Adhesion-induced instabilities and pattern formation in thin films of elastomers and gels

  • Manoj K. Chaudhury
  • Aditi Chakrabarti
  • Animangsu Ghatak
Colloquium

Abstract

A hydrostatically stressed soft elastic film circumvents the imposed constraint by undergoing a morphological instability, the wavelength of which is dictated by the minimization of the surface and the elastic strain energies of the film. While for a single film, the wavelength is entirely dependent on its thickness, a co-operative energy minimization dictates that the wavelength depends on both the elastic moduli and thicknesses of two contacting films. The wavelength can also depend on the material properties of a film if its surface tension has a pronounced effect in comparison to its elasticity. When such a confined film is subjected to a continually increasing normal displacement, the morphological patterns evolve into cracks, which, in turn, govern the adhesive fracture behavior of the interface. While, in general, the thickness provides the relevant length scale underlying the well-known Griffith-Kendall criterion of debonding of a rigid disc from a confined film, it is modified non-trivially by the elasto-capillary number for an ultra-soft film. Depending upon the degree of confinement and the spatial distribution of external stress, various analogs of the canonical instability patterns in liquid systems can also be reproduced with thin confined elastic films.

Graphical abstract

Keywords

Soft Matter: Interfacial Phenomena and Nanostructured Surfaces 

Supplementary material

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References

  1. 1.
    Lord Rayleigh, Proc. London Math. Soc. 10, 4 (1878).Google Scholar
  2. 2.
    G.P. Ivantsov, Dokl. Akad. Nauk USSR 58, 567 (1947).Google Scholar
  3. 3.
    W.W. Mullins, R.F. Sekerka, J. Appl. Phys. 34, 323 (1963).ADSGoogle Scholar
  4. 4.
    W. Thomson, Philos. Mag. 42, 362 (1871).Google Scholar
  5. 5.
    P.G. Saffman, G.I. Taylor, Proc. R. Soc. London A 245, 312 (1958).MathSciNetADSMATHGoogle Scholar
  6. 6.
    X. Cheng, L. Xu, A. Patterson, H.M. Jaeger, S.R. Nagel, Nat. Phys. 4, 234 (2008).Google Scholar
  7. 7.
  8. 8.
    B. Audoly, Y. Pomeau, Elasticity and Geometry: from Hair Curls to The Non-Linear Response of Shells (Oxford University Press, New York, 2010).Google Scholar
  9. 9.
    A.L. Volynskii, S. Bazhenov, O.V. Lebedeva, N.F. Bakeev, J. Mater. Sci. 35, 547 (2000).ADSGoogle Scholar
  10. 10.
    H. Huang, J.Y. Chung, A.J. Nolte, C.M. Stafford, Chem. Mater. 19, 6555 (2007).Google Scholar
  11. 11.
    J. Genzer, J. Groenewold, Soft Matter 2, 310 (2006).ADSGoogle Scholar
  12. 12.
    A.E. Cohen, L. Mahadevan, Proc. Natl. Acad. Sci. U.S.A. 100, 12141 (2003).ADSGoogle Scholar
  13. 13.
    M.A. Biot, Appl. Sci. Res. A 12, 168 (1963).MATHGoogle Scholar
  14. 14.
    J. Dervaux, M. Ben Amar, Annu. Rev. Condens. Matter Phys. 3, 311 (2012).Google Scholar
  15. 15.
