Structural and cooperative length scales in polymer gels

  • Baudouin Géraud
  • Loren Jørgensen
  • Christophe Ybert
  • Hélène Delanoë-Ayari
  • Catherine Barentin
Regular Article


Understanding the relationship between the material structural details, the geometrical confining constraints, the local dynamical events and the global rheological response is at the core of present investigations on complex fluid properties. In the present article, this problem is addressed on a model yield stress fluid made of highly entangled polymer gels of Carbopol which follows at the macroscopic scale the well-known Herschel-Bulkley rheological law. First, performing local rheology measurements up to high shear rates (\(\dot{\gamma} \geq 10^{2}\) s-1)and under confinement, we evidence unambiguously the breakdown of bulk rheology associated with cooperative processes under flow. Moreover, we show that these behaviors are fully captured with a unique cooperativity length \(\xi\) over the whole range of experimental conditions. Second, we introduce an original optical microscopy method to access structural properties of the entangled polymer gel in the direct space. Performing image correlation spectroscopy of fluorophore-loaded gels, the characteristic size D of carbopol gels microstructure is determined as a function of preparation protocol. Combining both dynamical and structural information shows that the measured cooperative length \(\xi\) corresponds to 2-5 times the underlying structural size D, thus providing a strong grounding to the “Shear Transformation Zones” modeling approach.

