Friction

pp 1–38 | Cite as

Advances in nonequilibrium molecular dynamics simulations of lubricants and additives

Open Access
Review Article

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.

Keywords

molecular dynamics nonequilibrium systems confined fluids boundary lubrication elastohydrodynamic lubrication tribology 

Notes

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.

References

  1. [1]
    Holmberg K, Erdemir A. Influence of tribology on global energy consumption, costs and emissions. Friction 5(3): 263–284 (2017)CrossRefGoogle Scholar
  2. [2]
    Urbakh M, Klafter J, Gourdon D, Israelachvili J. The nonlinear nature of friction. Nature 430(6999): 525–528 (2004)CrossRefGoogle Scholar
  3. [3]
    Aghababaei R, Warner D H, Molinari J F. Critical length scale controls adhesive wear mechanisms. Nat Commun 7: 11816 (2016)CrossRefGoogle Scholar
  4. [4]
    Allen M P, Tidesley D J. Computer Simulation of Liquids. Oxford (UK): Clarendon Press, 1989.Google Scholar
  5. [5]
    Metropolis N, Ulam S. The Monte Carlo method. J Am Stat Assoc 44(247): 335–341 (1949)MATHCrossRefGoogle Scholar
  6. [6]
    Goldstein M. Viscous liquids and the glass transition: A potential energy barrier picture. J Chem Phys 51(9): 3728–3739 (1969)CrossRefGoogle Scholar
  7. [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)CrossRefGoogle Scholar
  8. [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)CrossRefGoogle Scholar
  9. [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)CrossRefGoogle Scholar
  10. [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)CrossRefGoogle Scholar
  11. [11]
    Szlufarska I, Chandross M, Carpick R W. Recent advances in single-asperity nanotribology. J Phys D Appl Phys 41(12): 123001 (2008)CrossRefGoogle Scholar
  12. [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)CrossRefGoogle Scholar
  13. [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)CrossRefGoogle Scholar
  14. [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)CrossRefGoogle Scholar
  15. [15]
    Alder B J, Wainwright T E. Phase transition for a hard sphere system. J Chem Phys 27(5): 1208–1209 (1957)CrossRefGoogle Scholar
  16. [16]
    Frenkel D. Entropy-driven phase transitions. Phys. A 263(1–4): 26–38 (1999)CrossRefGoogle Scholar
  17. [17]
    Rahman A. Correlations in the motion of atoms in liquid argon. Phys Rev 136(2A): 405–411 (1964)CrossRefGoogle Scholar
  18. [18]
    Eyring H, Ree T. Significant liquid structures, VI. The vacancy theory of liquids. Proc Natl Acad Sci USA 47(4): 526–537 (1961)CrossRefGoogle Scholar
  19. [19]
    Ediger M D. Spatially heterogeneous dynamics in supercooled liquids. Annu Rev Phys Chem 51: 99–128 (2000)CrossRefGoogle Scholar
  20. [20]
    Edward J T. Molecular volumes and the Stokes-Einstein equation. J Chem Educ 47(4): 261 (1970)CrossRefGoogle Scholar
  21. [21]
    Hansen J P, McDonald I R. Theory of Simple Liquids. 4th ed. Amsterdam (Netherlands): Academic Press, 2013.MATHGoogle Scholar
  22. [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)CrossRefGoogle Scholar
  23. [23]
    Hefland E. Transport coefficients from dissipation in a canonical ensemble. Phys Rev 119(1): 1–9 (1960)MathSciNetCrossRefGoogle Scholar
  24. [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)MathSciNetCrossRefGoogle Scholar
  25. [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)MathSciNetCrossRefGoogle Scholar
  26. [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)CrossRefGoogle Scholar
  27. [27]
    Ashurst W T, Hoover W G. Dense-fluid shear viscosity via nonequilibrium molecular dynamics. Phys Rev A 11(2): 658–678 (1975)CrossRefGoogle Scholar
  28. [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)CrossRefGoogle Scholar
  29. [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)CrossRefGoogle Scholar
  30. [30]
    Evans D J, Morriss G P. Nonlinear-response theory for steady planar Couette flow. Phys Rev A 30(3): 1528–1530 (1984)CrossRefGoogle Scholar
  31. [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)CrossRefGoogle Scholar
  32. [32]
    Evans D J, Morriss G P. Statistical Mechanics of Nonequilibrium Liquids. 2nd ed. Cambridge (UK): Cambridge University Press, 2008.MATHCrossRefGoogle Scholar
  33. [33]
    Todd B D, Daivis P J. Nonequilibrium Molecular Dynamics: Theory, Algorithms and Applications. Cambridge (UK): Cambridge University Press, 2017.MATHCrossRefGoogle Scholar
  34. [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)CrossRefGoogle Scholar
  35. [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)CrossRefGoogle Scholar
  36. [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)CrossRefGoogle Scholar
  37. [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)CrossRefGoogle Scholar
  38. [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)CrossRefGoogle Scholar
  39. [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)CrossRefGoogle Scholar
