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Autonomous materials systems from active liquid crystals

Abstract

Liquid crystals (LCs) are ubiquitous in display technologies. The orientational ordering in the nematic phase of LCs gives rise to structural anisotropy, the ability to form topological defects and extraordinary sensitivity to interfacial events — three features that are not found in traditional, isotropic liquids. Active LC systems represent a particular class of active materials, in which some form of energy is transformed and used to generate motion, providing opportunities for new technologies and offering a platform to investigate matter far from equilibrium. In this Review, we discuss recent advances in the field of active LC systems, including natural systems, such as cell colonies, biopolymers and bacteria, and synthetic systems, which mimic the adaptive and autonomous behaviours found in nature. We investigate the properties of defects and flows, examine LC interfaces and emulsions, and discuss active LC colloids and composites. Finally, we highlight future possibilities and applications of active LC systems.

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Fig. 1: Applications of topological defects in passive and active liquid crystals.
Fig. 2: Defect properties in biopolymer-based active liquid crystals.
Fig. 3: Control of active matter through activity or anisotropy patterning.
Fig. 4: Emergent active structures in driven liquid crystals.
Fig. 5: Active LC emulsions and interfaces.
Fig. 6: Pattern formation in active nematics.

References

  1. 1.

    de Gennes, P. G. & Prost, J. The Physics of Liquid Crystals (Clarendon, 1993).

  2. 2.

    Kleman, M. & Lavrentovich, O. D. Soft Matter Physics: An Introduction (Springer, 2004).

  3. 3.

    Larsen, T. T., Bjarklev, A., Hermann, D. S. & Broeng, J. Optical devices based on liquid crystal photonic bandgap fibres. Opt. Express 11, 2589–2596 (2003).

    CAS  Article  Google Scholar 

  4. 4.

    Muševič, I. Liquid-crystal micro-photonics. Liq. Cryst. Rev. 4, 1–34 (2016).

    Article  CAS  Google Scholar 

  5. 5.

    Rey, A. D. & Denn, M. M. Dynamical phenomena in liquid-crystalline materials. Annu. Rev. Fluid Mech. 34, 233–266 (2002).

    Article  Google Scholar 

  6. 6.

    Lin, I.-H. et al. Endotoxin-induced structural transformations in liquid crystalline droplets. Science 332, 1297–1300 (2011).

    CAS  Article  Google Scholar 

  7. 7.

    Sadati, M. et al. Liquid crystal enabled early stage detection of beta amyloid formation on lipid monolayers. Adv. Funct. Mater. 25, 6050–6060 (2015).

    CAS  Article  Google Scholar 

  8. 8.

    Ware, T. H., McConney, M. E., Wie, J. J., Tondiglia, V. P. & White, T. J. Voxelated liquid crystal elastomers. Science 347, 982–984 (2015).

    CAS  Article  Google Scholar 

  9. 9.

    White, T. J. & Broer, D. J. Programmable and adaptive mechanics with liquid crystal polymer networks and elastomers. Nat. Mater. 14, 1087–1098 (2015).

    CAS  Article  Google Scholar 

  10. 10.

    Gelebart, A. H. et al. Making waves in a photoactive polymer film. Nature 546, 632–636 (2017).

    CAS  Article  Google Scholar 

  11. 11.

    Poulin, P., Stark, H., Lubensky, T. C. & Weitz, D. A. Novel colloidal interactions in anisotropic fluids. Science 275, 1770–1773 (1997).

    CAS  Article  Google Scholar 

  12. 12.

    Musevic, I., Skarabot, M., Tkalec, U., Ravnik, M. & Zumer, S. Two-dimensional nematic colloidal crystals self-assembled by topological defects. Science 313, 954–958 (2006).

    CAS  Article  Google Scholar 

  13. 13.

    Martínez-González, J. A. et al. Blue-phase liquid crystal droplets. Proc. Natl Acad. Sci. USA 112, 13195–13200 (2015).

    Article  CAS  Google Scholar 

  14. 14.

    Rahimi, M. et al. Nanoparticle self-assembly at the interface of liquid crystal droplets. Proc. Natl Acad. Sci. USA 112, 5297–5302 (2015).

    CAS  Article  Google Scholar 

  15. 15.

    Wang, X. et al. Topological defects in liquid crystals as templates for molecular self-assembly. Nat. Mater. 15, 106–112 (2016).

    CAS  Article  Google Scholar 

  16. 16.

    Wang, X. et al. Experimental insights into the nanostructure of the cores of topological defects in liquid crystals. Phys. Rev. Lett. 116, 147801 (2016).

    Article  CAS  Google Scholar 

  17. 17.

    Whitmer, J. K. et al. Nematic-field-driven positioning of particles in liquid crystal droplets. Phys. Rev. Lett. 111, 227801 (2013).

    Article  CAS  Google Scholar 

  18. 18.

    Tran, L. & Bishop, K. J. M. Swelling cholesteric liquid crystal shells to direct the assembly of particles at the interface. ACS Nano 14, 5459–5467 (2020).

    CAS  Article  Google Scholar 

  19. 19.

    Prost, J., Jülicher, F. & Joanny, J.-F. Active gel physics. Nat. Phys. 11, 131–139 (2015).

    Article  CAS  Google Scholar 

  20. 20.

    Marchetti, M. C. et al. Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189 (2013).

    CAS  Article  Google Scholar 

  21. 21.

    Ramaswamy, S. The mechanics and statistics of active matter. Annu. Rev. Condens. Matter Phys. 1, 323–345 (2010).

    Article  Google Scholar 

  22. 22.

    Doostmohammadi, A., Ignés-mullol, J., Yeomans, J. M. & Sagués, F. Active nematics. Nat. Commun. 9, 3246 (2018).

    Article  CAS  Google Scholar 

  23. 23.

    Bechinger, C. et al. Active particles in complex and crowded environments. Rev. Mod. Phys. 88, 045006 (2016).

    Article  Google Scholar 

  24. 24.

    Needleman, D. & Dogic, Z. Active matter at the interface between materials science and cell biology. Nat. Rev. Mater. 2, 17408 (2017).

    Article  CAS  Google Scholar 

  25. 25.

    Ignés-Mullol, J. & Sagués, F. Active, self-motile, and driven emulsions. Curr. Opin. Colloid Interface Sci. 49, 16–26 (2020).

    Article  CAS  Google Scholar 

  26. 26.

    Sengupta, A., Bahr, C. & Herminghaus, S. Topological microfluidics for flexible micro-cargo concepts. Soft Matter 9, 7251–7260 (2013).

    CAS  Article  Google Scholar 

  27. 27.

    Hernàndez-Navarro, S. et al. AC electrophoresis of microdroplets in anisotropic liquids: transport, assembling and reaction. Soft Matter 9, 7999–8004 (2013).

    Article  CAS  Google Scholar 

  28. 28.

    Gompper, G. et al. The 2020 motile active matter roadmap. J. Phys. Condens. Matter 32, 193001 (2020).

    CAS  Article  Google Scholar 

  29. 29.

    Ramaswamy, S. Active matter. J. Stat. Mech. Theory Exp. 2017, 054002 (2017).

    Article  Google Scholar 

  30. 30.

    Shaebani, M. R., Wysocki, A., Winkler, R. G., Gompper, G. & Rieger, H. Computational models for active matter. Nat. Rev. Phys. 2, 181–199 (2020).

    Article  Google Scholar 

  31. 31.

    Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I. & Shochet, O. Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75, 1226 (1995).

    CAS  Article  Google Scholar 

  32. 32.

