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Violation of the local electroneutrality condition in an inhomogeneous macroions solution

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Abstract

A simple mathematical model for a multivalent macroions solution, next to a charged wall of planar geometry, is solved through a well-established integral equation theory. The macroions structure and the charge induced into the fluid are obtained, as a function to the distance to the electrode. The macroions adsorption to the surface and the induced charge density, both show an atypical structure, not consistent with the predictions of the classical theory of Poisson–Boltzmann. In particular, the induced charge density exhibits an enormous charge overcompensation, localized just next to the electrode, implying a violation of the local electroneutrality condition. A breakdown of the charge neutrality, in confined, charged fluids, has been theoretically predicted in the past, by means of integral equations, density functional approaches, and computer simulations, and recently experimentally reported. However, the results presented here show a charge neutrality breakdown, in unconfined, inhomogeneous fluids. Our results are in qualitative agreement with experimental data for Langmuir films of amphiphilic molecules, in contact with a macroions solution.

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References

  1. E.J.W. Verwey, J.T.G. Overbeek, Theory of the Stability of Lyophobic Colloids (Dover, New York, 1948)

    Google Scholar 

  2. A. Münster, Statistical Thermodynamics, First, English edn. (Springer, Berlin, 1974)

    MATH  Google Scholar 

  3. D.C. Grahame, Chem. Rev. 41(3), 441 (1947)

    Google Scholar 

  4. G.M. Torrie, J.P. Valleau, J. Chem. Phys. 73, 5807 (1980)

    ADS  Google Scholar 

  5. J.P. Valleau, G.M. Torrie, J. Chem. Phys. 76(9), 4623 (1982)

    ADS  Google Scholar 

  6. M. Lozada-Cassou, R. Saavedra-Barrera, D. Henderson, J. Chem. Phys. 77, 5150 (1982)

    ADS  Google Scholar 

  7. M. Lozada-Cassou, J. Phys. Chem. 87, 3729 (1983)

    Google Scholar 

  8. P. Attard, in Advances in Chemical Physics, vol. XCII, ed. by I. Prigogine, S.A. Rice (Wiley, New York, 1996)

  9. D.A. McQuarrie, Statistical Mechanics (Harper and Row, New York, 1976)

    MATH  Google Scholar 

  10. V. Lobaskin, P. Linse, J. Chem. Phys. 111, 4300 (1999)

    ADS  Google Scholar 

  11. E. GonÃzlez-Tovar, M. Lozada-Cassou, Adv. Colloid Interface Sci. 270, 54 (2019). https://doi.org/10.1016/j.cis.2019.05.009

    Article  Google Scholar 

  12. C.W. Outhwaite, L.B. Bhuiyan, J. Chem. Phys. 84, 3461 (1986)

    ADS  Google Scholar 

  13. B. Hribar, V. Vlachy, L.B. Bhuiyan, C.W. Outhwaite, J. Phys. Chem. B 104, 11522 (2000)

    Google Scholar 

  14. L.B. Bhuiyan, C.W. Outhwaite, Condens. Matter Phys. 20(3), 33801(1) (2017)

    Google Scholar 

  15. B. Hribar, H. Krienke, Y. Kalyuzhnyi, V. Vlachy, J. Mol. Liq. 73–74, 277 (1997)

    Google Scholar 

  16. H. Greberg, R. Kjellander, J. Chem. Phys. 108, 2940 (1998)

    ADS  Google Scholar 

  17. D.M. Zuckerman, M.E. Fisher, S. Bekiranov, Phys. Rev. E 64, 011206 (2001)

    ADS  Google Scholar 

  18. J.P. Hansen, I.R. McDonald, Theory of Simple Liquids with Applications to Soft Matter, 4th edn. (Academic Press, London, 2013)