Graphical abstract


Flowing Matter: Liquids and Complex Fluids 


  1. 1.
    R.G. Larson, The Structure and Rheology of Complex Fluids (Oxford University Press, 1999)Google Scholar
  2. 2.
    S.A. Rogers, D. Vlassopoulos, P.T. Callaghan, Phys. Rev. Lett. 100, 128304 (2008)ADSCrossRefGoogle Scholar
  3. 3.
    M. Le Merrer, S. Cohen-Addad, R. Höhler, Phys. Rev. Lett. 108, 188301 (2012)ADSCrossRefGoogle Scholar
  4. 4.
    E.D. Knowlton, D.J. Pine, L. Cipelletti, Soft Matter 10, 6931 (2014)ADSCrossRefGoogle Scholar
  5. 5.
    P.C.F. Möller, S. Rodts, M.A.J. Michels, D. Bonn, Phys. Rev. E 77, 041507 (2008)ADSCrossRefGoogle Scholar
  6. 6.
    R. Besseling, L. Isa, P. Ballesta, G. Petekidis, M.E. Cates, W.C.K. Poon, Phys. Rev. Lett. 105, 268301 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    W.K. Kegel, A. van Blaaderen, Science 287, 290 (2000)ADSCrossRefGoogle Scholar
  8. 8.
    S.P. Meeker, R.T. Bonnecaze, M. Cloitre, J. Rheol. 48, 6 (2004)CrossRefGoogle Scholar
  9. 9.
    J. Goyon, A. Colin, G. Ovarlez, A. Ajdari, L. Bocquet, Nature 454, 84 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    B. Géraud, L. Bocquet, C. Barentin, Eur. Phys. J. E 36, 13030 (2013)CrossRefGoogle Scholar
  11. 11.
    G.C. Maitland, Curr. Opin. Colloid Interface Sci. 5, 301 (2000)CrossRefGoogle Scholar
  12. 12.
    A. Cuenca, H. Bodiguel, Phys. Rev. Lett. 108, 108304 (2013)ADSCrossRefGoogle Scholar
  13. 13.
    A. Muggeridge, A. Cockin, K. Webb, H. Frampton, I. Collins, T. Moulds, P. Salino, Philos. Trans. R. Soc. London A: Math. Phys. Eng. Sci. 372, 2006 (2013)CrossRefGoogle Scholar
  14. 14.
    A. Argon, Acta. Metall. 27, 47 (1979)CrossRefGoogle Scholar
  15. 15.
    V.V. Bulatov, A. Argon, Model. Simul. Mater. Sci. Eng. 2, 167 (1994)ADSCrossRefGoogle Scholar
  16. 16.
    P. Olsson, S. Teitel, Phys. Rev. Lett. 99, 178001 (2007)ADSCrossRefGoogle Scholar
  17. 17.
    A. Lemaitre, C. Caroli, Phys. Rev. Lett. 103, 065501 (2009)ADSCrossRefGoogle Scholar
  18. 18.
    P. Schall, D.A. Weitz, F. Spaepen, Science 318, 1895 (2007)ADSCrossRefGoogle Scholar
  19. 19.
    P. Jop, V. Mansard, P. Chaudhuri, L. Bocquet, A. Colin, Phys. Rev. Lett. 108, 148301 (2012)ADSCrossRefGoogle Scholar
  20. 20.
    V. Mansard, L. Bocquet, A. Colin, Soft Matter 10, 6984 (2014)ADSCrossRefGoogle Scholar
  21. 21.
    K.N. Nordstrom, J.P. Gollub, D.J. Durian, Phys. Rev. E 84, 021403 (2011)ADSCrossRefGoogle Scholar
  22. 22.
    P. Chaudhuri, V. Mansard, A. Colin, L. Bocquet, Phys. Rev. Lett. 109, 0360001 (2012)CrossRefGoogle Scholar
  23. 23.
    A. Nicolas, J.L. Barrat, Phys. Rev. Lett. 110, 138304 (2013)ADSCrossRefGoogle Scholar
  24. 24.
    J. Goyon, A. Colin, G. Ovarlez, A. Ajdari, L. Bocquet, Soft Matter 6, 2668 (2010)ADSCrossRefGoogle Scholar
  25. 25.
    K.A. Reddy, Y. Forterre, O. Pouliquen, Phys. Rev. Lett. 106, 108301 (2011)ADSCrossRefGoogle Scholar
  26. 26.
    K. Kamrin, G. Koval, Phys. Rev. Lett. 108, 178301 (2012)ADSCrossRefGoogle Scholar
  27. 27.
    Benjamin Dollet, J. Rheol. 54, 741 (2010)CrossRefGoogle Scholar
  28. 28.
    B. Dollet, A. Scagliarini, M. Sbragaglia, J. Fluid Mech. 766, 556 (2015)ADSCrossRefGoogle Scholar
  29. 29.
    A. Scagliarini, B. Dollet, M. Sbragaglia, Colloids Surf. A: Physicochem. Eng. Aspects 473, 133 (2015)CrossRefGoogle Scholar
  30. 30.
    R. Lespiat, S. Cohen-Addad, R. Höhler, Phys. Rev. Lett. 106, 148302 (2011)ADSCrossRefGoogle Scholar
  31. 31.
    K.N. Nordstrom, J.P. Gollub, D.J. Durian, Phys. Rev. Lett. 105, 175701 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    Lubrizol pharmaceutical bulletins, Technical report, Lubrizol Corporation (2002)Google Scholar
  33. 33.
    P. Möller, A. Fall, V. Chikkadi, D. Derks, D. Bonn, Philos. Trans. R. Soc. A 367, 5139 (2009)ADSCrossRefGoogle Scholar
  34. 34.
    M. Muramatsu, K. Kanada, A. Nishida, K. Ouchi, N. Saito, M. Yoshida, A. Shimoaka, T. Ozeki, H. Yuasa, Y. Kanaya, Int. J. Pharm. 199, 77 (2000)CrossRefGoogle Scholar
  35. 35.
    T. Divoux, D. Tamarii, C. Barentin, S. Teitel, S. Manneville, Soft Matter 8, 4151 (2012)ADSCrossRefGoogle Scholar
  36. 36.
    D. Lee, I.A. Gutowski, A.E. Bailey, L. Rubatat, J.R. de Bruyn, B.J. Frisken, Phys. Rev. E 83, 031401 (2011)ADSCrossRefGoogle Scholar
  37. 37.
    I.A. Gutowski, D. Lee, J.R. de Bruyn, B.J. Frisken, Rheol. Acta 51, 441 (2012)CrossRefGoogle Scholar
  38. 38.
    L. Baudonnet, J.L. Grossiord, F. Rodriguez, J. Dispersion Sci. Technol. 25, 183 (2004)CrossRefGoogle Scholar
  39. 39.
    W.H. Herschel, R. Bulkley, Kolloid-Zeitschrift 39, 291 (1926)CrossRefGoogle Scholar
  40. 40.
    V. Mansard, A. Colin, P. Chaudhuri, L. Bocquet, Soft Matter 9, 7489 (2013)ADSCrossRefGoogle Scholar
  41. 41.
    L. Bocquet, A. Colin, A. Ajdari, Phys. Rev. Lett. 103, 036001 (2009)ADSCrossRefGoogle Scholar
  42. 42.
    N.O. Petersen, P.L. Höddelius, P.W. Wiseman, O. Seger, K.-E. Magnusson, Biophys. J. 65, 1135 (1993)CrossRefGoogle Scholar
  43. 43.
    P.W. Wiseman, F. Capani, J.A. Squier, M.E. Martone, J. Microsc. 205, 177 (2002)CrossRefGoogle Scholar
  44. 44.
    M. Doi, S.F. Edwards, The Theory of Polymer Dynamics (Oxford Science Publications, 1988)Google Scholar
  45. 45.
    A.-L. Vayssade, C. Lee, E. Terriac, F. Monti, M. Cloitre, P. Tabeling, Phys. Rev. E 89, 052309 (2014)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Baudouin Géraud
    • 1
  • Loren Jørgensen
    • 1
  • Christophe Ybert
    • 1
  • Hélène Delanoë-Ayari
    • 1
  • Catherine Barentin
    • 1
  1. 1.Univ Lyon, Université Claude Bernard Lyon 1, CNRSInstitut Lumière MatièreVILLEURBANNEFrance

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