    Toner, J. & Tu, Y. Long-range order in a two-dimensional dynamical XY model: how birds fly together. Phys. Rev. Lett. 75, 4326–4329 (1995).

    CAS  Article  Google Scholar 

  33. 33.

    Narayan, V., Ramaswamy, S. & Menon, N. Long-lived giant number fluctuations in a swarming granular nematic. Science 317, 105–109 (2007).

    CAS  Article  Google Scholar 

  34. 34.

    Sanchez, T., Chen, D. T. N., DeCamp, S. J., Heymann, M. & Dogic, Z. Spontaneous motion in hierarchically assembled active matter. Nature 491, 431–434 (2012).

    CAS  Article  Google Scholar 

  35. 35.

    Kumar, N., Zhang, R., de Pablo, J. J. & Gardel, M. L. Tunable structure and dynamics of active liquid crystals. Sci. Adv. 4, eaat7779 (2018).

    CAS  Article  Google Scholar 

  36. 36.

    Dogic, Z., Sharma, P. & Zakhary, M. J. Hypercomplex liquid crystals. Annu. Rev. Condens. Matter Phys. 5, 137–157 (2014).

    CAS  Article  Google Scholar 

  37. 37.

    Simha, R. A. & Ramaswamy, S. Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles. Phys. Rev. Lett. 89, 058101 (2002).

    Article  CAS  Google Scholar 

  38. 38.

    Marenduzzo, D., Orlandini, E. & Yeomans, J. M. Hydrodynamics and rheology of active liquid crystals: a numerical investigation. Phys. Rev. Lett. 98, 118102 (2007).

    CAS  Article  Google Scholar 

  39. 39.

    Marenduzzo, D., Orlandini, E., Cates, M. & Yeomans, J. Steady-state hydrodynamic instabilities of active liquid crystals: hybrid lattice Boltzmann simulations. Phys. Rev. E 76, 031921 (2007).

    CAS  Article  Google Scholar 

  40. 40.

    Gao, T., Blackwell, R., Glaser, M. A., Betterton, M. D. & Shelley, M. J. Multiscale polar theory of microtubule and motor-protein assemblies. Phys. Rev. Lett. 114, 048101 (2015).

    Article  CAS  Google Scholar 

  41. 41.

    Tang, X. & Selinger, J. V. Theory of defect motion in 2D passive and active nematic liquid crystals. Soft Matter 15, 587–601 (2019).

    CAS  Article  Google Scholar 

  42. 42.

    Giomi, L., Bowick, M. J., Ma, X. & Marchetti, M. C. Defect annihilation and proliferation in active nematics. Phys. Rev. Lett. 110, 228101 (2013).

    Article  CAS  Google Scholar 

  43. 43.

    Zhang, R., Zhou, Y., Mohammad, R. & de Pablo, J. J. Dynamic structure of active nematic shells. Nat. Commun. 8, 15064 (2016).

    Google Scholar 

  44. 44.

    Kumar, N., Soni, H., Ramaswamy, S. & Sood, A. K. Flocking at a distance in active granular matter. Nat. Commun. 5, 4688 (2014).

    CAS  Article  Google Scholar 

  45. 45.

    Galanis, J., Nossal, R., Losert, W. & Harries, D. Nematic order in small systems: measuring the elastic and wall-anchoring constants in vibrofluidized granular rods. Phys. Rev. Lett. 105, 168001 (2010).

    Article  CAS  Google Scholar 

  46. 46.

    Warner, M. & Terentjev, E. M. Liquid Crystal Elastomers (Oxford Univ. Press, 2007).

  47. 47.

    Warner, M. Topographic mechanics and applications of liquid crystalline solids. Annu. Rev. Condens. Matter Phys. 11, 125–145 (2020).

    CAS  Article  Google Scholar 

  48. 48.

    Nédélec, F. J., Surrey, T., Maggs, A. C. & Leibler, S. Self-organization of microtubules and motors. Nature 389, 305–308 (1997).

    Article  Google Scholar 

  49. 49.

    Schaller, V., Weber, C., Semmrich, C., Frey, E. & Bausch, A. R. Polar patterns of driven filaments. Nature 467, 73–77 (2010).

    CAS  Article  Google Scholar 

  50. 50.

    Sumino, Y. et al. Large-scale vortex lattice emerging from collectively moving microtubules. Nature 483, 448–452 (2012).

    CAS  Article  Google Scholar 

  51. 51.

    Brugués, J. & Needleman, D. Physical basis of spindle self-organization. Proc. Natl Acad. Sci. USA 111, 18496–18500 (2014).

    Article  CAS  Google Scholar 

  52. 52.

    Janmey, P. A. Mechanical properties of cytoskeletal polymers. Curr. Opin. Cell Biol. 2, 4–11 (1991).

    Article  Google Scholar 

  53. 53.

    Zhang, R., Kumar, N., Ross, J. L., Gardel, M. L. & de Pablo, J. J. Interplay of structure, elasticity, and dynamics in actin-based nematic materials. Proc. Natl Acad. Sci. USA 115, E124–E133 (2018).

    CAS  Article  Google Scholar 

  54. 54.

    Shendruk, T. N., Thijssen, K., Yeomans, J. M. & Doostmohammadi, A. Onset of meso-scale turbulence in active nematics. Nat. Commun. 8, 15326 (2017).

    Article  CAS  Google Scholar 

  55. 55.

    Hemingway, E. J., Mishra, P., Marchetti, M. C. & Fielding, S. M. Correlation lengths in hydrodynamic models of active nematics. Soft Matter 12, 7943–7952 (2016).

    CAS  Article  Google Scholar 

  56. 56.

    Guillamat, P., Ignés-mullol, J. & Sagués, F. Control of active liquid crystals with a magnetic field. Proc. Natl Acad. Sci. USA 113, 5498–5502 (2016).

    CAS  Article  Google Scholar 

  57. 57.

    Guillamat, P., Ignés-Mullol, J. & Sagués, F. Taming active turbulence with patterned soft interfaces. Nat. Commun. 8, 564 (2017).

    CAS  Article  Google Scholar 

  58. 58.

    Doostmohammadi, A. & Yeomans, J. M. Coherent motion of dense active matter. Eur. Phys. J. Spec. Top. 227, 2401–2411 (2019).

    Article  Google Scholar 

  59. 59.

    Hudson, S. D. & Thomas, E. L. Frank elastic-constant anisotropy measured from transmission-electron-microscope images of disclinations. Phys. Rev. Lett. 62, 1993 (1993).

    Article  Google Scholar 

  60. 60.

    Zhou, S., Shiyanovskii, S. V., Park, H. & Lavrentovich, O. D. Fine structure of the topological defect cores studied for disclinations in lyotropic chromonic liquid crystals. Nat. Commun. 8, 14974 (2017).

    Article  Google Scholar 

  61. 61.

    Joshi, A., Putzig, E., Baskaran, A. & Hagan, M. F. The interplay between activity and filament flexibility determines the emergent properties of active nematics. Soft Matter 15, 94–101 (2019).

    CAS  Article  Google Scholar 

  62. 62.

    Pismen, L. M. Dynamics of defects in an active nematic layer. Phys. Rev. E 88, 050502(R) (2013).

    Article  CAS  Google Scholar 

  63. 63.

    Giomi, L., Bowick, M. J., Mishra, P., Sknepnek, R. & Marchetti, M. C. Defect dynamics in active nematics. Phil. Trans. R. Soc. A 372, 20130365 (2014).

    Article  CAS  Google Scholar 

  64. 64.

    Decamp, S. J., Redner, G. S., Baskaran, A., Hagan, M. F. & Dogic, Z. Orientational order of motile defects in active nematics. Nat. Mater. 14, 1110 (2015).

