Concept:
Chemistry (Polymers) - Addition Polymers and Copolymers.
Step 1: Identify the reacting monomers.
The given monomers are 1,3-butadiene ($CH_2=CH-CH=CH_2$) and acrylonitrile ($CH_2=CH-CN$).
Step 2: Determine the type of polymerization.
Since both monomers contain double bonds, they undergo an addition polymerization reaction. Because there are two different monomers involved, it is specifically a copolymerization.
Step 3: Analyze the reaction mechanism.
The reaction typically proceeds via a free-radical mechanism in the presence of a peroxide catalyst. The double bonds in 1,3-butadiene open up to form a continuous carbon chain, shifting a double bond to the central carbons, while the double bond in acrylonitrile also opens to link with the butadiene units.
Step 4: Formulate the polymer structure.
The repeating unit formed by linking 1,3-butadiene and acrylonitrile is $-[-CH_2-CH=CH-CH_2-CH_2-CH(CN)-]_n-$.
Step 5: Identify the common name of the polymer.
The synthetic rubber formed from Butadiene and acryloNitrile is commercially known as Buna-N (or Nitrile rubber). Here, 'Bu' stands for butadiene, 'na' for the sodium catalyst originally used in similar reactions, and 'N' for acrylonitrile.
$$
\therefore \text{The polymer obtained is Buna N.}
$$