Superlubricity

Graphic by Eric K. Drexler -- Citation: "Symmetric molecular bearings can exhibit low energy barriers that are insensitive to details of the potential energy function" <ref name="pdrag"> Drag mechanisms in symmetrical sleeve bearings: Drexler, K. E. (1992) Nanosystems: Molecular Machinery, Manufacturing, and Computation. Wiley/Interscience, pp.290–293.</ref>

A simulation made with the software "Nanoengineer-1"
Author Eric K. Drexler – An atomically precise slide bearing.

Coaxial nanotube bearing based nano-motors have been experimentally built and tested. While still very crude they already show very little friction. Much unlike the problems with stiction and wear in photolithographically produced MEMS systems. – Coaxial nanotubes are quite similar in characteristics to crystolecule bearing so the working nanotube bearings give experimental evidence for crystolecular elements working with low friction an wear-free.

Double logarithmic chart of several estimations for superlubric friction and its quadratic scaling. Note that at moderate speeds like 1m/s it is actually quite high but it quickly drops off going to lower (proposed) speeds around ~1mm/s. The black line (way higher up than all the others) is not superlubric friction but dynamic friction in fluids for comparison.

Up: Friction in gem-gum technology

Superlubricity (or superlubrication) is a state of extremely low friction that occurs when two atomically precise surfaces slide along each other in such a way that the "atomic bumps" do not mesh.
More precisely: When the lattices distances projected in the direction of movement are maximally incommensurate.

Ditching the trapdoors

🪤 No, superlubricity is not the general absence of friction and not even about vanishingly small friction
it is particularly about the very small level of static friction posibly even total absence in special cases.
And maybe about quickly falling friction when decreasing speed.

At speeds that would be considered modeate for macroscale bearings friction can actually be quite high.
Estimates for friction losses at 1m/s of speed fall in the range:
20W/m² … 1000W/m² – or equally – 0.2W/dm² … 10W/dm² (~palm of hand area)
Speeding up 10x from 1m/s (3.6km/h) to 10m/s (36km/h) would 100x these losses. But no worries.

By the same law dropping down to proposed speeds for productive nanosystems around 10mm/s … 1mm/s
these losses shrink by a factor of ten thousand to one million though.
Worried about excessive bearing area of nanomachinery?
See: Why larger bearing area of smaller machinery is not a problem

Key aspects of superlubricity

• Present in gem-gum-tec: Superlubricity is present in crystolecule bearings which are essential molecular machine elements in gemstone metamaterial technology.
• Eternally wear-free: Superlubricity features no "colliding mountain ranges" at the nanoscale that can mutually shear off their tips. Thus superlubricating bearings are fully wear-free. The dominating damage mechanism of superlubricating bearings is ionizing radiation or thermal destruction in extreme conditions (melting, evaporating, hot chemical dissolution, ..). There is damage over time but there is no wear from mechanical friction (and load) over time.

Examples exhibiting superlubricity

• two coplanar sheets of graphene rotated to one another to minimize meshing
• two appropriately chosen tightly fitting coaxial nanotubes (experimentally demonstrated)
  (wiki-TODO: add reference)
• diamondoid molecular bearings and other DMEs with sliding interfaces.
• an advanced metamaterial forming an infinitesimal bearing structure.

Low friction without superlubricity

There are a few notes about that on the page: "How friction diminishes at the nanoscale"

As long as the energy is efficiently recuperated when crossing repulsive angular locations
Even bearings with large waviness of potential can have low friction.
What absolutely must not happen is interfaces having such low stiffness that snapback is starting to occur.

What kind of friction are we even talking about here?

A good question.

Classical static Friction?

As soon as the waviness of the potential gets close and falls below
the thermal energy (equipartitioning theorem) there should be literally zero static friction.
There must be a point where a constant torque does not lead to unbounded acceleration.
(TODO: To investigate)

But superlubricity is supposed to not have a point where it (more or less suddenly)
falls to unmeasurably small levels like superconductivity.
(TODO: To investigate)

Friction from dynamic drag?

