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Research Article | Open Access

Quantum "contact" friction: The contribution of kinetic friction coefficient from thermal fluctuations

Skolkovo Institute of Science and Technology, Moscow 121205, Russia
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Abstract

A thermal model of kinetic friction is assigned to a classical loaded particle moving on a fluctuating smooth surface. A sinusoidal wave resembles surface fluctuations with a relaxation time. The Hamiltonian is approximated to the mean energy of the wave describing a system of Harmonic oscillators. The quantization of amplitudes yields in terms of annihilation and creation operators multiplied by a quantum phase. Further, we consider acoustic dispersion relation and evaluate the friction coefficient from the force autocorrelation function. While the sliding particle remains classical describing a nano-particle or a tip with negligible quantum effects like tunneling or delocalization in the wave function, the quantized model of the surface fluctuations results in the temperature dependence of the kinetic friction coefficient. It follows an asymptotic value for higher temperatures and supper-slipperiness at low temperatures.

Keywords

phononthermal modelkinetic friction coefficientfluctuation-dissipationquantum friction

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References

[1]
Car R, Parrinello M. Unified approach for molecular dynamics and density-functional theory. Phys Rev Lett 55(22): 2471–2474 (1985)
Crossref Google Scholar
[2]
Tambe N S, Bhushan B. Friction model for the velocity dependence of nanoscale friction. Nanotechnology 16(10): 2309–2324 (2005)
Crossref Google Scholar
[3]
Wu B, Niu Q. Nonlinear landau-zener tunneling. Phys Rev A 61(2): 023402 (2000)
Crossref Google Scholar
[4]
Zenesini A, Lignier H, Tayebirad G, Radogostowicz J, Ciampini D, Mannella R, Wimberger S, Morsch O, Arimondo E. Time-resolved measurement of Landau-Zener tunneling in periodic potentials. Phys Rev Lett 103(9): 090402 (2009)
Crossref Google Scholar
[5]
Zanca T, Pellegrini F, Santoro GE, Tosatti E. Frictional lubricity enhanced by quantum mechanics. Proc Natl Acad Sci USA 115(14): 3547–3550 (2018)
Crossref Google Scholar
[6]
Krim J, Solina D H, Chiarello R. Nanotribology of a Kr monolayer: A quartz-crystal microbalance study of atomic-scale friction. Phys Rev Lett 66(2): 181–184 (1991)
Crossref Google Scholar
[7]
Robbins M O, Krim J. Energy dissipation in interfacial friction. MRS Bull23(6): 23–26 (1998)
Crossref Google Scholar
[8]
Smith ED, Robbins MO, Cieplak M. Friction on adsorbed monolayers. Phys Rev B Condens Matter 54(11): 8252–8260 (1996)
Crossref Google Scholar
[9]
Matsukawa H, Fukuyama H. Theoretical study of friction: One-dimensional clean surfaces. Phys Rev B Condens Matter 49(24): 17286–17292 (1994)
Crossref Google Scholar
[10]
Hirano M, Shinjo K, Kaneko R, Murata Y. Observation of superlubricity by scanning tunneling microscopy. Phys Rev Lett 78(8): 1448–1451 (1997)
Crossref Google Scholar
[11]
Popov V L. Superslipperiness at low temperatures: Quantum mechanical aspects of solid state friction. Phys Rev Lett 83(8): 1632–1635 (1999)
Crossref Google Scholar
[12]
Lifshitz E M, Pitaevskii L P. Statistical Physics: Theory of the Condensed State Vol. 9. Elsevier, 2013.
[13]
Dayo A, Alnasrallah W, Krim J. Superconductivity-dependent sliding friction. Phys Rev Lett 80(8): 1690–1693 (1998)
Crossref Google Scholar
[14]
Renner R L, Rutledge J E, Taborek P. Quartz microbalance studies of superconductivity-dependent sliding friction. Phys Rev Lett 83(6): 1261 (1999)
Crossref Google Scholar
[15]
