Forget batteries: think supercapacitors. You can even power a bus with it. Key thing to remember: compared to a regular battery electron density is modest but charging a supercapacitor is a lot faster with much lower losses and more endurance. In a recent Science article El-Kady et al. describe the use of graphene as a potential electrode in a supercapacitor device (DOI). Graphene is a great conductor with potentially a high surface area. Problem to solve: in conventional graphite oxide to graphene conversion, the graphene sheet restack as fast as they exfoliate.
El-Kady deposited an aqueous solution of graphite oxide on a DVD disk, this disk was then laser-irradiated in a conventional DVD drive , converting the GO layer to a graphene layer and then the laser-scribed graphene (LSG) layer was peeled of. This material did not display restacking and a supercapacitor setup was constructed by sandwiching an ion porous PP sheet with an ionic liquid as electrolyte with two LSG sheets and then two PET sheets.
This device is able to deliver 4 volts with an energy sufficient to power a LED lamp for 30 minutes. Charging takes a couple of seconds, it does not lose capacitance with over 10,000 charging cycles. It also endures bending to up to 180 degrees without complaining which is important in potential applications in wearable technology.