The field of nonlinear dynamics deals with mathematical techniques to study the nonlinear equations that serve as models of physical systems. The benefits of using nonlinear dynamics concepts to interpret and predict probe oscillations in dynamic AFM [1] are becoming increasingly clear. Nonlinear dynamics lies at the heart of probe instabilities [2], tip-sample dissipation processes [3], and higher harmonic generation in AFM [4].

In this talk we will first review known experimental phenomena in dynamic AFM, and how a nonlinear dynamicist interprets them. We will then discuss recent experimental results that have established the existence of chaos in tapping mode AFM under reasonable operating conditions [5, 6]. We will also discuss parametric resonance, a phenomenon that underlies the physics of surface waves and of childrens swings, and its recent implementation in dynamic AFM [7]. While still in its infancy, this is a completely different way of oscillating an AFM probe that offers significant promise while posing specific challenges.

1. S. I. Lee, S. W. Howell, A. Raman, R. Reifenberger, "Nonlinear dynamics of microcantilevers in tapping mode atomic force microscopy: A comparison between theory and experiment", Phys. Rev B. 66, 115409, 2002.
2. A. San Paulo, R. Garcia, " High-resolution imaging of antibodies by tapping-mode atomic force microscopy: attractive and repulsive interaction regimes", Biophysical Journal 78, 1599-1605, 2000.
3. R. Garcia, C. J. Gomez, N. F. Martinez, et al., "Identification of nanoscale dissipation processes by dynamic atomic force microscopy", Phys. Rev. Lett. 97, 016103, 2006.
4. S. Crittenden, A. Raman, R. Reifenberger, "Probing attractive forces at the nanoscale using higher-harmonic dynamic force microscopy", Phys. Rev. B. 72, 235422, 2005.
5. S. Q. Hu and A. Raman, "Chaos in atomic force microscopy", Phys. Rev. Lett. 96, 036107, 2006.
6. F. Jamitzky, M. Stark, W. Bunk, et al., "Chaos in dynamic atomic force microscopy", Nanotechnology 17, S213-S220, 2006.
7. M. Moreno-Moreno, A. Raman, J. Gomez-Herrero, R. Reifenberger, "Parametric resonance based scanning probe microscopy", App. Phys. Lett. 88, 193108, 2006.

Researchers should cite this work as follows:

• Arvind Raman (2007), "SPMW Nonlinear dynamics in AFM - chaos and parametric resonance," http://nanohub.org/resources/2238.

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1. atomic force microscopy
2. experiments
3. research seminar