A free-standing membrane comprises a plurality of vertically aligned carbon nanotubes, each of the plurality of vertically aligned carbon nanotubes having a first terminus at a first side of the membrane and a second terminus at a second side of the membrane. The first and second terminuses are exposed. The free-standing membrane comprises a non-conducting, inert filler material disposed in the interstitial space between the nanotubes such that a barrier to electron, proton, and/or ion transport is formed, and so that conduction of electrons, protons, and/or ions only occurs through the plurality of vertically aligned carbon nanotubes and not through the inert filler material. Methods for fabricating the membrane comprise nanotube growth, epoxy coating, and exposure of the terminuses of the nanotubes.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
 The disclosed invention was made with government support under grant number DE-FG02-09ER16121 awarded by the Department of Energy. The government has certain rights in the invention.