Addition Polymerisation and Polythene (LDPE, HDPE)

Addition polymerisation (also called chain-growth polymerisation) builds a polymer by repeatedly adding molecules of an unsaturated monomer -- one containing a reactive $\text{C=C}$ double bond -- to a single growing chain, with no atom lost in the process; the polymer's molecular formula is therefore simply an exact multiple of the monomer's formula, e.g. $n\ \text{CH}_2{=}\text{CH}_2 \rightarrow -(\text{CH}_2-\text{CH}_2)_n-$ for polythene from ethene.

Free-radical mechanism. The industrial synthesis of polythene from ethene proceeds through a three-stage free-radical chain mechanism, closely paralleling the free-radical halogenation of alkanes met earlier in organic chemistry. Initiation: a small amount of an organic peroxide initiator (e.g. benzoyl peroxide) is heated to generate a reactive radical, $\text{R}^{\bullet}$, which adds to one ethene molecule's $\pi$ bond, opening it and generating a new, larger radical: $\text{R}^{\bullet} + \text{CH}_2{=}\text{CH}_2 \rightarrow \text{R--CH}_2{-}\text{CH}_2^{\bullet}$. Propagation: this new radical is itself reactive and adds to another ethene molecule in exactly the same way, and this step then repeats itself thousands of times over, each addition extending the SAME growing chain by one more $-\text{CH}_2-\text{CH}_2-$ unit and regenerating a radical at the growing end: $\text{R--}(\text{CH}_2\text{CH}_2)_{n}{-}\text{CH}_2{-}\text{CH}_2^{\bullet} + \text{CH}_2{=}\text{CH}_2 \rightarrow \text{R--}(\text{CH}_2\text{CH}_2)_{n+1}{-}\text{CH}_2{-}\text{CH}_2^{\bullet}$. Termination: the chain finally stops growing when two radical chain-ends collide and combine (or disproportionate), consuming both radicals without generating a new one. …