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In the case of both Silicon and Oxygen, the double bond is less stable than two single bonds. Consequently, surely both should polymerize, why don't they? What accounts for the difference between Carbon and Silicon in this context?

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Why does $\ce{Si2H4}$ readily polymerize at RTP but ethene does not?

$\ce{Si2H4}$, the silicon analogue of ethylene, is referred to as disilene, a member of the silene family.

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The silicon atoms in disilene are $\ce{sp^2}$ hybridized and the orbitals overlap to form both a sigma and pi bond, analogous to the hybridization and bonding in ethylene. However, the $\ce{Si=Si}$ bond length is significantly over 2 angstroms, whereas the double bond length in an ethylene is much shorter at 1.34 angstroms. This much larger double bond length in silenes results in extremely poor p-orbital overlap which yields an extremely weak silicon-silicon pi bond. While it takes energies on the order of 65-70 Kcal/mol to cause rotational cis-trans isomerization about a carbon-carbon double bond, it only takes 10-20 Kcal/mol to effect similar isomerization about the silene double bond.

Since the pi bond in a silene is so weak it doesn't require much energy to disrupt it making the molecule very reactive, much more so than an olefin. The molecule can polymerize or react with whatever else may be around such as oxygen, water, etc.

Replacing the 4 hydrogen atoms in disilene with bulky groups stabilizes the molecule and allows the molecule to be isolated and characterized. The bulky groups make it more difficult for another molecule to get close enough to react with the disilene pi bond.

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Still, even these sterically protected molecules react with oxygen and water at temperatures not far above room temperature. Here is a link to a full paper that discusses the preparation and reactivity of these sterically protected silenes.

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