Constraints in Molecular Dynamics, Nonequilibrium Processes in Fluids via Computer Simulations

  • Siegfried Hess


The basic features of computer simulations for fluids are presented based on the molecular dynamics approach. Technical details, in particular the interaction potentials and the scaling of physical variables, the application of constraints to the dynamics, e.g., in order to simulate a thermostat, and the choice of integrators for the numerical solution of the equations of motion are discussed. Some examples which can be used as numerical exercises are outlined. The method of nonequilibrium molecular dynamics (NEMD) is introduced. Simulations of relaxation phenomena are mentioned briefly. The main emphasis is on simulations of a plane Couette flow as an example of a stationary transport process. Procedures to extract rheological properties, such as the (non-Newtonian) viscosity, normal pressure differences, and information on shear-flow-induced structural changes, are given, firstly for fluids composed of spherical particles. This comprises simple liquids and dense colloidal dispersions, in which the states far away from equilibrium studied in NEMD are accessible in experiments. Secondly, simulations for complex fluids, in particular polymeric melts, nematic and smectic liquid crystals, as well as ferrofluids and magnetorheological fluids are discussed.


Shear Rate Nematic Liquid Crystal Pressure Tensor Static Structure Factor Magnetorheological Fluid 
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  1. [1]
    W.T. Ashurst and W.G. Hoover, Am. Phys. Soc. 17, 1196 (1972)Google Scholar
  2. [1]
    Phys. Rev. Lett. 31, 206 (1972)ADSCrossRefGoogle Scholar
  3. [2]
    A.W. Lees and S.F. Edwards, J. Phys. C 5, 1921 (1972)ADSCrossRefGoogle Scholar
  4. [3]
    G. Ciccotti, G. Jacucci, and I.R. McDonald, Phys. Rev. A 13, 426 (1975)ADSCrossRefGoogle Scholar
  5. [3a]
    J. Stat. Phys. 21, 1 (1979)ADSCrossRefGoogle Scholar
  6. [3b]
    C. Trozzi and G. Ciccotti, Phys. Rev. A 29, 916 (1984)ADSCrossRefGoogle Scholar
  7. [4]
    W.G. Hoover, Annu. Rev. Phys. Chem. 34, 103 (1983)ADSCrossRefGoogle Scholar
  8. [4a]
    D.J. Evans and G.P. Morriss, Comp. Phys. Rep. 1, 287 (1984)ADSCrossRefGoogle Scholar
  9. [4a]
    D.J. Evans and W.G. Hoover, Ann. Rev. Fluid Mech. 18, 243 (1986)ADSMathSciNetCrossRefGoogle Scholar
  10. [5]
    B.D. Holian and D.J. Evans, J. Chem. Phys. 78, 5157 (1983)ADSCrossRefGoogle Scholar
  11. [6]
    D.M. Heyes, J. Chem. Soc. Faraday II, 82, 1365 (1986)CrossRefGoogle Scholar
  12. [7]
    W.G. Hoover, Molecular Dynamics, (Springer, Berlin 1986)Google Scholar
  13. [7]
    Computational Statistical Mechanics, (Elsevier, Amsterdam 1991)Google Scholar
  14. [7]
    Physica A 194, 450 (1993)ADSCrossRefGoogle Scholar
  15. [8]
    M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids, (Clarendon, Oxford 1987)MATHGoogle Scholar
