collective behavior of such active molecules and predict, besides dynamic clusters, the existence of a so-far unknown state of active matter made of “active fractalytes”, which are motile crystallites featuring internal holes, gaps, and a fractal dimension. These structures could serve as a starting point for the creation of active materials with a low density and mechanical properties that can be designed through their fractal internal structure.
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References (66)
- E. Mach, The Science of Mechanics, edited by T. J. McCormack, Cambridge Library Collection—Physical Sciences (Cambridge University Press, Cambridge, 2013).
- A. V. Ivlev, J. Bartnick, M. Heinen, C. R. Du, V. Nosenko, and H. Löwen, Statistical Mechanics where Newton's Third Law is Broken, Phys. Rev. X 5, 011035 (2015).
- M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. Aditi Simha, Hydrodynamics of soft active matter, Rev. Mod. Phys. 85, 1143 (2013).
- J. Elgeti, R. G. Winkler, and G. Gompper, Physics of microswimmers-single particle motion and collective behavior: A review, Rep. Prog. Phys. 78, 056601 (2015).
- F. Schmidt, B. Liebchen, H. Löwen, and G. Volpe, Light-controlled assembly of active colloidal molecules, J. Chem. Phys. 150, 094905 (2019).
- S. Y. Reigh, P. Chupal, S. Thakur, and R. Kapral, Diffusiophoretically induced interactions between chemically active and inert particles, Soft Matter 14, 6043 (2018).
- J. Stürmer, M. Seyrich, and H. Stark, Chemotaxis in a binary mixture of active and passive particles, J. Chem. Phys. 150, 214901 (2019).
- D. P. Singh, U. Choudhury, P. Fischer, and A. G. Mark, Non-equilibrium assembly of light-activated colloidal mixtures, Adv. Mater. 29, 1701328 (2017).
- F. Hauke, H. Löwen, and B. Liebchen, Clustering-induced velocity-reversals of active colloids mixed with passive particles, J. Chem. Phys. 152, 014903 (2020).
- H. Löwen, Active colloidal molecules, Europhys. Lett. 121, 58001 (2018).
- J. R. Howse, R. A. L. Jones, A. J. Ryan, T. Gough, R. Vafabakhsh, and R. Golestanian, Self-Motile Colloidal Particles: From Directed Propulsion to Random Walk, Phys. Rev. Lett. 99, 048102 (2007).
- R. Golestanian, T. B. Liverpool, and A. Ajdari, Propulsion of a Molecular Machine by Asymmetric Distribution of Reaction Products, Phys. Rev. Lett. 94, 220801 (2005).
- R. Golestanian, T. B. Liverpool, and A. Ajdari, Designing phoretic micro- and nano-swimmers, New J. Phys. 9, 126 (2007).
- A. Würger, Self-Diffusiophoresis of Janus Particles in Near-Critical Mixtures, Phys. Rev. Lett. 115, 188304 (2015).
- G. Rückner and R. Kapral, Chemically Powered Nanodimers, Phys. Rev. Lett. 98, 150603 (2007).
- J. L. Moran, P. M. Wheat, and J. D. Posner, Locomotion of electrocatalytic nanomotors due to reaction induced charge autoelectrophoresis, Phys. Rev. E 81, 065302(R) (2010).
- W. F. Paxton, K. C. Kistler, C. C. Olmeda, A. Sen, S. K. St. Angelo, Y. Cao, T. E. Mallouk, P. E. Lammert, and V. H. Crespi, Catalytic nanomotors: Autonomous movement of striped nanorods, J. Am. Chem. Soc. 126, 13424 (2004).
- W. F. Paxton, A. Sen, and T. E. Mallouk, Motility of catalytic nanoparticles through self-generated forces, Chem. Eur. J. 11, 6462 (2005).
- D. Rings, R. Schachoff, M. Selmke, F. Cichos, and K. Kroy, Hot Brownian Motion, Phys. Rev. Lett. 105, 090604 (2010).
- P. Gaspard and R. Kapral, The stochastic motion of self-thermophoretic Janus particles, J. Stat. Mech. (2019) 074001.
