IMAGING A NANOSTRUCTURE BY THE LYAPUNOV EXPONENT COMPUTATION

Authors

  • Saša Nježić Banja Luka University, Faculty of Medicine, Save Mrkalja 14, 78000 Banja Luka
  • Dragana Malivuk Banja Luka University, Faculty of Science, Mladena Stojanovića 2, 78000 Banja Luka
  • Sreten Lekić Banja Luka University, Faculty of Science, Mladena Stojanovića 2, 78000 Banja Luka
  • Saša Sekulić Banja Luka University, Faculty of Science, Mladena Stojanovića 2, 78000 Banja Luka
  • Enes Škrgić Banja Luka University, Faculty of Science, Mladena Stojanovića 2, 78000 Banja Luka
  • Zoran Rajilić Banja Luka University, Faculty of Science, Mladena Stojanovića 2, 78000 Banja Luka

DOI:

https://doi.org/10.7251/COMEN1301058NJ

Abstract

A model of the AFM (atomic force microscope) with certain tip-nanostructure interaction, cantilever elasticity and damping of its oscillations is proposed. Stable and unstable motion of the AFM tip interacting with the graphene sheet is investigated by the Lyapunov exponent computation. In our approximation, a hundred Si atoms (top of the AFM tip) interact with C atoms of the nanostructure. Тhis interaction is described by Lennard-Jones potential, and the distance between the top and the center of the cantilever mass is a constant. Complex influence of the initial tip-nanostructure distance and nanostructure size on stability has been examined. We discuss a possible new mode of the AFM operation based on the Lyapunov exponent computation. Maxima and minima of the Lyapunov exponent show where certain parts of the elementary cells are placed.

References

[1] F. J. Giessibl, Advances in atomic force microscopy, Rev. Mod. Phys., Vol. 75 (2003) 949−983.

[2] R. Garcia and A. San Paulo, Dynamics of a vibrating tip near or in intermittent contact with a surface, Phys. Rev. B, Vol. 61 (2000) 13381−13384.

[3] Q.Q. Hu and L.Q. Chen, Bifurcation and chaos of atomic-force-microscope probes driven in Lennard-Jones potentials, Chaos, Solitons & Fractals, Vol. 36 (2008) 740−745.

[4] S. Hu and A. Raman, Chaos in Atomic Force Microscopy, Phys. Rev. Lett. Vol. 96 (2006) 036107 (4 pages).

[5] F. Jamitzky, M. Stark, W. Bunk, W. M. Heckl and R. W. Stark, Chaos in dynamic atomic force microscopy, Nanotechnology, Vol. 17 (2006) 213−220.

[6] R. W. Stark, Bistability, higher harmonics, and chaos in AFM, Materials Today, Vol. 13 (2010) 24−32.

[7] C. C. Wang, N. S. Pai and H. T. Yau, Chaos control in AFM system using sliding mode control by backstepping design, Comm. Nonl. Sci. Num. Sim., Vol. 15 (2010) 741−751.

[8] M. Liu and D. Chelidze, A new type of atomic force microscope based on chaotic motions, International Journal of Non-Linear Mechanics, Vol. 43 (2008) 521−526.

Downloads

Published

2013-06-01