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

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

6.2.2 Mechanical Energy Storage

6.2.2.1 Pendulums and Springs

Energy may also be stored in mechanical systems. A gravitational pendulum of cord length r with a bob of density r and characteristic diameter L that is tangentially displaced a distance Dx has potential energy ~r L³ g stored in a volume of order ~r L Dx for small Dx, hence energy density is approximately:

{Eqn. 6.2}

Taking r = 2000 kg/m³, g = 9.81 m/sec² and L = r = 1 micron, then E_storage = 2 x 10² joules/m³, the same as Eqn. 6.1, as expected.

Stretched springs provide significantly greater energy storage capacity. For example, a diamondoid spring of size ~L and stretching stiffness k_s has harmonic potential (1/2) k_s x² for a displacement x and volume L³, with energy density:

{Eqn. 6.3}

where (x/L) = strain and E = Young's modulus. Conservatively taking strain = 5% and E = 1.05 x 10¹² N/m² for diamond, then E_storage = 1.3 x 10⁹ joules/m³. However, strains may be applied in three dimensions as well as in tension, shear, or torsion, so total energy storage may be somewhat higher. The fracture surface energy of the weakest {111} diamond plane E_f = 5.3 joules/m², and the distance between {111} planes is L_plane ~ 0.24 nm given that there are ~1.8 x 10¹⁹ bonds/m²,¹⁰ so the theoretical maximum mechanical energy storage density in a diamond block is E_storage ~ E_f / L_plane = 2 x 10¹⁰ joules/m³.

Last updated on 18 February 2003