This is a cool idea. Strangely I think this was too long...
The idea of the 100 word post (as I understand it) is to give the skeleton, and let others flesh it out in their mind, or in their setting.
Great idea, I just think it could be better refined into a 100 words or better expanded into a longer post.
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Also, I think you meant that instead of the in the first line.
Clever concept. I was thinking that these could be used to grow crops in the vacuum of space. Basically infinite farmland. But it looks like you're shooting at a source of O2 and sugar (and possibly energy). That's actually a really cool idea, but why can't we have both? Green Sleeves seem more than capable vessles to accomplish food, oxygen, and energy.
I can think of a great number of uses for something like this, the first that comes to mind is as the power source for navigational beacons and bouys around star systems and and for interstellar travel. The power requirement to just run a basic ping is pretty low, and if it has a few capacitors it can charge up and release fairly 'loud' navigational pings. Some other ideas include powering scientific observation satellites, the sort of thing a starship would zip up and kick out and move on, while scientists elsewhere receive and decipher the data. Good thing for long term observations, or for providing satellites to frontier level worlds and colonies. It doesn't carry a lot of data, but a satellite with a bucky core could serve as the seed of global communications.
You've managed to make the battery novel, not an easy task.
I could see them used as an auxilliary battery in starships, something equivalent to having a second battery in your car to power just the lights. Although, in the case of spacefaring, it would be better served as life support. The incredibly long lifespan would mean that even used-spaceship buyers wouldn't have to worry about replacing them.
A few alternate wide spread uses for them:
-Gravity plating on starships: A nice emergency back up to keep gravity functioning at .3-.6 G's or so during a catastrophic system failure. While far from earth normal being able to move about normally allows crews to better effect repairs then attempting to maneuver in zero gravity.
Atmospheric terraforming equipment Perfect to run the gargantuan terraforming installations on uninhabitable worlds, as these batteries take very little maintenance, and will operate the terrafomring equipment reliably for the 100+ years it takes to turn a plant habitable. (and keep it that way.)
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Escape pods: While not generally the primary power supply, a bucky battery can provide sufficent power to a cryo capsule and maintain it's functionality for immense time spans, perfect to allow ample time for the pod to be rescued, or travel as slower then light speeds to an inhabitable planet. (Something that could take decades if not centuries depending on the location it is launched from and end velocity.)
A nice short and simple sub with widespread implications and use in a scifi world. Creative characters/players can no doubt find plenty of way to use "bucky bats" to optomize their ship and/or equipment.
A intuitive Gm can find plenty of places they would come in handy to make spacefaring society run smoothly.