[en] Odd materials feature antisymmetric response to perturbations. This anomalous property can stem from the nonequilibrium activity of their components, which is sustained by an external energy supply. These materials open the door to designing innovative engines which extract work by applying cyclic deformations, without any equivalent in equilibrium. Here, we reveal that the efficiency of such energy conversion, from local activity to macroscopic work, can be arbitrarily close to unity when the cycles of deformation are properly designed. We illustrate these principles in some canonical viscoelastic materials, which leads us to identify strategies for optimizing power and efficiency according to material properties and to delineate guidelines for the design of more complex odd engines.
Disciplines :
Physique
Auteur, co-auteur :
FODOR, Etienne ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
Souslov2, Anton; Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom
H. B. Callen, Thermodynamics and an Introduction to Thermostatics (John Wiley & Sons, New York, 1985).
S. Carnot, Réflexions sur la puissance motrice du feu (Bachelier, Paris, 1824).
V. Blickle and C. Bechinger, Realization of a micrometre-sized stochastic heat engine, Nat. Phys. 8, 143 (2011) 1745-2473 10.1038/nphys2163.
S. Krishnamurthy, S. Ghosh, D. Chatterji, R. Ganapathy, and A. K. Sood, A micrometre-sized heat engine operating between bacterial reservoirs, Nat. Phys. 12, 1134 (2016) 1745-2473 10.1038/nphys3870.
I. A. Martínez, É. Roldán, L. Dinis, D. Petrov, J. M. R. Parrondo, and R. A. Rica, Brownian Carnot engine, Nat. Phys. 12, 67 (2016) 1745-2473 10.1038/nphys3518.
I. A. Martínez, É. Roldán, L. Dinis, and R. A. Rica, Colloidal heat engines: A review, Soft Matter 13, 22 (2017) 1744-683X 10.1039/C6SM00923A.
M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, Hydrodynamics of soft active matter, Rev. Mod. Phys. 85, 1143 (2013) RMPHAT 0034-6861 10.1103/RevModPhys.85.1143.
C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, Active particles in complex and crowded environments, Rev. Mod. Phys. 88, 045006 (2016) RMPHAT 0034-6861 10.1103/RevModPhys.88.045006.
É. Fodor and M. C. Marchetti, The statistical physics of active matter: From self-catalytic colloids to living cells, Physica A 504, 106 (2018) PHYADX 0378-4371 10.1016/j.physa.2017.12.137.
X.-L. Wu and A. Libchaber, Particle Diffusion in a Quasi-Two-Dimensional Bacterial Bath, Phys. Rev. Lett. 84, 3017 (2000) PRLTAO 0031-9007 10.1103/PhysRevLett.84.3017.
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) RPPHAG 0034-4885 10.1088/0034-4885/78/5/056601.
A. Cavagna and I. Giardina, Bird flocks as condensed matter, Annu. Rev. Condens. Matter Phys. 5, 183 (2014) 1947-5454 10.1146/annurev-conmatphys-031113-133834.
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) PRLTAO 0031-9007 10.1103/PhysRevLett.110.238301.
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) SCIEAS 0036-8075 10.1126/science.1230020.
R. Zakine, A. Solon, T. Gingrich, and F. van Wijland, Stochastic Stirling engine operating in contact with active baths, Entropy 19, 193 (2017) ENTRFG 1099-4300 10.3390/e19050193.
D. Martin, C. Nardini, M. E. Cates, and É. Fodor, Extracting maximum power from active colloidal heat engines, Europhys. Lett. 121, 60005 (2018) EULEEJ 0295-5075 10.1209/0295-5075/121/60005.
P. Pietzonka, É. Fodor, C. Lohrmann, M. E. Cates, and U. Seifert, Autonomous Engines Driven by Active Matter: Energetics and Design Principles, Phys. Rev. X 9, 041032 (2019) 2160-3308 10.1103/PhysRevX.9.041032.
A. Saha and R. Marathe, Stochastic work extraction in a colloidal heat engine in the presence of colored noise, J. Stat. Mech. (2019) 094012 1742-5468 10.1088/1742-5468/ab39d4.
G. Szamel, Single active particle engine utilizing a nonreciprocal coupling between particle position and self-propulsion, Phys. Rev. E 102, 042605 (2020) 2470-0045 10.1103/PhysRevE.102.042605.
J. S. Lee, J.-M. Park, and H. Park, Brownian heat engine with active reservoirs, Phys. Rev. E 102, 032116 (2020) 2470-0045 10.1103/PhysRevE.102.032116.
