In the underwater scene in Mission: Impossible - Rogue Nation Ethan Hunt is told that he can't take any oxygen tanks because there are metal detectors.
So why does it have to be metal? I know this might be a little bit naive of me, but with all their technology they aren't able to use rubber bags/balloons of air maybe?
Just pump some air into a non-metal container and take it down with you!
Maybe I missed some detail, but was there any other constrains for the underwater scene?
In order to have sufficient air to breathe in underwater situations, the air is very highly pressurized (3000 psi on average). The first and second stage of the scuba regulator work to reduce the level of the pressure to the ambient level for the person using the air.
In order to hold that high-pressure air, it's necessary that the container be made of metal, otherwise it would explode... imagine an over-filled balloon.
At lower pressure levels, it's certainly possible that someone could create a heavy-duty plastic cylinder but many of the fittings on a regulator are also metal, at least in part, so you'd reduce the amount of metal by a huge amount but it still wouldn't be no metal.
Regardless, there's one other problem. Air is extremely buoyant. It does not want to stay underwater... it wants to float. As a test, take a capped, empty three liter soda bottle into a pool and try to stay submerged... it's not easy... and if you do manage to get deep enough, watch it compress under the water pressure.
Part of the benefit of the solid metal - the standard steel tanks generally weigh 30-40 pounds - is that it usually helps counteract this buoyancy. If Ethan had simply taken a plastic container of air down with him (despite likely only getting a couple of breaths), he'd spend a good amount of energy working to stay underwater, against the buoyancy of the air. And the more energy you expend underwater, the more air you need.*
Generally, when you scuba dive, this is counteracted with the weight of your equipment (generally around 50 pounds) and additional lead weights, if necessary. Neither of these are options for Ethan, who can't have any metal on him.
The density of the most dense non-metal is iodine, at 4.933 g/cm3. The density of lead is more than double that, 11.34 g/cm3. To combat the pull of the air, Ethan would have to haul around a ton of iodine... which, again, would take more work and more air. It's simply not feasible.
*In scuba training, they encourage you to move as little as possible and to keep your movements controlled and smooth because you will breathe less and go through your tank more slowly. When I dove in the Caribbean, I would use about 2500 psi at 60 feet over the course of about 50 minutes. Our dive master used half that, only about 1200 psi. Clearly he's a much more efficient diver than I am.
Firefighters use composite pressure tanks that are quite light, so there's no problem with finding non-metallic construction that will withstand SCUBA class pressures.
No, the problem is with the "take it down with you" part. Those firefighter cylinders weight very little in air, but in water they will have negative weight. That is, they float. In fact, a nearly-empty aluminum SCUBA tank will float, just barely. So if Ethan Hunt had a nonmetallic compressed gas tank with him, he'd need to also carry a lot of weight to get and stay underwater. While this could also be non-metallic, he'd need to carry 3-4 times the volume of rock compared to lead weights.
End result? He'd be carrying a small air tank and a couple of bowling balls. And I haven't even gotten to the non-metallic regulator he'd need...
It was entirely feasible for his purpose to bring nonmetal breathing devices:
The gallon of air would have given him enough strength to open the escape hatch.
Of course, this would have rendered the plot less exciting. But to demonstrate how a tiny little preparation could have spared him from dangerous risks, just consider my quick calculation below.
At the depth of around 50 feet underwater, the total pressure is about 2 atm. A plastic container filled with a gallon of air would have reduced to almost 1/2 of its size, which is around 2000mL. The buoyant force due to this is equivalent to the weight of 2000g of water. Since iodine has a density of almost 5 times the water, this would have required 400mL of iodine to balance out force. If I consider the buoyant force due to the volume of the iodine, this would be 500mL.
My point is, he could have brought cheap, nonmetal "equipment" with him so that he could spend more time underwater. He didn't need like 30 minutes to do the job; all he needed was 3 minutes and a few extra seconds. With the gallon of air and a bottle of iodine, he could have easily stayed for 4-5 minutes.
There are such materials as granite, carbon ceramic and graphite, all of which would be able to sustain high levels of pressure, and in the case of graphite be a true future-tech material that could be used in conjunction with some type of stone to counteract the buoyancy issue.
In short, see above for at least 2 viable solutions to a relatively trivial problem...
I think the answer provided by Catija is pretty good even though I'm going to argue that the opposite conclusion is true: in the scenario of MI 5, you absolutely could build a breathing apparatus for Ethan to use without requiring any metallic components. The reason why this is true despite everything in the conventional argument that says it's not being accurate is that people think of answers in terms of existing solutions. Mainly, they focus on that 3000 PSI of pressure held in SCUBA tanks.
