© 2003 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume IIA: Biocompatibility, Landes Bioscience, Georgetown, TX, 2003

15.5.8 Nanorobot-Nanorobot Mechanocompatibility

In clinical applications involving large populations of bloodborne diamondoid nanorobots simultaneously present inside the human body, nanorobots will regularly encounter one additional class of objects in their environment towards which mechanocompatibility must be proven: other nanorobots. For example, a maximum nanocrit bloodstream infusion involving a ~1000 terabot dosage (~10¹⁵ nanorobots) implies a mean collisional frequency for each device with its nanorobotic neighbors of ~40-200 collisions/sec (Section 9.4.2.2), mostly in regions close to vessel walls even at high shear (Section 9.4.1.3). Will such nanorobots survive in sanguo collisions with their neighboring devices?

Consider an elastic collision at relative velocity v_coll between two identical spherical nanorobots of radius R_bot and density rho_bot, each comprised of a diamondoid structure with failure strength sigma_bot, producing at the site of interaction a collisional dimple of radius r_coll and depth x_coll, and imposing a strain s_coll. The two nanorobots decelerate in a time t_coll = x_coll/v_coll with a negative acceleration of a_coll = v_coll² / (2 x_coll) = v_coll² / (2 s_coll R_bot). The collisional force of F_coll = m_bot a_coll is distributed over an interaction area of A_coll = pi r_coll², producing a collisional pressure P_coll <~ sigma_bot to avoid material failure, with m_bot = (4/3) pi rho_bot R_bot³. Hence the stress produced during a nanorobot-nanorobot collision is approximately s_coll = (2 rho_bot R_bot² v_coll²) / (3 sigma_bot r_coll²). For nanorobots of radius R_bot = 1 micron and density rho_bot ~ 2000 kg/m³, thermal velocity in blood at 37 ^oC is ~1 mm/sec (Section 3.2.1) and the anticipated relative collision velocity is 1-2 mm/sec (Section 9.4.2.2). Conservatively taking v_coll = 1 cm/sec, sigma_bot = 1000 atm (~10⁸ N/m²) and r_coll = 10 nm, and taking the maximum allowable strain for diamond s_max ~ 5%, then the collision time t_coll ~ 1 nanosec, deceleration a_coll ~ 4 x 10⁵ g’s, and strain s_coll ~ 0.001% << s_max ~ 5%, so such collisions appear to be easily survivable. Similar considerations may apply to interactions between individual nanorobots and macroscale nanorobotic organs or nanoaggregates. Interactions between nonspherical nanorobots having protruding surface features, extended manipulators, and the like should be examined in future studies.

Nonspecific aggregation or inelastic “clumping” of nanorobots in vivo should not be a major problem because nonbiological adhesive forces are greatly reduced in fluid environments (Section 9.2.3), and because nanorobot surface adhesive characteristics and biological adhesive forces are subject to design control and therefore to minimization (Section 15.2.2).

Last updated on 30 April 2004