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creating/storing/transporting them is much more efficient than transporting full building materials.
Right, it's really small and low density. Maybe it could be synthesized on Mars since there's lots of carbon dioxide.
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One approach I would imagine then would be to first transform the CO$_2$ into CO or methane CH$_4$ before using CVD to form carbon nanotubes...
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Looks like they will be making methane on Mars anyway before building anything permanent.
SpaceX_Mars_colonization_program
Methane was chosen for the Raptor engines because it is relatively inexpensive, produces a low amount of soot as compared to other hydrocarbons,[28] and can be created on Mars from carbon dioxide from the atmosphere and hydrogen via the Sabatier reaction.[29]
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methane
That was my thought too, after reading about the manufacturing process.
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Carbon nanotubes in general (to my admittedly non-physicist knowledge) are synthesized, but creating/storing/transporting them is much more efficient than transporting full building materials.