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Advances in nonequilibrium molecular dynamics simulations of lubricants and additives

  • Review Article
  • Open access
  • Published: 12 February 2018
  • Volume 6, pages 349–386, (2018)
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Friction Aims and scope
Advances in nonequilibrium molecular dynamics simulations of lubricants and additives
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  • J. P. Ewen1,
  • D. M. Heyes1 &
  • D. Dini1 
  • 4746 Accesses

  • 2 Altmetric

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Abstract

Nonequilibrium molecular dynamics (NEMD) simulations have provided unique insights into the nanoscale behaviour of lubricants under shear. This review discusses the early history of NEMD and its progression from a tool to corroborate theories of the liquid state, to an instrument that can directly evaluate important fluid properties, towards a potential design tool in tribology. The key methodological advances which have allowed this evolution are also highlighted. This is followed by a summary of bulk and confined NEMD simulations of liquid lubricants and lubricant additives, as they have progressed from simple atomic fluids to ever more complex, realistic molecules. The future outlook of NEMD in tribology, including the inclusion of chemical reactivity for additives, and coupling to continuum methods for large systems, is also briefly discussed.

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References

  1. Holmberg K, Erdemir A. Influence of tribology on global energy consumption, costs and emissions. Friction 5(3): 263–284 (2017)

    Google Scholar 

  2. Urbakh M, Klafter J, Gourdon D, Israelachvili J. The nonlinear nature of friction. Nature 430(6999): 525–528 (2004)

    Google Scholar 

  3. Aghababaei R, Warner D H, Molinari J F. Critical length scale controls adhesive wear mechanisms. Nat Commun 7: 11816 (2016)

    Google Scholar 

  4. Allen M P, Tidesley D J. Computer Simulation of Liquids. Oxford (UK): Clarendon Press, 1989.

    Google Scholar 

  5. Metropolis N, Ulam S. The Monte Carlo method. J Am Stat Assoc 44(247): 335–341 (1949)

    MATH  Google Scholar 

  6. Goldstein M. Viscous liquids and the glass transition: A potential energy barrier picture. J Chem Phys 51(9): 3728–3739 (1969)

    Google Scholar 

  7. Levesque D, Verlet L, Kürkijarvi J. Computer ”Experiments” on classical fluids. IV. Transport properties and timecorrelation functions of the Lennard-Jones liquid near its triple point. Phys Rev A 7(5): 1690–1700 (1973)

    Google Scholar 

  8. Siu S W I, Pluhackova K, Böckmann R A. Optimization of the OPLS-AA force field for long hydrocarbons. J Chem Theory Comput 8(4): 1459–1470 (2012)

    Google Scholar 

  9. Murzyn K, Bratek M, Pasenkiewicz-Gierula M. Refined OPLS all-atom force field parameters for n-pentadecane, methyl acetate, and dimethyl phosphate. J Phys Chem B 117(51): 16388–16396 (2013)

    Google Scholar 

  10. Ewen J P, Gattinoni C, Thakkar F M, Morgan N, Spikes H, Dini D. A comparison of classical force-fields for molecular dynamics simulations of lubricants. Materials 9(8): 651 (2016)

    Google Scholar 

  11. Szlufarska I, Chandross M, Carpick R W. Recent advances in single-asperity nanotribology. J Phys D Appl Phys 41(12): 123001 (2008)

    Google Scholar 

  12. 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)

    Google Scholar 

  13. Dong Y L, Li Q Y, Martini A. Molecular dynamics simulation of atomic friction: A review and guide. J Vac Sci Technol A, 31(3): 030801 (2013)

    Google Scholar 

  14. Sawyer W G, Argibay N, Burris D L, Krick B A. Mechanistic studies in friction and wear of bulk materials. Annu Rev Mater Res 44: 395–427 (2014)

    Google Scholar 

  15. Alder B J, Wainwright T E. Phase transition for a hard sphere system. J Chem Phys 27(5): 1208–1209 (1957)

    Google Scholar 

  16. Frenkel D. Entropy-driven phase transitions. Phys. A 263(1–4): 26–38 (1999)

    Google Scholar 

  17. Rahman A. Correlations in the motion of atoms in liquid argon. Phys Rev 136(2A): 405–411 (1964)

    Google Scholar 

  18. Eyring H, Ree T. Significant liquid structures, VI. The vacancy theory of liquids. Proc Natl Acad Sci USA 47(4): 526–537 (1961)

    Google Scholar 

  19. Ediger M D. Spatially heterogeneous dynamics in supercooled liquids. Annu Rev Phys Chem 51: 99–128 (2000)

    Google Scholar 

  20. Edward J T. Molecular volumes and the Stokes-Einstein equation. J Chem Educ 47(4): 261 (1970)

    Google Scholar 

  21. Hansen J P, McDonald I R. Theory of Simple Liquids. 4th ed. Amsterdam (Netherlands): Academic Press, 2013.

    MATH  Google Scholar 

  22. Alder B J, Gass D M, Wainwright T E. Studies in molecular dynamics. VIII. The transport coefficients for a hard-sphere fluid. J Chem Phys 53(10): 3813–3826 (1970)

    Google Scholar 

  23. Hefland E. Transport coefficients from dissipation in a canonical ensemble. Phys Rev 119(1): 1–9 (1960)

    MathSciNet  Google Scholar 

  24. Green M S. Markoff random processes and the statistical mechanics of time-dependent phenomena. II. Irreversible processes in fluids. J Chem Phys 22(3): 398–413 (1954)

    MathSciNet  Google Scholar 

  25. Kubo R. Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J Phys Soc Jpn 12(6): 570–586 (1957)

    MathSciNet  Google Scholar 

  26. Ladd A J C, Alley W E, Alder B J. Structural relaxation in dense hard-sphere fluids. J Stat Phys 48(5–6): 1147–1156 (1987)

    Google Scholar 

  27. Ashurst W T, Hoover W G. Dense-fluid shear viscosity via nonequilibrium molecular dynamics. Phys Rev A 11(2): 658–678 (1975)

    Google Scholar 

  28. Bitsanis I, Magda J J, Tirrell M, Davis H T. Molecular dynamics of flow in micropores. J Chem Phys 87(3): 1733–1750 (1987)

    Google Scholar 

  29. Ewen J P, Gattinoni C, Zhang J, Heyes D M, Spikes H A, Dini D. On the effect of confined fluid molecular structure on nonequilibrium phase behaviour and friction. Phys Chem Chem Phys 19(27): 17883–17894 (2017)

    Google Scholar 

  30. Evans D J, Morriss G P. Nonlinear-response theory for steady planar Couette flow. Phys Rev A 30(3): 1528–1530 (1984)

    Google Scholar 

  31. Lees A W, Edwards S F. The computer study of transport processes under extreme conditions. J Phys C Solid State Phys 5(15): 1921–1928 (1972)

    Google Scholar 

  32. Evans D J, Morriss G P. Statistical Mechanics of Nonequilibrium Liquids. 2nd ed. Cambridge (UK): Cambridge University Press, 2008.

    MATH  Google Scholar 

  33. Todd B D, Daivis P J. Nonequilibrium Molecular Dynamics: Theory, Algorithms and Applications. Cambridge (UK): Cambridge University Press, 2017.

    MATH  Google Scholar 

  34. Heyes D M, Kim J J, Montrose C J, Litovitz T A. Time dependent nonlinear shear stress effects in simple liquids: A molecular dynamics study. J Chem Phys 73(8): 3987–3996 (1980)

    Google Scholar 

  35. Maginn E J, Elliott J R. Historical perspective and current outlook for molecular dynamics as a chemical engineering tool. Ind Eng Chem Res 49(7): 3059–3078 (2010)

    Google Scholar 

  36. Götz A W, Williamson M J, Xu D, Poole D, Le Grand S, Walker R C. Routine microsecond molecular dynamics simulations with AMBER on GPUs. 1. Generalized born. J Chem Theory Comput 8(5): 1542–1555 (2012)

    Google Scholar 

  37. Bair S, McCabe C, Cummings P T. Comparison of nonequilibrium molecular dynamics with experimental measurements in the nonlinear shear-thinning regime. Phys Rev Lett 88(5): 058302 (2002)

    Google Scholar 

  38. Bair S, McCabe C, Cummings P T. Calculation of viscous EHL traction for squalane using molecular simulation and rheometry. Tribol Lett 13(4): 251–254 (2002)

    Google Scholar 

  39. Morriss G P, Evans D J. Application of transient correlation functions to shear flow far from equilibrium. Phys Rev A 35(2): 792–797 (1987)

    Google Scholar 

  40. Evans D J, Morriss G P. Transient-time-correlation functions and the rheology of fluids. Phys Rev A 38(8): 4142–4148 (1988)

    Google Scholar 

  41. Spikes H, Zhang J. History, origins and prediction of elastohydrodynamic friction. Tribol Lett 56(1): 1–25 (2014)

    Google Scholar 

  42. Taylor R, de Kraker B R. Shear rates in engines and implications for lubricant design. Proc Inst Mech Eng Part J J Eng Tribol 231(9): 1106–1116 (2017)

    Google Scholar 

  43. Andersen H C. Molecular dynamics simulations at constant pressure and/or temperature. J Chem Phys 72(4): 2384–2393 (1980)

