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you physics is a little bit off. Largest potential drop will most likely be in the electrolyte due to the double layer. The drop in oxide is usually pretty small.
To model it correctly, you will need explicitly specify the equation for the double layer.

you physics is a little bit off. Largest potential drop will most likely be in the electrolyte due to the double layer. The drop in oxide is usually pretty small.
To model it correctly, you will need explicitly specify the equation for the double layer.

Thanks. I see your point. As for the equation you are talking about for the double layers: I think I can make two more rectangles at both ends near the oxide, which will represent the double layers in the electrolyte and I can set the charge density in those rectangle to p = N * [exp(-q*u(r)/kT) - exp(q*u(r)/kT)]...with p = charge density, N = bulk ion concentration in the electrolyte, and u(r) being potential....that equation is the boltzmann equation for charge density in an electrolyte with a given ion concentration.

Would that be a valid way to insert the effect of the double layer into the overall model and then solve Poisson's equation for the whole?

You can use double layer equation in the entire electrolyte layer. Also be careful as the potential u(r) from the double layer is not the same as the one you will compute with COMSOL. u(r) should be a function defined for your electrolyte that includes screenings length and other electrolyte parameters.

You can use double layer equation in the entire electrolyte layer. Also be careful as the potential u(r) from the double layer is not the same as the one you will compute with COMSOL. u(r) should be a function defined for your electrolyte that includes screenings length and other electrolyte parameters.

Thanks. I sent you a private message with more details and my model. I seem to be getting the wrong results by using the Poisson-Boltzmann equation for the entire electrolyte layer...in my current results, ALL the applied potential drops in a small double layer and is 0 in the bulk. This is wrong...the double layer should not drop ALL the applied voltage...the drop should be small...the potential in the bulk electrolyte should be close to applied voltage...NOT 0. What am I doing wrong?

Maybe the key is in your warning about u(r)...could you please show me what you mean by the u(r) for the double layer not being the same as the one computed by COMSOL? How can both potentials be de-coupled?

I didn't get any private message, sorry. Better post directly here next time.

Are you sure that you are not confusing potential and electric field? E should be zero as ions will always move in such a way to zero it. It might be non-zero in the case when you have huge potential drop across the electrodes and there are no enough ions to neutralized the potential. Zero electric field means constant potential. That's what you should be getting.

To do it correctly in COMSOL, you should define a variable charge density that is a function of potential on the electrolyte-oxide interface. But that potential is not function of distance as you showed. In other words, your u(r)=const and does not depend on variable u (potential) from COMSOL. Instead, define charge density as exponentially decaying with distance function.

I think that is exactly what I am doing now. The potential in the charge density term is dependent on the potential at the boundary or interface...NOT the dependent variable u. But I am not getting the right result.

I am using the Gouy-Chapman equations on this site: www.ee.ucl.ac.uk/~mflanaga/java/GouyChapmanStern.html#s1.1.2

I have two interfaces to the electrolyte...one is the metal where the voltage is applied and the other is the oxide-electrolyte interface. I know the applied potential at the metal-electrolyte interface but not the surface charge density...but the surface charge density can be related to the potential at the interface by the equation in Section 1.1.2 (website above). Now, for the oxide-electrolyte interface, I know the surface charge density but not the potential...but the potential can be calculated for a known surface charge density by the equation in Section 2.1.2 (website above)...I make this calculated potential a dirichlet boundary condition at the oxide-electrolyte interface.

But the problem is there are 2 interfaces but only 1 electrolyte domain...and I can only define one source term for Poisson's equation in the electrolyte (charge density dependent on interface potential). So basically, one interface gets ignored because the I can only put in the potential of one interface in the charge density source term. Do you see what I mean? Please have a look at the model file...it will be obvious there.

I cannot attach the model here...but I uploaded it offsite...here is the download link for the model: www.adrive.com/public/BxMvSx.html

Sorry, can't open your model due to firewall: "Your request to URL "www.adrive.com/public/BxMvSx.html" has been blocked"

Hi

it's much easier to upload the model to the FORUM, try a edit Clear all solution Clear all mesh reset model and save witha new name, then upload the cleaned file mostly it arrives here ;)

--
Good luck
Ivar

AHA! Apparently the forum doesn't like firefox...I kept getting the file extension error because I was trying to upload with firefox. I tried with Chrome and it worked!

Please see the attached model Alexander. Thanks a lot for your continued guidance.

Now I can open it. Why in your model file you have only 2 domains? According to the very first picture you uploaded, you should have 5. Then the right setting would be to use one Poisson's equation for electrolyte and the second equation for other 4 domains. Then only for the electrolyte domain you should include source term. And only set one ground BC and one Dirichlet BC with Vapp. You don't need to set anything in between.

And general comment about the mess with units you have. Go to Poisson's equation Settings and change units to "Electric Potential (V)". Then make sure to get rid of those yellow-highlighted expressions by using correct units. For example, you expression for "Dirichlet Boundary Condition 3" gives NaN when evaluating it. Once your expressions turn from yellow to black, you can be sure in them. In general it helps to avoid unnecessary errors.

And finally, there is no need to simulate such long domain as your problem is y-symmetric. You can even use 1D geometry to solve this problem.

