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

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

5.3.2.2 Parasol Model

In the Parasol Model, the metamorphic surface consists of a series of overlapping plates pressed snugly together in the vertical dimension, but free to slide in the horizontal plane (Fig. 5.12). Each plate has at least one orthogonal stabilizing keel or "handle" through which the segment is connected to subsurface control (Section 5.3.3) or rigidification mechanisms. The minimum number of plate planes is two, which allows both one-dimensional and (limited) two-dimensional extensions. In the two-dimensional case, the lower plates are allowed to rotate codirectionally under a torsion-spring restoring force applied in the plane of the lower surface, keeping all edges tight under the upper plates to maintain leakproofness. A modest areal expansibility of e_area ~ 0.28(28%) is depicted. The maximum number of plate planes is limited by nanodevice radius (hence maximum stack depth) and operating specifications such as surface rigidity, rugosity, reactivity and controllability. Self-scraping plates produce a fouling-resistant dysopsonic design -- the device simply "shrugs" in all directions, neatly guillotining any biological adherents from their attachment points on the diamondoid surface. Vertical spring tensions are adjusted to keep plates pressed tightly together, ensuring watertightness even while in motion. Corrugation features can be added to the underside of each plate to increase contact area and watertightness during plate tipping in curved configurations. Related crudely analogous structures include systems of fixed scales (e.g., lizard or snake skins) and roof tile shingle patterns on houses.

Consider an annular cylindrical section of diameter D comprised of a two-plane (p = 2) parasol surface with square top plates of area L² and rectangular bottom plates of area L(L-h) where h is the width of the handle and also the minimum overlap of adjacent plates at full extension. Then A_min = N_plates L² = p D L and A_max = A_min + (N_plates - 1)(L² - 3hL), hence areal extensibility e_area = (A_max - A_min)/A_min = (N_plates - 1 / N_plates)(1 - 3h/L). For N_plates >> 1 and h << L, the theoretical limit for a 2-plane parasol is e_area ~ 1.00(100%).

Extensibility is greatly improved by using additional plate planes. In the compact configuration of Figure 5.13, for p >> 1, A_min = N_plates L², A_max ~ N_plates L (pL - p² h + h) and areal extensibility e_area = p - 1 - (h/L)(p² - 1), with maximum e_area occurring at p = L/2h. Hence for L = 10 nm and h = 1 nm, h/L = 0.1 and maximum e_area = 1.60(160%) using p = 5 plate planes; the minimum plausible h/L ~ 0.01, which gives maximum extensibility e_area = 24.00(2400%) using p = 50 plate planes, giving a maximum surface rugosity of ~98 nm at full distension if h = 2 nm.

If an external mechanical pressure is applied perpendicular to a parasol surface, the degree of deformation will depend strongly on various details of design. Given the extensive cabling and spring-loading of plates a surface stiffness of k_s ~ 10 N/m should be achievable, in which case a point force of 1 nN deforms the parasol surface by ~0.1 nm.

Last updated on 18 February 2003