    CAS  Article  Google Scholar 

  65. 65.

    Oza, A. U. & Dunkel, J. Antipolar ordering of topological defects in active liquid crystals. N. J. Phys. 18, 093006 (2016).

    Article  Google Scholar 

  66. 66.

    Shankar, S. & Marchetti, M. C. Hydrodynamics of active defects: from order to chaos to defect ordering. Phys. Rev. X 9, 041047 (2019).

    CAS  Google Scholar 

  67. 67.

    Putzig, E., Redner, G. S., Baskaran, A. & Baskaran, A. Instabilities, defects, and defect ordering in an overdamped active nematic. Soft Matter 12, 3854–3859 (2016).

    CAS  Article  Google Scholar 

  68. 68.

    Shankar, S., Ramaswamy, S., Marchetti, M. C. & Bowick, M. J. Defect unbinding in active nematics. Phys. Rev. Lett. 121, 108002 (2018).

    CAS  Article  Google Scholar 

  69. 69.

    Srivastava, P., Mishra, P. & Marchetti, M. C. Negative stiffness and modulated states in compressible active nematics. Soft Matter 12, 8214 (2016).

    CAS  Article  Google Scholar 

  70. 70.

    Doostmohammadi, A., Adamer, M. F., Thampi, S. P. & Yeomans, J. M. Stabilization of active matter by flow-vortex lattices and defect ordering. Nat. Commun. 7, 10557 (2016).

    CAS  Article  Google Scholar 

  71. 71.

    Green, R., Toner, J. & Vitelli, V. Geometry of thresholdless active flow in nematic microfluidics. Phys. Rev. Fluids 2, 104201 (2017).

    Article  Google Scholar 

  72. 72.

    Taylor, P., Sengupta, A., Herminghaus, S. & Bahr, C. Liquid crystal microfluidics: surface, elastic and viscous interactions at microscales. Liq. Cryst. Rev. 2, 73–110 (2014).

    Article  CAS  Google Scholar 

  73. 73.

    Tan, A. J. et al. Topological chaos in active nematics. Nat. Phys. 15, 1033–1039 (2019).

    CAS  Article  Google Scholar 

  74. 74.

    Aref, H. Stirring by chaotic advection. J. Fluid Mech. 143, 1–21 (1984).

    Article  Google Scholar 

  75. 75.

    Aref, H. et al. Frontiers of chaotic advection. Rev. Mod. Phys. 89, 025007 (2017).

    Article  Google Scholar 

  76. 76.

    Shendruk, T. N., Doostmohammadi, A., Thijssen, K. & Yeomans, J. M. Dancing disclinations in confined active nematics. Soft Matter 13, 3853–3862 (2017).

    CAS  Article  Google Scholar 

  77. 77.

    Chandragiri, S., Dootmohammadi, A., Yeomans, J. & Thampi, S. P. Active transport in a channel: stabilisation by flow or thermodynamics. Soft Matter 15, 1597–1604 (2019).

    CAS  Article  Google Scholar 

  78. 78.

    Sknepnek, R. & Henkes, S. Active swarms on a sphere. Phys. Rev. E 91, 022306 (2015).

    Article  CAS  Google Scholar 

  79. 79.

    Apaza, L. & Sandoval, M. Active matter on Riemannian manifolds. Soft Matter 14, 9928–9936 (2018).

    CAS  Article  Google Scholar 

  80. 80.

    Ehrig, S., Ferracci, J., Weinkamer, R. & Dunlop, J. W. C. Curvature-controlled defect dynamics in active systems. Phys. Rev. E 95, 062609 (2017).

    Article  Google Scholar 

  81. 81.

    Janssen, L. M. C., Kaiser, A. & Löwen, H. Aging and rejuvenation of active matter under topological constraints. Sci. Rep. 7, 5667 (2017).

    Article  CAS  Google Scholar 

  82. 82.

    Xi, W., Sonam, S., Beng Saw, T., Ladoux, B. & Teck Lim, C. Emergent patterns of collective cell migration under tubular confinement. Nat. Commun. 8, 1517 (2017).

    Article  CAS  Google Scholar 

  83. 83.

    Suzuki, K., Miyazaki, M., Takagi, J., Itabashi, T. & Ishiwata, S. Spatial confinement of active microtubule networks induces large-scale rotational cytoplasmic flow. Proc. Natl Acad. Sci. USA 114, 2922–2927 (2017).

    CAS  Article  Google Scholar 

  84. 84.

    Theillard, M., Alonso-Matilla, R. & Saintillan, D. Geometric control of active collective motion. Soft Matter 13, 363–375 (2017).

    CAS  Article  Google Scholar 

  85. 85.

    Wioland, H., Lushi, E. & Goldstein, R. E. Directed collective motion of bacteria under channel confinement. N. J. Phys. 18, 075002 (2016).

    Article  Google Scholar 

  86. 86.

    Wioland, H., Woodhouse, F. G., Dunkel, J. & Goldstein, R. E. Ferromagnetic and antiferromagnetic order in bacterial vortex lattices. Nat. Phys. 12, 341–345 (2016).

    CAS  Article  Google Scholar 

  87. 87.

    Lushi, E., Wioland, H. & Goldstein, R. E. Fluid flows created by swimming bacteria drive self-organization in confined suspensions. Proc. Natl Acad. Sci. USA 111, 9733–9738 (2014).

    CAS  Article  Google Scholar 

  88. 88.

    Hardoüin, J. et al. Reconfigurable flows and defect landscape of confined active nematics. Commun. Phys. 2, 121 (2019).

    Article  Google Scholar 

  89. 89.

    Ravnik, M. & Yeomans, J. M. Confined active nematic flow in cylindrical capillaries. Phys. Rev. Lett. 110, 026001 (2013).

    Article  CAS  Google Scholar 

  90. 90.

    Opathalage, A. et al. Self-organized dynamics and the transition to turbulence of confined active nematics. Proc. Natl Acad. Sci. USA 116, 4788–4797 (2019).

    CAS  Article  Google Scholar 

  91. 91.

    Norton, M. M. et al. Insensitivity of active nematic liquid crystal dynamics to topological constraints. Phys. Rev. E 97, 012702 (2018).

    CAS  Article  Google Scholar 

  92. 92.

    Chen, S., Gao, P. & Gao, T. Dynamics and structure of an apolar active suspension in an annulus. J. Fluid Mech. 835, 393–405 (2018).

    CAS  Article  Google Scholar 

  93. 93.

    Keber, F. C. et al. Topology and dynamics of active nematic vesicles. Science 345, 1135–1139 (2014).

    CAS  Article  Google Scholar 

  94. 94.

    Wu, K. et al. Transition from turbulent to coherent flows in confined three-dimensional active fluids. Science 355, eaal1979 (2017).

    Article  CAS  Google Scholar 

  95. 95.

    Khoromskaia, D. & Alexander, G. P. Vortex formation and dynamics of defects in active nematic shells. N. J. Phys. 19, 103043 (2017).

    Article  Google Scholar 

  96. 96.

    Henkes, S., Marchetti, M. C. & Sknepnek, R. Dynamical patterns in nematic active matter on a sphere. Phys. Rev. E 97, 042605 (2018).

    CAS  Article  Google Scholar 

  97. 97.

    Alaimo, F., Köhler, C. & Voigt, A. Curvature controlled defect dynamics in topological active nematics. Sci. Rep. 7, 5211 (2017).

    Article  CAS  Google Scholar 

  98. 98.

