Electrostatic and Van Der Waals Interactions of Nanoparticles in Electrolytes

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

Abstract

The electrostatic interaction between nanoparticles caused by the overlapping of double electric layers and the van der Waals interaction caused by quantum and thermodynamic fluctuations of electromagnetic fields are considered. The linearized Poisson–Boltzmann equation for particles with a fixed electric potential on their surface is used in the case of the electrostatic interaction. An exact solution of the problem has been obtained both for identical particles and for particles with strongly different sizes. The screening of static fluctuations and the retardation of electromagnetic fields for the dispersion part of the van der Waals interaction have been taken into account. The total interaction energy of two particles has been calculated for ion concentrations in an electrolyte from 10–6 to 10–2 mol/L and sizes of nanoparticles from 1 to 103 nm. It has been found that the van der Waals force exceeds the screened electrostatic repulsive force at high concentrations of the electrolyte from 10–3 to 10–2 mol/L at both small and large interparticle distances.

About the authors

A. V Filippov

State Research Center of the Russian Federation Troitsk Institute for Innovation and Fusion Research, 108840, Troitsk, Moscow, Russia; Joint Institute for High Temperatures, Russian Academy of Sciences, 125412, Moscow, Russia; Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudnyi, Moscow region, Russia

Email: fav@triniti.ru

V. M Starov

Department of Chemical Engineering, Loughborough University, LE11 3TU, Loughborough, United Kingdom

Author for correspondence.
Email: fav@triniti.ru

References

  1. J. N. Israelachvili, Intermolecular and surface forces, 3rd ed., Elsevier, Amsterdam (2011), p.191.
  2. B. Honig and A. Nicholls, Science 268(5214), 1144 (1995).
  3. I. Ledezma-Yanez, W. D. Z. Wallace, P. Sebasti'an-Pascual, V. Climent, J. M. Feliu, and M. T. Koper, Nat. Energy 2(4), 17031 (2017).
  4. B. Smit, J. A. Reimer, C. M. Oldenburg, and I. C. Bourg, Introduction to carbon capture and sequestration, World Scienti c, Singapore (2014), v. 1.
  5. M. Manciu and E.Ruckenstein, Langmuir 17(22), 7061 (2001).
  6. H. Wennerstrom, E. Vallina Estrada, J. Danielsson, and M. Oliveberg, Proc. Natl. Acad. Sci. USA 117(19), 10113 (2020).
  7. S. Su, I. Siretanu, D. van den Ende, B. Mei, G. Mul, and F. Mugele, Adv. Mater. 33, 2106229 (2021).
  8. D. F. Parsons, M. Bostr¨om, P. L. Nostro, and B. W. Ninham, Phys. Chem. Chem. Phys. 13(27), 12352 (2011).
  9. J. Klein, Friction 1(1), 1 (2013).
  10. K. Vo¨ıtchovsky, J. J. Kuna, S. A. Contera, E. Tosatti, and F. Stellacci, Nat. Nanotechnol. 5(6), 401 (2010).
  11. J. N. Israelachvili, Intermolecular and surface forces, Academic Press, Amsterdam (2015).
  12. Y. Liang, N. Hilal, P. Langston, and V. Starov, Adv. Colloid Interface Sci. 134-135, 151 (2007).
  13. N. M. Kovalchuk, D. Johnson, V. Sobolev, N. Hilal, and V. Starov, Adv. Colloid Interface Sci. 272, 102020 (2019).
  14. B. V. Derjaguin, N. V. Churaev, and V. M. Muller, Surface Forces, Consultants Bureau, N.Y. (1987).
  15. A. B. Glendinning and W. B.Russel, J. Colloid Interface Sci. 93(1), 95 (1983).
  16. S. L. Carnie and D. Y. C. Chan, J. Colloid Interface Sci. 161, 260 (1993).
  17. А. В. Филиппов, И. Н. Дербенев, ЖЭТФ 150, 1262 (2016).
  18. I. N. Derbenev, A. V. Filippov, A. J. Stace, and E. Besley, J. Chem. Phys. 145, 084103 (2016).
  19. А. В. Филиппов, И. Н. Дербенев, А. А. Паутов, М. М. Родин, ЖЭТФ 152, 607 (2017).
  20. I. N. Derbenev, A. V. Filippov, A. J. Stace, and E. Besley, Soft Matter 14, 5480 (2018).
  21. S. V. Siryk, A. Bendandi, A. Diaspro, and W. Rocchia, J. Chem. Phys. 155, 114114 (2021).
  22. W. R. Bowen and F. Jenner, Adv. Colloid Interface Sci. 56, 201 (1995).
  23. J. I. Kilpatrick, S.-H. Loh, and S. P. Jarvis, J. Am. Chem. Soc. 135(7), 2628 (2013).
  24. S. R. van Lin, K. K. Grotz, I. Siretanu, N. Schwierz, and F. Mugele, Langmuir 35(17), 5737 (2019).
  25. A. Klaassen, F. Liu, F. Mugele, and I. Siretan, Langmuir 38(3), 914 (2022).
  26. Г. Н. Ватсон, Теория бесселевых функций, Иностранная литература, М. (1949), т. 1
  27. G. N. Watson, A treatise on the theory of Bessel functions, Cambridge University Press, London (1922).
  28. D. Langbein, Theory of Van der Waals Attraction, Springer Tracts in Modern Physics, ed. by G. Hohler, Springer-Verlag, Berlin, Heidelberg, N.Y. (1974), v. 72.
  29. В. В. Батыгин, И. Н. Топтыгин, Сборник задач по электродинамике, Наука, М. (1970).
  30. L. N. McCartney and S. Levine, J. Colloid Interface Sci. 30(3), 345 (1969).
  31. G. M. Bell, S. Levine, and L. N. McCartney, J. Colloid.Interface Sci. 33(3), 335 (1970).
  32. H. C. Hamaker, Physica 4(10), 1058 (1937).
  33. Е. М. Лифшиц, ЖЭТФ 29, 94 (1955).
  34. И. Е. Дзялошинский, Е. М. Лифшиц, Л. П. Питаевский, ЖЭТФ 37, 229 (1959).
  35. Б. В. Дерягин, И. И. Абрикосова, Е. М. Лифшиц, УФН 185, 981 (2015).
  36. Ю. С. Бараш, В. Л. Гинзбург, УФН 143, 345 (1984).
  37. Н. В. Чураев, Успехи химии 73, 26 (2004).
  38. D. J. Mitchell and B. W. Ninham, J. Chem. Phys. 56, 1117 (1972).
  39. R. G. Horn and J. N. Israelachvili, J. Chem. Phys. 75(3), 1400 (1981).
  40. B. Vincent, J. Colloid.Interf. Sci. 42, 270 (1973).
  41. J. Chen and A. Anandarajah, J. Colloid Interface Sci. 180(2), 519 (1996).
  42. L. Bergstr¨om, Adv. Colloid Interface Sci. 70, 125 (1997).
  43. V. A. Parsegian and G. H. Weiss, J. Colloid.Interf. Sci. 81(1), 285 (1981).

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2023 Российская академия наук