Journal of Statistical Physics

, Volume 145, Issue 4, pp 946–966 | Cite as

Statistical Physics Problems in Adaptive Resolution Computer Simulations of Complex Fluids

Article

Abstract

Simulating complex fluids or in general complex molecular systems requires approaches covering decades of time and length scales. This usually cannot be achieved within one simulation model. Over the years many different methods and models have been developed ranging from rather generic models, representing most efficiently the universal statistical mechanical properties of e.g. polymers, to all atom models and even quantum mechanical treatments. While these allow for scientifically very important studies in their own right, only a combination and close link between models of different levels allows for a truly quantitative description of materials and processes. In the present contribution we discuss an adaptive resolution approach where different levels of detail are treated within one simulation and the molecules are free to diffuse between different regions in space, where the molecules interact with different interaction potentials.

Keywords

Coarse-graining Multiscale simulation Adaptive resolution AdResS 

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References

  1. 1.
    Baschnagel, J., Binder, K., Doruker, P., et al.: Bridging the gap between atomistic and coarse-grained models of polymers: status and perspectives. In: Viscoelasticity, Atomistic Models, Statistical Chemistry. Advances in Polymer Science, vol. 152, pp. 41–156. Springer, Berlin (2000) CrossRefGoogle Scholar
  2. 2.
    Broughton, J.Q., Abraham, F.F., Bernstein, N., Kaxiras, E.: Concurrent coupling of length scales: methodology and application. Phys. Rev. B 60, 2391–2403 (1999) ADSCrossRefGoogle Scholar
  3. 3.
    Cotrill-Shepherd, K., Naber, M.: Fractional differential forms. J. Math. Phys. 42, 2203–2212 (2001) MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Delgado-Buscalioni, R., Kremer, K., Praprotnik, M.: Concurrent triple-scale simulation of molecular liquids. J. Chem. Phys. 128, 114110 (2008) ADSCrossRefGoogle Scholar
  5. 5.
    Delgado-Buscalioni, R., Kremer, K., Praprotnik, M.: Coupling atomistic and continuum hydrodynamics through a mesoscopic model: application to liquid water. J. Chem. Phys. 131, 244107 (2009) ADSCrossRefGoogle Scholar
  6. 6.
    Delle Site, L.: Some fundamental problems for an energy-conserving adaptive-resolution molecular dynamics scheme. Phys. Rev. E 76, 047701 (2007) ADSCrossRefGoogle Scholar
  7. 7.
    Ensing, B., Nielsen, S.O., Moore, P.B., Klein, M.L., Parrinello, M.: Energy conservation in adaptive hybrid atomistic/coarse-grain molecular dynamics. J. Chem. Theory Comput. 3, 1100–1105 (2007) CrossRefGoogle Scholar
  8. 8.
    Español, P., Warren, P.: Statistical mechanics of dissipative particle dynamics. Europhys. Lett. 30, 191–196 (1995) ADSCrossRefGoogle Scholar
  9. 9.
    Fabritiis, G.D., Delgado-Buscalioni, R., Coveney, P.V.: Multiscale modeling of liquids with molecular specificity. Phys. Rev. Lett. 97, 134501 (2006) ADSCrossRefGoogle Scholar
  10. 10.
    Henderson, R.L.: A uniqueness theorem for fluid pair correlation functions. Phys. Lett. A 49, 197–198 (1974) ADSCrossRefGoogle Scholar
  11. 11.
    Hilfer, R. (ed.): Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000) MATHGoogle Scholar
  12. 12.
    Hoogerbrugge, P.J., Koelman, J.M.V.A.: Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhys. Lett. 19, 155–160 (1992) ADSCrossRefGoogle Scholar
  13. 13.
    Izvekov, S., Parrinello, M., Burnham, C.B., Voth, G.A.: Effective force fields for condensed phase systems from ab initio molecular dynamics simulation: a new method for force-matching. J. Chem. Phys. 120, 10896–10913 (2004) ADSCrossRefGoogle Scholar
  14. 14.
    Izvekov, S., Voth, G.A.: Multiscale coarse graining of liquid-state systems. J. Chem. Phys. 123, 134105 (2005) ADSCrossRefGoogle Scholar
  15. 15.
