Skip to main content
SpringerLink
Log in

Wrinkling of a charged elastic film on a viscous layer

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

A thin metallic film deposited on a compliant polymeric substrate begins to wrinkle under compression induced in curing process and afterwards cooling of the system. The wrinkle mode depends upon the thin film elasticity, thickness, compressive strain, as well as mechanical properties of the compliant substrate. This paper presents a simple model to study the modulation of the wrinkle mode of thin metallic films bonded on viscous layers in external electric field. During the procedure, linear perturbation analysis was performed for determining the characteristic relation that governs the evolution of the plane-strain wrinkle of the thin films under varying conditions, i.e., the maximally unstable wrinkle mode as a function of the film surface charge, film elasticity and thickness, misfit strain, as well as thickness and viscosity of the viscous layer. It shows that, in proper electric field, thin film may wrinkle subjected to either compression or tension. Therefore, external electric field can be employed to modulate the wrinkle mode of thin films. The present results can be used as the theoretical basis for wrinkling analysis and mode modulation in surface metallic coatings, drying adhesives and paints, and microelectromechanical systems (MEMS), etc.

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

Similar content being viewed by others

References

  1. Bowden N, Brittain S, Evans AG, Hutchinson JW, Whitesides GM, (1998) Spontaneous formation of ordered structures in thin films of metals supported on elastomeric polymer. Nature (London) 393(6681):146–149

    Article  ADS  Google Scholar 

  2. Cerda E, Ravi-Chandar K, Mahadevan L (2002) Thin films-wrinkling of an elastic sheet under tension. Nature (London) 419(6907):579–580

    Article  ADS  Google Scholar 

  3. Chan EP, Crosby AJ (2006) Spontaneous formation of stable aligned wrinkling patterns. Soft Matter 2:324–328

    Article  Google Scholar 

  4. Chen X, Hutchinson JW (2004) A family of herringbone patterns in thin films. Scr Mater 50:797–801

    Article  Google Scholar 

  5. Chen X, Hutchinson JW (2004) Herringbone buckling patterns of compressed thin films on compliant substrates. ASME J Appl Mech 71:597–603

    Article  MATH  Google Scholar 

  6. Chou SY, Zhuang L (1999) Lithographically induced self-assembly of periodic polymer micropillar arrays. J Vac Sci Technol B 17(6):3197–3202

    Article  Google Scholar 

  7. Chou SY, Zhuang L, Guo LJ (1999) Lithographically induced self-construction of polymer microstructures for resistless patterning. Appl Phys Lett 75(7):1004–1006

    Article  ADS  Google Scholar 

  8. Craster RV, Matar OK (2005) Electrically induced pattern formation in thin leaky dielectric films. Phys Fluids 17(3), Article No. 032104

  9. Genzer J, Groenewold J (2006) Soft matter with hard skin: from skin wrinkling to templating and material characterization. Soft Matter 2:310–323

    Article  Google Scholar 

  10. Gioia G, Ortiz M (1997) Delamination of compressed thin film. Adv Appl Mech 33:119–192

    Google Scholar 

  11. Huang R (2005a) Kinetic wrinkling of an elastic film on viscoelastic substrate. J Mech Phys Solids 53:63–89

    Article  MATH  ADS  Google Scholar 

  12. Huang R (2005b) Electrically induced surface instability of a conductive thin film on a dielectric substrate. Appl Phys Lett 87, Article No. 151911

  13. Huang R, Suo Z (2002a) Wrinkling of a compressed elastic film on a viscous layer. J Appl Phys 91(3):1135–1142

    Article  ADS  Google Scholar 

  14. Huang R, Suo Z (2002b) Instability of a compressed elastic film on a viscous layer. Int J Solids Struct 39(7):1791–1802

    Article  MATH  Google Scholar 

  15. Huang ZY, Hong W, Suo Z (2004) Evolution of wrinkles in hard films of soft substrates. Phys Rev E 70, Article No. 030601

  16. Huang ZY, Hong W, Suo Z (2005) Nonlinear analyses of wrinkles in a film bonded to a compliant substrate. J Mech Phys Solids 53:2101–2118

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. Huck WTS, Bowden N, Onck P, Pardoen T, Hutchinson JW, Whitesides GW (2000) Ordering of spontaneously formed buckles on planar surfaces. Langmuir 16(7):3497–3501