    Guillamat, P. et al. Active nematic emulsions. Sci. Adv. 4, eaao1470 (2018).

    Article  CAS  Google Scholar 

  99. 99.

    Senoussi, A., Kashida, S., Voituriez, R., Galas, J. & Maitra, A. Tunable corrugated patterns in an active nematic sheet. Proc. Natl Acad. Sci. USA 116, 22464–22470 (2019).

    CAS  Article  Google Scholar 

  100. 100.

    Strübing, T., Khosravanizadeh, A., Vilfan, A., Golestanian, R. & Guido, I. Wrinkling instability in 3D active nematics. Nano Lett. 20, 6281–6288 (2020).

    Article  CAS  Google Scholar 

  101. 101.

    Giomi, L. Geometry and topology of turbulence in active nematics. Phys. Rev. X 5, 031003 (2015).

    Google Scholar 

  102. 102.

    Ellis, P. W. et al. Curvature-induced defect unbinding and dynamics in active nematic toroids. Nat. Phys. 14, 85–90 (2018).

    CAS  Article  Google Scholar 

  103. 103.

    Pearce, D. J. G., Ellis, P. W., Fernandez-nieves, A. & Giomi, L. Geometrical control of active turbulence in curved topographies. Phys. Rev. Lett. 122, 168002 (2019).

    CAS  Article  Google Scholar 

  104. 104.

    Martínez-Prat, B., Ignés-Mullol, J., Casademunt, J. & Sagués, F. Selection mechanism at the onset of active turbulence. Nat. Phys. 15, 362–366 (2019).

    Article  CAS  Google Scholar 

  105. 105.

    Sokolov, A., Mozaffari, A., Zhang, R., de Pablo, J. J. & Snezhko, A. Emergence of radial tree of bend stripes in active nematics. Phys. Rev. X 9, 031014 (2019).

    CAS  Google Scholar 

  106. 106.

    Guillamat, P., Hardoüin, J., Prat, B. M., Ignés-Mullol, J. & Sagués, F. Control of active turbulence through addressable soft interfaces. J. Phys. Condens. Matter 29, 504003 (2017).

    CAS  Article  Google Scholar 

  107. 107.

    Pearce, D. J. G. Activity driven orientational order in active nematic liquid crystals on an anisotropic substrate. Phys. Rev. Lett. 122, 227801 (2019).

    CAS  Article  Google Scholar 

  108. 108.

    Thijssen, K., Metselaar, L., Yeomans, J. M. & Doostmohammadi, A. Active nematics with anisotropic friction: the decisive role of the flow aligning parameter. Soft Matter 16, 2065–2074 (2020).

    CAS  Article  Google Scholar 

  109. 109.

    Nakamura, M. et al. Remote control of myosin and kinesin motors using light-activated gearshifting. Nat. Nanotechnol. 9, 693–697 (2014).

    CAS  Article  Google Scholar 

  110. 110.

    Ross, T. D. et al. Controlling organization and forces in active matter through optically defined boundaries. Nature 572, 224–229 (2019).

    CAS  Article  Google Scholar 

  111. 111.

    Zhang, R. et al. Spatiotemporal control of liquid crystal structure and dynamics through activity patterning. Nat. Mater. https://doi.org/10.1038/s41563-020-00901-4 (2021).

    Article  Google Scholar 

  112. 112.

    Tang, X. & Selinger, J. V. Alignment of a topological defect by an activity gradient. Preprint at arXiv https://arXiv.org/abs/2007.09680 (2020).

  113. 113.

    Duclos, G., Garcia, S., Yevick, H. G. & Silberzan, P. Perfect nematic order in confined monolayers of spindle-shaped cells. Soft Matter 10, 2346–2353 (2014).

    CAS  Article  Google Scholar 

  114. 114.

    Kawaguchi, K., Kageyama, R. & Sano, M. Topological defects control collective dynamics in neural progenitor cell cultures. Nature 545, 327–331 (2017).

    CAS  Article  Google Scholar 

  115. 115.

    Liu, Y. J. et al. Confinement and low adhesion induce fast amoeboid migration of slow mesenchymal cells. Cell 160, 659–672 (2015).

    CAS  Article  Google Scholar 

  116. 116.

    Xi, W., Saw, T. B., Delacour, D., Lim, C. T. & Ladoux, B. Material approaches to active tissue mechanics. Nat. Rev. Mater. 4, 23–44 (2019).

    Article  Google Scholar 

  117. 117.

    Saw, T. B. et al. Topological defects in epithelia govern cell death and extrusion. Nature 544, 212–216 (2017).

    CAS  Article  Google Scholar 

  118. 118.

    Duclos, G., Erlenkämper, C., Joanny, J. F. & Silberzan, P. Topological defects in confined populations of spindle-shaped cells. Nat. Phys. 13, 58–62 (2017).

    CAS  Article  Google Scholar 

  119. 119.

    Nishiguchi, D., Nagai, K. H., Chaté, H. & Sano, M. Long-range nematic order and anomalous fluctuations in suspensions of swimming filamentous bacteria. Phys. Rev. E 95, 020601(R) (2017).

    Article  Google Scholar 

  120. 120.

    Blanch-Mercader, C. et al. Turbulent dynamics of epithelial cell cultures. Phys. Rev. Lett. 120, 208101 (2018).

    CAS  Article  Google Scholar 

  121. 121.

    Duclos, G. et al. Spontaneous shear flow in confined cellular nematics. Nat. Phys. 14, 728–732 (2018).

    CAS  Article  Google Scholar 

  122. 122.

    Voituriez, R., Joanny, J.-F. & Prost, J. Spontaneous flow transition in active polar gels. Europhys. Lett. 70, 404–410 (2005).

    CAS  Article  Google Scholar 

  123. 123.

    Wan, L. Q. et al. Micropatterned mammalian cells exhibit phenotype-specific left–right asymmetry. Proc. Natl Acad. Sci. USA 108, 12295–12300 (2011).

    CAS  Article  Google Scholar 

  124. 124.

    Hoffmann, L. A., Schakenraad, K., Merks, R. M. H. & Giomi, L. Chiral stresses in nematic cell monolayers. Soft Matter 16, 764–774 (2020).

    CAS  Article  Google Scholar 

  125. 125.

    Maitra, A. & Lenz, M. Spontaneous rotation can stabilise ordered chiral active fluids. Nat. Commun. 10, 920 (2019).

    Article  CAS  Google Scholar 

  126. 126.

    Doostmohammadi, A., Thampi, S. P. & Yeomans, J. M. Defect-mediated morphologies in growing cell colonies. Phys. Rev. Lett. 117, 048102 (2016).

    Article  CAS  Google Scholar 

  127. 127.

    Dell’Arciprete, D. et al. A growing bacterial colony in two dimensions as an active nematic. Nat. Commun. 9, 4190 (2018).

    Article  CAS  Google Scholar 

  128. 128.

    You, Z., Pearce, D. J. G., Sengupta, A. & Giomi, L. Geometry and mechanics of microdomains in growing bacterial colonies. Phys. Rev. X 8, 031065 (2018).

    CAS  Google Scholar 

  129. 129.

    Blow, M. L., Aqil, M., Liebchen, B. & Marenduzzo, D. Motility of active nematic films driven by ‘active anchoring’. Soft Matter 13, 6137–6144 (2017).

    CAS  Article  Google Scholar 

  130. 130.

    Copenhagen, K., Alert, R., Wingreen, N. S. & Shaevitz, J. W. Topological defects promote layer formation in Myxococcus xanthus colonies. Nat. Phys. https://doi.org/10.1038/s41567-020-01056-4 (2020).

