Latest revision as of 12:51, 13 October 2022

A scaling law.
When scaling things down the ratio between surface area and volume changes.
Specifically halving the size of an object doubles its surface to volume ratio.
This can be easily seen by:

• first cutting a cube into eight sub-cubes and
• then calculating the ratio between the surface to volume ratios before and after the cutting.

(wiki-TODO: add illustrative image)

As concern in regards to:
"macroscale style machinery at the nanoscale"

The potential consequences of rising surface area are one of the major concerns when it comes to
the assessment of the feasibility of macroscale style machinery at the nanoscale.

Potential issues include:

• first and foremost: rising friction power losses
• second: rising corrosion rates
• third: dirt and lubricants clogging machinery

Up: Macroscale style machinery at the nanoscale

Concern: Friction-power losses

There are no less than three factors that work against the growing surface area effect when it comes to increasing friction power losses.

• first and most importantly: the rising throughput per volume scaling law
• second: the superlubricity effect
• and third: infinitesimal bearings (an "invention" of this wikis author)

It should be possible to keep power losses low enough for a practical functioning nanofactory (with large safety margins). Even systems more efficient than biological diffusion based systems may be possible. For details why see here: (wiki-TODO: add link).

Counter-factor: Not the slightest need to fill up the whole volume with nanomachinery

Convergent assembly organized in assembly layers in a first conceptual approximation
features the exact same bearing area at every layer!
So even the lowermost nanomachinery layer has a total bearing area that is
just the same size as the bearing area of the topmost macroscale assembly chamber(s).

Even adding up over all of the convergent assembly layers gives not much more bearing area because
with the layers shrinking in thickness following a geometric series
the z axis goes into the area under the logarithm to the base of the branching factor.
And practical branching factors are big. 32 possibly.

So effectively summing up over all the layers the total bearing area grows
by a mediocre factor less than one decimal order of magnitude (maybe 4 to 6).

That on it's own pretty much solves the problem but there is more ...

Counter-factor: throughput per volume scaling law

(Main article: "Higher productivity of smaller machinery")

This law is less much less known than the scaling law for surface area per volume, but it plays a major role in compensating the rising friction effect of it.

• there is rising throughput-per-volume @ constant operation speeds
• or equivalently constant throughput-per-volume @ falling operation speeds
• this causes falling friction power losses -- quadratically falling :) since it is dynamic friction

Counter-factor: superlubicity

This is not exactly a scaling law but an effect that is only available at the nanoscale in atomically precise systems in dry sleeve bearings with non meshing atomic bumps. The effect is experimentally proven. For more details see the main article: Superlubrication.

Friction power losses can be lowered from three to five orders of magnitude compared to motion in a liquid.

Counter-factor: infinitesimal bearing

These machine elements distribute speed differences equally over multiple coplanar surfaces. Due to friction power falling quadratically with speed this kind of allows one to "cheat" scaling laws a bit.

Effect on transport

See main article: How small scale friction shapes advanced transport

Concern: Surface oxidation

Conter-factor: Non-oxidizing materials

This is one of the reasons why the choice for building materials falls mostly towards already oxidized materials -- flawless ceramics (aka gemstones) instead of metals.

Note: This is very much unlike macroscale machinery where unoxidized metals are usually the material of choice.

Conter-factor: Perfect sealings

Gas sealings are possible that are FAPP perfectly tight.

The interior space of gem-gum manufacturing devices (and their products) is exceptionally well sealable against outside gasses -- (wiki-TODO: add reference). So inside even oxidation sensitive materials can be used. (given they are not thermally sensitive that is they don't show surface diffusion).

Counter-factor: Compact products

Almost all of the machinery is not exposed the atmosphere.

In case of bulk products (most products) by far most nanomachinery surface is not located on the outside products surface, but in tightly sealed inside chambers. For the minute outside macro-product surfaces especially materials that are highly stable against oxidative (or other) chemical attack can be chosen.

Concern: Nanomachinery getting clogged

Lubricants (or solvents including water) may seem like gravel at the atomic scale. Small molecules are:

• very slippery (since there are very vew available DOFs for energy being dissipated into heat) and
• very strongly jostled by thermal motion (much faster than the machine motions)

thus they are unlikely to act like wrenches in gears(**). Nonetheless lubricants won't be used in nanofactories because with superlubrication one can achieve much lower friction levels (as already noted above in a previous section).

• Counter-factor: no lubricants present
• Counter-factor: no dirt present at inside machinery (FAPP perfectly sealed)

Dirt is somewhat of an issue at the outside of products and in the context of recycling where things may need to be pulled back in again.

(**) Off topic side note: Trapping solvent molecules on purpose should be possible despite the large speed differences (e.g. by tightly sealing big chambers).

Related

For quantitative calculations please consult Nanosystems (or its freely available predecessor paper).

Related pages:

• Friction
• Superlubricity
• Infinitesimal bearing
• Increasing bearing area to decrease friction