  16. [9]
    R. Haberlandt, S. Fritzsche, G. Peinel, and K. Heinzinger, Molekular-Dynamik, (Vieweg, Braunschweig 1995)Google Scholar
  17. [10]
    S. Hess and W. Loose, in Constitutive Laws and Micro structure, eds. D. Axelrad and W. Muschik, (Springer, Berlin 1988), p. 92Google Scholar
  18. [11]
    W. Loose and S. Hess, Phys. Rev. Lett. 58, 2443 (1988)ADSCrossRefGoogle Scholar
  19. [11]
    Phys. Rev. A 37, 2099 (1988)ADSCrossRefGoogle Scholar
  20. [12]
    S. Hess, in Rheological Modelling: Thermodynamical and Statistical Approaches, eds. J. Casas-Vázques and D. Jou, Lecture Notes in Physics 381, (Springer, Berlin 1991), p. 51CrossRefGoogle Scholar
  21. [12a]
    Physikal. Blätter 44, 325 (1988)Google Scholar
  22. [13]
    S. Hess and W. Loose, Physica A 162, 138 (1989)ADSCrossRefGoogle Scholar
  23. [14]
    W. Loose and S. Hess, Rheol. Acta 28, 91 (1989)CrossRefGoogle Scholar
  24. [14a]
    W. Loose and S. Hess, in Microscopic Simulation of Complex Flows, ed. M. Mareschal, NATO ASI series, (Plenum, New York 1990)Google Scholar
  25. [14b]
    S. Hess and W. Loose, Ber. Bunsenges. Phys. Chem. 94, 216 (1990)Google Scholar
  26. [15]
    W. Loose and G. Ciccotti, Phys. Rev. 45, 3859 (1992)ADSCrossRefGoogle Scholar
  27. [16]
    W.C. Gear, Numerical Initial Value Problems in Ordinary Differential Equations, (Prentice Hall, London 1971)MATHGoogle Scholar
  28. [17]
    S.K. Gray, D.W. Noid, and B.G. Sumpter, J. Chem. Phys. 101, 4062 (1994)ADSCrossRefGoogle Scholar
  29. [18]
    W.G. Hoover, O. Kum, and N.E. Owens, J. Chem. Phys. 103, 1530 (1995)ADSCrossRefGoogle Scholar
  30. [19]
    S. Hess, Physica A 127, 509 (1984)MATHADSCrossRefGoogle Scholar
  31. [19a] Physique 46, C3–191 (1985)Google Scholar
  32. [20]
    S. Hess, Phys. Lett. 105 A, 113 (1984)CrossRefGoogle Scholar
  33. [21]
    S. Hess, M. Kröger, W. Loose, C. Pereira Borgmeyer, R. Schramek, H. Voigt, and T. Weider, Simple and Complex Fluids Under Shear, in eds. K. Binder and G. Ciccotti in pressGoogle Scholar
  34. [22]
    G. Bossis, Y Grasselli, E. Lemaire, A. Meunier, J.F. Brady, and T. Phung, Physica Scripta T 49, 89 (1993)ADSCrossRefGoogle Scholar
  35. [23]
    O. Hess, W. Loose, T. Weider, and S. Hess, Physica B 156/157, 505 (1989)ADSCrossRefGoogle Scholar
  36. [23a]
    T. Weider, U. Stottut, W. Loose, and S. Hess, Physica A 174, 1 (1991)ADSCrossRefGoogle Scholar
  37. [23b]
    S. Hess, D. Baalss, O. Hess, W. Loose, J. F. Schwarzl, U. Stottut and T. Weider in Continuum Models and Discrete Systems, ed. G. A. Maugin, (Longman, Essex 1990), p. 18Google Scholar
  38. [24]
    H.M. Laun, R. Bung, S. Hess, W. Loose, O. Hess, K. Hahn, E. Hädicke, R. Hingmann, F. Schmidt, and P. Lindner, J. Rheol. 36, 743 (1992)ADSCrossRefGoogle Scholar
  39. [25]
    J.J. Erpenbeck, Phys. Rev. Lett. 52, 1333 (1984)ADSCrossRefGoogle Scholar