    Google Scholar 

  44. Berendsen H J C, Postma J P M, Van Gunsteren W F, DiNola A, Haak J R. Molecular dynamics with coupling to an external bath. J Chem Phys 81(8): 3684–3690 (1984)

    Google Scholar 

  45. 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)

    Google Scholar 

  46. Español P, Warren P. Statistical mechanics of dissipative particle dynamics. Eur Lett 30(4): 191–196 (1995)

    Google Scholar 

  47. Nosé S. A molecular dynamics method for simulations in the canonical ensemble. Mol Phys 52(2): 255–268 (1984)

    MathSciNet  Google Scholar 

  48. Hoover W G. Canonical dynamics: Equilibrium phase-space distributions. Phys Rev A 31(3): 1695–1697 (1985)

    Google Scholar 

  49. Mundy C J, Siepmann J I, Klein M L. Decane under shear: A molecular dynamics study using reversible NVT-SLLOD and NPT-SLLOD algorithms. J Chem Phys 103(23): 10192–10200 (1995)

    Google Scholar 

  50. Delhommelle J, Petravic J, Evans D J. On the effects of assuming flow profiles in nonequilibrium simulations. J Chem Phys 119(21): 11005–11010 (2003)

    Google Scholar 

  51. Delhommelle J, Petravic J, Evans D J. Reexamination of string phase and shear thickening in simple fluids. Phys Rev E 68(3): 031201 (2003)

    Google Scholar 

  52. Delhommelle J, Evans D J. Configurational temperature profile in confined fluids. II. Molecular fluids. J Chem Phys 114(14): 6236–6241 (2001)

    Google Scholar 

  53. Braga C, Travis K P. A configurational temperature Nosé-Hoover thermostat. J Chem Phys 123(13): 134101 (2005)

    Google Scholar 

  54. Yong X, Zhang L T. Thermostats and thermostat strategies for molecular dynamics simulations of nanofluidics. J Chem Phys 138(8): 084503 (2013)

    Google Scholar 

  55. Khare R, de Pablo J, Yethiraj A. Molecular simulation and continuum mechanics study of simple fluids in non-isothermal planar Couette flows. J Chem Phys 107(7): 2589–2596 (1997)

    Google Scholar 

  56. Bernardi S, Todd B D, Searles D J. Thermostating highly confined fluids. J Chem Phys 132(24): 244706 (2010)

    Google Scholar 

  57. Martini A, Hsu H Y, Patankar N A, Lichter S. Slip at high shear rates. Phys Rev Lett 100(20): 206001 (2008)

    Google Scholar 

  58. Berro H, Fillot N, Vergne P, Tokumasu T, Ohara T, Kikugawa G. Energy dissipation in non-isothermal molecular dynamics simulations of confined liquids under shear. J Chem Phys 135(13): 134708 (2011)

    Google Scholar 

  59. De Luca S, Todd B D, Hansen J S, Daivis P J. A new and effective method for thermostatting confined fluids. J Chem Phys 140(5): 054502 (2014)

    Google Scholar 

  60. Kantorovich L, Rompotis N. Generalized Langevin equation for solids. II. Stochastic boundary conditions for nonequilibrium molecular dynamics simulations. Phys Rev B 78(9): 094305 (2008)

    Google Scholar 

  61. Toton D, Lorenz C D, Rompotis N, Martsinovich N, Kantorovich L. Temperature control in molecular dynamic simulations of non-equilibrium processes. J Phys Condens Matter 22(7): 074205 (2010)

    Google Scholar 

  62. Gattinoni C, Maćkowiak S, Heyes D M, Brańka A C, Dini D. Boundary-controlled barostats for slab geometries in molecular dynamics simulations. Phys Rev E 90(4): 043302 (2014)

    Google Scholar 

  63. Lupkowski M, Van Swol F. Ultrathin films under shear. J Chem Phys 95(3): 1995–1998 (1991)

    Google Scholar 

  64. Gao J P, Luedtke W D, Landman U. Structure and solvation forces in confined films: Linear and branched alkanes. J Chem Phys 106(10): 4309–4318 (1997)

    Google Scholar 

  65. Snook I K, Van Megen W. Solvation forces in simple dense fluids. I. J Chem Phys 72(5): 2907–2913 (1980)

    Google Scholar 

  66. Gao J P, Luedtke W D, Landman U. Origins of solvation forces in confined films. J Phys Chem B 101(20): 4013–4023 (1997)

    Google Scholar 

  67. Persson B N J, Mugele F. Squeeze-out and wear: Fundamental principles and applications. J Phys Condens Matter 16(10): R295–R355 (2004)

    Google Scholar 

  68. Fajardo O Y, Bresme F, Kornyshev A A, Urbakh M. Electrotunable friction with ionic liquid lubricants: How important is the molecular structure of the ions? J Phys Chem Lett 6(20): 3998–4004 (2015)

    Google Scholar 

  69. Leng Y S. Hydration force and dynamic squeeze-out of hydration water under subnanometer confinement. J Phys Condens Matter 20(35): 354017 (2008)

    Google Scholar 

  70. Leng Y S, Xiang Y, Lei Y J, Rao Q. A comparative study by the grand canonical Monte Carlo and molecular dynamics simulations on the squeezing behavior of nanometers confined liquid films. J Chem Phys 139(7): 074704 (2013)

    Google Scholar 

  71. Lei Y J, Leng Y S. Stick-slip friction and energy dissipation in boundary lubrication. Phys Rev Lett 107(14): 147801 (2011)

    Google Scholar 

  72. Ewald P P. Die Berechnung optischer und elektrostatischer Gitterpotentiale. Ann Phys 369(3): 253–287 (1921)

    MATH  Google Scholar 

  73. Luty B A, Davis M E, Tironi I G, Van Gunsteren W F. A comparison of particle-particle, particle-mesh and Ewald methods for calculating electrostatic interactions in periodic molecular systems. Mol Simul 14(1): 11–20 (1994)

    Google Scholar 

  74. Feller S E, Pastor R W, Rojnuckarin A, Bogusz S, Brooks B R. Effect of electrostatic force truncation on interfacial and transport properties of water. J Phys Chem 100(42): 17011–17020 (1996)

    Google Scholar 

  75. Yeh I C, Berkowitz M L. Ewald summation for systems with slab geometry. J Chem Phys 111(7): 3155–3162 (1999)

    Google Scholar 

  76. Allen W, Rowley R L. Predicting the viscosity of alkanes using nonequilibrium molecular dynamics: Evaluation of intermolecular potential models. J Chem Phys 106(24): 10273–10281 (1997)

    Google Scholar 

  77. Payal R S, Balasubramanian S, Rudra I, Tandon K, Mahlke I, Doyle D, Cracknell R. Shear viscosity of linear alkanes through molecular simulations: Quantitative tests for n-decane and n-hexadecane. Mol Simulat 38(14–15): 1234–1241 (2012)

    Google Scholar 

  78. Fischer J, Paschek D, Geiger A, Sadowski G. Modeling of aqueous poly(oxyethylene) solutions: 1. Atomistic simulations. J Phys Chem B 112(8): 2388–2398 (2008)

    Google Scholar 

  79. Moore J D, Cui S T, Cochran H D, Cummings P T. Rheology of lubricant basestocks: A molecular dynamics study of C30 isomers. J Chem Phys 113(19): 8833–8840 (2000)

    Google Scholar 

  80. Ye X G, Cui S T, de Almeida V F, Khomami B. Effect of varying the 1–4 intramolecular scaling factor in atomistic simulations of long-chain N-alkanes with the OPLS-AA model. J Mol Model 19(3): 1251–1258 (2013)

    Google Scholar 

  81. Pan G A, McCabe C. Prediction of viscosity for molecular fluids at experimentally accessible shear rates using the transient time correlation function formalism. J Chem Phys 125(19): 194527 (2006)

    Google Scholar 

  82. Delhommelle J, Cummings P T. Simulation of friction in nanoconfined fluids for an arbitrarily low shear rate. Phys Rev B 72(17): 172201 (2005)

    Google Scholar 

  83. Bernardi S, Brookes S J, Searles D J, Evans D J. Response theory for confined systems. J Chem Phys 137(7): 074114 (2012)

    Google Scholar 

  84. Bocquet L, Barrat J L. Hydrodynamic boundary conditions, correlation functions, and Kubo relations for confined fluids. Phys Rev E 49(4): 3079–3092 (1994)

    Google Scholar 

  85. Petravic J, Harrowell P. On the equilibrium calculation of the friction coefficient for liquid slip against a wall. J Chem Phys 127(17): 174706 (2007)

    Google Scholar 

  86. Bocquet L, Barrat J L. On the Green-Kubo relationship for the liquid-solid friction coefficient. J Chem Phys 139(4): 044704 (2013)

    Google Scholar 

  87. Müller-Plathe F. Reversing the perturbation in nonequilibrium molecular dynamics: An easy way to calculate the shear viscosity of fluids. Phys Rev E 59(5): 4894–4898 (1999)

    Google Scholar 

  88. Bordat P, Müller-Plathe F. The shear viscosity of molecular fluids: A calculation by reverse nonequilibrium molecular dynamics. J Chem Phys 116(8): 3362–3369 (2002)

