How can Nanotubes store electicity ?

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Carbon nanotubes (CN) are cylindrical structures of carbon atoms that can store electricity by functioning as capacitors, leveraging their large surface area to mass ratio to enhance capacitance. While they can improve the performance of lithium-ion batteries, they do not store electricity more effectively than these batteries on their own. The unique property of electron tunneling allows nanotubes to propagate electrical signals at nanoscale levels. Their potential applications include serving as tiny wires and enhancing energy storage systems. Overall, carbon nanotubes present promising advancements in electrical storage technology, particularly in conjunction with existing battery systems.
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In they site they say nanotubes can store electricity http://www.calrecycle.ca.gov/reducewaste/Power/ElectricStor.htm

"Carbon nanotubes (CN) are cylinders of carbon atoms that are 1 or 2 nanometers in diameter. The molecular structure of the carbon atoms resembles wire mesh with six sided holes, similar to chicken wire. A carbon nanotube resembles an extremely tiny seamless tube of chicken wire. Carbon nanotubes have at least two potential uses. They can serve as tiny wires due to a property called electron tunneling, which let's them propagate electrical signals at scales where ordinary current flow is impossible. Carbon nanotubes can also store electrical energy."

So how does it store electricity? and does it store it better than Lithium batteries?
 
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Carbon nanotubes store electricity much the same way as anything does. i.e. they can be configured to act as capacitors. Surfaces made out of nanotubes have a large surface area to mass ratio, and capacitance increases with surface area.

In comparison to lithium-oin batteries, the short answer is no. However, they can be used to greatly improve the amount of electricity you can get out of one. eg:
http://www.scientificamerican.com/article.cfm?id=carbon-nanotubes-boost-power-of-lithium-battery
 
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