Fill it and Forget it

Everybody knows that a tire inflated with CO2 loses pressure over time a lot faster than one inflated with regular air, (If you don't know this, try inflating two tires to identical pressures, one with air and one with CO2, then check the pressure in about 3 days. The results will be unambiguous) but as I was re-inflating the tire I zapped with CO2 on the trail yesterday I got to wondering about why.

With the depth of my chemistry experience limited to the three classes I took in college (which, granted, is probably a whole lot more than the average person), my natural intuition is that CO2 would leak more slowly than air (78% nitrogen). I mean it's bigger, right? And bigger things have a harder time fitting through little holes [insert fat-kid or other similarly off-color joke here]. CO2, the ostensibly bigger one, has a molecular mass of 44 while Nitrogen (N2) has a molecular mass of only about 28. Pretty clear cut, right?

WRONG.

Even if my brain had survived the oxygen deprivation from the hundreds of zone4 hill sprints and near-blackout race finishes I've been involved in since college and I remembered that that the molecular mass of an atom often has little bearing on its size (in fact, O, N and C are all within about 15% of each other), CO2 still has THREE atoms in it while nitrogen only has TWO. Last time I graduated kindergarten THREE was bigger than TWO, but no longer!

It turns out that one of the major limiting factors for how fast (or if) a molecule goes through a permeable membrane like your tire is the molecule's "kinetic diameter". Simply defined, the kinetic diameter is the smallest limiting dimension of the molecule. For example, if you have a box with dimensions 12"x6"x"4", the kinetic diameter would be 4". If we look and N2 vs. CO2, both have atoms that are about the same size on their own, and both are linear in configuration. If we believe the kinetic diameter argument, the the fact that the two compounds have different numbers of atoms is of lesser importance, as the longest dimension of the molecule isn't what we should be focusing on. Instead one needs to look at the cross section, where the big clouds of electrons between atoms (in the bonds) are the limiting dimension. You may have seen those nifty little diagrams of pi and sigma bods in chemistry class like this one,

but in reality the electron clouds make big orbs around the nuclei that are not nearly as precisely shaped as the diagram above. Smart people have figured out how to model these orbs in "electron charge density" diagrams.



This is CO2






and this is N2



where the smaller spheres in the middle are the nuclei and the larger orbs are the electron clouds. I was unable to find numbers for the diameters of these clouds, but if one assumes these two drawings are to scale and that the nuclei are about the same size for the two molecules (because they are), then you would expect the N2 molecule to be much larger.

The polarity and overall charge of a molecule also affects permeability, but as these molecules are both symmetric and uncharged one would expect them to behave similarly with respect to those properties.

When thinking about a tire, the partial pressures of the gases matter to the extent that if you have a tire filled only with CO2 other gases from the air will actually want to leak into the tire (wild, right?) because each individual gas wants to equalize its own partial pressure across the membrane, but because the CO2 can get out much faster than other stuff can get in, you have a net loss of gas in the tire even with this factor included.

Some quantitative analysis for permeability in silicone rubber (didn't find a good comparison for butyl) can be found here. For Silicone rubber, the permeability of CO2 was about 11.5x that of N2, which agrees with the empirical evidence that your CO2 filled tire goes flat really fast.

Anyway, there's now a super-secret new product called StayFill that is supposed to have gas molecules so big that you only have to fill your tires once a year. Here's a MTBAction article about it. The stuff is 8.99 for a 25g cartridge, and my first reaction is $18/year to not have to pump up my tires?! But then, thinking about my commuter bike on which I get a flat maybe once every couple years, maybe that's almost worth it...

...and I'm spent.


Image credits:
http://www.cem.msu.edu/~reusch/VirtualText/intro3.htm
http://www.blacklightpower.com/theory/animations.shtml
http://www.discrete-labs.com/compbio/info/caddpaper/caddpaper.html