    Google Scholar 

  89. Müller T J, Müller-Plathe F. Determining the local shear viscosity of a lipid bilayer system by reverse non-equilibrium molecular dynamics simulations. ChemPhysChem 10(13): 2305–2315 (2009)

    Google Scholar 

  90. Voeltzel N, Giuliani A, Fillot N, Vergne P, Joly L. Nanolubrication by ionic liquids: Molecular dynamics simulations reveal an anomalous effective rheology. Phys Chem Chem Phys 17(35): 23226–23235 (2015)

    Google Scholar 

  91. Ramasamy U S, Len M, Martini A. Correlating molecular structure to the behavior of linear styrene–butadiene viscosity modifiers. Tribol Lett 65(4): 147 (2017)

    Google Scholar 

  92. Len M, Ramasamy U S, Lichter S, Martini A. Thickening mechanisms of polyisobutylene in polyalphaolefin. Tribol Lett 66(1): 5 (2018)

    Google Scholar 

  93. Tenney C M, Maginn E J. Limitations and recommendations for the calculation of shear viscosity using reverse nonequilibrium molecular dynamics. J Chem Phys 132(1): 014103 (2010)

    Google Scholar 

  94. Todd B D, Daivis P J. Nonequilibrium molecular dynamics simulations of planar elongational flow with spatially and temporally periodic boundary conditions. Phys Rev Lett 81(5): 1118–1121 (1998)

    Google Scholar 

  95. Bair S. Rheology and high-pressure models for quantitative elastohydrodynamics. Proc Inst Mech Eng Part J J Eng Tribol 223(4): 617–628 (2008)

    Google Scholar 

  96. Hajizadeh E, Todd B D, Daivis P J. Shear rheology and structural properties of chemically identical dendrimer-linear polymer blends through molecular dynamics simulations. J Chem Phys 141(19): 194905 (2014)

    Google Scholar 

  97. Hajizadeh E, Todd B D, Daivis P J. A molecular dynamics investigation of the planar elongational rheology of chemically identical dendrimer-linear polymer blends. J Chem Phys 142(17): 174911 (2015)

    Google Scholar 

  98. Baig C, Edwards B J, Keffer D J, Cochran H D. Rheological and structural studies of liquid decane, hexadecane, and tetracosane under planar elongational flow using nonequilibrium molecular-dynamics simulations. J Chem Phys 122(18): 184906 (2005)

    Google Scholar 

  99. Daivis P J, Todd B D. A simple, direct derivation and proof of the validity of the SLLOD equations of motion for generalized homogeneous flows. J Chem Phys 124(19): 194103 (2006)

    Google Scholar 

  100. Hunt T A, Bernardi S, Todd B D. A new algorithm for extended nonequilibrium molecular dynamics simulations of mixed flow. J Chem Phys 133(15): 154116 (2010)

    Google Scholar 

  101. Hartkamp R, Bernardi S, Todd B D. Transient-time correlation function applied to mixed shear and elongational flows. J Chem Phys 136(6): 064105 (2012)

    Google Scholar 

  102. Thompson P A, Robbins M O. Origin of stick-slip motion in boundary lubrication. Science 250(4982): 792–794 (1990)

    Google Scholar 

  103. Gee M L, McGuiggan P M, Israelachvili J N, Homola A M. Liquid to solid-like transitions of molecularly thin films under shear. J Chem Phys 93(3): 1895–1906 (1990)

    Google Scholar 

  104. Leng Y, Cummings P T. Fluidity of hydration layers nanoconfined between mica surfaces. Phys Rev Lett 94(2): 026101 (2005)

    Google Scholar 

  105. Stevens M J, Mondello M, Grest G S, Cui S T, Cochran H D, Cummings P T. Comparison of shear flow of hexadecane in a confined geometry and in bulk. J Chem Phys 106(17): 7303–7314 (1997)

    Google Scholar 

  106. Zhang J F, Todd B D, Travis K P. Viscosity of confined inhomogeneous nonequilibrium fluids. J Chem Phys 121(21): 10778–10786 (2004)

    Google Scholar 

  107. Zhang J F, Todd B D, Travis K P. Erratum: “Viscosity of confined inhomogeneous nonequilibrium fluids” [J Chem Phys 121: 10778 (2004)]. J Chem Phys 122(21): 219901 (2005)

    Google Scholar 

  108. Liem S Y, Brown D, Clarke J H R. Investigation of the homogeneous-shear nonequilibrium-molecular-dynamics method. Phys Rev A 45(6): 3706–3713 (1992)

    Google Scholar 

  109. Todd B D, Evans D J, Travis K P, Daivis P J. Comment on “Molecular simulation and continuum mechanics study of simple fluids in nonisothermal planar Couette flows” [J Chem Phys 107: 2589 (1997)]. J Chem Phys 111(23): 10730 (1999)

    Google Scholar 

  110. Cui S T, Cummings P T, Cochran H D, Moore J D, Gupta S A. Nonequilibrium molecular dynamics simulation of the rheology of linear and branched alkanes. Int J Thermophys 19(2): 449–459 (1998)

    Google Scholar 

  111. Mundy C J, Balasubramanian S, Bagchi K, Siepmann J I, Klein M L. Equilibrium and non-equilibrium simulation studies of fluid alkanes in bulk and at interfaces. Faraday Discuss 104: 17–36 (1996)

    Google Scholar 

  112. Todd B D, Daivis P J. Homogeneous non-equilibrium molecular dynamics simulations of viscous flow: Techniques and applications. Mol Simul 33(3): 189–229 (2007)

    MATH  Google Scholar 

  113. Morriss G P, Daivis P J, Evans D J. The rheology of n alkanes: Decane and Eicosane. J Chem Phys 94(11): 7420–7433 (1991)

    Google Scholar 

  114. Weeks J D, Chandler D, Andersen H C. Role of repulsive forces in determining the equilibrium structure of simple liquids. J Chem Phys 54(12): 5237–5247 (1971)

    Google Scholar 

  115. Khare R, de Pablo J, Yethiraj A. Rheological, thermodynamic, and structural studies of linear and branched alkanes under shear. J Chem Phys 107(17): 6956–6964 (1997)

    Google Scholar 

  116. Jorgensen W L, Madura J D, Swenson C J. Optimized intermolecular potential functions for liquid hydrocarbons. J Am Chem Soc 106(22): 6638–6646 (1984)

    Google Scholar 

  117. Siepmann J I, Karaborni S, Smit B. Simulating the critical behaviour of complex fluids. Nature 365(6444): 330–332 (1993)

    Google Scholar 

  118. McCabe C, Cui S T, Cummings P T. Characterizing the viscosity-temperature dependence of lubricants by molecular simulation. Fluid Phase Equilib 183–184: 363–370 (2001)

    Google Scholar 

  119. McCabe C, Cui S T, Cummings P T, Gordon P A, Saeger R B. Examining the rheology of 9-octylheptadecane to giga-pascal pressures. J Chem Phys 114(4): 1887–1891 (2001)

    Google Scholar 

  120. Liu P Z, Yu H L, Ren N, Lockwood F E, Wang Q J. Pressure-viscosity coefficient of hydrocarbon base oil through molecular dynamics simulations. Tribol Lett 60(1): 34 (2015)

    Google Scholar 

  121. Ramasamy U S, Bair S, Martini A. Predicting pressureviscosity behavior from ambient viscosity and compressibility: Challenges and opportunities. Tribol Lett 57(2): 11 (2015)

    Google Scholar 

  122. Bair S, Vergne P, Kumar P, Poll G, Krupka I, Hartl M, Habchi W, Larsson R. Comment on “History, origins and prediction of elastohydrodynamic friction” by Spikes and Jie. Tribol Lett 58(1): 16 (2015)

    Google Scholar 

  123. Spikes H, Zhang J. Reply to the comment by Scott Bair, Philippe Vergne, Punit Kumar, Gerhard Poll, Ivan Krupka, Martin Hartl, Wassim Habchi, Roland Larson on “History, origins and prediction of elastohydrodynamic friction” by Spikes and Jie in Tribology Letters. Tribol Lett 58(1): 17 (2015)

    Google Scholar 

  124. Voeltzel N, Vergne P, Fillot N, Bouscharain N, Joly L. Rheology of an Ionic Liquid with variable carreau exponent: A full picture by molecular simulation with experimental contribution. Tribol Lett 64(2): 25 (2016)

    Google Scholar 

  125. Spikes H A. Comment on: Rheology of an Ionic Liquid with Variable Carreau Exponent: A full picture by molecular simulation with experimental contribution, by Nicolas Voeltzel, Philippe Vergne, Nicolas Fillot, Nathalie Bouscharain, Laurent Joly, Tribology Letters (2016) 64: 25. Tribol Lett 65(2): 72 (2017)

    Google Scholar 

  126. Voeltzel N, Vergne P, Fillot N, Bouscharain N, Joly L. Reply to the “Comment on ‘Rheology of an ionic liquid with variable carreau exponent: A full picture by molecular simulation with experimental contribution’, by N. Voeltzel, P. Vergne, N. Fillot, N. Bouscharain, L. Joly, Tribology Letters (2016) 64: 25” by H. A. Spikes. Tribol Lett 65(2): 73 (2017)

    Google Scholar 

  127. Bird R B, Armstrong R C, Hassager O. Dynamics of Polymeric Liquids: Volume 1: Fluid Mechanics. 2nd ed. New York (USA): John Wiley and Sons, 1987.

