Thermodynamics and statistical mechanics of chemically powered synthetic nanomotors

References

• Kay ER, Leigh DA, Zerbetto F. Synthetic molecular motors and mechanical machines. Angew. Chem. Int. Ed. 2007;46:72–191.
   Google Scholar
• Sauvage JP, Gaspard P, editors. From non-covalent assemblies to molecular machines. Weinheim: Wiley-VCH; 2011.
   Google Scholar
• van Leeuwen PWNM. Homogeneous catalysis. Dordrecht: Kluwer Academic Publishers.; 2004.
   Google Scholar
• Dey KK, Pong FY, Breffke J, et al. Dynamic coupling at the Ångstrom scale. Angew Chem Int Ed. 2016;55:361–397.
   Web of Science ®Google Scholar
• Alberts B, Bray D, Johnson A, et al. Essential cell biology: an introduction to the molecular biology of the cell. New York: Garland Science; 1998.
   Google Scholar
• Jones RAL. Soft machines: nanotechnology and life. Oxford: Oxford University Press; 2004.
   Google Scholar
• Wang J. Nanomachines: fundamentals and applications. Weinheim, Germany: Wiley-VCH; 2013.
   Google Scholar
• Mareschal M, Malek Mansour M, Puhl A, et al. Molecular dynamics versus hydrodynamics in a two-dimensional Rayleigh-Bénard system. Phys Rev Lett. 1988;61:2550–2553.
   PubMed Web of Science ®Google Scholar
• Paxton WF, Kistler KC, Olmeda CC, et al. Catalytic motors: autonomous movement of striped nanorods. J Am Chem Soc. 2004;126:13424–13431.
   PubMed Web of Science ®Google Scholar
• Fournier-Bidoz S, Arsenault AC, Manners I, et al. Synthetic self-propelled nanorotors. Chem Commun. 2005;441–443.
   PubMed Web of Science ®Google Scholar
• Wang W, Duan W, Ahmed S, et al. Small power: autonomous nano- and micromotors propelled by self-generated gradients. Nano Today. 2013;8:531–554.
   Web of Science ®Google Scholar
• Sánchez S, Soler L, Katuri J. Chemically powered micro- and motors. Angew Chem Int Ed. 2014;54:1414–1444.
   PubMed Web of Science ®Google Scholar
• Colberg PH, Reigh SY, Robertson B, et al. Chemistry in motion: tiny synthetic motors. Acc Chem Res. 2014;47:3504–3511.
   PubMed Web of Science ®Google Scholar
• Abdelmohsen L, Peng F, Tu Y, et al. Micro- and nano-motors for biomedical applications. J Mater Chem B. 2014;2:2395.
   PubMed Web of Science ®Google Scholar
• Rückner G, Kapral R. Chemically powered nanodimers. Phys Rev Lett. 2007;98:150603.
   PubMed Web of Science ®Google Scholar
• Sumino Y, Magome N, Hamada T, et al. Self-running droplet: emergence of regular motion from nonequilibrium noise. Phys Rev Lett. 2005;94:068301.
   PubMed Web of Science ®Google Scholar
• Chen YJ, Nagamine Y, Yoshikawa K. Self-propelled motion of a droplet induced by Marangoni-driven spreading. Phys Rev E. 2009;80:016303.
   Web of Science ®Google Scholar
• Thutupalli S, Seemann R, Herminghaus S. Swarming behavior of simple model squirmers. New J Phys. 2011;13:073021.
   Web of Science ®Google Scholar
• Izri Z, van der Linden MN, Michelin S, et al. Self-propulsion of pure water droplets by spontaneous Marangoni-stress-driven motion. Phys Rev Lett. 2014;113:248302.
   PubMed Web of Science ®Google Scholar
• Landau LD, Lifshitz EM. Statistical physics, part 2. Oxford: Pergamon Press; 1980.
   Google Scholar
• Ortiz de Zárate JM, Sengers JV. Hydrodynamic fluctuations in fluids and fluid mixtures. Amsterdam: Elsevier; 2006.
   Google Scholar
• Kapral R. Perspective: motors without moving parts that propel themselves in solution. J Chem Phys. 2013;138:020901.
