Air is (mostly) nitrogen and oxygen. Atmospheric air also contains water vapour. Oxygen diffuses through the tyre casing faster than nitrogen so removing the oxygen means that the pressure in the tyre drops slightly slower over time. Slightly. Temperature effects are far more pronounced. Nitrogen is inert for all practical purposes. Oxygen under pressure, especially if combined with water vapour, is corrosive if the water vapour condenses. I’ve not seen an alloy wheel with internal corrosion for many years, and the TPMS will be suitably sealed. Applications where maintaining a fixed pressure is critical (racing cars, aircraft, construction equipment) may benefit from the reduced pressure adjustment frequency resulting from nitrogen fill. For the rest of us, just checking the tyre pressure and topping up/bleeding off with air as the ambient temperature changes (and do it on shaded tyres, not tyres soaking up direct solar energy) must surely be perfectly adequate, especially as we can read pressures in the car. There might be a case for using the heavier inert gases such as argon which could possibly offer some convective heat transmission effects but this is esoteric stuff for anything but world speed record attempts.
The most important thing is just to have the right tyre pressure for the conditions on the day. What’s in the tyre is pretty irrelevant, so long as it remains a mostly inert compressible gas; chlorine is likely to be a bad idea . A liquid might be interesting but wouldn’t do much for unsprung weight and ride might be, well, a little harsh, though I’d like to try a freon or similar gas that liquefies at low pressure, just to see what happens. Could even use propane but the flammability is a bit of an issue.
The whole discussion will soon be academic anyway as we move to airless tyres like the Michelin UPTIS which is due on the market in 2024.
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