Krim J. Krim replies. Phys Rev Lett 83(6): 1262 (1999)
Crossref Google Scholar
[16]
Novotný T, Velický B. Electronic sliding friction of atoms physisorbed at superconductor surface. Phys Rev Lett 83(20): 4112–4115 (1999)
Crossref Google Scholar
[17]
Sokoloff J B, Tomassone M S, Widom A. Strongly temperature dependent sliding friction for a superconducting interface. Phys Rev Lett 84(3): 515–517 (2000)
Crossref Google Scholar
[18]
Persson B N J. Electronic friction on a superconductor surface. Solid State Commun 115(3): 145–148 (2000)
Crossref Google Scholar
[19]
Fois G, Bruschi L, D’Apolito L, Mistura G, Torre B, Buatier de Mongeot F, Boragno C, Buzio R, Valbusa U. Low-temperature static friction of N2monolayers on Pb(111). J Phys: Condens Matter 19(30): 305013 (2007)
Crossref Google Scholar
[20]
Kisiel M, Gnecco E, Gysin U, Marot L, Rast S, Meyer E. Suppression of electronic friction on Nb films in the superconducting state. Nature Mater 10(2): 119–122 (2011)
Crossref Google Scholar
[21]
Pendry J B. Shearing the vacuum - quantum friction. J Phys: Condens Matter 9(47): 10301–10320 (1997)
Crossref Google Scholar
[22]
Volokitin A I, Persson B J. Theory of friction: The contribution from a fluctuating electromagnetic field. J Phys: Condens Matter 11(2): 345–359 (1999)
Crossref Google Scholar
[23]
Volokitin A I, Persson B N J. Near-field radiative heat transfer and noncontact friction. Rev Mod Phys 79(4): 1291–1329 (2007)
Crossref Google Scholar
[24]
Volokitin A I, Persson B N J. Theory of the interaction forces and the radiative heat transfer between moving bodies. Phys Rev B 78(15): 155437 (2008)
Crossref Google Scholar
[25]
Volokitin A I, Persson B N. Quantum friction. Phys Rev Lett 106(9): 094502 (2011)
Crossref Google Scholar
[26]
Silveirinha M G. Theory of quantum friction. New J Phys 16(6): 063011 (2014)
Crossref Google Scholar
[27]
Klatt J, Farías M B, Dalvit D A R, Buhmann S Y. Quantum friction in arbitrarily directed motion. Phys Rev A 95(5): 052510 (2017)
Crossref Google Scholar
[28]
Belén Farías M, Fosco C D, Lombardo F C, Mazzitelli F D, Rubio López A E. Functional approach to quantum friction: Effective action and dissipative force. Phys Rev D 91(10): 105020 (2015)
Crossref Google Scholar
[29]
Farias M B, Fosco C D, Lombardo F C, Mazzitelli F D. Quantum friction between graphene sheets. Phys Rev D 95(6): 065012 (2017)
Crossref Google Scholar
[30]
Farias M B, Kort-Kamp W J M, Dalvit D A R. Quantum friction in two-dimensional topological materials. Phys Rev B 97(16): 161407 (2018)
Crossref Google Scholar
[31]
Viotti L, Belén Farías M, Villar P I, Lombardo F C. Thermal corrections to quantum friction and decoherence: A closed-time-path approach to atom-surface interaction. Phys Rev D 99(10): 105005 (2019)
Crossref Google Scholar
[32]
Farías M B, Fosco C, Lombardo F C, Mazzitelli F D. Motion induced radiation and quantum friction for a moving atom. Phys Rev D 100(3): 036013 (2019)
Crossref Google Scholar
[33]
Farías M B, Lombardo F C, Soba A, Villar P I, Decca R S. Towards detecting traces of non-contact quantum friction in the corrections of the accumulated geometric phase. Npj Quantum Inf 6: 25 (2020)
Crossref Google Scholar
[34]
Gysin U, Rast S, Kisiel M, Werle C, Meyer E. Low temperature ultrahigh vacuum noncontact atomic force microscope in the pendulum geometry. Rev Sci Instrum 82(2): 023705 (2011)
Crossref Google Scholar
[35]
Kisiel M, Samadashvili M, Gysin U, Meyer E. Non-contact friction. In Noncontact Atomic Force Microscopy Volume 3. Springer, 2015: 93–110.
Crossref
[36]
Krylov S Y, Dijksman J A, van Loo W A, Frenken J W. Stick-slip motion in spite of a slippery contact: Do we get what we see in atomic friction? Phys Rev Lett 97(16): 166103 (2006)
