Atom placement frequency

For gemstone metamaterial on-chip factories to be able to put human scale objects together atom by atom in reasonable timespans they need to place atoms at mind boggling rates.

Compensating for a loss in parallelity

When going from "normal" (solution phase) chemistry to the unnatural chemistry
that piezochemical mechanosynthesis is than one has to deal with a loss of parallelism.
To elaborate:

In solution phase chemistry high throughputs are achieved via:

• massive spacial density of reaction locations (mixed dense liquides with many molecules in close contact)
• massive temporal density (frequency) of reaction attempts (molecules bouncing into each other)
  – (For gaining an intuition about how much bumping into each other down there actually is see: The speed of atoms)

A countering effect is:

• A low success rate per bump

In machine phase:

• spacial density is much more limited (due to the volume of the machinery needed to operate the tooltips) – Related: Fat finger problem
• temporal density is also more limited – See: Deliberate slowdown at the lowest assembly level

But making up for this big time is:

• An (extremely) high success rate per atom (or moiety) placement.

Fortunately when running the numbers in the end this works out nicely.

(wiki-TODO: Add a skech that is comparing spacial and temporal frequencies of natural and unnatural chemistry)

Example

Assuming f₀ = 1MHz atom placement frequency per mechanosynthesis core how many cores (N_core) does one need to reach the desired throughput of Q₀ = 1kg/h ?
N_core = Q₀ / (m_C * f₀) = ~1.4*10¹⁵ cores (about an 1.4 Petacore system). (m_C … mass of carbon atom.)
A core size of ~(32nm)³ = ~32000(nm³) seems to be a sensible guess for advanced APM systems.
All the cores together then take a volume of size ~45(mm³) = ~ 45microliters.
This can be spread out plenty to remove high levels of waste heat.
The effective atom placement frequency in this system is f₀*N_core = 1.4*10²¹ atoms per second (1.4ZHz – 1.4 Zettahertz – quite mind boggling) (>> 10⁹ Atoms/second).

Early mechanosynthetic systems will be several orders of magnitude lower in throughput though.

• They will have low temporal placement frequency
• they may be only two dimensional
• but they'll be already massively parallel

Note:
Despite the similarity in name mechanosynthesis core's are totally different (and much more complicated) in nature compared the "cores" we have in our computer processors (data processing arithmetic logic units ALUs). Mechanosynthesis core's are much more simple in nature and controlled in whole groups by contolling logic. Thus the enormous number of ~1.4*10¹⁵ cores is actually achievable. Not to say that bootstrapping to there will be easy.

Related

• Mechanosynthesis core
• Mechanosynthesis
• Convergent assembly
• Pages with math

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Nanosystems chapter 8 Mechanosynthesis
=> 8.3. Solution-phase synthesis and mechanosynthesis
=> 8.3.2.a. Basic constraints imposed by mechanosynthesis
=> 8.3.2.a. Loss of natural parallelism