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.

Loss of parallelism of natural chemistry and how to compensate

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 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.

(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 – 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