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#### Abstract

Tapping mode atomic force microscopy (TMAFM) in fluids has become an increasingly important technique, especially in studying biological samples under near physiological conditions. However, until recently the physics of tapping mode operation under fluids has not been well understood. The first part of this presentation will show that the key features of operating TMAFM in fluids can be captured by the simple single degree of freedom model of a driven harmonic oscillator model characterized by a low quality factor. Such a model can aid in clarifying the physics underlying the operation of TMAFM in fluids and could prove useful in the development of techniques to extract meaningful mechanical surface properties from tip/sample interactions.

The second part will be focused on a new approach to reconstruction of tip-sample force in TMAFM based on the determination of cantilever acceleration, and thus referred to as scanning probe acceleration microscopy (SPAM). This method utilizes the second derivative of the deflection signal to recover the tip acceleration trajectory. The challenge in such an approach is that with real, noisy data, the second derivative of the signal is strongly dominated by the noise. This problem is solved by taking advantage of the fact that most of the information about the deflection trajectory is contained in the higher harmonics, making it possible to filter the signal by “comb” filtering, i.e. by taking its Fourier transform, and inverting it while selectively retaining only the intensities at integer harmonic frequencies. Such a comb filtering method works particularly well in fluid TMAFM due to the highly distorted character of the deflection signal. The validity of this approach will be demonstrated through numerical simulations and in situ TMAFM experiments on supported lipid bilayer patches on mica.

The second part will be focused on a new approach to reconstruction of tip-sample force in TMAFM based on the determination of cantilever acceleration, and thus referred to as scanning probe acceleration microscopy (SPAM). This method utilizes the second derivative of the deflection signal to recover the tip acceleration trajectory. The challenge in such an approach is that with real, noisy data, the second derivative of the signal is strongly dominated by the noise. This problem is solved by taking advantage of the fact that most of the information about the deflection trajectory is contained in the higher harmonics, making it possible to filter the signal by “comb” filtering, i.e. by taking its Fourier transform, and inverting it while selectively retaining only the intensities at integer harmonic frequencies. Such a comb filtering method works particularly well in fluid TMAFM due to the highly distorted character of the deflection signal. The validity of this approach will be demonstrated through numerical simulations and in situ TMAFM experiments on supported lipid bilayer patches on mica.

#### Credits

This work was supported by NSF NIRT awards CTS-0304568 and DMR-9974457.

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