Skip to main content

Irreversible adsorption from dilute polymer solutions

Abstract.

We study irreversible polymer adsorption from dilute solutions theoretically. Universal features of the resultant non-equilibrium layers are predicted. Two broad cases are considered, distinguished by the magnitude of the local monomer-surface sticking rate Q: chemisorption (very small Q) and physisorption (large Q). Early stages of layer formation entail single-chain adsorption. While single-chain physisorption times \(\tau_{\rm ads}\) are typically micro- to milli-seconds, for chemisorbing chains of N units we find experimentally accessible times \(\tau_{\rm ads} = Q^{-1} N^{3/5}\), ranging from seconds to hours. We establish 3 chemisorption universality classes, determined by a critical contact exponent: zipping, accelerated zipping and homogeneous collapse. For dilute solutions, the mechanism is accelerated zipping: zipping propagates outwards from the first attachment, accelerated by occasional formation of large loops which nucleate further zipping. This leads to a transient distribution \(\omega(s) \sim s^{-7/5}\) of loop lengths s up to a maximum size \(s^{\max} \approx (Q t)^{5/3}\) after time t. By times of order \(\tau_{\rm ads}\) the entire chain is adsorbed. The outcome of the single-chain adsorption episode is a monolayer of fully collapsed chains. Having only a few vacant sites to adsorb onto, late-arriving chains form a diffuse outer layer. In a simple picture we find for both chemisorption and physisorption a final loop distribution \(\Omega(s) \sim s^{-11/5}\) and density profile \(c(z) \sim z^{-4/3}\) whose forms are the same as for equilibrium layers. In contrast to equilibrium layers, however, the statistical properties of a given chain depend on its adsorption time; the outer layer contains many classes of chain, each characterized by a different fraction of adsorbed monomers f. Consistent with strong physisorption experiments, we find the f values follow a distribution \(P(f) \sim f^{-4/5}\).

This is a preview of subscription content, access via your institution.

References

  1. P.G. de Gennes, Adv. Colloid Interface Sci. 27, 189 (1987).

    Article  Google Scholar 

  2. G.J. Fleer, M.A. Cohen Stuart, J.M.H.M. Scheutjens, T. Cosgrove, B. Vincent, Polymers at Interfaces (Chapman and Hall, London, 1993).

  3. E. Bouchaud, M. Daoud, J. Phys. (Paris) 48, 1991 (1987).

    MathSciNet  Article  Google Scholar 

  4. P.G. de Gennes, Some dynamical features of adsorbed polymers, in Molecular Conformation and Dynamics of Macromolecules in Condensed Systems, edited by N. Nagasawa (Elsevier, Amsterdam, 1988) pp. 315-331.

  5. P.G. de Gennes, Dynamics of adsorbed polymers, in New Trends in Physics and Physical Chemistry of Polymers, edited by Lieng-Huang Lee (Plenum Press, New York, 1989) pp. 9-18.