  40. [26]
    S. Hess, J. Mécanique Théor. Appl., Numéro spécial, 1 (1985)Google Scholar
  41. [26a]
    Int. J. Thermophys 6, 657 (1985)ADSCrossRefGoogle Scholar
  42. [27]
    S. Hess, J. Non-Newtonian Fluid Mech. 23, 187 (1987)MathSciNetCrossRefGoogle Scholar
  43. [28]
    P. Bartlett and P.N. Pusey, Physica A 194, 415 (1993)ADSCrossRefGoogle Scholar
  44. [29]
    J.P. Ryckaert, Mol. Phys. 55, 549 (1985)ADSCrossRefGoogle Scholar
  45. [30]
    M. Kröger and S. Hess, Physica A 195, 336 (1993)ADSCrossRefGoogle Scholar
  46. [31]
    M. Kröger, W. Loose, and S. Hess, J. Rheol. 37, 1057 (1993)ADSCrossRefGoogle Scholar
  47. [31a]
    M. Kröger, Rheologie und Struktur von Polymerschmelzen, (W&T, Berlin 1995)Google Scholar
  48. [32]
    M. Kröger, Rheology 95, 66 (1995)Google Scholar
  49. [33]
    K. Kremer and G.S. Grest, J. Chem. Phys. 92, 5057 (1990)ADSCrossRefGoogle Scholar
  50. [34]
    M. Kröger and H. Voigt, Macromol. Theory Simul. 3, 639 (1994)Google Scholar
  51. [35]
    R. Muller, J.J. Pesce, and C. Picot, Macromol. 26, 4356 (1993)ADSCrossRefGoogle Scholar
  52. [36]
    C. Pierleoni and J.P. Ryckaert, Phys. Rev. Lett. 71, 1724 (1993)ADSCrossRefGoogle Scholar
  53. [36a]
    Macromolecules 28, 5087 (1995)ADSCrossRefGoogle Scholar
  54. [37]
    C. Aust, Molekulardynamik-Untersuchungen von Polymerketten in strömenden Lösungen, Thesis, TU-Berlin, (1995)Google Scholar
  55. [38]
    M. Kröger and R. Makhloufi, Phys. Rev. E 53, 2531 (1996)ADSCrossRefGoogle Scholar
  56. [39]
    A. Affouard, M. Kröger, and S. Hess, in preparationGoogle Scholar
  57. [40]
    S. Hess, J. Non-Equilibr. Thermodyn. 11, 176 (1986)Google Scholar
  58. [41]
    D. Baalss and S. Hess, Phys. Rev. Lett. 57, 86 (1986)ADSCrossRefGoogle Scholar
  59. [41a]
    Z. Naturforsch. 43 a, 662 (1988)Google Scholar
  60. [41b]
    H. Sollich, D. Baalss, and S. Hess, Mol. Cryst. Liq. Cryst. 168, 189 (1989)Google Scholar
  61. [42]
    S. Hess, J. Schwarzl, and D. Baalss, J. Phys. Condens. Matter 2, 279 (1990)ADSGoogle Scholar
  62. [43]
    S. Hess, D. Frenkel, and M.P. Allen, Mol. Phys. 74, 765 (1991)ADSCrossRefGoogle Scholar
  63. [44]
    H. Ehrentraut and S. Hess, Phys. Rev. E 51, 2203 (1995)ADSCrossRefGoogle Scholar
  64. [45]
    S. Sarman and D.J. Evans, J. Chem. Phys. 99, 9021 (1993)ADSCrossRefGoogle Scholar
  65. [46]
    C. Pereira Borgmeyer, Thesis, TU-Berlin, unpublished, (1995)Google Scholar
  66. [47]
    S. Hess, J.B. Hayter, and R. Pynn, Mol. Phys. 53, 1527 (1984)ADSCrossRefGoogle Scholar
  67. [48]
    T. Weider, Molekulardynamik-Simulation kristalliner Strukturen unter dem Einfluss einer Scherströmung, Dissertation, TU-Berlin (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Siegfried Hess
    • 1
  1. 1.Institut für Theoretische PhysikTechnische Universität BerlinBerlinGermany

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