**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

**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_{b}^{3} metamorphic unit
surface blocks each L_{b}^{3} 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 micron^{3},
L_{b} = 10 nm, and d_{f} = 100 nm (p
d_{f} / L_{b} ~ 31 blocks per circumference), N_{b}
= 10^{4} 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 micron^{3}
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 micron^{3} to a high of 164 micron^{3}
when spherized, a 74% increase, but surface area rises from 135 micron^{2}
to just 145 micron^{2}, 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