    Janežič, D., Praprotnik, M., Merzel, F.: Molecular dynamics integration and molecular vibrational theory: I. New symplectic integrators. J. Chem. Phys. 122, 174101 (2005) ADSCrossRefGoogle Scholar
  16. 16.
    Junghans, C., Praprotnik, M., Kremer, K.: Transport properties controlled by a thermostat: an extended dissipative particle dynamics thermostat. Soft Matter 4, 156–161 (2008) CrossRefADSGoogle Scholar
  17. 17.
    Klapp, S.H.L., Diestler, D.J., Schoen, M.: Why are effective potentials ‘soft’? J. Phys., Condens. Matter 16, 7331–7352 (2004) ADSCrossRefGoogle Scholar
  18. 18.
    Lambeth, B., Junghans, C., Kremer, K., Clementi, C., Delle Site, L.: On the locality of hydrogen bond networks at hydrophobic interface. J. Chem. Phys. 133, 221101 (2010) ADSCrossRefGoogle Scholar
  19. 19.
    Lyubartsev, A.P., Laaksonen, A.: Calculation of effective interaction potentials from radial distribution functions: a reverse Monte Carlo approach. Phys. Rev. E 52, 3730–3737 (1995) ADSCrossRefGoogle Scholar
  20. 20.
    Marrink, S.J., Risselada, H.J., Yefimov, S., Tieleman, D.P., de Vries, A.H.: The martini force field: Coarse grained model for biomolecular simulations. J. Phys. Chem. B 111, 7812–7824 (2007) CrossRefGoogle Scholar
  21. 21.
    Marrink, S.J., de Vries, A.H., Mark, A.E.: Coarse grained model for semiquantitative lipid simulations. J. Phys. Chem. B 108, 750–760 (2004) CrossRefGoogle Scholar
  22. 22.
    Matysiak, S., Clementi, C., Praprotnik, M., Kremer, K., Delle Site, L.: Modeling diffusive dynamics in adaptive resolution simulation of liquid water. J. Chem. Phys. 128, 024503 (2008) ADSCrossRefGoogle Scholar
  23. 23.
    Müller-Plathe, F.: Coarse-graining in polymer simulation: from the atomistic to the mesoscopic scale and back. ChemPhysChem 3, 754–769 (2002) CrossRefGoogle Scholar
  24. 24.
    Mullinax, J.W., Noid, W.G.: Extended ensemble approach for deriving transferable coarse-grained potentials. J. Chem. Phys. 131, 104110 (2009) ADSCrossRefGoogle Scholar
  25. 25.
    Mullinax, J.W., Noid, W.G.: Generalized Yvon-Born-Green theory for molecular systems. Phys. Rev. Lett. 103, 198104 (2009) ADSCrossRefGoogle Scholar
  26. 26.
    Nielsen, S.O., Moore, P.B., Ensing, B.: Adaptive multiscale molecular dynamics of macromolecular fluids. Phys. Rev. Lett. 105, 237802 (2010) ADSCrossRefGoogle Scholar
  27. 27.
    Nonnenmacher, T.F.: Fractional integral and differential equations for a class of Levi-type probability densities. J. Phys. A, Math. Gen. 23, L697S–L700S (1990) MathSciNetADSCrossRefGoogle Scholar
  28. 28.
    Peter, C., Delle Site, L., Kremer, K.: Classical simulations from the atomistic to the mesoscale and back: coarse graining an azobenzene liquid crystal. Phys. Chem. Chem. Phys. 4, 859–886 (2008) Google Scholar
  29. 29.
    Peter, C., Kremer, K.: Multiscale simulation of soft matter systems. Faraday Discuss. 144, 9 (2010) ADSCrossRefGoogle Scholar
  30. 30.
    Poblete, S.: Thermodynamic concepts in adaptive resolution simulations. Ph.D. thesis, Johannes Gutenberg Universität Mainz, Mainz (2011) Google Scholar
  31. 31.
    Poblete, S., Praprotnik, M., Kremer, K., Delle Site, L.: Coupling different levels of resolution in molecular simulations. J. Chem. Phys. 132, 114101 (2010) ADSCrossRefGoogle Scholar
  32. 32.
    Poma, A.B., Delle Site, L.: Classical to path-integral adaptive resolution in molecular simulation: towards a smooth quantum-classical coupling. Phys. Rev. Lett. 104, 250201 (2010) ADSCrossRefGoogle Scholar
  33. 33.
    Poma, A.B., Delle Site, L.: Adaptive resolution simulation of liquid para-hydrogen: testing the robustness of the quantum-classical adaptive coupling. Phys. Chem. Chem. Phys. (2011). doi:10.1039/C0CP02865G Google Scholar
  34. 34.
    Praprotnik, M., Delle Site, L., Kremer, K.: Adaptive resolution molecular dynamics simulation: changing the degrees of freedom on the fly. J. Chem. Phys. 123, 224106 (2005) ADSCrossRefGoogle Scholar
  35. 35.
    Praprotnik, M., Delle Site, L., Kremer, K.: Adaptive resolution scheme (AdResS) for efficient hybrid atomistic/mesoscale molecular dynamics simulations of dense liquids. Phys. Rev. E 73, 066701 (2006) ADSCrossRefGoogle Scholar