    Article  Google Scholar 

  131. 131.

    Turiv, T. et al. Topology control of human fibroblast cells monolayer by liquid crystal elastomer. Sci. Adv. 6, eaaz6485 (2020).

    CAS  Article  Google Scholar 

  132. 132.

    Blanch-Mercader, C., Guillamat, P., Roux, A. & Kruse, K. Integer topological defects of cell monolayers: mechanics and flows. Phys. Rev. E 103, 012405 (2021).

    CAS  Article  Google Scholar 

  133. 133.

    Saw, T., Xi, W., Ladoux, B. & Lim, C. T. Biological tissues as active nematic liquid crystals. Adv. Mater. 30, 1802579 (2018).

    Article  CAS  Google Scholar 

  134. 134.

    Mizuno, D., Tardin, C., Schmidt, C. F. & MacKintosh, F. C. Nonequilibrium mechanics of active cytoskeletal networks. Science 315, 370–373 (2007).

    CAS  Article  Google Scholar 

  135. 135.

    Lenz, M., Thoresen, T., Gardel, M. L. & Dinner, A. R. Contractile units in disordered actomyosin bundles arise from F-actin buckling. Phys. Rev. Lett. 108, 238107 (2012).

    Article  CAS  Google Scholar 

  136. 136.

    Köhler, S., Schaller, V. & Bausch, A. R. Structure formation in active networks. Nat. Mater. 10, 462–468 (2011).

    Article  CAS  Google Scholar 

  137. 137.

    Mueller, R., Yeomans, J. M. & Doostmohammadi, A. Emergence of active nematic behavior in monolayers of isotropic cells. Phys. Rev. Lett. 122, 48004 (2019).

    CAS  Article  Google Scholar 

  138. 138.

    Comelles, J. et al. Epithelial colonies in vitro elongate through collective effects. eLife 10, e57730 (2021).

    Article  Google Scholar 

  139. 139.

    Volfson, D., Cookson, S., Hasty, J. & Tsimring, L. S. Biomechanical ordering of dense cell populations. Proc. Natl Acad. Sci. USA 105, 15346–15351 (2008).

    Article  Google Scholar 

  140. 140.

    Ginelli, F., Peruani, F., Bär, M. & Chaté, H. Large-scale collective properties of self-propelled rods. Phys. Rev. Lett. 104, 184502 (2010).

    Article  CAS  Google Scholar 

  141. 141.

    Lei, Q. L., Ciamarra, M. P. & Ni, R. Nonequilibrium strongly hyperuniform fluids of circle active particles with large local density fluctuations. Sci. Adv. 5, eaau7423 (2019).

    Article  Google Scholar 

  142. 142.

    Zhang, H. P., Be’er, A., Florin, E.-L. & Swinney, H. L. Collective motion and density fluctuations in bacterial colonies. Proc. Natl Acad. Sci. USA 107, 13626–13630 (2010).

    CAS  Article  Google Scholar 

  143. 143.

    Schaller, V. & Bausch, A. R. Topological defects and density fluctuations in collectively moving systems. Proc. Natl Acad. Sci. USA 110, 4488–4493 (2013).

    Article  CAS  Google Scholar 

  144. 144.

    Maitra, A. et al. A nonequilibrium force can stabilize 2D active nematics. Proc. Natl Acad. Sci. USA 115, 6934–6939 (2018).

    Article  CAS  Google Scholar 

  145. 145.

    Ginelli, F. & Chate, H. Simple model for active nematics: quasi-long-range order and giant fluctuations. Phys. Rev. Lett. 96, 180602 (2006).

    Article  CAS  Google Scholar 

  146. 146.

    Shi, X. & Ma, Y. Topological structure dynamics revealing collective evolution in active nematics. Nat. Commun. 4, 3013 (2013).

    Article  CAS  Google Scholar 

  147. 147.

    Li, H. et al. Data-driven quantitative modeling of bacterial active nematics. Proc. Natl Acad. Sci. USA 116, 777–785 (2019).

    CAS  Article  Google Scholar 

  148. 148.

    Cui, M., Emrick, T. & Russell, T. P. Stabilizing liquid drops in nonequilibrium shapes by the interfacial jamming of nanoparticles. Science 342, 460–463 (2013).

    CAS  Article  Google Scholar 

  149. 149.

    Porenta, T., Ravnik, M. & Zumer, S. Complex field-stabilised nematic defect structures in Laguerre–Gaussian optical tweezers. Soft Matter 8, 1865–1870 (2012).

    CAS  Article  Google Scholar 

  150. 150.

    Emeršič, T. et al. Sculpting stable structures in pure liquids. Sci. Adv. 5, eaav4283 (2019).

    Article  CAS  Google Scholar 

  151. 151.

    Čopar, S., Kos, Ž., Emeršič, T. & Tkalec, U. Microfluidic control over topological states in channel-confined nematic flows. Nat. Commun. 11, 59 (2020).

    Article  CAS  Google Scholar 

  152. 152.

    Lei, L., Changqing, S. & Gang, X. Generation and detection of propagating solitons in shearing liquid crystals. J. Stat. Phys. 39, 633–652 (1985).

    Article  Google Scholar 

  153. 153.

    Smalyukh, I. I. Review: knots and other new topological effects in liquid crystals and colloids. Rep. Prog. Phys. 83, 106601 (2020).

    Article  Google Scholar 

  154. 154.

    Helfrich, W. Conduction-induced alignment of nematic liquid crystals: basic model and stability considerations. J. Chem. Phys. 51, 4092 (1969).

    CAS  Article  Google Scholar 

  155. 155.

    Buka, A. & Kramer, L. Pattern Formation in Liquid Crystals (Springer, 1984).

  156. 156.

    Aya, S. & Araoka, F. Kinetics of motile solitons in nematic liquid crystals. Nat. Commun. 11, 3248 (2020).

    CAS  Article  Google Scholar 

  157. 157.

    Calderer, M.-C. & Earls, A. Three-dimensional solitons in nematic liquid crystals: linear analysis. Preprint at arXiv https://arxiv.org/abs/1910.05959 (2019).

  158. 158.

    Li, B. et al. Electrically driven three-dimensional solitary waves as director bullets in nematic liquid crystals. Nat. Commun. 9, 1038 (2018).

    Article  CAS  Google Scholar 

  159. 159.

    Li, B., Xiao, R., Paladugu, S., Shiyanovskii, S. V. & Lavrentovich, O. D. Three-dimensional solitary waves with electrically tunable direction of propagation in nematics. Nat. Commun. 10, 3749 (2019).

    Article  CAS  Google Scholar 

  160. 160.

    Foster, D. et al. Two-dimensional skyrmion bags in liquid crystals and ferromagnets. Nat. Phys. 15, 655–660 (2019).

    CAS  Article  Google Scholar 

  161. 161.

    Fukuda, J. I. & Žumer, S. Quasi-two-dimensional skyrmion lattices in a chiral nematic liquid crystal. Nat. Commun. 2, 246 (2011).

    Article  CAS  Google Scholar 

  162. 162.

    Kim, Y. H., Gim, M. J., Jung, H. T. & Yoon, D. K. Periodic arrays of liquid crystalline torons in microchannels. RSC Adv. 5, 19279–19283 (2015).

    CAS  Article  Google Scholar 

  163. 163.

    Smalyukh, I. I., Lansac, Y., Clark, N. A. & Trivedi, R. P. Three-dimensional structure and multistable optical switching of triple-twisted particle-like excitations in anisotropic fluids. Nat. Mater. 9, 139–145 (2010).

    CAS  Article  Google Scholar 

  164. 164.

