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Soft Active Materials

Soft Active Materials. Zhigang Suo Harvard University. II. Gels. 1. gel = network + solvent. solvent. gel. network. Solid-like : long polymers crosslinked by strong bonds . Retain shape Liquid like : polymers and solvent aggregate by weak bonds . Enable transport.

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Soft Active Materials

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  1. Soft Active Materials Zhigang Suo Harvard University II. Gels 1

  2. gel = network + solvent solvent gel network Solid-like: long polymers crosslinked by strong bonds. Retain shape Liquid like: polymers and solvent aggregate by weak bonds. Enable transport • Imbibe solvent, and swell • Exude solvent, and collapse Ono, Sugimoto, Shinkai, Sada, Nature Materials 6, 429 (2007)

  3. Gels in daily life food plants Contact lenses Wichterie, Lim, Nature 185, 117 (1960) Drug delivery Ulijn et al. Materials Today 10, 40 (2007) Tissues, natural or engineered

  4. Gels in engineering • Responsive to physiological variables: • pH • concentration of ions • temperature • light Gate in microfluidics packer in oil well Beebe, Moore, Bauer, Yu, Liu, Devadoss, Jo, Nature 404, 588 (2000) Shell, 2003

  5. Chemical potential of a molecular species in a system vapor wine cheese • A molecular species: water, or a type of alcohol, or a type of protein • A system: the wine, or the cheese, or the vapor, or the composite • Number of water molecules in a system, M • Helmholtz free energy of a system, F(M,…) • Chemical potential of water in a system, • In equilibrium, the chemical potential of water in the wine equals the chemical potential of water in the cheese, and equals the chemical potential of water in the vapor. • Measure the chemical potential of water in one system by equilibrating this system with another system in which the chemical potential of water is known.

  6. Chemical potential of a species in a one-species system weights piston vapor vapor liquid liquid State of reference liquid & vapor in equilibrium liquid only vapor only Relative humidity, Pressure of saturated vapor volume per solvent molecule

  7. The ascent of sap Henry Horatio Dixon • The air is dry. • The soil is wet. • The gradient of humidity pumps water up. Dixon and Joly, Phil. Trans. R. Soc. Lond. B 186, 563 (1895)

  8. Liquid water in tension Chemical potential of water in the air water-permeable solid When the liquid water in the void equilibrate with the water vapor in the air, xylem water s Chemical potential of water in the xylem

  9. Liquid water in tension Abe Stroock 10 20 30 40 • Axisymmertic deformation • Creasing • Cavitation Wheeler, Stroock. Nature 455, 208 (2008)

  10. Osmosis in a liquid solute Number of solute molecules, N Volume of the solution, V Volume per solvent molecule, v h osmotic pressure Van’t Hoff membrane solution solvent Chemical potential of water in the solution due to osmosis Chemical potential of water in the solution due to gravity Chemical potential of water in the solvent Jacobus H. Van’t Hoff, Osmotic pressure and chemical equilibrium, Nobel Lecture, 13 December 1901

  11. Osmosis in a gel Crosslink solution solvent membrane Osmosis balanced by elasticity Osmosis balanced by gravity

  12. Two ways of doing work work done by the pump Chemical potential of solvent Pump work done by the weight Solvent Helmholtz free energy of gel Condition of equilibrium Gel = Network + M solvent molecules Equations of state Weight Force

  13. Gels as transducers • A swelling gel is blocked by a hard material. • Blocking force. • Inhomogeneous deformation. Need to formulate boundary-value problems

  14. 2 ways of doing work Reference state Current state M=0 Equilibrium condition m pump Pump, m M L gel l P Helmholtz free energy per volume dl weight

  15. pump Gel Weight Inhomogeneous field Deformation gradient Concentration Free-energy function Gibbs (1878) Condition of equilibrium • How to prescribe ? • How to solve boundary-value problems? • What boundary-value problems to solve? Hong, Zhao, Zhou, Suo, JMPS 56, 1779 (2008)

  16. Free-energy function • Swelling decreases entropy by straightening polymers. • Swelling increases entropy by mixing solvent and polymers. Free energy of stretching Paul Flory Free-energy function Free energy of mixing Flory, Rehner, J. Chem. Phys., 11, 521 (1943)

  17. Assumptions: Individual solvent molecule and polymer are incompressible. Neglect volumetric change due to physical association Gel has no voids. (a gel is different from a sponge.) = + Vdry + Vsol = Vgel Molecular incompressibility Wei Hong v – volume per solvent molecule

  18. Stress-strain relation Hong, Zhao, Zhou, Suo, JMPS 56, 1779 (2008)

  19. Anisotropic swelling Free swelling Unidirectional swelling A gel imbibes a different amount of solvent under constraint. Treloar, Trans. Faraday Soc. 46, 783 (1950).

  20. Inhomogeneous swelling • Concentration is inhomogeneous even in equilibrium. • Stress is high near the interface (debond, cavitation). Sternstein, J. Macromolol. Soc. Phys. B6, 243 (1972) Zhao, Hong, Suo, APL 92, 051904 (2008 )

  21. Finite element method Equilibrium condition Legendre transform • A gel in equilibrium is analogous to an elastic solid • ABAQUS UMAT Hong, Liu, Suo, Int. J. Solids Structures 46, 3282 (2009) ABAQUS UMAT posted online http://imechanica.org/node/3163

  22. Swelling-induced buckling Zishun Liu Liu, Hong, Suo, Swaddiwudhipong, Zhang. Computational Materials Science. In press.

