1. 1 Soft Active Materials Zhigang Suo Harvard University I. Dielectric Elastomers

2. 2 Hard Machines C-3PO R2-D2

3. 3 Soft Machines Angelina JolieOctopus

4. 4 octopus Mäthger, Hanlon, Kuzirian – Marine Biological Laboratory, Woods Hole MA

5. 5 Squid changes color Expand pigmented sacs by contracting muscles Mathger, Denton, Marshall, Hanlon, J. R. Soc. Interface 6, S149 (2009)

6. 6 Elastomeric Optics Many stimuli cause deformation. Deformation affects optics. Wilbur, Jackman, Whitesides, Cheung, Lee, Prentiss Chem. Mater. 8, 1380 (1996) Aschwanden, Stemmer Optics letters 31, 2610 (2006) George Whitesides

7. 7 reversible elastomer = network gel = network + solvent solvent network gel

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

9. Oil Spill…Hair Phil McCrory, Inventor of the hairmats Lisa Gautier, Founder of Matter of Trust Hair adsorbs oil (~3g oil/1g hair) Polypropylene fibers absorb oil (~10g oil/1g polypropylene)

10. 10 Swelling packers in oil wells Cai, Lou, Ganguly, Robisson, Suo Forces generated by a swelling elastomer subject to constraint Journal of Applied Physics, in press

11. 11 Gels regulate flow in plants Zwieniecki, Melcher, Holbrook, Hydrogel control of xylem hydraulic resistance in plants Science 291, 1095 (2001) Missy Holbrook

12. 12 Self-regulating fluidics Beebe, Moore, Bauer, Yu, Liu, Devadoss, Jo, Nature 404, 588 (2000) David Beebe pH Salt Temperature light Responsive to Physiological variables: Many stimuli cause deformation. Deformation regulates flow.

13. 13 Soft Active Materials Soft: capable of large and reversible deformation (rubbers, gels,…) Active: response to diverse stimuli (electric field, temperature, pH, salt,…) Stimuli pH, E, T, C… SAM deforms Functions optics, flow… A stimulus causes deformation. Deformation provides a function. Better life through deformation

14. 14 Dielectric elastomer Compliant Electrode Dielectric Elastomer Reference StateCurrent State Pelrine, Kornbluh, Pei, Joseph High-speed electrically actuated elastomers with strain greater than 100%. Science 287, 836 (2000). Large strain Noise-less Cheap

15. Potential applications of dielectric elastomers Automobil:In- outside, Temp., Safety, Vandalism, Stupidity, … Aircraft:In- outside, Temp., Safety, Reliability, Failsave, … Space:Temp., Vacuum, Radiation, Reliability, Vibration, … Machine Tool:Vibration, Act-Speed, Positioning, Force, … Robot./Prosthetics:Safety, Act-Speed, Efficiency, Low Voltage, Force, … Tectile Displays:Safety, Low Voltage, Multifunction, Resolution, … Micro Actuation:Low Voltage, Small Size, Fabrication, … FFD:Multifunction, Safety, Responsetime, … Optics:Refractivity, Transmittanz, No Imperfections, … Energy Harvesting:Efficiency, Conductivity, Fatigue, … Sensing:Low Stiffness, No Viscosity, … Implants:Safety, Reliability, Very Low Voltage, Radio Control, … Gabor Kovacs, Winter School, Ascona, Switzerland, 10-16 January 2010

16. 16 Roll to Roll Manufacturing Danfoss PolyPower Roll coating of film Metallise electrodes Laminate metallised film Roll actuators

17. 17 Parallel-plate capacitor P P battery force electrode vacuum electrode Electric field Electric displacement field stress field  0, permittivity of vacuum Maxwell stress

18. 18 + + + + + + + + + - - - - - - + + + + + + + + + +-+- Maxwell stress Electrostriction Trouble with Maxwell stress in dielectrics In general,  varies with deformation. In general, E 2 dependence has no special significance. Wrong sign? Our complaints:

19. 19 An atom in an electric field Hydrogen atom + + + + + + + + + - - - - - - External electric field displaces positive and negative charges somewhat. Polarization: Induce more charge on the electrodes. Deformation: Distort the shape of the electron cloud. battery

