Correction of microrheological measurements of soft samples with atomic force microscopy for the hydrodynamic drag on the cantilever

Force measurements with atomic force microscopy (AFM) in liquid are subjected to the hydrodynamic dragforce artifact (F-d) due to viscous friction of the cantilever with the liquid. This artifact may be especially relevant in microrheological studies of soft samples. Common approaches estimate F-d at a certain distance above the sample and subtract its value from the contact force measured on the sample. However, this procedure can underestimate F-d at contact. The aim of this work was to assess the effect of the hydrodynamic drag in microrheological AFM measurements of soft samples in liquid at low Reynolds numbers (Re < 1). Drag forces of water on rectangular and V-shaped cantilevers were measured in noncontact when subjecting the substrate to low-amplitude (35 nm) sinusoidal oscillations at different frequencies (1-200 Hz) and tip-substrate distances (h) (0.2-3 mum). F-d increased proportionally with the relative velocity (v). Moreover, the drag factor b(h) defined as F-d/v rose when the cantilever approached the substrate. Thus, the hydrodynamic drag exhibited locally a pure viscous behavior. Drag factor dependence on distance was well-fitted (r(2) approximate to 0.95) by the scaled spherical model b(h) = 6pietaa(eff)(2)/(h + h(eff)), where eta is the viscosity of the liquid, a(eff) is the effective radius of the cantilever, and h(eff) is the effective height of the tip. Drag factor at contact was estimated as b(0) = 1.38 x 10(-6) (rectangular) and 1.55 x 10(-6) Ns/m (V-shaped) by extrapolating b(h) to h = 0. Drag factor measured at 2 mum underestimated b(0) by 30-50%. Thus, correction of the hydrodynamic artifact with drag factor measured a few micrometers above the surface could result in substantial errors in AFM microrheological measurements of soft samples. Our results suggest that drag artifact in contact microrheological measurements under low Re can be accurately estimated by b(0). Precise correction of drag artifact could lead to an improvement in scan speed in contact AFM imaging and in pulling speed in force spectroscopy studies.