Single-walled carbon nanotubes (SWNTs) have been chemically modified through the formation of carboxylic acid functionalities or by grafting octadecylamine and polystyrene onto them. We purified SWNTs with nitric acid to remove some remaining catalysts and amorphous carbon materials. After purification, we broke the carbon nanotubes and shortened their lengths by using a 3:1 mixture of concentrated sulfuric acid and nitric acid. During these purification and cutting processes, carboxylic acid units formed at the open ends of the SWNTs. Octa-decylamine and amino-terminated polystyrene were grafted onto the cut SWNTs by condensation reactions between the amine and carboxylic acid units. The cut SWNTs did not disperse in organic solvents, but the octadecylamine-grafted and polystyrene-grafted SWNTs dispersed well in dichloromethane and aromatic solvents (e.g., benzene, toluene). Composites were prepared by mixing polystyrene with the octadecylamine-grafted or polystyrene-grafted SWNTs. Each composite had a higher dynamic storage modulus than that of a pristine polystyrene. The composites exhibited enhanced storage moduli, complex viscosities, and unusual non-terminal behavior when compared with a monodisperse polystyrene matrix because of the good dispersion of carbon nanotubes in the polystyrene matrix.