Calculation of Water Transfer

[tadeoori]

Hi Guys,

I have a problem that I'm a bit stumped with...

I have a polymer surrounding an analyte that I wish to keep dry. Think of an M&M, where the chocolate is the analyte and the candy coating is the polymer. The unit will be submersed in salt water. I'm trying to model the rate of moisture uptake by the analyte. For example, let's assume the analyte is of a rather high molecular weight, like 100 kDa.

I'm a bit confused as to how to approach the problem. Let me explain what I've done, and perhaps my conundrum will become clear.

I have the WVTR for the polymer coating (typical g*mil/100 in^2/24 hr/atm type measurement). I can calculate the rate of water vapor transfer via WVTR*area*(p2-p1)/thickness, where p2 is the vapor pressure of water on the outside and p1 is the vapor pressure of water on the inside. But can I do the calculation when I'm submersed in water? Is being submersed the same as being in 100 % RH?

In a very short time, once a little bit of water reaches the analyte, the vapor pressure of the water (calculated via Raoult's law, i.e. via molar fraction) approaches 100 % RH, and this suggests that the rate of water vapor transfer would decrease substantially. However, if I calculate osmotic pressure, there is a high osmotic pressure in the analyte that will want to draw in more water. Experimentally, I find that the analyte draws in a lot of water and liquid water forms, and this happens at a rate much higher than I calculate using the equation above.

I'm I approaching this the right way? I'm trying to reconcile the WVTR calculation using partial pressures and the steady state result predicted by osmotic pressures. Osmotic pressure calculations don't give me a rate of transfer, and I'm concerned that the rate calculations don't take into account the osmotic pressure.

Perhaps Raoult's law isn't the right way to calculate the vapor pressure of the water, considering I'm staring with dry analyte? Since the mole fraction of water increases very rapidly (18 g/mol for water, versus 100,000 g/mol for the analyte), the model predicts a very small percentage of water uptake over a long period of time, however, experiments suggest the analyte draws in a lot of water and the uptake is much more rapid than my model predicts.

Perhaps I need to stick to diffusion calculations using chemical potentials of water, or something like that?

Any help or suggestions on how to reconcile these various ideas would be greatly appreciated!

Thank you,
Tadeo

 

[Demon3]

A couple of comments.

First modeling is only of use if it allows you predict something so you can save time and money doing the experiment. That doesn't seem to be the case here.

The literature values you have for the permeability may not apply when the polymer is submerged. Polymers can swell when in contact with liquid and the permeability will increase dramatically.

The answer, assuming this is a real-world problem is to use a different polymer, coat the polymer with e.g. a plasma deposited SiOx coating or cross-link the polymer to lower permeability. Another option is to add a platy filler to the polymer.

When I drop my M&Ms in a puddle I usually just go buy another pack (sorry, couldn't resist).

Chris DeArmitt - PhD FRSC CChem
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[tadeoori]

Hi Demon3, thanks for the quick response!

Yes, the purpose of the modeling is to predict something. There are many variables in the system I'm describing that I can manipulate that I didn't go into here: the polymer, of course, the composition of the analyte, the allowable amount of water uptake over a given time period, etc. Of course, experiments are being conducted in parallel, but understanding the physics is not isolated to modeling, but will also provide direction for the experiments.

The key is to understand the physics.

For example, does the osmotic potential of the analyte affect the rate of transfer? Or is it the vapor pressure of water? How do I calculate the vapor pressure of water when being absorbed into the analyte?

These are gonna be goooooood M&Ms!

Thanks again!

 

[IRstuff]

If your shell is supposed to keep your stuff dry, it seems weird that you'd be burning calories predicting mechanism of the intrusion

TTFN
faq731-376

 

[patprimmer]

What polymer have you used and how are you applying them.

Have you listed polymers by water vapour barrier properties.

Some of the polymers with the best theoretical barrier properties are quite fragile and or quite difficult to mould and might not be giving you an intact coating with no physical pores at the micro scale.

Regards
Pat
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[tadeoori]

Hi IRstuff, the question is dry for how long?? Dry is relative. There's very few materials that would keep it bone dry forever, and none of them are polymers. If I don't understand the mechanism of intrusion, I can't predict the relative performance of various implementations.

Hi patprimmer, yeah, I've been looking at their water vapor barrier properties, but if in a solution, is WVTR the appropriate way to approach the problem?

