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I was wondering how the chemical composition of a synthetic polymer such as nylon results in strength and durability.

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Polyamides (such as Nylon) are molecules containing a large number of amide functions:

Amide function

In those functions, the $\ce{C=O}$ bond is polarized (due to the difference in electronegativity between C and O) : $\ce{^{\delta+}C=O^\delta-}$. The N-H bond is polarized, too: $\ce{^{\delta-}N-H^\delta+}$. This leads to H-bonds between the chains:

H-bonds in polyamides

While H-bonds are weak interactions, their high number (as there are a lot of amides in polyamide chains) leads to strongly bonded chains, which results in increased strength and durability.

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