Skip to main content
SpringerLink
Log in

Effective Interactions for Large-Scale Simulations of Complex Fluids

  • Chapter
Book cover Bridging Time Scales: Molecular Simulations for the Next Decade

Part of the book series: Lecture Notes in Physics ((LNP,volume 605))

Abstract

The simulation of complex fluids naturally involves widely different length scales. Integrating out parts of the microscopic degrees of freedom leads to the concept of effective interactions and provides a “coarse-grained” picture which can be simulated much more efficiently than a full microscopic model. This approach bridges length scales in complex fluids. In this chapter, we justify this procedure on a Statistical Mechanics level and apply it to a variety of different systems ranging from charged colloidal dispersions and polymer solutions (including star polymers and dendrimers) to mixtures of colloids and polymers and binary colloidal mixtures. Problems arising when this concept is transferred to nano-scales are pointed out. Finally the much harder problem of bridging different time scales in complex fluids is briefly discussed.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. V. Lobaskin, A. Lyubartsev, P. Linse, Phys. Rev. E 63, 020401 (2001).

    Article  ADS  Google Scholar 

  2. C. W. J. Beenakker, P. Mazur, Physica 126A, 349 (1984).

    ADS  MathSciNet  Google Scholar 

  3. See e.g R. van Roij, M. Dijkstra, J.P. Hansen, Phys. Rev. E 59, 2010 (1999).

    Article  ADS  Google Scholar 

  4. For an extensive review of classical DFT see R. Evans in “Fundamentals of Inhomogeneous Fluids”, edited by D. Henderson (Marcel Decker, New York, 1992).

    Google Scholar 

  5. J. P. Hansen and E. Smargiassi, in “Monte Carlo and Molecular Dynamics of Condensed Matter Systems”, edited by K. Binder and G. Ciccotti (Societa Italiana di Fisica, Bologna, 1996).

    Google Scholar 

  6. See e.g. G. Galli and M. Parrinello, in “Computer Simulations in Materials Science”, P. 282, edited by M. Meyer and V. Pontikis (Kluwer, Dordrecht, 1991)

    Google Scholar 

  7. H. Löwen, J. P. Hansen, P. A. Madden, J. Chem. Phys. 98, 3275 (1993).

    Article  ADS  Google Scholar 

  8. F. Gygi, G. Galli, Phys. Rev. B 52, R 2229 (1995).

    Article  ADS  Google Scholar 

  9. S. Melchionna, J. P. Hansen, Phys. Chem. Chem. Phys. 2, 3465 (2000).

    Article  Google Scholar 

  10. R. Roth, R. Evans, S. Dietrich, Phys. Rev. E 62, 5360 (2000).

    Article  ADS  Google Scholar 

  11. D. Goulding, S. Melchionna, Phys. Rev. E 64, 011403 (2001).

    Article  ADS  Google Scholar 

  12. J. P. Hansen, H. Löwen, Ann. Rev. Phys. Chem. 51, 209 (2000).

    Article  ADS  Google Scholar 

  13. L. Belloni, J. Phys. Condens. Matter 12, R549 (2000).

    Article  ADS  Google Scholar 

  14. B. V. Derjaguin, L. D. Landau, Acta Physicochim. USSR 14, 633 (1941); E. J. W. Verwey and J. T. G. Overbeek, Theory of the Stability of Lyophobic. Colloids. (Elsevier, Amsterdam, 1948).

    Google Scholar 

  15. A. Delville, R. J. M. Pellenq, Molecular Simulation 24, 1 (2000); R. Messina, C. Holm, K. Kremer, Phys. Rev. Lett. 85, 872 (2000); T. Terao, T. Nakayama, Phys. Rev. E 63, 041401 (2001); B. Hribar, V. Vlachy, Langmuir 17, 2043 (2001).

