Advertisement

The tension of framed membranes from computer simulations

  • Daniel Hamkens
  • Claus Jeppesen
  • John H. Ipsen
Open Access
Regular Article
  • 110 Downloads

Abstract.

We have analyzed the behavior of a randomly triangulated, self-avoiding surface model of a flexible, fluid membrane subject to a circular boundary by Wang-Landau Monte Carlo computer simulation techniques. The dependence of the canonical free energy and frame tension on the frame area is obtained for flexible membranes. It is shown that for low bending rigidities the framed membrane is only stable above a threshold tension, suggesting a discontinuous transition from the collapsed (branched polymer) state to a finite tension extended state. In a tension range above this threshold tension the membranes display power-law characteristics for the equation of state, while higher tension levels includes both an extended linear (elastic) as well as a highly non-linear stretching regime. For semi-flexible membranes a transition from extended to buckled conformations takes place at negative frame tensions. Our analysis indicates that at zero frame tension the crumpling transition of fluid membranes show characteristics of both critical behavior and a discontinuous transition at low bending rigidities.

Graphical abstract

Keywords

Soft Matter: Interfacial Phenomena and Nanostructured Surfaces 

References

  1. 1.
    U. Glaus, J. Stat. Phys. 50, 1141 (1988)ADSCrossRefGoogle Scholar
  2. 2.
    J. O’Connell, F. Sullivan, D. Libes, E. Orlandini, M.C. Tesi, A.L. Stella, T.L. Einstein, J. Phys. A 24, 4619 (1991)ADSCrossRefGoogle Scholar
  3. 3.
    D.M. Kroll, G. Gompper, Phys. Rev. A 46, 3119 (1992)ADSCrossRefGoogle Scholar
  4. 4.
    C. Jeppesen, J.H. Ipsen, Europhys. Lett. 22, 713 (1993)ADSCrossRefGoogle Scholar
  5. 5.
    B. Durhuus, J. Frölich, T. Jonsson, Nucl. Phys. B 283, 185 (1983)ADSCrossRefGoogle Scholar
  6. 6.
    L. Peliti, S. Leibler, Phys. Rev. Lett. 54, 1690 (1985)ADSCrossRefGoogle Scholar
  7. 7.
    G. Gompper, D.M. Kroll, Phys. Rev. E 51, 514 (1995)ADSCrossRefGoogle Scholar
  8. 8.
    J.H. Ipsen, C. Jeppesen, J. Phys. I 5, 1563 (1995)Google Scholar
  9. 9.
    G. Gompper, D.M. Kroll, Phys. Rev. A 46, 7466 (1992)ADSCrossRefGoogle Scholar
  10. 10.
    B. Dammann, H.C. Fogedby, J.H. Ipsen, C. Jeppesen, J. Phys. I 4, 1139 (1994)Google Scholar
  11. 11.
    W. Cai, T.C. Lubensky, P. Nelson, T.R. Powers, J. Phys. II 4, 931 (1994)Google Scholar
  12. 12.
    O. Farago, P. Pincus, Eur. Phys. J. E 11, 399 (2003)CrossRefGoogle Scholar
  13. 13.
    C. Barbetta, A. Imparato, J.-B. Fournier, Eur. Phys. J. E 31, 333 (2010)CrossRefGoogle Scholar
  14. 14.
    J.-B. Fournier, C. Barbetta, Phys. Rev. 100, 078103 (2008)Google Scholar
  15. 15.
    H. Shiba, H. Noguchi, J.-B. Fournier, Soft Matter 12, 2373 (2016)ADSCrossRefGoogle Scholar
  16. 16.
    H. Koibuchi, A. Shobukhov, H. Sekino, J. Math. Chem. 54, 358 (2016)MathSciNetCrossRefGoogle Scholar
  17. 17.
    E. Evans, W. Rawicz, Phys. Rev. Lett. 64, 2094 (1990)ADSCrossRefGoogle Scholar
  18. 18.
    J.R. Henriksen, J.H. Ipsen, Eur. Phys. J. E 14, 149 (2004)CrossRefGoogle Scholar
