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Covalent surface modification of multiwall carbon nanotubes leads to enhanced nanotube dispersion in the polymer. Despite this, the mechanical properties of electrospun fibers made of polymethylmethacrylate containing surface modified nanotubes generally fall below those of fibers with pristine nanotubes, sometimes below those of pure polymer fibers. We show that covalent functionalization produces defects in the graphene structure, leading to mechanical weakening of the nanotube and, therefore, of the nanocomposite.