Advertisement

The European Physical Journal Special Topics

, Volume 225, Issue 8–9, pp 1527–1549 | Cite as

A hybrid particle-continuum resolution method and its application to a homopolymer solution

  • S. Qi
  • H. Behringer
  • T. Raasch
  • F. Schmid
Regular Article Hybrid and Adaptive Coarse Graining Methods
Part of the following topical collections:
  1. Modern Simulation Approaches in Soft Matter Science: From Fundamental Understanding to Industrial Applications

Abstract

We discuss in detail a recently proposed hybrid particle-continuum scheme for complex fluids and evaluate it at the example of a confined homopolymer solution in slit geometry. The hybrid scheme treats polymer chains near the impenetrable walls as particles keeping the configuration details, and chains in the bulk region as continuous density fields. Polymers can switch resolutions on the fly, controlled by an inhomogeneous tuning function. By properly choosing the tuning function, the representation of the system can be adjusted to reach an optimal balance between physical accuracy and computational efficiency. The hybrid simulation reproduces the results of a reference particle simulation and is significantly faster (about a factor of 3.5 in our application example).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Polymer Surfaces and Interfaces: Characterization, Modification and Application, edited by M. Stamm (Springer, Berlin, 2008)Google Scholar
  2. 2.
    G. Kickelbick, Progr. Pol. Science 28, 83 (2003)CrossRefGoogle Scholar
  3. 3.
    F. Mammeri, E. Le Bourhis, L. Rozes, C. Sanches, J. Mater. Chem. 15, 3787 (2005)CrossRefGoogle Scholar
  4. 4.
    T. Kulla, S. Bhadra, D.H. Yao, N.H. Kim, S. Bose, J.H. Lee, Progr. Polym. Sci. 35, 1350 (2010)CrossRefGoogle Scholar
  5. 5.
    P. van Rijn, H. Park, K.Ö Nazli, N.C. Mougin, A. Böker, Langmuir 29, 276 (2013)CrossRefGoogle Scholar
  6. 6.
    D. Guo, G. Xie, J. Luo, J. Phys. D: Appl. Phys. 47, 013001 (2014)ADSCrossRefGoogle Scholar
  7. 7.
    F. Mathias, A. Fokina, K. Landfester, W. Tremel, F. Schmid, K. Char, R. Zentel, Macrom. Rapid Comm. 36, 959 (2015)CrossRefGoogle Scholar
  8. 8.
    A. Warshel, M. Levitt, J. Mol. Biology 103, 227 (1976)CrossRefGoogle Scholar
  9. 9.
    M.J. Field, P.A. Bash, M. Karplus, J. Comp. Chem. 11, 700 (1990)CrossRefGoogle Scholar
  10. 10.
    J. Baschnagel, K. Binder, P. Doruker, A.A. Gusev, O. Hahn, K. Kremer, W.L. Mattice, F. Müller-Plathe, M. Murat, W. Paul, S. Santos, U.W. Suter, V. Tries Adv. Polym. Sci. 152, 41 (2000)CrossRefGoogle Scholar
  11. 11.
    W.E.B. Engquist, X. Li, W. Ren, E. Vanden-Eijnden, Comm. Comput. Phys. 2, 367 (2007)MathSciNetGoogle Scholar
  12. 12.
    S.A. Baeurle, J. Math. Chem. 46, 363 (2009)MathSciNetCrossRefGoogle Scholar
  13. 13.
    C. Peter, K. Kremer, Soft Matter 5, 4357 (2009)ADSCrossRefGoogle Scholar
  14. 14.
    D. Lockerby, A. Patronix, M.K. Borg, J.M. Reese, J. Comp. Phys. 284, 261 (2015)ADSCrossRefGoogle Scholar
  15. 15.
    M. Praprotnik, L. Delle Site, K. Kremer, Annu. Rev. Phys. Chem. 59, 545 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    M. Praprotnik, L. Delle Site, K. Kremer, J. Chem. Phys. 123, 224106 (2005)ADSCrossRefGoogle Scholar
  17. 17.
