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Logo: Institut für Baumechanik und Numerische Mechanik/Leibniz Universität Hannover
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Logo: Institut für Baumechanik und Numerische Mechanik/Leibniz Universität Hannover
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Modeling of electro-mechanical contact on a mesoscopic length-scale

Bearbeitung:ext. T. Helmich
Förderung durch:This work is supported by the Graduiertenkolleg 615 of the DFG (German Research Foundation).
Bild Modeling of electro-mechanical contact on a mesoscopic length-scale

The basic idea is to model the electro-mechanical contact on a microscale. The application for this project is the atomic force microscope (AFM), as a typical application for a contact force calculation on micro level. The AFM allows to measure forces down to 1 pN and geometries down to 0,1 nm and exceeds therefore optical microscopes in resolution, it is in common use in nearly all science fields. The AFM detects the surface of the sample mounted on a tube scanner by scanning the sample against a short tip at the end of a cantilever. A typical tip has a length of about 2 nanometer and a sharpness at its end of about one atom, the cantilever is 450 micrometer wide. The tip motion causes a cantilever distraction, which is measured by the help of a laser and a photo detector. The laser beam is lead to the tip and then reflected to the photo detector via mirrors and prisms, where the voltage difference is measured as a size of the contact force. The interaction between tip and surface is affected by coupled physical phenomena. A potential formulation of the van der Waals forces with a repulsive and attractive component in terms of a Lennard-Jones-potential is used to discribe the contact between tip and surface. In contrast to classical contact formulations the contact conditions are continuous and normal and tangential contact are coupled consistently. From this the often introduced artifial free energy potential for normal contact on macroscopic lengthscales can be argued.

Figure 1: Atomic Force microscope (AFM)

Figure 2: Contact forces on microlevel

Figure 3: van der Waals forces

Figure 4: Integration into a FEM environment

Figure 5: Matrix formulation

Figure 6: Numerical example

Figure 7: Contact forces: vertical tip motion

Figure 8: Contact potential: vertical tip motion

Figure 9: Tip motion and contact potential

Figure 10: Conclusion

Übersicht