    Article  Google Scholar 

  16. A. Delville, J. Phys. Chem. B 103, 8296 (1999); A. Delville, P. Levitz, J. Phys. Chem. B 105, 663 (2001)

    Article  Google Scholar 

  17. S. Meyer, P. Levitz, A. Delville, J. Phys. Chem. B 105, 10684 (2001).

    Article  Google Scholar 

  18. H. Löwen, E. Allahyarov, J. Phys.: Condensed Matter 10, 4147 (1998).

    Article  ADS  Google Scholar 

  19. R. D. Groot, J. Phys. 95, 9191 (1991).

    Google Scholar 

  20. M. J. Stevens, M. L. Falk, M. O. Robbins, J. Chem. Phys. 104, 5209 (1996).

    Article  ADS  Google Scholar 

  21. H. Löwen, G. Kramposthuber, Europhys. Lett. 23, 673 (1993).

    Article  ADS  Google Scholar 

  22. H. Löwen, Phys. Rev. Lett. 72, 424 (1994). J. Chem. Phys. 100, 6738 (1994).

    Article  ADS  Google Scholar 

  23. S. Kutter, J. P. Hansen, M. Sprik, E. Boek, J. Chem. Phys. 112, 311 (2001).

    Article  ADS  Google Scholar 

  24. M. Dijkstra, Current Opinion in Colloid and Interface Science 6, 372 (2001).

    Article  Google Scholar 

  25. For a review, see T. Tomasi, M. Perico, Chem. Rev. 94, 2027 (1994).

    Article  Google Scholar 

  26. M. Marchi, D. Borgis, N. Levy, P. Ballone, J. Chem. Phys. 114, 4377 (2001).

    Article  ADS  Google Scholar 

  27. D. M. York, M. Karplus, J. Phys. Chem. A 103, 11060 (1999).

    Article  Google Scholar 

  28. R. A. Marcus, J. Chem. Phys. 24, 966, 979 (1956).

    Article  ADS  Google Scholar 

  29. B. U. Felderhof, J. Chem. Phys. 67, 493 (1977).

    Article  ADS  Google Scholar 

  30. R. Allen, J. P. Hansen, S. Melchionna, Phys. Chem. Chem. Phys. 3, 4177 (2001).

    Article  Google Scholar 

  31. R. Allen, S. Melchionna, J. P. Hansen to be published.

    Google Scholar 

  32. C. Mischler, J. Baschnagel, K. Binder, Advances in Colloid and Interface Science 94, 197 (2001).

    Article  Google Scholar 

  33. P. J. Flory, W. R. Krigbaum, J. Chem. Phys 18, 1086 (1950).

    Article  ADS  Google Scholar 

  34. A. Y. Grosberg, P. G. Khalatur, A. R. Khokhlov, Makromol. Chem. Rapid Comm. 3, 709 (1982).

    Article  Google Scholar 

  35. J. Dautenhahn, C. K. Hall, Macromolecules 27, 5399 (1994), and references therein.

    Article  ADS  Google Scholar 

  36. A. A. Louis, P. G. Bolhuis, J. P. Hansen, E. J. Meijer, Phys. Rev Letters 85, 2522 (2000) P. G. Bolhuis, A. A. Louis, J. P. Hansen, E. J. Meijer, J. Chem. Phys. 114, 4296 (2001).