Friction losses from dynamic (speed dependent) drag can get quite high.
So drawing an analogy to superconduction here is far fetched.
See numbers on the page: Friction in gem-gum technology

Band-stiffness scattering drag (BSSD) can be reduced by tuning for superlubrication:
Interestingly there are two parameters. Not just the incommensurability.

• The velocity ratio of the alignment bands goes in quadratically
  <math> R = v_{bands} / v = |k_1| / |k_2 - k_1|</math> – Nanosystems (7.22)
• The relative amplitude of variations in stiffness of the interface at different angles goes in linearly
  <math> \Delta k_a / k_a</math> (wiki-TODO: add a sketch)

<math>P_{BSSdrag} \propto (\Delta k_a / k_a) R^2</math> – Nanosystems (10.23, 10.24)

Shear-reflection drag (SRD) is not influenced by these parameters.
It is the remnant friction that remains in a well designed bearing.

Oddly simulations of nanotube bearings (see math on page Friction in gem-gum technology)
are quite a bit above the point of dominance of shear-reflection drag.
And that despite this being a quite conservative (pessimistic) estimation for levels of drag.

(TODO: Resolve the many not unrelevant mysteries here. More reading and thinking needed.)

Superlubricity - vs - Superconductivity

The name "superlubricity" points to some weak analogies to superconductivity:

• similar: It is also a state of low energy dissipation during the motion of elemental particles
• dissimilar: It has no sharp onset/cutoff point and friction does not fall to unmeasurably low levels
• dissimilar: It is present at all (non destructive) temperatures including ~300K room temperature
• Superlubrication is reached by decrease of degree of intermeshment while superconductivity is reached by decrease of temperature.
• There is not a sharp cutoff in friction when decreasing the degree of intermeshment like the cutoff in superconductivity when decreasing temperature.

Thresholds?

smoothly sliding atoms – graphic by Erik K. Drexler

unsmoothly sliding atoms – graphic by Erik K. Drexler

When it comes to dynamic speed dependent friction the waviness of the energy potential is actually not that important.
As long as there is no snapback the energy needed to overcome the next angle of maximum energy can be recuperated.

There is no special threshold for superlubricity, but there are other special thresholds:

• The waviness of the energy over the turning angle is exactly equal to the thermal energy per degree of freedom
  (this is temperature dependent, but a constant for 300K room temperature)
• The interface is at the threshold to snapback
• The holding force of the remnant wavyness of the PES (potential energy surface) falls below the force of vdW suck-in

Activation of vdW suck-in

This is … – much less demanding than getting below characteristic thermal energy and enabling superlubric diffuson. – likely practiacally more relevant than getting below characteristic thermal energy

There are two edge cases:
– Large contact area but small incriease of contact area per slising distance:
There may be no vdW suck-in despite incommensurate interfaces.
– Small contact are but big increase in contact area per sliding distance:
There may be vdW suck-in despite commensurate interfaces.

To the latter case: In some application cases one may want the opposite
well conserved notching despite the presence of vdW suck-in forces.
This needs similar simulations and experiments just with commensurate surface contacts.

Thermal activation energy - vs - Angular energy waviness

If AP surfaces are designed or aligned to not mesh then the "perceived bumps" (the bumps that the surfaces perceive as a whole) become lower and their spatial frequency becomes higher (more bumps per length). If the surface pressure isn't extremely high the characteristic thermal energy k_BT can become a lot higher than the bumps energy barriers. Thus the (static) friction becomes so low that e.g. an unconstrained DMME bearing can be activated thermally and may start turning randomly in a Brownian fashion [to verify].

Choice of nanoscale passivation and snapback dissipation

Oxygen or sulfur with their two bonds in a plane parallel to the relative sliding direction are a good choice for surface termination of bearing interfaces since this configuration gives maximal stiffness in sliding direction.

