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Colloid Journal

, Volume 80, Issue 6, pp 625–635 | Cite as

An Electrical Double Layer between Spherical Particles. The Effect of Ion Sizes

  • A. I. DolinnyiEmail author
Article

Abstract

Using the modified Poisson–Boltzmann theory, which includes restrictions on the maximum attainable concentration of ionic species in the solution Cmax, determined by their effective dimensions, the spatial distributions of the electric potential and ions between spherical nanoparticles immersed in a 1 : 1 electrolyte solution have been investigated. It has been found that the pattern of the aforementioned distributions is governed by surface electric potential ψs of the particles, interparticle distance, and maximum concentration Cmax. Between weakly charged particles, the electric potential profiles are almost independent of the value of Cmax. As absolute value \(\left| {{{\psi }_{{\text{s}}}}} \right|\) increases, an effect associated with the ionic sizes manifests itself; i.e., for high \(\left| {{{\psi }_{{\text{s}}}}} \right|\) values, the electrical double layer expands into the solution, and, the lower Cmax (the larger the effective size of counterions), the higher the degree of expansion. This behavior is related to the fact that, near a particle surface, the profile of counterion concentration is developed with the following distinctly pronounced regions: the region of a plateau with width lc, which corresponds to the condensed part of the profile with C(x) = Cmax for 0 < x < lc, and the diffusion region with C(x) < Cmax for x > lc. When highly charged particles approach to each other up to such distances that their electrical double layers appear to be strongly overlapped, coions are completely displaced from the interparticle electrolyte layer, and only counterions are present in the layer.

Notes

REFERENCES

  1. 1.
    Verwey, E.J.W. and Overbeek, J.Th.G., Theory of the Stability of Lyophobic Colloids, New York: Elsevier, 1948.Google Scholar
  2. 2.
    Delahay, P., Double Layer and Electrode Kinetics, New York, 1965; Moscow: Mir, 1967.Google Scholar
  3. 3.
    Derjaguin, B.V., Churaev, N.V., and Muller, V.M., Surface Forces, New York: Consultants Bureau, 1987.CrossRefGoogle Scholar
  4. 4.
    Israelachvili, J.N., Intermolecular and Surface Forces, San Diego: Academic, 1991.Google Scholar
  5. 5.
    Ben-Yaakov, D., Andelman, D., Podgornik, R., and Harries, D., Curr. Opin. Colloid Interface Sci., 2010, vol. 16, p. 542.CrossRefGoogle Scholar
  6. 6.
    Muller, V.M., Martynov, G.A., Kuz’mina, G.L., and Bulatova, M.V., Kolloidn. Zh., 1976, vol. 38, p. 480.Google Scholar
  7. 7.
    Muller, V.M. and Derjaguin, B.V., Kolloidn. Zh., 1976, vol. 38, p. 1117.Google Scholar
  8. 8.
    Lima, E.R.A., Biscaia, E.C., Jr., Bostrom, M., Tavares, F.W., and Prausnitz, J.M., J. Phys. Chem. C, 2007, vol. 111, p. 16055.CrossRefGoogle Scholar
  9. 9.
    Lima, E.R.A., Tavares, F.W., and Biscaia, E.C., Phys. Chem. Chem. Phys., 2007, vol. 9, p. 3174.CrossRefGoogle Scholar
  10. 10.
    Eigen, M. and Wick, E., J. Phys. Chem., 1954, vol. 58, p. 702.CrossRefGoogle Scholar
  11. 11.
    Levine, S. and Bell, G.M., Discuss. Faraday Soc., 1966, vol. 42, p. 69.CrossRefGoogle Scholar
  12. 12.
    Frydel, D. and Levin, Y., J. Chem. Phys., 2012, vol. 137, p. 164703.CrossRefGoogle Scholar
  13. 13.
    Marcus, Y., Chem. Rev., 1988, vol. 88, p. 1475.CrossRefGoogle Scholar
  14. 14.
    Kilic, M.S., Bazant, M.Z., and Ajdari, A., Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 2007, vol. 75, p. 021502.CrossRefGoogle Scholar
  15. 15.
    Bikerman, J., Philos. Mag., 1942, vol. 33, p. 384.CrossRefGoogle Scholar
  16. 16.
    Kralj-Iglic, V. and Iglic, A., J. Phys. (France), 1996, vol. 6, p. 477.Google Scholar
  17. 17.
    Bohinc, K., Kralj-Iglic, V., and Iglic, A., Electrochim. Acta, 2000, vol. 46, p. 3033.CrossRefGoogle Scholar
  18. 18.
    Antypov, D., Barbosa, M.C., and Holm, C., Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 2005, vol. 71, p. 061106.CrossRefGoogle Scholar
  19. 19.
    Biesheuvel, P.M. and Van Soestbergen, M., J. Colloid Interface Sci., 2007, vol. 316, p. 490.CrossRefGoogle Scholar
  20. 20.
    Lue, L., Zoeller, N., and Blankschtein, D., Langmuir, 1999, vol. 15, p. 3726.CrossRefGoogle Scholar
  21. 21.
    López-García, J.J., Aranda-Rascon, M.J., and Hor-no, J., J. Colloid Interface Sci., 2007, vol. 316, p. 196.CrossRefGoogle Scholar
  22. 22.
    López-García, J.J., Aranda-Rascon, M.J., Grosse, C., and Horno, J., J. Phys. Chem. B, 2010, vol. 114, p. 7548.CrossRefGoogle Scholar
  23. 23.
    Borukhov, I., J. Polym. Sci., Part B: Polym. Phys., 2004, vol. 42, p. 3598.CrossRefGoogle Scholar
  24. 24.
    Borukhov, I., Andelman, D., and Orland, H., Electrochim. Acta, 2000, vol. 46, p. 221.CrossRefGoogle Scholar
  25. 25.
    Ibarra-Armenta, J.G., Martin-Molina, A., and Quesada-Perez, M., Phys. Chem. Chem. Phys., 2009, vol. 11, p. 309.CrossRefGoogle Scholar
  26. 26.
    Hoskin, N.E., Philos. Trans. R. Soc. London A, 1956, vol. 248, p. 433.CrossRefGoogle Scholar
  27. 27.
    Hoskin, N.E. and Levine, S., Philos. Trans. R. Soc. London A, 1956, vol. 248, p. 449.CrossRefGoogle Scholar
  28. 28.
    McCartney, L.N. and Levine, S., J. Colloid Interface Sci., 1969, vol. 30, p. 345.CrossRefGoogle Scholar
  29. 29.
    Ledbetter, J.E., Croxton, T.L., and McQuarrie, D.A., Can. J. Chem., 1981, vol. 59, p. 1860.CrossRefGoogle Scholar
  30. 30.
    Carnie, S.L., Chan, D.Y.C., and Stankovich, J., J. Colloid Interface Sci., 1994, vol. 165, p. 116.CrossRefGoogle Scholar
  31. 31.
    Stankovich, J. and Carnie, S.L., Langmuir, 1996, vol. 12, p. 1453.CrossRefGoogle Scholar
  32. 32.
    Warszynski, P. and Adamczyk, Z., J. Colloid Interface Sci., 1997, vol. 187, p. 283.CrossRefGoogle Scholar
  33. 33.
    Das, P.K., Bhattacharjee, S., and Moussa, W., Langmuir, 2003, vol. 19, p. 4162.CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of SciencesMoscowRussia

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