Noise-activated dissociation of soft elastic contacts

  • M. K. Chaudhury
  • P. S. Goohpattader
Regular Article

Abstract

Adhesive forces are capable of deforming a soft elastic object when it comes in contact with a flat rigid substrate. The contact is in stable equilibrium if the total energy of the system arising from the elastic and surface forces exhibits a minimum at a zero or at a slightly negative load. However, as the system is continually unloaded, the energy barrier decreases and it eventually disappears, thus leading to a ballistic separation of the contact. While this type of contact splitting has received wide recognition, what has not been much appreciated with these types of soft adhesion problems is that rupture of a contact can also occur at any finite sub critical load in the presence of a noise. The soft contact problems are unique in that the noise can be athermal, whereas the metastable and stable states of the thermodynamic potential can arise from the competition of the elastic and the interfacial energies of the system. Analysis based on Kramers' theory and simulations based on Langevin dynamics show that the contact rupture dynamics is amenable to an Eyring's form of a force and noise-induced escape of a particle from a potential well that is generic to various types of colloidal and macromolecular processes. These ideas are useful in understanding the results of a recent experiment involving the noise-activated rolling dynamics of a rigid sphere on a surface, where it is pinned by soft micro-fibrillar contacts.

Graphical abstract

Keywords

Soft Matter: Interfacial Phenomena and Nanostructured Surfaces 

References

  1. 1.
    K. Kendall, Molecular Adhesion and Its Applications (Kluwer Academic/Plenum Publishers, New York, 2001)Google Scholar
  2. 2.
    J.E. Gordon, The New Science of Strong Materials (Princeton University Press, Princeton, 1976)Google Scholar
  3. 3.
    A. Jagota, C.-Y. Hui, Mater. Sci. Engin. R: Reports 72, 253 (2011)Google Scholar
  4. 4.
    R. Thomson, C. Hsieh, V. Rana, J. Appl. Phys. 42, 3154 (1971)ADSCrossRefGoogle Scholar
  5. 5.
    R. Thomson, E.R. Fuller, Bull. Am. Phys. Soc. 22, 443 (1977)Google Scholar
  6. 6.
    K. Kendall, Proc. R. Soc. London, Ser. A 341, 409 (1975)ADSCrossRefGoogle Scholar
  7. 7.
    K.L. Johnson, Contact Mechanics (Cambridge University Press, Cambridge, 1985). The subject is rather vast and it would be impossible to review all the relevant works hereGoogle Scholar
  8. 8.
    D. Maugis, Contact, Adhesion and Rupture of Elastic Solids (Springer-Verlag, Berlin, 2000)Google Scholar
  9. 9.
    V.L. Popov, Contact Mechanics and Friction (Springer, Berlin, 2010)Google Scholar
  10. 10.
    K.L. Johnson, K. Kendall, A.D. Roberts, Proc. R. Soc. London, Ser. A 324, 301 (1971)ADSCrossRefGoogle Scholar
  11. 11.
    V.M. Muller, V.S. Yushchenko, B.V. Derjaguin, J. Colloid Interface Sci. 92, 92 (1983)CrossRefGoogle Scholar
  12. 12.
    M.E.R. Shanahan, J. Adhes. 79, 881 (2003)CrossRefGoogle Scholar
  13. 13.
    D. Maugis, M. Barquins, J. Phys. D: Appl. Phys. 16, 1843 (1983)ADSCrossRefGoogle Scholar
  14. 14.
    J. Shi, S. Muftu, K.T. Wan, J. Appl. Mech. 79, 041015 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    J.B. Pethica, A.P. Sutton, J. Vac. Sci. Technol. A 6, 2490 (1988)ADSCrossRefGoogle Scholar
  16. 16.
    J.R. Smith, G. Bozzolo, A. Banerjea, J. Ferrante, Phys. Rev. Lett. 63, 1269 (1989)ADSCrossRefGoogle Scholar
  17. 17.
    P. Attard, J.L. Parker, Phys. Rev. A 46, 7959 (1992)ADSCrossRefGoogle Scholar
  18. 18.
    J.N. Israelachvili, Intermolecular and Surface Forces, third edition (Academic Press, 2011) ISBN: 978-0-12-375182-9Google Scholar
  19. 19.
    H. Eyring, J. Chem. Phys. 4, 283 (1936)ADSCrossRefGoogle Scholar
  20. 20.
    M. Brillouin, Notice sur les Travaux Scientifiques (Gauthier-Villars, Paris, 1904). As cited in ref. 25Google Scholar
