**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

**5.3.2.2 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 L^{2}
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} L^{2} = p D L and A_{max}
= A_{min} + (N_{plates} - 1)(L^{2} - 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} L^{2},
A_{max} ~ N_{plates} L (pL - p^{2} h + h) and areal
extensibility e_{area} = p - 1 - (h/L)(p^{2} - 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