Influence of Electrocapillarity on the Water Meniscus Shape in the Atomic Force Microscopy

  • E. A. Eliseev Institute for Problems of Materials Science, Nat. Acad. of Sci. of Ukraine
Keywords: electrocapillarity, atomic force microscopy, water meniscus, Euler–Lagrange equation

Abstract

In the framework of the analytical theory of electrocapillarity phenomena that arise in atomic force microscopy (AFM) experiments, the formation of a water meniscus under the AFM probe has been considered, and its dependence on the applied voltage has been analyzed. The non-uniformity of the electric field produced by the AFM probe, the influences of gravitation forces on the meniscus height, and the dependence of the surface energy of a meniscus on its shape are taken into account self-consistently. The influence of a strong non-uniform electric field of the probe on the emergence conditions, size, and shape of the water meniscus is analyzed for the first time. The Euler–Lagrange partial differential equation and the corresponding boundary conditions making allowance for the non-uniform electric field of an AFM probe, the gravitation force, the meniscus surface tension, and the environmental humidity and describing the thermodynamics of the water meniscus formation in a self-consistent way are derived. The obtained numerical results are in agreement with known experimental data.

References

S.V. Kalinin, A.N. Morozovska, Long Qing Chen, and B.J. Rodriguez, Rep. Prog. Phys. 73, 056502 (2010).

http://dx.doi.org/10.1088/0034-4885/73/5/056502

A.N. Morozovska, G.S. Svechnikov, and E.A. Eliseev, Theory of Local Polar Properties of Ferroelectrics (Astroprint, Odessa, 2013) (in Russian).

B.L. Weeks, M.W. Vaughn, and J.J. DeYoreo, Langmuir 21, 8096 (2005).

http://dx.doi.org/10.1021/la0512087

Th. Stifter, O. Marti, and B. Bhushan, Phys. Rev. B 62, 13667 (2000).

http://dx.doi.org/10.1103/PhysRevB.62.13667

H.-J. Butt, M.B. Untch, A. Golriz, S.A. Pihan, and R. Berger, Phys. Rev. E 83, 061604 (2011).

http://dx.doi.org/10.1103/PhysRevE.83.061604

S. Gomez-Monivas and J.J. Saenz, Phys. Rev. Lett. 91, 056101 (2003).

http://dx.doi.org/10.1103/PhysRevLett.91.056101

Yu.V. Goryunov and B.D. Summ, Wetting (Znanie, Moscow, 1972) (in Russian); A.D. Zimon, Fluid Adhesion and Wetting (Khimiya, Moscow, 1974) (in Russian).

L.D. Landau and E.M. Lifshitz, Statistical Physics, Part 1 (Pergamon Press, Oxford, 1980).

J.N. Israelachvili, Intermolecular and Surface Science (Academic Press, London, 1991).

http://en.wikipedia.org/wiki/Kelvin_equation, https://en.wikipedia.org/wiki/Young-Laplace_equation.

E.A. Eliseev, S.V. Kalinin, S. Jesse, S.L. Bravina, and A.N. Morozovska, J. Appl. Phys. 102, 014109 (2007).

http://dx.doi.org/10.1063/1.2749463

E.J. Mele, Am. J. Phys. 69, 557 (2001).

http://dx.doi.org/10.1119/1.1341252

V.V. Batygin and I.N. Toptygin, Collection of Problems in Electrodynamics (Nauka, Moscow, 1970) (in Russian).

A.N. Morozovska, E.A. Eliseev, and S.V. Kalinin, J. Appl. Phys. 102, 074105 (2007).

http://dx.doi.org/10.1063/1.2785824

A.V. Ievlev, A.N. Morozovska, V.Ya. Shur, and S.V. Kalinin, Appl. Phys. Lett. 104, 092908 (2014).

http://dx.doi.org/10.1063/1.4867979

L. Elsgolts, Differential Equations and the Calculus of Variations (Mir Publishers, Moscow, 1970).

P.-G. de Gennes, Usp. Fiz. Nauk 151, 619 (1987).

http://dx.doi.org/10.3367/UFNr.0151.198704c.0619

Published
2019-01-15
How to Cite
Eliseev, E. (2019). Influence of Electrocapillarity on the Water Meniscus Shape in the Atomic Force Microscopy. Ukrainian Journal of Physics, 60(8), 796. https://doi.org/10.15407/ujpe60.08.0799
Section
Solid matter