**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

**9.5.3.3 Buoyant Nanoballoons**

Gravity may also be overcome by reducing density relative
to the surrounding medium. An object has neutral buoyancy when its density equals
that of the medium in which it is suspended, becoming "weightless" within that
medium. For example, a nanorobot whose interior volume consists 90% of vacuum
has a v_{t} ~10 times smaller than a completely solid object of equal
size.

What is the tiniest possible lighter-than-air balloon? J.S. Hall notes that for a one-atom-thick graphene shell the out-of-plane bending stiffness of the C-C bond is much lower than the in-plane stretching stiffness. This is why hollow fullerenes of submicron diameter are experimentally observed to collapse (and remain collapsed due to van der Waals forces) even when their interiors are not evacuated. Simple internal bracing sufficient to stabilize an evacuated structure outweighs the lift. For example, applying the Euler buckling formula (Eqn. 9.44) to three diamondoid orthogonal diametral stiffening rods inside a spherical evacuated nanoballoon gives a scale-invariant total beam mass ~6 times the mass of the displaced air, hence net lift is impossible for any device radius using this minimal crossbeam design although macroscale geodesic trusswork-stabilized vacuum balloons cannot be ruled out. (See also Section 10.3.5.)

Hall also observes that pressurizing nanoballoons to atmospheric
pressure removes most shell stress. This strategy also eliminates the need to
thicken the single-atom shell walls, up to a nanoballoon radius of at least
s_{w} t_{wall} / Dp
~ 100 microns, taking wall thickness t_{wall} = 0.17 nm, a conservative
diamondoid wall working stress s_{w} = 10^{10}
N/m^{2} (Table
9.3), and allowing a maximum environmental pressure fluctuation of Dp
~ 0.17 atm (vs. ~0.002 atm for 140 dB sound waves (Section
4.9.1.5), ~0.1 atm normal barometric variation (Section
4.9.1.6), and ~2 atm maximum sound pressure in air). Bursting strength of
pressure shells is briefly treated in Section 10.3.1.

The smallest atmospheric-pressurized atomic-walled nanoballoon
that can achieve neutral buoyancy has radius R_{min} = 3 r_{wall}
t_{wall} / (r_{air }- r_{gas}),
where r_{wall} is wall density, r_{air}
is air density (r_{air} = 1.2929 kg/m^{3}
for dry air at STP), and r_{gas} is the density
of the filling gas. Thus R_{min} = 1.6 micron for hydrogen gas with
r_{gas} = 0.0899 kg/m^{3}; R_{min}
= 1.7 micron for STP helium gas (r_{gas }=
0.1785 kg/m^{3}) which, in conjunction with a slightly thicker nondiamondoid
(e.g., sapphire) shell, eliminates flammability concerns at all device number
densities. Diffusion leakage must also be addressed (Section
10.3.4).

Nanoballoons of radius R > R_{min} can carry payloads
of mass:

For instance, a helium-filled R = 2.2-micron fullerene sphere
can lift a ~10^{-17} kg payload mass, representing a payload volume
of ~0.01 micron^{3} at r_{payload}
~ 1000 kg/m^{3}. Expanding nanoballoon radius to R = 6.8 microns increases
payload volume to ~1 micron^{3}. Pressurized buoyancy-based lift systems
may be useful either in early-generation aerial nanodevices that must rely upon
primitive energy supplies, or in default-float applications. However, the modest
power expenditure needed to overcome gravity in micron-size devices (Section
9.5.3.2) suggests that nonbuoyant active-propulsion designs will normally
be preferred.

Last updated on 22 February 2003