    Article  ADS  Google Scholar 

  37. B. Krüger, L. Schäfer, A. Baumgärtner, J. Phys. (Paris) 50, 319 (1989).

    Google Scholar 

  38. V. Krakoviack, A. A. Louis, J. P. Hansen, to be published.

    Google Scholar 

  39. C. H. Bennett, J. Comp. Phys. 22, 245 (1976).

    Article  ADS  Google Scholar 

  40. D. Frenkel, B. Smit, “Understanding Molecular Simulation”, 2d Edition (Academic Press, San Diego, 2001).

    Google Scholar 

  41. P. G. Bolhuis, A. A. Louis, J. P. Hansen, Phys. Rev. E 64, 021801 (2001).

    Article  ADS  Google Scholar 

  42. C. von Ferber, A. Jusufi, C. N. Likos, H. Löwen, M. Watzlawek, Europhys. Journal E 2, 311 (2000).

    ADS  Google Scholar 

  43. See e.g. J. P. Hansen, I. R. McDonald, “Theory of Simple Liquids” 2d edition (Academic Press, London, 1986).

    Google Scholar 

  44. A. A. Louis, P. G. Bolhuis, J. P. Hansen, Phys. Rev. E 62, 7961 (2000).

    Article  ADS  Google Scholar 

  45. C. N. Likos, Physics Reports 348, 267 (2001).

    Article  ADS  Google Scholar 

  46. R. L. Henderson, Phys. Lett. 49A, 197 (1974).

    ADS  Google Scholar 

  47. A. Jusufi, J. Dzubiella, C. N. Likos, C. von Ferber, H. Löwen, J. Phys.: Condensed Matter 13 6177 (2001).

    Article  ADS  Google Scholar 

  48. A. A. Louis, P. G. Bolhuis, E. J. Meyer, J. P. Hansen, cond-mat (011518).

    Google Scholar 

  49. For a review see K. S. Schweizer, J. G. Curro, Adv. Chem. Phys. 98, 1 (1997).

    Article  Google Scholar 

  50. V. Krakoviack, J. P. Hansen, A. A. Louis, cond-mat / 0110387

    Google Scholar 

  51. For a review see: G. S. Grest, L. J. Fetters, J. S. Huang, D. Richter, Advances in Chemical Physics, Volume XCIV, 67 (1996)).

    Article  Google Scholar 

  52. T. A. Witten, P. A. Pincus, Macromolecules 19, 2509 (1986).

    Article  ADS  Google Scholar 

  53. M. Dauod, J. P. Cotton, J. Phys. (Paris) 38, 983 (1977).

    Google Scholar 

  54. C. N. Likos, H. Löwen, M. Watzlawek, B. Abbas, O. Jucknischke, J. Allgaier, D. Richter, Phys. Rev. Letters 80, 4450 (1998).

