That graph shows grapheme caps topping out at about 4.5 Wh/Kg energy density.
Just for perspective, the best lithium polymer batteries deliver about 250 Wh/Kg.
The power density for supercaps is pretty good though, as is their longevity.
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I’m not getting this. If grapheme caps top out at about 4.5 Wh/Kg energy density....why are they so much more interesting/better/important/powerful than lithium polymer batteries which deliver about 250 Wh/Kg? Isn’t 250 Wh/Kg many orders of magnitude better/important/powerful than 4.5 Wh/Kg?
It’s not the energy storage that’s attractive, it’s the power density. Lithium batteries take hours to recharge. Supercaps can be recharged in seconds (or deliver their whole charge in seconds).
Batteries generally have fairly short lives; this is certainly true with lithium batteries, whose high performance characteristics are offset by the fact that they're really only just barely stable from a chemistry standpoint. There have been a number of spectacular fires resulting from damaged or overcharged lithium batteries; as they age they become less stable; most lithium battery packs include little special-purpose "smart power" chips to keep them from exploding. These chips monitor their temperature, charge state, and other parameters to keep them stable.
For that reason, I imagine that supercaps might find uses in satellites and other applications where maintenance is impossible.