   PubMed Web of Science ®Google Scholar
• Valadares LF, Tao YG, Zacharia NS, et al. Catalytic motors: self-propelled sphere dimers. Small. 2010;6:565–572.
   PubMed Web of Science ®Google Scholar
• Ke H, Ye S, Carroll RL, et al. Motion analysis of self-propelled Pt-silica particles in hydrogen peroxide solutions. J Phys Chem A. 2010;114:5462–5467.
   PubMed Web of Science ®Google Scholar
• Gao W, Pei A, Dong R, et al. Catalytic iridium-based Janus micromotors powered by ultralow levels of chemical fuels. J Am Chem Soc. 2014;136:2276–2279.
   PubMed Web of Science ®Google Scholar
• Mazur P, Bedeaux D. A generalization of Faxén’s theorem to nonsteady motion of a sphere through an incompressible fluid in arbitrary flow. Phys A. 1974;76:235–246.
   Google Scholar
• Bedeaux D, Mazur P. Brownian motion and fluctuating hydrodynamics. Phys A. 1974;76:247–258.
   Google Scholar
• Hills BP. A generalized Langevin equation for the angular velocity of a spherical Brownian particle from fluctuating hydrodynamics. Phys A. 1975;80:360–368.
   Google Scholar
• Felderhof BU. Force density induced on a sphere in linear hydrodynamics: I. Fixed sphere, stick boundary conditions. Phys A. 1976;84:557–568.
   Web of Science ®Google Scholar
• Felderhof BU. Force density induced on a sphere in linear hydrodynamics: II. Moving sphere, mixed boundary conditions. Phys. A 1976;84:569–576.
   Google Scholar
• Bedeaux D, Albano AM, Mazur P. Brownian motion and fluctuating hydrodynamics II; A fluctuation-dissipation theorem for the slip coefficient. Phys A. 1977;88:574–582.
   Google Scholar
• Bechinger C, Leonardo RD, Löwen H, et al. Active particles in complex and crowded environments. Rev Mod Phys. 2016;88:045006.
   Web of Science ®Google Scholar
• Campbell AI, Ebbens SJ. Gravitaxis in spherical Janus swimming devices. Langmuir. 2013;295:14066–14073.
   Google Scholar
• Prigogine I. Introduction to thermodynamics of irreversible processes. New York: Wiley; 1967.
   Google Scholar
• de Groot SR, Mazur P. Nonequilibrium thermodynamics. New York: Dover; 1984.
   Google Scholar
• Nicolis G. Irreversible thermodynamics. Rep Prog Phys. 1979;42:225–268.
   Web of Science ®Google Scholar
• Landau LD, Lifshitz EM. Statistical physics, part 1. 3rd ed. Oxford: Pergamon Press; 1980.
   Google Scholar
• Gardiner CW. Handbook of stochastic methods for physics, chemistry and the natural sciences. 3rd ed. Berlin: Springer; 2004.
   Google Scholar
• Onsager L. Reciprocal relations in irreversible processes I. Phys Rev. 1931;37:405–426.
   Google Scholar
• Onsager L. Reciprocal relations in irreversible processes II. Phys Rev. 1931;38:2265–2279.
   Google Scholar
• Casimir HBG. On Onsager’s principle of microscopic reversibility. Rev Mod Phys. 1945;17:343–350.
   Web of Science ®Google Scholar
• Waldmann L. Non-equilibrium thermodynamics of boundary conditions. Z Naturforschg A. 1967;22:1269–1280.
   PubMedGoogle Scholar
• Bedeaux D, Albano AM, Mazur P. Boundary conditions and non-equilibrium thermodynamics. Phys A. 1976;82:438–462.
   Web of Science ®Google Scholar
• Haase R. Thermodynamics of irreversible processes. New York: Dover; 1969.
   Google Scholar
• Callen HB, Welton TA. Irreversibility and generalized noise. Phys Rev. 1951;83:34–40.
   Web of Science ®Google Scholar
• Kovac J. Non-equilibrium thermodynamics of interfacial systems. Phys A. 1977;86:1–24.
   Web of Science ®Google Scholar
• Bedeaux D. Nonequilibrium thermodynamics and statistical physics of surfaces. Adv Chem Phys. 1986;64:47–109.
