Yes, this I'd love to hear as well.
First thing first. "air" is already ~80% nitrogen. What you are replacing is the remaining ~20% oxygen with nitrogen. Depending on the relative humidity when you inflate your tires with "air" there might also be a very slight amount of water vapor in there (~ 1%), and trace amounts of some other gasses (C02 being one of them

)
There was some BS at Costco about Nitrogen not leaking out as fast as "air." So, what they're saying is the molecular diameter of N2 is sufficiently different from O2 (it's not) that the leak around the bead and/or valve is significantly different. (Most of the leak is through the valve, the tolerances of which are not measured in Angstroms so both gasses will leak at the same rate

). Thankfully, tires themselves are not appreciably permeable to gasses.
Some other things I've seen written about:
Reducing tire heat and therefore decreasing rolling resistance. WTF? What is the basis for this? Nitrogen and Oxygen have about the same heat capacity. Water does have a higher heat capacity, but, again there is very little water in compressed air (~1%). And all of these gasses behave very close to the ideal gas law at the temps and pressures seen in a street tire.
Oxidation. This one has some truth to it. The INSIDE of the tire and wheel will be exposed to much less Oxygen if inflated with pure N2. So, if you were planning on keeping these items around for long enough to be bothered by the damage caused by this oxidation you should choose Nitrogen. Problem is, of course, you need to put the whole tire/wheel combo into a Nitrogen tank because the OUTSIDE of the thing will still be exposed to air (not to mention road debris, salt, oil, dead animals, paint and other more destructive environmental stuff.)
"But, racecars and jet planes use nitrogen so it must be better." Yes, to the extent that you can run around with a can of portable compressed N2 at very high pressure without a need for a power source or a staged compressor, yes it is better.
Does it sound cool to tell your friends you put nitrogen in your tires?
Yeah, about as cool as having red painted calipers with stock brakes, pads and all-season tires or an //M decal on a 325i.
Personally, I'd like to put Hydrogen in my tires because then when I burn rubber, I'd really BURN RUBBER :2: Or, to bottor from another BS industry, Xenon would be great because then I'd have HID tires!
