Which of the following polymers is synthesized using a free radical polymerization technique?

We start by recalling the basic theory of how different polymers are prepared. In polymer chemistry there are two broad routes:

1. Addition (chain-growth) polymerization, which is usually initiated by a free radical, a cation or an anion. The most common initiators in undergraduate courses are free radicals, generated, for example, from benzoyl peroxide or azo compounds. In a free-radical process, an initiator radical first attacks an unsaturated monomer containing a carbon-carbon double bond, creating a new radical at the chain end, and the chain grows rapidly by repeatedly adding more such monomer units.

2. Condensation (step-growth) polymerization, which involves the stepwise reaction of bifunctional (or polyfunctional) monomers with the elimination of a small molecule such as $$H_2O,$$ $$HCl,$$ or $$CH_3OH.$$ Free radicals are not involved here; instead, it is ordinary functional-group chemistry—esterification, amidation, etc.

With the theory in mind, we now examine each option one by one and decide whether its preparation mechanism involves free-radical addition or condensation.

Option A - Terylene
Terylene is the common name for polyethylene terephthalate, PET. It is made by the condensation of ethylene glycol $$HO-CH_2CH_2-OH$$ with terephthalic acid $$HOOC-C_6H_4-COOH.$$ During the process, molecules of water are eliminated, indicating a step-growth (condensation) polymerization. No free radicals are used. Hence, Terylene is not synthesized by a free-radical route.

Option B - Melamine polymer
The resin called melamine-formaldehyde is obtained by the condensation of melamine $$C_3N_3(NH_2)_3$$ with formaldehyde $$HCHO,$$ again liberating water. This is clearly a condensation polymerization. Free radicals are absent, so this option also does not match the required technique.

Option C - Nylon 6,6
Nylon 6,6 is produced by condensing hexamethylene diamine $$H_2N-(CH_2)_6-NH_2$$ with adipic acid $$HOOC-(CH_2)_4-COOH,$$ freeing molecules of water in the reaction. Consequently, Nylon 6,6 is another example of a step-growth (condensation) polymer. No free radicals appear in its synthetic route.

Option D - Teflon
Teflon is the trade name for polytetrafluoroethylene (PTFE). Its monomer is tetrafluoroethylene, represented as $$F_2C$$ $$=$$ $$CF_2.$$ Tetrafluoroethylene contains a carbon-carbon double bond, making it an unsaturated molecule. The industrial polymerization follows the typical free-radical chain-reaction steps:

• Initiation: A radical source such as $$ROO\cdot$$ generated from peroxide decomposes, producing a radical that attacks the $$C=C$$ bond of one $$CF_2=CF_2$$ molecule, giving a new radical $$\cdot CF_2-CF_2F_2$$ at the chain end.

• Propagation: The radical thus formed adds to another monomer unit:

$$\cdot CF_2-CF_2 + CF_2=CF_2 \rightarrow CF_2-CF_2-CF_2-CF_2\cdot$$

This step repeats many thousands of times, rapidly extending the chain.

• Termination: Two growing radical chains can combine, or a radical can be trapped by an inhibitor, ending the chain growth.

Because an unsaturated monomer is polymerized through a free-radical mechanism with no elimination of small molecules, Teflon is unequivocally synthesized via free-radical polymerization.

Summarizing our findings:

• Terylene - condensation, not free radical.
• Melamine polymer - condensation, not free radical.
• Nylon 6,6 - condensation, not free radical.
• Teflon - free-radical addition polymerization.

Therefore, among the given choices, only Teflon satisfies the condition stated in the question.

Hence, the correct answer is Option D.