Contact Mechanics · Nanotribology
Atomic-scale friction: stick-slip of an AFM tip on atoms
Drag a sharp tip on a spring over a row of atoms and watch it stick in the dips, then slip.
Why does an AFM tip stick and slip on atoms?
The Prandtl-Tomlinson model: a tip on a spring pulled over a row of atoms.
Try it: press Smooth: η drops to 0.63, the sawtooth becomes a smooth wave and the mean friction drops to 0.
Why does friction rise with speed and fall with temperature?
Heat shakes the tip, so it can hop over the last bit of barrier before the valley vanishes.
Try it: raise the speed from 1 nm/s to 100 µm/s: friction climbs from 0.14 to 0.50 nN.
Why does a rotated graphite flake slide with almost no friction?
Turn a graphite flake on graphite and its atoms stop fitting the dips together.
Try it: press 0°, then drag the angle to 8°: the shades mix and friction falls from 100% to 4.5%.
What to take away
η sets the regime
In the Tomlinson model, η above 1 gives stick-slip and energy loss; below 1, smooth sliding. Lower load lowers η.
Heat helps the slip
In this model, heat lets the tip hop early, so friction rises with the log of speed and falls with temperature.
Mismatch cancels forces
On a rotated flake, the pushes and pulls on its atoms mostly cancel.
More detail: the equations and the limits of these models
The Prandtl-Tomlinson model
The tip at position x feels E(x) = −(U0/2) cos(2πx/a) + (k/2)(X − x)², where X is the support position and U0 is the full height of the energy ripple, from valley to crest. The lateral force is F = k(X − x). The tip has only one valley to sit in when k is larger than the steepest curvature of the ripple, 2π²U0/a². That gives η = 2π²U0/(k a²): above 1, valleys vanish one after another and the tip jumps. Some papers write the ripple as U cos(2πx/a); then η = 4π²U/(k a²), the same thing. k is the effective stiffness: cantilever, tip and contact in series.
Picture 1 is the slow (quasi-static) limit at zero temperature: the tip always rolls down to the nearest valley. The mean friction is the average of F over many lattice spacings; times a it equals the energy lost per atom passed. Socoliuc et al. (2004) saw the change from stick-slip to smooth sliding on NaCl by lowering the load, which lowers U0.
Thermal activation
Picture 2 uses the parameters of Sang et al. (2001): a = 0.4 nm, k = 0.86 N/m, U0 = 0.54 eV (they write −U cos(2πx/a) with U = 0.27 eV, half the full ripple), and an attempt rate of 1.1 × 106 per second, the frequency scale they quote. Holding the attempt rate constant is a simplification of their Kramers-type rate. At each support position the page computes the exact barrier ΔE between the valley and the next crest. The chance per unit time of a hop is f0 exp(−ΔE/kT). The page adds up the chance of still sticking and takes the mean force at the slip. Near the no-heat limit the barrier shrinks as (Fc − F)3/2, so F ≈ Fc − (const · kT ln(vc/v))2/3 (Sang et al.). Over a few decades this looks like the logarithmic rise Gnecco et al. (2000) measured on NaCl. Hops back to the old valley are ignored. The model leaves out contact ageing and changes of the contact with temperature, which can make real friction go up with temperature in some tests.
Structural superlubricity
Picture 3 treats the flake as rigid. Each flake atom feels V(r) = −V0 Σ cos(gj·r), the first Fourier terms of the graphite surface (a = 0.246 nm). The flake is pushed along x, and the page plots the largest force against the sliding, relative to 0°. When aligned, all atoms pull together. When rotated, the forces mostly cancel, and what is left comes from the edge. Bigger flakes give narrower peaks, roughly as a / (flake width) in radians. Dienwiebel et al. (2004) measured peaks of 306 ± 40 pN at 0° and 203 ± 20 pN at 61°, and friction close to their 15 pN force resolution in between; their model flake had 96 atoms, as the default here. Real flakes and surfaces bend a little, so the measured drop is smaller than the rigid model gives.
