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Convergent assembly can quickly build large products from nanoscale parts

The above illustration (available for use) shows one way in which mechanisms can be organized to quickly build large products from nanoscale parts, using an approach suggested by Ralph Merkle in which small parts converge to form larger parts in a simple, systematic pattern. It is perhaps best explained by starting at the end and working backwards.

In the final stage (on the right), a pair of arms operating in a vacuum environment assembles 8 half-size blocks to form a full-size product object. The blocks must be designed to fit together and adhere. The resulting junctions can be extremely strong, with seam lines of molecular scale (Nanosystems, pp. 412–414). A wide range of structures can be formed from such blocks, including machines containing parts that are freed for motion after assembly is complete.

The 8 half-size blocks are assembled by 4 half-size arm-pairs in the preceding stage. Moving at the same speed as the full-size arms (in m/s), but traveling half the distance, these arms complete a motion cycle in half the time — this conforms to basic scaling laws. Thus, it takes as much time for the 4 half-size pairs to do their work (assembling 64 quarter-size blocks to form 8 half-size blocks) as it takes the full-size pair to do their work (assembling 8 half-size blocks to form one full-size block). As shown above, each stage occupies half the volume of its successor, yet it processes material at the same rate.

This pattern can be extended down to arms and blocks of submicron size. Below that scale (and even above it), simpler assembly mechanisms have advantages. Fixed-track conveyors are simpler, more efficient, and can be smaller than programmable arms. At the smallest scales, mill-style machines can be used to prepare molecular building blocks in the nanometer size range.

Size-doubling assembly operations make meter-scale products from nanoscale blocks in only 30 stages. How long will this take? Assume (in round numbers) that each motion-cycle of a full-size arm takes about 4 seconds, so that the arm-pair completes its 8 assembly operations in 16 seconds. Since each stage takes the same amount of time, the total time required for assembly cannot be more than 480 seconds (8 minutes). In fact, however, the stages overlap. The final stage takes 16 seconds to produce a full-size block. It begins when the preceding stage has produced its first half-size block, which takes 8 seconds, and so on. The total time from start to finish is thus very nearly 16⋅(1 + 1/2 + 1/4 + ...) = 32 seconds.

Concerns that molecular manufacturing will be impractically slow seem misplaced.

Exercise: Describe how to modify the simple scheme shown here to achieve the most of the energy-efficiency benefits of slower motion while only slightly increasing the product delivery time and the total volume of the system.

The advanced approach (with full, updated text):

Merkle, R.C., “Convergent assembly” Nanotechnology 8:18-22 (1997).

The primitive version:

Drexler, K. E. (1992) Nanosystems: Molecular Machinery, Manufacturing, and Computation. Wiley/Interscience, pp.416–418.