Nanomedicine, Volume I: Basic Capabilities
© 1999 Robert A. Freitas Jr. All Rights Reserved.
Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999
10.1.2.3 Acoustic Transmission Line Oscillators
Drexler10 describes a diamondoid acoustic transmission line in which a ~2 nN force pulse is initiated at one end, travels to the far end at vsound ~ 17,300 m/sec, then is received by a mechanical displacement probe, possibly with significant energy recovery. Such lines may also be used to generate precisely delayed acoustic signal sets suitable for clocking applications.
Consider a "starter" pulse applied to a short feeder line that symmetrically bifurcates into a set of nline = 10 lines each of length ln = (1730 n) nm (n = 1, 2, ..., nline), requiring a total length Lline = (1730) nline (nline + 1) / 2 = 95,150 nm of transmission line to obtain a set of lines having all nline time delays. The bifurcated pulses arrive at the end of each line in 0.1 nanosec (n = 1), 0.2 nanosec (n = 2), ..., 1.0 nanosec (n = 10); any of these pulses may be drawn off and used for diverse clocking purposes, or may be fed back into the initiation mechanism and used either to trigger the next starter pulse or to achieve more robust error correction. If acoustic lines have a cross-sectional area of ~30 nm2, then the total volume of all ten lines is ~3,000,000 nm3, which may be coiled into ~0.3% of the volume of a 1 micron3 nanorobot. Such diamondoid acoustic power transmission lines are essentially lossless (Section 184.108.40.206). If a complete set of lines containing all nline delays is not required, any desired single delay time may be obtained by connecting up to nline segments end to end, or by bouncing a pulse off of the ends of a single line up to nline times.
Aside from the many potential frequency instabilities inherent in pulse detection, signal re-initiation, and acoustic interferometry mechanisms, two fundamental sources of frequency instability include:
1. changes in the velocity of sound due to thermal variations, and;
2. changes in acoustic path length due to elastic longitudinal displacements of thermally excited transmission rods.
First, the speed of transverse sound waves in an isotropic elastic medium having Poisson's ratio cPoisson (~0.1 for diamond) is given by:10
where Young's modulus E = 1.05 x 1012 N/m2 and density r = 3510 kg/m3 for diamond. In addition to the thermal dependency of E, r varies as (1 + bthermal T)-1 where T is temperature, because volume changes according to the volume coefficient of thermal expansion bthermal = 3.5 x 10-6 K-1 for diamond, 1.56 x 10-5 K-1 for sapphire. In an uncorrected oscillator system, Dn / n ~ Dvsound / vsound ~ (1/2) bthermal DT ~ 10-5 for diamondoid transmission lines, assuming that DT ~ 6 K temperature variations are typically encountered inside the human body (Table 8.11). Correcting oscillator timing using independent temperature sensors accurate to DTmin / T ~ 10-6 (Section 4.6), and ignoring other possible sources of frequency instability (which may be significant), could reduce measurement DT to ~310 microkelvins at T ~ 310 K, thus improving Dn / n significantly for this source of frequency instability.
Second, longitudinal displacements DL / Lrod ~ 10-4 - 10-5 at 300 K for rods of length Lrod = 1.73-17.3 microns and cross-section Arod ~ 30 nm2 (Figure 5.8 in Drexler10); J. Soreff observes that DL / Lrod ~ (kT / E Lrod Arod)1/2 ~ 10-6 for ~0.01 micron3-volume systems. For the zeroth longitudinal vibrational mode,10 these displacements occur on a timescale nosc-1 = 4 Lrod (r / E)1/2 = 0.4-4 nanosec, comparable to signal transit times, taking r and E for diamond as above and Lrod = (1730 n) nm with n = 1, 2, ..., nline. This may restrict Dn / n to ~ 10-6 unless transmission lines can be further rigidized by end-clamping, sheathing, or latticed bracing at intervals, all of which, in effect, enlarge Arod.
Last updated on 23 February 2003