  21. 21.
    G.A. Tomlinson, Philos. Mag. 7, 905 (1929)CrossRefGoogle Scholar
  22. 22.
    L.Z. Prandtl, Angew Math. Mech. 8, 85 (1928)CrossRefGoogle Scholar
  23. 23.
    T.D. Blake, J.M. Haynes, J. Colloid Interface Sci. 30, 421 (1969)CrossRefGoogle Scholar
  24. 24.
    A. Schallamach, Wear 6, 375 (1963)CrossRefGoogle Scholar
  25. 25.
    C. Caroli, P. Nozieres, in Physics of Sliding Friction, edited by B.N.J. Persson, E. Tosatti, Proceedings of the NATO Advanced Research Workshop and Adriatico Research Conference, Miramare, Trieste, Italy, June 20-23, 1995, Series: Nato Science Series E, Vol. 311, ISBN 978-0-7923-3935-9Google Scholar
  26. 26.
    B.N.J. Persson, Phys. Rev. B 51, 13568 (1995)ADSCrossRefGoogle Scholar
  27. 27.
    B.N.J. Persson, Sliding Friction: Physical Principles and Applications (Springer, Berlin, 2000)Google Scholar
  28. 28.
    M. Srinivasan, S. Walcott, Phys. Rev. E 80, 046124 (2009)ADSCrossRefGoogle Scholar
  29. 29.
    M.H. Muser, Phys. Rev. B 84, 125419 (2011)ADSCrossRefGoogle Scholar
  30. 30.
    A.K. Singh, V.A. Juvekar, Soft Matter 7, 10601 (2011)ADSCrossRefGoogle Scholar
  31. 31.
    B. Lawn, Fracture of Brittle Solids (Cambridge University Press, Cambridge, 1993)Google Scholar
  32. 32.
    G.I. Bell, Science 200, 618 (1978)ADSCrossRefGoogle Scholar
  33. 33.
    E. Evans, K. Ritchie, Biophys. J. 72, 1541 (1997)CrossRefGoogle Scholar
  34. 34.
    H.A. Kramers, Physica 7, 284 (1940)ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    R. Zwanzig, Nonequilibrium Statistical Mechanics (Oxford University Press, New York, 2001)Google Scholar
  36. 36.
    A. Garg, Phys. Rev. B 51, 15592 (1995)ADSCrossRefGoogle Scholar
  37. 37.
    A. Ghatak, K. Vorvolakos, H. She, D.L. Malotky, M.K. Chaudhury, J. Phys. Chem. B 104, 4018 (2000)CrossRefGoogle Scholar
  38. 38.
    O.K. Dudko, A.E. Filippov, J. Klafter, M. Urbakh, Proc. Natl. Acad. Sci. U.S.A. 100, 11378 (2003)ADSCrossRefGoogle Scholar
  39. 39.
    O.K. Dudko, G. Hummer, A. Szabo, Proc. Natl. Acad. Sci. U.S.A. 105, 15755 (2008)ADSCrossRefGoogle Scholar
  40. 40.
    L.B. Freund, Proc. Natl. Acad. Sci. U.S.A. 106, 8818 (2009)ADSCrossRefGoogle Scholar
  41. 41.
    H.J. Lin, H.Y. Chen, Y.J. Sheng, H.K. Tsao, Phys. Rev. Lett. 98, 088304 (2007)ADSCrossRefGoogle Scholar
  42. 42.
    D.J. Lacks, J. Willis, M.P. Robinson, J. Phys. Chem. B 114, 10821 (2010)CrossRefGoogle Scholar
  43. 43.
    M.H. Muser, Phys. Rev. B 84, 125419 (2011)ADSCrossRefGoogle Scholar
  44. 44.
    P.S. Goohpattader, S. Mettu, M.K. Chaudhury, Eur. Phys. J. E 34, 120 (2011)CrossRefGoogle Scholar
  45. 45.
    P.S. Goohpattader, M.K. Chaudhury, Eur. Phys. J. E. 35, 67 (2012)CrossRefGoogle Scholar
  46. 46.
    K. Kendall, J. Phys. D: Appl. Phys. 4, 1186 (1971)ADSCrossRefGoogle Scholar
  47. 47.
    D. Maugis, M. Barquins, J. Phys. Lett. 42, L95 (1981)CrossRefGoogle Scholar
  48. 48.
    S. Kim et al., Proc. Natl. Acad. Sci. U.S.A. 107, 17095 (2010)ADSCrossRefGoogle Scholar
  49. 49.
    N.J. Glassmaker, A. Jagota, C.Y. Hui, W.L. Noderer, M.K. Chaudhury, Proc. Natl. Acad. Sci. U.S.A. 104, 10786 (2007)ADSCrossRefGoogle Scholar
  50. 50.
    W.L. Noderer, L. Shen, S. Vajpayee, N.J. Glassmaker, A. Jagota, C.Y. Hui, Proc. R. Soc. London, Ser. A 463, 2631 (2007)ADSCrossRefGoogle Scholar
  51. 51.
    J.A. Greenwood, K.L. Johnson, S.-H. Choi, M.K. Chaudhury, J. Phys. D 42, 035301 (2009)ADSCrossRefGoogle Scholar
  52. 52.
    P. Sharma, S. Ghosh, S. Bhattacharya, Nat. Phys. 4, 960 (2008)CrossRefGoogle Scholar
  53. 53.
    J.A. Greenwood, J. Phys. D: Appl. Phys. 40, 1769 (2007)ADSCrossRefGoogle Scholar
  54. 54.
    H. Sakaguchi, J. Phys. Soc. Jpn. 75, 124006 (2006)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • M. K. Chaudhury
    • 1
  • P. S. Goohpattader
    • 1
  1. 1.Department of Chemical EngineeringLehigh UniversityBethlehemUSA

Personalised recommendations