2020 Impact factor 1.890
Soft Matter and Biological Physics
Eur. Phys. J. E 9, 435-441 (2002)
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. Johannsmann

Max-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  $\mu $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 $\xi (\omega)$. The variation of the drag coefficient $\xi (\omega)$ 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 $\xi (\omega)$, 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 $\xi (\omega)$ 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.

PACS
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