Tilt of atomic force microscope cantilevers: effect on spring constant and adhesion measurements

In atomic force microscopy, the cantilevers are mounted under a certain tilt angle alpha with respect to the sample surface. In this paper, we show that this increases the effective spring constant by typically 10-20%. The effective spring constant of a rectangular cantilever of length L can be obtained by dividing the measured spring constant by cos2 alpha(1 - 2D tan alpha/L). Here, alpha is the tilt angle and D is the size of the tip. In colloidal probe experiments, D has to be replaced by the radius of the attached particle. To determine the effect of tilt experimentally, the adhesion force between spherical borosilicate particles and planar silicon oxide surfaces was measured at tilt angles between 0 degrees and 35 degrees. The experiments revealed a significant decrease of the mean apparent adhesion force with a tilt of typically 20-30% at alpha = 20 degrees. In addition, they demonstrate that the adhesion depends drastically on the precise position of contact on the particle surface.