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Polymer composites containing variable amounts of multiwalled carbon nanotubes (MWNTs) have been prepared using solution dispersion and melt-shear mixing. Various polymer composites with 1 wt % MWNTs have been found to dissolve homogeneously in organic solvents. The amount of polymer coated or wrapped MWNTs dissolved in the solution was quantified using UV-vis absorbance at 500 nm and the concentration ratio of [MWNTs]solution/[MWNTs]composite was close to 1. A nonspecific polymer adsorption through multiple-weak molecular interactions of CH groups with MWNTs in the composites has been identified through FTIR spectroscopy. The composites of polybutadiene with different wt % of MWNTs showed slight changes in the CH bending vibrations, indicating the presence of intermolecular CH-π interactions. The dissolution of various polymer composites containing low concentration of MWNTs in organic solvents was attributed to polymer coating on the MWNTs via noncovalent and nonspecific CH-π interactions. The dissolution of MWNTs in organic solvents using common polymers used in this study indicates that the coating or wrapping is a general phenomenon occurring between polymers and carbon nanotubes.