Carbon nanostructures free of an adhered growth substrate can include a plurality of carbon nanotubes that are branched, crosslinked, and share common walls with one another. Under applied shear, crosslinks between the carbon nanotubes in carbon nanostructures can break to form fractured carbon nanotubes that are branched and share common walls. Methods for making polymer composites from carbon nanostructures can include combining a polymer matrix and a plurality of carbon nanostructures that are free of an adhered growth substrate, and dispersing the carbon nanostructures in the polymer matrix under applied shear. The applied shear breaks crosslinks between the carbon nanotubes to form a plurality of fractured carbon nanotubes that are dispersed as individuals in the polymer matrix. Polymer composites can include a polymer matrix and a plurality of fractured carbon nanotubes dispersed as individuals in the polymer matrix.