General scaling law for stiffness measurement of small bodies with applications to the atomic force microscope

John E. Sader, Jessica Pacifico, Christopher P. Green, Paul Mulvaney
2005 Journal of Applied Physics  
A general scaling law connecting the stiffness and dissipative properties of a linear mechanical oscillator immersed in a viscous fluid is derived. This enables the noninvasive experimental determination of the stiffness of small elastic bodies of arbitrary shape by measuring their resonant frequency and quality factor in fluid ͑typically air͒. In so doing, we elucidate the physical basis of the method of Sader et al. ͓Rev. Sci. Instrum. 70, 3967 ͑1999͔͒ for determining the stiffness of
more » ... tiffness of rectangular atomic force microscope cantilevers, and discuss its applicability. The validity of the derived general technique is demonstrated by calibrating atomic force microscope cantilevers with complex geometries, and its implications to small bodies in general are discussed.
doi:10.1063/1.1935133 fatcat:laeqxtdr7ncgdgyhz5jycuhl2a