Step 1: Understanding the Question:
The question asks us to identify which of the given monomers does not polymerize via a vinyl polymerization mechanism.
Step 2: Key Formula or Approach:
Vinyl polymerization is a type of chain-growth addition polymerization that involves unsaturated monomer molecules containing a carbon-carbon double bond (C=C). The rearrangement occurs when the $\pi$-bonds open up to link with neighboring monomers without losing any small molecular side-products.
Step 3: Detailed Explanation:
Let's analyze the structural nature of each monomer:
(B) Vinyl cyanide (Acrylonitrile, $\text{CH}_2\text{=CH-CN}$): Contains a vinyl group with a double bond. It undergoes vinyl chain-growth addition polymerization to yield Polyacrylonitrile (PAN, or Orlon).
(C) Tetrafluoroethylene ($\text{CF}_2\text{=CF}_2$): A fully fluorinated alkene. The double bond opens up during chain-growth polymerization to form Polytetrafluoroethylene (PTFE, or Teflon).
(D) Ethylene ($\text{CH}_2\text{=CH}_2$): The simplest alkene monomer. It undergoes standard free-radical addition polymerization to form Polyethylene.
(A) $\varepsilon$-Caprolactam ($\text{C}_6\text{H}_{11}\text{NO}$): This is a cyclic amide (lactam) that does not contain a carbon-carbon double bond (C=C). Instead, it polymerizes via a ring-opening condensation mechanism at elevated temperatures to form Nylon-6. Because it lacks a vinyl double bond, it cannot undergo vinyl polymerization.
Therefore, option (A) is the correct choice.
Step 4: Final Answer:
$\varepsilon$-Caprolactam does not undergo vinyl polymerization, which corresponds to option (A).