Crossref Google Scholar
[37]
Krylov S Y, Frenken J W M. Thermal contact delocalization in atomic scale friction: A multitude of friction regimes. New J Phys 9(10): 398 (2007)
Crossref Google Scholar
[38]
Rabinowicz E. Friction and Wear of Materials 2nd ed. John Wiley & Sons, inc., 1995.
[39]
Berman A, Drummond C, Israelachvili J. Amontons' law at the molecular level. Tribol Lett 4(2): 95–101 (1998)
Crossref Google Scholar
[40]
Krim J. Friction and energy dissipation mechanisms in adsorbed molecules and molecularly thin films. Adv Phys 61(3): 155–323 (2012)
Crossref Google Scholar
[41]
Krim J. Resource letter: FMMLS-1: Friction at macroscopic and microscopic length scales. Am J Phys 70(9): 890–897 (2002)
Crossref Google Scholar
[42]
Prandtl, L. A conceptual model to the kinetic theory of solid bodies. Z Angew Math Mech 8: 85–106 (1928) (In German).
Crossref Google Scholar
[43]
Popov V L, Gray J A T. Prandtl-tomlinson model: History and applications in friction, plasticity, and nanotechnologies. Z Angew Math Mech 92(9): 683–708 (2012)
Crossref Google Scholar
[44]
Tabor D. Friction as a dissipative process. In Fundamentals of Friction: Macroscopic and Microscopic Processes. Dordrecht: Springer Netherlands, 1992: 3–24.
Crossref
[45]
Tomlinson G A. CVI.A molecular theory of friction. Lond Edinb Dublin Philos Mag J Sci 7(46): 905–939 (1929)
Crossref Google Scholar
[46]
Brilliantov N V, Budkov Y A, Seidel C. Theoretical and numerical analysis of nano-actuators based on grafted polyelectrolytes in an electric field. Faraday Discuss 199: 487–510 (2017)
Crossref Google Scholar
[47]
Brilliantov N V, Budkov Y A, Seidel C. Generation of mechanical force by grafted polyelectrolytes in an electric field: Application to polyelectrolyte-based nano-devices. Philos Trans Royal Soc A Math Phys Eng Sci 374(2080): 20160143 (2016)
Crossref Google Scholar
[48]
Johnson K L, Kendall K, Roberts A. Surface energy and the contact of elastic solids. Proc Royal Soc London A Math Phys Sci 324(1558): 301–313 (1971)
Crossref Google Scholar
[49]
Popov V L. A note by K. L. Johnson on the history of the JKR theory. Tribol Lett 69(4): 1–3 (2021)
Crossref Google Scholar
[50]
Derjaguin B V, Muller V M, Toporov Y P. Effect of contact deformations on the adhesion of particles. J Colloid Interface Sci 53(2): 314–326 (1975)
Crossref Google Scholar
[51]
Maugis D. Adhesion of spheres: The JKR-DMT transition using a dugdale model. J Colloid Interface Sci 150(1): 243–269 (1992)
Crossref Google Scholar
[52]
Lee C G, Wei X D, Kysar J W, Hone J. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321(5887): 385–388 (2008)
Crossref Google Scholar
[53]
Lee J U, Yoon D, Cheong H. Estimation of young’s modulus of graphene by Raman spectroscopy. Nano Lett 12(9): 4444–4448 (2012)
Crossref Google Scholar
[54]
Clark N, Oikonomou A, Vijayaraghavan A. Ultrafast quantitative nanomechanical mapping of suspended graphene. Phys Status Solidi B 250(12): 2672–2677 (2013)
Crossref Google Scholar
[55]
Zhang G P, Wei Z X, Ferrell R E. Elastic modulus and hardness of muscovite and rectorite determined by nanoindentation. Appl Clay Sci 43(2): 271–281 (2009)
Crossref Google Scholar
[56]
Young T J, Monclus M A, Burnett T L, Broughton W R, Ogin S L, Smith P A. The use of the PeakForceTM quantitative nanomechanical mapping AFM-based method for high-resolution Young’s modulus measurement of polymers. Meas Sci Technol 22(12): 125703 (2011)
Crossref Google Scholar
[57]
Landau L D, Lifshitz E M. Course of Theoretical Physics Vol 7: Theory and Elasticity. Pergamon press, 1959.
[58]