    Google Scholar 

  128. Carreau P J. Rheological equations from molecular network theories. J Rheol 16(1): 99–127 (1972)

    Google Scholar 

  129. Liu P Z, Lu J, Yu H L, Ren N, Lockwood F E, Wang Q J. Lubricant shear thinning behavior correlated with variation of radius of gyration via molecular dynamics simulations. J Chem Phys 147(8): 084904 (2017)

    Google Scholar 

  130. Bair S, Winer W O. A quantitative test of the Einstein-Debye relation using the shear dependence of viscosity for low molecular weight liquids. Tribol Lett 26(3): 223–228 (2007)

    Google Scholar 

  131. Jadhao V, Robbins M O. Probing large viscosities in glass-formers with nonequilibrium simulations. Proc Natl Acad Sci USA 114(30): 7952–7957 (2017)

    Google Scholar 

  132. Eyring H. Viscosity, plasticity, and diffusion as examples of absolute reaction rates. J Chem Phys 4(4): 283–291 (1936)

    Google Scholar 

  133. Travis K P, Todd B D, Evans D J. Departure from Navier-Stokes hydrodynamics in confined liquids. Phys Rev E 55(4): 4288–4295 (1997)

    Google Scholar 

  134. Abraham F F. The interfacial density profile of a Lennard- Jones fluid in contact with a (100) Lennard-Jones wall and its relationship to idealized fluid/wall systems: A Monte Carlo simulation. J Chem Phys 68(8): 3713–3716 (1978)

    Google Scholar 

  135. Horn R G, Israelachvili J N. Direct measurement of structural forces between two surfaces in a nonpolar liquid. J Chem Phys 75(3): 1400–1411 (1981)

    Google Scholar 

  136. Magda J J, Tirrell M, Davis H T. Molecular dynamics of narrow, liquid-filled pores. J Chem Phys 83(4): 1888–1901 (1985)

    Google Scholar 

  137. Bitsanis I, Somers S A, Davis H T, Tirrell M. Microscopic dynamics of flow in molecularly narrow pores. J Chem Phys 93(5): 3427–3431 (1990)

    Google Scholar 

  138. Berro H. A molecular dynamics approach to nano-scale lubrication. Ph.D Thesis. Lyon (France): L’Institut National des Sciences Appliquées de Lyon, 2010.

    Google Scholar 

  139. Israelachvili J N. Measurement of the viscosity of liquids in very thin films. J Colloid Interface Sci 110(1): 263–271 (1986)

    Google Scholar 

  140. Somers S A, Davis H T. Microscopic dynamics of fluids confined between smooth and atomically structured solid surfaces. J Chem Phys 96(7): 5389–5407 (1992)

    Google Scholar 

  141. Jabbarzadeh A, Harrowell P, Tanner R I. Crystal bridge formation marks the transition to rigidity in a thin lubrication film. Phys Rev Lett 96(20): 206102 (2006)

    Google Scholar 

  142. Granick S. Motions and relaxations of confined liquids. Science 253(5026): 1374–1379 (1991)

    Google Scholar 

  143. Klein J, Kumacheva E. Simple liquids confined to molecularly thin layers. I. Confinement-induced liquid-tosolid phase transitions. J Chem Phys 108(16): 6996–7009 (1998)

    Google Scholar 

  144. Klein J, Kumacheva E. Confinement-induced phase transitions in simple liquids. Science 269(5225): 816–819 (1995)

    Google Scholar 

  145. Thompson P A, Grest G S, Robbins M O. Phase transitions and universal dynamics in confined films. Phys Rev Lett 68(23): 3448–3451 (1992)

    Google Scholar 

  146. Gao J P, Luedtke W D, Landman U. Layering transitions and dynamics of confined liquid films. Phys Rev Lett 79(4): 705–708 (1997)

    Google Scholar 

  147. Docherty H, Cummings P T. Direct evidence for fluidsolid transition of nanoconfined fluids. Soft Matter 6(8): 1640–1643 (2010)

    Google Scholar 

  148. Van Alsten J, Granick S. Molecular tribometry of ultrathin liquid films. Phys Rev Lett 61(22): 2570–2573 (1988)

    Google Scholar 

  149. Lin Z Q, Granick S. Platinum nanoparticles at mica surfaces. Langmuir 19(17): 7061–7070 (2003)

    Google Scholar 

  150. Cummings P T, Docherty H, Iacovella C R, Singh J K. Phase transitions in nanoconfined fluids: The evidence from simulation and theory. AIChE J 56(4): 842–848 (2010)

    Google Scholar 

  151. Jabbarzadeh A, Atkinson J D, Tanner R I. The effect of branching on slip and rheological properties of lubricants in molecular dynamics simulation of Couette shear flow. Tribol Int 35(1): 35–46 (2002)

    Google Scholar 

  152. Gupta S A, Cochran H D, Cummings P T. Shear behavior of squalane and tetracosane under extreme confinement. II. Confined film structure. J Chem Phys 107(23): 10327–10334 (1997)

    Google Scholar 

  153. Gao J P, Luedtke W D, Landman U. Structures, solvation forces and shear of molecular films in a rough nanoconfinement. Tribol Lett 9(1–2): 3–13 (2000)

    Google Scholar 

  154. Jabbarzadeh A, Atkinson J D, Tanner R I. Effect of the wall roughness on slip and rheological properties of hexadecane in molecular dynamics simulation of Couette shear flow between two sinusoidal walls. Phys Rev E 61(1): 690–699 (2000)

    Google Scholar 

  155. Cui S T, McCabe C, Cummings P T, Cochran H D. Molecular dynamics study of the nano-rheology of n-dodecane confined between planar surfaces. J Chem Phys 118(19): 8941–8944 (2003)

    Google Scholar 

  156. Zhu Y X, Granick S. Superlubricity: A paradox about confined fluids resolved. Phys Rev Lett 93(9): 096101 (2004)

    Google Scholar 

  157. Jabbarzadeh A, Harrowell P, Tanner R I. Very low friction state of a dodecane film confined between mica surfaces. Phys Rev Lett 94(12): 126103 (2005)

    Google Scholar 

  158. Jabbarzadeh A, Harrowell P, Tanner R I. Low friction lubrication between amorphous walls: Unraveling the contributions of surface roughness and in-plane disorder. J Chem Phys 125(3): 034703 (2006)

    Google Scholar 

  159. Jabbarzadeh A, Harrowell P, Tanner R I. The structural origin of the complex rheology in thin dodecane films: Three routes to low friction. Tribol Int 40(10–12): 1574–1586 (2007)

    Google Scholar 

  160. Martini A, Liu Y, Snurr R Q, Wang Q J. Molecular dynamics characterization of thin film viscosity for EHL simulation. Tribol Lett 21(3): 217–225 (2006)

    Google Scholar 

  161. Hu Y Z, Zhu D. A full numerical solution to the mixed lubrication in point contacts. J Tribol 122(1): 1–9 (1999)

    Google Scholar 

  162. Robbins M O, Smith E D. Connecting molecular-scale and macroscopic tribology. Langmuir 12(19): 4543–4547 (1996)

    Google Scholar 

  163. Rosenhek-Goldian I, Kampf N, Yeredor A, Klein J. On the question of whether lubricants fluidize in stick-slip friction. Proc Natl Acad Sci USA 112(23): 7117–7122 (2015)

    Google Scholar 

  164. Jee A Y, Lou K, Granick S. Scrutinizing evidence of no dilatancy upon stick–slip of confined fluids. Proc Natl Acad Sci USA 112(36): E4972 (2015)

    Google Scholar 

  165. Dhinojwala A, Bae S C, Granick S. Shear-induced dilation of confined liquid films. Tribol Lett 9(1–2): 55–62 (2000)

    Google Scholar 

  166. Zhu Y X, Granick S. Rate-dependent slip of Newtonian liquid at smooth surfaces. Phys Rev Lett 87(9): 096105 (2001)

    Google Scholar 

  167. Neto C, Evans D R, Bonaccurso E, Butt H J, Craig V S J. Boundary slip in Newtonian liquids: A review of experimental studies. Rep Prog Phys 68(12): 2859–2897 (2005)

    Google Scholar 

  168. Savio D, Fillot N, Vergne P, Zaccheddu M. A model for wall slip prediction of confined n-alkanes: Effect of wallfluid interaction versus fluid resistance. Tribol Lett 46(1): 11–22 (2012)

    Google Scholar 

  169. Fillot N, Berro H, Vergne P. From continuous to molecular scale in modelling elastohydrodynamic lubrication: Nanoscale surface slip effects on film thickness and friction. Tribol Lett 43(3): 257–266 (2011)

    Google Scholar 

  170. Washizu H, Hyodo S A, Ohmori T, Nishino N, Suzuki A. Macroscopic no-slip boundary condition confirmed in full atomistic simulation of oil film. Tribol Online 9(2): 45–50 (2014)