If the two bonds of the atoms are instead in a plane normal to the sliding direction the lower stiffness may lead to higher energy dissipation (friction). Singly bonded hydrogen fluorine or chlorine passivations have even lower stiffness, see: E. Drexlers's blog: snap back dissipation. This can be deliberately used in dissipative elements (friction brakes). There's a critical point at which snapping back starts to occur [todo: simulation results needed].

Main power dissipation mechanisms

(TODO: Integrate infos from Nanosystems and the "evaluating friction ..." paper.)

Main article: Friction mechanisms

Design principles

Non-stressed non-strained crystolecules for linear bearings

There are a few options to get good incommensurability for superlubric iterfaces.

Crystal axis mismatching:
Intentional parallel alignment of diffenent crystal axis directions for the sliding-axis.
For cubic systems this gives basic simplemost pairings and respective incommensuralities of:
<100>+<110> 1/√2, <110>+<111> 1/√3, <111>+<100> √3/√2
Side-note: Sliding-rods for the <111> directions can not have right angles
in the cross sectional shape unless going to higher miller indices for the sliding-rod or sliding-rail faces.
I.e. not just {110} faces (which only alow for triangles and hexagons as crosssections) but also {210} faces.
Side-note: Sliding rods or rails in <110> directiin can inly be rectangular not square which can complicate design.

Lattice mismatch material pairing:
Using two diffeent materials with mismatchig lattices
like e.g. lonsdaleite and hexagonal moissanite
this allows one to pair the same crystal axes parallely
in sliding direction and to still gain incommesurability.
An issue here is that while V-groove self centering for the sliding-rail
works across different lattice spacings
the W-groove self centering method is not applicable
as the spacing of the two peaks or two troughs always mismatch between the materials.

Incommensuralization spacer-shims
Using spacers to do
– crystal axis mismatching and/or
– lattice mismatch material pairing.
One side should be locke in place
e.g. by inset holes or by W groove self centering
transversal to sliding direction.

Incomensurally spaced rail segments:
Transversal to sliding direction spaced out placement
of sliding rail segments.
e.g. by inset holes or W groove self centering
could be used but this may just shift the problem.

Nonbonded interface commensurality breaking:
Using non-bonded interface-connections to introcudce
overall noncomensurality over longer length ranges.
Nontrivial constraints: – The sliding-rail-segments lengths must be shorther than the slider-rod.
… otherwise the rod will go commensurate whenever fully on just one rail segment
– The sliding-rail-segments must notably stronger vdW bond to housing matrix base (and themselves) than to the slider-rod.
… otherwise the sliding-rail-segment may be pulled in to be locally commensurate with the slider-rod.

Stressed and strained rings

Incommensurality tends to fall out by itself for smaller rings.
Some symmetry considerations can be made for balanced behaviour.
(wiki-TODO: Add more discussion here. Particularly conent from an old article (only printout left).)

Superlubricating crystolecule machine elements

Atomically precise gemstone bearings

Interestingly Van der Waals forces allow for stable designs in which the axle in gemstone bearings is pulled outward in all directions instead of compressed inward.
This allows for lower friction at the cost of less load bearing capacity.

Stretching terminology a bit this could be counted as one form of Levitation.

• Q: How much can friction be lowered by this strategy?
• Q: Might resonant vibrations start to occur at high operation speeds?

Atomically precise gemstone gears

Gears with straight rows of teeth, while reducing atomic bumps due to being roughly shape complementary, do not smooth out atomic bumps beyond that.
Helical gears in contrast can smooth out and do smooth out atomic bumps.
Up to some point the longer the contact between gear teeth the better the smoothing.
This is a motivation to not make gears at the absolute minimal size possible but a bit above that.

As a side-note: Another reason for making gears a bit above the absolute minimal size is that stiffness of the intermeshing gear teeth interface can be matched to the stiffness of the axles (preventing flex wave reflections in higher frequency operations).