  40. [40]
    Evans D J, Morriss G P. Transient-time-correlation functions and the rheology of fluids. Phys Rev A 38(8): 4142–4148 (1988)CrossRefGoogle Scholar
  41. [41]
    Spikes H, Zhang J. History, origins and prediction of elastohydrodynamic friction. Tribol Lett 56(1): 1–25 (2014)CrossRefGoogle Scholar
  42. [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)CrossRefGoogle Scholar
  43. [43]
    Andersen H C. Molecular dynamics simulations at constant pressure and/or temperature. J Chem Phys 72(4): 2384–2393 (1980)CrossRefGoogle Scholar
  44. [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)CrossRefGoogle Scholar
  45. [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)CrossRefGoogle Scholar
  46. [46]
    Español P, Warren P. Statistical mechanics of dissipative particle dynamics. Eur Lett 30(4): 191–196 (1995)CrossRefGoogle Scholar
  47. [47]
    Nosé S. A molecular dynamics method for simulations in the canonical ensemble. Mol Phys 52(2): 255–268 (1984)MathSciNetCrossRefGoogle Scholar
  48. [48]
    Hoover W G. Canonical dynamics: Equilibrium phase-space distributions. Phys Rev A 31(3): 1695–1697 (1985)CrossRefGoogle Scholar
  49. [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)CrossRefGoogle Scholar
  50. [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)CrossRefGoogle Scholar
  51. [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)CrossRefGoogle Scholar
  52. [52]
    Delhommelle J, Evans D J. Configurational temperature profile in confined fluids. II. Molecular fluids. J Chem Phys 114(14): 6236–6241 (2001)CrossRefGoogle Scholar
  53. [53]
    Braga C, Travis K P. A configurational temperature Nosé-Hoover thermostat. J Chem Phys 123(13): 134101 (2005)CrossRefGoogle Scholar
  54. [54]
    Yong X, Zhang L T. Thermostats and thermostat strategies for molecular dynamics simulations of nanofluidics. J Chem Phys 138(8): 084503 (2013)CrossRefGoogle Scholar
  55. [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)CrossRefGoogle Scholar
  56. [56]
    Bernardi S, Todd B D, Searles D J. Thermostating highly confined fluids. J Chem Phys 132(24): 244706 (2010)CrossRefGoogle Scholar
  57. [57]
    Martini A, Hsu H Y, Patankar N A, Lichter S. Slip at high shear rates. Phys Rev Lett 100(20): 206001 (2008)CrossRefGoogle Scholar
  58. [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)CrossRefGoogle Scholar
  59. [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)CrossRefGoogle Scholar
  60. [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)CrossRefGoogle Scholar
  61. [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)CrossRefGoogle Scholar
  62. [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)CrossRefGoogle Scholar
  63. [63]
    Lupkowski M, Van Swol F. Ultrathin films under shear. J Chem Phys 95(3): 1995–1998 (1991)CrossRefGoogle Scholar
  64. [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)CrossRefGoogle Scholar
  65. [65]
    Snook I K, Van Megen W. Solvation forces in simple dense fluids. I. J Chem Phys 72(5): 2907–2913 (1980)CrossRefGoogle Scholar
  66. [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)CrossRefGoogle Scholar
  67. [67]
    Persson B N J, Mugele F. Squeeze-out and wear: Fundamental principles and applications. J Phys Condens Matter 16(10): R295–R355 (2004)CrossRefGoogle Scholar
  68. [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)CrossRefGoogle Scholar
  69. [69]
    Leng Y S. Hydration force and dynamic squeeze-out of hydration water under subnanometer confinement. J Phys Condens Matter 20(35): 354017 (2008)CrossRefGoogle Scholar
  70. [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)CrossRefGoogle Scholar
  71. [71]
    Lei Y J, Leng Y S. Stick-slip friction and energy dissipation in boundary lubrication. Phys Rev Lett 107(14): 147801 (2011)CrossRefGoogle Scholar
  72. [72]
    Ewald P P. Die Berechnung optischer und elektrostatischer Gitterpotentiale. Ann Phys 369(3): 253–287 (1921)MATHCrossRefGoogle Scholar
  73. [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)CrossRefGoogle Scholar
  74. [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)CrossRefGoogle Scholar
  75. [75]
    Yeh I C, Berkowitz M L. Ewald summation for systems with slab geometry. J Chem Phys 111(7): 3155–3162 (1999)CrossRefGoogle Scholar
  76. [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)CrossRefGoogle Scholar
  77. [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)CrossRefGoogle Scholar
  78. [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)CrossRefGoogle Scholar
  79. [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)CrossRefGoogle Scholar
  80. [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)CrossRefGoogle Scholar
  81. [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)CrossRefGoogle Scholar
  82. [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)CrossRefGoogle Scholar