On this site: Why friction is not a material constant · Asperities and the real area of contact · Dislocations and Burgers vectors · Flash temperature · Lubrication regimes and the Stribeck curve
Questions people ask
What is atomic stick-slip?
An AFM tip dragged over a crystal stays in one atomic dip while its spring loads up. Then it jumps to the next dip. The lateral force signal looks like a sawtooth with the period of the lattice.
What is the Prandtl-Tomlinson model?
A model of a single point (the tip) pulled by a spring over a periodic energy ripple. Prandtl (1928) and Tomlinson (1929) used it to explain why friction loses energy even though atoms are elastic. It is still the standard starting point for AFM friction.
What is superlubricity?
Sliding with friction far below normal values, often below 0.01 in friction coefficient. Structural superlubricity comes from two crystal surfaces that do not fit, so the atom forces cancel. The word does not mean zero friction.
Why does nanoscale friction grow with the log of speed?
The tip can hop early with help from heat. At slow speed it waits longer, so it gets more chances to hop at a lower force. The waiting time scales with 1/v, and the barrier it can cross grows with the log of that time.
What does the Tomlinson parameter η mean?
It compares how steep the atomic ripple is with how stiff the spring is. Above 1 the tip has more than one valley to sit in, so it must jump. Below 1 it slides smoothly and, in the slow limit, loses no energy.
Is superlubricity why graphite is a good lubricant?
It is part of the story. Rotated graphite layers slide with very low friction in vacuum, as Dienwiebel et al. showed. In everyday use, water and other molecules between layers also matter, and a flake can rotate back into register and lock.
References
Show the 8 references
- L. Prandtl, Ein Gedankenmodell zur kinetischen Theorie der festen Körper, Zeitschrift für Angewandte Mathematik und Mechanik 8, 85 to 106 (1928). doi:10.1002/zamm.19280080202
- G. A. Tomlinson, A molecular theory of friction, Philosophical Magazine 7, 905 to 939 (1929). doi:10.1080/14786440608564819
- A. Socoliuc, R. Bennewitz, E. Gnecco and E. Meyer, Transition from stick-slip to continuous sliding in atomic friction: entering a new regime of ultralow friction, Physical Review Letters 92, 134301 (2004). doi:10.1103/PhysRevLett.92.134301
- E. Gnecco, R. Bennewitz, T. Gyalog, Ch. Loppacher, M. Bammerlin, E. Meyer and H.-J. Güntherodt, Velocity dependence of atomic friction, Physical Review Letters 84, 1172 (2000). doi:10.1103/PhysRevLett.84.1172
- Y. Sang, M. Dubé and M. Grant, Thermal effects on atomic friction, Physical Review Letters 87, 174301 (2001). doi:10.1103/PhysRevLett.87.174301
- M. Dienwiebel, G. S. Verhoeven, N. Pradeep, J. W. M. Frenken, J. A. Heimberg and H. W. Zandbergen, Superlubricity of graphite, Physical Review Letters 92, 126101 (2004). doi:10.1103/PhysRevLett.92.126101
- G. S. Verhoeven, M. Dienwiebel and J. W. M. Frenken, Model calculations of superlubricity of graphite, Physical Review B 70, 165418 (2004). doi:10.1103/PhysRevB.70.165418
- I. Szlufarska, M. Chandross and R. W. Carpick, Recent advances in single-asperity nanotribology, Journal of Physics D: Applied Physics 41, 123001 (2008). doi:10.1088/0022-3727/41/12/123001
BibTeX
@misc{tripathy2026atomicfriction,
author = {Tripathy, Manisha},
title = {Atomic-Scale Friction Lab},
year = {2026},
howpublished = {\url{https://untetheredatom.com/tribology/atomic-scale-friction}},
note = {Interactive web tool}
}