A method of forming a nanotube grid includes placing a plurality of catalyst nanoparticles on a grid framework, contacting the catalyst nanoparticles with a gas mixture that includes hydrogen and a carbon source in a reaction chamber, forming an activated gas from the gas mixture, heating the grid framework and activated gas, and controlling a growth time to generate a single-wall carbon nanotube array radially about the grid framework. A filter membrane may be produced by this method.