Sunday, May 13, 2007

science detour - the carbon nanotube as a Hookean spring

Here is an experiment to get an approximation of the spring constant for a nanotube positioned as shown. The tube is 20A long and is being subjected to a constant force of 1000 pN. NanoEngineer 1 has jigs that measure distances and angles during simulations. Unfortunately these jigs are not showing up in the pov files used to make these animations, but plots of their values are available.

While the tube is 20A long, the actual distance from the anchored base to where the force is applied hovers around 18.5A. The tube makes a maximum deflection of 11.32 degrees before returning back to near equilibrium. However late in the simulation the tube slips to 11.52 degrees before becoming unstable and breaking apart. Here is the deflection/time plot:

These data points are also available in a text file, but there doesn't seem to be a way to export them to another application like Excel. I am ball-parking the average angle of deflection to be seven degrees, or 2.3 A. This gives a spring constant for the tube of 4.3 N/m.

A cursory search for similar experiments has not turned up anything, but I was able to find a company that sells carbon nanotube AFM probes with a spring constant of 2.8 N/m. If I can find a way to get the raw data out of NE1, or ever need to kill a couple hours by typing it into a spreadsheet, I will perform a more rigorous calculation.

I would like to thank Perry for providing the motivation for this post.

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