Application to Polymer Crystallization

[Erik Anderson]

Hi PRISMS-PF users,

I am very new to phase field modeling and I have been reading papers on application of the phase-field approach to polymer crystallization. I wanted to know if some of the models I'm finding in these papers would be able to be readily implemented in PRISMS-PF. The main things I would be interested in trying to implement would be a model that captures the growth of spherulites both in the bulk phase as well as on particles that serve as nucleation sites. The goal would be to try to create a model that produces similar statistics for the crystallite size distribution, interfacial area, or other observables. 

Sincerely,

Erik J. Anderson

[David Montiel]

Hello, Erik

It sounds like it would be possible to implement a model to simulate what you are describing in PRISMS-PF. 

It would help us If you could share one or more references where such model(s) are described in more detail.

Best,

David

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[Erik Anderson]

David, 

Thanks for the quick response these are some of the models I've been looking at. I've seen a few references that combine lattice Boltzmann simulation to incorporate the effects of flow as well. The main things I would be interested in simulating would be a system where both homogeneous nucleation in the bulk is observed as well as heterogeneous nucleation on a surface also occur.

https://www.sciencedirect.com/science/article/abs/pii/S0927025621004122

https://pubs.acs.org/doi/epdf/10.1021/ma202476t?ref=article_openPDF

https://www.mdpi.com/2227-7390/10/17/3181

Sincerely,

Erik J. Anderson

[Erik Anderson]

Daniel,

Would something like this be possible to encode into PRISMS-PF?

https://www.sciencedirect.com/science/article/pii/S0017931017318823

Sincerely,

Erik J. Anderson

On Monday, September 30, 2024 at 8:48:30 PM UTC-4 dmontiel wrote:

[David Montiel]

Hello, Erik

Looks like your last two messages were identified as possible spam. I will look into the references and get back to you later this week. 

Best, 

David

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[Erik Anderson]

David,

Great! Thanks so much.

Sincerely,

Erik 

[David Montiel]

Hello, Erik

Sorry for the late reply.

Yes, the model described in this paper https://www.sciencedirect.com/science/article/pii/S0017931017318823 can definitely be integrated into PRISMS-PF. For reference, please see the application CHiMaD_benchmark3, in which a very similar model is implemented for dendritic solidification of a pure material. I believe that you would just need to extend the dimensions in the code and the model equations from 2 to 3. 

We are also planning to release an example where convection is incorporated.

Let me know if you have any questions. 

Best,

David

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[Erik Anderson]

David,

One more question specifically on PRISMS-PF's capabilities. So I have been looking at the PDF's associated with the applications and I was looking at the alloy solidification example where you are modeling solidification in a constant temperature gradient. As I was looking through the assumptions for this model, I noted that it is assumed that the temperature gradient is constant because latent heat diffuses a lot faster than the rate at which solidification occurs. While this seems like a very reasonable assumption for metals, I don't think that would hold for polymers that have a much lower thermal conductivity. Can this modeling framework handle both the phase-field and coupled heat transfer problem or is that not supported?

Sincerely,

Erik 

[David Montiel]

Hello, Erik 

Yes, in fact the application CHiMaD_benchmark3 is an example of a model that couples order parameter and heat transfer equations (see equation 5 of the documentation, in which the right-hand side contains a term for latent heat).

Let me know if you have any questions.

David

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[Erik Anderson]

David,

I'm running that simulation right now to see what it looks like and if there are some things that I could adapt for what I want to do. I have a couple questions. 

1. Could I add a noise term to the gradient terms to include the effect of thermal noise in the crystal growth? Would this lead to any numerical issues within PRISMS-PF? 

2. Can the thermal diffusivity be made to be some function of the order parameter?

3. Can I import a volume of some other material that does not undergoing phase change, but is capable of transferring heat. 

3.b Can I make the surface of that volume have a higher nucleation probability?

Sincerely,

Erik J. Anderson 

[David Montiel]

Hello, Erik

Please see my inline replies below. I'll be glad to answer more specific questions about your implementation. 

Best,

David

On Tue, Nov 12, 2024 at 4:54 PM Erik Anderson <ejan...@udel.edu> wrote:

David,

I'm running that simulation right now to see what it looks like and if there are some things that I could adapt for what I want to do. I have a couple questions. 

1. Could I add a noise term to the gradient terms to include the effect of thermal noise in the crystal growth? Would this lead to any numerical issues within PRISMS-PF? 

Yes, but you have to be careful relating the noise magnitude with the element size. This is particularly challenging in adaptive mesh. For an example of how to add noise (although this is done only in the initial conditions) see the spinodalDecomposition app.

 

2. Can the thermal diffusivity be made to be some function of the order parameter?

Yes, this should be trivial, although you may have to derive the weak formulation of the governing equation carefully

3. Can I import a volume of some other material that does not undergoing phase change, but is capable of transferring heat. 

I am not sure I fully understand what you mean by "importing a volume". In principle, you can import any field (though it must be defined in a mesh within a vtk file) using the settings described in the Loading Initial Conditions from File section of the parameters.prm file (see this page for details). This field must also be declared as a field variable in the loadVariableAttributes function of equations.cc.

 

3.b Can I make the surface of that volume have a higher nucleation probability?

Yes, you can make the nucleation probability function dependent on a field that is larger at the surface. See the nucleationModel and nucleationModel_preferential applications.

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[Jason Landini]

I'll chime in for David's 1st point.

The element volume of the cell you're currently working on is available in equations.cc through element_volume in the latest release (v2.4). If you add noise, you can scale it with the element volume to use AMR (adaptive meshing).

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Jason Landini

Ph.D. Pre-Candidate, Thornton Group

Materials Science & Engineering

University of Michigan

land...@umich.edu