Adhesion forces between a parabolic-shaped AFM tip scanning a grooved gold surface: Comparison of a model and an experiment

Adhesion forces largely depend on the precise geometry of contact between two surfaces; however, this relationship has not yet been systematically studied. In this paper, the adhesion forces between a parabolic-shaped tip and a grooved gold surface were measured on an atomic force microscope (AFM) under ambient conditions. Experimental results show that the fluctuation in mean adhesion force corresponds to the substrate's profile (which is symmetric), yet is asymmetric. A numerical model is proposed based on geometry of the contact zone. Adhesion force was found to be largely dependent on the combined effects of tip radius, profile and tilt angle, and the concavity, principal curvatures and slope of the substrate surface. Moreover, adhesion force is increased by the superposition of the concave upward profile, and vice versa; while its variation in magnitude depends on the principal curvature. The adhesion force increases if the tip's contact point becomes further away from its vertex due to the slope of the curved sample. The slope has an additional effect due to the difference between the contact normal and pull-off directions. The adhesion force distribution is asymmetric for a tilted tip due to the asymmetric distribution of contact points on the tip. The modelled results of the adhesion forces estimated to occur while scanning along the curved surface are in reasonable accordance with the experimental results. The proposed model may allow better quantitative comparisons of adhesion forces measured experimentally and those estimated theoretically.