II$.(10$ pts$)$ Chain configuration

$($a$)$ Briefly explain the difference between configuration and conformation?

$($b$)$ Assume there are $3$ isomers $($e$.$g$.$ cis$-,$ trans$-,$ vinyl$-)$ of a monomer. You synthesized $5$

grams of polymer from these monomers $($with molar mass $100\frac{g}{m}ol)$ with degree of

polymerization $N=100$ by adding monomers randomly to the growing chains. What is

the probability that you synthesized two identical chains? Explain briefly.

$($c$)$ Consider the polypropylene molecules with different stereoregularities shown below.

Identify which polystyrene is atactic, syndiotactic and isotactic.

$($d$)$ Suppose these polymers are heated to form amorphous melt and then rapidly cooled

below their glass transition temperature. You notice that one of these polymers is fully

transparent while the others have white$-$ish color due to scattering from crystalline

regions. Which polymer forms the fully transparent glass? Briefly explain. Solve all please:$)$