Skip to main content
Log in

Phase behaviour of a dispersion of charge-stabilised colloidal spheres with added non-adsorbing interacting polymer chains

  • Regular Article
  • Published:
The European Physical Journal E Aims and scope Submit manuscript

Abstract.

We present a theory for the phase behaviour of mixtures of charge-stabilised colloidal spheres plus interacting polymer chains in good and θ -solvents within the framework of free-volume theory. We use simple but accurate combination rules for the depletion thickness around a colloidal particle and for the osmotic pressure up to the semi-dilute concentration regime. Hence, we obtain expressions for the free energy for mixtures of charged colloidal particles and non-adsorbing interacting polymers. From that, we calculate the phase behaviour, and discuss its topology in dependence on the competition between the charge-induced repulsion and the polymer-induced attraction. The homogeneous mixture of colloids and polymers becomes more stabilised against demixing when increasing the electrostatic repulsion. This charge-induced stabilisation is strongest for small polymer-to-colloid size ratios and is more pronounced for charged colloids mixed with polymers in a good solvent than for polymers in a θ -solvent. For the weakly charged regime we find that the phase diagram becomes salt-concentration-independent in the protein limit for charged colloids plus polymers in a θ -solvent. The liquid window, i.e., the concentration regimes where a colloidal liquid exists, is narrowed down upon increasing the charge-induced repulsion. Also this effect is more pronounced when charged colloids are mixed with polymer chains in a good solvent. In summary, we demonstrate that the solvent quality significantly influences the phase behaviour of mixtures of charged colloids plus non-adsorbing polymers if the range of the screened electrostatic repulsion becomes of the order of the range of the depletion-induced attraction.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. W.B. Russel, D.A. Saville, W.R. Schowalter, Colloidal Dispersions (Cambridge University Press, Cambridge, 1992).

