Hi Yigu,

Great analysis. There is a distinct difference in them, but both are referring to electrons and its state of being.

Basically, in metallic bonding, we think of it as an electron-sea model is as you described. Electrons just exist in the matrix, as droplets exist in the sea, and moves about freely. This explains the malleability we see with metals. Because its so free moving, we are able to bend and shape it to our will. This is without addition of electric field

With polarizability, this is referring to the atom/molecules capability to produce a dipole moment under the influence of electric field. You see this a lot in dipole-dipole interactions, where because one atom's electrons have more electrons on the left side vs. the right side, other atoms in close contact will preferrentially have electrons move slightly towards the areas where that first atom is deficient in electrons, since opposites attract, and the first atom's positive core is now exposed.

These kind of dipoles occur randomly by chance, or could be caused through polar-bonding in molecules. Larger atoms and molecules are more polarizable just due to the sheer number of electrons that are present. Having more electrons means more chance for that imbalance to happen, and more chance for one side to be significantly more or less charged than the other.

Hope this helps,

Molly