© 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 v_sound ~ 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 n_line = 10 lines each of length l_n = (1730 n) nm (n = 1, 2, ..., n_line), requiring a total length L_line = (1730) n_line (n_line + 1) / 2 = 95,150 nm of transmission line to obtain a set of lines having all n_line 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 7.2.5.3). If a complete set of lines containing all n_line delays is not required, any desired single delay time may be obtained by connecting up to n_line segments end to end, or by bouncing a pulse off of the ends of a single line up to n_line 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 c_Poisson (~0.1 for diamond) is given by:¹⁰

{Eqn. 10.8}

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 + b_thermal T)^-1 where T is temperature, because volume changes according to the volume coefficient of thermal expansion b_thermal = 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 ~ Dv_sound / v_sound ~ (1/2) b_thermal 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 DT_min / 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 / L_rod ~ 10^-4 - 10^-5 at 300 K for rods of length L_rod = 1.73-17.3 microns and cross-section A_rod ~ 30 nm² (Figure 5.8 in Drexler¹⁰); J. Soreff observes that DL / L_rod ~ (kT / E L_rod A_rod)^1/2 ~ 10^-6 for ~0.01 micron³-volume systems. For the zeroth longitudinal vibrational mode,¹⁰ these displacements occur on a timescale n_osc^-1 = 4 L_rod (r / E)^1/2 = 0.4-4 nanosec, comparable to signal transit times, taking r and E for diamond as above and L_rod = (1730 n) nm with n = 1, 2, ..., n_line. 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 A_rod.

Last updated on 23 February 2003