    T. Tanaka, S.T. Sun, Y. Hirokawa, S. Katayama, J. Kucera, Y. Hirose, T. Amiya, Nature 325, 796 (1987).ADSGoogle Scholar
  16. 16.
    B. Li, Y.P. Cao, X.Q. Feng, H.J. Gao, Soft Matter 8, 5728 (2012).ADSGoogle Scholar
  17. 17.
    V. Trujillo, J. Kim, R.C. Hayward, Soft Matter 4, 564 (2008).ADSGoogle Scholar
  18. 18.
    W. Hong, X. Zhao, Z. Suo, Appl. Phys. Lett. 95, 111901 (2009).ADSGoogle Scholar
  19. 19.
    A.N. Gent, I.S. Cho, Rubber Chem. Technol. 72, 253 (1999).Google Scholar
  20. 20.
    M. Taffetani, P. Ciarletta, Phys. Rev. E 91, 032413 (2015).ADSGoogle Scholar
  21. 21.
    P. Ciarletta, L. Foret, M. Ben Amar, J. R. Soc. Interface 8, 345 (2011).Google Scholar
  22. 22.
    T. Tallinen, J.Y. Chung, J.S. Biggins, L. Mahadevan, Proc. Natl. Acad. Sci. U.S.A. 111, 12667 (2014).ADSGoogle Scholar
  23. 23.
    E. Hannezo, J. Prost, J.F. Joanny, Phys. Rev. Lett. 107, 078104 (2011).ADSGoogle Scholar
  24. 24.
    R.J. Asaro, W.A. Tiller, Metall. Trans. 3, 1789 (1972).Google Scholar
  25. 25.
    M. Grinfeld, J. Nonlinear Sci. 3, 35 (1993).MathSciNetADSMATHGoogle Scholar
  26. 26.
    D. Srolovitz, Acta Metall. 37, 621 (1989).Google Scholar
  27. 27.
    J.C. Ramirez, Int. J. Solids Struct. 25, 579 (1989).MATHGoogle Scholar
  28. 28.
    S.S. Park, D.J. Durian, Phys. Rev. Lett. 72, 3347 (1994).ADSGoogle Scholar
  29. 29.
    A. Ghatak, M.K. Chaudhury, V. Shenoy, A. Sharma, Phys. Rev. Lett. 85, 4329 (2000).ADSGoogle Scholar
  30. 30.
    W. Mönch, S. Herminghaus, Europhys. Lett. 53, 525 (2001).ADSGoogle Scholar
  31. 31.
    V. Shenoy, A. Sharma, Phys. Rev. Lett. 89, 119 (2001).ADSGoogle Scholar
  32. 32.
    A. Ghatak, M.K. Chaudhury, Langmuir 19, 2621 (2003).Google Scholar
  33. 33.
    J.Y. Chung, M.K. Chaudhury, J. Adhesion 81, 1119 (2005).Google Scholar
  34. 34.
    A. Ghatak, L. Mahadevan, J.Y. Chung, M.K. Chaudhury, V. Shenoy, Proc. R. Soc. London A 460, 2725 (2004).ADSMATHGoogle Scholar
  35. 35.
    J. Sarkar, V. Shenoy, A. Sharma, Phys. Rev. E 67, 031607 (2003).ADSGoogle Scholar
  36. 36.
    M. Gonuguntla, A. Sharma, J. Sarkar, S.A. Subramanian, M. Ghosh, V. Shenoy, Phys. Rev. Lett. 97, 018303 (2006).ADSGoogle Scholar
  37. 37.
    J.E. Longley, L. Mahadevan, M.K. Chaudhury, EPL 104, 46002 (2013).ADSGoogle Scholar
  38. 38.
    J.Y. Chung, K.H. Kim, M.K. Chaudhury, J. Sarkar, A. Sharma, Eur. Phys. J. E 20, 47 (2006).Google Scholar
  39. 39.
    M.K. Chaudhury, K.H. Kim, Eur. Phys. J. E 23, 175 (2007).Google Scholar
  40. 40.
    M.K. Chaudhury, J.Y. Chung, Langmuir 23, 8061 (2007).Google Scholar
  41. 41.
    J.Y. Chung, M.K. Chaudhury, J. R. Soc. Interface 2, 55 (2005).Google Scholar
  42. 42.
    J. Sarkar, A. Sharma, Langmuir 26, 8464 (2010).Google Scholar
  43. 43.
    N. Arun, A. Sharma, V.B. Shenoy, K.S. Narayan, Adv. Mater. 18, 660 (2006).Google Scholar
  44. 44.
    C. Creton, H. Lakrout, J. Polym. Sci., Part B: Polym. Phys. 38, 965 (2000).ADSGoogle Scholar
  45. 45.
