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Antoine equation for D2O and D2O diffusion measured by a QMS

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Do you need to calculate or are you just looking for values? Values for heavy water vapor pressure in your temperature range of interest exist:

--- Quote ---In a vacuum system, when diffusing D2O through a film and measuring the current on the other side with a quadrupole mass spectrometer, the mass 19 is always higher than the deuterium oxide, regardless of the time of pumping before. Any  idea of why this happens?
--- End quote ---

Could you elaborate on this point, particularly the bolded part? I don't understand what you mean. Maybe describing your experiment setup and what you're trying to do would be helpful.

Hi Corribus,
I could find values and they are in accordance with the paper you gave me, thanks! I was trying to find a way to calculate them, but I think that I'll content myself with the values.

You're right, that was too short.
I have several polymer films, whose I want to evaluate the permeability to water (m/z 18), thanks to a mass spectrometer. In order to differentiate  easily the residual water present in the room and the water used for the measure, I use D2O (m/z 20).
On the graph, m/z 19 is clearly higher than D2O, even if the diffusion is made with pure D2O. Do you have an idea why? (% openening correpsonds to the opening of a butterfly valve that reduce or not the pumping speed in the measuring room)

My off the cuff guess would be exchange reaction to form semi-heavy water, since you have not taken steps to remove regular (not heavy) water:

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.

This sounds like a very complicated and possibly flawed way to do what is a fairly standard assessment of water vapor permeability. Aside from the fact that keeping water and heavy water separate is impossible, you are assuming that water and heavy water have the same permeation properties. This may be true in some cases but particularly in polymers that interact strongly with water, I'm not sure this is a good assumption. At the least, it should be justified. I guess it depends on what kind of error you would be willing to accept. I feel heavy water is unnecessary any way, because you can just baseline the background water vapor concentration, which should be as close to zero as possible anyway, since any water vapor on the other end of the polymer will affect the diffusion/permeation rate.

There are instruments solely designed to make a water vapor transmission rate measurement. Of course, not everyone has one of these. The typical way to do it "poor man style" is to find a container with a circular opening of known cross-sectional area, fill it with a known weight of water, press your film across the opening, and monitor the weight of water in the container as a function of time. As the water passes through the film, the water weight in the container drops. From this you can calculate the transmission rate and permeability of the film. This doesn't work great with films of very low permeability, but it can give you a reasonable measurement of permeability in most cases. It is best to do it in a low humidity, well-ventilated external environment so that you have very little water vapor pressure on the distal side of the film.

(You can also do this the opposite way - put a moisture absorber like calcium chloride in the container, seal with your polymer, and then place the whole assembly in a humidity chamber, measure the weight gain of the absorber over time. I seem to recall the two methods differ in whether you are interested in earlier or later time points in the diffusion curve based on the accuracy of measuring weight gain versus weight loss.)


Here's a method that uses tritiated water to measure WVTR and directly compares to gravimetric method. This may be a better way to go since any exchange of a tritiated water and regular water will result in same species, in most cases you won't be forming something new.

I guess the assumption that heavy and regular water permeation kinetics are identical is probably OK for hydrophobic polymers like HDPE used in the linked study. I'd be more careful with the assumption in cases where the polymer is hydrophilic, since binding capacity/kinetics may be different for heavy water compared to regular water. I didn't find anything to support or refute that based on quick search, but it might be something to keep in mind. This is also discussed a little at the end of the article.

Thank you so much Corribus, this is such a great exaplation! That is very helpful.

We actually did remove as much water as possible, by heating up the whole system to 80°C and having a pressure of 10^-8 mbar into the measurement chamber thanks to a turbo pump. But I guess this is still not enough.

The polymer parylene is actually rather hydrophobic. Which properties should I look at to determine if the binding capacity of the D2O is similar to water?

The study you mentionned is very interesting. If I understood it correctly, it works the same as the measure of total body water with diluted tritiated water. So is it correct when I say that, opposite to the behaviour of D2O, the amount of diluated tritiated water doesn't diminish when it is together with water?

The tritiated water used in the paper is only singly tritiated, not doubly as in your case. Although the paper doesn't say this explicitly, it is probably heavily diluted with water, such that the concentration of HTO is probably quite low. If you have a large amount of water and a small fraction is singly tritiated water, you will still have exchange reactions. There are four possibilities here:
(1)   H2O + H2O = H2O + H2O
(2)   H2O + HTO = HTO + H2O
(3)   HTO + HTO = HTO + HTO
(4)   HTO + HTO = H2O + T2O
Process (1) is trivial and does not affect the concentration of H2O or HTO.
Process (2) and (3) likewise is trivial for the same reason.
Process (4) is not trivial as it affects the concentration of H2O and HTO, but if the concentration of HTO is very low, the effect will be insignificant because the probability of HTO encountering another HTO will be very low.

In your experimental setup, the effect is evidently not insignificant because your fully deuterated and regular water concentrations are both high enough that the probability of exchange events is high. (Although see far below for another idea here.)

The method in that paper detects permeated water vapor using a scintillation counter. An implicit assumption seems to be that the mole fraction of HTO on both sides of the film is the same at all times. Using this assumption they can calculate the total mass of water vapor that crosses through the polymer per time at steady state conditions by scaling with the scintillation rate of known pressures of water vapor. This assumption would fail if:
(1) There is considerable frequency of exchange reactions between different water species (which would occur if the concentration of tritiated water is high).
(2) The diffusion coefficients of HTO and H2O within the polymer are significantly different.
(3) If the gas sorption coefficient (partition coefficient) of the two species are different. I.e., if the solubility of HTO in the polymer is different from that of H2O.
(4) Diffusion is so slow that it is competitive with the radiation half-life of tritium. Which would be impressive since the half-life of tritium is a decade.
(5) If the polymer interacts with water so strongly that it can facilitate proton exchange reactions with HTO.

I think these would only really become a potential problem for a very hydrophilic polymer that has significant swelling in water. Your polymer doesn't seem like it would fit in this category (although you can do a simple swelling experiment - go you have a TGA? - to rule it out).

I wonder - instead of using pure heavy water, have you considered using diluted heavy water (with enough equilibration time to allow must species to be HDO)? This would essentially replicate what they're doing with tritiated water, except you'd be using mass spec for HDO instead of scintillation counting with HTO. You'd just have make some calibration curves to determine the relationship between HDO and total water vapor concentration. The only downside I would see is sensitivity. I'm not sure what concentrations of HDO would be detectable with your equipment. Also, you'd probably have a non-negligible background because there's a sizeable concentration of semiheavy water naturally.

On the other hand, I wonder whether the exchange to form semiheavy water really matters here. If the exchange to form HDO from D2O and water is happening in your source mixture, you can probably still get a good measurement of permeability by scaling your measured concentrations of D2O accordingly. I.e., as long as you know the "constant" concentration/pressure of D2O on one side of the film, and the evolving concentration on the other side, the concentration of other species doesn't matter, as long as it is constant. I would just want to check and see if the mole fractions of HDO and D2O are the same on both sides of the film.

Also, I could imagine scenarios where water may not be the only source of proton exchange. Exchange can happen if protons in the polymer or any polymer additives are labile. (For example, a lot of polymer UV blockers or antioxidants are fully of hydroxyl groups. These could easily undergo exchange reactions with D2O.) Some things to think about.


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