Friction

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The essence: Higher throughput of smaller machinery is the main compensating factor
and overcompensating factor for rise in friction from higher bearing surface area of smaller machinery.
Plus there are some more (over)compensating factors.

Qualitatively

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.)

  • It is true that physics changes when the size-scale changes. But who says it changes for the worse?
  • It is true that surface area grows with shrinking structure sizes, But there are other effects that overcompensate growing surface area and these are very often overlooked.
  • 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 machine phase systems allow keeping and reuse of the change.
  • 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 very big 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, ...
  • 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.

Concretely (and qualitatively) the effects that overcompensate the growing area friction increasing effect are:

Rising productivity with scaling down machinery is an especially important factor. It allows for ...

  • reducing the speed of the machinery => quadratic drop in friction power losses (due to dynamic superlubricicating friction scaling that way)
  • reducing the number of machinery => linear drop in friction power losses
  • Infinitesimal bearings can be used to reduce friction at the intermediary scales (maybe to to extraordinary low levels)

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

Qnatitatively: 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 Δk{sub}a{\sub}/k{sub}a{\sub} = 0.4) or
  • P = 5.8*10⁻16 W / (m/s)^2 -- (for Δk{sub}a{\sub}/k{sub}a{\sub} = 0.003)

So how much waste heat would one get for a reasonable desktop nanofactory? The book Nanosystems does not even give an answer on that since energy recuperation inefficiencies in force applying mechanosynthesis and "covalent welding" block assembly likely dominate.

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

The issue

With shrinking size of machinery the surface area of this machinery rises. Doubling the surface area doubles the friction (a scaling law).

Extrapolating from speeds and friction levels of macroscale machinery leads to impractically high levels of waste heat generation.

This is one of the elephants in the room when introducing an audience to advanced APM.

Such an extrapolation is the first thing that any person knowledgeable in other micro- and nanotechnologies is likely do. Since this is not the only point where a first "quick" glance reveals a strongly discouraging result and experts usually are busy and have little time at hand to dig deeper, the situation sometimes leads these people to quickly deem all nanomachinery impossible, that looks superficially similar to macro scale cog-and-gear-machinery.

Especially using micro-machionery (tech term: MEMS micro-electro-mechanical systems) as scaling trend leads to hugely misleading results.

What makes it work despite the issue

There are several effect working against this explosion of friction which are repeatedly overlooked.

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

One needs to slow down anyway to prevent an explosion of productivity

Rising productivity allows to slow down motion speeds (e.g. to just few mm per second) while keeping throughput constant. Slowing down to halve the speed drops drops the fiction to a fourth (a quadratic scaling law – tech term: dynamic drag).

Main article: "Higher productivity of smaller machinery".

Dropping speeds further by smart arrangements

By dividing relative speeds up in several layers each taking a proportional part of the speed area goes up, yes, but the drop in speed has a bigger effect.

See main article: "Infinitesimal bearings"

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"

Related

External links

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