© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

3.5.6 Minimum Feature Size and Positioning Accuracy

Maximum displacement measurement accuracy in nanoscale devices is ~0.01 nm (Section 4.3.1), and RMS thermal displacement in diamondoid bonds is ~0.01 nm at 310 K (Section 3.5.4). Thermal displacements in 10-nm long diamondoid rods are ~0.01 nm at a 1-nm rod width, ~0.02 nm at 0.5-nm width, and ~0.10 nm at 0.3-nm width.¹⁰ However, it is possible to construct components to even narrower tolerances.

For instance, a single C-O bond inserted into a diamondoid rod in a collinear carbon chain extends rod length by 0.1402 nm, the C-O bond length. An adjacent rod into which an N-N bond is similarly inserted is extended by 0.1381 nm, the N-N bond length. By bonding these rods (aligned at one end) it is possible to build diamondoid structures having 0.002-nm features* (at the other end), which at 310 K will nonetheless suffer thermal displacements of ~0.01 nm or more. Similarly tiny displacements can be induced in binding cavity surfaces by inserting a foreign atom deep inside the bulk diamondoid structure, causing dislocation strains that decline in magnitude at greater distances from the compositional disturbance.**

* For even finer feature control, the ground state atomic radius R_a depends on nuclear mass (m_n), proton mass (m_p) and electron mass (m_e) through the reduced mass of the electron m_e = m_e m_n / (m_e + m_n) ~ m_e (1 - (1836 A_mass)^-1), or R_a ~ 1/m_e, where A_mass is nucleus mass number and m_p/m_e = 1836. Thus, a 25-nm rod consisting of 162 planes of C¹² atoms is ~0.1 picometer (pm) longer than a 162-plane rod of C¹³ atoms; a single ground-state deuterium atom is measured as ~0.4 pm smaller than a hydrogen atom. SQUIDs and X-ray interferometers have been used to measure displacements of 10^-7 nm, or ~1% of the nuclear diameter.⁴⁴⁵

** J. Soreff points out that such strain fields have components at various spatial frequencies, and that at high spatial frequencies there is much design freedom but the effects decay exponentially with a short characteristic length, hence design choices are not spread uniformly throughout the constraint space but rather are clustered. As a result, it may not be possible to achieve a 0.01-nm designed receptor topography simultaneously everywhere across an entire binding surface, nor may it be possible via surface binding alone to distinguish molecules which differ only deep in their interiors.

It is also possible to translate diamondoid components through a picometer step size,⁴³³ much smaller than the unavoidable RMS thermal displacements, using any of several methods; for example:

A. Levers -- Consider a 10-nm lever joined to a fixed bar by a pivot at one end, and driven axially by a ratchet interposed between lever and bar at the other end. Ratchet movements translate to smaller displacements at positions along the lever distant from the ratchet. Thus a follower rod attached to the lever 1 nm from the pivot and driven by a ratchet with 0.01-nm steps moves ~0.001 nm per ratchet step.

B. Screws -- Consider a 3-nm diameter cylindrical screw with a 1-nm pitch. Rotating the screw through a 0.01-nm circumferential displacement causes the screw to move laterally by ~0.001 nm, which may be transmitted elsewhere in the machine by an attached follower rod. Of course, nanoscale screws or gears are sensitive to the precise cancellation of the potentials and hence cannot be perfectly smooth and circular, producing some unavoidable "knobbiness" under load.

C. Gear Trains -- Consider a 32-nm diameter worm gear with 1-nm teeth. One rotation of the gear requires 100 rotations of the worm; hence a 0.1 nm displacement applied to the worm produces a 0.001 nm displacement in the gear. More efficient (and coaxial) compound planetary gear trains commonly employed in transmissions achieve displacement ratios up to 10,000:1, a hundred times better than the above example.

D. Hydraulics -- Consider a sealed, fluid-filled, tapered pipe. A piston 1000 nm² in area is mounted at one end; another piston 10 nm² in area lies at the other end. A displacement of 0.1 nm applied to the smaller piston produces a 0.001 nm displacement in the larger piston. (Here again the finite size of molecules may produce "knobby" performance as fluid particles slip from one stable configuration to the next.)

E. Compression -- Consider a rod upon which a compressive force of 100 nN/nm² (near the maximum diamondoid strength) has been imposed. Affixed to the rod are two crossbars spaced 4 nm apart. If the force on the rod is increased to 101 nN/nm², the gap between the crossbars compresses by ~0.001 nm.

Last updated on 19 February 2003