  2. W.C.K. Poon, J. Phys.: Condens. Matter 14, R859 (2002).

  3. R. Tuinier, J. Rieger, C.G. de Kruif, Adv. Colloid Interface Sci. 103, 1 (2003).

    Google Scholar 

  4. S. Asakura, F. Oosawa, J. Chem. Phys. 22, 1255 (1954).

    Google Scholar 

  5. S. Asakura, F. Oosawa, J. Polym. Sci. 33, 183 (1958).

    Google Scholar 

  6. A. Vrij, Pure Appl. Chem. 48, 471 (1976).

    Google Scholar 

  7. A.P. Gast, C.K. Hall, W.B. Russel, J. Colloid Interface Sci. 96, 251 (1983).

    Google Scholar 

  8. H. de Hek, A. Vrij, J. Colloid Interface Sci. 84, 409 (1981).

    Google Scholar 

  9. B. Vincent, Colloids Surf. 24, 269 (1987).

  10. B. Vincent, J. Edwards, S. Emmett, R. Croot, Colloids Surf. 31, 267 (1988).

    Google Scholar 

  11. H.N.W. Lekkerkerker, W.C.K. Poon, P.N. Pusey, A. Stroobants, P.W. Warren, Europhys. Lett. 20, 559 (1992).

    Google Scholar 

  12. H.L. Reiss, H. Frisch, J.L. Lebowitz, J. Chem. Phys. 31, 369 (1959).

    Google Scholar 

  13. J.L. Lebowitz, E. Helfand, E. Praestgaard, J. Chem. Phys. 43, 774 (1965).

    Google Scholar 

  14. E.J. Meijer, D. Frenkel, J. Chem. Phys. 100, 6873 (1994).

    Google Scholar 

  15. R.C.L. Vink, J. Horbach, J. Chem. Phys. 121, 3253 (2004).

    Google Scholar 

  16. M. Dijkstra, J.M. Brader, R. Evans, J. Phys.: Condens. Matter 11, 10079 (1999).

    Google Scholar 

  17. M. Dijkstra, R. van Roij, R. Evans, Phys. Rev. E 59, 5744 (1999).

    Google Scholar 

  18. M. Dijkstra, R. van Roij, R. Evans, Phys. Rev. Lett. 82, 117 (1999).

    Google Scholar 

  19. M. Dijkstra, R. van Roij, R. Evans, J. Chem. Phys. 113, 4799 (2000).

    Google Scholar 

  20. M. Dijkstra, R. van Roij, R. Roth, A. Fortini, Phys. Rev. E 73, 041404 (2006).

    Google Scholar 

  21. A. Moncho-Jordá, A.A. Louis, P.G. Bolhuis, R. Roth, J. Phys.: Condens. Matter 15, S3429 (2003).

  22. M. Fuchs, K.S. Schweizer, J. Chem. Phys. 106, 347 (1997).

    Google Scholar 

  23. M. Fuchs, K.S. Schweizer, Europhys. Lett. 51, 621 (2000).

    Google Scholar 

  24. M. Fuchs, K.S. Schweizer, Phys. Rev. E 64, 021514 (2001).

    Google Scholar 

  25. Y.L. Chen, K.S. Schweizer, J. Chem. Phys. 118, 3880 (2003).

    Google Scholar 

  26. M. Fuchs, K.S. Schweizer, J. Phys.: Condens. Matter 14, R239 (2002).

  27. S. Ramakrishnan, M. Fuchs, K.S. Schweizer, C.F. Zukoski, Langmuir 18, 1082 (2002).

  28. S. Ramakrishnan, M. Fuchs, K.S. Schweizer, C.F. Zukoski, J. Chem. Phys. 116, 2201 (2002).

    Google Scholar 

  29. S.A. Shah, S. Ramakrishnan, Y.L. Chen, K.S. Schweizer, C.F. Zukoski, Langmuir 19, 5128 (2003).

  30. C.P. Royall, D.G.A.L. Aarts, H. Tanaka, Nat. Phys. 3, 636 (2007).

    Google Scholar 

  31. D. Pini, F. Lo Verso, M. Tau, A. Parola, L. Reatto, Phys. Rev. Lett. 100, 055703 (2008).

    Google Scholar 

  32. V.B. Tolstoguzov, Food Hydrocolloids 4, 429 (1991).

  33. V. Ya Grinberg, V.B. Tolstoguzov, Food Hydrocolloids 11, 145 (1997).

    Google Scholar 

  34. D. Marenduzzo, K. Finan, P.R. Cook, J. Cell. Biol. 175, 681 (2006).

    Google Scholar 

  35. T. Odijk, Biophys. J. 73, 23 (1988).

  36. R. de Vries, Biophys. J. 80, 1186 (2001).

  37. A. McPherson, Crystallization of Biological Macromolecules, 1st edition (Cold Spring Harbor Laboratory Press, New York, 1999).

  38. P.G. Bolhuis, A.A. Louis, Macromolecules 35, 1860 (2002).

  39. P.G. Bolhuis, A.A. Louis, J.P. Hansen, E.J. Meijer, J. Chem. Phys. 114, 4296 (2001).

    Google Scholar 

  40. A.A. Louis, P.G. Bolhuis, J.P. Hansen, E.J. Meijer, Phys. Rev. Lett. 85, 2522 (2000).

    Google Scholar 

  41. P.G. Bolhuis, A.A. Louis, J.P. Hansen, Phys. Rev. Lett. 89, 128302 (2002).

    Google Scholar 

  42. M. Schmidt, M. Fuchs, J. Chem. Phys. 117, 6308 (2002).

    Google Scholar 

  43. D.G.A.L. Aarts, R. Tuinier, H.N.W. Lekkerkerker, J. Phys.: Condens. Matter 14, 7551 (2002).

    Google Scholar 

  44. E. Eisenriegler, A. Hanke, S. Dietrich, Phys. Rev. E 54, 1134 (1996).

    Google Scholar 

  45. A. Hanke, E. Eisenriegler, S. Dietrich, Phys. Rev. E 59, 6853 (1999).

    Google Scholar 

  46. F.W. Tavares, S.I. Sandler, AIChE J. 43, 218 (1997).

    Google Scholar 

  47. P.G. Ferreira, M. Dymitrowska, L. Belloni, J. Chem. Phys. 113, 9849 (2000).

    Google Scholar 

  48. Ferreira and Belloni have chosen a system of highly charged and weakly screened colloids and non-adsorbing polymer chains (a=10nm, R g =10nm, Z=50, c s=0.01mol/l, T=298K). These values lead to a factor of m=7.5, and, thus, cannot be described by our simple model because the Coulomb interactions are no longer short ranged with respect to the colloid size. Therefore, we cannot compare with their calculated gas-liquid spinodal for Z=0 and Z=50 (see Fig. 11 on page 9860 in ferreira:2000).