   Google Scholar
• Albano AM, Bedeaux D, Mazur P. On the motion of a sphere with arbitrary slip in a viscous incompressible fluid. Phys A. 1975;80:89–97.
   Web of Science ®Google Scholar
• Gaspard P, Kapral R. Nonequilibrium thermodynamics and boundary conditions for reaction and transport in heterogeneous media. J Chem Phys. 2018;148:194114.
   PubMed Web of Science ®Google Scholar
• Anderson JL. Colloid transport by interfacial forces. Ann Rev Fluid Mech. 1989;21:61–99.
   Web of Science ®Google Scholar
• Anderson JL, Prieve DC. Diffusiphoresis caused by gradients of strongly absorbing solutes. Langmuir. 1991;7:403–406.
   Google Scholar
• Ajdari A, Bocquet L. Giant amplification of interfacially driven transport by hydrodynamic slip: diffusio-osmosis and beyond. Phys Rev Lett. 2006;96:186102.
   PubMed Web of Science ®Google Scholar
• Gaspard P, Kapral R. Fluctuating chemohydrodynamics and the stochastic motion of self-diffusiophoretic particles. J Chem Phys. 2018;148:134104.
   PubMed Web of Science ®Google Scholar
• Lighthill MJ. On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers. Commun Pure Appl Math. 1952;5:109–118.
   Web of Science ®Google Scholar
• Blake JR. A spherical envelope approach to ciliary propulsion. J Fluid Mech. 1971;46:199–208.
   Web of Science ®Google Scholar
• Reigh SY, Huang MJ, Schofield J, et al. Microscopic and continuum descriptions of Janus motor fluid flow fields. Phil Trans R Soc A. 2016;374:20160140.
   Google Scholar
• Campbell AI, Ebbens SJ, Illien P, et al. Experimental observation of flow fields around Janus spheres. arXiv:1802.04600. 2018.
   Google Scholar
• Anderson JL. Transport mechanisms of biological colloids. Ann N Y Acad Sci. 1986;469:166–177.
   PubMed Web of Science ®Google Scholar
• Jülicher F, Ajdari A, Prost J. Modeling molecular motors. Rev Mod Phys. 1997;69:1269.
   Web of Science ®Google Scholar
• Huang MJ, Schofield J, Gaspard P, et al. From single particle motion to collective dynamics in Janus motor systems. J Chem Phys. 2019;150:124110.
   PubMed Web of Science ®Google Scholar
• Gaspard P, Kapral R. Mechanochemical fluctuation theorem and thermodynamics of self-phoretic motors. J Chem Phys. 2017;147:211101.
   PubMed Web of Science ®Google Scholar
• Huang MJ, Schofield J, Gaspard P, et al. Dynamics of Janus motors with microscopically reversible kinetics. J Chem Phys. 2018;149:024904.
   PubMed Web of Science ®Google Scholar
• Malevanets A, Kapral R. Mesoscopic model for solvent dynamics. J Chem Phys. 1999;110:8605–8613.
   Web of Science ®Google Scholar
• Kapral R. Multiparticle collision dynamics: simulation of complex systems on mesoscales. Adv Chem Phys. 2008;140:89–146.
   Web of Science ®Google Scholar
• Gompper G, Ihle T, Kroll DM, et al. Multi-particle collision dynamics: a particle- based mesoscale simulation approach to the hydrodynamics of complex fluids. Adv Polym Sci. 2009;221:1–87.
   Web of Science ®Google Scholar
• Tao YG, Kapral R. Dynamics of chemically powered nanodimer motors subject to an external force. J Chem Phys. 2009;131:024113.
   PubMed Web of Science ®Google Scholar
• Sabass B, Seifert U. Dynamics and efficiency of a self-propelled, diffusiophoretic swimmer. J Chem Phys. 2012;136:064508.
   PubMed Web of Science ®Google Scholar
• Farage TFF, Krinninger P, Brader JM. Effective interactions in active Brownian suspensions. Phys Rev E. 2015;91:042310.
   Web of Science ®Google Scholar
• Marconi UMB, Gnan N, Paoluzzi M, et al. Velocity distribution in active particles systems. Sci Rep. 2016;6:23297.