  36. 36.
    Praprotnik, M., Delle Site, L., Kremer, K.: A macromolecule in a solvent: adaptive resolution molecular dynamics simulation. J. Chem. Phys. 126, 134902 (2007) ADSCrossRefGoogle Scholar
  37. 37.
    Praprotnik, M., Delle Site, L., Kremer, K.: Multiscale simulation of soft matter: from scale bridging to adaptive resolution. Annu. Rev. Phys. Chem. 59, 545–571 (2008) ADSCrossRefGoogle Scholar
  38. 38.
    Praprotnik, M., Junghans, C., Delle Site, L., Kremer, K.: Simulation approaches to soft matter: generic statistical properties vs. chemical details. Comput. Phys. Commun. 179, 51–60 (2008) ADSCrossRefGoogle Scholar
  39. 39.
    Praprotnik, M., Kremer, K., Delle Site, L.: Adaptive molecular resolution via a continuous change of the phase space dimensionality. Phys. Rev. E 75, 017701 (2007) ADSCrossRefGoogle Scholar
  40. 40.
    Praprotnik, M., Kremer, K., Delle Site, L.: Fractional dimensions of phase space variables: a tool for varying the degrees of freedom of a system in a multiscale treatment. J. Phys. A, Math. Theor. 40, F281–F288 (2007) MathSciNetADSMATHCrossRefGoogle Scholar
  41. 41.
    Praprotnik, M., Matysiak, S., Delle Site, L., Kremer, K., Clementi, C.: Adaptive resolution simulation of liquid water. J. Phys., Condens. Matter 19, 292201 (2007) CrossRefGoogle Scholar
  42. 42.
    Reith, D., Pütz, M., Müller-Plathe, F.: Deriving effective mesoscale potentials from atomistic simulations. J. Comput. Chem. 24, 1624–1636 (2003) CrossRefGoogle Scholar
  43. 43.
    Rottler, J., Barsky, S., Robbins, M.O.: Cracks and crazes: on calculating the macroscopic fracture energy of glassy polymers from molecular simulations. Phys. Rev. Lett. 89, 148304 (2002) ADSCrossRefGoogle Scholar
  44. 44.
    Ruhle, V., Junghans, C., Lukyanov, A., Kremer, K., Andrienko, D.: Versatile object-oriented toolkit for coarse-graining applications. J. Chem. Theory Comput. 5, 3211–3223 (2009) CrossRefGoogle Scholar
  45. 45.
    Soddemann, T., Dünweg, B., Kremer, K.: Dissipative particle dynamics: a useful thermostat for equilibrium and nonequilibrium molecular dynamics simulations. Phys. Rev. E 68, 046702 (2003) ADSCrossRefGoogle Scholar
  46. 46.
    Soper, A.K.: Empirical Monte Carlo simulation of fluid structure. Chem. Phys. 202, 295–306 (1996) ADSCrossRefGoogle Scholar
  47. 47.
    Tarasov, V.E.: Fractional generalization of Liouville equations. Chaos 14, 123–127 (2004) ADSCrossRefGoogle Scholar
  48. 48.
    Tarasov, V.E.: Fractional systems and fractional Bogoliubov hierarchy equations. Phys. Rev. E 71, 011102 (2005) MathSciNetADSCrossRefGoogle Scholar
  49. 49.
    Tschöp, W., Kremer, K., Batoulis, J., Bürger, T., Hahn, O.: Simulation of polymer melts. I. Coarse-graining procedure for polycarbonates. Acta Polym. 49, 61–74 (1998) CrossRefGoogle Scholar
  50. 50.
    Tschöp, W., Kremer, K., Hahn, O., Batoulis, J., Bürger, T.: Simulation of polymer melts. II. From coarse-grained models back to atomistic description. Acta Polym. 49, 75–79 (1998) CrossRefGoogle Scholar
  51. 51.
    van der Vegt, N.F.A., Peter, C., Kremer, K.: Structure-based coarse- and fine-graining in soft matter simulation. In: Voth, G.A. (ed.) Coarse-Graining of Condensed Phase and Biomolecular Systems. Chapman & Hall/CRC Press, London (2008) Google Scholar
  52. 52.
    Villa, A., Peter, C., van der Vegt, N.F.A.: Transferability of nonbonded interaction potentials for coarse-grained simulations: benzene in water. J. Chem. Theory Comput. 6, 2434–2444 (2010) CrossRefGoogle Scholar
  53. 53.
    Villa, A., van der Vegt, N.F.A., Peter, C.: Self-assembling dipeptides: including solvent degrees of freedom in a coarse-grained model. Phys. Chem. Chem. Phys. 11, 2068–2076 (2009) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.National Institute of ChemistryLjubljanaSlovenia
  2. 2.Max-Planck-Institut für PolymerforschungMainzGermany

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