---
title: "Superlubric Flakes: How a Twist Cuts Atomic Friction Interactive Lab | Sandbox Physics"
description: "Why does a twisted flake glide while an aligned one sticks? Because its atoms stop pulling in step."
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language: "en"
page_type: "lab"
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  zh-CN: "https://sandboxphysics.com/zh/labs/twisted-flake-superlubricity/"
last_modified: "2026-10-31"
---

FR40 · Structural superlubricity

# Superlubric Flakes: How a Twist Cuts Atomic Friction

**Why does a twisted flake glide while an aligned one sticks?** Because its atoms stop pulling in step. On an aligned flake every atom sits in a hollow at once and the barriers add up. Twisted, the atoms sit everywhere at once and their pushes cancel except near the edge, so the flake no longer sticks. Friction drops a long way but not to zero, and vacancies or rough edges bring some of it back.

Twist a crystal flake on a matching crystal and watch its atoms stop pulling together. The barrier collapses, stick-slip stops, and only defects and edges bring friction back.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

The flake is a rigid crystal of hexagonal, triangular, disk-shaped or rough outline on a rigid triangular substrate potential, following the model of de Wijn (2012). Every flake atom feels the same three-cosine potential, the flake is pulled by a spring at its centre and loses energy through a damping term, and its twist is held fixed. All quantities are in reduced units: substrate spacing, single-atom corrugation, atom mass and the matching time. Without stick-slip the friction left is the model damping, which stands in for phonon and electronic losses that are not modelled; real flakes can also rotate back into registry, which this model leaves out.

Barrier against twist angle

Barrier against flake size at 10°

Drag force on the flake

Physics tutorial

## When atoms stop pulling together

**Background** A single tip feels the full corrugation of the surface under it. A flake of many atoms feels the sum of all their corrugations. If the flake fits the substrate, every atom sits in a hollow at the same time and the barriers add. If it is twisted, the atoms sit at all possible places at once and most of their pushes and pulls cancel.

**Why it matters** Experiments with graphite flakes on graphite found high friction with stick-slip only near the angles where the two lattices match, and friction below 50 pN at most other angles, as reviewed by Vanossi et al. (2013). This structural superlubricity is one of the few known routes to very low dry friction.

Start with the essentials

- **Focus question**: Why does a twisted flake glide while an aligned one sticks?
- **One-sentence intuition**: The flake energy is a sum of waves, one per atom, with phases set by where each atom sits. Aligned atoms share one phase and the waves add to N times the single-atom barrier. Twisted atoms spread their phases evenly across the flake, so the interior cancels and only an edge term is left. With the barrier gone the spring no longer stores energy, stick-slip stops and only the damping of the model is left.

### Core mathematical model

#### Flake energy as a structure factor

$$
U(\mathbf R)=-\frac{2V_0}{9}\sum_{l=1}^{3}\mathrm{Re}\!\left[S_l\,e^{i\mathbf G_l\cdot\mathbf R}\right],\qquad S_l=\sum_{j=1}^{N}e^{i\mathbf G_l\cdot\mathbf r_j}
$$

Summing the substrate potential over the atoms of a rigid flake gives this exact form, the one de Wijn (2012) uses. Aligned, $|S_l|=N$ and the corrugation is $NV_0$. Twisted, the phases of $S_l$ wind around the flake and $|S_l|$ stays of the order of the edge.

#### Width of the friction peak

$$
\tan\Delta\Phi\approx\frac{1}{D}
$$

Vanossi et al. (2013) estimate the angular width of the friction peak from the flake diameter $D$ in lattice spacings. For disk flakes the model puts the first zero of the corrugation at 6.01°, 3.01° and 1.51° for $D=10,\,20,\,40$, so the width halves when the diameter doubles.

