Revision as of 21:08, 17 September 2021

Graphic by Eric K. Drexler -- Citation: "Symmetric molecular bearings can exhibit low energy barriers that are insensitive to details of the potential energy function" ^[1]

Erik K. Drexlers superlubricating "big bearing" - This is a photo of a 3D printed model. See: http://www.thingiverse.com/thing:631715

A simulation made with the software "Nanoengineer-1"
Author Eric K. Drexler

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 sticktion 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.

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.

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 fee: Superlubricity features no "collinding mountainranges" 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, evaporationg, 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 minimally mesh
• two appropriately chosen tightly fitting coaxial nanotubes (experimantally demonstrated)
  (wiki-TODO: add reference)
• diamondoid molecular bearings and other DMEs with sliding interfaces.
• an advanced metamaterial forming an infinitesimal bearing structure.

Dynamic drag in superlubricating gemstone bearings - vs - viscous drag in liquids

There is at least 2,000.0 to 100,000.0 times less friction in gemstone bearings compared to movement at the same speed in water.

So when it comes to peak performance parameters
soft nanotechnologies and artificial synthetic biology derived from molecular biology,
is fundamentally massively inferior to gemstone metamaterial technology

Yes, this much lower friction is still more than the zero friction that is as present in diffusion transport.
But this misses a crucial point.
For diffusion transport to happen it still needs to "expend" energy (still needs to devaluate free energy).
It is just that the free energy expense need to be payed up at the pitstops (when crossing cell- and vesticle-membranes) rather than during the transport motion. (see external links)

So:
Diffusion transport driven by concentration gradients does NOT make biological nanosystems fundamentally more efficient than conveyorbelt style transport in stiff dry artificial nanosystems in a vacuum.

Associated math

Source: ^[2]

Rotating sphere in Water: (Source: ^[3])

• [math] \omega = v/R [/math]
• Drag-torque: [math] M_{flow} = -8 \pi \eta R^3 \omega [/math]
• Dissipation: [math] P_{flow} = M_{flow} \omega = 8 \pi \eta R v^2 [/math]

With: [math] \eta \approx 10 \times 10^{-3} Pa \cdot s [/math] and [math] R = 2nm [/math]

• Dissipation: [math] P_{flow} \approx 5 \times 10^{-11} v^2 W = 5 \times 10^{-11} W/(m/s)^2[/math]

Gemstone sleeve nearing: (Source: ^[1])

• [math] P_{drag} = 5.8 \times 10^{-16} W/(m²(m/s)²) -- \Delta k_a / k_a = 0.003[/math]
• [math] P_{drag} = 2.7 \times 10^{-14} W/(m²(m/s)²) -- \Delta k_a / k_a = 0.4 [/math]

Ratio:

• [math] P_{flow} / P_{drag} \approx 2000 … 100000[/math]

Despite superlubricity dynamic drag can be significant

While static friction in superlubricity falls to nigh zero,
Dynamic (speed dependent) friction can be quite significant for higher speeds.

For higher speeds and bearings that do not resort to:

• some mean of levitation ( only possible for low loads ) or
• bearing stratification ( only possible for bigger nearings )

... the friction per area can actually get quite high for higher speeds.

• [math] P_{drag} = 23 W/(m²(m/s)²) -- \Delta k_a / k_a = 0.003[/math]
• [math] P_{drag} = 1080 W/(m²(m/s)²) -- \Delta k_a / k_a = 0.4 [/math]

Source: Nanosystems Equation (10.27) ^[1] -- But here calculated backwards to friction per area from friction per bearing.
Note: These are highly conservative estimates. Real values should be quite a bit lower.

Halving the linear speed (in units of m/s) quaters the friction losses.
And going down from 1m/s to 1mm/s the friction losses fall by a factor of a million (1,000,000).
More technically: Dynamic friction for crystolecules scales quadratically with speed.

Why this is not a problem

Worry #1: Looking at the table friction per area for small speeds like 1m/s is quite high.

Friction can be massively massively reduced by reducing the linear speed of motions (speed in units m/s NOT Hz!).
And we can totally afford to reduce the linear speed of motion in advanced productive nanosystems because all the machinery that is needed for practical levels of throughput fits in a super thin layer at the very bottom of the convergent assembly of a gem-gum factory chip.
(Reason: Higher throughput of smaller machinery - things scale favorably here)

We just need to make the bottom layer gem-gum factory chip a bit thicker
to compensate for the loss of speed and we are back at the original throughput.
(We want to do that anyway because many different specialized assembly lines need space.)

One totally can afford to slow down so much in advanced productive nanosystems like gem-gum factories
because there is plenty of space to compensate by just adding more nanomachinery.

Q: But what about the additional bearing area?
A: Yes, the total bearing area increases.
But while 10x the amount of nanomachinery gives 10x the bearing area
the friction per area falls by 100x due to 1/10th the speed.
So overall friction falls by 10x.

PS: Also note that the table above gives conservative (pessimistic) estimates on levels of friction.

Worry #2: Nanotech has a lot of surface area per volume. Won't that cause friction to become excessive?

Q: Shouldn't there be massive amounts of bearing surface area?
It's nanomachinery after all, and and for nanotechnology the surface to volume ratio gets extremely high?
A: Surface per volume is indeed high. BUT: We barely need any volume to achieve practical levels of throughput.
(Reason: Higher throughput of smaller machinery - things scale favorably here)

Looking at convergent assembly in a first naive approximation every layer has exactly the same bearing area.
So the bottom-most nanomachinery layer has exactly the same bearing area as the topmost macroscale assembly chamber.
In practice one would want to deviate form naive convergent assembly by making the bottom layer thicker,
which, as described above, only improves the situation with friction losses from dynamic drag.

As for the bearing area of the convergent assembly layers higher up:

• (1) There are only a few convergent assembly layers present (take 32nm chambers times 32 four times and you are at 32mm).
• (2) Bigger bearings can infinitesimal bearings. Again. Same trick. Area x10 & speed x1/10 => overall friction x1/10.

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?

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.

Thee 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

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 spacial 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 starts 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

Superlubricating crystolecule machine elements

Atomically precise gemstone bearings

Interestingly Van der Waals forces allow for stable designs in which the axle in gemstome 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 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

• 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

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

External links

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

• 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 simpified results from the Fluctuation-dissipation_theorem (Wikipedia-link)

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

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

References

1. ↑ ^{1.0 1.1 1.2} Drag mechanisms in symmetrical sleeve bearings: Drexler, K. E. (1992) Nanosystems: Molecular Machinery, Manufacturing, and Computation. Wiley/Interscience, pp.290–293.
2. ↑ Eric Drexlers former homepage (webarchive): Phonon drag in sleeve bearings can be orders of magnitude smaller than viscous drag in liquids
3. ↑ Viscous torque on a sphere: Landau, L, and Lifshitz, E (1987) Fluid Mechanics, 2nd ed. Pergamon Press p.91.