V. Holubec, S. Steffenoni, G. Falasco, and K. Kroy, Active Brownian heat engines, Phys. Rev. Res. 2, 043262 (2020) 2643-1564 10.1103/PhysRevResearch.2.043262.
T. Ekeh, M. E. Cates, and É. Fodor, Thermodynamic cycles with active matter, Phys. Rev. E 102, 010101 (R) (2020) 2470-0045 10.1103/PhysRevE.102.010101.
G. Gronchi and A. Puglisi, Optimization of an active heat engine, Phys. Rev. E 103, 052134 (2021) 2470-0045 10.1103/PhysRevE.103.052134.
P. Malgaretti, P. Nowakowski, and H. Stark, Mechanical pressure and work cycle of confined active Brownian particles, Europhys. Lett. 134, 20002 (2021) EULEEJ 0295-5075 10.1209/0295-5075/134/20002.
É. Fodor and M. E. Cates, Active engines: Thermodynamics moves forward, Europhys. Lett. 134, 10003 (2021) EULEEJ 0295-5075 10.1209/0295-5075/134/10003.
G. Kokot, S. Das, R. G. Winkler, G. Gompper, I. S. Aranson, and A. Snezhko, Active turbulence in a gas of self-assembled spinners, Proc. Natl. Acad. Sci. USA 114, 12870 (2017) PNASA6 0027-8424 10.1073/pnas.1710188114.
V. Soni, E. S. Bililign, S. Magkiriadou, S. Sacanna, D. Bartolo, M. J. Shelley, and W. T. M. Irvine, The odd free surface flows of a colloidal chiral fluid, Nat. Phys. 15, 1188 (2019) 1745-2473 10.1038/s41567-019-0603-8.
Y. Chen, X. Li, C. Scheibner, V. Vitelli, and G. Huang, Realization of active metamaterials with odd micropolar elasticity, Nat. Commun. 12, 5935 (2021) 2041-1723 10.1038/s41467-021-26034-z.
J. E. Avron, R. Seiler, and P. G. Zograf, Viscosity of Quantum Hall Fluids, Phys. Rev. Lett. 75, 697 (1995) PRLTAO 0031-9007 10.1103/PhysRevLett.75.697.
D. Banerjee, A. Souslov, A. G. Abanov, and V. Vitelli, Odd viscosity in chiral active fluids, Nat. Commun. 8, 1573 (2017) 2041-1723 10.1038/s41467-017-01378-7.
N. H. P. Nguyen, D. Klotsa, M. Engel, and S. C. Glotzer, Emergent Collective Phenomena in a Mixture of Hard Shapes Through Active Rotation, Phys. Rev. Lett. 112, 075701 (2014) PRLTAO 0031-9007 10.1103/PhysRevLett.112.075701.
B. C. van Zuiden, J. Paulose, W. T. M. Irvine, D. Bartolo, and V. Vitelli, Spatiotemporal order and emergent edge currents in active spinner materials, Proc. Natl. Acad. Sci. USA 113, 12919 (2016) PNASA6 0027-8424 10.1073/pnas.1609572113.
C. Scheibner, A. Souslov, D. Banerjee, P. Surowka, W. T. M. Irvine, and V. Vitelli, Odd elasticity, Nat. Phys. 16, 475 (2020) 1745-2473 10.1038/s41567-020-0795-y.
M. Brandenbourger, C. Scheibner, J. Veenstra, V. Vitelli, and C. Coulais, Active impact and locomotion in robotic matter with nonlinear work cycles, arXiv:2108.08837.
T. G. Rogers and A. C. Pipkin, Asymmetric relaxation and compliance matrices in linear viscoelasticity, Z. Angew. Math. Phys. 14, 334 (1963) ZAMPA8 0044-2275 10.1007/BF01603090.
W. A. Day, Restrictions on relaxation functions in linear viscoelasticity, Quart. J. Mech. Appl. Math. 24, 487 (1971) QJMMAV 0033-5614 10.1093/qjmam/24.4.487.
M. Fabrizio and A. Morro, Thermodynamic restrictions on relaxation functions in linear viscoelasticity, Mech. Res. Commun. 12, 101 (1985) MRCOD2 0093-6413 10.1016/0093-6413(85)90077-1.
A. Parmeggiani, F. Jülicher, A. Ajdari, and J. Prost, Energy transduction of isothermal ratchets: Generic aspects and specific examples close to and far from equilibrium, Phys. Rev. E 60, 2127 (1999) 1063-651X 10.1103/PhysRevE.60.2127.
