© 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 = 10¹⁰ N/m² (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/m³ 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/m³; R_min = 1.7 micron for STP helium gas (r_gas = 0.1785 kg/m³) 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:

{Eqn.9.87}

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 micron³ at r_payload ~ 1000 kg/m³. Expanding nanoballoon radius to R = 6.8 microns increases payload volume to ~1 micron³. 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