    Google Scholar 

  171. Jabbarzadeh A, Atkinson J D, Tanner R I. Wall slip in the molecular dynamics simulation of thin films of hexadecane. J Chem Phys 110(5): 2612–2620 (1999)

    Google Scholar 

  172. Pit R, Hervet H, Leger L. Direct experimental evidence of slip in hexadecane: Solid interfaces. Phys Rev Lett 85(5): 980–983 (2000)

    Google Scholar 

  173. Blake T D. Slip between a liquid and a solid: D. M. Tolstoi’s (1952) theory reconsidered. Colloids Surf 47: 135–145 (1990)

    Google Scholar 

  174. Spikes H, Granick S. Equation for slip of simple liquids at smooth solid surfaces. Langmuir 19(12): 5065–5071 (2003)

    Google Scholar 

  175. De Gennes P G. On fluid/wall slippage. Langmuir 18(9): 3413–3414 (2002)

    Google Scholar 

  176. Wang F C, Zhao Y P. Slip boundary conditions based on molecular kinetic theory: The critical shear stress and the energy dissipation at the liquid–solid interface. Soft Matter 7(18): 8628–8634 (2011)

    Google Scholar 

  177. Vadakkepatt A, Dong Y L, Lichter S, Martini A. Effect of molecular structure on liquid slip. Phys Rev E 84(6): 066311 (2011)

    Google Scholar 

  178. Majumdar A, Bhushan B. Role of fractal geometry in roughness characterization and contact mechanics of surfaces. J Tribol 112(2): 205–216 (1990)

    Google Scholar 

  179. Savio D, Pastewka L, Gumbsch P. Boundary lubrication of heterogeneous surfaces and the onset of cavitation in frictional contacts. Sci Adv 2(3): e1501585 (2016)

    Google Scholar 

  180. Reynolds O. On the theory of lubrication and its application to Mr. Beauchamp Tower’s experiments, including an experimental determination of the viscosity of olive oil. Proc Roy Soc Lond 40(242–245): 191–203 (1886)

    MATH  Google Scholar 

  181. Zhu Y X, Granick S. Limits of the hydrodynamic no-slip boundary condition. Phys Rev Lett 88(10): 106102 (2002)

    Google Scholar 

  182. Savio D, Fillot N, Vergne P, Hetzler H, Seemann W, Morales-Espejel G E. A multiscale study on the wall slip effect in a ceramic-steel contact with nanometer-thick lubricant film by a nano-to-elastohydrodynamic lubrication approach. J Tribol 137(3): 031502 (2015)

    Google Scholar 

  183. Ponjavic A, Wong J S S. The effect of boundary slip on elastohydrodynamic lubrication. RSC Adv 4(40): 20821–20829 (2014)

    Google Scholar 

  184. Wong P L, Li X M, Guo F. Evidence of lubricant slip on steel surface in EHL contact. Tribol Int 61: 116–119 (2013)

    Google Scholar 

  185. Martinie L, Vergne P. Lubrication at extreme conditions: A discussion about the limiting shear stress concept. Tribol Lett 63(2): 21 (2016)

    Google Scholar 

  186. Heyes D M, Smith E R, Dini D, Spikes H A, Zaki T A. Pressure dependence of confined liquid behavior subjected to boundary-driven shear. J Chem Phys 136(13): 134705 (2012)

    Google Scholar 

  187. Gattinoni C, Heyes D M, Lorenz C D, Dini D. Traction and nonequilibrium phase behavior of confined sheared liquids at high pressure. Phys Rev E 88(5): 052406 (2013)

    Google Scholar 

  188. Maćkowiak S, Heyes D M, Dini D, Brańka A C. Non-equilibrium phase behavior and friction of confined molecular films under shear: A non-equilibrium molecular dynamics study. J Chem Phys 145(16): 164704 (2016)

    Google Scholar 

  189. Thompson P A, Robbins M O. Shear flow near solids: Epitaxial order and flow boundary conditions. Phys Rev A 41(12): 6830–6837 (1990)

    Google Scholar 

  190. Butler S, Harrowell P. Factors determining crystal-liquid coexistence under shear. Nature 415(6875): 1008–1011 (2002)

    Google Scholar 

  191. Butler S, Harrowell P. Simulation of the coexistence of a shearing liquid and a strained crystal. J Chem Phys 118(9): 4115–4126 (2003)

    Google Scholar 

  192. Butler S, Harrowell P. Structure and stability of the interface between a strained crystal and a shearing liquid. Phys Rev E 67(5): 051503 (2003)

    Google Scholar 

  193. Varnik F, Bocquet L, Barrat J L, Berthier L. Shear localization in a model glass. Phys Rev Lett 90(9): 095702 (2003)

    Google Scholar 

  194. Rottler J, Robbins M O. Shear yielding of amorphous glassy solids: Effect of temperature and strain rate. Phys Rev E 68(1): 011507 (2003)

    Google Scholar 

  195. Heyes D M. The Liquid State: Applications of Molecular Simulations. New York (USA): Wiley, 1998.

    Google Scholar 

  196. Bair S, Winer W O. The high pressure high shear stress rheology of liquid lubricants. J Tribol 114(1): 1–9 (1992)

    Google Scholar 

  197. Bair S, Qureshi F, Winer W O. Observations of shear localization in liquid lubricants under pressure. J Tribol 115(3): 507–513 (1993)

    Google Scholar 

  198. Bair S, McCabe C. A study of mechanical shear bands in liquids at high pressure. Tribol Int 37(10): 783–789 (2004)

    Google Scholar 

  199. Ponjavic A, Chennaoui M, Wong J S S. Through-thickness velocity profile measurements in an elastohydrodynamic contact. Tribol Lett 50(2): 261–277 (2013)

    Google Scholar 

  200. Ponjavic A, di Mare L, Wong J S S. Effect of pressure on the flow behavior of polybutene. J Polym Sci B Polym Phys 52(10): 708–715 (2014)

    Google Scholar 

  201. Galmiche B, Ponjavic A, Wong J S S. Flow measurements of a polyphenyl ether oil in an elastohydrodynamic contact. J Phys Condens Matter 28(13): 134005 (2016)

    Google Scholar 

  202. Šperka P, Křupka I, Hartl M. Evidence of plug flow in rolling-sliding elastohydrodynamic contact. Tribol Lett 54(2): 151–160 (2014)

    Google Scholar 

  203. Sperka P, Krupka I, Hartl M. Lubricant flow in thin-film elastohydrodynamic contact under extreme conditions. Friction 4(4): 380–390 (2016)

    Google Scholar 

  204. Zhang J, Tan A, Spikes H. Effect of base oil structure on elastohydrodynamic friction. Tribol Lett 65(1): 13 (2017)

    Google Scholar 

  205. Spikes H, Tysoe W. On the commonality between theoretical models for fluid and solid friction, wear and tribochemistry. Tribol Lett 59(1): 14 (2015)

    Google Scholar 

  206. Washizu H, Ohmori T, Suzuki A. Molecular origin of limiting shear stress of elastohydrodynamic lubrication oil film studied by molecular dynamics. Chem Phys Lett 678: 1–4 (2017)

    Google Scholar 

  207. Bodnarchuk M S, Heyes D M, Breakspear A, Chahine S, Dini D. A molecular dynamics study of CaCO3 nanoparticles in a hydrophobic solvent with a stearate co-surfactant. Phys Chem Chem Phys 17(20): 13575–13581 (2015)

    Google Scholar 

  208. Bodnarchuk M S, Dini D, Heyes D M, Breakspear A, Chahine S. Molecular dynamics studies of overbased detergents on a water surface. Langmuir 33(29): 7263–7270 (2017)

    Google Scholar 

  209. Tomlinson A, Danks T N, Heyes D M, Taylor S E, Moreton D J. Interfacial characterization of succinimide surfactants. Langmuir 13(22): 5881–5893 (1997)

    Google Scholar 

  210. Tomlinson A, Scherer B, Karakosta E, Oakey M, Danks T N, Heyes D M, Taylor S E. Adsorption properties of succinimide dispersants on carbonaceous substrates. Carbon 38(1): 13–28 (2000)

    Google Scholar 

  211. Ramasamy U S, Lichter S, Martini A. Effect of molecularscale features on the polymer coil size of model viscosity index improvers. Tribol Lett 62(2): 23 (2016)

    Google Scholar 

  212. Jiang S Y, Frazier R, Yamaguchi E S, Blanco M, Dasgupta S, Zhou Y H, Cagin T, Tang Y C, Goddard III W A. The SAM model for wear inhibitor performance of dithiophosphates on iron oxide. J Phys Chem B 101(39): 7702–7709 (1997)

    Google Scholar 

  213. Zhou Y H, Jiang S Y, Çaǧın T, Yamaguchi E S, Frazier R, Ho A, Tang Y C, Goddard III W A. Application of the self-assembled monolayer (SAM) model to dithiophosphate and dithiocarbamate engine wear inhibitors. J Phys Chem A 104(11): 2508–2524 (2000)

    Google Scholar 

  214. Minfray C, Le Mogne T, Martin J M, Onodera T, Nara S, Takahashi S, Tsuboi H, Koyama M, Endou A, Takaba H, et al. Experimental and molecular dynamics simulations of tribochemical reactions with ZDDP: Zinc phosphate–iron oxide reaction. Tribol Trans 51(5): 589–601 (2008)

