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Complex dewetting scenarios captured by thin-film models

Abstract

In the course of miniaturization of electronic and microfluidic devices, reliable predictions of the stability of ultrathin films have a strategic role for design purposes. Consequently, efficient computational techniques that allow for a direct comparison with experiment become increasingly important. Here we demonstrate, for the first time, that the full complex spatial and temporal evolution of the rupture of ultrathin films can be modelled in quantitative agreement with experiment. We accomplish this by combining highly controlled experiments on different film-rupture patterns with computer simulations using novel numerical schemes for thin-film equations. For the quantitative comparison of the pattern evolution in both experiment and simulation we introduce a novel pattern analysis method based on Minkowski measures. Our results are fundamental for the development of efficient tools capable of describing essential aspects of thin-film flow in technical systems.

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Figure 1: Dewetting morphology of a thin film.
Figure 2: Satellite holes.
Figure 3: Analysis by Minkowski measures.

References

  1. Kagan, C.R., Mitzi, D.B. & Dimitrakopoulos, C.D. Organic-inorganic hybrid materials as semi-conducting channels in thin-film field-effect transistors. Science 286, 945–947 (1999).

    CAS  Article  Google Scholar 

  2. Seemann, R., Herminghaus, S. & Jacobs, K. Dewetting patterns and molecular forces: a reconcialiation. Phys. Rev. Lett. 86, 5534–5537 (2001).

    CAS  Article  Google Scholar 

  3. Acheson, D.J. Elementary Fluid Dynamics (Oxford Univ. Press, Oxford, 1990).

    Google Scholar 

  4. Oron, A., Davis, S. & Bankoff, S.G. Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931–980 (1997).

    CAS  Article  Google Scholar 

  5. Dussan V, E.B. & Davis, S. On the motion of a fluid-fluid interface along a solid surface. J. Fluid. Mech. 65, 71–95 (1974).

    Article  Google Scholar 

  6. Bernis, F. & Friedman, A. Higher order nonlinear degenerate parabolic equations. J. Differ. Equations 83, 179–206 (1990).

    Article  Google Scholar 

  7. Dal Passo, R., Garcke, H. & Grün, G. On a fourth order degenerate parabolic equation: global entropy estimates and qualitative behavior of solutions. SIAM J. Math. Anal. 29, 321–342 (1998).

    Article  Google Scholar 

  8. Bertozzi, A.L. & Pugh, M. The lubrication approximation for thin viscous films: regularity and long time behaviour of weak solutions. Comm. Pure Appl. Math. 49, 85–123 (1996).

    Article  Google Scholar 

  9. Grün, G. & Rumpf, M. Nonnegativity preserving convergent schemes for the thin film equation. Num. Math. 87, 113–152 (2000).

    Article  Google Scholar 

  10. Grün, G. On the convergence of entropy consistent schemes for lubrication type equations in multiple space dimensions. Math. Comp. (in the press).

  11. Seemann, R., Herminghaus, S. & Jacobs, K. Gaining control of pattern formation of dewetting liquid films. J. Phys. Condens. Mat. 13, 4925–4938 (2001).

    CAS  Article  Google Scholar 

  12. Herminghaus, S., Seemann, R. & Jacobs, K. The glass transition of thin polymer films: some questions and a possible answer. Eur. Phys. J. E 5, 531–538 (2001).

    CAS  Article  Google Scholar 

  13. Vrij, A. Possible mechanism for the spontaneous rupture of thin, free liquid films. Discuss. Faraday Soc. 42, 23–33 (1966).

    Article  Google Scholar 

  14. Ruckenstein E. & Jain, R.K. Spontaneous rupture of thin liquid films. J. Chem. Soc. Faraday Trans. II 132–147 (1974).

  15. Brochard, F. & Daillant, J. Drying of solids wetted by thin liquid films. Can. J. Phys. 68, 1084–1088 (1990).

    Article  Google Scholar 

  16. Reiter, G. Dewetting of thin polymer films. Phys. Rev. Lett. 68, 751–754 (1992).

    Article  Google Scholar 

  17. Bischof, J., Scherer, D., Herminghaus, S. & Leiderer, P. Dewetting modes of thin metallic films: nucleation of holes and spinodal dewetting. Phys. Rev. Lett. 77, 1536–1539 (1996).

