Web Release Date: January 10,
Correction of Microrheological Measurements of Soft Samples with Atomic Force Microscopy for the Hydrodynamic Drag on the Cantilever
and
Unitat de Biofísica i Bioenginyeria, Facultat de Medicina, Universitat de Barcelona-IDIBAPS, Casanova 143, E-08036 Barcelona, Spain, and Laboratorio de Nuevas Microscopías, Departamento de Física de la Materia Condensada, C-III, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
Received July 16, 2001
In Final Form: October 21, 2001
Abstract:
Force measurements with atomic force microscopy (AFM) in liquid are subjected to the hydrodynamic
drag force artifact (Fd) 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 Fd at a certain distance
above the sample and subtract its value from the contact force measured on the sample. However, this
procedure can underestimate Fd 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 
m). Fd increased proportionally with the relative velocity (v). Moreover,
the drag factor b(h) defined as Fd/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 (r2 
0.95) by the scaled spherical model b(h) = 6
aeff2/(h + heff), where is the viscosity of
the liquid, aeff is the effective radius of the cantilever, and heff is the effective height of the tip. Drag factor
at contact was estimated as b(0) = 1.38 × 10-6 (rectangular) and 1.55 × 10-6 Ns/m (V-shaped) by extrapolating
b(h) to h = 0. Drag factor measured at 2 m 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.
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