Skip to main content
SpringerLink
Log in

Kinetic Model of Structural Relaxation in Diblock Copolymer Film

  • THEORY AND SIMULATIONS
  • Published:
Polymer Science, Series A Aims and scope Submit manuscript

Abstract

A relaxation model for the structure ripening under annealing of a microphase-separated polymer film has been developed. Equations have been derived that describe the appearance and annihilation of defects in the kinetically controlled mode based on the experimental data on the hexagonal structure evolution. Using that equations, the time dependences of the defect-free area size have been analyzed. It has been found that the predominance of the defect annihilation upon their triple contact leads to the power-law dependence of the orientation correlation length ξor ~ t1/4, which is observed experimentally at high annealing temperatures. A more detailed analysis of the evolution of two types of defects (dislocations and disclinations) shows that this dependence can also be realized in a model that takes into account the annihilation of disclination pairs and quadruples providing that dislocations influence this process. The results demonstrate that macrokinetic models can describe structural rearrangements in block copolymer films.

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

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.

Similar content being viewed by others

REFERENCES

  1. P. W. Majewski and K. G. Yager, J. Phys.: Condens. Matter 28, Article 403002 (2016).

    Google Scholar 

  2. P. W. Majewski and K. G. Yager, ACS Nano 9, 3896 (2015).

    Article  CAS  Google Scholar 

  3. Z. Cheng, S. Sethuraman, D. A. Huse, P. M. Chaikin, D. A. Vega, J. M. Sebastian, R. A. Register, and D. H. Adamson, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 66, Article 011706 (2002).

  4. C. T. Black and K. W. Guarini, J. Polym. Sci., Part A: Polym. Chem. 42, 1970 (2004).

    Article  CAS  Google Scholar 

  5. R. Ruiz, J. K. Bosworth, and C. T. Black, Phys. Rev. B: Condens. Matter Mater. Phys. 77, 054204 (2008).

    Article  CAS  Google Scholar 

  6. C. Harrison, D. E. Angelescu, M. Trawick, Z. Cheng, D. A. Huse, P. M. Chaikin, D. A. Vega, J. M. Sebastian, R. A. Register, and D. H. Adamson, Europhys. Lett. 67, 800 (2004).

    Article  CAS  Google Scholar 

  7. S. Ji, C.-C. Liu, W. Liao, A. L. Fenske, G. S. W. Craig, and P. F. Nealey, Macromolecules 44, 4291 (2011).

    Article  CAS  Google Scholar 

  8. A. S. Merekalov, Y. I. Derikov, A. A. Ezhov, E. N. Govorun, and Y. V. Kudryavtsev, Polym. Sci., Ser. A 60, 723 (2018).

    Article  CAS  Google Scholar 

  9. A. A. Rudov, E. S. Patyukova, I. V. Neratova, P. G. Khalatur, D. Posselt, C. M. Papadakis, and I. I. Potemkin, Macromolecules 46, 5786 (2013).

    Article  CAS  Google Scholar 

  10. B. C. Berry, A. W. Bosse, J. F. Douglas, R. L. Jones, and A. Karim, Nano Lett 7, 2789 (2007).

    Article  CAS  Google Scholar 

  11. S. Samant, J. Strzalka, K. G. Yager, K. Kisslinger, D. Grolman, M. Basutkar, N. Salunke, G. Singh, B. Berry, and A. Karim, Macromolecules 49, 8633 (2016).

