© 2004 Robert A. Freitas Jr. and Ralph C. Merkle. All Rights Reserved.

Robert A. Freitas Jr., Ralph C. Merkle, Kinematic Self-Replicating Machines, Landes Bioscience, Georgetown, TX, 2004.

B.4.3.3.2 Operational Regimes Defined

The interaction of the piston plate with the physisorbed n-octane monolayer during the piston return stroke will be governed by the characteristic diffusion time t_diffusion|| of the adsorbed n-octane molecules parallel to the surface. According to the well-known Einstein-Smoluchowski diffusion equation [228], t_diffusion|| ~ (Dx)² / (2 D_diffusion||) where Dx is the distance diffused in a fluid having lateral diffusion constant D_diffusion||. For an adsorbed monolayer, Dx may be taken as the mean intermolecular separation distance within the monolayer, or Dx ~ a_octane^1/2 ~ 0.77 nm for n-octane. t_diffusion|| is thus the mean time for a physisorbed molecule to diffuse one intermolecular separation distance. Although no studies of any kind have been done on the physisorption of n-octane on diamond surfaces, estimates from molecular dynamics and other theoretical investigations have found, for example, that D_diffusion|| ~ 0.57 x 10^-9 m²/sec for 1.3 monolayers coverage of liquid n-octane physisorbed on a-Al₂O₃(0001) at 300 K [3234], D_diffusion|| ~ 7.5 x 10^-9 m²/sec for an n-octane monolayer on Cu(111) surface at 200 K [3235], D_diffusion|| ~ 1.7 x 10^-9 m²/sec for butane at 149 K or hexane at 215 K adsorbed on graphite [3236], D_diffusion|| ~ 2.1 x 10^-9 m²/sec for butane at 150 K on Pt(111) at close to monolayer coverage [3237], D_diffusion|| ~ 10 x 10^-9 m²/sec for 1.0 monolayer coverage of liquid benzene on the basal plane of graphite at 250 K [3238], and D_diffusion|| ~ 2.8 x 10^-9 m²/sec for the translational self-diffusion coefficient for liquid ethylene adsorbed on the basal plane of graphite at 75 K [3239]. Conservatively taking D_diffusion|| ~ 1.0 x 10^-9 m²/sec for liquid octane adsorbed on hydrogen terminated diamond at 300 K, then t_diffusion|| ~ 0.3 x 10^-9 sec.

The characteristic time required for the piston plate to travel one intermolecular separation distance (Dx) is t_piston = Dx / v_piston. This defines three distinct operating regimes for the piston relative to the surface-adsorbed n-octane monolayer, as discussed further, below:

I. Desorption Regime: t_piston << t_diffusion|| (~ 0.3 x 10^-9 sec)
II. Transitional Regime: t_piston ~ t_diffusion|| (~ 0.3 x 10^-9 sec)
III. Viscous Regime: t_piston >> t_diffusion|| (~ 0.3 x 10^-9 sec)

Last updated on 13 August 2005