  83. [83]
    Bernardi S, Brookes S J, Searles D J, Evans D J. Response theory for confined systems. J Chem Phys 137(7): 074114 (2012)CrossRefGoogle Scholar
  84. [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)CrossRefGoogle Scholar
  85. [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)CrossRefGoogle Scholar
  86. [86]
    Bocquet L, Barrat J L. On the Green-Kubo relationship for the liquid-solid friction coefficient. J Chem Phys 139(4): 044704 (2013)CrossRefGoogle Scholar
  87. [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)CrossRefGoogle Scholar
  88. [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)CrossRefGoogle Scholar
  89. [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)CrossRefGoogle Scholar
  90. [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)CrossRefGoogle Scholar
  91. [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)CrossRefGoogle Scholar
  92. [92]
    Len M, Ramasamy U S, Lichter S, Martini A. Thickening mechanisms of polyisobutylene in polyalphaolefin. Tribol Lett 66(1): 5 (2018)CrossRefGoogle Scholar
  93. [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)CrossRefGoogle Scholar
  94. [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)CrossRefGoogle Scholar
  95. [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)CrossRefGoogle Scholar
  96. [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)CrossRefGoogle Scholar
  97. [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)CrossRefGoogle Scholar
  98. [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)CrossRefGoogle Scholar
  99. [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)CrossRefGoogle Scholar
  100. [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)CrossRefGoogle Scholar
  101. [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)CrossRefGoogle Scholar
  102. [102]
    Thompson P A, Robbins M O. Origin of stick-slip motion in boundary lubrication. Science 250(4982): 792–794 (1990)CrossRefGoogle Scholar
  103. [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)CrossRefGoogle Scholar
  104. [104]
    Leng Y, Cummings P T. Fluidity of hydration layers nanoconfined between mica surfaces. Phys Rev Lett 94(2): 026101 (2005)CrossRefGoogle Scholar
  105. [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)CrossRefGoogle Scholar
  106. [106]
    Zhang J F, Todd B D, Travis K P. Viscosity of confined inhomogeneous nonequilibrium fluids. J Chem Phys 121(21): 10778–10786 (2004)CrossRefGoogle Scholar
  107. [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)CrossRefGoogle Scholar
  108. [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)CrossRefGoogle Scholar
  109. [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)CrossRefGoogle Scholar
  110. [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)CrossRefGoogle Scholar
  111. [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)CrossRefGoogle Scholar
  112. [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)MATHCrossRefGoogle Scholar
  113. [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)CrossRefGoogle Scholar
  114. [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)CrossRefGoogle Scholar
  115. [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)CrossRefGoogle Scholar
  116. [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)CrossRefGoogle Scholar
  117. [117]
    Siepmann J I, Karaborni S, Smit B. Simulating the critical behaviour of complex fluids. Nature 365(6444): 330–332 (1993)CrossRefGoogle Scholar
  118. [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)CrossRefGoogle Scholar
  119. [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)CrossRefGoogle Scholar
  120. [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)CrossRefGoogle Scholar
  121. [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)CrossRefGoogle Scholar
  122. [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)CrossRefGoogle Scholar
  123. [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)CrossRefGoogle Scholar
  124. [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)CrossRefGoogle Scholar
  125. [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)CrossRefGoogle Scholar
  126. [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)CrossRefGoogle Scholar
  127. [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. [128]
    Carreau P J. Rheological equations from molecular network theories. J Rheol 16(1): 99–127 (1972)Google Scholar
  129. [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)CrossRefGoogle Scholar
  130. [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)CrossRefGoogle Scholar
  131. [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)CrossRefGoogle Scholar
  132. [132]
    Eyring H. Viscosity, plasticity, and diffusion as examples of absolute reaction rates. J Chem Phys 4(4): 283–291 (1936)CrossRefGoogle Scholar
