Conducting transition analysis of thin films composed of long flexible macromolecules: Percolation study

  • Yuki NorizoeEmail author
  • Hiroshi Morita
Regular Article


By simulating percolation and critical phenomena of labelled species inside films composed of single-component linear homogeneous macromolecules using the molecular Monte Carlo method in 3 dimensions, we study the dependence of these conducting transition and critical phenomena upon both thermal movements, i.e. spontaneous mobility, and extra-molecular topological constraints of the molecules. Systems containing topological constraints and/or composed of immobile particles, e.g. lattice models and chemical gelation, were studied in conventional works on percolation. Coordinates of the randomly distributed particles in the conventional lattice models are limited to discrete lattice points. Moreover, each particle is spatially fixed at the distributed position, which results in a temporally unchanged network structure. Although each polymer in the chemical gels can spontaneously move in the continuous space, the network structure is fixed when cross-linking reaction ends. By contrast to these conventional systems, all the molecules in the present system freely move and spontaneously diffuse in the continuous space. The network structure of the present molecules continues changing dynamically. The percolation and critical phenomena of such dynamic network structures are examined here. We reveal that these phenomena also occur in the present system, and that both the universality class and percolation threshold are independent of the extra-molecular topological constraints.

Graphical abstract


Soft Matter: Polymers and Polyelectrolytes 


  1. 1.
    S.-M. Hur, G.S. Khaira, A. Ramírez-Hernández, M. Müller, P.F. Nealey, J.J. de Pablo, ACS Macro Lett. 4, 11 (2015)CrossRefGoogle Scholar
  2. 2.
    A.P. Marencic, P.M. Chaikin, R.A. Register, Phys. Rev. E 86, 021507 (2012)ADSCrossRefGoogle Scholar
  3. 3.
    N. Lefevre, K.C. Daoulas, M. Müller, J.-F. Gohy, C.-A. Fustin, Macromolecules 43, 7734 (2010)ADSCrossRefGoogle Scholar
  4. 4.
    X. Gu, I. Gunkel, A. Hexemer, W. Gu, T.P. Russell, Adv. Mater. 26, 273 (2014)CrossRefGoogle Scholar
  5. 5.
    J.K. Bosworth, M.Y. Paik, R. Ruiz, E.L. Schwartz, J.Q. Huang, A.W. Ko, D.-M. Smilgies, C.T. Black, C.K. Ober, ACS Nano 2, 1396 (2008)CrossRefGoogle Scholar
  6. 6.
    D. Stauffer, A. Aharony, Introduction to Percolation Theory (Taylor & Francis, London, 1994)Google Scholar
  7. 7.
    M. Sahimi, Applications of Percolation Theory (Taylor & Francis, London, 1994). Google Scholar
  8. 8.
    Y. Norizoe, T. Kawakatsu, J. Chem. Phys. 137, 024904 (2012)ADSCrossRefGoogle Scholar
  9. 9.
    Y. Norizoe, T. Kawakatsu, Europhys. Lett. 72, 583 (2005)ADSCrossRefGoogle Scholar
  10. 10.
    Y. Norizoe, H. Jinnai, A. Takahara, J. Chem. Phys. 140, 054904 (2014)ADSCrossRefGoogle Scholar
  11. 11.
    Y. Norizoe, H. Jinnai, A. Takahara, EPL 101, 16006 (2013)ADSCrossRefGoogle Scholar
  12. 12.
    G. Kondrat, J. Chem. Phys. 117, 6662 (2002)ADSCrossRefGoogle Scholar
  13. 13.
    P. Adamczyk, P. Polanowski, A. Sikorski, J. Chem. Phys. 131, 234901 (2009)ADSCrossRefGoogle Scholar
  14. 14.
    S. Zerko, P. Polanowski, A. Sikorski, Soft Matter 8, 973 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    P. Polanowski, E. Wawrzyńska, A. Sikorski, Macromol. Theor. Simul. 22, 238 (2013)CrossRefGoogle Scholar
  16. 16.
    A. Yethiraj, Macromolecules 36, 5854 (2003)ADSCrossRefGoogle Scholar
  17. 17.
    P. Polanowski, A. Sikorski, Soft Matter 14, 8249 (2018)ADSCrossRefGoogle Scholar
  18. 18.
    J.M. Drouffe, A.C. Maggs, S. Leibler, Science 254, 1353 (1991)ADSCrossRefGoogle Scholar
  19. 19.
    K.C. Daoulas, M. Müller, Adv. Polym. Sci. 224, 197 (2010)Google Scholar
  20. 20.
    Y. Norizoe, Measuring the Free Energy of Self-assembling Systems in Computer Simulation, PhD Thesis, Institute for Theoretical Physics, University of Göttingen, Göttingen, Germany (2010) available on-line at
  21. 21.
    Y. Norizoe, K.C. Daoulas, M. Müller, Faraday Discuss. 144, 369 (2010)ADSCrossRefGoogle Scholar
  22. 22.
    D. Murakami, Y. Norizoe, Y. Higaki, A. Takahara, H. Jinnai, Macromolecules 49, 4862 (2016)ADSCrossRefGoogle Scholar
  23. 23.
    M. Doi, Introduction to Polymer Physics (Oxford University Press, Oxford, 1996)Google Scholar
  24. 24.
    M. Müller, K.C. Daoulas, Y. Norizoe, Phys. Chem. Chem. Phys. 11, 2087 (2009)CrossRefGoogle Scholar
  25. 25.
    R.D. Groot, P.B. Warren, J. Chem. Phys. 107, 4423 (1997)ADSCrossRefGoogle Scholar
  26. 26.
    R.D. Groot, T.J. Madden, J. Chem. Phys. 108, 8713 (1998)ADSCrossRefGoogle Scholar
  27. 27.
    M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids (Oxford University Press, Oxford, 1989)Google Scholar
  28. 28.
    D. Frenkel, B. Smit, Understanding Molecular Simulation: From Algorithms to Applications (Academic Press, London, 2002)Google Scholar
  29. 29.
    M. Matsumoto, T. Nishimura, ACM Trans. Model. Comput. Simul. 8, 3 (1998)CrossRefGoogle Scholar
  30. 30.
    M. Matsumoto, Y. Kurita, ACM Trans. Model. Comput. Simul. 2, 179 (1992)CrossRefGoogle Scholar
  31. 31.
    M. Matsumoto, Y. Kurita, ACM Trans. Model. Comput. Simul. 4, 254 (1994)CrossRefGoogle Scholar
  32. 32.
    T. Kawakatsu, Statistical Physics of Polymers: An Introduction (Springer, 2004)Google Scholar
  33. 33.
    R. Zallen, The Physics of Amorphous Solids (Wiley, 1998)Google Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Technology Research Association for Single Wall Carbon Nanotubes (TASC) - Central 2-1Tsukuba, IbarakiJapan
  2. 2.National Institute of Advanced Industrial Science and Technology (AIST) - Central 2-1Tsukuba, IbarakiJapan

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