Exploring the tip-sample interaction regimes in the presence of hysteretic forces in the tapping mode atomic force microscopy

Abstract

In this article, the tip-sample interaction regimes in the presence of hysteretic forces are investigated using atomic force microscopy in the tapping mode. For this purpose, two samples that cause the formation of hysteretic forces, namely, silicon (stiff sample) with an adsorbed water film and polyethylene (compliant sample), are used. Also, for deriving the equation of motion of the microcantilever, the continuous beam model is used, and for determining the contact forces, depending on the sample under investigation, the Derjaguin–Muller–Toporov and Johnson–Kendall–Roberts contact mechanics models are used. The results indicate that the hysteretic interaction forces generate high-periodic and irregular responses at certain tip-sample separation distances. In fact, at these distances, a family of steady-state attractors is found that can be observed in one branch on the minimum tip-sample separation curves and in two separate branches on the average force curves. The reason for this occurrence might be the alternate formation of a liquid column between the probe tip and the sample (in the presence of ambient moisture), and for the compliant sample, the reason might be the alternate formation of an adhesion neck. In this article, the role of hysteretic forces in producing the hysteresis of the amplitude-separation curves is also explored.