The reaction between fluorinated single-wall carbon nanotubes (F-SWNTs) and branched (M-w = 600, 1800, 10000, and 25000 Da) or linear (M-w = 25000 Da) polyethyleneimine (PEI) yields the covalent attachment of the polymer to the sidewalls of the nanotubes. The resulting PEI-functionalized SWNTs (PEI-SWNTs) were characterized by solid-state C-13 NMR, Raman spectroscopy, X-ray photoelectron spectroscopy, UV-vis spectroscopy, atomic force microscopy, transmission electron microscopy, and thermal gravimetric analysis studies. As expected, the number of polymer molecules per SWNT is larger for low molecular weight PEI than for high molecular weight PEI. However, above 1800 Da, the number of polymer molecules per SWNT does not vary as much. This is supported by Raman spectral data that shows the D:G ratio is relatively insensitive of the molecular weight for M-w > 1800 Da. The PEI-SWNTs are shown to have solubility in aqueous media of up to 0.4 mg . mL(-1). Solid-state A NMR shows the presence of carboxylate substituents that have been attributed to carbarnate formation as a consequence of the reversable CO, absorption to the primary amine substituents of the PEI. Desorption of CO2 is accomplished by heating under argon at 75 degrees C, while the dependence of the quantity of CO2 absorbed on temperature and the molecular weight of the PEI is reported. Under the conditions investigated the maximum absorption of 9.2% w/w is observed for PEI(25000)-SWNT at 27 degrees C. The possible CO2 absorption applications of the PEI-SWNTs is discussed.