Scaling and criticality of the Manning transition

Regular Article
  • 16 Downloads

Abstract.

We consider a system consisting of a charged cylinder in the presence of neutralizing counterions. This system is well known to exhibit the Manning transition of counterion condensation onto the charged cylinder. We study the criticality and the scaling properties of the Manning transition, analyzing involved thermodynamic quantities such as condensed fraction, its fluctuation, and heat capacity. Through the Monte Carlo simulations and finite-size scaling analysis, we find that near the transition point the examined quantities exhibit scale-invariant behaviors with specific exponents, which provides an evidence that the Manning transition is a critical phenomenon having a scale-invariant property, analogous to bulk phase transitions. Furthermore, we numerically confirm that such scaling properties are not affected by the coupling strength.

Graphical abstract

Keywords

Soft Matter: Polymers and Polyelectrolytes 

References

  1. 1.
    G.S. Manning, J. Chem. Phys. 51, 924 (1969)ADSCrossRefGoogle Scholar
  2. 2.
    G.S. Manning, J. Chem. Phys. 51, 3249 (1969)ADSCrossRefGoogle Scholar
  3. 3.
    F. Oosawa, Polyelectrolytes (Marcel Dekker, New York, 1971)Google Scholar
  4. 4.
    D. Andelman, in Soft Condensed Matter Physics in Molecular and Cell Biology, edited by W.C.K. Poon, D. Andelman (Taylor & Francis, New York, 2006)Google Scholar
  5. 5.
    V.A. Bloomfield, Biopolymers 31, 1471 (1991)CrossRefGoogle Scholar
  6. 6.
    V.A. Bloomfield, Curr. Opin. Struct. Biol. 6, 334 (1996)CrossRefGoogle Scholar
  7. 7.
    J.-L. Barrat, J.-F. Joanny, Adv. Chem. Phys. 94, 1 (1996)Google Scholar
  8. 8.
    D. Andelman, in Handbook of Physics of Biological Systems, edited by R. Lopowsky, E. Sackmann (Elsevier, New York, 1995)Google Scholar
  9. 9.
    Y. Levin, Physica A 257, 408 (1998)ADSCrossRefGoogle Scholar
  10. 10.
    R.M. Fuoss, A. Katchalsky, S. Lifson, Proc. Natl. Acad. Sci. U.S.A. 37, 579 (1951)ADSCrossRefGoogle Scholar
  11. 11.
    T. Alfrey, P.W. Berg, H. Morawetz, J. Polym. Sci. 7, 543 (1951)ADSCrossRefGoogle Scholar
  12. 12.
    A.D. MacGillivray, J. Chem. Phys. 56, 80 (1972)ADSCrossRefGoogle Scholar
  13. 13.
    A.D. MacGillivray, J. Chem. Phys. 56, 83 (1972)ADSCrossRefGoogle Scholar
  14. 14.
    G.V. Ramanathan, C.P. Woodbury, J. Chem. Phys. 77, 4133 (1982)ADSCrossRefGoogle Scholar
  15. 15.
    C.P. Woodbury, G.V. Ramanathan, Macromolecules 15, 82 (1982)ADSCrossRefGoogle Scholar
  16. 16.
    B.H. Zimm, M. Le Bret, J. Biomol. Struct. Dyn. 1, 461 (1983)CrossRefGoogle Scholar
  17. 17.
    M. Le Bret, B.H. Zimm, Biopolymers 23, 287 (1984)CrossRefGoogle Scholar
  18. 18.
    P.L. Hansen, R. Podgornik, V.A. Parsegian, Phys. Rev. E 64, 021907 (2001)ADSCrossRefGoogle Scholar
  19. 19.
    A. Deshkovski, S. Obukov, M. Rubinstein, Phys. Rev. Lett. 86, 2341 (2001)ADSCrossRefGoogle Scholar
  20. 20.
    M.L. Henle, C.D. Santan-gelo, D.M. Patel, P.A. Pincus, Europhys. Lett. 66, 284 (2004)ADSCrossRefGoogle Scholar
  21. 21.
    B. OShaughnessy, Q. Yang, Phys. Rev. Lett. 94, 048302 (2005)ADSCrossRefGoogle Scholar
  22. 22.
    E. Trizac, G. Téllez, Phys. Rev. Lett. 96, 038302 (2006)ADSCrossRefGoogle Scholar
  23. 23.
    Y. Burak, H. Orland, Phys. Rev. E 73, 010501(R) (2006)ADSCrossRefGoogle Scholar
  24. 24.
    M. Deserno, C. Holm, S. May, Macromolecules 33, 199 (2000)ADSCrossRefGoogle Scholar
  25. 25.
    Q. Liao, A.V. Dobrynin, M. Rubinstein, Macromolecules 36, 3399 (2003)ADSCrossRefGoogle Scholar
  26. 26.
    J.P. Mallarino, G. Téllez, E. Trizac, J. Phys. Chem. B 117, 12702 (2013)CrossRefGoogle Scholar
  27. 27.
    A. Naji, R.R. Netz, Phys. Rev. Lett. 95, 185703 (2005)ADSCrossRefGoogle Scholar
  28. 28.
    A. Naji, R.R. Netz, Phys. Rev. E 73, 056105 (2006)ADSCrossRefGoogle Scholar
  29. 29.
    K. Huang, Statistical Mechanics (John Wiley & Sons, New York, 1987)Google Scholar
  30. 30.
    N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group (Addison-Wesley, New York, 1992)Google Scholar
  31. 31.
    R.R. Netz, H. Orland, Eur. Phys. J. E 1, 203 (2000)CrossRefGoogle Scholar
  32. 32.
    R.R. Netz, Eur. Phys. J. E 5, 557 (2001)CrossRefGoogle Scholar
  33. 33.
    A. Moreira, R. Netz, Phys. Rev. Lett. 87, 078301 (2001)ADSCrossRefGoogle Scholar
  34. 34.
    A. Moreira, R. Netz, Eur. Phys. J. E 8, 33 (2002)Google Scholar
  35. 35.
    M.E.J. Newman, G.T. Barkema, Monte Carlo Methods in Statistical Physics (Oxford University Press, New York, 1999)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Graduate School of Nanoscience and TechnologyKorea Advanced Institute of Science and TechnologyDeajeonKorea
  2. 2.Department of PhysicsPusan National UniversityBusanKorea

Personalised recommendations