11 Soft Active Materials Zhigang Suo Harvard University III. Polyelectrolytes

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

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

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 Zwieniecki, Melcher, Holbrook, Hydrogel control of xylem hydraulic resistance in plants Science 291, 1095 (2001) Missy Holbrook

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

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

9 Ion exchanger

10 pH-sensitive gel fixedmobile

11 pH-sensitive hydrogel

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

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

14 Electric potential Electrochemical potential Gibbs (1878) electrode battery,  pump,  electrons,  q Ions,  M electroneutrality equilibrium Material A Material B electrode Battery does work on electrons,  q Pump does work on ions,  M Helmholtz free energy of system, F

15 Lithium-ion battery Electrolyte Li-ion Load Negative electrode Positive electrode Wang, Wu, Wang, Chen, Journal of Power Sources 140, 125 Chan et al., Nature Nanotechnology 3, 31 electron LiFePO 4 Silicon John B. Goodenough

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

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

18 microscopic processes 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 gel external solution

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

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

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

22 Debye length x gel external solution

23 In gel, near interface x infinity liquidgel

24 pH-sensitive hydrogel fixedmobile

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

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

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