An extremely high surface area. WTH does that mean?
In a capacitor, you have two conductive plates separated by a dielectric layer to store an electric field. Graphene makes a plate that has a large surface area in a very thin form factor. You can make a very substantial capacitor that way. Super capacitors are already in use to backup CMOS RAM to save configuration info on modern computer devices.
Probably that it’s ALL surface. Every atom is at the surface. There is practically no thickness, no volume to speak of.
Unlike most structures, where there is a thickness which is a practical waste of space when it’s the surface that matters.
Say the structure shown in #5 above was instead, oh, 3 atoms thick (that’s pretty darned thin) - that would have 1/3rd the surface per volume as this stuff does.
Sorta like the difference between, say, writing a book on paper vs stone tablets: if it’s a 100 page book, the paper version is compact while the stone tablet version is utterly useless.
Something that is effectively a two-dimensional plane has a very high surface-to-volume ratio.
You'll need a ladder to charge it.