In this type of polymerization,molecules of the same or different monomers add together on a large scale to form a polymer.
The monomers used are unsaturated compounds,e.g.,alkenes,alkadienes,and their derivatives.
This mode of polymerization leads to an increase in chain length,and chain growth can occur through the formation of free radicals or ionic species.
Free radical mechanism: $A$ variety of alkenes or dienes and their derivatives are polymerized in the presence of a free radical generating initiator (catalyst) like benzoyl peroxide,acetyl peroxide,$tert-butyl$ peroxide,etc.
For example,the polymerization of ethene to polythene consists of heating or exposing to light a mixture of ethene with a small amount of benzoyl peroxide initiator.
$1$. Chain initiation step: The process starts with the addition of a phenyl free radical,formed by the peroxide,to the ethene double bond,generating a new and larger free radical.
$C_6H_5-CO-O-O-CO-C_6H_5$ $\rightarrow 2C_6H_5-CO-O^{\bullet}$ $\rightarrow 2C_6H_5^{\bullet} + 2CO_2$
$C_6H_5^{\bullet} + CH_2=CH_2 \rightarrow C_6H_5-CH_2-\dot{C}H_2$
$2$. Chain propagating step: As this radical reacts with another molecule of ethene,a larger radical is formed. The repetition of this sequence carries the reaction forward.
$C_6H_5-CH_2-\dot{C}H_2 + n(CH_2=CH_2) \rightarrow C_6H_5-(CH_2-CH_2)_n-CH_2-\dot{C}H_2$
$3$. Chain terminating step: At some stage,the product radical reacts with another radical to form the polymerized product.
$C_6H_5-(CH_2-CH_2)_n-CH_2-\dot{C}H_2 + C_6H_5-(CH_2-CH_2)_n-CH_2-\dot{C}H_2$ $\rightarrow C_6H_5-(CH_2-CH_2)_n-CH_2-CH_2-CH_2-CH_2-(CH_2-CH_2)_n-C_6H_5$