20. 20 A dipole in an electric field Polar molecules + + + + + + + + + - - - - - - External electric field reorients dipoles. Polarization: Induce more charge on the electrodes. Deformation: Distort the shape of the sample. battery

21. 21 Field equations in vacuum, Maxwell (1873) A field of forces maintain equilibrium of a field of charges Electrostatic field P P Maxwell stress

22. 22 Include Maxwell stress in force balance h “Free-body” diagram

23. 23 James Clerk Maxwell (1831-1879) “I have not been able to make the next step, namely, to account by mechanical considerations for these stresses in the dielectric. I therefore leave the theory at this point…” A Treatise on Electricity & Magnetism (1873), Article 111

24. 24 Trouble with electric force in dielectrics In a vacuum, external force is needed to maintain equilibrium of charges +Q In a solid dielectric, force between charges is NOT an operational concept PP

25. 25 The Feynman Lectures on Physics Volume II, p.10-8 (1964) “It is a difficult matter, generally speaking, to make a unique distinction between the electrical forces and mechanical forces due to solid material itself. Fortunately, no one ever really needs to know the answer to the question proposed. He may sometimes want to know how much strain there is going to be in a solid, and that can be worked out. But it is much more complicated than the simple result we got for liquids.”

26. 26 All troubles are gone if we use measurable quantities Reference State Current State equilibrate elastomer and loads equations of state divide by volume name quantities Nominal True Suo, Zhao, Greene, J. Mech. Phys. Solids 56, 467 (2008)

27. 27 The nominal vs. the true Reference StateCurrent State Battery does work True electric field and true electric displacement are NOT work-conjugate Nominal electric field and nominal electric displacement are work-conjugate Battery does work

28. 28 Dielectric constant is insensitive to stretch Kofod, Sommer-Larsen, Kornbluh, Pelrine Journal of Intelligent Material Systems and Structures 14, 787 (2003). VHB 4910

29. 29 Elasticity Polarization Ideal dielectric elastomer Dielectric behavior is liquid-like, unaffected by deformation. For an ideal dielectric elastomer, electromechanical coupling is purely a geometric effect: incompressibility

30. 30 Ideal dielectric elastomer In terms of nominal quantities In terms of true quantities

31. 31 Maxwell stress represented in three ways Compliant Electrode Dielectric Elastomer Reference State Current State For incompressible material, the 3 states of stress give the same state of deformation Uniaxial stress biaxial stresstriaxial stress

32. 32 Stress-stretch curve Elastomer is incompressible

33. 33 Deformation of actuation Equation of state Maxwell stress voltage

34. 34 Experimentally observed deformation of actuation Ceramics, <1%. Zhenyi, et al. (1994), polymer ~3%. Zhang, et al. (1998),polymer ~7%. Pelrine, et al. (1998), low modulus, high dielectric strength, ~30%. Pelrine, et al. (2000), pre-stress, ~100%. Ha, et al. (2006), interpenetrating networks, ~100%. What is the theoretical limit? How about 1000%? Zhao and Suo, PRL 104, 178302 (2010)

35. 35 Two modes of failure  polarizing thinning  polarizing Electrical breakdown Hard material Pull-in instability Soft material Stark & Garton, Nature 176, 1225 (1955)

36. 36 Electrical breakdown Kofod, Plante… To measure dielectric strength, one must suppress electromechanical instability by fixing stretch.

37. 37 Pull-in instability limits deformation of actuation Calculation: Zhao & Suo Appl. Phys Lett. 91, 061921 (2007) Experiment: Pelrine, Kornbluh, Joseph, Sensors & Actuators A 64, 77 (1998)  Linear elastic model Xuanhe Zhao

38. 38 Interpretation: Zhao, Hong, Suo Physical Review B 76, 134113 (2007) Coexistent states: flat and wrinkled Observation: Plante, Dubowsky, Int. J. Solids and Structures 43, 7727 (2006) thickthin  Top view Cross section Coexistent states polarizing thinning stiffening

39. 39 Three types of behavior Zhao and Suo, PRL 104, 178302 (2010).

