Hydrodynamic corrections to contact resonance atomic force microscopy measurements of viscoelastic loss tangent

We present a method to improve accuracy in measurements of nanoscale viscoelastic material properties with contact resonance atomic force microscope methods. Through the use of the two-dimensional hydrodynamic function, we obtain a more precise estimate of the fluid damping experienced by the cantilever-sample system in contact resonance experiments, leading to more accurate values for the tip-sample damping and related material properties. Specifically, we consider the damping and added mass effects generated by both the proximity of the cantilever to the sample surface and the frequency dependence on the hydrodynamic loading of the system. The theoretical correction method is implemented on experimental contact resonance measurements. The measurements are taken on a thin polystyrene film and are used to determine the viscoelastic loss tangent, tan δ, of the material. The magnitude of the corrections become significant on materials with low tan δ (<0.1) and are especially important for measurements made with the first flexural mode of vibration.