Friction in gem-gum technology

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(wiki-TODO: This page needs major cleanup - several parts need to be merged and completed and factored out)

Macroscale style machinery at the nanoscale has in the past received some seriously bad reputation because it comes with a bunch of mental trapdoors that led a a number of very smart reputational and vocal people to bad conclusions. One of these bad conclusions is that macroscale style machinery at the nanoscale would lead to exorbitant amounts of friction. A very wrong conclusion, as I will try to show below. (There are other misled criticisms to the idea beside the false conclusion of exorbitant friction. For a discussion of those you may want to check out the main page about macroscale style machinery at the nanoscale.)

Qualitatively

Dodge the trapdoors

  • Yes, It is true that physics changes when the size-scale changes.
    But who says it changes for the worse when it comes to macroscale style machinery at the nanoscale?
  • Yes, It is true that surface area grows with shrinking structure sizes, and that this contributes to friction.
    But there are other effects that overcompensate growing surface area and these are very often overlooked.
  • Yes, It is true that unlike diffusion transport there is friction all the time along the whole way.
    But it's often overlooked that diffusion must devaluate chunks of energy at its "pit-stops" to prevent transport from running backwards and that the "change money" energy that gets left over at these "pit-stops" cannot be kept and used reused.
    Whereas in machine phase systems keeping and reuseing the energetic change money may be possible.
  • Yes, It is true that there is no natural example of macro style machinery at the nanoscale (similar to the one proposed).
    But concluding from that that it's not possible or a worse solution is a fallacy. There are plenty of human invented things that exceed capabilities of nature by orders of magnitude. To give just a few examples: Bicycles, combustion engines (spaceships), copper wires (superconductors), wheels and streets, ...
  • Yes, It is true that MEMS (microelectromechanical systems) have high friction (and very bad wear).
    But in case of MEMS this is due to MEMS not having atomically precise suberbublicating bearings but instead have a really bad signal to noise ratio in their geometry due to them being manufactured top-down.

Overcompensating increased friction from increased bearing area

See main page: How friction diminishes at the nanoscale

The two core physical facts that provide the lion-share of lowering friction

  • higher throughput of smaller machinery
    Halving the size of the robotics has doubles the throughput per volume when robotic keeping speeds (NOT frequencies) constant.
    This means that in a naive first approximation the total bearing area of nanomchinery in a gem-gum factory is no bigger than the bearing area of macromachinery. It's desirable to deviate quite a bit from that first approximation, but as it turns out that only drops friction even further despite increasing bearing area.
  • power losses from friction scale quadratic with speed
    that is: 1/2 the speed of the machinery => 1/4th friction power losses

The two main tricks that apply and combine these physical facts to great avail

The second trick: Infinitesimal bearings: 2x the number of layers => 1/2x the friction. This is because the drop in friction from reduced speed (x1/4) overcompensates the rise in friction from increased bearing area (x2).
  • In both cases there is more then sufficient space avaiblable to do so.
  • In both cases speed falls linearly with the number of bearing layers.
    This gives simultaneously a linear increase (more bearing area) and a quadratic fall (less bearing speed) of friction losses.
    That is: overall a linear fall of friction losses.

Smaller contributions

  • Bearing can be tuned for good superlubricity
  • minimization of travel-distance needed per chemical synthesis operation
    dissipation falls linearly with the path traveled

Minimization of travel-distance leads towards the nanofactory design and away from the molecular assembler design.
(wiki-TODO: elaborate on that)

Qnatitatively (Math and Numbers)

Highly conservative form Nanosystems

Assumed:

  • A crystolecule bearing with 2nm radius and 2nm length
  • Bearing stiffness k = 1000N/m
  • Bearing bumpiness incommensurability: R = abs(m/(m-n)) = 10
  • Bearing operating temperature: Roomtemperature 300K

The dominant power loss contributions (Nanosystems 10.4.6.f.) give:

  • P = 2.7*10⁻14 W / (m/s)^2 -- (for Δka/ka = 0.4) or
  • P = 5.8*10⁻16 W / (m/s)^2 -- (for Δka/ka = 0.003)

So how much waste heat would one get for a reasonable desktop gemstone metamaterial on-chip factory?
It is not calculated in Nanosystems since energy recuperation inefficiencies

  • in force applying mechanosynthesis and
  • "covalent welding" block assembly

likely dominates.

But let's confirm that:
The proposed nanofactory convergent assembly system architecture (Nanosystems Table 14.1.) lists (as reasonable) a few times 10^17 units at the lowest assembly levels. Nanosystems provides no info about how many bearings per unit to assume. But Let's assume 100 bearings per unit. This kinda seems like a reasonable (that is pessimistic and on the safe side) assumption. (applied Exploratory engineering) This gives:

  • P = TODO
  • P = TODO

Note that this is (on purpose) a rather pessimistic ("conservative") estimation.

Also the assumed 1019 bearings give a total internal bearing sliding surface area of about:
S = 200m^2 -- Which intuitively feels like quite a lot but not overly excessive.


