Reactive, chemical connections, which exist separately are called monomers.
Monomers are low-molecular and will be combined by a chemical reaction to branched or unbranched polymers.
Most monomers do have a C=C double bond.
Plastic melt might contain residual monomer. At higher temperatures, they will evaporate, which can be realized in many cases by its smell.

Monomer in Injection Molding

Plastic: Single Ethylen-Monomers

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This glossary of plastic industry is provided by PLEXPERT Canada Inc.