G. Lebon, C. Perez-Garcia, and J. Casas-Vazquez, On a new thermodynamic description of viscoelastic materials, Physica A 137, 531 (1986) PHYADX 0378-4371 10.1016/0378-4371(86)90093-2.
M. E. Gurtin and W. J. Hrusa, On the thermodynamics of viscoelastic materials of single-integral type, Quart. Appl. Math. 49, 67 (1991) QAMAAY 0033-569X 10.1090/qam/1096233.
M. Han, M. Fruchart, C. Scheibner, S. Vaikuntanathan, W. Irvine, J. de Pablo, and V. Vitelli, Fluctuating hydrodynamics of chiral active fluids, Nat. Phys. 17, 1260 (2021) 1745-2473 10.1038/s41567-021-01360-7.
D. Bi, J. H. Lopez, J. M. Schwarz, and M. L. Manning, A density-independent rigidity transition in biological tissues, Nat. Phys. 11, 1074 (2015) 1745-2473 10.1038/nphys3471.
D. Bi, X. Yang, M. C. Marchetti, and M. L. Manning, Motility-Driven Glass and Jamming Transitions in Biological Tissues, Phys. Rev. X 6, 021011 (2016) 2160-3308 10.1103/PhysRevX.6.021011.
D. Banerjee, V. Vitelli, F. Jülicher, and P. Surówka, Active Viscoelasticity of Odd Materials, Phys. Rev. Lett. 126, 138001 (2021) PRLTAO 0031-9007 10.1103/PhysRevLett.126.138001.
T. Schmiedl and U. Seifert, Efficiency at maximum power: An analytically solvable model for stochastic heat engines, Europhys. Lett. 81, 20003 (2008) EULEEJ 0295-5075 10.1209/0295-5075/81/20003.
M. Esposito, R. Kawai, K. Lindenberg, and C. Van den Broeck, Efficiency at Maximum Power of Low-Dissipation Carnot Engines, Phys. Rev. Lett. 105, 150603 (2010) PRLTAO 0031-9007 10.1103/PhysRevLett.105.150603.
S. Tong, N. K. Singh, R. Sknepnek, and A. Kosmrlj, Linear viscoelastic properties of the vertex model for epithelial tissues, arXiv:2102.11181.
B. Liebchen and D. Levis, Collective Behavior of Chiral Active Matter: Pattern Formation and Enhanced Flocking, Phys. Rev. Lett. 119, 058002 (2017) PRLTAO 0031-9007 10.1103/PhysRevLett.119.058002.
Performances of odd standard linear solids: Power (Equation presented), and efficiency (Equation presented).
B. D. Hoffman, G. Massiera, K. M. Van Citters, and J. C. Crocker, The consensus mechanics of cultured mammalian cells, Proc. Natl. Acad. Sci. USA 103, 10259 (2006) PNASA6 0027-8424 10.1073/pnas.0510348103.
M. Balland, N. Desprat, D. Icard, S. Féréol, A. Asnacios, J. Browaeys, S. Hénon, and F. Gallet, Power laws in microrheology experiments on living cells: Comparative analysis and modeling, Phys. Rev. E 74, 021911 (2006) PLEEE8 1539-3755 10.1103/PhysRevE.74.021911.
É. Fodor, W. W. Ahmed, M. Almonacid, M. Bussonnier, N. S. Gov, M.-H. Verlhac, T. Betz, P. Visco, and F. van Wijland, Nonequilibrium dissipation in living oocytes, Europhys. Lett. 116, 30008 (2016) EULEEJ 0295-5075 10.1209/0295-5075/116/30008.
W. W. Ahmed, É Fodor, M. Almonacid, M. Bussonnier, M.-H. Verlhac, N. Gov, P. Visco, F. van Wijland, and T. Betz, Active mechanics reveal molecular-scale force kinetics in living oocytes, Biophys. J. 114, 1667 (2018) BIOJAU 0006-3495 10.1016/j.bpj.2018.02.009.
Y. Basar and D. Weichert, Nonlinear Continuum Mechanics of Solids: Fundamental Mathematical and Physical Concepts (Springer, Berlin, 2013).
J. E. Soussou, F. Moavenzadeh, and M. H. Gradowczyk, Application of Prony series to linear viscoelasticity, Trans. Soc. Rheol. 14, 573 (1970) TSRHAZ 0038-0032 10.1122/1.549179.
Performances of odd power-law solids: power (Equation presented), and efficiency (Equation presented).
