Skip to main content
SpringerLink
Log in

Concurrent coupling between a particle simulation and a continuum description

  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

We introduce a numerical scheme that concurrently couples a particle simulation of a multi-component polymer melt to a continuum description. We use a soft, coarse-grained model in the particle simulation and a time-dependent Ginzburg-Landau approach for the continuum description. The coupling between the particle coordinates and the order-parameter field, m, allows us to estimate the parameters the free-energy functional, \({\cal F}_{\rm GL}[m]\), of the Ginzburg-Landau approach and it makes the particle model follow the time-evolution of the order-parameter field. The algorithm exploits the time-scale separation between the fast kinetics of the order-parameter field and the slow temporal variations of the parameters of the free-energy functional. A detailed analysis is presented for the spinodal decomposition of a binary polymer blend based on the Random-Phase Approximation and Monte-Carlo simulations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R.W. Cahn, P. Haasen, E.J. Kramer, Materials Science and Technology: A Comprehensive Treatment, (VCH, Weinheim, 1993), p. 12

    Google Scholar 

  2. F. Garbassi, M. Morra, E. Occhiello, Polymer Surface: From Physics to Technology (Wiley, Chichester, 2000)

    Google Scholar 

  3. 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)

    Article  Google Scholar 

  4. F. Müller-Plathe, Chem. Phys. Chem. 3, 754 (2002)

    Google Scholar 

  5. P.C. Hohenberg, B.I. Halperin, Rev. Mod. Phys. 49, 435 (1977)

    Article  ADS  Google Scholar 

  6. R. Petschek, H. Metiu, J. Chem. Phys. 79, 3443 (1983)

    Article  ADS  Google Scholar 

  7. R. Toral, A. Chakrabarti, J.D. Gunton, Phys. Rev. Lett. 60, 2311 (1988)

    Article  ADS  Google Scholar 

  8. M.C. Cross, P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993)

    Article  ADS  Google Scholar 

  9. L. Granasy, T. Borzsonyi, T. Pusztai, Phys. Rev. Lett. 88 (2002)

  10. H. Emmerich, Adv. Phys. 57, 1 (2008)

    Article  ADS  Google Scholar 

  11. E.M. Arruda, M.C. Boyce, R. Jayachandran, Mech. Mater. 19, 193 (1995)

    Article  Google Scholar 

  12. M.C. Boyce, E.M. Arruda, Rubber Chem. Technol. 73, 504 (2000)

    Google Scholar 

  13. C. Miehe, S. Goktepe, F. Lulei, J. Mech. Phys. Solids 52, 2617 (2004)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  14. M. Bol, S. Reese, J. Mat. Sci. 40, 5933 (2005)

    Article  ADS  Google Scholar 

  15. E. Vanden-Eijnden, Comm. Math. Sci. 5, 495 (2007)

    MATH  MathSciNet  Google Scholar 

  16. W.E.B. Engquist, X.T. Li, W.Q. Ren, E. Vanden-Eijnden, Comm. Comp. Phys. 2, 367 (2007)

    MATH  MathSciNet  Google Scholar 

  17. P.G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca and London, 1979)

    Google Scholar 

  18. M. Müller, G.D. Smith, J. Polym. Sci. B: Polym. Phys. 43, 934 (2005)

    Article  Google Scholar 

  19. K.Ch. Daoulas, M. Müller, J. Chem. Phys. 125, 184904 (2006)

    Article  ADS  Google Scholar 

  20. K.Ch. Daoulas, M. Müller, J.J. de Pablo, P.F. Nealey, G.D. Smith, Soft Matter 2, 573 (2006)

    Article  Google Scholar 

  21. F.A. Detcheverry, K.Ch. Daoulas, M. Müller, J.J. de Pablo, Macromolecules 41, 4989 (2008)

    Article  ADS  Google Scholar 

  22. F.A. Detcheverry, D.Q. Pike, M. Müller, P.F. Nealey, J.J. de Pablo, Phys. Rev. Lett. 102, 197801 (2009)

    Article  ADS  Google Scholar 

  23. M. Müller, K. Binder, L. Schäfer, Macromolecules 33, 4568 (2000)

    Article  Google Scholar 

  24. J.P. Wittmer, H. Meyer, J. Baschnagel, A. Johner, S. Obukhov, L. Mattioni, M. Müller, A.N. Semenov, Phys. Rev. Lett. 93, 147801 (2004)