Puttock M J, Thwaite E G. Elastic Compression of Spheres and Cylinders at Point and Line Contact. Melbourne: Commonwealth Scientific and Industrial Research Organization, 1969.
[59]
Lee C G, Li Q Y, Kalb W, Liu X Z, Berger H, Carpick R W, Hone J. Frictional characteristics of atomically thin sheets. Science 328(5974): 76–80 (2010)
Crossref Google Scholar
[60]
Li Q Y, Lee C G, Carpick R W, Hone J. Substrate effect on thickness-dependent friction on graphene. Phys Stat Sol (b) 247(11–12): 2909–2914 (2010)
Crossref Google Scholar
[61]
Filleter T, McChesney J L, Bostwick A, Rotenberg E, Emtsev K V, Seyller T, Horn K, Bennewitz R. Friction and dissipation in epitaxial graphene films. Phys Rev Lett 102(8): 086102 (2009)
Crossref Google Scholar
[62]
Filleter T, Bennewitz R. Structural and frictional properties of graphene films on SiC(0001) studied by atomic force microscopy. Phys Rev B 81(15): 155412 (2010)
Crossref Google Scholar
[63]
Smolyanitsky A, Killgore J P, Tewary V K. Effect of elastic deformation on frictional properties of few-layer graphene. Phys Rev B 85(3): 035412 (2012)
Crossref Google Scholar
[64]
Dong Y L. Effects of substrate roughness and electron–phonon coupling on thickness-dependent friction of graphene. J Phys D: Appl Phys 47(5): 055305 (2014)
Crossref Google Scholar
[65]
Mori H. Transport, collective motion, and Brownian motion. Prog Theor Phys 33(3): 423–455 (1965)
Crossref Google Scholar
[66]
Vanossi A, Manini N, Urbakh M, Zapperi S, Tosatti E. Colloquium: Modeling friction: From nanoscale to mesoscale. Rev Mod Phys 85(2): 529–552 (2013)
Crossref Google Scholar
[67]
Schwartz M. Lecture 10: Energy and power in waves. Information on https://scholar.harvard.edu/files/schwartz/files/lecture10-power.pdf.
[68]
Schneider T, Stoll E. Molecular-dynamics study of a three-dimensional one-component model for distortive phase transitions. Phys Rev B 17(3): 1302–1322 (1978)
Crossref Google Scholar
[69]
Intravaia F, Behunin R, Henkel C, Busch K, Dalvit D. Failure of local thermal equilibrium in quantum friction. Phys Rev Lett 117(10): 100402 (2016)
Crossref Google Scholar
[70]
Ashcroft N W, Mermin N D. Solid State Physics. New York: Holt, Rinehart and Winston, 1976.
[71]
Morita S, Giessibl F J, Meyer E, Wiesendanger R. Noncontact Atomic Force Microscopy Volume 3. Springer, 2015
Crossref
[72]
Pitaevskii L, Lifshitz E. Physical Kinetics: Volume 10. Butterworth-Heinemann, 2012.
[73]
Lynch R. The quantum phase problem: A critical review. Phys Rep 256(6): 367–436 (1995)
Crossref Google Scholar
[74]
Hong C K, Mandel L. Generation of higher-order squeezing of quantum electromagnetic fields. Phys Rev A Gen Phys 32(2): 974–982 (1985)
Crossref Google Scholar
[75]
Feynman R P. Statistical Mechanics: A Set of Lectures. Chapman and Hall/CRC, 2018.
Crossref
[76]
Davydov A S. Quantum Mechanics, Vol. 1. Pergamon Press, 1965.
Crossref
[77]
Brilliantov N V, Pöschel T. Rolling friction of a viscous sphere on a hard plane. Europhys Lett 42(5): 511–516 (1998)
Crossref Google Scholar
[78]
Brilliantov NV, Albers N, Spahn F, Pöschel T. Collision dynamics of granular particles with adhesion. Phys Rev E Stat Nonlin Soft Matter Phys 76(5): 051302 (2007)
Crossref Google Scholar
[79]
Manini N, Braun OM, Tosatti E, Guerra R, Vanossi A. Friction and nonlinear dynamics. J Phys Condens Matter 28(29): 293001 (2016)
Crossref Google Scholar
[80]
Leggett A J, Chakravarty S, Dorsey A T, Fisher M P A, Garg A, Zwerger W. Dynamics of the dissipative two-state system. Rev Mod Phys 59(1): 1–85 (1987)
Crossref Google Scholar
[81]
Gorokhov D A, Fisher D S, Blatter G. Quantum collective creep: A quasiclassical Langevin equation approach. Phys Rev B 66(21): 214203 (2002)
Crossref Google Scholar
[82]
