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

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.

The generalized continuous multiple step (GCMS) potential: model systems and benchmarks

“…Finally, we comment on systems where an interaction potential might consist of an empirically derived representation [145][146][147][148][149][150][151][152] which may be sparsely evaluated. Another possibility is that the system is characterized by multiple steps, such as those encountered in systems with inherent periodicity or entropic barriers [153][154][155][156][157][158].…”

Simultaneous quantification of Young’s modulus and dispersion forces with nanoscale spatial resolution

“…This is an important results because it demonstrates that the method is capable of distinguishing the contributions of local nanoscale features, something usually neglected by existing measurement techniques and models [76][77][78][79][80][81][82][83][84][85][86][87][88]. Previous dynamic and contact mode AFM studies have highlighted the fact that H values tend to be affected by roughness and nanoscale features [89,90]. This was achieved by implementing an AFM system within a transmission electron microscope (TEM), with the measurements performed in vacuum.…”

Reduced Radial Curves of Diatomic Molecules

“…25 The same approach can obviously be used for modeling any pair potential, including interaction potentials measured by atomic force spectroscopy; 26 note that potentials modeled this way significantly deviate from those produced by the usually used Lennard−Jones model. 27 The aim of this study is to adopt the RPC approach for molecular electric dipole moment (μ(r)), quadrupole moment (Θ(r)), and dipole polarizability (α zz (r)) functions. Like the potential energy function, μ(r), Θ(r), and α zz (r) are fundamental molecular characteristics (see, e.g., ref 28 and references therein) and have been studied both experimentally and theoretically in some detail (see, e.g., refs 29−36 and references therein).…”

“…Where potential energy functions of diatomic molecules are concerned, this procedure certainly appears to be a suitable tool when it is based on the RPC method of Jenč. ,, For instance, it has enabled the proper spectral assignment of highly excited vibrational states using the experimental s -wave scattering length and has helped to reveal the existence of the 12th vibrational state of the beryllium dimer and its two rotational states . The same approach can obviously be used for modeling any pair potential, including interaction potentials measured by atomic force spectroscopy; note that potentials modeled this way significantly deviate from those produced by the usually used Lennard–Jones model …”