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

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

6.4.3.1 Electrical Tethers

One of the most obvious methods for providing energy to nanodevices is simply to attach a power cord to each machine. The bending moment of a wire is proportional to its radius to the fourth power,⁶⁴² so molecular nanowires^1740,2866 are much more flexible than macroscopic wires. These power cables could be made of traditional metallic conductors (15-nm thick gold wires have been fabricated on a Si substrate) or doped polyacetylene chains (Section 10.2.3.3) and other organic conductors which have been used to make LEDs and polymer batteries.³⁸²

For an uninsulated single conductor of length L, square cross-sectional area A_w, surface area A (~ 4 L A_w^1/2 for L >> A_w^1/2), resistivity r_e, and surface emissivity e_r, carrying a steady current I (amps) across a potential V (volts) and a resistance R (ohms), developing power P (watts), transmitted power intensity P_Aw (watts/m²), and volumetric power density D (watts/m³), which heats the wire from ambient temperature T₀ up to the maximum desired operating temperature T_max, then from the standard electrical formulas and Eqn. 6.19:

{Eqn. 6.36}

{Eqn. 6.37}

{Eqn. 6.38}

{Eqn. 6.39}

{Eqn. 6.40}

{Eqn. 6.41}

where s = 5.67 x 10^-8 watt/m²-K⁴ (Stefan-Boltzmann constant). Thus for a silver wire 1 micron in diameter and 1 meter long, with r_e = 1.6 x 10^-8 ohm-m, e_r = 0.02 for polished silver, T_max = 373 K (boiling point of water) and T₀ = 310 K (body temperature), then R = 16,000 ohms, I = 50 microamps (current density I_d ~ 5 x 10⁷ amps/m²), A_w = 1 micron², A ~ 4 mm², V = 0.9 volt, P = 50 microwatts (sufficient power to operate a load of ~45 electrostatic motors ~390 nm in diameter, as described in Section 6.3.5), and D = 5 x 10⁷ watts/m³. Note that the minimum quantum unit of resistance in atomic or molecular-scale wires is ~h/2e² ~ 13,000 ohms, where h = 6.63 x 10^-34 joule-sec (Planck's constant) and e = 1.6 x 10^-19 joule/eV, due to quantized conductance (e.g., Coulomb blockade) in narrow channels whose characteristic transverse dimension approaches the electronic wavelength.¹⁷⁴⁰ By 1998, metallic wires down to ~20 nm in width had been fabricated.¹⁵¹⁷

Wires with electrical and thermal insulation can safely carry higher currents in vivo (Section 6.5.5). If the wire in the preceding example is wrapped with a thermal insulator of thickness d_insul and thermal conductivity K_t, then the maximum current increases to:

{Eqn. 6.42}

Using water as the thermal insulator (K_t = 0.623 watt/m-K at 310 K), a d_insul = 1 micron layer allows the wire to rise to 373 K while the outside of the insulating jacket remains near 310 K. A 100-micron thick water jacket allows electrical current and voltage to safely rise by a factor of 10, thus power to rise by a factor of 100.

Another possibility is the fullerene (pure carbon) conductors (Section 10.2.2.1). For example, 7-12 nm nanotube ropes 200-500 nm in length at ~310 K conduct ~50 nanoamperes at ~1 millivolt, transmitting a total power of ~50 pW.⁶⁴¹ Boron nitride coated carbon nanotube wires should be highly oxidation-resistant.¹³⁰⁸ Field emission from room temperature carbon atomic wires has been measured as 0.1-1 microamperes at 80 volts, or ~10 microwatts.⁶⁴³ Nanowires a few nm wide and hundreds of microns long have already been fabricated, and continuous meter-length threads (and longer) have been proposed; current densities >10¹⁴ amps/m² have been pulled through a single chain of carbon atoms.⁶⁴³

If fullerene nanowires are doped with metal atoms, adding electrons or holes so that the charge carrier density is high, electrical conductivity may be precisely engineered from semiconductor levels up to equal or better than copper in the plane of the graphene sheet. Multitube cables may display a quantum confinement effect that sharply reduces the resistance, possibly giving an electrical conductivity 10-100 times that of copper at room temperatures, and may provide shielding comparable to coax. Doped electron-rich conductors are easily oxidized on the nanometer scale, but wrapping such conductors in a second concentric undoped outer nanotube provides an insulating jacket that is effectively chemically impermeable under normal conditions. By 1998, coaxial nanocables ~30 nm in diameter had been fabricated in lengths up to 50 microns.²⁰¹⁶ Boron-nitrogen (BN) equivalents of fullerene nanotubes are physically strong and good insulators. Low-temperature superconductivity has been demonstrated in doped⁶⁴⁴ and undoped³²⁴⁰ fullerenes.

An interesting alternative is a conveyor belt system for direct mechanical charge transport, crudely analogous to the charging system of a Van de Graaff generator. Nanoscale conveyor belts (Section 3.4.3) could transport ~10⁶ electrons/sec at a belt speed of 4 mm/sec, comparable to the ~1 cm/sec drift speed of electrons flowing in macroscale wires (Section 6.5.5). This gives a 0.2 picoampere current through a device with cross-sectional area ~(10 nm)², a modest current density of ~10³ amperes/m² and electrostatic belt stress of ~1 atm between adjacent charges spaced ~4 nm apart. If a much smaller belt can be designed of a scale comparable to the 150 micron long computer data storage tape (Section 7.2.6) described by Drexler,¹⁰ a belt speed of ~10 m/sec and charge density of ~1 electron/nm² (~amino acid density) on a 1 nm² belt gives a current of ~2 nanoamperes and a current density of ~10⁹ amperes/m², comparable to the electromigration-limited ~10¹⁰ amperes/m² maximum current density in bulk aluminum,* with an electrostatic belt stress of ~3600 atm. Net belt mechanical energy dissipation may be as low as ~10^-6 zJ/nm of travel for each ~nanometer-scale charge carrying device (Section 3.4.3).

* This "maximum" may be quite conservative: "A single crystal metal wire surrounded by a strongly bonded, lattice-matched sheath should be stable at far greater current densities than a conventional wire of the same material".¹⁰

Last updated on 18 February 2003