I'm gonna go out on a limb and say you killed it. If it broke at the bottom half way through, its likely you severed the pathways for the nutrients from the roots and I don't think its reparable. Even if it was, I don't think duct tape would be the bandage of choice. I'd take the tape off and use maybe like a wet paper towel or something to hold it. If its too heavy to hold by itself, maybe try using some kind of splint held on the top and bottom with twist ties. You should use something wet I would think.

I could be wrong (and probably am). Hope someone can provide a more informed answer.