    Article  Google Scholar 

  18. Hutchinson JW, Suo Z (1992) Mixed-mode cracking in layered materials. Adv Appl Mech 29:63–191

    Article  MATH  Google Scholar 

  19. Kim D, Lu W (2006) Three-dimensional model of electrostatically induced pattern formation in thin polymer films. Phys Rev B 73, Article No. 035206

  20. Landau LD, Lifshitz EM, Pitaevskii LP (1993) Electrodynamics of continuous media, 2nd edn. Butterworth-Heinemann, Oxford, pp. 29–33

    Google Scholar 

  21. Liang J, Huang R, Yin H, Sturm JC, Hobart KD, Suo Z (2002) Relaxation of compressed elastic islands on a viscous layer. Acta Mater 50(11):2933–2944

    Article  Google Scholar 

  22. Pease LF, Russel WB (2002) Linear stability analysis of thin leaky dielectric films subjected to electric fields. J Non-Newtonian Fluid Mech 102(2):233–250

    Article  MATH  Google Scholar 

  23. Pease LF, Russel WB (2003) Electrostatically induced submicron patterning of thin perfect and leaky dielectric films: a generalized linear stability analysis. J Chem Phys 118(8):3790–3803

    Article  ADS  Google Scholar 

  24. Schaffer E, Thurn-Albrecht T, Russell TP, Steiner U (2000) Electrically induced structure formation and pattern transfer. Nature (London) 403(6772):874–877

    Article  ADS  Google Scholar 

  25. Schaffer E, Thurn-Albrecht T, Russell TP, Steiner U (2001) Electrohydrodynamic instabilities in polymer films. Europhys Lett 53(4):518–524

    Article  ADS  Google Scholar 

  26. Sridhar N, Srolovitz DJ, Suo Z (2001) Kinetics of buckling of a compressed film on a viscous substrate. Appl Phys Lett 78(17):2482–2484

    Article  ADS  Google Scholar 

  27. Timoshenko S, Woinowsky-Krieger S (1987) Theory of plates and shells, 2nd edn. McGraw-Hill, New York, pp 378–380

    Google Scholar 

  28. Wu L, Chou SY (2003) Dynamic modeling and scaling of nanostructure formation in the lithographically induced self-assembly and self-construction. Appl Phys Lett 82(19):3200–3202

    Article  ADS  Google Scholar 

  29. Wu L, Chou SY (2005) Electrohydrodynamic instability of a thin film of viscoelastic polymer underneath a lithographically manufactured mask. J Non-Newtonian Fluid Mech 125(2–3):91–99

    Article  MATH  Google Scholar 

  30. Wu N, Russel WB (2005) Dynamics of the formation of polymeric microstructures induced by electrohydrodynamic instability. Appl Phys Lett 86, Article No. 241912

  31. Wu N, Pease LF, Russel WB (2005) Electric-filed-induced patterns in thin polymer films: weakly nonlinear and fully nonlinear evolution. Langmuir 21(26):12290–12302

    Article  Google Scholar 

  32. Wu N, Pease LF, Russel WB (2006) Toward large-scale alignment of electrohydrodynamic patterning of thin polymer films. Adv Funct Mater 16(15):1992–1999

    Article  Google Scholar 

  33. Wu XF, Dzenis YA (2005) Electrohydrodynamic instability of thin conductive liquid film. J Phys D Appl Phys 38(16):2848–2850

    Article  ADS  Google Scholar 

  34. Yoo PJ, Suh KY, Park SY, Lee HH (2002) Physical self-assembly of microstructures by anisotropic buckling. Adv Mater (Weinhein, Germany) 14(19):1383–1387

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering Mechanics, Center for Materials Research and Analysis, University of Nebraska-Lincoln, Lincoln, NE, 68588-0526, USA

    Xiang-Fa Wu & Yuris A. Dzenis

  2. Department of Mechanical Engineering and Department of Mathematics and Statistics, University of Nebraska-Lincoln, Lincoln, NE, 68588-0323, USA

    Kyle W. Strabala

Authors
  1. Xiang-Fa Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuris A. Dzenis
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kyle W. Strabala
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiang-Fa Wu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, XF., Dzenis, Y.A. & Strabala, K.W. Wrinkling of a charged elastic film on a viscous layer. Meccanica 42, 273–282 (2007). https://doi.org/10.1007/s11012-007-9054-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-007-9054-x

Keywords

Search

Navigation