- H.-R. Jiang, N. Yoshinaga, and M. Sano, Active Motion of a Janus Particle by Self-Thermophoresis in a Defocused Laser Beam, Phys. Rev. Lett. 105, 268302 (2010).
- A. Würger, Thermophoresis in Colloidal Suspensions Driven by Marangoni Forces, Phys. Rev. Lett. 98, 138301 (2007).
- S. Auschra, A. Bregulla, K. Kroy, and F. Cichos, Thermotaxis of Janus particles, Eur. Phys. J. E 44, 90 (2021).
- M. Fränzl and F. Cichos, Hydrodynamic manipulation of nano-objects by optically induced thermo-osmotic flows, Nat. Commun. 13, 656 (2022).
- M. Braun and F. Cichos, Optically controlled thermophoretic trapping of single nano-objects, ACS Nano 7, 11200 (2013).
- J. Grauer, F. Schmidt, J. Pineda, B. Midtvedt, H. Löwen, G. Volpe, and B. Liebchen, Active droploids, Nat. Commun. 12, 6005 (2021).
- R. Niu, A. Fischer, T. Palberg, and T. Speck, Dynamics of binary active clusters driven by ion-exchange particles, ACS Nano 12, 10932 (2018).
- R. Soto and R. Golestanian, Self-assembly of active colloidal molecules with dynamic function, Phys. Rev. E 91, 052304 (2015).
- R. Soto and R. Golestanian, Self-Assembly of Catalytically Active Colloidal Molecules: Tailoring Activity Through Surface Chemistry, Phys. Rev. Lett. 112, 068301 (2014).
- H. D. Vuijk, S. Klempahn, H. Merlitz, J.-U. Sommer, and A. Sharma, Active colloidal molecules in activity gradients, Phys. Rev. E 106, 014617 (2022).
- S. Gonzales and R. Soto, Directed assembly of active colloidal molecules, New J. Phys. 21, 033041 (2019).
- A. Varma, T. D. Montenegro-Johnson, and S. Michelin, Clustering-induced self-propulsion of isotropic autophoretic particles, Soft Matter 14, 7155 (2018).
- Z. Wang, Z. Wang, J. Li, C. Tian, and Y. Wang, Active colloidal molecules assembled via selective and directional bonds, Nat. Commun. 11, 2670 (2020).
- R. Niu, T. Palberg, and T. Speck, Self-Assembly of Colloidal Molecules due to Self-Generated Flow, Phys. Rev. Lett. 119, 028001 (2017).
- S. Saha, J. Agudo-Canalejo, and R. Golestanian, Scalar Active Mixtures: The Nonreciprocal Cahn-Hilliard Model, Phys. Rev. X 10, 041009 (2020).
- M. Fruchart, R. Hanai, P. B. Littlewood, and V. Vitelli, Non-reciprocal phase transitions, Nature (London) 592, 363 (2021).
- J. Agudo-Canalejo and R. Golestanian, Active Phase Separation in Mixtures of Chemically Interacting Particles, Phys. Rev. Lett. 123, 018101 (2019).
- K. L. Kreienkamp and S. H. L. Klapp, Clustering and flocking of repulsive chiral active particles with non-reciprocal couplings, New J. Phys. 24, 123009 (2022).
- S. A. M. Loss and S. H. L. Klapp, Irreversibility, heat and information flows induced by non-reciprocal interactions, New J. Phys. 22, 123051 (2020).
- Z. You, A. Baskaran, and M. C. Marchetti, Nonreciprocity as a generic route to traveling states, Proc. Natl. Acad. Sci. USA 117, 19767 (2020).
- S. A. M. Loos, S. H. L. Klapp, and T. Martynec, Long-Range Order and Directional Defect Propagation in the Nonreciprocal XY Model with Vision Cone Interactions, Phys. Rev. Lett. 130, 198301 (2023).
- I. Theurkauff, C. Cottin-Bizonne, J. Palacci, C. Ybert, and L. Bocquet, Dynamic Clustering in Active Colloidal Suspensions with Chemical Signaling, Phys. Rev. Lett. 108, 268303 (2012).
- I. Buttinoni, J. Bialké, F. Kümmel, H. Löwen, C. Bechinger, and T. Speck, Dynamical Clustering and Phase Separation in Suspensions of Self-Propelled Colloidal Particles, Phys. Rev. Lett. 110, 238301 (2013).