  19. 19.
    J.-B. Fournier, A. Ajdari, L. Peliti, Phys. Rev. Lett. 86, 4970 (2001)ADSCrossRefGoogle Scholar
  20. 20.
    W. Helfrich, Z. Naturforsch. A 33, 305 (1978)ADSCrossRefGoogle Scholar
  21. 21.
    F. Wang, D.P. Landau, Phys. Rev. Lett. 86, 2050 (2001)ADSCrossRefGoogle Scholar
  22. 22.
    P.N. Vorontsov-Velyaminov, N.A. Volkov, A.A. Yurchenko, J. Phys. A: Math. Gen. 37, 1573 (2004)ADSCrossRefGoogle Scholar
  23. 23.
    A.D. Swetnam, M.P. Allen, J. Comput. Chem. 32, 816 (2011)CrossRefGoogle Scholar
  24. 24.
    B. Nielsen, C. Jeppesen, J.H. Ipsen, J. Biol. Phys. 32, 465 (2006)CrossRefGoogle Scholar
  25. 25.
    B. Krüger, K. Mecke, Phys. Rev. D 93, 085018 (2016)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    H. Koibuchi, J. Stat. Phys. 140, 676 (2010)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    W. Helfrich, Z. Naturforsch. C 28, 693 (1973)CrossRefGoogle Scholar
  28. 28.
    P. Canham, J. Theor. Biol. 26, 21 (1970)CrossRefGoogle Scholar
  29. 29.
    E. Evans, Biophys. J. 14, 923 (1974)ADSCrossRefGoogle Scholar
  30. 30.
    J. Ambjørn, B. Durhuus, J. Frölich, Nucl. Phys. B 257, 433 (1985)ADSCrossRefGoogle Scholar
  31. 31.
    F. David, Phys. Lett. B 159, 303 (1985)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    V.A. Kazakov, K. Kostov, A.A. Migdahl, Phys. Lett. B 157, 295 (1985)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    M. Nielsen, L. Miao, J.H. Ipsen, O.G. Mouritsen, M.J. Zuckermann, Phys. Rev. E 54, 6889 (1996)ADSCrossRefGoogle Scholar
  34. 34.
    D. Nelson, T. Piran, S. Weinberg (Editors), Statistical Mechanics of Membranes and Surfaces, 2nd edition (World Scientific, Singapore, 2003)Google Scholar
  35. 35.
    N. Ramakrishnan, P.B. Sunil Kumar, J.H. Ipsen, Phys. Rev. E 81, 041922 (2010)ADSCrossRefGoogle Scholar
  36. 36.
    M. Meyer, M. Desbrun, P. Schröder, A.H. Barr, Vis. Math. 3, 34 (2004)Google Scholar
  37. 37.
    A.I. Bobenko, B.A. Springborn, Discrete Comput. Geom. 38, 740 (2007)MathSciNetCrossRefGoogle Scholar
  38. 38.
    J. Lee, Phys. Rev. 71, 211 (1993)ADSGoogle Scholar
  39. 39.
    F. David, S. Leibler, J. Phys. II 1, 959 (1991)Google Scholar
  40. 40.
    P. Pincus, Macromoleculs 9, 386 (1976)ADSCrossRefGoogle Scholar
  41. 41.
    Y. Kantor, M. Kardar, D.R. Nelson, Phys. Rev. A 35, 3056 (1987)ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    J. Banavar, A. Maritan, A.L. Stella, Science 252, 825 (1991)ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    O. Farago, Y. Kantor, Phys. Rev. E 3, 253 (2000)Google Scholar
  44. 44.
    F.H. Stillinger jr., Z.W. Salsburg, R.L. Kornegay, J. Chem. Phys. 43, 932 (1965)ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    F. David, E. Guitter, Europhys. Lett. 3, 1169 (1987)ADSCrossRefGoogle Scholar
  46. 46.
    F. David, E. Guitter, Nucl. Phys. B 295, 332 (1988)ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Daniel Hamkens
    • 1
  • Claus Jeppesen
    • 1
  • John H. Ipsen
    • 1
  1. 1.MEMPHYS - Center for Biomembrane Physics, Department of Physics, Chemistry and PharmacyUniversity of Southern DenmarkOdense MDenmark

Personalised recommendations