    Article  ADS  Google Scholar 

  55. A. Jusufi, M. Watzlawek, H. Löwen, Macromolecules 32, 4470 (1999).

    Article  ADS  Google Scholar 

  56. M. Watzlawek, C. N. Likos, H. Löwen, Phys. Rev. Letters. 82, 5289 (1999).

    Article  ADS  Google Scholar 

  57. M. Watzlawek, H. Löwen, C. N. Likos, J. Phys. Condensed Matter 10, 8189 (1998).

    Article  ADS  Google Scholar 

  58. G. A. McConnell, A. P. Gast, Macromolecules 30, 435 (1997).

    Article  ADS  Google Scholar 

  59. S. T. Milner, T. A. Witten, M. E. Cates, Macromolecules 21, 2610 (1988).

    Article  ADS  Google Scholar 

  60. J. Mewis, W. J. Frith, T. A. Strivens, W. B. Russel, A. I. Ch. E. J. 35, 415 (1989).

    Google Scholar 

  61. U. Genz, B. D’Aguanno, J. Mewis, R. Klein, Langmuir 10, 2206 (1994).

    Article  Google Scholar 

  62. C. N. Likos, H. Löwen, A. Poppe, L. Willner, J. Roovers, B. Cubitt, D. Richter, Phys. Rev. E 58, 6299 (1998).

    Article  ADS  Google Scholar 

  63. A. Jusufi, C. N. Likos, H. Löwen, Phys. Rev. Letters (in press).

    Google Scholar 

  64. P. Pincus, Macromolecules 24, 2912 (1991).

    Article  ADS  Google Scholar 

  65. C. N. Likos, M. Schmidt, H. Löwen, M. Ballauff, D. Pötschke, P. Lindner, Macromolecules 34, 2914 (2001).

    Article  ADS  Google Scholar 

  66. C. N. Likos, private communication.

    Google Scholar 

  67. A. Lang, C. N. Likos, M. Watzlawek, H. Löwen, J. Phys. Condensed Matter 12, 5087 (2000).

    Article  ADS  Google Scholar 

  68. S. Asakura, F. Oosawa, J. Chem. Phys. 22, 1255 (1954).

    ADS  Google Scholar 

  69. M. Dijkstra, J. M. Brader, R. Evans, J. Phys.: Condensed Matter 11, 10079 (1999).

    Article  ADS  Google Scholar 

  70. M. Dijkstra, to be published.

    Google Scholar 

  71. I. Götze, Diploma Thesis, University of Düsseldorf, 2002.

    Google Scholar 

  72. H. N. W. Lekkerkerker, W. C. K. Poon, P. N. Pusey, A. Stroobants, P. B. Warren, Europhys. Lett. 20, 559 (1992).

    Article  ADS  Google Scholar 

  73. M. Schmidt, H. Löwen, J. M. Brader, R. Evans, Phys. Rev. Letters 85, 1934 (2000).

    Article  ADS  Google Scholar 

  74. Y. Rosenfeld, M. Schmidt, H. Löwen, P. Tarazona, Phys. Rev. E 55, 4245 (1997).

    Article  ADS  Google Scholar 

  75. M. Schmidt, H. Löwen, J. M. Brader, R. Evans, J. Phys.: Condensed Matter 14, L1 (2002).

    Article  Google Scholar 

  76. A. A. Louis, R. Finken, J. P. Hansen, Phys. Rev. E 61, R1028 (2000).

    Article  ADS  Google Scholar 

  77. E. J. Meijer, D. Frenkel, Physica A 213, 130 (1995).

    Article  ADS  Google Scholar 

  78. A. Johner, J. F. Joanny, S. Diez Orrite, J. BonetAvalos, Europhys. Letters 56, 549 (2001).

    Article  ADS  Google Scholar 

  79. J. Dzubiella, A. Jusufi, C. N. Likos, C. von Ferber, H. Löwen, J. Stellbrink, J. Allgaier, D. Richter, A. B. Schofield, P. A. Smith, W. C. K. Poon, P. N. Pusey, Phys. Rev. E 64, 01040 (2001).

    Google Scholar 

  80. J. Dzubiella, C. N. Likos, H. Löwen, to be published.

    Google Scholar 

  81. M. Fuchs, K. S. Schweizer, Phys. Rev. E 64, 021514 (2001).

    Article  ADS  Google Scholar 

  82. A. Hanke, E. Eisenriegler, S. Dietrich, Phys. Rev. E 59, 6853 (1999).

    Article  ADS  Google Scholar 

  83. H. Xu, M. Baus, J. Phys.: Condensed Matter 4, L663 (1992).

    Article  ADS  Google Scholar 

  84. M. D. Eldridge, P. A. Madden, D. Frenkel, Mol. Phys. 79, 105 (1993).

    Article  ADS  Google Scholar 

  85. P. Bartlett, R. H. Ottewill, P. N. Pusey, Phys. Rev. Lett. 68, 3801 (1992).

    Article  ADS  Google Scholar 

  86. R. Dickman, P. Attard, V. Simonian, J. Chem. Phys. 107, 205 (1997).

    Article  ADS  Google Scholar 

  87. E. Allahyarov, H. Löwen, Phys. Rev. E 63, 041403 (2001).

    Article  ADS  Google Scholar 

  88. J. C. Crocker, J. A. Matteo, A. D. Dinsmore, A. G. Yodh, Phys. Rev. Letters 82, 4352 (1999).

    Article  ADS  Google Scholar 

  89. M. Dijkstra, R. van Roij, R. Evans, Phys. Rev. E 59, 5744 (1999).

    Article  ADS  Google Scholar 

  90. N. G. Almarza, E. Enciso, Phys. Rev. E 59, 4426 (1999).

    Article  ADS  Google Scholar 

  91. P. Bolhuis, M. Hagen, D. Frenkel, Phys. Rev. E 50, 4880 (1994).

    Article  ADS  Google Scholar 

  92. C. N. Likos, Z. T. N’emeth, H. Löwen, J. Phys. Condensed Matter 6, 10965 (1994).

    Article  ADS  Google Scholar 

  93. D. Goulding, J. P. Hansen, Mol. Phys. 99, 865 (2001).

    Article  ADS  Google Scholar 

  94. A. A. Louis, R. Roth, E. Allahyarov, H. Löwen, to be published.

    Google Scholar 

  95. E. Allahyarov, H. Löwen, J. Phys. Condensed Matter 13, L277 (2001).

    Article  ADS  Google Scholar 

  96. H. Löwen, E. Allahyarov, J. Dzubiella, C. von Ferber, A. Jusufi, C. N. Likos, M. Heni, Philos. Trans. R. Soc. Lond. A 359, 909 (2001).

    Article  ADS  Google Scholar 

  97. E. Allahyarov, H. Löwen, A. A. Louis, J. P. Hansen, Discrete charge patterns, Coulomb correlations and interactions in protein solutions, Europhys. Letters (in press).

    Google Scholar 

  98. A. George, W. W. Wilson, Acta Cryst. D 50, 361 (1994); G. A. Vliegenthart, H. N. W. Lekkerkerker, J. Chem. Phys. 112, 5364 (2000).

