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Soft Active Materials

Soft Active Materials. Zhigang Suo Harvard University. III. Polyelectrolytes. 1. Polyelectrolyte: polymer with electrolyte group. polymer chain. covalent bond. ionic bond. In a solvent, the electrolyte dissociates. solvent. co-ion. fixed charge. counterion. counterion .

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Soft Active Materials

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  1. Soft Active Materials Zhigang Suo Harvard University III. Polyelectrolytes 1

  2. Polyelectrolyte: polymer with electrolyte group polymer chain covalent bond ionic bond In a solvent, the electrolyte dissociates. solvent co-ion fixed charge counterion counterion

  3. Polyelectrolyte gel A network of polymers Solvent (e.g., water) Crosslinks Fixed charges Counterions Co-ions - + -

  4. Many tissues are polyelectrolyte gels • Structure and function: • Cartilage is polyelectrolyte. • Does this fact have anything to • do with low friction of a joint?

  5. Plant cell walls are polyelectrolytes Pectin

  6. Gels regulate flow in plants Missy Holbrook Zwieniecki, Melcher, Holbrook, Hydrogel control of xylem hydraulic resistance in plants Science 291, 1095 (2001)

  7. Osmosis in a polyelectrolyte gel fixed charge water crosslink - - + solution + - - + - + - + + - + + network - + solvent - - counterion • Network tatters fixed charges. • To maintain electroneutrality, fixed charges are balanced by counterions. • Counterions cause osmosis membrane Osmosis balanced by gravity Osmosis balanced by elasticity

  8. Super absorbent diaper Sodium polyacrylate: polyelectrolyte Masuda, Trends in the development of superabsorbent polymers for diapers, pp. 88-89, Superabsorbent polymers: science and technology (1994).

  9. Ion exchanger

  10. pH-sensitive gel fixed mobile

  11. pH-sensitive hydrogel

  12. pH-sensitive valves in microfluidics David Beebe Deformation and force regulated by physiological variables (pH, salt, temperature…) Mechanics and chemistry Beebe, Moore, Bauer, Yu, Liu, Devadoss, Jo, Nature 404, 588 (2000)

  13. Adaptive optics with soft materials Dong, Agarwal, Beebe, Jiang, Nature 442, 551 (2006)

  14. Electric potential Electrochemical potential Gibbs (1878) Material B • Battery does work on electrons, Fdq • Pump does work on ions, mdM • Helmholtz free energy of system, F electrode equilibrium Ions, dM electrons, dq electroneutrality battery, F pump, m electrode Material A

  15. Lithium-ion battery electron Negative electrode Positive electrode John B. Goodenough Load Silicon Li-ion Electrolyte LiFePO4 Chanet al., 2008. Nature Nanotechnology3, 31 Wang, Wu, Wang, Chen, 2005. Journal of Power Sources 140, 125

  16. 3 ways of doing work to a gel Hong, Zhao, Suo. J. Mech. Phys. Solids 58 (2010) 558-577.

  17. A field theory of thermodynamic equilibrium Gauss’s law Deformation gradient Concentrations Material model: Equilibrium: Equivalent conditions of equilibrium Hong, Zhao, Suo. J. Mech. Phys. Solids 58 (2010) 558-577.

  18. - - microscopic processes - - gel external solution • Swelling increases entropy by mixing solvent and polymers. • Swelling decreases entropy by straightening the polymers. • Redistributing mobile ions increases entropy by mixing. • Neutrality reduces electrostatic energy.

  19. Free-energy function Free-energy function • Free energy of stretching • Free energy of mixing • Free energy of polarization Flory, Rehner, J. Chem. Phys., 11, 521 (1943) Zhao, Hong, Suo, Physical Review B 76, 134113 (2007)

  20. Swelling regulated by concentration of ions Concentration of fixed ions Swelling ratio nonionic gel Concentration of ions in external solution

  21. Concentration of fixed ions Constrained swelling gel External solution Swelling ratio Concentration of ions in external solution

  22. Debye length - + - + - - + + 0 x - - + - + + + gel external solution

  23. In gel, near interface - + - + infinity - - + + 0 x - gel liquid - + - + + +

  24. pH-sensitivehydrogel fixed mobile

  25. Osmosis is balanced by elasticity Donnan equilibrium Electroneutrality Conservation of particles Constant of acidic dissociation Ricka, Tanaka,Macromolecules17, 2916 (1984). Marcombe, Cai, Hong, Zhao, Lapusta, Suo, Soft Matter 6, 784 (2010)

  26. Free swelling

  27. Constrained swelling

  28. Finite element method Condition of equilibrium Legendre transformation Shengqiang Cai Marcombe, Cai, Hong, Zhao, Lapusta, Suo, Soft Matter 6, 784 (2010) ABAQUS UMAT posted online.

  29. Channel wall B D A pillar gel pH-sensitive valve pH = 2 pH = 6

  30. Summary • Couple large deformation and electrochemistry. • Swelling regulated by concentration of ions. • Swelling regulated by pH.

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