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Homogeneous dispersion of carbon nanotubes (CNTs) in polymers has significantly improved their processing and application as nanomaterials. Generally, CNTs tend to agglomerate due to their high aspect ratios and strong van der Waals interaction. Surface functionalization appears to be a solution to this problem. This study presents a controlled dispersion of carbon nanotubes in polyethylene through surface modification using a mixture of concentrated acid and octadecylamine (ODA). CNTs were characterized by Fourier transform infrared, Raman and X-ray photoelectron spectroscopy, and transmission electron microscopy. The results confirmed that carboxyl and alkane groups were successfully introduced on CNT surfaces. The acid- and amine-functionalized carbon nanotubes were dispersed in four solvents with different polarities (water, ethanol, acetone, and xylene) to correlate the degree of dispersion of CNT with their polarity. The results showed that CNT dispersion stability strongly depends on solvent and carbon nanotube polarities after the functionalization step. The nanohardness and tensile tests showed that the addition of CNTs, especially the functionalized with ODA, leaded the polymer harder, increasing its Young’s modulus and tensile strength. However, its toughness and deformation capacity were reduced. The potential applications of CNT-based polymer nanocomposites broaden considerably due to the surface engineering of carbon nanotubes.