  133. [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)CrossRefGoogle Scholar
  134. [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)CrossRefGoogle Scholar
  135. [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)CrossRefGoogle Scholar
  136. [136]
    Magda J J, Tirrell M, Davis H T. Molecular dynamics of narrow, liquid-filled pores. J Chem Phys 83(4): 1888–1901 (1985)CrossRefGoogle Scholar
  137. [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)CrossRefGoogle Scholar
  138. [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. [139]
    Israelachvili J N. Measurement of the viscosity of liquids in very thin films. J Colloid Interface Sci 110(1): 263–271 (1986)CrossRefGoogle Scholar
  140. [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)CrossRefGoogle Scholar
  141. [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)CrossRefGoogle Scholar
  142. [142]
    Granick S. Motions and relaxations of confined liquids. Science 253(5026): 1374–1379 (1991)CrossRefGoogle Scholar
  143. [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)CrossRefGoogle Scholar
  144. [144]
    Klein J, Kumacheva E. Confinement-induced phase transitions in simple liquids. Science 269(5225): 816–819 (1995)CrossRefGoogle Scholar
  145. [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)CrossRefGoogle Scholar
  146. [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)CrossRefGoogle Scholar
  147. [147]
    Docherty H, Cummings P T. Direct evidence for fluidsolid transition of nanoconfined fluids. Soft Matter 6(8): 1640–1643 (2010)CrossRefGoogle Scholar
  148. [148]
    Van Alsten J, Granick S. Molecular tribometry of ultrathin liquid films. Phys Rev Lett 61(22): 2570–2573 (1988)CrossRefGoogle Scholar
  149. [149]
    Lin Z Q, Granick S. Platinum nanoparticles at mica surfaces. Langmuir 19(17): 7061–7070 (2003)CrossRefGoogle Scholar
  150. [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. [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)CrossRefGoogle Scholar
  152. [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)CrossRefGoogle Scholar
  153. [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)CrossRefGoogle Scholar
  154. [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)CrossRefGoogle Scholar
  155. [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)CrossRefGoogle Scholar
  156. [156]
    Zhu Y X, Granick S. Superlubricity: A paradox about confined fluids resolved. Phys Rev Lett 93(9): 096101 (2004)CrossRefGoogle Scholar
  157. [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)CrossRefGoogle Scholar
  158. [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)CrossRefGoogle Scholar
  159. [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)CrossRefGoogle Scholar
  160. [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)CrossRefGoogle Scholar
  161. [161]
    Hu Y Z, Zhu D. A full numerical solution to the mixed lubrication in point contacts. J Tribol 122(1): 1–9 (1999)CrossRefGoogle Scholar
  162. [162]
    Robbins M O, Smith E D. Connecting molecular-scale and macroscopic tribology. Langmuir 12(19): 4543–4547 (1996)CrossRefGoogle Scholar
  163. [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)CrossRefGoogle Scholar
  164. [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)CrossRefGoogle Scholar
  165. [165]
    Dhinojwala A, Bae S C, Granick S. Shear-induced dilation of confined liquid films. Tribol Lett 9(1–2): 55–62 (2000)CrossRefGoogle Scholar
  166. [166]
    Zhu Y X, Granick S. Rate-dependent slip of Newtonian liquid at smooth surfaces. Phys Rev Lett 87(9): 096105 (2001)CrossRefGoogle Scholar
  167. [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)CrossRefGoogle Scholar
  168. [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)CrossRefGoogle Scholar
  169. [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)CrossRefGoogle Scholar
  170. [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)CrossRefGoogle Scholar
  171. [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)CrossRefGoogle Scholar
  172. [172]
    Pit R, Hervet H, Leger L. Direct experimental evidence of slip in hexadecane: Solid interfaces. Phys Rev Lett 85(5): 980–983 (2000)CrossRefGoogle Scholar
  173. [173]
    Blake T D. Slip between a liquid and a solid: D. M. Tolstoi’s (1952) theory reconsidered. Colloids Surf 47: 135–145 (1990)CrossRefGoogle Scholar
  174. [174]
    Spikes H, Granick S. Equation for slip of simple liquids at smooth solid surfaces. Langmuir 19(12): 5065–5071 (2003)CrossRefGoogle Scholar
  175. [175]
    De Gennes P G. On fluid/wall slippage. Langmuir 18(9): 3413–3414 (2002)CrossRefGoogle Scholar
  176. [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)CrossRefGoogle Scholar
  177. [177]
    Vadakkepatt A, Dong Y L, Lichter S, Martini A. Effect of molecular structure on liquid slip. Phys Rev E 84(6): 066311 (2011)CrossRefGoogle Scholar
  178. [178]
