**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

**5.3.2.1 Accordion Model**

The Accordion Model is characterized by a surface folded in
a repeating-W pattern, as in a Japanese fan or butterfly wing pleating; photographic
and accordion bellows use what is known in origami* as a "basic fold." Point/line
vertices may employ rigid hinges or flexural members.^{1251}
Fold geometry may be double-triangular, triangular-square, or double-square;
may consist of segments of varying lengths; or may consist of a series of hinged
blocks (Fig.
5.11). This surface remains flexible even near full distension, provided
that obtuse angles may be continuously accessed. The main drawback of this model
is its likely propensity to surface fouling in vivo due to the large number
of concave pockets formed during flexure.

* The ancient practice of origami (the art
of folding three-dimensional objects out of paper without cutting or pasting)
has systematically explored the geometries of folded flat sheets;^{1102-1105}
the mathematics of origami is well-studied.^{1106-1111}

Folding or unfolding may require no sliding surfaces. Treating
the model as a simple spherical surface expanding into a watery medium, from
Section 5.3.1.4 a radial distension velocity of v_{drag}
~ 0.3 cm/sec may be expected for a 1-micron nanodevice with a 0.1 pW metamorphic
power budget. If N_{segment} is the total number of segments in a maximally
extended surface of area A_{max}, then for square segments of area L^{2}
and thickness H, N_{segment} = A_{max} / L^{2} and the
fully folded surface has area A_{min} = L H N_{segment}. For
L = 10 nm, H = 1 nm, and A_{max} = 10 micron^{2} (N_{segment}
= 10^{5}), then A_{min} = 1 micron^{2} and a 0.1-pW
power budget allows one full-range motion from A_{min} to A_{max}
in t_{motion} = (A_{max}^{1/2} - A_{min}^{1/2})
/ (2 p^{1/2} v_{drag})~ 0.2 millisec.
For the accordion model, areal extensibility e_{area} ~ (L - H) / H
= 9.00(900%) in this example.

Last updated on 17 February 2003