    B. Ensing, S.O. Nielsen, P.B. Moore, M.L. Klein, M. Parrinello, J. Chem. Theory Comput. 3, 1100 (2007)CrossRefGoogle Scholar
  18. 18.
    A. Heyden, D.G. Truhlar, J. Chem. Theory Comput. 4, 217 (2008)CrossRefGoogle Scholar
  19. 19.
    M. Praprotnik, L. Delle Site, K. Kremer, Phys. Rev. E. 73, 066701 (2006)ADSCrossRefGoogle Scholar
  20. 20.
    A.B. Poma, L. Delle Site, Phys. Rev. Lett. 104, 250201 (2010)ADSCrossRefGoogle Scholar
  21. 21.
    A.B. Poma, L. Delle Site, Phys. Chem. Chem. Phys. 13, 10510 (2011)CrossRefGoogle Scholar
  22. 22.
    C.S. Peskin, Acta Numerica 11, 479 (2002)MathSciNetCrossRefGoogle Scholar
  23. 23.
    P.J. Atzberger, P.R. Kramer, C.S. Peskin, J. Comput. Phys. 224, 1255 (2007)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    S.W. Sides, B.J. Kim, E.J. Kramer, G.H. Fredrickson, Phys. Rev. Lett. 96, 250601 (2006)ADSCrossRefGoogle Scholar
  25. 25.
    G.J.A. Sevink, M. Charlaganov, J.G.E.M. Fraaije, Soft Matter 9, 2816 (2013)ADSCrossRefGoogle Scholar
  26. 26.
    W.E, Z. Huang, Phys. Rev. Lett. 87, 135501 (2001)ADSCrossRefGoogle Scholar
  27. 27.
    V. Ganesan, V. Pryamitsyn, J. Chem. Phys. 118, 4345 (2003)ADSCrossRefGoogle Scholar
  28. 28.
    B. Narayanan, V.A. Pryamitsyn, V. Ganesan, Macromolecules 37, 10180 (2004)ADSCrossRefGoogle Scholar
  29. 29.
    M. Müller, G.D. Smith, J. Polym. Sci.: Part B: Polym. Phys. 43, 934 (2005)ADSCrossRefGoogle Scholar
  30. 30.
    K. Ch Daoulas, M. Müller, J. Chem. Phys. 125 184904 (2006)ADSCrossRefGoogle Scholar
  31. 31.
    G. Milano, T. Kawakatsu, J. Chem. Phys. 130, 214106 (2009)ADSCrossRefGoogle Scholar
  32. 32.
    G. Milano, T. Kawakatsu, J. Chem. Phys. 133, 214102 (2010)ADSCrossRefGoogle Scholar
  33. 33.
    G. Milano, T. Kawakatsu, A. de Nicola, Phys. Biol. 10, 045007 (2013)ADSCrossRefGoogle Scholar
  34. 34.
    R. Delgado-Buscalioni, P.V. Coveney, Phys. Rev. E 67, 046704 (2003)ADSCrossRefGoogle Scholar
  35. 35.
    G. De Fabritiis, R. Delgado-Buscalioni, P.V. Coveney, Phys. Rev. Lett. 97, 134501 (2006)ADSCrossRefGoogle Scholar
  36. 36.
    R. Delgado-Buscalioni, G. De Fabritiis, Phys. Rev. E 76, 036709 (2007)ADSCrossRefGoogle Scholar
  37. 37.
    R. Delgado-Buscalioni, K. Kremer, M. Praprotnik, J. Chem. Phys. 128, 114110 (2009)ADSCrossRefGoogle Scholar
  38. 38.
    L.D. Landau, E.M. Lifshitz, Statistical Physics Part 2 Theory of Condensed State, Second edition (Pergamon Press, 1980)Google Scholar
  39. 39.
    S. Qi, H. Behringer, F. Schmid, New J. Phys. 15, 125009 (2013)ADSCrossRefGoogle Scholar
  40. 40.
    S.F. Edwards, Proc. Phys. Soc. 85, 613 (1965)ADSMathSciNetCrossRefGoogle Scholar
  41. 41.
    G.H. Fredrickson, H. Orland, J. Chem. Phys. 140, 084902 (2014)ADSCrossRefGoogle Scholar
  42. 42.
    P.G. de Gennes, Rep. Prog. Phys. 32, 187 (1969)ADSCrossRefGoogle Scholar
  43. 43.
    S.F. Edwards, Proc. Phys. Soc. 88, 265 (1966)ADSCrossRefGoogle Scholar
  44. 44.
    M. Muthukumar, S.F. Edwards, J. Chem. Phys. 76, 2760 (1982)ADSMathSciNetGoogle Scholar
  45. 45.
    K. Freed, Renormalization Group Theory of Macromolecules (New York: Wiley, 1987)Google Scholar
  46. 46.
    M. Laradji, H. Guo, M.J. Zuckermann, Phys. Rev. E. 49, 3199 (1994)ADSCrossRefGoogle Scholar
  47. 47.
    M.P. Stoykovich, M. Müller, S.O. Kim, H.H. Solak, E.W. Edwards, J.J. de Pablo, P.F. Nealey, Science 308, 1442 (2005)ADSCrossRefGoogle Scholar
