I only own one microwave and I use it to make food in. Not really equipped to experiment making membranes. If someone has a spare they're not afraid to fry, they'd be hero to the cause.
From the patent they say gamma rays or ions. Let's call microwaves ions for our purposes. So we evacuate the air, nuke the polyethylene sheet. Maybe a few times. I think we want it to look aged/yellowish but not melted, so probably medium to low setting, for like 10 minutes at a time? The micro-cheese holed plastic when soaked in acid, gets sulfur atoms that attach to the main polymer chain/backbone. Those are what conduct the sulfate ions. Otherwise the material is fairly impervious.
Keep it in vacuum until ready to soak in acid. Actually only .5% - 1.5% acid, in trichloethane. (Don't know if trichlorethylene would work but rhymes with poly-ethylene; available in paint dept. of hardware stores.
Weak acid supposedly causes more uniform sulfonation throughout the material. Water not recommended, contains oxygen, that competes with sulfer atoms.
How long to soak? Says one hour, then raise temp and soak for another hour, then soak in acetone or other solvent, then evaporate, and wash in water to remove any acid. One example they sulfonated for 5 hours. By guess and by gosh I'd say.
Sides of plastic milk jugs might be cut into 4" disks, would fit nicely into PVC pipe, H - cell design. Laminated layers.
Good one Kevin!