    Ackerman, P. J., Boyle, T. & Smalyukh, I. I. Squirming motion of baby skyrmions in nematic fluids. Nat. Commun. 8, 673 (2017).

    Article  CAS  Google Scholar 

  165. 165.

    Sohn, H. R. O., Liu, C. D. & Smalyukh, I. I. Schools of skyrmions with electrically tunable elastic interactions. Nat. Commun. 10, 4744 (2019).

    CAS  Article  Google Scholar 

  166. 166.

    Sohn, H. R. O., Liu, C. D., Voinescu, R., Chen, Z. & Smalyukh, I. I. Optically enriched and guided dynamics of active skyrmions. Opt. Express 28, 6306 (2020).

    Article  Google Scholar 

  167. 167.

    Shen, Y. & Dierking, I. Dynamics of electrically driven solitons in nematic and cholesteric liquid crystals. Commun. Phys. 3, 14 (2020).

    CAS  Article  Google Scholar 

  168. 168.

    Ackerman, P. J. & Smalyukh, I. I. Diversity of knot solitons in liquid crystals manifested by linking of preimages in torons and hopfions. Phys. Rev. X 7, 011006 (2017).

    Google Scholar 

  169. 169.

    Kim, Y., Wang, X., Mondkar, P., Bukusoglu, E. & Abbott, N. L. Self-reporting and self-regulating liquid crystals. Nature 557, 539–544 (2018).

    CAS  Article  Google Scholar 

  170. 170.

    Khoromskaia, D. & Alexander, G. P. Motility of active fluid drops on surfaces. Phys. Rev. E 92, 062311 (2015).

    Article  CAS  Google Scholar 

  171. 171.

    Yoshinaga, N. Self-propulsion of an active polar drop. J. Chem. Phys. 150, 184904 (2019).

    Article  CAS  Google Scholar 

  172. 172.

    Negro, G., Carenza, L. N., Lamura, A., Tiribocchi, A. & Gonnella, G. Rheology of active polar emulsions: from linear to unidirectional and inviscid flow, and intermittent viscosity. Soft Matter 15, 8251–8265 (2019).

    CAS  Article  Google Scholar 

  173. 173.

    Fialho, A. R., Blow, M. L. & Marenduzzo, D. Anchoring-driven spontaneous rotations in active gel droplets. Soft Matter 13, 5933–5941 (2017).

    CAS  Article  Google Scholar 

  174. 174.

    Mushenheim, P. C. & Abbott, N. L. Hierarchical organization in liquid crystal-in-liquid crystal emulsions. Soft Matter 10, 8627–8734 (2014).

    CAS  Article  Google Scholar 

  175. 175.

    Huber, L., Suzuki, R., Krüger, T., Frey, E. & Bausch, A. R. Emergence of coexisting ordered states in active matter systems. Science 361, 255–258 (2018).

    CAS  Article  Google Scholar 

  176. 176.

    Peng, C., Turiv, T., Guo, Y., Wei, Q. & Lavrentovich, O. D. Command of active matter by topological defects and patterns. Science 354, 882–885 (2016).

    CAS  Article  Google Scholar 

  177. 177.

    Kim, Y., Noh, J., Nayani, K. & Abbott, N. L. Soft matter from liquid crystals. Soft Matter 15, 6913–6929 (2019).

    CAS  Article  Google Scholar 

  178. 178.

    Hardoüin, J., Guillamat, P., Sagués, F. & Ignés-Mullol, J. Dynamics of ring disclinations driven by active nematic shells. Front. Phys. 7, 165 (2019).

    Article  Google Scholar 

  179. 179.

    Giomi, L. & Desimone, A. Spontaneous division and motility in active nematic droplets. Phys. Rev. Lett. 112, 147802 (2014).

    Article  CAS  Google Scholar 

  180. 180.

    Blow, M. L., Thampi, S. P. & Yeomans, J. M. Biphasic, lyotropic, active nematics. Phys. Rev. Lett. 113, 248303 (2014).

    Article  CAS  Google Scholar 

  181. 181.

    Gao, T. & Li, Z. Self-driven droplet powered by active nematics. Phys. Rev. Lett. 119, 108002 (2017).

    Article  Google Scholar 

  182. 182.

    Carenza, L. N., Gonnella, G., Marenduzzo, D. & Negro, G. Rotation and propulsion in 3D active chiral droplets. Proc. Natl Acad. Sci. USA 116, 22065–22070 (2019).

    CAS  Article  Google Scholar 

  183. 183.

    De Magistris, G. et al. Spontaneous motility of passive emulsion droplets in polar active gels. Soft Matter 10, 7826–7837 (2014).

    Article  CAS  Google Scholar 

  184. 184.

    Peddireddy, K., Kumar, P., Thutupalli, S., Herminghaus, S. & Bahr, C. Solubilization of thermotropic liquid crystal compounds in aqueous surfactant solutions. Langmuir 28, 12426–12431 (2012).

    CAS  Article  Google Scholar 

  185. 185.

    Herminghaus, S. et al. Interfacial mechanisms in active emulsions. Soft Matter 10, 7008–7022 (2014).

    CAS  Article  Google Scholar 

  186. 186.

    Krüger, C., Klös, G., Bahr, C. & Maass, C. C. Curling liquid crystal microswimmers: a cascade of spontaneous symmetry breaking. Phys. Rev. Lett. 117, 048003 (2016).

    Article  CAS  Google Scholar 

  187. 187.

    Jin, C., Krüger, C. & Maass, C. C. Chemotaxis and autochemotaxis of self-propelling droplet swimmers. Proc. Natl Acad. Sci. USA 114, 5089–5094 (2017).

    CAS  Article  Google Scholar 

  188. 188.

    Hokmabad, B. V., Baldwin, K. A., Krüger, C., Bahr, C. & Maass, C. C. Topological stabilization and dynamics of self-propelling nematic shells. Phys. Rev. Lett. 123, 178003 (2019).

    CAS  Article  Google Scholar 

  189. 189.

    Lazo, I., Peng, C., Xiang, J., Shiyanovskii, S. V. & Lavrentovich, O. D. Liquid crystal-enabled electro-osmosis through spatial charge separation in distorted regions as a novel mechanism of electrokinetics. Nat. Commun. 5, 5033 (2014).

    CAS  Article  Google Scholar 

  190. 190.

    Conklin, C. et al. Electrokinetic effects in nematic suspensions: single-particle electro-osmosis and interparticle interactions. Phys. Rev. E 98, 022703 (2018).

    CAS  Article  Google Scholar 

  191. 191.

    Lehmann, O. Structure, system and magnetic behaviour of liquid crystals and their miscibility with the solid ones. Ann. Phys. 2, 649–705 (1900).

    CAS  Article  Google Scholar 

  192. 192.

    Oswald, P. & Dequidt, A. Measurement of the continuous Lehmann rotation of cholesteric droplets subjected to a temperature gradient. Phys. Rev. Lett. 100, 217802 (2008).

    Article  CAS  Google Scholar 

  193. 193.

    Yoshioka, J. & Araoka, F. Topology-dependent self-structure mediation and efficient energy conversion in heat-flux-driven rotors of cholesteric droplets. Nat. Commun. 9, 432 (2018).

    Article  CAS  Google Scholar 

  194. 194.

    Oswald, P., Ignés-Mullol, J. & Dequidt, A. Lehmann rotation of cholesteric droplets driven by Marangoni convection. Soft Matter 15, 2591–2604 (2019).

    CAS  Article  Google Scholar 

  195. 195.

