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

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

7.2.5.3 Acoustic Cables and Transmission Lines

Consider an acoustic compression signal of frequency n_acoust traveling down a fluid-filled transmission cable of length l_cable and radius r_cable. In order to be detected at a signal/noise ratio SNR = 2, each pulse cycle must transfer a minimum energy kT e^SNR to a receiver of volume L³ at the cable terminus; hence from Eqn. 4.29, the maximum detectable pulse frequency n_acoust = I_rec L² / kT e^SNR (Hz), where I_rec is the acoustic power intensity at the receiver. To obtain this intensity at the receiver, the input signal power at the other end of the cable must be P₀ > p r_cable² I_trans (watts) where I_trans is the power intensity of the signal transmitter. Combining these relations with Eqn. 6.44 for acoustic attenuation in cables gives

{Eqn. 7.18}

where a_tube is given by Eqn. 6.45 with a ~n_acoust^1/2 dependency. To avoid cavitation in pure water (Section 6.4.3.3) and to ensure safety in the unlikely event of cable detachment in vivo, maximum I_trans = 10⁴ watts/m² of acoustic energy (Fig. 6.8). For a cable of diameter 1 micron terminating on a receiver of volume (680 nm)³ sensitive to 10^-6 atm displacements (Section 4.5.1), then n_acoust ~ 1 GHz (10⁹ bits/sec) for a cable of length l_cable = 14 microns (~8000 zJ/bit). A 1000-micron long cable can transmit up to ~1 MHz; n_acoust ~ 1 KHz at l_cable ~ 5 cm; and n_acoust ~ 1 Hz at l_cable ~ 2 meters. For intradevice communications, n_acoust ~ 1 GHz for L = 300 nm, l_cable = 1 micron, and r_tube = 50 nm, though pure diamond fiber may be more efficient in this case.

A solid diamond acoustic transmission line transfers signals over great distances at GHz frequencies with almost no power losses, in part because of the extreme stiffness of diamond. Consider a rod of volume V_rod at temperature T_rod, made of a material with a thermal coefficient of volume expansion b and heat capacity C_V, to which a pressure pulse DP is applied at one end that travels at velocity v_sound (~17,300 m/sec for diamond) to the other end. In the worst-case thermodynamic cycle, Drexler ¹⁰ gives the total energy dissipation per pulse W_max as

{Eqn. 7.19}

For diamond at T_rod = 310 K, b = 3.5 x 10^-6 /K and C_V = 1.8 x 10⁶ joule/m³-K.^460,567 Thus a 1-atm pulse that is applied to a transmission line consisting of a diamond rod 1 micron in length and (10 nm)² in cross sectional area (V_rod = 10^-22 m³) requires a pulse input energy of ~10,000 zJ, but suffers an energy loss during transmission of at most W_max = 2 x 10^-6 zJ. Under smooth mechanical cycling, nanomechanical systems may approach the isothermal limit and significantly reduce dissipation still further,¹⁰ to ~1% W_max at ~1 GHz and ~0.001% W_max at ~1 MHz. Thus even at n_rod ~ 1 GHz the losses using 1-atm pulses amount to only ~20 zJ and the transmission of energy is still ~99.8% efficient.

Last updated on 19 February 2003