    Google Scholar 

  215. Berro H, Fillot N, Vergne P. Molecular dynamics simulation of surface energy and ZDDP effects on friction in nano-scale lubricated contacts. Tribol Int 43(10): 1811–1822 (2010)

    Google Scholar 

  216. Ramachandran S, Tsai B L, Blanco M, Chen H, Tang Y C, Goddard III W A. Self-assembled monolayer mechanism for corrosion inhibition of iron by imidazolines. Langmuir 12(26): 6419–6428 (1996)

    Google Scholar 

  217. Ramachandran S, Tsai B L, Blanco M, Chen H, Tang Y C, Goddard III W A. Atomistic simulations of oleic imidazolines bound to ferric clusters. J Phys Chem A 101(1): 83–89 (1997)

    Google Scholar 

  218. Xia S W, Qiu M, Yu L M, Liu F G, Zhao H Z. Molecular dynamics and density functional theory study on relationship between structure of imidazoline derivatives and inhibition performance. Corros Sci 50(7): 2021–2029 (2008)

    Google Scholar 

  219. Spikes H. Friction modifier additives. Tribol Lett 60(1): 5 (2015)

    Google Scholar 

  220. Beltzer M, Jahanmir S. Role of dispersion interactions between hydrocarbon chains in boundary lubrication. ASLE Trans 30(1): 47–54 (1987)

    Google Scholar 

  221. Lundgren S M, Ruths M, Danerlöv K, Persson K. Effects of unsaturation on film structure and friction of fatty acids in a model base oil. J Colloid Interface Sci 326(2): 530–536 (2008)

    Google Scholar 

  222. Campen S, Green J H, Lamb G D, Spikes H A. In situ study of model organic friction modifiers using liquid cell AFM; Saturated and Mono-unsaturated carboxylic acids. Tribol Lett 57(2): 18 (2015)

    Google Scholar 

  223. Wood M H, Casford M T, Steitz R, Zarbakhsh A, Welbourn R J L, Clarke S M. Comparative adsorption of saturated and unsaturated fatty acids at the iron oxide/oil interface. Langmuir 32(2): 534–540 (2016)

    Google Scholar 

  224. Rai B, Pradip P. Modeling self-assembly of surfactants at interfaces. Curr Opin Chem Eng 15: 84–94 (2017)

    Google Scholar 

  225. Briscoe B J, Evans D C B. The shear properties of Langmuir-Blodgett layers. Proc Roy Soc A Math Phys Eng Sci 380(1779): 389–407 (1982)

    Google Scholar 

  226. Moller M A, Tildesley D J, Kim K S, Quirke N. Molecular dynamics simulation of a langmuir-blodgett film. J Chem Phys 94(12): 8390–8401 (1991)

    Google Scholar 

  227. Karaborni S, Verbist G. Effect of chain conformation on the tilt behaviour in langmuir monolayers. Eur Lett 27(6): 467–472 (1994)

    Google Scholar 

  228. Davidson J E, Hinchley S L, Harris S G, Parkin A, Parsons S, Tasker P A. Molecular dynamics simulations to aid the rational design of organic friction modifiers. J Mol Graphics Modell 25(4): 495–506 (2006)

    Google Scholar 

  229. Greenfield M L, Ohtani H. Molecular dynamics simulation study of model friction modifier additives confined between two surfaces. Tribol Lett 7(2–3): 137–145 (1999)

    Google Scholar 

  230. Ruths M, Ohtani H, Greenfield M, Granick S. Exploring the “friction modifier” phenomenon: Nanorheology of n-alkane chains with polar terminus dissolved in n-alkane solvent. Tribol Lett 6(3–4): 207–214 (1999)

    Google Scholar 

  231. Greenfield M L, Ohtani H. Packing of simulated friction modifier additives under confinement. Langmuir 21(16): 7568–7578 (2005)

    Google Scholar 

  232. Doig M, Camp P J. The structures of hexadecylamine films adsorbed on iron-oxide surfaces in dodecane and hexadecane. Phys Chem Chem Phys 17(7): 5248–5255 (2015)

    Google Scholar 

  233. Wood M H, Welbourn R J L, Charlton T, Zarbakhsh A, Casford M T, Clarke S M. Hexadecylamine adsorption at the iron oxide-oil interface. Langmuir 29(45): 13735–13742 (2013)

    Google Scholar 

  234. Bradley-Shaw J L, Camp P J, Dowding P J, Lewtas K. Molecular dynamics simulations of glycerol monooleate confined between mica surfaces. Langmuir 32(31): 7707–7718 (2016)

    Google Scholar 

  235. Bradley-Shaw J L, Camp P J, Dowding P J, Lewtas K. Glycerol monooleate reverse micelles in nonpolar solvents: Computer simulations and small-angle neutron scattering. J Phys Chem B 119(11): 4321–4331 (2015)

    Google Scholar 

  236. Glosli J N, McClelland G M. Molecular dynamics study of sliding friction of ordered organic monolayers. Phys Rev Lett 70(13): 1960–1963 (1993)

    Google Scholar 

  237. Kong Y C, Tildesley D J, Alejandre J. The molecular dynamics simulation of boundary-layer lubrication. Mol Phys 92(1): 7–18 (1997)

    Google Scholar 

  238. Kong Y C, Tildesley D J. The effect of molecular geometry on boundary layer lubrication. Mol Simul 22(2): 149–168 (1999)

    Google Scholar 

  239. Eder S J, Vernes A, Betz G. On the derjaguin offset in boundary-lubricated nanotribological systems. Langmuir 29(45): 13760–13772 (2013)

    Google Scholar 

  240. Eder S, Vernes A, Vorlaufer G, Betz G. Molecular dynamics simulations of mixed lubrication with smooth particle post-processing. J Phys Condens Matter 23(17): 175004 (2011)

    Google Scholar 

  241. Doig M, Warrens C P, Camp P J. Structure and friction of stearic acid and oleic acid films adsorbed on iron oxide surfaces in squalane. Langmuir 30(1): 186–195 (2014)

    Google Scholar 

  242. Campen S, Green J, Lamb G, Atkinson D, Spikes H. On the Increase in Boundary Friction with Sliding Speed. Tribol Lett 48(2): 237–248 (2012)

    Google Scholar 

  243. Ewen J P, Gattinoni C, Morgan N, Spikes H, Dini D. Nonequilibrium molecular dynamics simulations of organic friction modifiers adsorbed on iron oxide surfaces. Langmuir 32(18): 4450–4463 (2016)

    Google Scholar 

  244. Ewen J P, Echeverri Restrepo S, Morgan N, Dini D. Nonequilibrium molecular dynamics simulations of stearic acid adsorbed on iron surfaces with nanoscale roughness. Tribol Int 107: 264–273 (2017)

    Google Scholar 

  245. Koike A, Yoneya M. Molecular dynamics simulations of sliding friction of Langmuir-Blodgett monolayers. J Chem Phys 105(14): 6060–6067 (1996)

    Google Scholar 

  246. Koike A, Yoneya M. Effects of molecular structure on frictional properties of langmuir-Blodgett monolayers. Langmuir 13(6): 1718–1722 (1997)

    Google Scholar 

  247. Lewis J B, Vilt S G, Rivera J L, Jennings G K, McCabe C. Frictional properties of mixed fluorocarbon/hydrocarbon silane monolayers: A simulation study. Langmuir 28(40): 14218–14226 (2012)

    Google Scholar 

  248. Lorenz C D, Chandross M, Grest G S, Stevens M J, Webb III E B. Tribological properties of alkylsilane self-assembled monolayers. Langmuir 21(25): 11744–11748 (2005)

    Google Scholar 

  249. Lorenz C D, Chandross M, Lane J M D, Grest G S. Nanotribology of water confined between hydrophilic alkylsilane self-assembled monolayers. Modell Simul Mater Sci Eng 18(3): 034005 (2010)

    Google Scholar 

  250. Black J E, Iacovella C R, Cummings P T, McCabe C. Molecular dynamics study of alkylsilane monolayers on realistic amorphous silica surfaces. Langmuir 31(10): 3086–3093 (2015)

    Google Scholar 

  251. Summers A Z, Iacovella C R, Billingsley M R, Arnold S T, Cummings P T, McCabe C. Influence of surface morphology on the shear-induced wear of alkylsilane monolayers: Molecular dynamics study. Langmuir 32(10): 2348–2359 (2016)

    Google Scholar 

  252. Tupper K J, Brenner D W. Molecular dynamics simulations of friction in self-assembled monolayers. Thin Solid Films 253(1–2): 185–189 (1994)

    Google Scholar 

  253. Ramin L, Jabbarzadeh A. Frictional properties of two alkanethiol self assembled monolayers in sliding contact: Odd-even effects. J Chem Phys 137(17): 174706 (2012)

    Google Scholar 

  254. Ramin L, Jabbarzadeh A. Effect of water on structural and frictional properties of self assembled monolayers. Langmuir 29(44): 13367–13378 (2013)

    Google Scholar 

  255. Kroto H W, Heath J R, O’Brien S C, Curl R F, Smalley R E. C60: Buckminsterfullerene. Nature 318(6042): 162–163 (1985)

