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.
REFERENCES
J. N. Israelachvili, Intermolecular and Surface Forces, 3rd ed. (Elsevier, Amsterdam, 2011), p.191.
B. Honig and A. Nicholls, Science (Washington, DC, U. S.) 268 (5214), 1144 (1995).
I. Ledezma-Yanez, W. D. Z. Wallace, P. Sebastián-Pascual, V. Climent, J. M. Feliu, and M. T. Koper, Nat. Energy 2, 17031 (2017).
B. Smit, J. A. Reimer, C. M. Oldenburg, and I. C. Bourg, Introduction to Carbon Capture and Sequestration (World Scientific, Singapore, 2014), Vol. 1.
M. Manciu and E. Ruckenstein, Langmuir 17, 7061 (2001).
H. Wennerstrom, E. Vallina Estrada, J. Danielsson, and M. Oliveberg, Proc. Natl. Acad. Sci. U. S. A. 117, 10113 (2020).
S. Su, I. Siretanu, D. van den Ende, B. Mei, G. Mul, and F. Mugele, Adv. Mater. 33, 2106229 (2021).
D. F. Parsons, M. Boström, P. L. Nostro, and B. W. Ninham, Phys. Chem. Chem. Phys. 13, 12352 (2011).
J. Klein, Friction 1, 1 (2013).
K. Voitchovsky, J. J. Kuna, S. A. Contera, E. Tosatti, and F. Stellacci, Nat. Nanotechnol. 5, 401 (2010).
J. N. Israelachvili, Intermolecular and Surface Forces (Academic, Amsterdam, 2015).
Y. Liang, N. Hilal, P. Langston, and V. Starov, Adv. Colloid Interface Sci. 134–135, 151 (2007).
N. M. Kovalchuk, D. Johnson, V. Sobolev, N. Hilal, and V. Starov, Adv. Colloid Interface Sci. 272, 102020 (2019).
B. V. Derjaguin, N. V. Churaev, and V. M. Muller, Surface Forces (Consultants Bureau, New York, 1987).
A. B. Glendinning and W. B. Russel, J. Colloid Interface Sci. 93, 95 (1983).
S. L. Carnie and D. Y. C. Chan, J. Colloid Interface Sci. 161, 260 (1993).
A. V. Filippov and I. N. Derbenev, J. Exp. Theor. Phys. 123, 1099 (2016).
I. N. Derbenev, A. V. Filippov, A. J. Stace, and E. Besley, J. Chem. Phys. 145, 084103 (2016).
A. V. Filippov, I. N. Derbenev, A. A. Pautov, and M. M. Rodin, J. Exp. Theor. Phys. 125, 518 (2017).
I. N. Derbenev, A. V. Filippov, A. J. Stace, and E. Besley, Soft Matter 14, 5480 (2018).
S. V. Siryk, A. Bendandi, A. Diaspro, and W. Rocchia, J. Chem. Phys. 155, 114114 (2021).
W. R. Bowen and F. Jenner, Adv. Colloid Interface Sci. 56, 201 (1995).
J. I. Kilpatrick, S.-H. Loh, and S. P. Jarvis, J. Am. Chem. Soc. 135, 2628 (2013).
S. R. van Lin, K. K. Grotz, I. Siretanu, N. Schwierz, and F. Mugele, Langmuir 35, 5737 (2019).
A. Klaassen, F. Liu, F. Mugele, and I. Siretan, Langmuir 38, 914 (2022).
G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge Univ. Press, London, 1922), Vol. 1.
D. Langbein, Springer Tracts Mod. Phys., 72 (1974).
V. V. Batygin and I. N. Toptygin, Problems in Electrodynamics, 2nd ed. (Nauka, Moscow, 1970; Academic, London, 1978).
L. N. McCartney and S. Levine, J. Colloid Interface Sci. 30, 345 (1969).
G. M. Bell, S. Levine, and L. N. McCartney, J. Colloid. Interface Sci. 33, 335 (1970).
H. C. Hamaker, Physica (Amsterdam, Neth.) 4, 1058 (1937).
E. M. Lifshits, Sov. Phys. JETP 2, 73 (1955).
I. E. Dzyaloshinskii, E. M. Lifshits, and L. P. Pitaevskii, Sov. Phys. JETP 10, 161 (1959).
B. V. Derjaguin, I. I. Abrikosova, and E. M. Lifshitz, Phys. Usp. 58, 906 (2015).
Yu. S. Barash and V. L. Ginzburg, Sov. Phys. Usp. 27, 467 (1984).
N. V. Churaev, Russ. Chem. Rev. 73, 25 (2004).
D. J. Mitchell and B. W. Ninham, J. Chem. Phys. 56, 1117 (1972).
R. G. Horn and J. N. Israelachvili, J. Chem. Phys. 75, 1400 (1981).
B. Vincent, J. Colloid Interface Sci. 42, 270 (1973).
J. Chen and A. Anandarajah, J. Colloid Interface Sci. 180, 519 (1996).
L. Bergström, Adv. Colloid Interface Sci. 70, 125 (1997).
V. A. Parsegian and G. H. Weiss, J. Colloid Interface Sci. 81, 285 (1981).
Funding
This work was supported by the Russian Science Foundation (project no. 22-22-01000, A.V. Filippov) and by the European Space Agency (projects NanoPaInt Marie Curie, ЕС, and MAP EVAPORATION, V. M. Starov).
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Filippov, A.V., Starov, V.M. Electrostatic and Van Der Waals Interactions of Nanoparticles in Electrolytes. Jetp Lett. 117, 598–605 (2023). https://doi.org/10.1134/S002136402360074X
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DOI: https://doi.org/10.1134/S002136402360074X