Three stages:

Initiation: Benzoyl peroxide (C6H5COO)2 → 2 C6H5COO* (homolytic cleavage at 60-80 degC). The radical attacks the C=C of monomer: R* + CH2=CHX → R-CH2-CHX* (new radical at chain end).

Propagation: Chain radical adds to another monomer: R-CH2-CHX* + CH2=CHX → R-CH2-CHX-CH2-CHX*. Repeats thousands of times. Each addition is exothermic (pi bond broken, sigma bond formed).

Termination: (a) Combination: two chain radicals couple — R* + R* → R-R. (b) Disproportionation: H-atom transfer between two radicals → one saturated + one unsaturated chain end. (c) Chain transfer: radical abstracts H from middle of another chain → branching (this is why LDPE is branched — radical polymerization at high pressure).

HDPE uses Ziegler-Natta catalyst $\frac{TiCl4}{AlEt3}$ instead of free radicals → coordination polymerization → linear chains with no branching → higher density, crystallinity, and melting point.