    K.R. Shull, C. Creton, J. Polym. Sci., Part B: Polym. Phys. 42, 4023 (2004).ADSGoogle Scholar
  46. 46.
    H. Lakrout, P. Sergot, C. Creton, J. Adhes. 69, 307 (1999).Google Scholar
  47. 47.
    G.H. McKinley, Dynamics of Complex Fluids.Google Scholar
  48. 48.
    S.J. Muller, R.G. Larson, E.S.G. Shaqfeh, Rheol. Acta 28, 499 (1989).Google Scholar
  49. 49.
    A. Zosel, J. Adhes. 30, 135 (1989).Google Scholar
  50. 50.
    Y. Urahama, J. Adhes. 31, 47 (1989).Google Scholar
  51. 51.
    B.-M. Zhang Newby, M.K. Chaudhury, H.R. Brown, Science 269, 1407 (1995).ADSGoogle Scholar
  52. 52.
    D.H. Kaelble, Trans. Soc. Rheol. 4, 45 (1960).ADSGoogle Scholar
  53. 53.
    C. Gay, L. Leibler, Phys. Rev. Lett. 82, 936 (1999).ADSGoogle Scholar
  54. 54.
    S. Mora, T. Phou, J.M. Fromental, L.M. Pismen, Y. Pomeau, Phys. Rev. Lett. 105, 214301 (2010).ADSGoogle Scholar
  55. 55.
    S. Mora, T. Phou, J.M. Fromental, Y. Pomeau, Phys. Rev. Lett. 113, 178301 (2014).ADSGoogle Scholar
  56. 56.
    S. Mora, M. Abkarian, H. Tabuteau, Y. Pomeau, Soft Matter 7, 10612 (2011).ADSGoogle Scholar
  57. 57.
    N. Nadermann, C.-Y. Hui, A. Jagota, Proc. Natl. Acad. Sci. U.S.A. 110, 10541 (2013).ADSGoogle Scholar
  58. 58.
    A. Jagota, D. Paretkar, A. Ghatak, Phys. Rev. E 85, 051602 (2012).ADSGoogle Scholar
  59. 59.
    J.B. Bostwick, M. Shearer, K.E. Daniels, Soft Matter 10, 7361 (2014).ADSGoogle Scholar
  60. 60.
    T. Kajiya, P. Brunet, L. Royon, A. Daerr, M. Receveur, L. Limat, Soft Matter 10, 8888 (2014).Google Scholar
  61. 61.
    R.W. Style, R. Boltyanskiy, B. Allen, K.E. Jensen, H.P. Foote, J.S. Wettlaufer, E.R. Dufresne, Nat. Phys. 11, 82 (2014).Google Scholar
  62. 62.
    J.-M.Y. Carrillo, A.V. Dobrynin, Langmuir 28, 10881 (2012).Google Scholar
  63. 63.
    T. Salez, M. Benzaquen, É. Raphaël, Soft Matter 9, 10699 (2013).ADSGoogle Scholar
  64. 64.
    C.-Y. Hui, T. Liu, T. Salez, E. Raphael, A. Jagota, Proc. R. Soc. A 471, 20140727 (2015).MathSciNetADSGoogle Scholar
  65. 65.
    D. Chen, S. Cai, Z. Suo, R.C. Hayward, Phys. Rev. Lett. 109, 038001 (2012).ADSGoogle Scholar
  66. 66.
    J.A. Zimberlin, A.J. Crosby, J. Polym. Sci. B Polym. Phys. 48, 1423 (2010).ADSGoogle Scholar
  67. 67.
    A. Majumder, A.K. Tiwari, K. Korada, A. Ghatak, J. Adhes. Sci. Technol. 24, 2681 (2010).Google Scholar
  68. 68.
    Q. Wang, X. Zhao, Sci. Rep. 5, 8887 (2015).ADSGoogle Scholar
  69. 69.
    A.A. Griffith, Philos. Trans. R. Soc. London Ser. A 221, 163 (1921).ADSGoogle Scholar
  70. 70.
    A.D. Kerr, Ingenieur-Archiv 54, 455 (1984).MATHGoogle Scholar
  71. 71.
    C.Q. Ru, J. Appl. Phys. 90, 6098 (2001).ADSGoogle Scholar
  72. 72.
    F. Yang, J.C.M. Li, Langmuir 17, 6524 (2001).Google Scholar
  73. 73.
    A.N. Gent, P.B. Lindley, Proc. R. Soc. London A 249, 195 (1959).ADSGoogle Scholar
  74. 74.
    K.R. Shull, C.M. Flanigan, A.J. Crosby, Appl. Phys. Lett. 84, 3057 (2000).Google Scholar
  75. 75.
    J.S. Biggins, B. Saintyves, Z. Wei, E. Bouchaud, L. Mahadevan, Proc. Natl. Acad. Sci. U.S.A. 110, 12545 (2013).ADSGoogle Scholar
