Validity of point-mass model in off-resonance dynamic atomic force microscopy

The quantitative measurement of viscoelasticity nano-scale entities is an important goal nanotechnology research and there considerable progress with advent dynamic atomic force microscopy. hydrodynamics cantilever, the sensor in AFM measurements, plays a pivotal role estimates viscoelasticity. point-mass (PM) model, wherein cantilever approximated as mass-less spring widely used analysis its validity, particularly liquid environments, debated. It suggested that must be treated continuous rectangular beam to obtain accurate materials it probing. Here, we derived equations, which relate stiffness damping coefficient material under investigation measured parameters, by approximating also considering full geometric details. These equations are for both tip-excited well base-excited cantilevers. We have performed off-resonance spectroscopy on single protein molecule investigate validity PM model. measurements AFMs equipped different excitation methods detection schemes measure response. data was analyzed using both, model found models yield same results when experiments truly regime small amplitudes much higher than interaction stiffness. Our findings suggest simple approximation based adequate describe dynamics, provided care taken while performing so approximations these valid.