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Antoine equation for D2O and D2O diffusion measured by a QMS

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Dear Corribus,
Once again, thank you so much for your answer!

Unfortunately, I think that dilution of D2O is not a possibility.  We already have problems with sensitivity (the QMS doesn't have a multiplier) and even at a pressure of several tens of mbar for the D2O, the detection is extremely low.

The penultimate paragraph is very interesting also. The level of pressure before and after the film are actually very different (1*10-1 to 30 mbar before the film, and after around 1*10-7 mbar), so I guess that the mole fractions are quite different. However, do you think there is still a way to calculate which amount of D2O from the begining actually contributes to the signal of HDO and D2O?

After your explanation, considering that our polymer is rather hydrophobic and it doesn't contain any hydroxyl group, I will assume that water and D2O have the same diffusive properties.

Something is still unclear from one of your previous answer:

--- Quote from: Corribus on September 14, 2022, 11:12:49 AM ---
H2O + D2O :rarrow: 2HDO

This reaction is thermodynamically favorable (ΔG ~ -4.2 kJ/mol in gas phase at 298 K based on standard values published at NIST), mostly due to entropy contribution.

--- End quote ---
I understand what it means, but I couldn't find the information myself.
This is the data I found about free energy reactions for water at NIST. I'm afraid to ask, but where did you find the info about its reaction with D2O?

It's a little hard to be real specific because I am still not exactly understanding your experiment (for instance, the figure you supplied above). But just doing a thought experiment here, supposing you start with a single species A on one side of your film, and you end up with two species A + B on the other side of the film, it stands to reason that something is happening while A is permeating through the film. Since both A and B come from A, you might be able to use a mass balance approach and calculate your permeability metrics as the sum of A + B. In principle whatever causes the conversion of A to B would be subject to laws of chemical kinetics so I'd have to think a bit about the assumptions involved. But, it may OK.

Just curious, is there a reason you don't ditch heavy water altogether and just do regular water? If you are pumping your system down to remove atmospheric (background) water, I don't see why you can't just use the residual as a baseline for your measurement. It's the concentration (pressure) difference across the film that matters. If your baseline is the same on both sides of the film, then the baseline can just be subtracted out.

Regarding the Gibbs energy calculation, you can just look up standard heats of formation and standard entropy values for each species (make sure they're at the right temperature and phase). From these you can determine the enthalpy and entropy changes for the reaction, and then the Gibbs energy change.


--- Quote from: Corribus on September 30, 2022, 10:36:43 AM ---Just curious, is there a reason you don't ditch heavy water altogether and just do regular water?

--- End quote ---
Because that was the proposal of my work and now I need to explain why it doesn't work  :)
But I'll surely try with normal water to have a comparison.

Regarding the Gibbs energy, I couldn't get if it was a calculation or a given value, so thank you for the hint!

For the same work, I'll probably need to compare D2O/water diffusion to helium diffusion, both measured with a QMS. Would you say that this is comaprable, or the nature of the molecule and the element are too different?

Permeation of gas through polymer depends on two basic factors: diffusion coefficient of the gas within the polymer and solubility of gas within the polymer. You might crudely think of the diffusion coefficient as being related to how fast individual gas molecules are able to move through transient pore spaces in the polymer (although, to be clear, the diffusion coefficient is not a rate). The solubility coefficient may be thought of as representing how many gas molecules can fit within a certain volume of polymer. To take an analogy, if a farmer is trying to shuttle her goats across a river using a raft, the diffusion coefficient represents how fast the raft can move through the water, and the solubility coefficient is how many goats can fit on the raft. So, even if she can row the raft really fast, if she can only fit one goat on the raft, it will still take a long time to get her goats across the river.

In a Fickian model, the diffusion coefficient is most related to how big each gas molecule is compared to the average pore space of the polymer. Smaller molecules have tend to have larger diffusion coefficients - they can physically move through the polymer more quickly than larger molecules, which tend to collide with polymer strands more frequently. The solubility coefficient is most related to how polar the gas molecule is compared to how polar the polymer is, although size does also play a role here. Solubility coefficients are a little harder to guess at, particularly for molecules that have similar polarity. But in any case, all things being equal: small, nonpolar molecules will permeate through nonpolar polymers faster than large, polar molecules will. And the pore space size of the polymer - which depends not only on the polymer structure but also how it is processed - also makes a big difference.

Consider polyethylene as a typical example. You can see some gas permeabilities, diffusion coefficients, and solubility coefficients here:

Notice, for instance that helium has a much larger diffusion coefficient than argon. Both are nonpolar but the argon atom is much larger than a helium atom, therefore has a smaller diffusion coefficient. A nitrogen molecule is slightly larger than an argon atom and has both a slightly lower diffusion coefficient and a slightly lower solubility. And so on. You can also see differences between low, medium, and high density polyethylene. The higher the polymer density, the less space there is for gas molecules to fit, with consequences to both the diffusion coefficient and (less so) solubility.

On its face, then, you would guess that water, being small and highly polar, would have a large diffusion coefficient but low solubility. Indeed the solubility of water in a nonpolar polymer like LDPE is quite low, which is why polyethylene is such a great moisture barrier (go back to the small but fast raft analogy of getting goats across a river). The interesting thing is that while the diffusion coefficient of water is pretty large (compared to large molecules, say), it is still much smaller than comparably sized nonpolar molecules. For instance, from data I found, diffusion coefficient of nitrogen (size ~300 pm) in LDPE is 2-3 orders of magnitude larger than water (size ~275 pm) at the same temperature. What gives here?

Water is a funky molecule. Whereas nonpolar permeants like helium or nitrogen gas tend to diffuse as individual molecules, it is thought that the strong hydrogen bonding of water combined with the highly hydrophobic LDPE environment means that when water partitions into LDPE, it does so as tightly bound water clusters. So, the effective size of the permeant is much larger than that of individual water molecules, with a correspondingly smaller diffusion coefficient - the diffusion coefficient decreases exponentially as a function of the permeant diameter. Moreover those water clusters may change size as they permeate through the polymer. In this situation diffusion isn't really Fickian any more so a lot of those elementary considerations about diffusion coefficients and permeant size kind of go out the window. You may read more about this here ( | Wang et al. Ind. Eng. Chem. Res. 2011, 50, 6447–6454,

Maybe that helps you think about diffusion and permeation of helium and water through your polymer. Hopefully you are learning that permeation is complicated and more difficult to measure than many people realize. :)


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