Which one of the following is a chain growth polymerisation?

Polymerisation reactions are classified mainly into two mechanisms.

Step-growth (condensation) polymerisation: Monomers possessing two or more functional groups react step-by-step. Small molecules such as $$H_2O$$, $$HCl$$ etc. are often eliminated. Typical products are proteins, starch, nylon-6,6, polyesters, etc.

Chain-growth (addition) polymerisation: Unsaturated monomers (usually containing $$C=C$$) add to one another through a free-radical, ionic or coordination mechanism. The reaction proceeds via an active centre; high molecular mass polymer is produced rapidly without loss of small molecules. Typical products are polyethylene, polyvinyl chloride, polystyrene, etc.

Now analyse each option:

Option A (Nucleic acid): Formed by condensation of nucleotide units with elimination of $$H_2O$$ ⇒ step-growth.

Option B (Polystyrene): Styrene $$CH_2=CH-C_6H_5$$ undergoes free-radical addition to give long chains without elimination of by-products ⇒ chain-growth.

Option C (Protein): Amino acids link through peptide (amide) bonds with loss of $$H_2O$$ ⇒ step-growth.

Option D (Starch): Glucose units join by glycosidic links with elimination of $$H_2O$$ ⇒ step-growth.

Therefore only polystyrene is produced by chain-growth (addition) polymerisation.

Option B which is: Polystyrene