Superglue is a runny liquid of small monomer molecules. Spread it thin and within seconds they join into long polymer chains, and the trigger is a trace of water.
Most superglue is ethyl 2-cyanoacrylate, and some brands use methyl 2-cyanoacrylate, which has a methyl group in place of the ethyl. The molecule has a C=C double bond, like ethene, so it can join into a chain by addition, the way ethene makes poly(ethene). One carbon of the double bond carries two strong electron-pullers: a -C≡N group and an ester group with its C=O.
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Those two groups draw electrons out of the double bond, so the CH₂ carbon at the far end is δ+, an electron-poor place. Almost every surface in air carries a film of water a few molecules thick, and water always holds a few hydroxide ions, OH⁻. A hydroxide ion is a nucleophile: its lone pair reaches for the δ+ CH₂ carbon.
As one bond of the C=C opens, its pair of electrons moves onto the other carbon, which ends up with a lone pair and a − charge. The -C≡N and ester groups next to it spread that charge out over their nitrogen and oxygen atoms, which steadies it. The new chain end is a nucleophile in its turn, so it adds to the CH₂ of the next monomer, and the chain grows by thousands of monomers in a few seconds.
Thin layers set fastest
Each chain starts at the surface, where the water is. A thin layer sets within a minute and reaches full strength in about a day. A thick blob sets slowly, because water from the surface takes time to reach its middle. In the tube, the glue stays dry, and a trace of acid mixed in mops up any hydroxide ions that get in.
Skin is always slightly moist, which is why superglue sticks fingers together in seconds. Surgeons close cuts with a related glue, 2-octyl cyanoacrylate, approved for skin in the United States in 1998. Its longer 8-carbon chain makes a softer polymer that bends with the skin.