  23. Gel and nano-rods • Joanna Aizenberg • Experiment: Sidorenko, Krupenin, Taylor, Fratzl, Aizenberg, Science 315, 487 (2007). • Theory: Hong, Zhao, Suo, JAP104, 084905 (2008) .

  24. Critical humidity can be tuned

  25. Swelling-induced bifurcation Shu Yang Zhang, Matsumoto, Peter, Lin, Kamien, Yang, Nano Lett. 8, 1192 (2008).

  26. Swelling-induced bifurcation Experiment: Zhang, Matsumoto, Peter, Lin, Kamien, Yang, Nano Lett. 8, 1192 (2008). Simulation: Hong, Liu, Suo, Int. J. Solids Structures 46, 3282 (2009)

  27. Time-dependent process Shape change: short-range motion of solvent molecules, fast Volume change: long-range motion of solvent molecules, slow Hong, Zhao, Zhou, Suo, JMPS 56, 1779 (2008)

  28. Concurrent deformation and migration Deformation of network Conservation of solvent Maurice Biot JAP 12, 155 (1941) pump Gel Nonequilibrium thermodynamics Weight Rate process Local equilibrium Hong, Zhao, Zhou, Suo, JMPS 56, 1779 (2008)

  29. ideal kinetic model Solvent molecules migrate in a gel by self-diffusion Diffusion in true quantities Conversion between true and nominal quantities Hong, Zhao, Zhou, Suo, JMPS 56, 1779 (2008)

  30. Finite element method for concurrent deformation and migration Hanqing Jiang Zhang, Zhao, Suo, Jiang, JAP 105, 093522 (2009)

  31. AAD ++ Ca ( ) Na+ Irreversible Alginate Hydrogels David Mooney Ionic crosslinks Covalent crosslinks

  32. Stress-relaxation test strain Impermeable Rigid plates Gel disk PBS time stress time Zhao, Huebsch, Mooney, Suo, J. Appl. Phys. In press.

  33. Elasticity, plasticity, fracture Ionic crosslinks 10mm Swollen state 45% compressive strain 50% compressive strain Covalent crosslinks Swollen state 15% compressive strain 20% compressive strain

  34. Stress Relaxation Covalent ~102 Ionic Strain: 15% Radius: 6mm

  35. Size effect R

  36. Gel with covalent crosslinks relaxes stress by migration of water

  37. h F indenter t h migration of solvent gel water Indent a gel Yuhang Hu Indent into a gel by a certain depth Joost Vlassak F Record force as a function of time F(0) F(∞) t Hu, Zhao, Vlassak, Suo. Applied Physics Letters 96, 121904 (2010)

  38. Linear poroelasticity Small deformation Mass conservation Force Balance Kinetics Local equilibrium Incompressibility of solvent molecules and polymers Free energy Constitutive relations Biot, JAP 12, 155 (1941). Originally developed for soil. Now adapted for gels.

  39. PDEs 3 poroelastic constants:

  40. Initial state Instantaneous deformation Equilibrium state Poisson’s ratio of a gel

  41. covalently crosslinked alginate hydrogel • viscoelasticity • Poroelasticity 41 Hu, Zhao, Vlassak, Suo. Applied Physics Letters 96, 121904 (2010)

  42. From relaxation curve to poroelastic constants F R h 2a F R h 2a F θ h 2a F R h 2a (a) Plane-strain cylindrical indenter (b) Cylindrical punch Hui , Lin, Chuang, Shull, Ling. J. Polymer Sci B: Polymer Phys. 43, 359 (2006) Y.Y. Lin, B.-W. Hu, J. Non-Crystalline Solids 352 4034 (2006). (d) Spherical indenter (c) Conical indenter 42 Hu, Zhao, Vlassak, Suo. Applied Physics Letters 96, 121904 (2010)

  43. Covalently crosslinked alginate gel F(0) F(∞)

  44. Crease Liang Fen (凉粉), a starch gel A food popular in northern China

  45. Dough Zhigang, I was making bread this weekend, and realized that when the rising dough was constrained by the bowl it formed the creases that you were talking about in New Orleans. -- An email from Michael Thouless

  46. Brain

  47. Face

  48. Crease: theory and experiment Biot, Appl. Sci. Res. A 12, 168 (1963). Theory: linear perturbation analysis Maurice Biot Gent, Cho, Rubber Chemistry and Technology 72, 253 (1999) Ghatak, Das, PRL 99, 076101 (2007) Experiments: bending rods of rubber and gel Alan Gent

  49. What’s wrong with Biot’s theory? Homogeneous deformation Mahadevan Crease: Large strain from the state of homogeneous deformation Biot’s theory: infinitesimal strain from the state of homogeneous deformation Hohlfeld, Mahadevan (2008): crease is an instability different from that analyzed by Biot.

  50. An energetic model of crease • Neo-Hookean material • Plane strain conditions Hong, Zhao, Suo, Applied Physics Letters 95, 111901 (2009)

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