However, I have just consulted my HSC Conquering Chemistry textbook, initiators are mainly used for the production of Low Density Polyethylene(LDPE) and within the textbook, it clearly states that in this process the 'initiator' is not strictly a catalyst because it gets incorporated into the actual polymer formed-one initiator molecule per one or two polymer molecules, equivalent to 2000/3000 monomer units. Because by your deduction that it gets removed-then it will not be called an 'initiator' but rather a catalyst-since catalyst doesn't get consumed in the chemical reaction it is speeding up, and in this instance, I don't think the initiator can be classified as a catalyst in the scientific sense of defining a catalyst as a substance that accelerates the rate of a chemical reaction without being consumed by the reaction.
I think rather than the removal of the organic peroxide-addition of inhibitors or lowering the pressure and temperature, or when the free peroxide radicals attached monomer chains collide to combine to form non-activated species-which results in chain termination and stops the polymerisation process seems to be a more logical process. I have consulted with various HSC chemistry textbooks and they seem to suggest that the OP is on the right track.
Chemistry Contexts says this:
"Production and uses of low-density polyethylene
The polymerisation process consists of three stages: initiation, propagation
and termination. During the production of LDPE, the reaction is initiated
with a catalyst, usually an organic peroxide. These peroxides produce free
radicals (molecules with at least one unpaired electron). The radical R–O•,
where R represents an alkyl group and • represents an unpaired electron,
is electron defi cient and attacks the double bond in the ethylene. This
causes one of the bonds between carbon atoms in the CH2=CH2 molecule
to break, and a covalent bond is formed between one of the carbon atoms
and the radical. The resulting molecule, R–O–CH2CH2• , is itself a radical
and will attack the double bond in another ethylene molecule, resulting in
the ‘addition’ of another –CH2CH2– group. This process continues and so
the polymer chain rapidly grows. These reactions are referred to as chain
propagating reactions.
As the chains grow, they often curl back on themselves so that the radical end
of the chain removes a hydrogen atom from a CH2 group within the chain, as
shown in Figure 2.21. This leaves the within-chain group with an unpaired electron
which will react with an ethylene molecule, and so a new branch will begin to grow
from this point. This process, called ‘backbiting’, results in branches being formed
approximately every fifty or so atoms.
At various times it is possible for two free radical polymers to react to form
a covalent bond. This type of reaction is called a chain terminating reaction".
It says catalyst but it doesn't refer to anything about it becoming engulfed. Then again, Contexts could have possibly not included that piece of information that it is engulfed in the chain.
Need a few more confirmations :/