  48. 48.
    F.A. Detcheverry, D.Q. Pike, P.F. Nealey, M. Müller, J.J. de Pablo, Phys. Rev. Lett. 102, 197801 (2009)ADSCrossRefGoogle Scholar
  49. 49.
    P. Gemünden, H. Behringer, J. Chem. Phys. 138, 024904 (2013)ADSCrossRefGoogle Scholar
  50. 50.
    S. Qi, L.I. Klushin, A.M. Skvortsov, A.A. Polotsky, F. Schmid, Macromolecules 48, 3775 (2015)CrossRefGoogle Scholar
  51. 51.
    E. Helfand, J. Chem. Phys. 62, 999 (1975)ADSCrossRefGoogle Scholar
  52. 52.
    G. Besold, H. Guo, M.J. Zuckermann, J. Poly. Sci. Part B: Polym. Phys. 38, 1053 (2000)ADSCrossRefGoogle Scholar
  53. 53.
    D. Frenkel, B. Smit, Understanding Molecular Simulation: From Algorithms to Applications, (New York: Academic Press, 2002)Google Scholar
  54. 54.
    G.H. Fredrickson, The Equilibrium Theory of Inhomogeneous Polymers (Oxford University Press, Oxford, 2006)Google Scholar
  55. 55.
    G.H. Fredrickson, V. Ganesan, F. Drolet, Macromolecules 35, 16 (2002)ADSCrossRefGoogle Scholar
  56. 56.
    F. Schmid, J. Phys. Condens. Matter 10, 8105 (1998)ADSCrossRefGoogle Scholar
  57. 57.
    K.M. Hong, J. Noolandi, Macromolecules 14, 727 (1981)ADSCrossRefGoogle Scholar
  58. 58.
    A. Alexander-Katz, A.G. Moreira, S.W. Sides, G.H. Fredrickson, J. Chem. Phys. 122, 014904 (2005)ADSCrossRefGoogle Scholar
  59. 59.
    Z.-G. Wang, J. Chem. Phys. 117, 481 (2002)ADSCrossRefGoogle Scholar
  60. 60.
    A. Kudlay, S. Stepanow, J. Chem. Phys. 118, 4272 (2003)ADSCrossRefGoogle Scholar
  61. 61.
    P. Grzywacz, J. Qin, D.C. Morse, Phys. Rev. E 76, 061802 (2007)ADSCrossRefGoogle Scholar
  62. 62.
    V. Ganesan, G.H. Frederickson, Europhys. Lett. 55, 814 (2001)ADSCrossRefGoogle Scholar
  63. 63.
    K. Freed, Adv. Chem. Phys. 22, 1 (1972)Google Scholar
  64. 64.
    F.A. Detcheverry, H. Kang, K. Ch Daoulas, M. Müller, P.F. Nealey, J.J. de Pablo, Macromolecules 41, 4989 (2008)ADSCrossRefGoogle Scholar
  65. 65.
    M. Müller, J. Stat. Phys. 145, 967 (2011)ADSCrossRefGoogle Scholar
  66. 66.
    P.J. Rossky, J.D. Doll, H.L. Friedman, J. Chem. Phys. 69, 4628 (1978)ADSCrossRefGoogle Scholar
  67. 67.
    D.A. Kofke, E.D. Glandt, Mol. Phys. 64, 1105 (1988)ADSCrossRefGoogle Scholar
  68. 68.
    K.Ch. Daoulas, D.N. Theodorou, V.A. Harmandaris, N.Ch. Karayiannis, V.G. Mavrantzas, Macromolecules 38, 7134 (2005)ADSCrossRefGoogle Scholar
  69. 69.
    S. Fritsch, S. Poblete, C. Junghans, G. Ciccotti, L. Delle Site, K. Kremer, Phys. Rev. Lett. 108, 170602 (2012)ADSCrossRefGoogle Scholar
  70. 70.
    N.M. Maurits, J.G.E.M. Fraaije, J. Chem. Phys. 108, 5879 (1997)ADSCrossRefGoogle Scholar
  71. 71.
    L. Zhang, A. Sevink, F. Schmid, Macromolecules 44, 9434 (2011)ADSCrossRefGoogle Scholar
  72. 72.
    N.D. Petsev, L.G. Leal, M.S. Shell, J. Chem. Phys. 142, 044101 (2015)ADSCrossRefGoogle Scholar
  73. 73.
    U. Alekseeva, R.G. Winkler, G. Sutmann, J. Comput. Phys. 314, 14 (2016)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2016

Authors and Affiliations

  1. 1.Institut für Physik, Johannes Gutenberg-Universität MainzMainzGermany
  2. 2.KITPCBeijingChina
  3. 3.CUI, Universität HamburgHamburgGermany
  4. 4.Institut für Mathematik, Johannes Gutenberg-Universität MainzMainzGermany

Personalised recommendations