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Journal of Statistical Physics

, Volume 165, Issue 5, pp 970–989 | Cite as

Charge Renormalization and Charge Oscillation in Asymmetric Primitive Model of Electrolytes

  • Mingnan Ding
  • Yihao Liang
  • Bing-Sui Lu
  • Xiangjun Xing
Article

Abstract

Debye charging method is generalized to study the linear response properties of the asymmetric primitive model for electrolytes. Analytic results are obtained for the effective charge distributions of constituent ions inside the electrolyte, from which all static linear response properties of the system follow. It is found that, as the ion density increases, both the screening length and the dielectric constant receive substantial renormalization due to ionic correlations. Furthermore, the valence of larger ion is substantially renormalized upward by ionic correlations, while those of smaller ions remain approximately the same. For sufficiently high density, the system exhibits charge oscillations. The threshold ion density for charge oscillation is much lower than the corresponding values for symmetric electrolytes. Our results agree well with large-scale Monte Carlo simulations, and find good agreement in general, except for the case of small ion sizes (\(d = 4\,\AA \)) near the charge oscillation threshold.

Keywords

Charge renormalization Primitive model Electrolyte Charging oscillation Debye charging 

Notes

Acknowledgements

We thank the NSFC (Grants Nos. 11174196 and 91130012) for their financial support. We also thank Wei Cai for interesting discussions.

References

  1. 1.
    Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York (1964). ISBN 0-486-61272-4, Chapter 5MATHGoogle Scholar
  2. 2.
    Baus, M., Hansen, J.-P.: Statistical mechanics of simple Coulomb systems. Phys. Rep. 59(1), 1–94 (1980)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Benjamin, B.P., Fisher, M.E.: Charge oscillations in Debye–Hückel theory. Europhys. Lett. 39(6), 611 (1997)CrossRefGoogle Scholar
  4. 4.
    Debye, P.W., Huckel, E.: Phys. Z. 24, 185 (1923)Google Scholar
  5. 5.
    Ding, M., Liang, Y., Xing, X.: Surfaces with Ion-specific Interactions, Their Effective Charge Distributions and Effective Interactions, to be submitted (2016)Google Scholar
  6. 6.
    Ennis, J., Kjellander, R., Mitchell, D.J.: Dressed ion theory for bulk symmetric electrolytes in the restricted primitive model. J. Chem. Phys. 102(2), 975 (1995)ADSCrossRefGoogle Scholar
  7. 7.
    Hall, D.G.: A modification of Debye–Hckel theory based on local thermodynamics. Z. Phys. Chem. 174(Part_1), 89–98 (1991)CrossRefGoogle Scholar
  8. 8.
    Hansen, J.-P., McDonald, I.R.: Theory of Simple Liquids: With Applications to Soft Matter. Academic Press, London (2013)MATHGoogle Scholar
  9. 9.
    Henderson, D., Blum, L., Lebowitz, J.L.: An exact formula for the contact value of the density profile of a system of charged hard spheres near a charged wall. J. Electroanal. Chem. Interfacial Electrochem. 102(3), 315–319 (1979)CrossRefGoogle Scholar
  10. 10.
    Kékicheff, P., Ninham, B.W.: The double-layer interaction in asymmetric electrolytes. Europhys. Lett. 12(5), 471 (1990)ADSCrossRefGoogle Scholar
  11. 11.
    Kirkwood, J.G.: Statistical mechanics of liquid solutions. Chem. Rev. 19(3), 275–307 (1936)CrossRefGoogle Scholar
  12. 12.
    Kjellander, R.: Modified Debye–Hckel approximation with effective charges: an application of dressed ion theory for electrolyte solutions. J. Phys. Chem. 99(25), 10392–10407 (1995)CrossRefGoogle Scholar
  13. 13.
    Kjellander, R.: Distribution function theory of electrolytes and electrical double layers: charge renormalisation and dressed ion theory. In: Holm, C., Kkicheff, P., Podgornik, R. (eds.) Electrostatic Effects in Soft Matter and Biophysics. NATO Science Series, pp. 317–364. Kluwer Academic Publishers, Dordrecht (2001)CrossRefGoogle Scholar
  14. 14.
    Kjellander, R., Mitchell, D.J.: An exact but linear and Poisson–Boltzmann-like theory for electrolytes and colloid dispersions in the primitive model. Chem. Phys. Lett. 200(1), 76–82 (1992)ADSCrossRefGoogle Scholar
  15. 15.
    Kjellander, R., Mitchell, D.J.: Dressed ion theory for electrolyte solutions: a Debye–Hückel-like reformulation of the exact theory for the primitive model. J. Chem. Phys. 101(1), 603–626 (1994)ADSCrossRefGoogle Scholar
  16. 16.
    Liang, Y., Xing, X., Li, Y.: A GPU-based large-scale Monte Carlo simulation method for systems with long-range interactions. J. Comput. Phys. (submitted)Google Scholar
  17. 17.
    Mitchell, D.J., Ninham, B.W.: Asymptotic behavior of the pair distribution function of a classical electron gas. Phys. Rev. 174(1), 280–289 (1968)ADSCrossRefGoogle Scholar
  18. 18.
    Stell, G., Lebowitz, J.L.: Equilibrium properties of a system of charged particles. J. Chem. Phys. 49(8), 3706–3717 (1968)ADSCrossRefGoogle Scholar
  19. 19.
    Stone, M., Goldbart, P.M.: Mathematics for Physics. Cambridge University Press, Cambridge (2009)CrossRefMATHGoogle Scholar
  20. 20.
    Ulander, J., Kjellander, R.: Screening and asymptotic decay of pair distributions in asymmetric electrolytes. J. Chem. Phys. 109(21), 9508–9522 (1998)ADSCrossRefGoogle Scholar
  21. 21.
    Varela, L.M., Garca, M., Mosquera, V.: Exact mean-field theory of ionic solutions: non-Debye screening. Phys. Rep. 382(1), 1–111 (2003)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Mingnan Ding
    • 1
  • Yihao Liang
    • 1
  • Bing-Sui Lu
    • 2
  • Xiangjun Xing
    • 1
  1. 1.Institute of Natural Sciences and Department of Physics and AstronomyShanghai Jiaotong UniversityShanghaiChina
  2. 2.School of Physical and Mathematical SciencesNanyang Technological UniversitySingaporeSingapore

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