Looking for an adhesive, glue, epoxy, whatever that will bond a soft thermoplastic polyurethane and a neoprene closed cell sponge rubber. Any wisdom from the forum on this front?

I highly recommend you search 3M transfer tape. when you get to the 3M website, you can select the two substrates and it will filter down to the transfer tapes recommended for the application. I am assuming you are looking to bond 2 sheet-like materials together.

If not, you should go to Loctite website and do the same thing for liquid adhesives. they can also provide a compatibility cross-reference.

be warned, that using incompatible adhesives between two plastics can create a real gooey mess since the reactive chemicals in adhesive will often "melt" and\or attack the plasticizers and UV stabilizers found in flexible plastics. Make sure you know exactly what the plastics are. Ex: santoprene and neoprene are similar but not the same, santoprene is a modified neoprene but doesn't have the same compatibility with adhesives.

Ken

Not sure it is what you're looking for but I have used Aquaseal many times to glue pockets on my wetsuits. Never had it fail. Wetsuits have worn out and the pocket I glues on is still on there. Tried to remove a pocket off an old suit once. No-go that stuff was too strong of a bond.

Aquaseal

3M™ Neoprene High Performance Rubber and Gasket Adhesive 1300
but make a small test panel as always for this type of bonding the actual components matter.

 
Barge is a contact cement used by saddlemakers, and will bond just about anything to just about anything else. I forms a very strong bond.

I work with shoes & orthotics & we use Barge. There a a few different ones depending on your intended uses. Of all the things I do, gluing is what I am least confident with doing. With Barge, you have to apply it to both surfaces & wait til it feels almost dry. I think I don't wait long enough so I usually set a timer. Every time I have set a timer, it works. Go figure. Barge is made to glue things together that still need to flex & bend.

Great suggestions. Thank you.

I will also add that with wetsuits and I'm not sure how close that is to what you're doing getting the material flat and smooth is very important.

I would also lay a piece of cardboard and then books on what I glued. The books for weight and the cardboard to protect them in case any glue made a mess.

I'm actually trying to devise a cell phone mount for my mountain bikes that damps vibrations. There are very few (one, that I can find, really) solutions out there. The only viable one I can find is the Quad Lock Out Front Pro, really intended for road bikes. If I combined that with their dampener, really intended for motorcycles, it achieves the desired effect. But that setup won't allow me to mount a phone where I want it.