Certain specific embodiments of the invention will now be discussed. For example, a process of preparing a copolymer composition that includes a diene-modified polypropylene copolymer is described, which process includes: contacting a metallocene catalyst compound with a polymerization medium that includes at least a propylene monomer and 2-methyl-1,5-hexadiene monomer or an .alpha., internal non-conjugated diene monomer; and conducting polymerization of the monomers in the presence of the metallocene catalyst compound for a time sufficient to provide a diene-modified polypropylene random copolymer that includes monomeric units derived from each of the monomers, and having from 0.0 wt % to 2.0 wt % ethylene and a heat of fusion of 25 J/g or more.