The Jump-to-Contact Distance in Atomic Force Microscopy Measurement

Abstract

The jump-to-contact phenomenon of atomic force microscopy measurement is investigated. The force-approach relation for the adhesive contact based on the Lennard-Jones potential with the Derjaguin approximation is analyzed. For a small Tabor parameter, the force-approach relation is similar to that with the van der Waals force between two rigid spheres. For a large Tabor parameter, the force-approach relation is similar to that with the van der Waals force between two deformable spheres. Empirical formulas for the approaching part of the force-approach curve are proposed. The jump-to-contact distance can be obtained by using the semi-empirical formulas. The jump-to-contact distance for a fixed grips device and for large Tabor parameter is also obtained.

Keywords:

• AFM
• Contact mechanics
• Jump-to-contact
• Numerical simulation

ACKNOWLEDGMENTS

This research was supported by the National Science Council, Taiwan. The author also thanks the National Center for High-Performance Computing, Taiwan, for providing the computer facility.

Notes

¹Tabor [18] proposed this parameter which can explain the discrepancies between the JKR [9] and the Bradley [16] models. Muller et al. [19] subsequently performed a numerical simulation and confirmed that Tabor's parameter does govern the transition.

² H and A have the same “unit.” and 's unit is H ^1/2. The unit for Eq. (9) is . Thus, by setting , the Tabor parameter, μ, can be omitted.