Nanomedicine, Volume I: Basic Capabilities

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 ke is given by

{Eqn.6.7}

where e0 = 8.85 x 10-12 farad/m (permittivity constant) and dielectric constant ke = 5.7 for diamond. Electrostatic motors (Section 6.3.5) in nanomechanical systems may exhibit an electric field strength of ~0.2 x 109 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 109 volts/m for diamond537 (about the highest known for any material), giving a maximum electric storage density of 1.0 x 108 joules/m3.

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 Mdipole and number density Ndipole producing a flux density B at 100% saturation is given by

{Eqn. 6.8}

For iron atoms with bulk density 7860 kg/m3, then Ndipole = 8.5 x 1028 atoms/m3 and Mdipole = 1.8 x 10-23 ampere-m2,1662 giving Estorage = 2.1 x 106 joules/m3.

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 Rloop and thickness dwire carrying current I, and following the notation of Eqn. 4.44, peak magnetic flux density is B = m0 I / 2 Rloop at the center of the loop,1662 so the peak energy density is given by:

{Eqn. 6.9}

Aluminum conductors in integrated circuits are limited to Id ~ 3 x 109 ampere/m2 due to electromigration; thin-film high-temperature superconductors550 have achieved Id > 3 x 1010 ampere/m2. Taking I = (Id ~ 1010 ampere/m2) {p (dwire/2)2} ~ 10-4 amperes for dwire = 100 nm, m0 = 1.26 x 10-6 henry/m, and Rloop = 0.5 micron, then Estorage = 6.3 x 10-3 joules/m3.

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 23S state of solid He4 at 19.8 eV has a 2.3-hour lifetime and thus a theoretical storage density of 5 x 1011 joules/m3 for 100% electronically excited solid helium.661

Last updated on 18 February 2003