I am attaching the revised model. I took care of the units...sorry, it was a careless mistake. I guess I really need help with the physics...the potential in the electrolyte in the result becomes much higher than the applied voltage...and I feel it is not correct because the charge density term doesn't use the correct potential and it ignores the second interface.

The top domain is oxide, then electrolyte, then oxide and then silicon. The top and bottom boundaries of the stack are applied potential and ground. I have defined 3 Poisson equations. The oxides are assumed to have some internal charge. Si is modeled with internal depletion charge. And I have used the modified Poisson-Boltzmann equation for the electrolyte. I am using the equation described in the attached comsol conference paper. I also double checked the equation with Kornyshev's paper titled "Double-Layer in Ionic Liquids: Paradigm Change?"...he actually acknowledges you in that paper! I keep checking my equation and it is correctly input and matches the equations in those papers...but I get a strange result. Could you please take a look?

I also have these key questions:

1) What about the other double layer at the second interface (bottom oxide-electrolyte interface)? The charge density defined for the electrolyte domain using any double layer equation is defined dependent on the surface potential at an interface...so the equation is technically only valid for one interface.

2) Due to the top oxide dropping some of the applied voltage, the charge density term in the electrolyte is actually wrong because I use Vapp. In reality it should be the potential at the top oxide-electrolyte interface, which is only calculated after the potential drop in the top oxide...so how do I do that?

No, I don't think its me who mentioned in Kornyshev's paper. I don't know him personally. Just a coincidence, I guess :)

You improved your model but still didn't do it as I suggested in my previous message. I believe that after you do so, you should be getting something very close to real situation. What you have now is wrong in several places.

And again, make sure you completely get rid of those yellow-highlighted expressions by using correct units.

To your questions:
1) You charge density in entire electrolyte domain should be defined as sum of two exponents: exponent for positive charge at one of the interfaces and exponent for negative charge at the other one. Both exponents are function of distance y.
2) Potential drop in oxide should be pretty small in your geometry. First, I'd ignore it. Then define a variable for potential on electrolyte surface and solve two coupled equations using it.

Sorry I keep asking so many questions. I'm very new to both comsol and electrolyte modeling...and there is a big disconnect between what I need to do the develop the model and what I read in papers...so I'm learning as I go. I've been trying to follow papers until now...I've read about 10 of them...all of them are only concerned with one interface and so they only include one charge in their charge density term...I guess this is exactly where the key difference is. I'll try with the charge density term including both charges.

1.) But I'm afraid I still don't know exactly what you mean by the exponents being a function of distance y...I've never seen that in papers. I suppose its a special condition for me because of the 2 interfaces and the fact that I'm trying to use the double layer equation for the WHOLE electrolyte? Do you mean include position "variables" in each exponential so I can pre-define where they go to 0, so that at one interface one of the exponentials always goes to 0? Like below?:

charge density in electrolyte = ((q*z*N*Cb) / (eps0 * epsrwater))* (exp1+exp2) [N = avogadro's number, Cb is bulk ion concentration]

exp1 = exp ( (q * Vapp * Pos1) / (k*T) ) -> exponential for top oxide
exp2 = exp ( (q * VIntf2 * Pos2 ) / (k*T) ) -> exponential or bottom oxide

Pos1 = 1 and Pos2 = 0 at top oxide-electrolyte boundary
Pos1 =0 and Pos2 =1 at bottom oxide-electrolyte boundary

OR can you provide a reference where I can read about this approach?

2.) You suggested to define a "variable" for potential on the electrolyte surfaces...I've would like to define VIntf2 (in equation shown above) as the potential at the bottom oxide-electrolyte interface. Do I do this with the local variable? I read the Comsol User Guide section on variables but I'm not sure how to define a variable that will store the value of a dependent variable (potential) at a boundary while the simulation is running. I tried define a local variable with geometric scope only at the interface boundary with expression VIntf2 = mean(V) but it is not working.

1) charge density in the electrolyte is given by c1*exp(-(y-y1)/c2)-c3*exp((y-y2)/c4) , where constants c1-c4 depend on the properties of your electrolyte and y1 and y2 are the coordinates of two boundaries. What you are writing is the charge density at one point (at the interface).

2) I believe the best way will be to use coupling variables for that. There are plenty of discussions on the forum about using them.

Ah! I see now...I should have understood this earlier! You opened my eyes. I fully understand what you mean now. You're modeling the charge density at each point in the domain with a sinh(y) function with appropriate coefficients. Although I think I will try to make the charge density a cosh(y) function because the charge at both oxide interfaces is the same sign. I'll let you know how it goes.

Dear All,

I am trying to simulate a structure electrolyte/oxyde/semiconductor. I would like to plot potential profile in this structure.

You said that the charge density in the electrolyte c1*exp(-(y-y1)/c2)-c3*exp((y-y2)/c4), but how will change.
Sir Krutarth Trivedi, it is possible to give your model resolution to be able to know more


Could someone please help? I really appreciate your time!

Hi,
Did anyone get a working model for the Electrolyte-Insulator-Semiconductor system. I urgently need help to model this. Please help.

Thanks in advance
Anup Kumar