Certain specific embodiments of the invention will now be discussed. For example, a process of preparing a polymer composition that includes a branched crystalline diene-modified polypropylene random terpolymer is described, which process includes: contacting a metallocene catalyst compound with a polymerization medium that includes at least a propylene monomer, a first diene monomer, and a second diene monomer; and conducting polymerization of the monomers in the presence of the metallocene catalyst compound for a time sufficient to provide a branched crystalline diene-modified polypropylene random terpolymer 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 30 J/g or more.