    CAS  Article  Google Scholar 

  18. Jacobs, K., Mecke, K.R. & Herminghaus, S. Thin liquid polymer films rupture via defects. Langmuir 14, 965–969 (1998).

    CAS  Article  Google Scholar 

  19. Herminghaus, S. et al., Spinodal dewetting in liquid crystal and liquid metal films. Science 82, 916–919 (1998).

    Article  Google Scholar 

  20. Sharma, A. & Khanna, R. Pattern formation in unstable liquid films. Phys. Rev. Lett. 81, 3463–3466 (1998).

    CAS  Article  Google Scholar 

  21. Ghatak, A., Khanna, R. & Sharma, A. Dynamics and morphology of holes in dewetting of thin films. J. Colloid Interface Sci. 212, 483–494 (1999).

    CAS  Article  Google Scholar 

  22. Kargupta, K. & Sharma, A. Creation of ordered patterns by dewetting of thin films on homogeneous and heterogeneous substrates. J. Colloid Interface Sci. 245, 99–115 (2002).

    CAS  Article  Google Scholar 

  23. Blossey, R. Nucleation at first-order wetting transitions. Int. J. Mod. Phys. B 9, 3489–3525 (1995).

    CAS  Article  Google Scholar 

  24. Seemann, R., Herminghaus, S. & Jacobs, K. Shape of a liquid front upon dewetting. Phys. Rev. Lett. 81, 1251–1254 (2001).

    Google Scholar 

  25. Mecke, K.R. Integral geometry and statistical physics. Int. J. Mod. Phys. B 12, 861–899 (1998).

    Article  Google Scholar 

  26. Mecke, K.R. & Stoyan, D. (eds.) Statistical Physics and Spatial Statistics - The Art of Analysing and Modelling Spatial Structures and Pattern Formation Lecture Notes in Physics, Vol. 554, (Springer, Berlin, 2000).

    Google Scholar 

  27. Mecke, K.R. Morphological characterization of patterns in reaction-diffusion systems. Phys. Rev. E 53, 4794–4800 (1996).

    CAS  Article  Google Scholar 

  28. Gau, H., Herminghaus, S., Lenz, P. & Lipowsky, R. Liquid morphologies on structured surfaces. Science 283, 46–49 (1999)

    CAS  Article  Google Scholar 

  29. Herminghaus, S., Seemann, R. & Jacobs, K. Generic morphologies of viscoelastic dewetting fronts. Phys. Rev. Lett. 89, 056101 (2002).

  30. Barrett, J.W., Blowey, J.F. & Garcke, H. Finite element approximation of a fourth order nonlinear degenerate parabolic equation. Num. Math. 80, 525–556 (1998).

    Article  Google Scholar 

  31. Zhornitskaja, L. & Bertozzi, A.L. Positivity preserving numerical schemes for lubrication-type equations. SIAM J. Num. Anal. 37, 523–555 (2000).

    Article  Google Scholar 

  32. Grün, G. & Rumpf, M. Simulation of singularities and instabilities in thin film flow. Europ. J. Appl. Math. 12, 293–320 (2001).

    Article  Google Scholar 

  33. Oron, A. Three-dimensional nonlinear dynamics of thin liquid films. Phys. Rev. Lett. 85, 2108–2111 (2000).

    CAS  Article  Google Scholar 

Download references

Acknowledgements

We thank Stephan Herminghaus for many stimulating discussions and Renate Konrad for help in calculating the Minkowski measures. This work was supported by the Priority Program Wetting and Structure Formation at Interfaces of the German Science Foundation through individual research grants to the participating groups. This program provided an ideal forum for the interaction of mathematicians, theoretical and experimental physicists which lead to this interdisciplinary work.

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Correspondence to Ralf Blossey.

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Becker, J., Grün, G., Seemann, R. et al. Complex dewetting scenarios captured by thin-film models. Nature Mater 2, 59–63 (2003). https://doi.org/10.1038/nmat788

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