This looks like it would make a useful material for an electrodynamic tether:
Working with Teijin Aramid, the Rice group has now made carbon-nanotube fibers that have more of the properties of individual nanotubes. They have an electrical conductivity close to copper’s, but are much stronger. They’re not quite as strong as conventional carbon fibers, but they’re much less brittle. And they’re more thermally conductive than metal or carbon fiber. That means nanotube fibers could replace these materials in existing applications in aerospace and electronics, and enable new technologies that take advantage of the fibers’ unique combination of strength, flexibility, and thermal and electrical conductivity. Pasquali envisions washable electronic textiles, lightweight wiring for planes, and eventually, more efficient wires for the electrical grid.