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Large deformation and electrochemistry of polyelectrolyte gels

Wei Hong's picture

Immersed in an ionic solution, a network of polyelectrolyte polymers imbibes the solution and swells, resulting in a polyelectrolyte gel. The swelling is reversible, and is regulated by ionic concentrations, mechanical forces, and electric potentials. This paper develops a field theory to couple large deformation and electrochemistry. A specific material model is described, including the effects of stretching the network, mixing the polymers with the solvent and ions, and polarizing the gel. We show that the notion of osmotic pressure in a gel has no experimental significance in general, but acquires a physical interpretation within the specific material model. The theory is used to analyze several phenomena: a gel swells freely in an ionic solution, a gel swells under a constraint, electric double layer at the interface between the gel and the external solution, and swelling of a gel of a small size.

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Hua Li's picture

Hi Wei,

How is it going? This really is a interesting work, from which I have learnt a lot. Could I have tow questions here?

1) In page 6, you said that "Both the gel and the external solution are included in the domain under consideration", but Eq (2.1) cover the gel network domain only. How to understand that the external solution is covered in your problem domain?

2) It is difficult for me to understand the assumption that the gel is an ionic conductor and also is an electronic insulator (see the pages 6 and 7). Could I have more details info.

Thanks,

Hua  

Wei Hong's picture

Thank you for your interest in our paper, Hua!  Let me try to answer your questions:

1)  For a fluid, Eq. (2.1) is no longer defined. However, since there is not elasticity in the external solution, the displacement field is no longer an unknown needs to be determined.  In the solvent, we only solve for concentration (true concentration) and electric potential.

2) What we mean here is that the solvent is an insulator if no ions are present.  In other words, the gel is only conductive by ion transportation.  There is no free electron as in a metal.  Water molecules, if there is no dissociation, are dielectric and can be polarized when an electric field is present.

Hope these short answers can address your concern.

Wei

Hua Li's picture

Hi Wei,

Thank you for your time.

May I understand that your word "solvent" means the interstitial solvent within the gel? If yes, and see Eq (6.1) for mixing the polymers and the solvent and mixing the solvent and ions, how to understand "if no ions are present"? If no, may I understand that your gel is not conductive by the solvent transportation without ions?

Thanks again,

Hua

Wei Hong's picture

Hi Hua,

The solvent means the mobile molecules in and out of the gel.  For a hydrogel, the solvent is water moleucle (not H+ or OH- ions).  We made the insulating assumption so that we can define the electrostatic energy stored in a gel.

The situition when "no ions are present" is only an extreme I mentioned to help understand the insulating assumption of the solvent.  In this extreme the energy of mixing is not physically meaningful, it has singularity due to the ideal solution model.

Yes, you are right.  The gel is not conductive by solvent transportation alone without ions.

Wei

Hua Li's picture

Hi Wei,

ok, I get your point now.

The reseon I have this question on "solvent" is youe Equations (6.1) & (6.4), which include the term "Wion".

Hua 

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