X-Message-Number: 21076
Date: Thu, 06 Feb 2003 23:38:55 +0100
From: Henri Kluytmans <>
Subject: Nano robotic-arm precision

Yvan Bozzonetti explained that a macroscopic system with many atom lengths 
can have a precision better than a nanometer, but that downscaling 
reduces stiffness and increases positional uncertainty. He is right 
about that of course. And my example of a piezoelectric crystal was a 
bad one. 

Bending stiffness scales down proportional with size. And positional 
uncertainty due to thermal noice is inversely proportional to the 
square root of the stiffness.

But because MNT devices will be made from materials with very 
high stiffness (Young's modulus of diamond = 10^12 N/m2 ) 100 nm 
sized manipulator arms with atomic positional precision (<0.1nm)
are still feasible.

The robotic arm example in Nanosystems (although not optimal) is 
100 nm long and 35 nm diameter. Although it is hollow and contains 
joints, it still has an overal stiffness of 25 N/m. 
(For comparison, a solid rod of diamond 100nm by 35nm diameter 
would have a stiffness of 9000 N/m )

Positional uncertainty due to thermal noice is : 
sigma^2  =  kT / ks    at room temp.  sigma = sqrt( 4 10^-21 / 25 ) = ~0.01

This is only a modest fraction of an atomic diameter, and quite enough 
to allow placement with atomic resolution. However one should have to 
add positional uncertainty due to workpeace (the object) and tool 
(i.e. reactive moiety). But overall the total positional uncertainty 
can be kept under 0.03 nm, still enough for atomic resolution.

Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=21076