Addition polymerisation involves double bonds reacting to give chain growth, usually initiated by free radicals. Polycarbonate synthesis is NOT addition polymerisation.
The synthesis of polycarbonate is a step-growth polymerisation, from most often bisphenol A and phosgene to make LEXAN™.
The first step in the synthesis of polycarbonate from bisphenol A is treatment of bisphenol A with sodium hydroxide. This deprotonates the hydroxyl groups of the bisphenol A molecule, this deprotonated oxygen reacts with phosgene to form a chloroformate. The chloroformate is then attacked by another deprotonated bisphenol A, eliminating the remaining chloride ion and forming a dimer of bisphenol A with carbonate linkage and two molecules of sodium chloride.
Repetition of this process yields polycarbonates, hence step growth polymerisation.
Addition or chain growth polymerisation needs a monomer and initiator and gives a ploymer chain.
Condensation or step growth polymerisation need two different types of chemical to reacts to give a polymer chain plus small molecules such as, but not always, water.