**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

**6.2.2 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 L^{3} g stored in
a volume of order ~r L Dx for small Dx,
hence energy density is approximately:

Taking r = 2000 kg/m^{3},
g = 9.81 m/sec^{2} and L = r = 1 micron, then E_{storage} =
2 x 10^{2 }joules/m^{3}, 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} x^{2} for a
displacement x and volume L^{3}, with energy density:

where (x/L) = strain and E = Young's modulus. Conservatively
taking strain = 5% and E = 1.05 x 10^{12} N/m^{2} for diamond,
then E_{storage} = 1.3 x 10^{9} joules/m^{3}. 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/m^{2},
and the distance between {111} planes is L_{plane} ~ 0.24 nm given that
there are ~1.8 x 10^{19} bonds/m^{2},^{10}
so the theoretical maximum mechanical energy storage density in a diamond block
is E_{storage} ~ E_{f} / L_{plane} = 2 x 10^{10}
joules/m^{3}.

Last updated on 18 February 2003