How friction diminishes at the nanoscale
While the total surface area per volume of bearings in nanomachinery rises there are other factors that more than compensate for that
(wiki-TODO: Elaborate on that here. A lot is in the as of yet unpublished ReChain zim-wiki)
- 1 Factors reducing friction of gemstone based nanomachinery
- 2 TODO integrate chapters below
- 3 The issue
- 4 Related
Factors reducing friction of gemstone based nanomachinery
The main (over)compensating factors for rise in friction from higher bearing surface area of smaller machinery are:
- (1) Convergent assembly or equivalently ...
- (2) Higher throughput of smaller machinery and ...
- (X) Superlubricity
- (Y) other effects ... ?
Falling friction from "convergent assembly"
- In first approximation all convergent assembly layers have the same total bearing area as the top macroscale one
- There is no need for a large number of convergent assembly layers
And diverging from that first approximation:
A bottom layer stacked of chambers of the same size only further reduces friction
This trick gives a tuning parameter of: nanomachinery_operation_speed times bearing_area per chip_area.
(wiki-TODO: elaborate on that)
Falling friction from "higher throughput of smaller machinery"
To reach practical levels of throughput
there is not no need to fill up the whole of the macroscale assembly chamber with nanomachinery.
The "volumetric throughput density" (how much product per time can be processed per how much volume of nanomachinery) of gemstone based nanomachinery is very high.
Note: This is the same effect as in the former section but in different formulation.
Basically tracing down convergent assembly one finds high volumetric throughput density.
This one is a bit of a mystery.
Static friction or dynamic drag?
This is likely about static classical friction µ rather than dynamic drag.
Friction from dynamic drag (per unit of area) can actually be quite high when looking at higher speeds.
But is can become very low for low speeds. And low speeds are very affordable to choose,
because there is plenty of space for more nanomachinery. This just increases a nanoscale thickness layer to a microscale thickness layer at worst.
Low friction despite notches matching up with grooves
Even in cases where grooves and notches of shaft and sleeve match up (commensurate situation)
low friction can be present. It's just essential that the notches and grooves are stiff enough
- for the energy to be completely recuperated when going across a notch-facing-notch-barrier.
- for there to be no snapback
(Technical formulation: one needs a conservative energy potential.")
At the macroscale a strong waviness of potential over the turning angle
(like e.g. felt when turning a shaft of a stepper motor)
most definitely leads to higher dissipation.
Especially a light rotor does not turn long in face of strong waviness of potential.
But this dissipation mostly comes from a non stiff damping coupling of the sleve to the surrounding framework. Especially it this surrounding framework is a human Hand.
In Nanosystems dissipation from acoustic radiation has been analyzed and found to be not a dominant contributor for the targested operational speed range (~5mm/s).
Waviness of potential not necessarily meaning higher energy dissipation losses
is good news for molecular gears with tooth made up of single rows of atoms.
These are harder design to have get atom count incommensurability.
(Well not impossible with herringbone style gears probably (TODO: design one))
Other effects that could potentially reduce friction
There are other perhaps more deep reasons for friction to diminish at the nanoscale. It's about the issue that in systems small enough ...
- there are few degrees of freedom for energy to be dispersed into (thermalized/devaluated/dissipated) and
- there can be the quantum effect of a minimum activation energy that needs to be overcome before a degree of freedom becomes available. Likely only relevant for low temperature applications.
(This can be seem in the plots of heat capacity over temperature for polyatomic gases where steps represent the "quantum activation" of degrees of freedom).
TODO integrate chapters below
With shrinking size of machinery the surface area of this machinery (and total bearing area) rises.
Doubling the bearing surface area doubles the friction (a scaling law).
Plus: Extrapolating from speeds and friction levels of macroscale machinery
down to the nanoscale 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 nanotechnology experts to quickly deem all nanomachinery impossible, that looks superficially similar to macro scale cog-and-gear-machinery.
Especially looking at friction (and wear) in micro-machinery (technical term: MEMS micro-electro-mechanical systems) as a scaling trend is misleading.
What makes it work despite the issue
There are several effect working against this explosion of friction which are repeatedly overlooked.
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"
- Low speed efficiency limit (wiki-TODO: maybe move stuff over to here?) the interplanetary analogy ...
- There are a plethora of friction mechanisms but all those seem less fundamental than what is discussed here.
- Equipartitioning theorem (every degree of freedom gets an energy of kBT on average)