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


10.3.5 Vacuum Pumping and Storage

It will frequently be necessary to establish and maintain vacuum conditions inside nanorobots. Vacuum-enclosing shells were briefly considered in Section and were found incapable of providing sufficient buoyant lift in normal air due to buckling instabilities. However, nanoscale pressure hulls capable of retaining vacuum may be surprisingly thin-walled. In the simplest case, consider a circular cylindrical diamondoid tube of inside radius rtube, wall thickness htube, Young's modulus E = 1.05 x 1012 N/m2 and Poisson's ratio cPoisson ~ 0.1.10 When the relative external pressure on the hull is so large that the cylinder becomes neutrally unstable, a small deformation into an elliptical cylinder is possible. The critical pressure of buckling is given by:361

{Eqn. 10.20}

Taking rtube = 500 nm and pcrit <~ 1 atm for a vacuum vessel surrounded by normal atmospheric pressure, a hull thickness of htube >~ 3.7 nm will not buckle. Such a hull has a mass ~60 times greater than the mass of the displaced air.

How fast can the vacuum be established? Consider a cubical vessel of volume Vbox = Lbox3 = 1 micron3 containing gas at molecular number density ngas, which is to be evacuated. Molecular sorting rotors (Section 3.4.2) are embedded in the six walls, with each rotor mechanism of area Arotor = 100 nm2 having at least one binding site of area Areceptor = 0.1 nm2 always exposed to the box interior. There are Nrotor = (6 Lbox2 / Arotor) = 60,000 sorting rotors in the box walls. Gas molecules of thermal velocity vthermal (Eqn. 3.3) nearest the walls travel one mean free path lgas (Eqn. 9.23) and impact a rotor mechanism. On average, after Arotor/Areceptor impacts a binding site is hit; after nencounter = 10 independent hits, the molecule is finally captured by the receptor. Thus the time required for a receptor to capture a gas molecule is tbind ~ nencounter lgas Arotor / vthermal Areceptor and the time required to evacuate the box is approximately:

{Eqn. 10.21}

At 1 atm and 310 K, ngas = 2.4 x 1025 molecules/m3 (Table 10.2) and lgas = 200 nm; for pressures <0.2 atm, lgas ~ Lbox in the ballistic regime. Taking lgas ~ 1 micron and vthermal = 490 m/sec for O2 at 310 K gives tbind ~ 20 microsec and the box is evacuated in tvac ~ 10 millisec. Note that for microscale vessels at atmospheric pressure, tvac scales as ~Lbox2.

Tank wall material sublimates into the vacuum, the solid establishing equilibrium with its vapor at a temperature-dependent vapor pressure. However, this process produces negligible effluent at moderate temperatures for likely nanorobot building materials. A volumetric number density of one wall-material atom per micron3 of vacuum, representing a minimum detectable contamination in a ~1 micron3 box, equals a contaminant partial pressure of 4 x 10-8 atm. To reach this vapor pressure, carbon must be heated to 2480 K, aluminum to 1040 K (liquid), silver and corundum (e.g., ruby, sapphire) to 800 K, and even zinc (a soft, low melting point, metal) to 500 K.763 At 310 K, the vapor pressure of tank-wall carbon is only ~10-116 atm, aluminum ~10-39 atm, corundum ~10-19 atm, and zinc ~10-16 atm. Many organic materials evaporate or sublimate more readily. At a vapor pressure of 0.001 atm, ethanol (C2H5OH) vaporizes at or above 241.9 K, vs. 253 K for water-ice, 259.2 K for octane (C8H18), 313.1 K for phenol (C6H5OH), but 426.8 K for palmitic acid (CH3(CH2)14COOH), a typical fatty acid.763 A water-ice surface exposed to hard vacuum sublimates at the rate of 6.5 nm/day at 134 K, 1.4 microns/day at 152 K, and 1.2 mm/day at 183 K.2320


Last updated on 24 February 2003