© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

4.2.6 Spatial Concentration Gradients

Medical nanodevices can detect both extremely steep and extremely shallow spatial concentration gradients. For example, a receptor array sensor (Section 4.2.1) consisting of 10 steric probe units has a total volume of ~1000 nm³ including its prorated share of drive systems, housings, etc. In just a few measurement cycles, adjacent sensors can detect a maximum concentration change from 10^-2 nm^-3 to 10^-11 nm^-3 across a mean nanosensor separation of 10 nm on a nanodevice surface, a steep chemical spatial gradient of ~10¹⁰% per nanometer. J. Soreff points out that maintaining a steep concentration gradient of a freely diffusing species implies a power dissipation of ~kT per molecule per time to diffuse a concentration-halving distance. For a common, small, tethered molecule with c_ligand ~ 3 x 10^-3 molecules/nm³ that diffuses ~1 nm in t_diff ~ 1 nanosec, implied power density D_mol ~ kT c_ligand / t_diff ~ 10¹³ watts/m³, a power density that might possibly be encountered in the vicinity of chemoelectric transducers (Section 6.3.4.5). (Such high power densities never occur on macroscale dimensions, and heat rapidly diffuses at nanoscale dimensions; Sections 4.6.1.)

Similarly, counting rotor sensors (Section 4.2.3) for small common serum molecules like glucose deployed at opposite ends of a 1-micron nanodevice can detect a concentration differential of ~10^-4 over a ~1 sec measurement period, a shallow chemical spatial gradient of only ~10^-5 % per nanometer. Even lower gradients may be detected by communication (Chapter 7) between physically separated cooperating nanodevices.

Last updated on 17 February 2003