**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

**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/m^{2}), and volumetric
power density D (watts/m^{3}), which heats the wire from ambient temperature
T_{0} up to the maximum desired operating temperature T_{max},
then from the standard electrical formulas and Eqn.
6.19:

where s = 5.67 x 10^{-8}
watt/m^{2}-K^{4} (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 T_{0} = 310 K (body temperature),
then R = 16,000 ohms, I = 50 microamps (current density I_{d} ~ 5 x
10^{7} amps/m^{2}), A_{w} = 1 micron^{2}, A
~ 4 mm^{2}, 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 10^{7} watts/m^{3}. Note that the minimum
quantum unit of resistance in atomic or molecular-scale wires is ~h/2e^{2}
~ 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:

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 >10^{14} amps/m^{2} 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 doped^{644} and undoped^{3240}
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 ~10^{6} 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 ~10^{3} amperes/m^{2}
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/nm^{2} (~amino acid density)
on a 1 nm^{2} belt gives a current of ~2 nanoamperes and a current density
of ~10^{9} amperes/m^{2}, comparable to the electromigration-limited
~10^{10} amperes/m^{2} 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