    Majumdar A, Bhushan B. Role of fractal geometry in roughness characterization and contact mechanics of surfaces. J Tribol 112(2): 205–216 (1990)CrossRefGoogle Scholar
  179. [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)CrossRefGoogle Scholar
  180. [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)MATHCrossRefGoogle Scholar
  181. [181]
    Zhu Y X, Granick S. Limits of the hydrodynamic no-slip boundary condition. Phys Rev Lett 88(10): 106102 (2002)CrossRefGoogle Scholar
  182. [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)CrossRefGoogle Scholar
  183. [183]
    Ponjavic A, Wong J S S. The effect of boundary slip on elastohydrodynamic lubrication. RSC Adv 4(40): 20821–20829 (2014)CrossRefGoogle Scholar
  184. [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)CrossRefGoogle Scholar
  185. [185]
    Martinie L, Vergne P. Lubrication at extreme conditions: A discussion about the limiting shear stress concept. Tribol Lett 63(2): 21 (2016)CrossRefGoogle Scholar
  186. [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)CrossRefGoogle Scholar
  187. [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)CrossRefGoogle Scholar
  188. [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)CrossRefGoogle Scholar
  189. [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)CrossRefGoogle Scholar
  190. [190]
    Butler S, Harrowell P. Factors determining crystal-liquid coexistence under shear. Nature 415(6875): 1008–1011 (2002)CrossRefGoogle Scholar
  191. [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)CrossRefGoogle Scholar
  192. [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)CrossRefGoogle Scholar
  193. [193]
    Varnik F, Bocquet L, Barrat J L, Berthier L. Shear localization in a model glass. Phys Rev Lett 90(9): 095702 (2003)CrossRefGoogle Scholar
  194. [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)CrossRefGoogle Scholar
  195. [195]
    Heyes D M. The Liquid State: Applications of Molecular Simulations. New York (USA): Wiley, 1998.Google Scholar
  196. [196]
    Bair S, Winer W O. The high pressure high shear stress rheology of liquid lubricants. J Tribol 114(1): 1–9 (1992)CrossRefGoogle Scholar
  197. [197]
    Bair S, Qureshi F, Winer W O. Observations of shear localization in liquid lubricants under pressure. J Tribol 115(3): 507–513 (1993)CrossRefGoogle Scholar
  198. [198]
    Bair S, McCabe C. A study of mechanical shear bands in liquids at high pressure. Tribol Int 37(10): 783–789 (2004)CrossRefGoogle Scholar
  199. [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)CrossRefGoogle Scholar
  200. [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)CrossRefGoogle Scholar
  201. [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)CrossRefGoogle Scholar
  202. [202]
    Šperka P, Křupka I, Hartl M. Evidence of plug flow in rolling-sliding elastohydrodynamic contact. Tribol Lett 54(2): 151–160 (2014)CrossRefGoogle Scholar
  203. [203]
    Sperka P, Krupka I, Hartl M. Lubricant flow in thin-film elastohydrodynamic contact under extreme conditions. Friction 4(4): 380–390 (2016)CrossRefGoogle Scholar
  204. [204]
    Zhang J, Tan A, Spikes H. Effect of base oil structure on elastohydrodynamic friction. Tribol Lett 65(1): 13 (2017)CrossRefGoogle Scholar
  205. [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)CrossRefGoogle Scholar
  206. [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)CrossRefGoogle Scholar
  207. [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)CrossRefGoogle Scholar
  208. [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)CrossRefGoogle Scholar
  209. [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)CrossRefGoogle Scholar
  210. [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)CrossRefGoogle Scholar
  211. [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)CrossRefGoogle Scholar
  212. [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)CrossRefGoogle Scholar
  213. [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)CrossRefGoogle Scholar
  214. [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)CrossRefGoogle Scholar
  215. [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)CrossRefGoogle Scholar
  216. [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)CrossRefGoogle Scholar
  217. [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)CrossRefGoogle Scholar
  218. [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)CrossRefGoogle Scholar
  219. [219]
    Spikes H. Friction modifier additives. Tribol Lett 60(1): 5 (2015)CrossRefGoogle Scholar
  220. [220]
    Beltzer M, Jahanmir S. Role of dispersion interactions between hydrocarbon chains in boundary lubrication. ASLE Trans 30(1): 47–54 (1987)CrossRefGoogle Scholar
  221. [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)CrossRefGoogle Scholar
  222. [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)CrossRefGoogle Scholar