  49. A.R. Denton, M. Schmidt, J. Chem. Phys. 122, 244911 (2005).

    Google Scholar 

  50. A. Fortini, M. Dijkstra, R. Tuinier, J. Phys.: Condens. Matter 17, 7783 (2005).

    Google Scholar 

  51. G.J. Fleer, R. Tuinier, Phys. Rev. E 76, 041802 (2007).

    Google Scholar 

  52. G.J. Fleer, A.M. Skvortsov, R. Tuinier, Macromol. Theory Simul. 16, 531 (2007).

    Google Scholar 

  53. R. Tuinier, P.A. Smith, W.C.K. Poon, S.U. Egelhaaf, D.G.A.L. Aarts, H.N.W. Lekkerkerker, G.J. Fleer, Europhys. Lett. 82, 68002 (2008).

    Google Scholar 

  54. J.A. Barker, D. Henderson, J. Chem. Phys. 47, 4714 (1967).

    Google Scholar 

  55. H.N.W. Lekkerkerker, Colloids Surf. 51, 419 (1990).

  56. S.M. Oversteegen, R. Roth, J. Chem. Phys. 122, 214502 (2005).

    Google Scholar 

  57. J.M. Brader, M. Dijkstra, R. Evans, Phys. Rev. E 63, 041405 (2001).

    Google Scholar 

  58. A.A. Louis, P.G. Bolhuis, E.J. Meijer, J.P. Hansen, J. Chem. Phys. 117, 1893 (2002).

    Google Scholar 

  59. N.F. Carnahan, K.E. Starling, J. Chem. Phys. 51, 635 (1969).

    Google Scholar 

  60. W.W. Wood, J. Chem. Phys. 20, 1334 (1952).

    Google Scholar 

  61. D. Frenkel, A.J.C. Ladd, J. Chem. Phys. 81, 3188 (1984).

    Google Scholar 

  62. G.J. Fleer, R. Tuinier, Physica A 379, 52 (2007).

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

    Google Scholar 

  64. P.G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, 1979).

  65. G.J. Fleer, A.M. Skvortsov, R. Tuinier, Macromolecules 36, 7857 (2003).

    Google Scholar 

  66. A.A. Louis, P.G. Bolhuis, E.J. Meijer, J.P. Hansen, J. Chem. Phys. 116, 10547 (2002).

    Google Scholar 

  67. T. Taniguchi, T. Kawakatsu, K. Kawasaki, Slow Dynamics in Condensed Matter, AIP Conf. Ser., Vol. 256 (American Institute of Physics, New York, 1992) p. 503.

  68. G.J. Fleer, R. Tuinier, in press, Adv. Colloid Interface Sci. (2008) doi: 10.1016/j.cis.2008.07.001, 2008.

  69. P.G. Bolhuis, E.J. Meijer, A.A. Louis, Phys. Rev. Lett. 90, 068304 (2003).

    Google Scholar 

  70. W.G. Hoover, F.H. Ree, J. Chem. Phys. 49, 3609 (1968).

    Google Scholar 

  71. A.P. Hynninen, M. Dijkstra, Phys. Rev. E 68, 021407 (2003).

    Google Scholar 

  72. A.A. Louis, J. Phys.: Condens. Matter 14, 9187 (2002).

    Google Scholar 

  73. D. Frenkel, Physica A 313, 1 (2002).

  74. A.R. Hoskins, I.D. Robb, P.A. Williams, Biopolymers 45, 97 (1998).

  75. C.L.A. Berli, J.A. Deiber, M.C. Anon, Food Hydrocolloids 13, 507 (1999).

    Google Scholar 

  76. H. Chick, C.J. Martin, Biochem. J. 7, 92 (1913).

    Google Scholar 

  77. E. Nordmeier, J. Phys. Chem. 97, 5770 (1993).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gögelein, C., Tuinier, R. Phase behaviour of a dispersion of charge-stabilised colloidal spheres with added non-adsorbing interacting polymer chains. Eur. Phys. J. E 27, 171–184 (2008). https://doi.org/10.1140/epje/i2008-10367-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epje/i2008-10367-6

PACS.

Navigation