    Oswald, P., Dequidt, A. & Poy, G. Lehmann effect in nematic and cholesteric liquid crystals: a review. Liq. Cryst. Rev. 7, 142–166 (2019).

    CAS  Article  Google Scholar 

  196. 196.

    Lavrentovich, O. D. Transport of particles in liquid crystals. Soft Matter 10, 1264–1283 (2014).

    CAS  Article  Google Scholar 

  197. 197.

    Lavrentovich, O. D. Active colloids in liquid crystals. Curr. Opin. Colloid Interface Sci. 21, 97–109 (2016).

    CAS  Article  Google Scholar 

  198. 198.

    Wu, X.-L. & Libchaber, A. Particle diffusion in a quasi-two-dimensional bacterial bath. Phys. Rev. Lett. 84, 3017 (2000).

    CAS  Article  Google Scholar 

  199. 199.

    Valeriani, C., Li, M., Novosel, J., Arlt, J. & Marenduzzo, D. Colloids in a bacterial bath: simulations and experiments. Soft Matter 7, 5228–5238 (2011).

    CAS  Article  Google Scholar 

  200. 200.

    Mozaffari, A., Sharifi-Mood, N., Koplik, J. & Maldarelli, C. Self-propelled colloidal particle near a planar wall: a Brownian dynamics study. Phys. Rev. Fluids 3, 014104 (2018).

    Article  Google Scholar 

  201. 201.

    Rivas, D. P., Shendruk, T. N., Henry, R. R., Reich, D. H. & Leheny, R. L. Driven topological transitions in active nematic films. Soft Matter 16, 9331–9338 (2020).

    CAS  Article  Google Scholar 

  202. 202.

    Thampi, S. P., Doostmohammadi, A., Shendruk, T. N., Golestanian, R. & Yeomans, J. M. Active micromachines: microfluidics powered by mesoscale turbulence. Sci. Adv. 2, e1501854 (2016).

    Article  Google Scholar 

  203. 203.

    Sokolov, A., Apodaca, M. M., Grzybowski, B. A. & Aranson, I. S. Swimming bacteria power microscopic gears. Proc. Natl Acad. Sci. USA 107, 969–974 (2010).

    CAS  Article  Google Scholar 

  204. 204.

    Leonardo, R. D. I. et al. Bacterial ratchet motors. Proc. Natl Acad. Sci. USA 107, 9541–9545 (2010).

    Article  Google Scholar 

  205. 205.

    Hernàndez-Navarro, S., Tierno, P., Farrera, J. A., Ignøs-mullol, J. & Sagués, F. Reconfigurable swarms of nematic colloids controlled by photoactivated surface patterns. Angew. Chem. Int. Ed. 53, 10696–10700 (2014).

    Article  CAS  Google Scholar 

  206. 206.

    Toner, J., Löwen, H. & Wensink, H. H. Following fluctuating signs: anomalous active superdiffusion of swimmers in anisotropic media. Phys. Rev. E 93, 062610 (2016).

    Article  CAS  Google Scholar 

  207. 207.

    Ferreiro-Córdova, C., Toner, J., Löwen, H. & Wensink, H. H. Long-time anomalous swimmer diffusion in smectic liquid crystals. Phys. Rev. E 97, 062606 (2018).

    Article  Google Scholar 

  208. 208.

    Jones, T. B. Electromechanics of Particles (Cambridge Univ. Press, 2005).

  209. 209.

    Jákli, A., Senyuk, B., Liao, G. & Lavrentovich, O. D. Colloidal micromotor in smectic A liquid crystal driven by DC electric field. Soft Matter 4, 2471–2474 (2008).

    Article  CAS  Google Scholar 

  210. 210.

    Rasna, M. V., Ramudu, U. V., Chandrasekar, R. & Dhara, S. Propelling and spinning of microsheets in nematic liquid crystals driven by ac electric field. Phys. Rev. E 95, 012710 (2017).

    CAS  Article  Google Scholar 

  211. 211.

    Driscoll, M. et al. Unstable fronts and motile structures formed by microrollers. Nat. Phys. 13, 375–379 (2016).

    Article  CAS  Google Scholar 

  212. 212.

    Banerjee, D., Souslov, A., Abanov, A. G. & Vitelli, V. Odd viscosity in chiral active fluids. Nat. Commun. 8, 1573 (2017).

    Article  CAS  Google Scholar 

  213. 213.

    Soni, V. et al. The odd free surface flows of a colloidal chiral fluid. Nat. Phys. 15, 1188–1194 (2019).

    CAS  Article  Google Scholar 

  214. 214.

    Trivedi, R. R., Maeda, R., Abbott, N. L., Spagnolie, S. E. & Weibel, D. B. Bacterial transport of colloids in liquid crystalline environments. Soft Matter 11, 8404–8408 (2015).

    CAS  Article  Google Scholar 

  215. 215.

    Sokolov, A., Zhou, S., Lavrentovich, O. D. & Aranson, I. S. Individual behavior and pairwise interactions between microswimmers in anisotropic liquid. Phys. Rev. E 91, 013009 (2015).

    Article  CAS  Google Scholar 

  216. 216.

    Aranson, I. S. Harnessing medium anisotropy to control active matter. Acc. Chem. Res. 51, 3023–3030 (2018).

    CAS  Article  Google Scholar 

  217. 217.

    Sahu, D. K., Ramaswamy, S. & Dhara, S. Omnidirectional transport and navigation of Janus particles through a nematic liquid crystal film. Phys. Rev. Res. 2, 032009 (2020).

    CAS  Article  Google Scholar 

  218. 218.

    Zhou, S., Sokolov, A., Lavrentovich, O. D. & Aranson, I. S. Living liquid crystals. Proc. Natl Acad. Sci. USA 111, 1265–1270 (2014).

    CAS  Article  Google Scholar 

  219. 219.

    Mushenheim, P. C., Trivedi, R. R., Tuson, H. H., Weibel, D. B. & Abbott, N. L. Dynamic self-assembly of motile bacteria in liquid crystals. Soft Matter 10, 88–95 (2014).

    CAS  Article  Google Scholar 

  220. 220.

    Zhou, S. et al. Dynamic states of swimming bacteria in a nematic liquid crystal cell with homeotropic alignment. N. J. Phys. 19, 055006 (2017).

    Article  CAS  Google Scholar 

  221. 221.

    Mushenheim, P. C. et al. Effects of confinement, surface-induced orientations and strain on dynamical behaviors of bacteria in thin liquid crystalline films. Soft Matter 11, 6821–6831 (2015).

    CAS  Article  Google Scholar 

  222. 222.

    Guo, Y. et al. High-resolution and high-throughput plasmonic photopatterning of complex molecular orientations in liquid crystals. Adv. Mater. 28, 2353–2358 (2016).

    CAS  Article  Google Scholar 

  223. 223.

    Turiv, T. et al. Polar jets of swimming bacteria condensed by a patterned liquid crystal. Nat. Phys. 16, 481–487 (2020).

    CAS  Article  Google Scholar 

  224. 224.

    Endresen, K. D., Kim, M. & Serra, F. Topological defects of integer charge in cell monolayers. Preprint at arXiv https://arxiv.org/abs/1912.03271 (2019).

  225. 225.

    Koizumi, R. et al. Control of microswimmers by spiral nematic vortices: transition from individual to collective motion and contraction, expansion, and stable circulation of bacterial swirls. Phys. Rev. Res. 2, 033060 (2020).

    CAS  Article  Google Scholar 

  226. 226.

    Weirich, K. L. et al. Liquid behavior of cross-linked actin bundles. Proc. Natl Acad. Sci. USA 114, 2131–2136 (2017).