Rods in sleeves

Challenges:

• Using the same material for rod and sleeve (and the same crystallographic sliding direction) can lead to pretty much the same spacing and no good superlubrication.
• Getting a fit of just the right tightness with a compact sleeve around a thin reciprocative rod may be more difficult than getting just the right fit with a big stator sleeve around a big diameter rotor. Bigger loops can be finer adjusted in a relative sense.

Snapping into place

As mentioned before there is always a slight remaining ripple in the position dependant potential energy of the bearing (in its potential energy surface - PES). This energy corresponds to the (very low) temperature under which the bearing starts to snap into place. (If quantum zero point energy isn't too high?)

Quantum effects in (rotative) gemstone nanomachinery

Quantisation of angular momentum is usually not present except for very small free rotating elements at very low temperatures. Axels in nanomechanical systems are usually coupled to a bigger system making their moment of inertia rather big. Free rotations will often be suppressed which leaves only torsional vibrations as possible degree of freedom.

See:

• Estimation of nanomechanical quantisation.
• Nanomechanics is barely mechanical quantummechanics

Related

• VdW suck-in

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• More friction due to rising surface area.
• Less friction: How friction diminishes at the nanoscale.
• Gem-like molecular elements or for short on this wiki here: crystolecules
• Superlubrication goes perfectly together with infinitesimal bearings, reducing friction even further.
• Negative pressure bearings
• Levitation

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• Superelasticity ... another performance parameter that can be unusually elevated at the nanoscale

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• Atomic corrugation indexing … sort of the opposite of superlubric incommensurality,
  but it can also be low dissipation if operated both slowly and reversibly without snapbacks.

Concrete examples

In atomically precise bearings like:

• The whole raceway of atomically precise slide bearings
• The flanks of bigger atomically precise roller gearbearings

Some of the the moving examples of diamondoid molecular machine elements
feature tuned incommensurability and thus superlubricity.

Nanosystems section to decypher (Page 292)

10.4.6. Mechanisms of energy dissipation
c. Band-stiffness scattering

"The parameter <math>\Delta k_a / k_a</math> can be estimated from variations in the stiffness of nonbonded interactions between rows of equally spaced atoms as a function of their offset from alignment. Like many differential quantities, it is strongly dependent on the spacial frequencies involved. For first-row atoms (taking carbon as a model) <math>\Delta k_a / k_a \approx 0.3 \ to \ 0.4</math> (at a stifness-per-atom of 1 and 10 N/m, respectively) where d_a = 0.25nm, and ~0.001 to 0.003 where d_a = 0.125 nm. This vaue of d_a cannot be physicaly achieved in coplanar rings, but it correctly models a ring sandwitched between two other equidistant rings having d_a = 0.25 nm and a rotational offset of 0.125nm."

External links

(wiki-TODO: Find again and link the paper on nanostructured HOPG structures demonstrating presence and absence of superlubricity and VdW suck-in.)

Related pages on E. Drexlers homepage (internet archive):

• Phonon drag in sleeve bearings can be orders of magnitude smaller than viscous drag in liquids
• Symmetric molecular bearings can exhibit low energy barriers that are insensitive to details of the potential energy function
• Stiffly supported sliding atoms have a smooth interaction potential
• Softly supported sliding atoms can undergo abrupt transitions in energy -- Related page: Snapback

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• Paper: "Evaluating the Friction of Rotary Joints in Molecular Machines" (2017-01-27)
  arXiv:1701.08202 [cond-mat.soft]; ResearchGate; pubs.rsc.org; Google Scholar
  This uses simplified results from the Fluctuation-dissipation_theorem (Wikipedia-link)

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• Zyvex: A Proof About Molecular Bearings by Ralph C. Merkle -- 1993

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• Wikipedia: Superlubricity
• Wikipedia: Carbon nanotube nanomotor
• Experiments with nanotubes: Superlubricity on the macroscale

References

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