  19. N. Cuvillier, F. Rondelez, Thin Solid Films 327–329, 19 (1998)

    ADS  Google Scholar 

  20. N. Cuvillier, F. Rondelez, Langmuir 15, 5547 (1999)

    Google Scholar 

  21. N. Cuvillier, F. Millet, V. Petkova, M. Nedyalkov, J.J. Benattar, Langmuir 16, 5029 (2000)

    Google Scholar 

  22. N. Cuvillier, C. Mingotaud, P. Delhaes, Eur. Phys. J. E 15, 149 (2004)

    Google Scholar 

  23. M. Lozada-Cassou, J. Chem. Phys. 80, 3344 (1984)

    ADS  Google Scholar 

  24. M. Lozada-Cassou, W. Olivares, B. Sulbarán, Phys. Rev. E 53, 522 (1996)

    ADS  Google Scholar 

  25. J. Yu, L. Degrève, M. Lozada-Cassou, Phys. Rev. Lett. 79, 3656 (1997)

    ADS  Google Scholar 

  26. T. Colla, M. Girotto, A.P. dos Santos, Y. Levin, J. Chem. Phys. 145, 094704 (2016)

    ADS  Google Scholar 

  27. T. Takamichi, N. Tsuneyoshi, Phys. Rev. E 65, 021405(1) (2002)

    ADS  Google Scholar 

  28. Z.X. Luo, Y.Z. Xing, Y.C. Ling, A. Kleinhammes, Y. Wu, Nat. Commun. 6, 7358(1) (2015)

    Google Scholar 

  29. F. Jiménez-Ángeles, M. Lozada-Cassou, J. Phys. Chem B. 108, 7286 (2004)

    Google Scholar 

  30. O. Lenz, C. Holm, Eur. Phys. J. E 26, 191 (2008)

    Google Scholar 

  31. Z.Y. Wang, J. Wu, J. Chem. Phys. 147, 024703 (2017)

    ADS  Google Scholar 

  32. H.L. Friedman, A Course in Statistical Mechanics (Prentice-Hall Inc, Upper Saddle River, 1985)

    Google Scholar 

  33. M. Lozada-Cassou, J. Chem. Phys. 75, 1412 (1981)

    ADS  Google Scholar 

  34. L. Blum, Mol. Phys. 30, 1529 (1975)

    ADS  Google Scholar 

  35. L. Blum, J. Phys. Chem. 81(2), 136–147 (1977). https://doi.org/10.1021/j100517a009

    Article  Google Scholar 

  36. D. Henderson, L. Blum, J. Chem. Phys. 69(12), 5441 (1978). https://doi.org/10.1063/1.436535

    Article  ADS  Google Scholar 

  37. R. Kjellander, S. Marčelja, J. Chem. Phys. 82, 2122 (1985)

    ADS  Google Scholar 

  38. D. Henderson, Fundamentals of Inhomogeneous Fluids (Marcel Dekker, New York, 1992)

    Google Scholar 

  39. E. Wernersson, R. Kjellander, J. Lyklema, J. Phys. Chem. C 114, 1849 (2010)

    Google Scholar 

  40. M. Lozada-Cassou, in Fundamentals of Inhomogeneous Fluids, chap. 8, ed. by D. Henderson (Marcel Dekker, New York, 1992)

  41. S.L. Carnie, D.Y.C. Chan, D.J. Mitchell, B.W. Ninham, J. Chem. Phys. 74, 1472 (1981)

    ADS  Google Scholar 

  42. G. Odriozola, M. Lozada-Cassou, Fortschr. Phys. 65(6–8), 1600072 (2017)

    Google Scholar 

  43. K. Hiroike, Mol. Phys. 33, 1195 (1977)

    ADS  MathSciNet  Google Scholar 

  44. H. Manzanilla-Granados, M. Lozada-Cassou, J. Phys. Chem. B 117, 11812 (2013)

    Google Scholar 

  45. M. Deserno, F. Jiménez-Ángeles, C. Holm, M. Lozada-Cassou, J. Phys. Chem. B 105, 10983 (2001)

    Google Scholar 

  46. E. González-Tovar, L.B. Bhuiyan, C.W. Outhwaite, M. Lozada-Cassou, J. Mol. Liq. 228, 160 (2017)

    Google Scholar 

  47. J.N. Israelachvili, Intermolecular and Surface Forces, 2nd edn. (Academic Press, New York, 1992)

    Google Scholar 

  48. I. Borukhov, D. Andelman, Phys. Rev. Lett. 79, 435 (1997)

    ADS  Google Scholar 

  49. I. Borukhov, D. Andelman, H. Orland, Electrochim. Acta 46(46), 221 (2000)

    Google Scholar 

Download references

Acknowledgements

We gratefully acknowledge the support of CONACyT, México, through the Project 169125.

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Author notes

  1. Alfredo González-Calderón

    Present address: CONACyT-Centro de Ingeniería y Desarrollo Industrial (CIDESI), sede Campeche, Ctra. Carmen Puerto Real km 7.5, Mundo Maya, Cd. del Carmen, 24153, Campeche, Mexico

Authors and Affiliations

  1. Instituto de Energías Renovables, Universidad Nacional Autónoma de México (U.N.A.M.), 62580, Temixco, Mor., Mexico

    Alfredo González-Calderón & Marcelo Lozada-Cassou

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  1. Alfredo González-Calderón
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  2. Marcelo Lozada-Cassou
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Correspondence to Marcelo Lozada-Cassou.

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González-Calderón, A., Lozada-Cassou, M. Violation of the local electroneutrality condition in an inhomogeneous macroions solution. Eur. Phys. J. Spec. Top. 230, 1113–1120 (2021). https://doi.org/10.1140/epjs/s11734-021-00089-x

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