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What can I use for a diaphragm in an air cannon?

I've built a pretty good air cannon before, but I want to go bigger and better.
I saw this guy who used a rubber-like diaphragm to release air into the chamber, but I don't know what I could use for that, or if you can just buy something like that.

It shows how this works here:
http://www.xinventions.com/main/spud/how_a_spud_gun_works.htm

 Check out the link given in the spud gun url:
 http://www.xinventions.com/main/spud/pac5.htm1/4"
which says, "Hard neoprene with cloth insert (1000PSI) was used for the diaphragm material. This material is much stronger and is actually pressure tested to withstand the extreme pressures. Do not use wetsuit neoprene for it is far too weak."

I get an uncomfortable feeling looking at the design.  It might blow up in your face.  Be careful!