Someone will be along to correct me any minute now, but...
My understanding is that a capacitor stores charge in the dielectric
between a pair of plates.
A battery involves electron exchange chemistry.

My (limited) understanding is that graphene in a capacitor is being used to
either alter the small scale structure of the plates such that you can
increase effective plate area, and/or as a secret sauce in the dielectric
to increase the dielectric constant.

I read a pamphlet once (tm) that talked about using graphene in batteries
as a sort of "scaffold" to mechanically support the rest of the device.
e.g. it wasn't actively involved in the chemistry.

Add salt to taste. :-)

-Denny
--=20
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