Insanely-high surface area materials exist, the best example I can think of is activated charcoal https://en.wikipedia.org/wiki/Activated_charcoal#Properties but batteries are using it too http://spectrum.ieee.org/nanoclast/semiconductors/nanotechno... "Solids" like you mention are aerogels https://en.wikipedia.org/wiki/Aerogel#Alumina and this new aerographite http://www.extremetech.com/extreme/133056-aerographite-six-t...