  223. [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)CrossRefGoogle Scholar
  224. [224]
    Rai B, Pradip P. Modeling self-assembly of surfactants at interfaces. Curr Opin Chem Eng 15: 84–94 (2017)CrossRefGoogle Scholar
  225. [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)CrossRefGoogle Scholar
  226. [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)CrossRefGoogle Scholar
  227. [227]
    Karaborni S, Verbist G. Effect of chain conformation on the tilt behaviour in langmuir monolayers. Eur Lett 27(6): 467–472 (1994)CrossRefGoogle Scholar
  228. [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)CrossRefGoogle Scholar
  229. [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)CrossRefGoogle Scholar
  230. [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)CrossRefGoogle Scholar
  231. [231]
    Greenfield M L, Ohtani H. Packing of simulated friction modifier additives under confinement. Langmuir 21(16): 7568–7578 (2005)CrossRefGoogle Scholar
  232. [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)CrossRefGoogle Scholar
  233. [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)CrossRefGoogle Scholar
  234. [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)CrossRefGoogle Scholar
  235. [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)CrossRefGoogle Scholar
  236. [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)CrossRefGoogle Scholar
  237. [237]
    Kong Y C, Tildesley D J, Alejandre J. The molecular dynamics simulation of boundary-layer lubrication. Mol Phys 92(1): 7–18 (1997)CrossRefGoogle Scholar
  238. [238]
    Kong Y C, Tildesley D J. The effect of molecular geometry on boundary layer lubrication. Mol Simul 22(2): 149–168 (1999)CrossRefGoogle Scholar
  239. [239]
    Eder S J, Vernes A, Betz G. On the derjaguin offset in boundary-lubricated nanotribological systems. Langmuir 29(45): 13760–13772 (2013)CrossRefGoogle Scholar
  240. [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)CrossRefGoogle Scholar
  241. [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)CrossRefGoogle Scholar
  242. [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)CrossRefGoogle Scholar
  243. [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)CrossRefGoogle Scholar
  244. [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)CrossRefGoogle Scholar
  245. [245]
    Koike A, Yoneya M. Molecular dynamics simulations of sliding friction of Langmuir-Blodgett monolayers. J Chem Phys 105(14): 6060–6067 (1996)CrossRefGoogle Scholar
  246. [246]
    Koike A, Yoneya M. Effects of molecular structure on frictional properties of langmuir-Blodgett monolayers. Langmuir 13(6): 1718–1722 (1997)CrossRefGoogle Scholar
  247. [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)CrossRefGoogle Scholar
  248. [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)CrossRefGoogle Scholar
  249. [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)CrossRefGoogle Scholar
  250. [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)CrossRefGoogle Scholar
  251. [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)CrossRefGoogle Scholar
  252. [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)CrossRefGoogle Scholar
  253. [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)CrossRefGoogle Scholar
  254. [254]
    Ramin L, Jabbarzadeh A. Effect of water on structural and frictional properties of self assembled monolayers. Langmuir 29(44): 13367–13378 (2013)CrossRefGoogle Scholar
  255. [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)CrossRefGoogle Scholar
  256. [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)CrossRefGoogle Scholar
  257. [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)CrossRefGoogle Scholar
  258. [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)CrossRefGoogle Scholar
  259. [259]
    Coffey T, Krim J. C60 molecular bearings and the phenomenon of nanomapping. Phys Rev Lett 96(18): 186104 (2006)CrossRefGoogle Scholar
  260. [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)CrossRefGoogle Scholar
  261. [261]
    Zhmud B, Pasalskiy B. Nanomaterials in lubricants: An industrial perspective on current research. Lubricants 1(4): 95–101 (2013)CrossRefGoogle Scholar
  262. [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)CrossRefGoogle Scholar
  263. [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)CrossRefGoogle Scholar
  264. [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)CrossRefGoogle Scholar
  265. [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)CrossRefGoogle Scholar
  266. [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)CrossRefGoogle Scholar
  267. [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)CrossRefGoogle Scholar
  268. [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)CrossRefGoogle Scholar
  269. [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)CrossRefGoogle Scholar
