© 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 L² and thickness H, N_segment = A_max / L² and the fully folded surface has area A_min = L H N_segment. For L = 10 nm, H = 1 nm, and A_max = 10 micron² (N_segment = 10⁵), then A_min = 1 micron² 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