DOI: 10.1140/epje/i2002-10096-x
Hydrodynamic interaction of AFM cantilevers with solid walls: An investigation based on AFM noise analysis
F. Benmouna and D. JohannsmannMax-Planck-Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany johannsmann@pc.tu-clausthal.de
(Received 5 September 2002 and Received in final form 20 November 2002 / Published online: 4 February 2003)
Abstract
The noise power spectrum of the thermally activated motion of an
AFM cantilever has been analyzed with respect to viscoelastic and
hydrodynamic coupling between the cantilever and a substrate surface.
Spheres with radii between 5 and 25
m were glued to the cantilever to
provide a well-defined geometry. The cantilever is modeled as a harmonic
resonator with a frequency-dependent complex drag coefficient
.
The variation of the drag coefficient
with the
tip-sample distance,
D, and the sphere radius,
R, can be expressed as a
function of the single dimensionless parameter
D/R. However, this scaling
breaks down close to the surface. There are two sources of a frequency
dependence of
, which are viscoelastic memory and
hydrodynamics. Viscoelastic relaxation is observed when the surface is
covered with a soft polymer layer. In the absence of such a soft layer one
still finds a frequency dependence of
which is caused by
hydrodynamics. At large substrate-cantilever distances, the drag
coefficient increases with frequency because of inertial effects. At small
distances, on the other hand, the drag coefficient decreases with increasing
frequency, which is explained by the reflection of shear waves from the
substrate surface. In liquids, inertial effects can be important when
performing dynamic AFM experiments.
05.40.Jc - Brownian motion.
68.37.Ps - Atomic force microscopy (AFM).
81.40.Pq - Friction, lubrication, and wear.
47.35.+i - Hydrodynamic waves.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2002