- J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, Living Crystals of Light-Activated Colloidal Surfers, Science 339, 936 (2013).
- F. Ginot, I. Theurkauff, F. Detcheverry, C. Ybert, and C. Cottin-Bizonne, Aggregation-fragmentation and individual dynamics of active clusters, Nat. Commun. 9, 696 (2018).
- H. Stark, Artificial Chemotaxis of Self-Phoretic Active Colloids: Collective Behavior, Acc. Chem. Res. 51, 2681 (2018).
- O. Pohl and H. Stark, Dynamic Clustering and Chemotactic Collapse of Self-Phoretic Active Particles, Phys. Rev. Lett. 112, 238303 (2014).
- G. Foffano, J. S. Lintuvuori, K. Stratford, M. E. Cates, and D. Marenduzzo, Dynamic clustering and re-dispersion in concentrated colloid-active gel composites, Soft Matter 15, 6896 (2019).
- B. Liebchen, D. Marenduzzo, I. Pagonabarraga, and M. E. Cates, Clustering and Pattern Formation in Chemorepulsive Active Colloids, Phys. Rev. Lett. 115, 258301 (2015).
- O. Pohl and H. Stark, Self-phoretic active particles interacting by diffusiophoresis: A numerical study of the collapsed state and dynamic clustering, Eur. Phys. J. E 38, 93 (2015).
- M.-J. Huang, J. Schofield, and R. Kapral, Chemotactic and hydrodynamic effects on collective dynamics of self-diffusiophoretic Janus motors, New J. Phys. 19, 125003 (2017).
- Z. Ma, M. Yang, and R. Ni, Dynamic Assembly of Active Colloids: Theory and Simulation, Adv. Theory Simul. 3, 2000021 (2020).
- B. Liebchen and H. Löwen, Modeling Chemotaxis of Microswimmers: From Individual to Collective Behavior, in Chemical Kinetics (World Scientific Europe, London, 2019), p. 493.
- B. Liebchen and H. Löwen, Which interactions dominate in active colloids? J. Chem. Phys. 150, 061102 (2019).
- B. Liebchen and A. K. Mukhopadhyay, Interactions in active colloids, J. Phys.: Condens. Matter 34, 083002 (2022).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L032038 for details about simulations and data analysis.
- C. H. Meredith, P. G. Moerman, J. Groenewold, Y.-J. Chiu, W. K. Kegel, A. nav Blaaderen, and L. D. Zarzar, Predator-prey interactions between droplets driven by non-reciprocal oil exchange, Nat. Chem. 12, 1136 (2020).
- M. Knežević, T. Welker, and H. Stark, Collective motion of active particles exhibiting non-reciprocal orientational interactions, Sci. Rep. 12, 19437 (2022).
- A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolintineanu, W. M. Brown, P. S. Crozier, P. J. in 't Veld, A. Kohlmeyer, S. G. Moore, T. D. Nguyen, et al., LAMMPS—A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales, Comput. Phys. Commun. 271, 108171 (2022).
- B. M. Smirnov, The properties of fractal clusters, Phys. Rep. 188, 1 (1990).
- A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO—The Open Visualization Tool, Modelling Simul. Mater. Sci. Eng. 18, 015012 (2010).
- T. A. Witten and L. M. Sander, Diffusion-limited aggregation, Phys. Rev. B 27, 5686 (1983).
- T. A. Witten and L. M. Sander, Diffusion-Limited Aggregation, a Kinetic Critical Phenomenon, Phys. Rev. Lett. 47, 1400 (1981).
- S. Jungblut, J. O. Joswig, and A. Eychmüller, Diffusion-limited cluster aggregation: Impact of rotational diffusion, J. Phys. Chem. C 123, 950 (2019).
- M. Kolb, R. Botet, and R. Jullien, Scaling of Kinetically Growing Clusters, Phys. Rev. Lett. 51, 1123 (1983).
- M. Paoluzzi, M. Leoni, and M. C. Marchetti, Fractal aggregation of active particles, Phys. Rev. E 98, 052603 (2018).