A few more notes: carbon black is is not your ordinary chimney soot, but a different variety. It forms during incomplete combustion of some kinds.
It is quite conductive electrically and self-organizes into fractal tree-like structures inside cracks within drying cement. They predict that 45 cubic meters can store 10 KWh of energy - but large scale studies haven't been made yet.
I don't currently know what dielectric material they used between two castings of cement, but I imagine they used some type of plastic. It should be noted that you need a fair amount of carbon:
the “sweet spot” is around 10 percent carbon black in the mix