   PubMed Web of Science ®Google Scholar
• Wittmann R, Maggi C, Sharma A, et al. Effective equilibrium states in the colored-noise model for active matter I. Pairwise forces in the Fox and unified colored noise approximations. J Stat Mech Exp. 2017;11:113207.
   Google Scholar
• Lebowitz JL, Spohn H. A Gallavotti-Cohen-type symmetry in the large deviation functional for stochastic dynamics. J Stat Phys. 1999;95:333–365.
   Web of Science ®Google Scholar
• Andrieux D, Gaspard P. A fluctuation theorem for currents and non-linear response coefficients. J Stat Mech Theory Exp. 2007;2007:P02006.
   Google Scholar
• Andrieux D, Gaspard P. Fluctuation theorem and Onsager reciprocity relations. J Chem Phys. 2004;121:6167–6174.
   PubMed Web of Science ®Google Scholar
• Jarzynski C. Equalities and inequalities: irreversibility and the second law of thermodynamics at the nanoscale. Annu Rev Condens Matter Phys. 2011;2:329–351.
   Web of Science ®Google Scholar
• Seifert U. Stochastic thermodynamics, fluctuation theorems and molecular machines. Rep Prog Phys. 2012;75:126001.
   PubMed Web of Science ®Google Scholar
• Gaspard P. Multivariate fluctuation relations for currents. New J Phys. 2013;15:115014.
   Web of Science ®Google Scholar
• Falasco G, Pfaller R, Bregulla AP, et al. Exact symmetries in the velocity fluctuations of a hot Brownian swimmer. Phys Rev E. 2016;94:030602(R).
   Web of Science ®Google Scholar
• Andrieux D, Gaspard P. Temporal disorder and fluctuation theorem in chemical reactions. Phys Rev E. 2008;77:031137.
   Web of Science ®Google Scholar
• Gaspard P, Kapral R. Finite-time fluctuation theorem for diffusion-infuenced surface reactions. J Stat Mech Exp. 2018;2018:083206.
   Google Scholar
• Gaspard P, Grosfils P, Huang MJ, et al. Finite-time fluctuation theorem for diffusion-influenced surface reactions on spherical and Janus catalytic particles. J Stat Mech Exp. 2018;2018:123206.
   Google Scholar
• Hill TL. Free energy transduction and biochemical cycle kinetics. New York: Dover; 2005.
   Google Scholar
• Lacoste D, Lau AWC, Mallick K. Fluctuation theorem and large deviation function for a solvable model of a molecular motors. Phys Rev E. 2008;78:011915.
   Web of Science ®Google Scholar
• Astumian RD. Thermodynamics and kinetics of molecular motors. Biophys J. 2010;98:2401–2409.
   PubMed Web of Science ®Google Scholar
• Gerritsma E, Gaspard P. Chemomechanical coupling and stochastic thermodynamics of the F1-ATPase molecular motor with an applied external torque. Biophys Rev Lett. 2010;5:163–208.
   Google Scholar
• Andrieux D, Gaspard P. Fluctuation theorems and the nonequilibrium thermodynamics of molecular motors. Phys Rev E. 2006;74:011906.
   Web of Science ®Google Scholar
• Zwanzig R. Diffusion past an entropy barrier. J Phys Chem. 1992;96:3926–3930.
   Web of Science ®Google Scholar
• Reguera D, Rubí JM. Kinetic equations for diffusion in the presence of entropic barriers. Phys Rev E. 2001;64:061106.
   Web of Science ®Google Scholar
• Rubí JM, Lervik A, Bedeaux D, et al. Entropy facilitated active transport. J Chem Phys. 2017;146:185101.
   Web of Science ®Google Scholar
• Theurkauff I, Cottin-Bizonne C, Palacci J, et al. Dynamic clustering in active colloidal suspensions with chemical signaling. Phys Rev Lett. 2012;108:268303.
   PubMed Web of Science ®Google Scholar
• Elgeti J, Winkler RG, Gompper G. Physics of microswimmers–single particle motion and collective behavior: a review. Rep Prog Phys. 2015;78:056601.
