**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

**6.2.4 Electric and Magnetic
Energy Storage**

The energy density in a static electric field of strength
E traversing a material of dielectric constant k_{e}
is given by

where e_{0} = 8.85 x 10^{-12}
farad/m (permittivity constant) and dielectric constant k_{e}
= 5.7 for diamond. Electrostatic motors (Section 6.3.5)
in nanomechanical systems may exhibit an electric field strength of ~0.2 x 10^{9}
volts/m.^{10} However, the maximum field
that may be employed in an electrostatic energy storage device is limited by
the dielectric strength or breakdown voltage E = 2 x 10^{9} volts/m
for diamond^{537} (about the highest
known for any material), giving a maximum electric storage density of 1.0 x
10^{8} joules/m^{3}.

What about magnetic storage density? Since isolated magnetic
poles (analogous to the electron) are not known to exist, magnetic field energy
can be stored only in an array of aligned atomic dipoles. The energy density
of the static magnetic field of a permanent magnet comprised of atoms with dipole
moment M_{dipole} and number density N_{dipole} producing a
flux density B at 100% saturation is given by

For iron atoms with bulk density 7860 kg/m^{3}, then
N_{dipole} = 8.5 x 10^{28} atoms/m^{3} and M_{dipole}
= 1.8 x 10^{-23} ampere-m^{2},^{1662}
giving E_{storage} = 2.1 x 10^{6} joules/m^{3}.

Only a negligible amount of magnetic energy is stored in a
magnetic field created by a permanent current loop in a nanoscale ring of superconducting
material. For a wire loop of radius R_{loop} and thickness d_{wire}
carrying current I, and following the notation of Eqn.
4.44, peak magnetic flux density is B = m_{0}
I / 2 R_{loop} at the center of the loop,^{1662}
so the peak energy density is given by:

Aluminum conductors in integrated circuits are limited to
I_{d} ~ 3 x 10^{9} ampere/m^{2} due to electromigration;
thin-film high-temperature superconductors^{550}
have achieved I_{d} > 3 x 10^{10} ampere/m^{2}. Taking
I = (I_{d} ~ 10^{10} ampere/m^{2}) {p
(d_{wire}/2)^{2}} ~ 10^{-4} amperes for d_{wire}
= 100 nm, m_{0} = 1.26 x 10^{-6}
henry/m, and R_{loop} = 0.5 micron, then E_{storage} = 6.3 x
10^{-3} joules/m^{3}.

Electromagnetic waveguides, radiator cavities and fiberoptic
closed loops are too lossy or of inappropriate scale to permit direct nanodevice
photonic energy storage. Energy stored in excited or partially ionized molecular
or atomic states, coherent (lasing) and fluorescing media, and enzymatic activated
complexes (e.g. at peak activation energy) generally also lack sufficient duration
or stability to be useful, although the metastable excited electronic 2^{3}S
state of solid He^{4} at 19.8 eV has a 2.3-hour lifetime and thus a
theoretical storage density of 5 x 10^{11} joules/m^{3} for
100% electronically excited solid helium.^{661}

Last updated on 18 February 2003