  6. A.N. Semenov, J.-F. Joanny, J. Phys. II 5, 859 (1995).

    Google Scholar 

  7. L.T. Lee, O. Guiselin, B. Farnoux, A. Lapp, Macromolecules 24, 2518 (1991).

    ADS  Article  Google Scholar 

  8. L. Auvray, J.P. Cotton, Macromolecules 20, 202 (1987).

    ADS  Article  Google Scholar 

  9. M. Kawaguchi, A. Takahashi, Macromolecules 16, 1465 (1983).

    ADS  Article  Google Scholar 

  10. P.G. de Gennes, Macromolecules 14, 1637 (1981).

    ADS  Article  Google Scholar 

  11. P.G. de Gennes, P. Pincus, J. Phys. (Paris) Lett. 44, L241 (1983).

  12. E. Eisenriegler, J. Chem. Phys. 79, 1052 (1983).

    ADS  Article  Google Scholar 

  13. P.G. de Gennes, C. R. Acad. Sci. Paris Ser. II 294, 1317 (1982).

    Google Scholar 

  14. M. Aubouy, O. Guiselin, E. Raphael, Macromolecules 29, 7261 (1996).

    ADS  Article  Google Scholar 

  15. A.N. Semenov, J.-F. Joanny, Europhys. Lett. 29, 279 (1995).

    ADS  Article  Google Scholar 

  16. J.M.H.M. Scheutjens, G.J. Fleer, J. Phys. Chem. 83, 1619 (1979).

    Article  Google Scholar 

  17. J.M.H.M. Scheutjens, G.J. Fleer, J. Phys. Chem. 84, 178 (1980).

    Article  Google Scholar 

  18. I.S. Jones, P. Richmond, J. C. S. Faraday Trans. II 73, 1062 (1977).

    Article  Google Scholar 

  19. A.N. Semenov, J. Bonet-Avalos, A. Johner, J.F. Joanny, Macromolecules 29, 2179 (1996).

    ADS  Article  Google Scholar 

  20. A. Johner, J. Bonet-Avalos, C.C. van der Linden, A.N. Semenov, J.F. Joanny, Macromolecules 29, 3629 (1996).

    ADS  Article  Google Scholar 

  21. P.-Y. Lai, J. Chem. Phys. 103, 5742 (1995).

    ADS  Article  Google Scholar 

  22. R. Zajac, A. Chakrabarti, J. Chem. Phys. 104, 2418 (1996).

    ADS  Article  Google Scholar 

  23. J. de Joannis, C.-W. Park, J. Thomatos, I.A. Bitsanis, Langmuir 17, 69 (2001).

    Article  Google Scholar 

  24. E. Pefferkorn, A. Carroy, R. Varoqui, J. Polym. Sci. Polym. Phys. Ed. 23, 1997 (1985).

    ADS  Article  Google Scholar 

  25. E. Pefferkorn, A. Haouam, R. Varoqui, Macromolecules 22, 2677 (1989).

    ADS  Article  Google Scholar 

  26. R. Varoqui, E. Pefferkorn, Progr. Colloid Polym. Sci. 83, 96 (1990).

    Article  Google Scholar 

  27. P. Frantz, S. Granick, Phys. Rev. Lett. 66, 899 (1991).

    ADS  Article  Google Scholar 

  28. P. Frantz, S. Granick, Macromolecules 27, 2553 (1994).

    ADS  Article  Google Scholar 

  29. H.M. Schneider, S. Granick, Macromolecules 25, 5054 (1992).

    ADS  Article  Google Scholar 

  30. H.E. Johnson, S. Granick, Macromolecules 23, 3367 (1990).

    ADS  Article  Google Scholar 

  31. H.M. Schneider, P. Frantz, S. Granick, Langmuir 12, 994 (1996).

    Article  Google Scholar 

  32. J.F. Douglas, H.M. Schneider, P. Frantz, R. Lipman, S. Granick, J. Phys. Condens. Matter 9, 7699 (1997).

    ADS  Article  Google Scholar 

  33. P. Frantz, S. Granick, Macromolecules 28, 6915 (1995).

    ADS  Article  Google Scholar 

  34. I. Soga, S. Granick, Macromolecules 31, 5450 (1998).

    ADS  Article  Google Scholar 

  35. I. Soga, S. Granick, Colloids Surf. A 170, 113 (2000).

    Article  Google Scholar 

  36. Z. Fu, M. Santore, Macromolecules 31, 7014 (1998).

    ADS  Article  Google Scholar 

  37. Z. Fu, M. Santore, Macromolecules 32, 1939 (1999).

    ADS  Article  Google Scholar 

  38. E. Mubarekyan, M.M. Santore, Macromolecules 34, 4978 (2001).

    ADS  Article  Google Scholar 

  39. E. Mubarekyan, M.M. Santore, Macromolecules 34, 7504 (2001).

    ADS  Article  Google Scholar 

