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Van der Waals Radii / Molecular Geometry to Filter Homogenous Gases?


I was wondering why it's not possible to filter homogenous gases using their molecular geometries?

Oxygen has a Van der Waals radius of 152 pm, Nitrogen of 155, and Carbon 170.

Air is a mixture of O2, N2, and CO2 (sort of*). The diatoms can only stretch or compress in their molecular vibration, but the triatomic CO2 has more ways of expressing vibrational energy. When air is at STP there should be quite a bit of movement in the CO2 relative to the others.

My question is, why isn't it possible to manufacture a cube with a permeable membrane on one face, where the molecular openings are large enough to allow N2 and O2 through but small enough prevent CO2 passage - at least in a statistically relevant way? For example, if you have an input on another face of the cube which increases the pressure of the gas inside, pumping in air under pressure, and the N2 and the O2 can escape (slowly, over time, through the membrane face) then you will eventually reach a high partial pressure of CO2. This seems to me to be an obvious way of concentrating CO2 out of air with a relatively low maintenance (non-energy intensive) process.

One of the things I wonder about is the correct temperature to maintain for ideal effectiveness. Since the CO2 has multiple bonds, it would seem to me to get "longer" faster than the diatomic molecules as it has twice as many bonds to stretch. (Discounting the synchronous asymmetrical situation where the stretch of one is negated by simultaneous compression of the other - after all, we are looking for a statistically relevant solution, not a perfect one!) So I think perhaps an elevated temperature would be more effective.

I'm envisioning something like a sheet of graphene but where the voids are designed to be approximately 160 pm across (from a Van Der Waals radius perspective) and the diatoms wiggle through lengthwise. Maybe as you increase temperature the molecular vibration of the membrane reduces its effectiveness as (is phonons the right word?) energy waves through membrane constructively interfere to create extra large openings. Maybe that would be fixable by layering membrane together, but maybe you would just end up with CO2 molecules plugging it up partway and suffer something analogous to catalyst poisoning?

Perhaps I am overthinking this and there is some simple explanation for why there isn't a filter which can hold back CO2 and allow N2 and O2 through?

Thanks in advance for any replies!

*I have excluded Argon from consideration since it's monatomic but it's 188pm radius could present a problem. I still think cheaply producing a gas mixture of 96% argon and 4% CO2 would be valuable.

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Contributor III

Re: Van der Waals Radii / Molecular Geometry to Filter Homogenous Gases?

First of all, yes, we do have and use membranes for many different gas separations, including carbon dioxide.

Secondly, because any membrane permeability flux is dependent on relative concentrations, extracting/separating 400ppm of anything is not very energetically favorable.

Third, you are using the wrong radii, as the pure element Vander Waal radius is not the same (and larger) than the Covalent Radius that results when it forms a compound like diatomic oxygen (radius 66pm), diatomic nitrogen (71pm) and carbon in covalent bonds (like carbon dioxide) with a covalent radius of 69-77pm, depending on the atomic arrangement.  Linearly, CO2 is 232pm, so besides the similarity in minimum radius to the other air molecules, it has to further orientate itself in a particular direction before it can pass through.

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