#### How the barrier grows with area

$$
\Delta U\propto A^{\beta},\qquad \beta=1\ \text{aligned},\quad \beta=0\ \text{twisted regular},\quad \beta=\tfrac14\ \text{twisted rough}
$$

These are the exponents de Wijn (2012) derives for a twisted flake whose outline is regular or irregular, and for an aligned flake. Fitting the model at 10° gives $\beta=1.000$, $0.12\pm0.25$ and $0.21\pm0.03$. Random vacancies give $0.43\pm0.04$, close to the $\tfrac12$ of a random sum.

### Common difficulties

#### Superlubric means frictionless

**Typical misconception** A twisted flake slides with zero friction.

**Better mental model** Twisting removes the stick-slip channel only. In this model the friction left is the damping drag, which stands for sound and electronic losses; Vanossi et al. stress that real superlubric friction is reduced, not zero.

#### Bigger flakes always rub harder

**Typical misconception** Friction grows with contact area, so a larger flake must stick more.

**Better mental model** That holds for an aligned flake, whose barrier grows as N. A twisted flake with a regular outline keeps a barrier of edge size that does not grow on average; only defects and rough edges make it grow, and more slowly than the area.

### Run the experiment

1. 01

   #### Watch the sweep

   Leave Twist sweep running and watch the force chart while the twist passes a few degrees.

   **What to observe:** At 0° the 127-atom flake sticks and slips with friction about 245 times the viscous drag. By 5° the sawtooth is gone and the ratio is about 1. A weak sawtooth returns between about 6° and 8.5°, near 10 times the drag at 7°, and is gone again beyond 9°.

2. 02

   #### Predict, then change the lattice

   Guess whether a flake with a different lattice can stick at 0°, then choose Gold on graphite.

   **What to observe:** With a lattice ratio of 1.17 the atoms are out of step even without a twist, and friction stays at about 1.7 times the viscous drag.

3. 03

   #### Explain the defects

   Compare Twisted flake glides with Vacancies bring friction back and Rough edges bring friction back.

   **What to observe:** On the softer spring, the perfect 1027-atom flake slides at 0.97 times the viscous drag, while 10% vacancies raise it to about 3.0 times and a rough edge to about 3.1 times. The cancellation is broken and stick-slip returns.

Physical conclusion

A flake sticks when its atoms pull in step. Twisting it or changing its lattice puts them out of step, the barrier collapses to an edge term and stick-slip stops. Defects and rough edges partly restore the barrier, and the damping left behind means friction is reduced, not removed.

## Related experiments and articles

Nanofriction · Reading path

### From one sticking tip to a twisted flake that glides

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **How the friction of a crystal flake adds up from its atoms**](https://sandboxphysics.com/stories/nanofriction/from-one-tip-to-a-flake/)
2. [Article **Twisted flakes and structural superlubricity**](https://sandboxphysics.com/stories/nanofriction/twisted-flakes-and-structural-superlubricity/)

Motion & dynamics · Starter path

## From a falling ball to an orbit

Start by measuring gravity and splitting motion into components. Then add contact forces and collisions, and follow the same laws all the way to an orbit.

[Start here → **Free Fall & Measuring Gravity** Capture a few drops and fit the camera positions to estimate gravitational acceleration. Then add air damping and watch the fit drift from the truth. Observe · 14 min](https://sandboxphysics.com/labs/free-fall/)

1. [1 Free Fall & Measuring Gravity](https://sandboxphysics.com/labs/free-fall/)
2. [2 Projectile Flight Designer](https://sandboxphysics.com/labs/projectile-flight/)
3. [3 Inclined Plane & Friction](https://sandboxphysics.com/labs/inclined-plane/)
4. [4 One-Dimensional Collision Bench](https://sandboxphysics.com/labs/collision-bench/)
5. [5 Mass–Spring Oscillator](https://sandboxphysics.com/labs/mass-spring/)
6. [6 How Orbits Take Shape](https://sandboxphysics.com/labs/orbit/)

[View the full path →](https://sandboxphysics.com/topics/mechanics/#starter-path)