© 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 9.5.3.3 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 r_tube, wall thickness h_tube, Young's modulus E = 1.05 x 10¹² N/m² and Poisson's ratio c_Poisson ~ 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 r_tube = 500 nm and p_crit <~ 1 atm for a vacuum vessel surrounded by normal atmospheric pressure, a hull thickness of h_tube >~ 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 V_box = L_box³ = 1 micron³ containing gas at molecular number density n_gas, which is to be evacuated. Molecular sorting rotors (Section 3.4.2) are embedded in the six walls, with each rotor mechanism of area A_rotor = 100 nm² having at least one binding site of area A_receptor = 0.1 nm² always exposed to the box interior. There are N_rotor = (6 L_box² / A_rotor) = 60,000 sorting rotors in the box walls. Gas molecules of thermal velocity v_thermal (Eqn. 3.3) nearest the walls travel one mean free path l_gas (Eqn. 9.23) and impact a rotor mechanism. On average, after A_rotor/A_receptor impacts a binding site is hit; after n_encounter = 10 independent hits, the molecule is finally captured by the receptor. Thus the time required for a receptor to capture a gas molecule is t_bind ~ n_encounter l_gas A_rotor / v_thermal A_receptor and the time required to evacuate the box is approximately:

{Eqn. 10.21}

At 1 atm and 310 K, n_gas = 2.4 x 10²⁵ molecules/m³ (Table 10.2) and l_gas = 200 nm; for pressures <0.2 atm, l_gas ~ L_box in the ballistic regime. Taking l_gas ~ 1 micron and v_thermal = 490 m/sec for O₂ at 310 K gives t_bind ~ 20 microsec and the box is evacuated in t_vac ~ 10 millisec. Note that for microscale vessels at atmospheric pressure, t_vac scales as ~L_box².

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