  40. U. Raviv, J. Klein, T.A. Witten, Eur. Phys. J. E 9, 405

  41. P.O. Brown, D. Botstein, Nat. Genet. Suppl. 21, 33 (1999).

    Article  Google Scholar 

  42. V. Hlady, J. Buijs, Curr. Opin. Biotechnol. 7, 72 (1996).

    Article  Google Scholar 

  43. M.D. Joesten, L.J. Schaad, Hydrogen Bonding (Marcel Dekker, New York, 1974).

  44. T.J. Lenk, V.M. Hallmark, J.F. Rabolt, Macromolecules 26, 1230 (1993).

    ADS  Article  Google Scholar 

  45. J.B. Schlenoff, J.R. Dharia, H. Xu, L. Wen, M. Li, Macromolecules 28, 4290 (1995).

    ADS  Article  Google Scholar 

  46. J.S. Shaffer, A.K. Chakraborty, Macromolecules 26, 1120 (1993).

    ADS  Article  Google Scholar 

  47. P.M. Adriani, A.K. Chakraborty, J. Chem. Phys. 98, 4263 (1993).

    ADS  Article  Google Scholar 

  48. T. Cosgrove, C.A. Prestidge, A.M. King, B. Vincent, Langmuir 8, 2206 (1992).

    Article  Google Scholar 

  49. R. Laible, K. Hamann, Adv. Colloid Interface Sci. 13, 65 (1980).

    Article  Google Scholar 

  50. C. Creton, E.J. Kramer, H.R. Brown, C.-Y. Hui, Adv. Polym. Sci. 156, 53 (2001).

    Article  Google Scholar 

  51. U. Sundararaj, C. Macosko, Macromolecules 28, 2647 (1995).

    ADS  Article  Google Scholar 

  52. B. O'Shaughnessy, D. Vavylonis, Macromolecules 32, 1785 (1999).

    ADS  Article  Google Scholar 

  53. I. Lee, R.P. Wool, Macromolecules 33, 2680 (2000).

    ADS  Article  Google Scholar 

  54. S. Wu, Polymer Interface Adhesion (Marcel Dekker, New York, 1982).

  55. D.C. Edwards, J. Mater. Sci. 25, 4175 (1990).

    ADS  Article  Google Scholar 

  56. J.P. Cohen Addad, Polymer 30, 1820 (1989).

    Article  Google Scholar 

  57. J.P. Cohen Addad, L. Dujourdy, Polym. Bull. 41, 253 (1998).

    Article  Google Scholar 

  58. L. Auvray, P. Auroy, M. Cruz, J. Phys. I 2, 943 (1992).

    Google Scholar 

  59. L. Auvray, M. Cruz, P. Auroy, J. Phys. II 2, 1133 (1992).

    Google Scholar 

  60. C.J. Durning, B. O'Shaughnessy, U. Sawhney, D. Nguyen, J. Majewski, G.S. Smith, Macromolecules 32, 6772 (1999).

    ADS  Article  Google Scholar 

  61. C. Marzolin, P. Auroy, M. Deruelle, J.P. Folkers, L. Léger, A. Menelle, Macromolecules 34, 8694 (2001).

    ADS  Article  Google Scholar 

  62. L. Léger, E. Raphaël, H. Hervet, Adv. Polym. Sci. 138, 185 (1999).

    Article  Google Scholar 

  63. M. Deruelle, M. Tirrell, Y. Marciano, H. Hervet, L. Léger, Faraday Discuss. 98, 55 (1994).

    ADS  Article  Google Scholar 

  64. O. Guiselin, Europhys. Lett. 17, 225 (1992).

    ADS  Article  Google Scholar 

  65. J.P. Cohen Addad, P.G. de Gennes, C. R. Acad. Sci. Paris Ser. II 319, 25 (1994).

    Google Scholar 

  66. B. O'Shaughnessy, D. Vavylonis, submitted to Europhys. Lett., cond-mat/0303094.

  67. W. Barford, R.C. Ball, C.M.M. Nex, J. Chem. Soc., Faraday Trans. 1 82, 3233 (1986).

    Article  Google Scholar 

  68. W. Barford, R.C. Ball, J. Chem. Soc., Faraday Trans. 1 83, 2515 (1987).

    Article  Google Scholar 

  69. K. Konstadinidis, S. Prager, M. Tirrell, J. Chem. Phys. 97, 7777 (1992).

    ADS  Article  Google Scholar 

  70. J.S. Shaffer, Macromolecules 27, 2987 (1994).

    ADS  Article  Google Scholar 

  71. A.L. Ponomarev, T.D. Sewell, C.J. Durning, Macromolecules 33, 2662 (2000).

    ADS  Article  Google Scholar 

  72. J. Talbot, G. Tarjus, P.R. Van Tassel, P. Viot, Colloids Surf. 165, 287 (2000).

    Article  Google Scholar 

  73. K. Konstadinidis, B. Thakkar, A. Chakraborty, L.W. Potts, R. Tannenbaum, M. Tirrell, J.F. Evans, Langmuir 8, 1307 (1992).

