Abstract
The idea behind the atomic force microscope (AFM) is to measure the force between the surface and the scanning tip in order to track the surface topography. Before we describe the atomic force microscopy technique in detail, we consider the forces acting between tip and sample as well as the tip-sample contact mechanics. We consider also the snap-to-contact phenomenon, which can occur due to attractive tip-sample forces.
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Notes
- 1.
We use here the coordinate z for the distance between the tip and sample instead of r previously used for the Lennard-Jones potential between two atoms in (10.5).
- 2.
In our analysis we treat the spring constant k and the parameters of the Lennard-Jones potential (\(U_0\) and \(z_a\)) as constants.
References
J. Cugnon, The Casimir effect and the vacuum energy: duality in the physical interpretation. Few-Body Syst. 53, 181 (2012). https://doi.org/10.1007/s00601-011-0250-9
J. Israelachvili, Intermolecular and Surface Forces, 3rd edn. (Academic Press, London, 2011). ISBN 9780123919274
R. Reifenberger, Fundamentals of Atomic Force Microscopy: Part I: Foundations (World Scientific, Singapore, 2015). https://doi.org/10.1142/9343
H. Hertz, Über die Berührung fester elastischer Körper (On the contact of elastic solids). J. Reine Angew. Math. 92, 156 (1881)
B.V. Derjaguin, V.M. Muller, Y.P. Toporov, Effect of contact deformations on the adhesion of particles. J. Colloid Interface Sci. 53, 314 (1975). https://doi.org/10.1016/0021-9797(75)90018-1
B.V. Derjaguin, V.M. Muller, Y.P. Toporov, On the role of molecular forces in contact deformations (critical remarks concerning Dr. Tabor’s report). J. Colloid Interface Sci. 67, 378 (1978). https://doi.org/10.1016/0021-9797(78)90021-8
B.V. Derjaguin, V.M. Muller, Y.P. Toporov, On different approaches to the contact mechanics. J. Colloid Interface Sci. 73, 293 (1980). https://doi.org/10.1016/0021-9797(80)90157-5
V.M. Muller, B.V. Derjaguin, Y.P. Toporov, On two methods of calculation of the force of sticking of an elastic sphere to a rigid plane. Colloids Surf. 7, 251 (1983). https://doi.org/10.1016/0166-6622(83)80051-1
D. Maugis, Adhesion of spheres: the JKR-DMT transition using a dugdale model. J. Colloid Interface Sci. 150, 243 (1992). https://doi.org/10.1016/0021-9797(92)90285-T
B. Derjaguin, Untersuchungen über die Reibung und Adhäsion, IV (Investigations on friction and adhesion). Kolloid Z. 69, 155 (1934). https://doi.org/10.1007/BF01433225
D. Tabor, Surface forces and surface interactions. J. Colloid Interface Sci. 58, 2 (1977). https://doi.org/10.1016/0021-9797(77)90366-6
K.L. Johnson, K. Kendall, A.D. Roberts, Surface energy and the contact of elastic solids. Proc. R. Soc. Lond. Ser. A 324, 301 (1971). https://doi.org/10.1098/rspa.1971.0141
V.M. Muller, V.S. Yuschenko, B.V. Derjaguin, On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane. J. Colloid Interface Sci. 77, 91 (1980). https://doi.org/10.1016/0021-9797(80)90419-1
U.D. Schwarz, A generalized analytical model for the elastic deformation of an adhesive contact between a sphere and a flat surface. J. Colloid Interface Sci. 261, 99 (2003). https://doi.org/10.1016/S0021-9797(03)00049-3
D.S. Dugdale, Yielding of steel sheets containing slits. J. Mech. Phys. Sol. 8, 100 (1960). https://doi.org/10.1016/0022-5096(60)90013-2
D.B. Asay, S.H. Kima, Effects of adsorbed water layer structure on adhesion force of silicon oxide nanoasperity contact in humid ambient. J. Chem. Phys. 124, 174712 (2006). https://doi.org/10.1063/1.2192510
L. Zitzler, S. Herminghaus, F. Mugele, Capillary forces in tapping mode atomic force microscopy. Phys. Rev. B 66, 155436 (2002). https://doi.org/10.1103/PhysRevB.66.155436
T. Ondarcuhu, L. Fabiein, in Surface Tension in Microsystems, Microtechnology and MEMS, ed. by P. Lambert (Springer, Berlin, 2013). https://doi.org/10.1007/978-3-642-37552-1_14
M. Saint Jean, S. Hudlet, C. Guthmann, J. Berger, Van der Waals and capacitive forces in atomic force microscopies. J. Appl. Phys. 86, 5245 (1999). https://doi.org/10.1063/1.371506
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Voigtländer, B. (2019). Forces Between Tip and Sample. In: Atomic Force Microscopy. NanoScience and Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-13654-3_10
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DOI: https://doi.org/10.1007/978-3-030-13654-3_10
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