  76. 76.
    P. Attard, J.L. Parker, Phys. Rev. A 46, 7959 (1992).ADSGoogle Scholar
  77. 77.
    A. Chakrabarti, M.K. Chaudhury, Langmuir 29, 6926 (2013).Google Scholar
  78. 78.
    T. Vilmin, F. Ziebert, E. Raphaël, Langmuir 26, 3257 (2009).Google Scholar
  79. 79.
    K. Kendall, J. Phys. D: Appl. Phys. 4, 1186 (1971).ADSGoogle Scholar
  80. 80.
    D. Maugis, M. Barquins, J. Phys. D: Appl. Phys. 16, 1843 (1983).ADSGoogle Scholar
  81. 81.
    K. Kendall, Molecular Adhesion and Its Applications (Kluwer Academic/Plenum Publishers, New York, 2001).Google Scholar
  82. 82.
    D. Maugis, Contact, Adhesion and Rupture of Elastic Solids (Springer-Verlag, Berlin, 2000).Google Scholar
  83. 83.
    G.J. Lake, A.G. Thomas, Proc. R. Soc. London A 300, 108 (1967).ADSGoogle Scholar
  84. 84.
    A. Ghatak, K. Vorvolakos, H. She, D.L. Malotky, M.K. Chaudhury, J. Phys. Chem. B 104, 4018 (2000).Google Scholar
  85. 85.
    M.K. Chaudhury, J. Phys. Chem. B 103, 6562 (1999).Google Scholar
  86. 86.
    H. She, D. Malotky, M.K. Chaudhury, Langmuir 14, 3090 (1998).Google Scholar
  87. 87.
    A. Ghatak, K. Vorvolakos, H. She, D.L. Malotky, M.K. Chaudhury, J. Phys. Chem. B 104, 4018 (2000).Google Scholar
  88. 88.
    M.E.R. Shanahan, F. Michel, Int. J. Adhes. 11, 170 (1991).Google Scholar
  89. 89.
    K. Vorvolakos, M.K. Chaudhury, Langmuir 19, 6778 (2003).Google Scholar
  90. 90.
    K.H. Kim, M.K. Chaudhury, J. Adhes. 85, 792 (2009).Google Scholar
  91. 91.
    T. Takigawa, Y. Morino, K. Urayama, T. Masuda, Polym. Gels Netw. 4, 1 (1996).Google Scholar
  92. 92.
    R.J. Fields, M.F. Ashby, Philos. Mag. 33, 33 (1976).ADSGoogle Scholar
  93. 93.
    R. Menikoff, R.C. Mjolsness, D.H. Sharp, C. Zemach, Phys. Fluids 20, 2000 (1977).ADSMATHGoogle Scholar
  94. 94.
    A.J. Babchin, A.L. Frenkel, B.G. Levich, Phys. Fluids 26, 3159 (1983).ADSMATHGoogle Scholar
  95. 95.
    H.R. Brown, Phys. Fluids A 1, 895 (1989).ADSGoogle Scholar
  96. 96.
    M.M. Denn, Annu. Rev. Fluid Mech. 33, 265 (2001).ADSGoogle Scholar
  97. 97.
    A. Ghatak, PhD thesis, Lehigh University (2003).Google Scholar
  98. 98.
    A. Ghatak, Phys. Rev. E 73, 041601 (2006).ADSGoogle Scholar
  99. 99.
    A. Ghatak, M.K. Chaudhury, J. Adhes. 83, 679 (2007).Google Scholar
  100. 100.
    J. Nase, A. Lindner, C. Creton, Phys. Rev. Lett. 101, 074503 (2008).ADSGoogle Scholar
  101. 101.
    F. Varela Lopez, L. Pauchard, M. Rosen, M. Rabaud, J. Non-Newtonian Fluid Mech. 103, 123 (2002).MATHGoogle Scholar
  102. 102.
    K.-T. Wan, D.T. Smith, B.R. Lawn, J. Am. Ceram. Soc. 75, 667 (1992).Google Scholar
  103. 103.
    K.-T. Wan, N. Aimard, S. Lathabai, R.G. Horn, B.R. Lawn, J. Mater. Res. 5, 172 (1990).ADSGoogle Scholar
  104. 104.
    J.W. Obreimoff, Proc. R. Soc. London A 127, 290 (1930).ADSGoogle Scholar
  105. 105.
    D.A. Dillard, J. Appl. Mech. 56, 382 (1989).ADSMATHGoogle Scholar
  106. 106.
