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Polyelectrolyte gels

Polyelectrolyte gels. Yuhang Hu Advisor: Zhigang Suo May 21, 2009. Based on Zhigang’s notes, ucsb talk and an on going paper by Zhigang, Wei and Xuanhe. Outline. Introduction (microstructure and applications)

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Polyelectrolyte gels

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  1. Polyelectrolyte gels Yuhang Hu Advisor: Zhigang Suo May 21, 2009 Based on Zhigang’s notes, ucsb talk and an on going paper by Zhigang, Wei and Xuanhe

  2. Outline • Introduction (microstructure and applications) • A field theory of gels coupling large deformation and electrochemistry of ions and solvent • Homogeneous field in the interior of a gel and solution • Inhomogeneous field near interface between gel and external solution

  3. solution polyelectrolyte + - - + + or weak polyelectrolyte strong polyelectrolyte Polyelectrolyte gels = polyelectrolyte + solvent hydrogel + - - - - + + + + • Network • Solvent • Fixed ions • Mobile ions http://en.wikipedia.org/wiki/Polyelectrolyte

  4. Articular cartilage Negatively charged proteins Repulsion retain water during compression. And thus maintain small friction. 4

  5. Ion-exchange resin 5

  6. Field theory of polyelectrolyte gels coupling large deformation and electrochemistry of ions and solvent

  7. Electrochemical potential Electrochemical potential: Mechanical work done by bringing one ion from a standard state to a specified concentration and electric potential electrolyte • work done by the pump, mdM • work done by the battery, Fdq • Helmholtz free energy, F equilibrium Ions, dM neutrality electrons, dq battery, F pump, m electrode Gibbs (1878) standard electrolyte

  8. System = gel + weight + battery + pumps work done by the pumps work done by the weight work done by the battery Helmholtz free energy of the gel l Applicable to a single macromolecule, a cell or a large system

  9. deformation gradient Inhomogeneous internal field x(X, t) Marker X • nominal concentrations Reference state(Dry state) Current state • nominal electric field x(X+dX, t) Free-energy density ground

  10. A field of weights: stress Define the stress siK, such that holds for any test function i (X) Apply divergence theorem, one obtains that in volume on interface

  11. A field of charges: electric displacement Define the electric displacement, such that + + + - - - + holds for any test function z(X). Apply divergence theorem, one obtains that in volume on interface

  12. A field of pumps: conservation of ions Number of ions is conserved: in volume on interface The above two equations is equivalent to holds for any test function

  13. Total net electric charges fixed mobile in volume by pumps by battery on interface 13

  14. Work done by the weights Work done by the batteries Work done by the pumps Work done to a gel a field of weights, pumps and batteries

  15. Thermodynamics of non-equilibrium processes Free energy density change of the gel element: Free energy change of the composite system: work done by weights work done by batteries work done by pumps Thermodynamics:

  16. Local Equilibrium: Kinetic law: 16

  17. Summary of equations A field of markers A field of batteries A field of ions & molecules A field of weights A field of charges A field of pumps net electric charges Local equilibrium Kinetics law equilibrium

  18. Free energy function Free-energy function • Free energy of stretching • microscopic effect • Swelling increases entropy by mixing solvent and polymers, • but decreases entropy by straightening the polymers. • Redistributing mobile ions increases entropy by mixing, • but increase polarization energy • Free energy of mixing • Free energy of dissolving ions • Free energy of polarization (Ideal dielectric material) Flory-Rhner

  19. = + + - + - + + - - Vdry + Vsol = Vgel Incompressibility of particles va – volume per particle of species a Assumptions: • Individual solvent molecule and polymer are incompressible. • Gel has no voids. • An ion occupies a same volume in the solvent or in the gel

  20. Equations of state solvent ions

  21. Using the field theory to study different regions in polyelectrolyte gels and solution system • In liquid far from interface between gel and solvent • In liquid near interface • In gel far from interface • In gel near interface

  22. Solution far from interface – liquid electrolyte Infinity in liquid State equations In equilibrium & Π=E=D=0

  23. Solution near Liquid-gel interface _ _ _ _ _ _ _ _ infinity + + + + + + + + 0 x gel solution General solution: Debye length: LD When |Φ| << kT/e fast decay electric field in liquid near interface Stress near the interface Negative surface tension!

  24. Gel far from interface - free swelling infinity in gel Infinity in liquid Electric field vanishes and electric charge neutral gel swells uniformly incompressibility

  25. Gel far from interface - free swelling Concentration of fixed ions Swelling ratio nonionic gel Concentration of ions in external solution

  26. Gel near Liquid-gel interface Inhomogeneous field _ _ _ _ _ _ _ _ infinity incompressibility + + + + + + + + 0 x gel solution LD Deep in gel, electric filed vanishes and no net charge + External solution

  27. Gel near Liquid-gel interface _ _ _ _ _ _ _ _ infinity + + + + + + + + 0 x gel solution LD

  28. Load Li-ion Electrolyte A discharging Li-ion cell. Relation to my research Hydrogel : poroelasticity Li battery : field theory coupling large deformation and electrochemistry of ions and solvent

  29. Q&A Thank you!

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