   PubMed Web of Science ®Google Scholar
• Wang W, Duan W, Ahmed S, et al. From one to many: dynamic assembly and collective behavior of self-propelled colloidal motors. Acc Chem Res. 2015;48:1938–1946.
   PubMed Web of Science ®Google Scholar
• Zöttl A, Stark H. Emergent behavior in active colloids. J Phys Condens Matter. 2016;28:253001.
   Web of Science ®Google Scholar
• Liebchen B, Marenduzzo D, Pagonabarraga I, et al. Clustering and pattern formation in chemorepulsive active colloids. Phys Rev Lett. 2015;115:258301.
   PubMed Web of Science ®Google Scholar
• Jones RAL. Soft condensed matter. Oxford UK: Oxford University Press; 2002.
   Google Scholar
• Huang MJ, Schofield J, Kapral R. Chemotactic and hydrodynamic effects on collective dynamics of self-diffusiophoretic Janus motors. New J Phys. 2017;19:125003.
   Web of Science ®Google Scholar
• Cates ME, Tailleur J. When are active Brownian particles and run-and-tumble particles equivalent? consequences for motility-induced phase separation. EPL. 2013;101:20010.
   Web of Science ®Google Scholar
• Bialké J, Löwen H, Speck T. Microscopic theory for the phase separation of self-propelled repulsive disks. EPL. 2013;103:30008.
   Web of Science ®Google Scholar
• Speck T, Menzel AM, Bialké J, et al. Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles. J Chem Phys. 2015;142:224109.
   PubMed Web of Science ®Google Scholar
• Saha S, Golestanian R, Ramaswamy S. Clusters, asters, and collective oscillations in chemotactic colloids. Phys Rev E. 2014;89:062316.
   Web of Science ®Google Scholar
• Pohl O, Stark H. Self-phoretic active particles interacting by diffusiophoresis: a numerical study of the collapsed state and dynamic clustering. Eur Phys J E. 2015;38:93.
   PubMed Web of Science ®Google Scholar
• Bedeaux D, Kapral R, Mazur P. The effective shear viscosity of a uniform suspension of spheres. Phys A. 1977;88:88–121.
   Web of Science ®Google Scholar
• Einstein A. Investigations on the theory of the Brownian movement. New York: Dover; 1956.
   Google Scholar
• Landau LD, Lifshitz EM. Fluid mechanics. 2nd ed. Oxford: Pergamon Press; 1987.
   Google Scholar
• Lebenhaft JR, Kapral R. Diffusion-controlled processes among partially absorbing stationary sinks. J Stat Phys. 1979;20:25–56.
   Web of Science ®Google Scholar
• Happel J, Brenner H. Low Reynolds number hydrodynamics. The Hague: Martinus Nijhoff Publishers; 1983.
   Google Scholar
• Dhont JKG. An introduction to dynamics of colloids. Amsterdam: Elsevier; 1996.
   Google Scholar
• Nägele G. Colloidal hydrodynamics. In: Bechinger C, Sciortino F, Ziherl P, editors. Physics of complex colloids, proc. of the int. school of physics “Enrico Fermi”. Amsterdam: IOS Press; 2013. p. 507–601.
   Google Scholar
• Ramaswamy S. The mechanics and statistics of active matter. Annu Rev Condens Matter Phys. 2010;1:323–345.
   Web of Science ®Google Scholar
• Thakur S, Kapral R. Collective dynamics of self-propelled sphere-dimer motors. Phys Rev E. 2012;85:026121.
   Web of Science ®Google Scholar
• Colberg P, Kapral R. Many-body dynamics of chemically-propelled motors. J Chem Phys. 2017;147:064910.
   PubMed Web of Science ®Google Scholar
• Robertson B, Huang MJ, Chen JX, et al. Synthetic motors: working together through chemistry. Acc Chem Res. 2018;51:2355–2364.
   PubMed Web of Science ®Google Scholar
• Li T, Raizen MG. Brownian motion at short time scales. Ann Phys. 2013;525:281–295.
   Google Scholar
• Li W, Davis EJ. The effects of gas and particle properties on thermophoresis. J Aerosol Sci. 1995;26:1085–1099.
   Web of Science ®Google Scholar