    Article  ADS  Google Scholar 

  25. M. Müller, C. Pastorino, Europhys. Lett. 81, 28002 (2008)

    Article  ADS  Google Scholar 

  26. M. Müller, K.C. Daoulas, J. Chem. Phys. 128, 024903 (2008)

    Article  ADS  Google Scholar 

  27. J.M. Dawson, Rev. Mod. Phys. 55, 403 (1983)

    Article  ADS  Google Scholar 

  28. J.W. Eastwood, R.W. Hockney, D.N. Lawrence, Comp. Phys. Comm. 19, 215 (1980)

    Article  ADS  Google Scholar 

  29. M. Deserno, C. Holm, J. Chem. Phys. 109, 7678 (1998)

    Article  ADS  Google Scholar 

  30. L. Miao, H. Guo, M.J. Zuckermann, Macromolecules 29 2289 (1996)

    Article  ADS  Google Scholar 

  31. P.J. Rossky, J.D. Doll, H.L. Friedman, J. Chem. Phys. 69, 4628 (1978)

    Article  ADS  Google Scholar 

  32. M. Müller, K.Ch. Daoulas, J. Chem. Phys. 129, 164906 (2008)

    Article  ADS  Google Scholar 

  33. G. Gompper, M. Schick, Phys. Rev. Lett. 65, 1116 (1990)

    Article  ADS  Google Scholar 

  34. M. Seul, D. Andelman, Science 267, 476 (1995)

    Article  ADS  Google Scholar 

  35. T. Ohta, K. Kawasaki, Macromolecules 19, 2621 (1986)

    Article  ADS  Google Scholar 

  36. P.G. de Gennes, J. Chem. Phys. 72, 4756 (1980)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  37. P. Pincus, J. Chem. Phys. 75, 1996 (1981)

    Article  ADS  Google Scholar 

  38. K. Binder, J. Chem. Phys. 79, 6387 (1983)

    Article  ADS  Google Scholar 

  39. J.Z. Zhu, L.Q. Chen, J. Shen, V. Tikare, Phys. Rev. E 60, 3564 (1999)

    Article  ADS  Google Scholar 

  40. B.P. Vollmayr-Lee, A.D. Rutenberg, Phys. Rev. E 68, 066703 (2003)

    Article  ADS  Google Scholar 

  41. M.W. Cheng, A.D. Rutenberg, Phys. Rev. E 72 (2005)

  42. L. Maragliano, E. Vanden-Eijnden, Chem. Phys. Lett. 426, 168 (2006)

    Article  ADS  Google Scholar 

  43. E. Reister, M. Müller, K. Binder, Phys. Rev. E 64, 041804 (2001)

    Article  ADS  Google Scholar 

  44. T. Hashimoto, T. Izumitani, Macromolecules 26, 3631 (1993)

    Article  ADS  Google Scholar 

  45. T. Izumitani, T. Hashimoto, Macromolecules 27, 1744 (1994)

    Article  ADS  Google Scholar 

  46. T. Kawakatsu, Phys. Rev. E 50, 2856 (1994)

    Article  ADS  Google Scholar 

  47. T. Ohta, A. Ito, Phys. Rev. E 52, 5250 (1995)

    Article  ADS  Google Scholar 

  48. S.M. Wood, Z.-G. Wang, J. Chem. Phys. 116, 2289 (2002)

    Article  ADS  Google Scholar 

  49. M. Müller, L.G. Mac Dowell, P. Virnau, K. Binder, J. Chem. Phys. 117, 5480 (2002)

    Article  ADS  Google Scholar 

  50. R.A. Wickham, A.C. Shi, Z.G. Wang, J. Chem. Phys. 118, 10293 (2003)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Georg-August-Universität, 37077, Göttingen, Germany

    M. Müller

Authors
  1. M. Müller
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Müller.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Müller, M. Concurrent coupling between a particle simulation and a continuum description. Eur. Phys. J. Spec. Top. 177, 149–164 (2009). https://doi.org/10.1140/epjst/e2009-01172-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2009-01172-9

Keywords

Search

Navigation