    Google Scholar 

  256. Ghaednia H, Babaei H, Jackson R L, Bozack M J, Khodadadi J M. The effect of nanoparticles on thin film elasto-hydrodynamic lubrication. Appl Phys Lett 103(26): 263111 (2013)

    Google Scholar 

  257. Ewen J P, Gattinoni C, Thakkar F M, Morgan N, Spikes H A, Dini D. Nonequilibrium molecular dynamics investigation of the reduction in friction and wear by carbon nanoparticles between iron surfaces. Tribol Lett 63(3): 38 (2016)

    Google Scholar 

  258. Liang Q, Tsui O K C, Xu Y B, Li H N, Xiao X D. Effect of C60 molecular rotation on nanotribology. Phys Rev Lett 90(14): 146102 (2003)

    Google Scholar 

  259. Coffey T, Krim J. C60 molecular bearings and the phenomenon of nanomapping. Phys Rev Lett 96(18): 186104 (2006)

    Google Scholar 

  260. Lee K, Hwang Y, Cheong S, Choi Y, Kwon L, Lee J, Kim S H. Understanding the role of nanoparticles in nano-oil lubrication. Tribol Lett 35(2): 127–131 (2009)

    Google Scholar 

  261. Zhmud B, Pasalskiy B. Nanomaterials in lubricants: An industrial perspective on current research. Lubricants 1(4): 95–101 (2013)

    Google Scholar 

  262. Tevet O, Von-Huth P, Popovitz-Biro R, Rosentsveig R, Wagner H D, Tenne R. Friction mechanism of individual multilayered nanoparticles. Proc Natl Acad Sci USA 108(50): 19901–19906 (2011)

    Google Scholar 

  263. Lahouij I, Bucholz E W, Vacher B, Sinnott S B, Martin J M, Dassenoy F. Lubrication mechanisms of hollow-core inorganic fullerene-like nanoparticles: Coupling experimental and computational works. Nanotechnology 23(37): 375701 (2012)

    Google Scholar 

  264. Joly-Pottuz L, Bucholz E W, Matsumoto N, Phillpot S R, Sinnott S B, Ohmae N, Martin J M. Friction properties of carbon nano-onions from experiment and computer simulations. Tribol Lett 37(1): 75–81 (2010)

    Google Scholar 

  265. Bucholz E W, Phillpot S R, Sinnott S B. Molecular dynamics investigation of the lubrication mechanism of carbon nano-onions. Comput Mater Sci 54: 91–96 (2012)

    Google Scholar 

  266. Bucholz E W, Sinnott S B. Computational investigation of the mechanical and tribological responses of amorphous carbon nanoparticles. J Appl Phys 113(7): 073509 (2013)

    Google Scholar 

  267. Hu C Z, Bai M L, Lv J Z, Liu H, Li X J. Molecular dynamics investigation of the effect of copper nanoparticle on the solid contact between friction surfaces. Appl Surf Sci 321: 302–309 (2014)

    Google Scholar 

  268. Hu C Z, Bai M L, Lv J Z, Kou Z H, Li X J. Molecular dynamics simulation on the tribology properties of two hard nanoparticles (diamond and silicon dioxide) confined by two iron blocks. Tribol Int 90: 297–305 (2015)

    Google Scholar 

  269. Eder S J, Feldbauer G, Bianchi D, Cihak-Bayr U, Betz G, Vernes A. Applicability of macroscopic wear and friction laws on the atomic length scale. Phys Rev Lett 115(2): 025502 (2015)

    Google Scholar 

  270. Barwell F T. Wear of metals. Wear 1(4): 317–332 (1958)

    Google Scholar 

  271. Bowden F P, Tabor D. The Friction and Lubrication of Solids. Oxford (UK): Oxford University Press, 1950.

    MATH  Google Scholar 

  272. Hunter C N, Check M H, Hager C H, Voevodin A A. Tribological properties of carbon nanopearls synthesized by nickel-catalyzed chemical vapor deposition. Tribol Lett 30(3): 169–176 (2008)

    Google Scholar 

  273. Hu C Z, Bai M L, Lv J Z, Wang P, Li X J. Molecular dynamics simulation on the friction properties of nanofluids confined by idealized surfaces. Tribol Int 78: 152–159 (2014)

    Google Scholar 

  274. Hu C Z, Bai M L, Lv J Z, Li X J. Molecular dynamics simulation of mechanism of nanoparticle in improving load-carrying capacity of lubricant film. Comput Mater Sci 109: 97–103 (2015)

    Google Scholar 

  275. Peña-Parás L, Gao H Y, Maldonado-Cortés D, Vellore A, García-Pineda P, Montemayor O E, Nava K L, Martini A. Effects of substrate surface roughness and nano/micro particle additive size on friction and wear in lubricated sliding. Tribol Int 119: 88–98 (2018)

    Google Scholar 

  276. Horstemeyer M F. Integrated Computational Materials Engineering (ICME) for Metals: Using Multiscale Modeling to Invigorate Engineering Design with Science. Honoken (USA): Wiley, 2012.

    Google Scholar 

  277. Neville A, Morina A, Haque T, Voong Q. Compatibility between tribological surfaces and lubricant additives— How friction and wear reduction can be controlled by surface/lube synergies. Tribol Int 40(10–12): 1680–1695 (2007)

    Google Scholar 

  278. Van Duin A C T, Dasgupta S, Lorant F, Goddard III W A. ReaxFF: A reactive force field for hydrocarbons. J Phys Chem A 105(41): 9396–9409 (2001)

    Google Scholar 

  279. Senftle T P, Hong S, Islam M M, Kylasa S B, Zheng Y X, Shin Y K, Junkermeier C, Engel-Herbert R, Janik M J, Aktulga H M, Verstraelen T, Grama A, Van Duin A C T. The ReaxFF reactive force-field: Development, applications and future directions. NPJ Comput Mater 2(1): 15011 (2016)

    Google Scholar 

  280. Liang T, Shin Y K, Cheng Y T, Yilmaz D E, Vishnu K G, Verners O, Zou C Y, Phillpot S R, Sinnott S B, Van Duin A C T. Reactive potentials for advanced atomistic simulations. Annu Rev Mater Res 43: 109–129 (2013)

    Google Scholar 

  281. Böhm O, Pfadenhauer S, Leitsmann R, Plänitz P, Schreiner E, Schreiber M. ReaxFF+—A new reactive force field method for the accurate description of ionic systems and its application to the hydrolyzation of aluminosilicates. J Phys Chem C 120(20): 10849–10856 (2016)

    Google Scholar 

  282. Chenoweth K, Van Duin A C T, Goddard III W A. ReaxFF reactive force field for molecular dynamics simulations of hydrocarbon oxidation. J Phys Chem A 112(5): 1040–1053 (2008)

    Google Scholar 

  283. Yeon J, He X, Martini A, Kim S H. Mechanochemistry at solid surfaces: Polymerization of adsorbed molecules by mechanical shear at tribological interfaces. ACS Appl Mater Interfaces 9(3): 3142–3148 (2017)

    Google Scholar 

  284. Yue D C, Ma T B, Hu Y Z, Yeon J, Van Duin A C T, Wang H, Luo J B. Tribochemistry of phosphoric acid sheared between quartz surfaces: A reactive molecular dynamics study. J Phys Chem C 117(48): 25604–25614 (2013)

    Google Scholar 

  285. Yeon J, Adams H L, Junkermeier C E, Van Duin A C T, Tysoe W T, Martini A. Development of a ReaxFF force field for Cu/S/C/H and reactive MD simulations of methyl thiolate decomposition on Cu(100). J Phys Chem B 122(2): 888–896 (2018)

    Google Scholar 

  286. Ostadhossein A, Rahnamoun A, Wang Y X, Zhao P, Zhang S L, Crespi V H, Van Duin A C T. ReaxFF reactive force-field study of molybdenum disulfide (MoS2). J Phys Chem Lett 8(7): 631–640 (2017)

    Google Scholar 

  287. Mosey N J, Woo T K. Finite temperature structure and dynamics of zinc dialkyldithiophosphate wear inhibitors: A density functional theory and ab initio molecular dynamics study. J Phys Chem A 107(25): 5058–5070 (2003)

    Google Scholar 

  288. Mosey N J, Müser M H, Woo T K. Molecular mechanisms for the functionality of lubricant additives. Science 307(5715): 1612–1615 (2005)

    Google Scholar 

  289. Mosey N J, Woo T K. Insights into the chemical behavior of zinc dialkyldithiophosphate anti-wear additives in their isomeric and decomposed forms through molecular simulation. Tribol Int 39(9): 979–993 (2006)

    Google Scholar 

  290. Mosey N J, Woo T K. An ab initio molecular dynamics and density functional theory study of the formation of phosphate chains from metathiophosphates. Inorg Chem 45(18): 7464–7479 (2006)

    Google Scholar 

  291. Levita G, Righi M C. Effects of water intercalation and tribochemistry on MoS2 lubricity: An ab initio molecular dynamics investigation. ChemPhysChem 18(11): 1475–1480 (2017)