    CAS  Article  Google Scholar 

  227. 227.

    Weirich, K. L., Dasbiswas, K., Witten, T. A., Vaikuntanathan, S. & Gardel, M. L. Self-organizing motors divide active liquid droplets. Proc. Natl Acad. Sci. USA 166, 11125–11130 (2019).

    Article  CAS  Google Scholar 

  228. 228.

    Ludwig, N. B. et al. Nucleation and shape dynamics of model nematic tactoids around adhesive colloids. J. Chem. Phys. 152, 084901 (2019).

    Article  CAS  Google Scholar 

  229. 229.

    Lighthill, M. J. On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers. Commun. Pure Appl. Math. 5, 109–118 (1952).

    Article  Google Scholar 

  230. 230.

    Lintuvuori, J. S., Würger, A. & Stratford, K. Hydrodynamics defines the stable swimming direction of spherical squirmers in a nematic liquid crystal. Phys. Rev. Lett. 119, 068001 (2017).

    CAS  Article  Google Scholar 

  231. 231.

    Daddi-Moussa-Ider, A. & Menzel, A. M. Dynamics of a simple model microswimmer in an anisotropic fluid: implications for alignment behavior and active transport in a nematic liquid crystal. Phys. Rev. Fluids 3, 094102 (2018).

    Article  Google Scholar 

  232. 232.

    Chi, H., Potomkin, M., Zhang, L., Berlyand, L. & Aranson, I. S. Surface anchoring controls orientation of a microswimmer in nematic liquid crystal. Commun. Phys. 3, 162 (2020).

    Article  Google Scholar 

  233. 233.

    Duclos, G. et al. Topological structure and dynamics of three dimensional active nematics. Science 367, 1120–1124 (2020).

    CAS  Article  Google Scholar 

  234. 234.

    Krzic, U., Gunther, S., Saunders, T. E., Streichan, S. J. & Hufnagel, L. Multiview light-sheet microscope for rapid in toto imaging. Nat. Methods 9, 730–733 (2012).

    CAS  Article  Google Scholar 

  235. 235.

    Simon, Č., Aplinc, J., Kos, Ž., Slobodan, Ž. & Ravnik, M. Topology of three-dimensional active nematic turbulence confined to droplets. Phys. Rev. X 9, 031051 (2019).

    Google Scholar 

  236. 236.

    Krajnik, Ž., Kos, Ž. & Ravnik, M. Spectral energy analysis of bulk three-dimensional active nematic turbulence. Soft Matter 16, 9059–9068 (2020).

    CAS  Article  Google Scholar 

  237. 237.

    Binysh, J., Kos, Ž., Čopar, S., Ravnik, M. & Alexander, G. P. Three-dimensional active defect loops. Phys. Rev. Lett. 124, 088001 (2019).

    Article  Google Scholar 

  238. 238.

    Genkin, M. M., Sokolov, A., Lavrentovich, O. D. & Aranson, I. S. Topological defects in a living nematic ensnare swimming bacteria. Phys. Rev. X 7, 011029 (2017).

    Google Scholar 

  239. 239.

    Zhang, R., Roberts, T., Aranson, I. S. & De Pablo, J. J. Lattice Boltzmann simulation of asymmetric flow in nematic liquid crystals with finite anchoring. J. Chem. Phys. 144, 084905 (2016).

    Article  CAS  Google Scholar 

  240. 240.

    Kos, Ž. & Ravnik, M. Field generated nematic microflows via backflow mechanism. Sci. Rep. 10, 1446 (2020).

    CAS  Article  Google Scholar 

  241. 241.

    Lavrentovich, O. D., Lazo, I. & Pishnyak, O. P. Nonlinear electrophoresis of dielectric and metal spheres in a nematic liquid crystal. Nature 467, 947–950 (2010).

    CAS  Article  Google Scholar 

  242. 242.

    Whitfield, C. A. et al. Hydrodynamic instabilities in active cholesteric liquid crystals. Eur. Phys. J. E 40, 50 (2017).

    Article  CAS  Google Scholar 

  243. 243.

    Metselaar, L., Doostmohammadi, A. & Yeomans, J. M. Topological states in chiral active matter: dynamic blue phases and active half-skyrmions. J. Chem. Phys. 150, 064909 (2019).

    Article  CAS  Google Scholar 

  244. 244.

    Li, Z., Zhang, D., Lin, S. & Li, B. Pattern formation and defect ordering in active chiral nematics. Phys. Rev. Lett. 125, 098002 (2020).

    CAS  Article  Google Scholar 

  245. 245.

    Carenza, L. N., Gonnella, G., Marenduzzo, D. & Negro, G. Chaotic and periodical dynamics of active chiral droplets. Phys. A 559, 125025 (2020).

    CAS  Article  Google Scholar 

  246. 246.

    Napoli, G. & Turzi, S. Spontaneous helical flows in active nematics lying on a cylindrical surface. Phys. Rev. E 101, 022701 (2020).

    CAS  Article  Google Scholar 

  247. 247.

    Markovich, T., Tjhung, E. & Cates, M. E. Chiral active matter: microscopic ‘torque dipoles’ have more than one hydrodynamic description. N. J. Phys. 21, 112001 (2019).

    CAS  Article  Google Scholar 

  248. 248.

    Romanczuk, P., Chaté, H., Chen, L., Ngo, S. & Toner, J. Emergent smectic order in simple active particle models. N. J. Phys. 18, 063015 (2016).

    Article  CAS  Google Scholar 

  249. 249.

    Sokolov, A. & Aranson, I. S. Reduction of viscosity in suspension of swimming bacteria. Phys. Rev. Lett. 103, 148101 (2009).

    Article  CAS  Google Scholar 

  250. 250.

    López, H. M., Gachelin, J., Douarche, C., Auradou, H. & Clément, E. Turning bacteria suspensions into superfluids. Phys. Rev. Lett. 115, 028301 (2015).

    Article  CAS  Google Scholar 

  251. 251.

    Loisy, A., Eggers, J. & Liverpool, T. B. Active suspensions have nonmonotonic flow curves and multiple mechanical equilibria. Phys. Rev. Lett. 121, 018001 (2018).

    CAS  Article  Google Scholar 

  252. 252.

    Rafaï, S., Jibuti, L. & Peyla, P. Effective viscosity of microswimmer suspensions. Phys. Rev. Lett. 104, 098102 (2010).

    Article  CAS  Google Scholar 

  253. 253.

    Boyland, P., Aref, H. & Stremler, M. Topological fluid mechanics of stirring. J. Fluid Mech. 403, 277–304 (2000).

    Article  Google Scholar 

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Acknowledgements

The work on active living liquid crystals is supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), Division of Materials Science and Engineering. Support from the DOE, BES, Division of Materials Science and Engineering DE-SC0019762 for development of responsive chiral liquid crystals far from equilibrium, from the US Army Research Office (MURI: W911NF-15-1-0568) for design of triggerable materials based on liquid crystals, from the National Science Foundation (NSF) grant DMR-1710318 for development of lyotropic liquid crystal models and from the University of Chicago’s Materials Research Science and Engineering Center for development of activity patterning in active liquid crystals (NSF award DMR-1420709) is also gratefully acknowledged. R.Z. also acknowledges the financial support of the Hong Kong RGC under grant no. 26302320.

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Correspondence to Juan J. de Pablo.

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Zhang, R., Mozaffari, A. & de Pablo, J.J. Autonomous materials systems from active liquid crystals. Nat Rev Mater 6, 437–453 (2021). https://doi.org/10.1038/s41578-020-00272-x

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