Nanoscale Capacitors.

[swestrup]

So, for little good reason other than the fact that I like to speculate on future energy technologies, I spent an hour or two yesterday doing back-of-the-envelope calculations on the theoretical maximum energy storage of traditional two-plate capacitors. Assuming nanostructured fractal metal plates of roughly 100nm feature size and a dielectric made of semiconductors heterostructured for a maximal dielectric constant of 10^8 (ie 100 million times better than vacuum), I came up with a 1 cm^3 capacitor with an astounding 3 MEGAFarad capacitance. However, when I then did the math to figure out how much energy such a capacitor would store, I got a lousy 50 Joules, and that was assuming that a carefully designed nanostructured dielectric could have as high a dielectric strength as Teflon (largest value I could find).

It turns out that this was because my capacitor would have a breakdown voltage of 3 millivolts. I was surprised to find that optimizing for capacitance did not equate to optimizing for energy storage as there are tradeoffs having to do with the thickness of the dielectric. When I get some time I'm going to redo the calculations with the same assumptions and an eye towards optimizing for storage capacity. Hopefully, one can get a few more orders of magnitude storage out of one of these things.

Comments

[tjernobyl.livejournal.com]

I was looking at ultracapacitors the other day with the goal of figuring out how to power an electric car with them. The average rating is around 3V. Energy =~ V^2, so it's looking like that's the parameter to improve right now.

[swestrup]

Breakdown voltage increases as the minimum dielectric width increases, but that decreases capacitance. Total energy storage = .5CV^2, so in maximizing capacitance I rather minimized voltage. I need to generate a formula for energy storage based only on the geometry and assumed material properties, and then find a local maxima. Not hard, but I need to be more awake first.