It's no surprise that this actually happens -- probably more often than you might think.
Super glue definitely deserves its name -- a 1-square-inch bond can hold more than a ton. So, what if find yourself in a super-sticky situation?
The main ingredient in Super glue is cyanoacrylate (C5H5NO2, for you chemistry buffs). Cyanoacrylate is an acrylic resin that cures (forms its strongest bond) almost instantly. The only trigger it requires is the hydroxyl ions in water, which is convenient since virtually any object you might wish to glue will have at least trace amounts of water on its surface. Air also contains water in the form of humidity.
White glues, such as Elmer's, bond by solvent evaporation. The solvent in Elmer's all-purpose school glue is water. When the water evaporates, the polyvinylacetate latex that has spread into a material's crevices forms a flexible bond. Super glue, on the other hand, undergoes a process called anionic polymerization. The chemical process of polymerization produces a certain amount of heat. If a large enough amount of super glue makes contact with your skin, it can actually cause burns.
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Cyanoacrylate molecules start linking up when they come into contact with water, and they whip around in chains to form a durable plastic mesh. The glue thickens and hardens until the thrashing molecular strands can no longer move.