  270. [270]
    Barwell F T. Wear of metals. Wear 1(4): 317–332 (1958)CrossRefGoogle Scholar
  271. [271]
    Bowden F P, Tabor D. The Friction and Lubrication of Solids. Oxford (UK): Oxford University Press, 1950.MATHGoogle Scholar
  272. [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)CrossRefGoogle Scholar
  273. [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)CrossRefGoogle Scholar
  274. [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)CrossRefGoogle Scholar
  275. [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)CrossRefGoogle Scholar
  276. [276]
    Horstemeyer M F. Integrated Computational Materials Engineering (ICME) for Metals: Using Multiscale Modeling to Invigorate Engineering Design with Science. Honoken (USA): Wiley, 2012.CrossRefGoogle Scholar
  277. [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)CrossRefGoogle Scholar
  278. [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)CrossRefGoogle Scholar
  279. [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)CrossRefGoogle Scholar
  280. [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)CrossRefGoogle Scholar
  281. [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)CrossRefGoogle Scholar
  282. [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)CrossRefGoogle Scholar
  283. [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)CrossRefGoogle Scholar
  284. [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)CrossRefGoogle Scholar
  285. [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)CrossRefGoogle Scholar
  286. [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)CrossRefGoogle Scholar
  287. [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)CrossRefGoogle Scholar
  288. [288]
    Mosey N J, Müser M H, Woo T K. Molecular mechanisms for the functionality of lubricant additives. Science 307(5715): 1612–1615 (2005)CrossRefGoogle Scholar
  289. [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)CrossRefGoogle Scholar
  290. [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)CrossRefGoogle Scholar
  291. [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)CrossRefGoogle Scholar
  292. [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)CrossRefGoogle Scholar
  293. [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)CrossRefGoogle Scholar
  294. [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)CrossRefGoogle Scholar
  295. [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)CrossRefGoogle Scholar
  296. [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)CrossRefGoogle Scholar
  297. [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)CrossRefGoogle Scholar
  298. [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)CrossRefGoogle Scholar
  299. [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)CrossRefGoogle Scholar
  300. [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)CrossRefGoogle Scholar
  301. [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)CrossRefGoogle Scholar
  302. [302]
    Bernstein N, Kermode J R, Csányi G. Hybrid atomistic simulation methods for materials systems. Rep Prog Phys 72(2): 026501 (2009)CrossRefGoogle Scholar
  303. [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)CrossRefGoogle Scholar
  304. [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)CrossRefGoogle Scholar
  305. [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)CrossRefGoogle Scholar
  306. [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)CrossRefGoogle Scholar
  307. [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)CrossRefGoogle Scholar
  308. [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)CrossRefGoogle Scholar
  309. [309]
    Smith E R, Heyes D M, Dini D, Zaki T A. Controlvolume representation of molecular dynamics. Phys Rev E 85(5): 056705 (2012)CrossRefGoogle Scholar
  310. [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)CrossRefGoogle Scholar
  311. [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)CrossRefGoogle Scholar
  312. [312]
    Flekkøy E G, Wagner G, Feder J. Hybrid model for combined particle and continuum dynamics. Europhys Lett 52(3): 271–276 (2000)CrossRefGoogle Scholar
  313. [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)MATHCrossRefGoogle Scholar
  314. [314]
    Ren W Q. Analytical and numerical study of coupled atomistic-continuum methods for fluids. J Comput Phys 227(2): 1353–1371 (2007)MathSciNetMATHCrossRefGoogle Scholar
  315. [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)CrossRefGoogle Scholar
  316. [316]
    Smith E R, Trevelyan D, Ramos E. cpl-library. https://doi.org/10.5281/zenodo.46573, 2016.Google Scholar

Copyright information

© The author(s) 2018

Open Access: The articles published in this journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringImperial College LondonLondonUK

Personalised recommendations