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Polyethylene or polyethene is a thermoplastic commodity made by the chemical industry and probably the polymer you see most in daily life. Polyethylene is a polymer consisting of long chains of the monomer ethylene, see about introduction to polymer structure of polyethylene. Polyethylene is created through polymerization of ethene. It can be produced through 3 methods
• radical polymerization,
• anionic addition polymerization,
• Ion coordination polymerization or cationic addition polymerization.
At this post you will learn radical polymerization of polyethene.

Radical polymerization
is a type of polymerization in which the reactive center of a polymer chain consists of a radical. then what is reactive centre
A reactive center in chemistry is a particular location, usually an atom, within a chemical compound that is the likely center of a reaction in which the chemical is involved. In chain-growth polymer chemistry this is also the point of propagation for a growing chain. The reactive center is commonly radical, anionic, or cationic in nature, but can also take other forms (wikipedia)

Technical scale
The necessary pressure is generally kept around 180 to 350MPa and the temperature ranges from 180 to 350 C, The high-pressure polymerization of ethene proceeds via a radical chain mechanism. In this case chain propagation is regulated by disproportionation or recombination.
Radically created polyethene typically contains a total number of 10 to 50 branches per 1000 C atoms. Of these, 10% are ethyl, 50% are butyl, and 40% are longer side chains, Intermolecular and intramolecular chain transfer take place simultaneously

To prevent self-degeneration,
the temperature should not exceed 350C. Ethene
and intitiator are introduced by a piston or membrane compressor. An in-built sapphire window makes it possible to observe the phase relation. After the polymerization is finished, the reaction mixture is released in two steps. Temperature increases are due to a negative Joule Thompson effect. At 26MPa, ethene separates from the 250 C hot polymer melt. After further decompression down to normal pressure, the residual ethane is removed

Initiation is the creation of free radicals necessary for propagation. The radicals can be created from radical initiators, such as organic peroxide molecules, or other molecules containing an O-O single bond or by reacting oxygen with ethene, the polymerization reaction is initiated by three classes of free-radical initiators,

Oxygen or peroxides are used as the initiators. Initiation is very similar to that
in many other free-radical polymerizations at different temperatures according to their half-live times. based on handbook of polymer synthesis, below is half time table of peroxide initiators

you also can see online simulation of radical polymerization by the following link

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