I don't mean to be difficult, but I would like to keep the discussion more focused on theory than the various experiments I've performed... If someone were to ask whether XX were theoretically possible, experimenting isn't a good way to answer the question. All you could say is that what you tried didn't work. How many times have you accomplished something that someone else assumed wasn't possible. ;-)

 

[patprimmer]

But I tried it and it did work. I don't really know why is generally a not ideal, but acceptable answer in the real world.

Are you sure your theory and practice don't line up is because your theory is wrong. My suggestion is the lack of correlation might well be error with the practical test procedure.

I would have thought the relevant theoretical considerations are.

Diffusion rate through the matrix.

Concentration gradient.

Temperatures.

Affinity for water between the two surfaces or driving force

Is there an air interface inside the container so the moisture is being transferred from water, through plastic to air then to analyte.

It does not help that I have no idea what analyte is other than it must be very hygroscopic.

My money is on some sort of porosity in the plastic due to method of encapsulation.

Regards
Pat
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[btrueblood]

No, water vapor transmission is not a valid model for liquid water.

 

[tadeoori]

btrueblood, do you know what a valid model for liquid water would be?

 

[btrueblood]

I'd think diffusion as you have alluded to. I don't know of any big depository for diffusion coefficients of liquid water through polymers, and yes I've looked. As Chris and Pat have mentioned, the processing of polymers and pore sizes developed have a lot to do (almost as much, if not more, than the formulation) with the permeability of polymers. Chris (Demon3) would be a very good guy to talk to, or better yet, hire, to help you research and find the most cost effective solution for your needs.

 

[tadeoori]

Yeah, I would, too... But I have been researching water diffusion through polymers with regard to osmosis and I've found some interesting papers that state rather emphatically that water flow due to osmosis is bulk flow rather than diffusion. Makes sense, when you consider that a hydrostatic pressure equal to the osmotic pressure will halt the flow of water.

In fact, my research has shown that osmosis is a poorly understood phenomenon. Thermodynamics predicts accurate results, but there is no valid kinetic model that doesn't break down on closer examination.

I think bulk flow jives with pores within the polymer, or perhaps even more fundamental, the structure of the polymer allows bulk flow on a sub-microscopic level. (I've seen analysis of water diffusion refer to "clustering" of water molecules as an explanation for deviations in diffusion constants at different relative humidity. Perhaps the clustering accounts for bulk flow phenomena, as well?)

I'm thinking now that I could measure the flow of water through the polymer due to an osmotic pressure gradient, as calculate the time course with the osmotic pressure differential being the driving force.

I'll keep Chris in mind.

Thank you for the input!

 

[Demon3]

Take a potato and cut a pocket in it and fill that with table salt. It will fill with water due to osmosis. I don't see that as bulk diffusion. The water's coming out through the cell walls.

Chris DeArmitt - PhD FRSC CChem
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[tadeoori]

Yeah, it's coming out of the cell walls due to osmosis, but probably not via diffusion... Probably via bulk flow through "holes" in the cell wall (aquaporins). The rapid destruction of red blood cells when placed in DI water was one of the motivators that suggested there were water channels in cell walls.

 

[IRstuff]

Osmosis just gets it out past the wall, filling the hole still requires diffusion. Even though osmosis is treated as a pressure driven problem, the pressure arise from the concentration gradient, and diffusion is concentration gradient driven.

As a first order, you could possibly estimate the diffusion coefficient of the polymer based on the moisture uptake:

http://www.fpl.fs.fed.us/documnts/pdf1999/liu99c.pdf

TTFN
faq731-376

 

[patprimmer]

IR

I am not sure affinity and diffusion are directly related although affinity impacts on diffusion in that it alters equilibrium.

My understanding of diffusion is that it can only truly happen at the individual molecule level.

I never studied or seriously considered osmosis, so I will not comment in that regard.

Regards
Pat
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[cloa]

Why does the shell have to be a plastic?

 

[tadeoori]

IR, I used to think that osmosis was a concentration gradient driven process, i.e. diffusion, as well. Turns out, there is considerably controversy on this subject. As an example from one of the papers that I read, they mention that there are solutes known to *increase* the concentration of water (by causing water molecules to cluster around the solute), yet still generate the osmotic pressure one would expect.

Water, being incompressible, would require tremendous pressure to increase the concentration. For very, very dilute solutions, I might be able to see the concentration increasing sufficiently due to hydrostatic pressure to balance concentration gradients and halt diffusion. But it seems unlikely, and I am becoming more and more skeptical that osmosis is diffusion based.