    Article  CAS  Google Scholar 

  12. J. D. Hill and P. C. Millett, Sci. Rep. 7, Article 5250 (2017).

    Article  CAS  Google Scholar 

  13. X. Wan, T. Gao, L. Zhang, and J. Lin, Phys. Chem. Chem. Phys. 19, 6707 (2017).

    Article  CAS  Google Scholar 

  14. N. Dixit, A. Pape, L. Rong, E. Joseph, and S. M. Martin, Macromolecules 48, 1144 (2015).

    Article  CAS  Google Scholar 

  15. A. Singh, R. Krishnan, and S. Puri, Eur. Polym. Lett. 109, 26006 (2015).

    Article  CAS  Google Scholar 

  16. W. Li, P. F. Nealey, J. J. Pablo, and M. Müller, Phys. Rev. Lett. 113, Article No. 168301 (2014).

    Article  CAS  Google Scholar 

  17. A. V. Berezkin, C. M. Papadakis, and I. I. Potemkin, Macromolecules 49, 415 (2016).

    Article  CAS  Google Scholar 

  18. A. Checco, B. M. Ocko, A. Rahman, C. T. Black, M. Tasinkevych, A. Giacomello, and S. Dietrich, Phys. Rev. Lett. 112, Article 216101 (2014).

    Article  CAS  Google Scholar 

  19. C. K. Jeong, H. M. Jin, J.-H. Ahn, T. J. Park, H. G. Yoo, M. Koo, Y.-K. Choi, S. O. Kim, and K. J. Lee, Small 10, 337 (2014).

    Article  CAS  Google Scholar 

  20. P. W. Majewski, A. Rahman, C. T. Black, and K. G. Yager, Nat. Commun. 6, 7448 (2015).

    Article  CAS  Google Scholar 

  21. S. M. Allen and J. W. Cahn, Acta Metall. 27, 1085 (1979).

    Article  CAS  Google Scholar 

  22. G. Gonnella, E. Orlandini, and J. M. Yeomans, Phys. Rev. Lett. 78, 1695 (1997).

    Article  Google Scholar 

  23. A. G. Xu, G. Gonnella, A. Lamura, G. Amati, and F. Massaioli, Europhys. Lett. 71, 651 (2005).

    Article  CAS  Google Scholar 

  24. G. F. Mazenko, Phys. Rev. Lett. 78, 401 (1997).

    Article  CAS  Google Scholar 

  25. H. Qian and G. F. Mazenko, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 68, Article 021109 (2003).

  26. B. Yurke, A. N. Pargellis, T. Kovacs, and D. A. Huse, Phys. Rev. E: Stat. Phys., Plasma, Fluids, Relat. Interdiscip. Top. 47, 1525 (1993).

    CAS  Google Scholar 

  27. B. Kim, N. Laachi, K. T. Delaney, M. Carilli, E. J. Kramer, and G. H. Fredrickson, J. Appl. Polym. Sci. 131, 40790 (2014).

    Google Scholar 

  28. J. Shackelford, Introduction to Materials Science for Engineers (Pearson Prentice Hall, Upper Saddle River, 2009).

    Google Scholar 

  29. Y. V. Kudryavtsev, E. N. Govorun, and A. D. Litmanovich, Polym. Sci., Ser. A 42, 412 (2000).

    Google Scholar 

Download references

Funding

E.N. Govorun and Y.V. Kudryavtsev acknowledge the Russian Foundation for Basic Research for financial support (project 16-03-00531). Numerical calculations were performed by D.A. Filatov with financial support of the Ministry of Science and Higher Education of the Russian Federation.

Author information

Authors and Affiliations

  1. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, 119991, Moscow, Russia

    D. A. Filatov

  2. Faculty of Physics, Moscow State University, 119991, Moscow, Russia

    E. N. Govorun

  3. Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, 119991, Moscow, Russia

    Y. V. Kudryavtsev

Authors
  1. D. A. Filatov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. N. Govorun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Y. V. Kudryavtsev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. N. Govorun.

Additional information

Translated by V. Avdeeva

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Filatov, D.A., Govorun, E.N. & Kudryavtsev, Y.V. Kinetic Model of Structural Relaxation in Diblock Copolymer Film. Polym. Sci. Ser. A 62, 140–148 (2020). https://doi.org/10.1134/S0965545X20010046

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965545X20010046

Search

Navigation