    Z. Zong, C.-L. Chen, M.R. Dokmeci, K.-T. Wan, J. Appl. Phys. 107, 026104 (2010).ADSGoogle Scholar
  107. 107.
    T. Yamaguchi, S. Ohmata, M. Doi, J. Phys.: Condens. Matter 21, 205105 (2009).ADSGoogle Scholar
  108. 108.
    A. Schallamach, Wear 17, 301 (1971).Google Scholar
  109. 109.
    M. Barquins, Mater. Sci. Engg. 73, 45 (1985).Google Scholar
  110. 110.
    C.J. Rand, A.J. Crosby, Soft Matter 89, 261907 (2006).Google Scholar
  111. 111.
    K. Viswanathan, A. Mahato, S. Chandrasekar, Phys. Rev. E 91, 012408 (2015).ADSGoogle Scholar
  112. 112.
    K.L. Johnson, J.A. Greenwood, J. Colloid Interface Sci. 192, 326 (1997).Google Scholar
  113. 113.
    B.-M. Zhang Newby, M.K. Chaudhury, Langmuir 14, 4865 (1998).Google Scholar
  114. 114.
    J. Nase, O. Ramos, C. Creton, A. Lindner, Eur. Phys. J. E 36, 103 (2013).Google Scholar
  115. 115.
    A. Ghatak, L. Mahadevan, M.K. Chaudhury, Langmuir 21, 1277 (2005).Google Scholar
  116. 116.
    T. Tang, A. Jagota, M.K. Chaudhury, C.-Y. Hui, J. Adhes. 82, 671 (2006).Google Scholar
  117. 117.
    D.A. Hill, T. Hasegawa, M.M. Denn, J. Rheol. 34, 891 (1990).ADSGoogle Scholar
  118. 118.
    M. Barquins, R. Courtel, Wear 32, 133 (1975).Google Scholar
  119. 119.
    J.H. Gittus, Philos. Mag. 31, 317 (1975).ADSGoogle Scholar
  120. 120.
    B. Best, P. Meijers, A.R. Savkoor, Wear 65, 385 (1981).Google Scholar
  121. 121.
    M. Barquins, A.D. Roberts, J. Phys. D 19, 547 (1986).ADSGoogle Scholar
  122. 122.
    A.D. Roberts, S.A. Jackson, Nature London 257, 119 (1975).ADSGoogle Scholar
  123. 123.
    G.A.D. Briggs, B.J. Briscoe, Nature London 262, 381 (1976).ADSGoogle Scholar
  124. 124.
    B.J. Briscoe, D.C.B. Evans, Proc. R. Soc. London A 380, 389 (1982).ADSGoogle Scholar
  125. 125.
    K. Kendall, Philos. Mag. A 43, 713 (1981).ADSGoogle Scholar
  126. 126.
    G.J. Lake, A. Stevenson, J. Adhes. 12, 13 (1981).Google Scholar
  127. 127.
    N.J. Balmforth, R.V. Craster, I.J. Hewitt, Proc. R. Soc. A 471, 20140740 (2015).MathSciNetADSGoogle Scholar
  128. 128.
    A. Ghatak, A.L. Das, Phys. Rev. Lett. 99, 076101 (2007).ADSGoogle Scholar
  129. 129.
    D.P. Holmes, A.J. Crosby, Phys. Rev. Lett. 105, 038303 (2010).ADSGoogle Scholar
  130. 130.
    M.K. Chaudhury, A. Chakrabarti, S. Daniel, Langmuir DOI:10.1021/la504925u (2015).
  131. 131.
    M. Cavallaro, M.A. Gharbi, D.A. Beller, S. Copar, Z. Shi, T. Baumgart, S. Yang, R.D. Kamien, K.J. Stebe, Proc. Natl. Acad. Sci. U.S.A. 110, 18804 (2013).ADSGoogle Scholar
  132. 132.
    M.A. Lohr, M. Cavallaro, D.A. Beller, K.J. Stebe, R.D. Kamien, P.J. Collings, A.G. Yodh, Soft Matter 10, 3477 (2014).ADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Manoj K. Chaudhury
    • 1
  • Aditi Chakrabarti
    • 1
  • Animangsu Ghatak
    • 2
  1. 1.Department of Chemical and Biomolecular EngineeringLehigh UniversityBethlehemUSA
  2. 2.Department of Chemical EngineeringIndian Institute of TechnologyKanpurIndia

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