Polypropylene $($PP$)$ is placed in a solvent at $20C$ below its $-$temperature of $28C.$ You

notice the PP precipitates in solution at this temperature, forming globular particles with a

radius $R_{gl}.$ Assuming the globular PP particles do not interact and can be treated as

monodisperse hard spheres, what is the excluded volume of the PP "particles" $(v_{PP})?$ Assume

the degree of polymerization, $N=1500,=66,l=0\mathrm{.}154nm.$