The reason why SCUBA tanks are engineered to hold that much pressure isn't because it's some esoteric requirement of underwater breathing technology, it's simply so that a diver can bring about 1 hour of breathable air with them. The technology surrounding basic SCUBA gear is pretty straight forward, really. Bring a bunch of air and some way to consume it at normal breathing rates. The only way to bring a lot of air with you is to heavily compress it, and the only way to consume the compressed air is to step down the pressure to breathable pressures. Tanks and regulators.
So let's think about the regulator. It's comprised of stages that reduce the pressure coming from the tank to what's called ambient pressure, or the pressure surrounding the diver. The first stage connects directly to the tank and it's function is to step down the pressure to an intermediate pressure. This reduction is performed purely by mechanical design that can be explained by some science beyond the scope of this explanation, but the use of metal occurs in the first stage body which will hold the gas, the yoke that connects the regulator to the tank, and the yoke screw that tightens the yoke to the tank. The rest of the first stage components are non-metallic caps and ports. The ports connect the first stage to the second stage, an alternate or "octopus" for giving your diving buddy air if he/she needs it, the pressure gauge, and a low pressure inflator which is part of buoyancy control. We only need concern ourselves here with the second stage.
The second stage contains the mouthpiece divers use to breath air. It's comprised of a purge button that floods the second stage with air to push out any water that might have gotten in, a pressure fine tuning knob that allows the diver to slightly increase or decrease the pressure of air they're breathing, an exhaust valve, and the actual mouthpiece the diver breathes from. Second stages also perform pressure reduction from the intermediate pressure (120-150 PSI) hose coming from the first stage, but on a much less strenuous level and components here need not be metal, and this fact will be the main thrust of my conclusion.
The exact amount of breathing time you get from a full tank of air depends on how much physical exertion you experience and the depth you will be diving to. Divers consume more air the deeper they go, but in the case of Ethan he will never be more than maybe 5 meters deep so gas compression won't be much of an issue. We can assume he will be undergoing some physical exertion though, so let's assume that in net he's consuming twice the amount of air of a typical diver. As I said, a tank typically holds about an hour of air for a shallow (under 10 meters) diver not overly exerting themselves. But Ethan only needs about 3 minutes according to the movie to get in and do his superspy stuff, which is 5% of a full tanks capacity. Doubling that because of exertion means he only needs 10% of a regular tanks capacity, or 300 PSI, for breathing.
From an engineering perspective, this is a much less strenuous requirement than the normal 3000 PSI, and means that all the components that require metal in SCUBA gear can be replaced by non-metallic components operating under only 10%-20% of the pressure requirements, both in the tank and in the regulator. For reference, your typical 2 liter soda bottle is built to withstand 150 PSI, and polycarbonate plastics are widely available (since the 1950's) that have a tensile strength (pressure before it breaks) of around 9000 PSI and a yield tensile strength (pressure before it permanently deforms) of about 8000-9000 PSI. This leaves some wiggle room in the PSI you'd use for this application, which is good because of the way first stage regulators are designed, which uses a rubber diaphragm and a couple of springs in a chamber to step down the pressure to a steady equilibrium flow for the intermediate pressure hose, meaning that there is a minimum pressure required to achieve air flow. You might be able to redesign those pressure requirements for the non-metallic version, but for now let's just say you'll want 300 PSI of additional gas pressure for safety. Ultimately, the material specs suggest that you could go up to 900 PSI without any trouble if required.
This just leaves the buoyancy problem mentioned by others, but like the reduced strength requirements, the fact that we're only bringing in 10%-20% of the regular amount of air means a corresponding reduction in the buoyancy problem. In fact, you could probably put the tank in a backpack and surround it with rocks to counter the negative pressure. Sure, it wouldn't be fun to walk around with out of the water, but underwater it would be a minimal drag and the extra weight would, of course, be countered by the air.
Now, to be sure you'd be cutting it close, with just enough air for Ethan to get in and do his thing and quickly get out, but this is a highly specialized job we're talking about and given the choice between free diving it or taking 3 minutes of air I'd choose the latter every time.
Well the limitation is scientific in nature, You need a material that can sustain the pressure of pressurized air, what balloons do is actually bring the internal gas to terms with the atmospheric pressure by inflating in size(increasing volume), but to sustain a few minutes of breathing you're gonna need a large number of molecules and that's only possible when the gas is possibly liquified and there is no other material barring metals that is scientifically viable towards storing pressurized air.
