Quantitative determination of the interaction potential between two surfaces using frequency-modulated atomic force microscopy

Nicholas Chan; Carrie Lin; Tevis Jacobs; Robert W Carpick; Philip Egberts

doi:10.3762/bjnano.11.60

Quantitative determination of the interaction potential between two surfaces using frequency-modulated atomic force microscopy

Beilstein J Nanotechnol. 2020 May 6:11:729-739. doi: 10.3762/bjnano.11.60. eCollection 2020.

Authors

Nicholas Chan¹, Carrie Lin¹, Tevis Jacobs², Robert W Carpick³, Philip Egberts¹

Affiliations

¹ Department of Mechanical and Manufacturing Engineering, University of Calgary, 40 Research Place NW, Calgary, Alberta T2L 1Y6, Canada.
² Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA 15621, USA.
³ Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, 220 S. 33rd Street, Philadelphia, Pennsylvania 19104, USA.

Abstract

The interaction potential between two surfaces determines the adhesive and repulsive forces between them. It also determines interfacial properties, such as adhesion and friction, and is a key input into mechanics models and atomistic simulations of contacts. We have developed a novel methodology to experimentally determine interaction potential parameters, given a particular potential form, using frequency-modulated atomic force microscopy (AFM). Furthermore, this technique can be extended to the experimental verification of potential forms for any given material pair. Specifically, interaction forces are determined between an AFM tip apex and a nominally flat substrate using dynamic force spectroscopy measurements in an ultrahigh vacuum (UHV) environment. The tip geometry, which is initially unknown and potentially irregularly shaped, is determined using transmission electron microscopy (TEM) imaging. It is then used to generate theoretical interaction force-displacement relations, which are then compared to experimental results. The method is demonstrated here using a silicon AFM probe with its native oxide and a diamond sample. Assuming the 6-12 Lennard-Jones potential form, best-fit values for the work of adhesion (W _adh) and range of adhesion (z ₀) parameters were determined to be 80 ± 20 mJ/m² and 0.6 ± 0.2 nm, respectively. Furthermore, the shape of the experimentally extracted force curves was shown to deviate from that calculated using the 6-12 Lennard-Jones potential, having weaker attraction at larger tip-sample separation distances and weaker repulsion at smaller tip-sample separation distances. This methodology represents the first experimental technique in which material interaction potential parameters were verified over a range of tip-sample separation distances for a tip apex of arbitrary geometry.

Keywords: Lennard-Jones; adhesion; atomic force microscopy; diamond; frequency-modulated AFM; interaction potential; surfaces.

Grants and funding

The following sources of funding are acknowledged: P.E. would like to acknowledge funding from the Natural Sciences and Engineering Research Council (NSERC) of Canada through the Discovery Grant program, NSERC Postdoctoral fellowship, and funding from the University of Calgary Seed Grant program and University of Calgary Startup Funding. C.L. would like to acknowledge funding from the NSERC Undergraduate Student Research Award (USRA). N.C. would like to acknowledge support from the NSERC Canada Graduate Students PhD (CGS-D) program, as well as the Queen Elizabeth II (QE2) program. R.W.C. would like to acknowledge funding from grant AFOSR FA2386-18-1-4083.