|water / oxygen diffusion through OLED multilaminate|
Posting by Jasper Michels on 01 Oct 2008 at 14:34:13.
In the framework of thin film flexible electronic devices (think of OLED's and polymer based photovoltaics) I'm interested in a theoretical description of transient diffusion of a vapour through material interfaces of multilaminates of different materials, that each have a different solubility coefficient towards this vapour. e.g. How does the vapour accumulate at the interface? What does the surface concentration discontinuity look like as a function of time? etc.
Does anyone know any relevant literature on this?
follow up posts
Many thanks for your post.
I think the following case: hydrogen diffusion in polyamide on steel is of your interest. Specifically the part on diffusion, and probably the analytical multilayer solution presented in the appendix.
One comment to this concept paper (originally produced for JEC Composites in April 2008): if the interface between two layers is tight, you may assume that the solubility coefficients are governed by Henry's Law. If the interface is not tight, you have to add another "sheet" (vacuum in this case) to the laminate. In this specific case it is shown that both situations do not have a large influence on the total mass flux and time lag. However, this depends on the specific configuration and materials used.
Sijmon van der Wal
Thanks for your reply. Your reference on multilayer diffusion is helpful. I'd like to check whether I understand things by posing a little case:
If you put two layers of different materials together (Henrian interface), each with their own solubility coefficient S and both layers contain the same initial diffusant concentration, will there then be a spontaneous redistribution of the diffusant over the two layers until C1 = S1/S2 * C2 (with a concentration discontinuity at the interface)? This means that there is transport of material despite the absence of an (initial) concentration difference?
Looking forward to your answer,
Yes, correct. The ratio S1 / S2 is in diffusion literature often denoted as K, the distribution coefficient. K is dependent on temperature and pressure.
The concentration is indeed discontinuous. The rate at which the discontinuous equilibrium is obtained, depends on the layer thickness and diffusion coefficients in each layer.
However, if one material swells at the interface of two materials, the swelling stress usually exceeds - if no adhesive, surface roughening etc. is present - the interfacial strength (interfacial surface energies). Hence, holes appear, and the interface is not Henry like anymore.
In case of one sided water diffusion, in 50 micrometer polyimide, used as a solar cell substrate, the swelling stress at the subsequent material interface is zero - during a day-night cycle - due to the dual mode character of water diffusion in polyimide. Note that specifically high barrier polymers, like epoxy resin, liquid crystalline polymers and polyimide, demonstrate dual mode sorption (the diffusion rate is so slow that other phenomena like internal adsorption become visible...).
Sijmon van der Wal
Thanks Composite Analytica for the valuable feedback. I have some additional rather fundamental questions / remarks on diffusion, time lag and water /oxygen / carbon dioxide / nitrogen transmission rates through mutilayer laminate structures under exterme high pressure (50 to 100 bar). The materials we are interested in:
- Aluminum oxide (transparant Al2O3) on top of Polyethylene Naphthalate
- SiOx (Quartz) - Polyethylene Terephthalate (plasma coated PET)
- Aluminum oxide - Polyimide - Aluminum Oxide
- HDPE - Ethylene Vinyl Alcohol Polymer (EVOH) - HDPE
The question are as follows:
- What is the physical meaning of time lag? Time lag and breakthrough times are often used to indicate the tightness or barrier performance of a laminate, but the interpretation of the figure varies.
-Can you determine the time lag (or a better defined constant, see my first question) of a multilayer composite (say 3 layers) under high pressure (so swelling of layers may take place or the dual mode sorption as you showed us...pretty good stuff you did, I must admit ;-])?
-Sorry to bother you with a question on water vapour transmission rates. As I know you don't like them; is this due to the fact that the underlying moisture diffusion coefficient is key to barrier questions? At least time lag and final mass transfer or package migration are related to the diffusion coefficient and the squared thickness of a sheet of laminate. Solubility (only) seems to govern the type of diffusion process (Fick, Flory Huggins etc.)...?
Thanks for the follow-up. My apologies for the fact that I haven't got much time to study your post or for putting the library figures in the IDC â€“ SAC simulation program.
Time lag is a practical measure for breakthrough time of chemicals diffusing through a layer. But realize that time lag isn't the time that the first molecules appear. They appear much faster on the other side than the "lag" time, and the first molecule will be on the other side within one second...(read more on this in Einstein's article on Brownian Motion). If the first molecules are already causing problems in the application (which is possible) the Penetration theory for diffusion will be more helpful than the time lag theory.
Time lag origins from experimental determination of permeation rate, diffusion coefficient and water solubility. In this method (e.g. ASTM E96, ASTM D1434, ASTM D471) a plane sheet is exposed on one side to the chemical (or chemicals mixture) and subsequently being continuously measured (with a mass spectrometer MS or gas chromatography GC) on the downstream side of the sheet. From extrapolation of the detected mass, the diffusion coefficient is determined can be determined using the time lag formula.
Regarding time lag for multilayer structures. They can be determined using the chemical-physical simulation tool, as well as for example the total water permeation in aluminum oxide and polyimide layer.
Sorry, this is all for now. In the forthcoming post on moisture and oxygen diffusion in multilayer laminates, I will add the explanation and graphs for determining time lag in multilayer composites or laminate materials.
Further to my posting yesterday, hereby the method for moisture or oxygen time lag calculation for a multilayer laminate. The time lag (or "breakthrough time") follows from:
(1) The stationary chemicals concentration profile in the laminate. The concentration graph enables calculation of the mean square displacement. Note that in case of anomalous moisture permeation steady state concentration profiles are curved (inward for dual model sorption, outward for Flory Huggins, etc.)
(2) The mean overall diffusivity. Again in case of anomalous diffusion, the diffusion coefficient isn't often constant, hence the weighted average diffusivity as function of the chemical activity (potential) or concentration.
Thanks this is very helpful. We will be in touch shortly.
I really appreciate your questions on this nice forum... Can you explain what the high pressure has to do with moisture and gas diffusion in solar cell substrates / polymer based photovoltaics ;-)?
Secondly, I want to add something. If we would really go green, why not suggest a bio plastic for solar cell substrate material? What do you think of a multilayer laminate composed of polylactide or furan based coating resins (i.e. SiOx plasma coated)? Can you perform time lag and mass flux calculation, especially with regard to water, for these composite plastics also?
Keep up the good work!
The 50-100 bars pressure was for accelerated ageing weathering conditions for diffusion, permeation and chemical corrosion, but is obviously wrong. Nevertheless, I am curious to accelerated exposure conditions concerning water, oxygen and carbon dioxide. Hence, let us increase temperature from ambient to say 80 degrees Celsius. I am sure CheFEM is able to transpose these figures back to more ambient environmental conditions using some sort of William - Landel - Ferry (WLF) equation (the WLF formula should be adjusted for the glassy polymers) and something more...
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