adding styrofoam to heavy clary garden soil a good idea?

I am having a hard time dealing with styrofoam. If I buy any appliance I am stuck with the stuff in big huge chunks, and I was wondering what my fellow gardeners thought of breaking it up into small pieces and adding it to the soil to help keep it light and aerated. I double dig as I have heavy clay under my topsoil. What do you think? Couldn't I just dump all my collected styrofoam into the clay subsoil to keep it less sticky? I don't think it would hurt anything, would it? Here I can either send it to the burn plant or the landfill. Both terrible ideas. Thanks for any feedback.