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Surface interactions between two like-charged polyelectrolyte gels
Due to the migration of mobile molecules and ions, a thin diffusive layer of distributed charge - the electric double layer - forms at the interface between a polyelectrolyte gel and a liquid ionic solution. When two polyelectrolyte gels are brought closely together, the electric double layers overlap and interact with each other, resulting in an effective repulsion. The multiphysics coupling nature of soft gels makes their surface interactions significantly different from the interactions between rigid solids. Using the recently formulated nonlinear theory, this paper develops a continuum model to study the surface interactions between two like-charged polyelectrolyte gels, accounting for the coupled electric, concentration, and deformation fields in both the gels and the liquid. Numerical solutions of the surface interactions are obtained and compared with a qualitative scaling law derived via linearization. The results suggest that the structure of double layers, as well as their interactions, depends not only on the concentration of liquid solutions, but more on the bulk properties of the gels such as stiffness and fixed-charge density. This model also provides insights to the mechanism of the low-friction phenomena on the surface of a polyelectrolyte gel.
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Osmotic pressure due to mixing of ions with solvent
Dear Wei,
Some researchers such as Tanaka et al. (Macromolecules, 1984, 17(12) ) decomposed the osmotic pressure into three parts: osmotic pressure due to mixing of polymer with solvent, osmotic pressure due to mixing of ions with solvent and the osmotic pressure due to elasticity. The osmotic pressure due to mixing of ions with solvent, Pi_ion, was given as Pi_ion=RT(c_i-c'_i), where c_i and c'_i are true concentration of the ith ion inside and outside the gel.Can your free energy of mixing of ions with solvent, W_ion, yield the same expression of Pi_ion? Can the osmotic pressure defined in your this and previous paper be understood as the total osmotic pressure?
Regards,
Jinxiong
Re: osmotic pressure
Dear Jinxiong,
Our osmotic pressure due to mixing (as a part of the stress) is the same as the one you show, it is shown in the last term of Eq. (3) - kT/v*(C+ + C-)/Cs.
I don't see the definition of the total osmotic pressure in Tanaka's paper. He did not decompose the osmotic pressure into the three parts in this paper.
The osmotic pressure mentioned in this paper and the previous paper has two contributions: mixing between solvent and network, mixing between solvent and ions. In the equilibrium of a free-swelling case, it is balanced with the stress contribution from elastically deforming the network (Tanaka called it swelling pressure). It is similar to Tanaka's treatment in this case, although it is not the same in a constrained inhomogeneous deformation state.
Let me know if this resovles your concern.
Thanks,
Wei