Krajewski F R, Müser M H. Quantum dynamics in the highly discrete, commensurate Frenkel Kontorova model: A path-integral molecular dynamics study. J Chem Phys 122(12): 124711 (2005)
Crossref Google Scholar
[83]
Deng S J, Chenu A, Diao P P, Li F, Yu S, Coulamy I, del Campo A, Wu H B. Superadiabatic quantum friction suppression in finite-time thermodynamics. Sci Adv 4(4): eaar5909 (2018)
Crossref Google Scholar
[84]
Fogler M M, Butov L V, Novoselov K S. High-temperature superfluidity with indirect excitons in van der Waals heterostructures. Nat Commun 5: 4555 (2014)
Crossref Google Scholar
[85]
Berman O L, Kezerashvili R Y. High-temperature superfluidity of the two-component bose gas in a transition metal dichalcogenide bilayer. Phys Rev B 93(24): 245410 (2016)
Crossref Google Scholar
[86]
Li J I A, Taniguchi T, Watanabe K, Hone J, Dean C R. Excitonic superfluid phase in double bilayer graphene. Nat Phys 13(8): 751–755 (2017)
Crossref Google Scholar
[87]
Liu X M, Watanabe K, Taniguchi T, Halperin B I, Kim P. Quantum hall drag of exciton condensate in graphene. Nat Phys 13(8): 746–750 (2017)
Crossref Google Scholar
[88]
Popov V L. Contact Mechanics and Friction. Springer, 2010.
Crossref
[89]
Zuev L B. Autowave mechanics of plastic flow in solids. Phys Wave Phen 20(3): 166–173 (2012)
Crossref Google Scholar
[90]
Ostermeyer G P, Popov V L, Shilko E V, Vasiljeva O S. Multiscale Biomechanics and Tribology of Inorganic and Organic Systems: In Memory of Professor Sergey Psakhie. Springer Nature, 2021.
Crossref
[91]
Pustovalov V V. Serrated deformation of metals and alloys at low temperatures (Review). Low Temp Phys 34(9): 683–723 (2008)
Crossref Google Scholar
[92]
Granot E. Shearing a Fermionic gas and quantized friction. Europhys Lett 77(3): 36002 (2007)
Crossref Google Scholar
[93]
Jia J F, Li S C, Zhang Y F, Xue Q K. Quantum size effects induced novel properties in two-dimensional electronic systems: Pb thin films on Si(111). J Phys Soc Jpn 76(8): 082001 (2007)
Crossref Google Scholar
[94]
Han T Z, Dong G C, Shen Q T, Zhang Y F, Jia J F, Xue Q K. Adhesion modulation by quantum size effects in Pb/Si(111) system. Appl Phys Lett 89(18): 183109 (2006)
Crossref Google Scholar
[95]
Steverding B. Quantization of stress waves and fracture. Mater Sci Eng 9: 185–189 (1972)
Crossref Google Scholar
[96]
Schwinger J. Brownian motion of a quantum oscillator. J Math Phys 2(3): 407–432 (1961)
Crossref Google Scholar
[97]
Umezawa H, Matsumoto H, Tachiki M. Thermo Field Dynamics and Condensed States. Amsterdam: North-Holland, 1982.
[98]
Khanna F C. Thermal Quantum Field Theory: Algebraic Aspects and Applications. World Scientific, 2009.
Crossref
[99]
Barnett S M, Pegg D T. Phase in quantum optics. J Phys A: Math Gen 19(18): 3849–3862 (1986)
Crossref Google Scholar
[100]
Susskind L, Glogower J. Quantum mechanical phase and time operator. Physics 1(1): 49–61 (1964)
Crossref Google Scholar
[101]
Nieto M M. Quantum phase and quantum phase operators: Some physics and some history. Phys Scr T48: 5–12 (1993)
Crossref Google Scholar
[102]
Barnett S M, Vaccaro J A. The Quantum Phase Operator: A Review. Taylor and Francis, 2007.
Crossref
Friction
Volume 11 Issue 10,
October 2023
Pages 1877-1894
DOI: 10.1007/s40544-022-0719-1
Cite this article:
KHEIRI R. Quantum "contact" friction: The contribution of kinetic friction coefficient from thermal fluctuations. Friction, 2023, 11(10): 1877-1894. https://doi.org/10.1007/s40544-022-0719-1

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Received: 09 February 2022
Revised: 14 July 2022
Accepted: 02 November 2022
Published: 05 May 2023
© The author(s) 2022.

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