    Google Scholar 

  292. Onodera T, Morita Y, Suzuki A, Koyama M, Tsuboi H, Hatakeyama N, Endou A, Takaba H, Kubo M, Dassenoy F, et al. A computational chemistry study on friction of h-MoS2. Part I. Mechanism of single sheet lubrication. J Phys Chem B 113(52): 16526–16536 (2009)

    Google Scholar 

  293. Onodera T, Morita Y, Suzuki A, Sahnoun R, Koyama M, Tsuboi H, Hatakeyama N, Endou A, Takaba H, Del Carpio C A, et al. Tribochemical reaction dynamics of molybdenum dithiocarbamate on nascent iron surface: A hybrid quantum chemical/classical molecular dynamics study. J Nanosci Nanotechnol 10(4): 2495–2502 (2010)

    Google Scholar 

  294. Onodera T, Morita Y, Nagumo R, Miura R, Suzuki A, Tsuboi H, Hatakeyama N, Endou A, Takaba H, Dassenoy F, et al. A computational chemistry study on friction of h-MoS2. Part II. Friction anisotropy. J Phys Chem B 114(48): 15832–15838 (2010)

    Google Scholar 

  295. Onodera T, Martin J M, Minfray C, Dassenoy F, Miyamoto A. Antiwear chemistry of ZDDP: Coupling classical MD and tight-binding quantum chemical MD methods (TB-QCMD). Tribol Lett 50(1): 31–39 (2013)

    Google Scholar 

  296. Loehle S, Matta C, Minfray C, Le Mogne T, Martin J M, Iovine R, Obara Y, Miura R, Miyamoto A. Mixed lubrication with C18 fatty acids: Effect of unsaturation. Tribol Lett 53(1): 319–328 (2014)

    Google Scholar 

  297. Loehlé S, Matta C, Minfray C, Le Mogne T, Iovine R, Obara Y, Miyamoto A, Martin J M. Mixed lubrication of steel by C18 fatty acids revisited. Part I: Toward the formation of carboxylate. Tribol Int 82: 218–227 (2015)

    Google Scholar 

  298. Loehlé S, Matta C, Minfray C, Le Mogne T, Iovine R, Obara Y, Miyamoto A, Martin J M. Mixed lubrication of steel by C18 fatty acids revisited. Part II: Influence of some key parameters. Tribol Int 94: 207–216 (2016)

    Google Scholar 

  299. Knight C, Maupin C M, Izvekov S, Voth G A. Defining condensed phase reactive force fields from ab initio molecular dynamics simulations: The case of the hydrated excess proton. J Chem Theory Comput 6(10): 3223–3232 (2010)

    Google Scholar 

  300. Ma C R, Martin-Samos L, Fabris S, Laio A, Piccinin S. QMMMW: A wrapper for QM/MM simulations with QUANTUM ESPRESSO and LAMMPS. Comput Phys Commun 195: 191–198 (2015)

    Google Scholar 

  301. Makov G, Gattinoni C, De Vita A. Ab initio based multiscale modelling for materials science. Modell Simul Mater Sci Eng 17(8): 084008 (2009)

    Google Scholar 

  302. Bernstein N, Kermode J R, Csányi G. Hybrid atomistic simulation methods for materials systems. Rep Prog Phys 72(2): 026501 (2009)

    Google Scholar 

  303. Lin H, Truhlar D G. QM/MM: What have we learned, where are we, and where do we go from here? Theor Chem Acc 117(2): 185–199 (2007)

    Google Scholar 

  304. Singh M K, Ilg P, Espinosa-Marzal R M, Kröger M, Spencer N D. Polymer brushes under shear: Molecular dynamics simulations compared to experiments. Langmuir 31(16): 4798–4805 (2015)

    Google Scholar 

  305. Singh M K, Ilg P, Espinosa-Marzal R M, Spencer N D, Kröger M. Influence of chain stiffness, grafting density and normal load on the tribological and structural behavior of polymer brushes: A nonequilibrium-molecular-dynamics study. Polymers 8(7): 254 (2016)

    Google Scholar 

  306. Farrow M R, Chremos A, Camp P J, Harris S G, Watts R F. Molecular simulations of kinetic-friction modification in nanoscale fluid layers. Tribol Lett 42(3): 325–337 (2011)

    Google Scholar 

  307. Everaers R, Sukumaran S K, Grest G S, Svaneborg C, Sivasubramanian A, Kremer K. Rheology and microscopic topology of entangled polymeric liquids. Science 303(5659): 823–826 (2004)

    Google Scholar 

  308. Holland D M, Lockerby D A, Borg M K, Nicholls W D, Reese J M. Molecular dynamics pre-simulations for nanoscale computational fluid dynamics. Microfluid Nanofluidics 18(3): 461–474 (2015)

    Google Scholar 

  309. Smith E R, Heyes D M, Dini D, Zaki T A. Controlvolume representation of molecular dynamics. Phys Rev E 85(5): 056705 (2012)

    Google Scholar 

  310. Smith E R, Heyes D M, Dini D, Zaki T A. A localized momentum constraint for non-equilibrium molecular dynamics simulations. J Chem Phys 142(7): 074110 (2015)

    Google Scholar 

  311. O’Connell S T, Thompson P A. Molecular dynamicscontinuum hybrid computations: A tool for studying complex fluid flows. Phys Rev E 52(6): R5792–R5795 (1995)

    Google Scholar 

  312. Flekkøy E G, Wagner G, Feder J. Hybrid model for combined particle and continuum dynamics. Europhys Lett 52(3): 271–276 (2000)

    Google Scholar 

  313. Nie S Y, Chen S Y, W N E, Robbins M O. A continuum and molecular dynamics hybrid method for micro- and nano-fluid flow. J Fluid Mech 500: 55–64 (2004)

    MATH  Google Scholar 

  314. Ren W Q. Analytical and numerical study of coupled atomistic-continuum methods for fluids. J Comput Phys 227(2): 1353–1371 (2007)

    MathSciNet  MATH  Google Scholar 

  315. Mohamed K M, Mohamad A A. A review of the development of hybrid atomistic-continuum methods for dense fluids. Microfluid Nanofluidics 8(3): 283–302 (2010)

    Google Scholar 

  316. Smith E R, Trevelyan D, Ramos E. cpl-library. https://doi.org/10.5281/zenodo.46573, 2016.

    Google Scholar 

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Acknowledgements

J. P. E thanks the Engineering and Physical Sciences Research Council (EPSRC) for financial support through a Doctoral Prize Fellowship. D. D. acknowledges the EPSRC for an Established Career Fellowship EP/N025954/1. The authors also thank Hugh A. Spikes and B. D. Todd for helpful discussions.

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  1. Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London, SW7 2AZ, UK

    J. P. Ewen, D. M. Heyes & D. Dini

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James P. EWEN. He is an EPSRC Doctoral Prize Fellow in the Tribology Group at Imperial College London. He gained his master degree in chemistry from the University of Bath in 2014 and his PhD degree from Imperial College in 2017 with a Thesis entitled “Molecular dynamics simulations of lubricants and additives”. His research involves utilising molecular simulations to investigate the structure, flow, and friction behaviour of a range of tribological systems.

David. M HEYES. He is a Principal Research Fellow in the Tribology Group at Imperial College London. He received his PhD degree from the University of Manchester in 1977. He has held postdoctoral research positions in the Vitreous State Laboratory, Department of Physics, Catholic University of America, Washington DC, USA, Department of Physical Chemistry at the University of Amsterdam, and at the Department of Chemistry, Royal Holloway, University of London. He was a Royal Society (London) University Research Fellow between 1983 and 1992, first at Royal Holloway. His research interests are in the development of computer-based theoretical and modelling techniques applied to condensed matter liquid systems, principally in the areas of phase equilibria, and structural and transport properties of bulk and confined systems.

Daniele DINI. He is Head of the Tribology Group at Imperial College London. Prior to joining Imperial College in 2006, Professor Dini received the DPhil degree from the Department of Engineering Science at the University of Oxford in 2004. He now leads the advanced modelling research within the Tribology Group and collaborates closely with its experimentalists. His current individual research portfolio supports a large team of researchers focused on studies related to the modelling of tribological systems and materials. Most of these projects are multidisciplinary and range from atomic and molecular simulation of lubricant, additives and surfaces to the modelling of machine or biomechanical components. His group performs fundamental research, while successfully supporting the application of tribology in industry; the strong links with industrial partners have been recently recognised by the Imperial College President’s Award and Medal for Excellence in External Collaboration and Partnerships (2017). Professor Dini has also been the recipient of a number of other individual awards, he has also been elected a Fellow of the IMechE in 2014, and is the recipient of the prestigious EPSRC Established Career Fellowship, awarded in 2016.

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Ewen, J.P., Heyes, D.M. & Dini, D. Advances in nonequilibrium molecular dynamics simulations of lubricants and additives. Friction 6, 349–386 (2018). https://doi.org/10.1007/s40544-018-0207-9

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  • Received: 12 September 2017

  • Revised: 13 December 2017

  • Accepted: 26 December 2017

  • Published: 12 February 2018

  • Issue Date: December 2018

  • DOI: https://doi.org/10.1007/s40544-018-0207-9

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Keywords

  • molecular dynamics
  • nonequilibrium systems
  • confined fluids
  • boundary lubrication
  • elastohydrodynamic lubrication
  • tribology
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