Dear Godfrey Osatohamwen Otabor many thanks for asking this interesting technical question. Before you decide (I assume that you will decide in close cooperation with your PhD supervisor) you should carefully check and read the current literature about this topic. What I want say is that in general this topic is not new, and a lot of work has already been done in this area. Apparently the capture of CO2 using carbon nanotubes is a hot topic which is quite popular. For some relevant articles in this field please have a look at the following publications:
A CO2 Capture Technology Using Multi-walled Carbon Nanotubes with Polyaspartamide Surfactant
Article A CO2 Capture Technology Using Multi-walled Carbon Nanotubes...
and
Comparative Study of CO2 Capture by Carbon Nanotubes, Activated Carbons, and Zeolites
Article Comparative Study of CO2 Capture by Carbon Nanotubes, Activa...
The first article has been posted as public full text on RG and can be freely downloaded as pdf file.
You may focus on calcium oxide for carbon dioxide capture. You may fınctionalize the surface using carbon nanotube for promoting capture efficiency. Literature has many studies on this topic. Good luck with your investigation.