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
3.2.5 Nanocentrifugal Sortation
Nanoscale centrifuges offer yet another method for rapid molecular sortation, by biasing diffusive forces with a strong external field. The well-known effect of gravitational acceleration on spherical particles suspended in a fluid is described by Stokes' Law for Sedimentation:
where vt is terminal velocity, g is the acceleration of gravity (9.81 m/sec2), R is particle radius, rparticle and rfluid are the particle and fluid densities (kg/m3), and h is coefficient of viscosity of the fluid. Particles which are more dense than the suspending liquid tend to fall. Those which are less dense tend to rise (rparticle / rfluid ~0.8 for lipids, up to ~1.5 for proteins, and ~1.6 for carbohydrates in water).
This separation process may be greatly enhanced by rapidly spinning the mixed-molecule sample in a nanocentrifuge device. For ideal solutions (e.g., obeying Raoult's law) at equilibrium:390
where c2 is the concentration at distance r2 from the axis of a spinning centrifuge (molecules/m3), c1 is the concentration at distance r1 (nearer the axis), MWkg is the molecular weight of the desired molecule in kg/mole, w is the angular velocity of the vessel (rad/sec), T is temperature (K) and the universal gas constant Rg = 8.31 joule/mole-K. The approximate spinning time ts required to reach equilibrium is
where Sd is the sedimentation coefficient, usually given in units of 10-13 sec or svedbergs (Table 3.5). Research ultracentrifuges have reached accelerations of ~109 g's.
Consider a cylindrical diamondoid vessel of density rvessel = 3510 kg/m3, radius rc = 200 nm, height h = 100 nm, and wall thickness xwall = 10 nm, securely attached to an axial drive shaft of radius ra = 50 nm (schematic in Fig. 3.2). A fluid sample containing desired molecules enters the vessel through a hollow conduit in the drive shaft, and the device is rapidly spun. If rim speed vr = 1000 m/sec (max), then w = vr / rc = 5 x 109 rad/sec (w / 2 p = 8 x 108 rev/sec). The maximum bursting force Fb ~ 0.5 rvessel vr2 = 2 x 109 N/m2, well below the 50 x 109 N/m2 diamondoid tensile strength conservatively assumed by Drexler.10 Since Sd ranges from 0.1-200 x 10-13 sec for most particles of nanomedical interest (Table 3.5), minimum separation time using acceleration ar / g = vr2 / g rc = 5 x 1011 g's, when r2 = rc and r1 = ra, is ts = 0.003-6.0 x 10-6 sec. Fluid sample components migrate at ~0.1 m/sec.
Maximum centrifugation energy per particle Ec = (MWkg / NA) ar (rc - ra) ~ 10,000 zJ/molecule, or ~10 zJ/bond for proteins, well below the 180-1800 zJ/bond range for covalent chemical bonds (Section 3.5.1). However, operating the nanocentrifuge at peak speed may disrupt the weakest noncovalent bonds (including hydrophobic, hydrogen, and van der Waals) which range from 4-50 zJ/bond. The nanocentrifuge has mass ~10-17 kg, requires ~3 picojoules to spin up to speed (bearing drag consumes ~10 nanowatts of power, and fluid drag through the internal plumbing contributes another ~5 nanowatts), completes each separation cycle in ~104 revs (~10-5 sec), and processes ~300 micron3/sec which is ~1013 small molecules/sec (at 1% input concentration) or ~109 large molecules/sec (at 0.1% input concentration).
From Eqn. 3.11, the nanocentrifuge separates salt from seawater with c2/c1 ~ 300 across the width of the vessel (rc - ra = 150 nm); extracting glucose from water at 310 K, c2/c1 ~105 over 150 nm. For proteins with rparticle ~ 1500 kg/m3, separation product removal ports may be spaced, say, 10 nm apart along the vessel radius while maintaining c2/c1 ~ 103 between each port. Vacuum isolation of the unit in an isothermal environment and operation in continuous-flow mode could permit exchange of contents while the vessel is still moving, sharply reducing remixing, vibrations, and thermal convection currents between product layers. A complete design specification of product removal ports, batch and continuous flow protocols, compression profiles, etc. is beyond the scope of this book.
Variable gradient density centrifugation may be used to trap molecules of a specific density in a specific zone for subsequent harvesting, allowing recovery of each molecular species from complex mixtures of substances that are close in density. The traditional method is a series of stratified layers of sucrose or cesium chloride solutions that increase in density from the top to the bottom of the tube. A continuous density gradient may also be used, with the density of the suspension fluid calibrated by physical compression. For example, the coefficient of isothermal compressibility k = (DVl/Vl ) / DPl = (Drfluid / rfluid) / DPl = 4.492 x 10-5 atm-1 for water at 1 atm and 310 K (compressibility is pressure- and temperature-dependent). Applying Pl = 12,000 atm to the vessel raises fluid density to 1250 kg/m3,567 sufficient to partially regulate protein zoning. A multistage cascade (Section 3.2.4) may be necessary for complete compositional separation. Protein denaturation between 5000-15,000 atm585 due to hydrogen bond disruption may limit nanocentrifugation rotational velocity. Protein compressibility may further reduce separability. The balance between the differential densities and the differential compressibilities will determine the equilibrium radius of the protein in the centrifuge; in the limiting case of equal compressibilities for a given target protein and water, there is no stable equilibrium radius.
The nanocentrifuge may also be useful in isotopic separations. For a D2O/H2O mixture, c2/c1 = 1.415 per pass through the device; c2/c1 = 106 is achieved in a 40-unit cascade. Tracer glycine containing one atom of C14 is separated from natural glycine using a 113-unit cascade, achieving c2/c1 = 106.
Last updated on 7 February 2003