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

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