(a) (i) Explain the various steps involved in benzoyl peroxide-initiated polymerization of ethylene to give polyethylene. (10…

Radical polymerization and tacticity. Benzoyl peroxide-initiated ethylene polymerization is a free-radical chain process. Heat or initiator decomposition gives (PhCOO)₂ → 2 PhCOO•; benzoyloxy radicals decarboxylate to phenyl radicals, Ph•. The phenyl radical adds to ethylene, CH₂=CH₂, to give PhCH₂CH₂•, the first propagating radical. Propagation continues as the terminal radical adds to another ethylene, Ph(CH₂CH₂)ₙCH₂CH₂•, extending the chain. Chain transfer is important in ethylene: the growing radical can abstract hydrogen from solvent/impurity or, more importantly, back-bite its own chain to form a mid-chain radical; reinitiation produces short-chain branches characteristic of LDPE, or a dead chain. Termination occurs by coupling of two chain radicals to a longer saturated chain or by disproportionation to give one saturated and one vinyl-terminated chain. Industrially this high-pressure radical route gives branched LDPE, while HDPE is made by coordination catalysts; Indian producers such as Reliance and GAIL use such polyolefin processes for packaging, films and pipes.

Tacticity controls physical properties because phenyl side groups must pack regularly. Isotactic polystyrene has all phenyl groups on the same side of the chain; it packs well, is crystalline, has a higher Tm, greater density and stiffness, and is less transparent. Syndiotactic polystyrene has alternating phenyl groups; it is less regularly packed than isotactic but still semi-crystalline, with moderate Tm and strength. Atactic polystyrene has random stereochemistry, cannot crystallize, is amorphous and transparent, has no Tm, and its Tg is about 100°C, similar to the stereoregular forms; it is softer and used for disposable cups and packaging.

Photochemical formation of B and C. For the drawn A, a bicyclic hydroxy ketone in which the tertiary alcohol at the ring junction is positioned to reach the carbonyl, hν excites the C=O to an nπ* singlet and then triplet state. The excited carbonyl is strongly polarized: the carbonyl carbon is electrophilic/radical-like and the α-carbon has enolate/radical character. In the pathway to B, the hydroxyl oxygen, hydrogen-bonded to the carbonyl, attacks the excited carbonyl carbon; the C=O π bond opens to oxygen. Proton transfer from the attacking OH to the carbonyl oxygen and radical/electron recombination give the neutral bicyclic hemiacetal/lactol B, in which a new O–C bond to the former carbonyl carbon has closed a five-membered oxygen-containing ring and the original C=O is now an ether/alkoxy linkage. In the pathway to C, the excited carbonyl undergoes intramolecular α-H abstraction (Norrish–Yang type) to a ketyl–enolate 1,4-biradical. The hydroxyl oxygen then attacks the α-carbon; collapse of the enolate and loss of the proton from oxygen form the C=C bond between the former carbonyl carbon and the α-carbon, giving bicyclic enol ether C. Thus B and C are regioisomeric photochemical cyclization products of A: B is the lactol from O–carbonyl bond formation, C is the enol ether from O–α-carbon bond formation.

Reaction sequence and NaBH₄ mechanism. A is cyclohexanone. NaBH₄/MeOH reduces it to cyclohexanol; acid-catalysed dehydration of cyclohexanol gives B, cyclohexene. Reagent C is NBS/hν (allylic bromination), converting cyclohexene to 3-bromocyclohexene. mCPBA epoxidizes the double bond to D, 3-bromocyclohexene oxide, correctly named 2-bromo-7-oxabicyclo[4.1.0]heptane. In the first step, a hydride from BH₄⁻ attacks the planar carbonyl carbon of cyclohexanone while the C=O π electrons move to oxygen, forming a tetrahedral alkoxide–boron intermediate. Methanol protonates the alkoxide to give cyclohexanol; boron remains as borate ester/borate by-products rather than being regenerated. Attack can occur from either face; in the chair-like product the equatorial alcohol is favoured, but cyclohexanol rapidly ring-flips.

The overall sequence shows how radical, photochemical and ionic mechanisms convert simple functional groups into polymers, cyclic ethers and epoxides; in Indian industry the same logic underlies polyolefin and polystyrene manufacture, where control of chain structure determines packaging, insulation and pipe performance.