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
220.127.116.11 Acoustic Cables and Transmission Lines
Consider an acoustic compression signal of frequency nacoust traveling down a fluid-filled transmission cable of length lcable and radius rcable. In order to be detected at a signal/noise ratio SNR = 2, each pulse cycle must transfer a minimum energy kT eSNR to a receiver of volume L3 at the cable terminus; hence from Eqn. 4.29, the maximum detectable pulse frequency nacoust = Irec L2 / kT eSNR (Hz), where Irec 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 rcable2 Itrans (watts) where Itrans is the power intensity of the signal transmitter. Combining these relations with Eqn. 6.44 for acoustic attenuation in cables gives
where atube is given by Eqn. 6.45 with a ~nacoust1/2 dependency. To avoid cavitation in pure water (Section 18.104.22.168) and to ensure safety in the unlikely event of cable detachment in vivo, maximum Itrans = 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 nacoust ~ 1 GHz (109 bits/sec) for a cable of length lcable = 14 microns (~8000 zJ/bit). A 1000-micron long cable can transmit up to ~1 MHz; nacoust ~ 1 KHz at lcable ~ 5 cm; and nacoust ~ 1 Hz at lcable ~ 2 meters. For intradevice communications, nacoust ~ 1 GHz for L = 300 nm, lcable = 1 micron, and rtube = 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 Vrod at temperature Trod, made of a material with a thermal coefficient of volume expansion b and heat capacity CV, to which a pressure pulse DP is applied at one end that travels at velocity vsound (~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 Wmax as
For diamond at Trod = 310 K, b = 3.5 x 10-6 /K and CV = 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 (Vrod = 10-22 m3) requires a pulse input energy of ~10,000 zJ, but suffers an energy loss during transmission of at most Wmax = 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% Wmax at ~1 GHz and ~0.001% Wmax at ~1 MHz. Thus even at nrod ~ 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