    Article  Google Scholar 

  74. B. O'Shaughnessy, D. Vavylonis, Europhys. Lett. 45, 638 (1999).

    ADS  Article  Google Scholar 

  75. B. O'Shaughnessy, Bulk and interfacial polymer reaction kinetics, in Theoretical and Mathematical Models in Polymer Science, edited by A. Grosberg (Academic Press, New York, 1998) Chapt. 5, pp. 219-275.

  76. B. O'Shaughnessy, D. Vavylonis, Phys. Rev. Lett. 90, 056103 (2003).

    ADS  Article  Google Scholar 

  77. B. Duplantier, J. Stat. Phys. 54, 581 (1989).

    ADS  Article  Google Scholar 

  78. K. De'Bell, T. Lookman, Rev. Mod. Phys. 65, 87 (1993).

    ADS  Article  Google Scholar 

  79. P.G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, New York, 1985).

  80. Equation loops describes a fragmentation process and appears in many branches of physics, e.g. the Altarelli-Parisi equation in QCD. (Z. Cheng, S. Redner, J. Phys. A 23, 1233 (1990)

    MathSciNet  Article  Google Scholar 

  81. M. Doi, S.F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1986).

  82. J.S. Shaffer, A.K. Chakraborty, M. Tirrell, H.T. Davis, J.L. Martins, J. Chem. Phys. 95, 8616 (1991).

    ADS  Article  Google Scholar 

  83. A.K. Chakraborty, J.S. Shaffer, P.M. Adriani, Macromolecules 24, 5226 (1991).

    ADS  Article  Google Scholar 

  84. M.-W. Tsao, K.-H. Pfeifer, J.F. Rabolt, D.G. Castner, L. Haussling, H. Ringsdorf, Macromolecules 30, 5913 (1997).

    ADS  Article  Google Scholar 

  85. T. Cosgrove, C.A. Prestidge, B. Vincent, J. Chem. Soc. Faraday Trans. 86, 1377 (1990).

    Article  Google Scholar 

  86. T. Cosgrove, A. Patel, J.R.P. Webster, A. Zarbakhsh, Langmuir 9, 2326 (1993).

    Article  Google Scholar 

  87. B. O'Shaughnessy, D. Vavylonis, Phys. Rev. Lett. 84, 3193 (2000).

    ADS  Article  Google Scholar 

  88. B. O'Shaughnessy, D. Vavylonis, Eur. Phys. J. E 1, 159 (2000).

    Article  Google Scholar 

  89. P.G. de Gennes, J. Chem. Phys. 76, 3316 (1982).

    ADS  Article  Google Scholar 

  90. D.J. Amit, G. Parisi, L. Peliti, Phys. Rev. B 27, 1635 (1983).

    ADS  MathSciNet  Article  Google Scholar 

  91. L. Pietronero, Phys. Rev. Lett. 55, 2025 (1985).

    ADS  Article  Google Scholar 

  92. W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 2, 2nd ed. (John Wiley & Sons, Inc., New York, 1971).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to B. O'Shaughnessy.

Additional information

Received: 13 January 2003, Published online: 8 July 2003

PACS:

82.35.-x Polymers: properties; reactions; polymerization - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 68.08.-p Liquid-solid interfaces

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

O'Shaughnessy, B., Vavylonis, D. Irreversible adsorption from dilute polymer solutions. Eur. Phys. J. E 11, 213–230 (2003). https://doi.org/10.1140/epje/i2003-10015-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epje/i2003-10015-9

Keywords

  • Chemisorption
  • Universality Class
  • Loop Length
  • Irreversible Adsorption
  • Dilute Polymer Solution