Side-notes regarding the Numbers given above

In Nanosystems 10.4.6. some examples are calculated for 1m/s sliding speed (it gives about 80MHz for the r=2nm l=2nm bearing). It's worth to note that a sliding speed of 1m/s is already quite fast. The actually proposed speeds are more on the order of about 1mm/s (1000 times slower). This makes power losses no less than one million times lower (since the two dominant drag mechanisms scales quadratically with speed).

According to Nanosystems 10.4.6.f. the two dominating effects of for friction in crystolecule bearings (at speeds of interest ) are:

  • band-stiffness scallering and
  • shear-reflection drag

Other drag mechanisms (acoustic radiation, band-flutter scattering, thermoelastic damping) all give negligible contributions (at least for the speeds of interest).

Numbers from papers -- less safe (since more optimistic)

For much more optimistic but less absolutely certainly on the safe side numbers there is work on coaxial carbon nanotubes: Also in contrast to crystolecule bearings nanotube bearings are already somewhat accessible to experiments.

The following is from the paper:
"Evaluating the Friction of Rotary Joints in Molecular Machines"

Assumed:

  • A nanotube bearing with 0.6nm radius and 5nm length
  • Bearing operating temperature: Roomtemperature 300K
  • Simulation was done at the rather high speed of 30m/s ~ 8GHz
  • P = 2.9(+-1.5)*10^-33 W/(rad/s)^2

Or converted into the same units as used in Nanosystems :

  • P = 7.25*10^-12 W/(m/s)^2

For the above assumed 10^19 bearings this gives:

  • P = TODO

TODO update chapters below

Flawless surfaces drop friction significantly

In contrast to etched micro-systems where the relative manufacturing error gets bigger with shrinking size. Atomically precise machinery has no error allow superlubrication which drops friction at least three orders of magnitude

Evolved molecular biology is not a proof that diffusion transport is the ideal solution with minimal losses

With those aforementioned effects cog-and-gear nanomachinery could potential feature smaller losses than diffusion driven natural systems (more on that comparison further down). To quantify that more in depth investigations are needed.

The issue

Nature is often (probably mostly out of psychological reasons) seen as unsurpassable. But actually it is completely unknowable whether nature as a whole will be "surpassed" by artificial technology in the far future (get side-tracked). Regardless of that, specific aspects of nature definitively can (and have been) surpassed by artificial technologies (there are countless examples).

Evolution ended up with diffusion transport and not cog-and-gear-machinery. Taken the former in to consideration that does by no means imply that this is the best or only solution. Actually evolution is facing severe limitations (lock-in-effect, incrementalism, ...).

(This is only one of the many cases where bio-analogies can have a problematic effect on perception.)

Why cog-and-gear transport may be more efficient

While diffusion transport features no friction during the transport process itself diffusion transport is not at all lossless. At intermediate passing stations some energy always needs to be converted to heat (tech term: dissipated). Otherwise the chemical reactions would not have a preferred direction to go and all the molecular "machinery" would cease to do anything.

Of course cog-and gear nanomachinery has exactly the same requirement. The big difference is that in biological systems energy often comes in discrete disconnected chunks. If ther's more than needed the excess is dissipated without being used for some desired effect. In a crude analogy it's like being unable to accept the change money.

In cog-and-gear nanomachinery everything is linked together in one big machine phase There energy can be drawn in a continuous rather than discrete fashion. The dissipation necessary for forward moving operation (arrow of time) can be balanced and minimized further down to the absolutely unconditionally required minimum. See main article: "Low speed efficiency limit"

Proposed machine speeds are WAY below speeds of thermal motion

In gemstone based nanomachinery one usually wants the operation frequencies to be well below the thermal motion frequencies. Otherwise the mechanical motions couple too strongly into thermal motions and things will get very hot very quickly. The frequencies of thermal motions can be seen in oscillation infrared spectra. Typical covalent bonds are located in the wavelength range of 3µm-30µm. This corresponds to 10THz-0.1PHz.

Related: Stroboscopic illusion in animations of diamondoid molecular machine elements

Typical operation frequencies

This is strongly depending on the method of bearing (superlubrication / single sp3 bonds as bearings / some for m of levitation / ... ) and efficiency of operations.

  • For mechanosynthetic mills in a nanofactory where larger forces are present and potentially slightly inefficient mechanosynthesis is performed the low MHz range is a good target.
  • For low friction bearings (like in nanomechanical computing) one can go up into the high MHz to low GHz range. This still leaves a gap of three orders of magnitude to the oszillative thermal motion DOFs.

Less soft nanomachinery => less drag

Unlike compliant bio-molecules in water stiff structures like carbon nanotubes (or bearings out of gemstone) in dry vacuum do not provide low energy low frequency rotative degrees of freedom (DOFs) to couple into. Those DOFs could (if they where present like in water) go down all the way to the microwave range: ~ 3cm & 10GHz. So overlap of mechanical motion with rotative thermal motion isn't so much of a problem even at higher operation frequencies.

Note that existing simulations of crystolecules can show a a stroboscopic effect. That can lead one to believe machine motion and thermal motion lie very close together and that consequently friction would be horrendous. This is not the case. It's just an artifact of the simulation.

Related

Nanosystems – Chapter 7 – Energy Dissipation – (page 161 to 190)

External links

  • (TODO: Add ref's to relevant chapters in "Nanosystems")
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