    Article  Google Scholar 

  99. B. Guo, S. Kao, H. McDonald, A. Asanov, L. L. Combs, W. W. Wilson, J. Cryst. Growth 196, 424 (1999); D. N. Petsev, B. R. Thomas, S. T. Yau, P. G. Vekilov, Biophysical Journal 78, 2060 (2000).

    Article  ADS  Google Scholar 

  100. For a review, see P. N. Pusey, in “Liquids, Freezing and the Glass Transition”, edited by J. P. Hansen, D. Levesque and J. Zinn-Justin (North Holland, Amsterdam, 1991).

    Google Scholar 

  101. J. K. G. Dhont, “An Introduction to Dynamics of Colloids”, Elsevier, Amsterdam, 1996.

    Book  Google Scholar 

  102. G. Nägele, Physics Reports, 272, 215 (1996).

    Article  ADS  Google Scholar 

  103. A. J. C. Ladd, R. Verberg, J. Stat. Phys. 104, 1191 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  104. See e.g.: R. Pesch’e, G. Nägele, Europhys. Lett. 51, 584 (2000); H. M. Schaink, P. A. Nommensen, R. J. J. Jongschaap, J. Mellema, J. Chem. Phys. 113, 2484 (2000).

    Article  ADS  Google Scholar 

  105. P. B. Warren, Current Opinion in Colloid and Interface Science 3, 620 (1998).

    Article  Google Scholar 

  106. H. Tanaka, T. Araki, Phys. Rev. Lett. 85, 1338 (2000).

    Article  ADS  Google Scholar 

  107. H. Löwen, J. P. Hansen, J. N. Roux, Phys. Rev. A 44, 1169 (1991).

    Article  ADS  Google Scholar 

  108. H. Löwen, G. Szamel, J. Phys. Condensed Matter 5, 2295 (1993).

    Article  ADS  Google Scholar 

  109. S. Butler, P. Harrowell, J. Chem. Phys. 103, 4653 (1995); J. Chem. Phys. 105, 605 (1996).

    Article  ADS  Google Scholar 

  110. S. R. Rastogi, N. Wagner, S. R. Lustig, J. Chem. Phys. 104, 9234 (1996).

    Article  ADS  Google Scholar 

  111. N. Olivi-Tran, R. Botet, B. Cabane, Phys. Rev. E 57, 1997 (1998).

    Article  ADS  Google Scholar 

  112. H. Löwen, G. Hoffmann, Phys. Rev. E 60, 3009 (1999).

    Article  ADS  Google Scholar 

  113. J. Dzubiella, G. P. Hoffmann, H. Löwen, Lane formation in binary colloidal. mixtures driven by an external field, Phys. Rev. E (in press).

    Google Scholar 

  114. N. G. van Kampen, “Stochastic Processes in Physics and Chemistry (North Holland, Amsterdam, 1990).

    Google Scholar 

  115. W. Hess and R. Klein, Adv. Phys. 32, 173 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  116. For a review, see L. Bocquet and J. P. Hansen, in “Dynamics: Models and Kinetic Methods for Non-Equilibrium Many-Body Systems”, edited by J. Karkheck (Kluwer Academic, Dordrecht, 2000).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemistry, Lensfield Road, Cambridge, CB2 1EW, UK

    Jean-Pierre Hansen

  2. Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225, Düsseldorf, Germany

    Hartmut Löwen

Authors
  1. Jean-Pierre Hansen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hartmut Löwen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Lehrstuhl für Theoretische Physik Fachbereich Physik, Universität Konstanz, 78457, Konstanz, Germany

    Peter Nielaba

  2. CECAM, Ecole Normale Supérieure de Lyon, 46 Allée d’Italie, 69364, Lyon Cedex 07, France

    Michel Mareschal

  3. Dipartimento di Fisica, Universitá La Sapienza, Piazzale Aldo Moro, 00185, Roma, Italy

    Giovanni Ciccotti

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Hansen, JP., Löwen, H. (2002). Effective Interactions for Large-Scale Simulations of Complex Fluids. In: Nielaba, P., Mareschal, M., Ciccotti, G. (eds) Bridging Time Scales: Molecular Simulations for the Next Decade. Lecture Notes in Physics, vol 605. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45837-9_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-45837-9_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44317-9

  • Online ISBN: 978-3-540-45837-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation