Nanoporous carbon-based scaffolds or structures, and specifically carbon aerogels and their manufacture and use thereof. Embodiments include a cathode material within a lithium-air battery, where the cathode is formed of a binder-free, monolithic, polyimide-derived carbon aerogel. The carbon aerogel includes pores that improve the oxygen transport properties of electrolyte solution and improve the formation of lithium peroxide along the surface and/or within the pores of the carbon aerogel. The cathode and underlying carbon aerogel provide optimal properties for use within the lithium-air battery.