Accurate force spectroscopy in tapping mode atomic force microscopy in liquids

Existing force spectroscopy methods in tapping mode atomic force microscopy (AFM) such as higher harmonic inversion [M. Stark, R. W. Stark, W. M. Heckl, and R. Guckenberger, Proc. Natl. Acad. Sci. U. S. A. 99, 8473 (2002)] or scanning probe acceleration microscopy [J. Legleiter, M. Park, B. Cusick, and T. Kowalewski, Proc. Natl. Acad. Sci. U. S. A. 103, 4813 (2006)] or integral relations [M. Lee and W. Jhe, Phys. Rev. Lett. 97, 036104 (2006); S. Hu and A. Raman, Nanotechnology 19, 375704 (2008); H. Holscher, Appl. Phys. Lett. 89, 123109 (2006); A. J. Katan, Nanotechnology 20, 165703 (2009)] require and assume as an observable the tip dynamics in a single eigenmode of the oscillating microcantilever. We demonstrate that this assumption can distort significantly the extracted tip-sample interaction forces when applied to tapping mode AFM with soft cantilevers in liquid environments. This exception is due to the fact that under these conditions the second eigenmode is momentarily excited and the observed tip dynamics clearly contains contributions from the fundamental and second eigenmodes. To alleviate this problem, a simple experimental method is proposed to screen the second eigenmode contributions in the observed tip deflection signal to allow accurate tip-sample force reconstruction in liquids. The method is implemented experimentally to reconstruct interaction forces on polymer, bacteriorhodopsin membrane, and mica samples in buffer solutions.