Nanomedicine, Volume I: Basic Capabilities

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 nanowires1740,2866 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 Aw, surface area A (~ 4 L Aw1/2 for L >> Aw1/2), resistivity re, and surface emissivity er, carrying a steady current I (amps) across a potential V (volts) and a resistance R (ohms), developing power P (watts), transmitted power intensity PAw (watts/m2), and volumetric power density D (watts/m3), which heats the wire from ambient temperature T0 up to the maximum desired operating temperature Tmax, 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 re = 1.6 x 10-8 ohm-m, er = 0.02 for polished silver, Tmax = 373 K (boiling point of water) and T0 = 310 K (body temperature), then R = 16,000 ohms, I = 50 microamps (current density Id ~ 5 x 107 amps/m2), Aw = 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 dinsul and thermal conductivity Kt, then the maximum current increases to:

{Eqn. 6.42}

Using water as the thermal insulator (Kt = 0.623 watt/m-K at 310 K), a dinsul = 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