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

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

5.3.1.3 Extensibility

The most useful property of a flexible metamorphic surface is its extensibility, defined here as the percentage length increase of a fully stretched material relative to its length at zero stretch. Maximum values for natural materials used to construct the human body include 7% for cartilage, 10% for collagen, 30% for muscle, 60%-100% for skin, and up to 170% for arterial wall material if muscles are artificially relaxed.³⁶⁴ Linear elasticities of ~1000% are commonplace in artificial gels,⁵²⁸ rubbers, and other elastic materials, corresponding to ~1000-fold enclosed-volumetric changes. The El Tor strain of the Vibrio cholerae microbe shrinks 300-fold to the size of a large virus when plunged suddenly into cold salt water and remains viable in that state.³⁸⁴

If the shape of a metamorphic surface can be controlled to ~r_min (Section 5.3.1.1), then nanodevices may extrude these surfaces to define useful working subvolumes such as manipulatory appendages (e.g., prehensile fingers; see below), locomotive appendages (e.g., nanopseudopods; Section 9.3.1.6), large exterior hydrodynamic features (e.g., stabilizing fins), tools (e.g., a screw-shaped prow for easier cell penetration; Section 9.4.5.2), reconfigurable mechanical data arrays (e.g., Braille-like surface texturing), engulf formations (Section 5.3.4), perimeter contact bumpers (Section 5.4), or even entire second skins (see below). In theory, such extrusions can be quite large relative to device size.

For example, consider a nanodevice of volume V_n with an onboard pocket of volume V_f = f V_n containing N_b = f V_n / L_b³ metamorphic unit surface blocks each L_b³ in size. This is sufficient metamorphic material to extend a hollow cylindrical (hemisphere-capped) finger of diameter d_f out a total length l_f = f V_n / p d_f L_b. For f = 0.01(1%), V_n = 1 micron³, L_b = 10 nm, and d_f = 100 nm (p d_f / L_b ~ 31 blocks per circumference), N_b = 10⁴ blocks in the pocket and l_f = 3 microns maximum linear extension. Thus in theory, a finger which can extend three times the body length of the entire nanorobot can be stored in a (215 nm)³ pocket at the nanodevice surface. Ten such fingers, functionally equivalent to two micro-sized human hands, would occupy only (10/6) f ^2/3 ~ 0.08(8%) of total nanodevice surface area and 10f ~ 0.10(10%) of nanodevice volume.

Note also that a volume V_f of metamorphic blocks could be used to construct an enlarged second skin surrounding the entire nanodevice, enclosing an expanded volume V_e = (V_f / 6 L_b)^3/2 if the shell is of thickness L_b. For V_n = 1 micron³ and L_b = 10 nm, nanorobot volume may double (V_e/V_n = 2) if 9.5% of device volume is meta-morphic blocks; nanorobot volume may expand up to tenfold if ~28% of its volume is in controllable metamorphic blocks.

There are two limiting cases of extensibility. The first case is isoareal expansion, in which total surface area remains constant while volume increases dramatically. An example is the erythrocyte, which under osmotic stress expands from its normal disk shape into a sphere due to the influx of water. Volume rises from 94 micron³ to a high of 164 micron³ when spherized, a 74% increase, but surface area rises from 135 micron² to just 145 micron², a mere 7% increase.

The second limiting case is isovolemic extension, wherein surface area expands at constant volume, a transition of perhaps more relevance to nanodevices containing an irreducible fixed volume of onboard nanomachinery. For instance, if a spherical device of radius r_s morphs into a disk of equal volume with height h_d and radius r_d = a r_s, surface area increases by a factor of:

{Eqn. 5.3}

For a = 4.7, h_d ~ r_s / 17 and areal extensibility e_area = 10.2 (1020%) while enclosed volume remains unchanged.

Last updated on 17 February 2003