40. 40 Experimentally observed deformation of actuation Ceramics, <1%. Type I Zhenyi, et al. (1994), polymer ~3%. Type I Zhang, et al. (1998),polymer ~7%. Type I Pelrine, et al. (1998), ~30%. Type II Pelrine, et al. (2000), pre-stress, ~100%. Type III Ha, et al. (2006), interpenetrating networks, ~100%. Type III Zhao and Suo, PRL 104, 178302 (2010)

41. 41 Interpenetrating networks Ha, Yuan, Pei, Pelrine, Adv. Mater. 18, 887 (2006). Suo, Zhu. APL 95, 232909 (2009). Zhao and Suo, PRL 104, 178302 (2010).

42. 42 When stretched, a polymer stiffens n links Langevin Gauss released stretched fully stretched

43. 43 Kuhn, Grun, Kolloid-Z. 101, 248 (1942) Arruda, Boyce, J. Mech. Phys. Solids 41, 389 (1993) Arruda-Boyce model

44. 44 Change contour length of polymer chain n = 5n = 5 50 500

45. 45 Effect of Prestress n = 50

46. 46 Desired stress-stretch curve soft hard Soft: enable deformation. Hard: avert excessive deformation. Ear lobe

47. 47 Design materials for desirable stress-stretch curve

48. 48 Kuhn, Grun, Kolloid-Z. 101, 248 (1942) Arruda, Boyce, J. Mech. Phys. Solids 41, 389 (1993) Zhao and Suo, PRL 104, 178302 (2010). Dielectric gel

49. 49 Zhao and Suo, PRL 104, 178302 (2010). Dielectric gel

50. 50 Energy harvesting Generate electricity from walkingGenerate electricity from waves Pelrine, Kornbluh…

51. 51 Maximal energy that can be converted by a dielectric elastomer R LT EB E=0 EMI Koh, Zhao, Suo, Appl. Phys. Lett. 94, 262902 (2009) 1 J/g, Elastomer 1 mJ/g ceramics Cheap Reliable Adrian Koh

52. 52 VHB and Natural Rubber Koh, Keplinger, Li, Bauer, Suo, submitted (2010) (a)(b)

53. 53 VHB and Natural Rubber Koh, Keplinger, Lii, Bauer, Suo, submitted (2010)

54. 54 Generator X Koh, Keplinger, Lii, Bauer, Suo, submitted (2010)

55. 55 + + + + + + + + + - - - - - - + + + + + + + + + +-+- Maxwell stress Electrostriction

56. 56 Non-ideal dielectric elastomer Dielectric constant Area ratio Wissler, Mazza, Sens. Actuators, A 138, 384 (2007). deformation affects dielectric constant

57. 57 Quasi-linear dielectric elastomer Zhao, Suo, JAP 104, 123530 (2008)

58. 58 A field of markers: stretch Reference stateCurrent state Xx(X, t) X+dX x(X+dX, t) L l

59. 59 A field of batteries: electric field X x(X, t) X+dX x(X+dX, t) ground Reference stateCurrent state L l

60. 60 3D inhomogeneous field Need to specify a material model Condition of thermodynamic equilibrium

61. 61 PDEs Suo, Zhao, Greene, J. Mech. Phys. Solids 56, 467 (2008) Toupin (1956), Eringen (1963), Tiersten (1971), Goulbourne, Mockensturm and Frecker (2005), Dorfmann & Ogden (2005), McMeeking & Landis (2005) …

62. 62 Conditions of thermodynamic equilibrium Finite element method Solve for Legendre transformation Zhao, ABAQUS user-supplied subroutine, http://imechanica.org/node/4234http://imechanica.org/node/4234

63. 63 States of equilibrium Simple LayerRing Sphere Zhao and Suo, APL 93, 251902 (2008)

64. 64 Oscillating Balloon Zhao and Suo, APL 93, 251902 (2008) Zhu, Cai, Suo, Polymer International 59, 378-383 (2010) Excitation by sinusoidal voltage Oscillation of the balloon

65. 65 Programmable deformation Design: Kofod, Wirges, Paajanen, Bauer APL 90, 081916 (2007) Simulation: Zhao, Suo APL 93, 251902 (2008)

66. 66 Summary Soft active materials (SAMs) have many functions (soft robots, adaptive optics, self-regulating fluidics, programmable haptics, oil recovery, energy harvesting, drug delivery, tissue regeneration, low-cost diagnosis, oil spill cleanup … ) SAMs is interesting and challenging to study (mechanics, electrostatics, chemistry; large deformation, mass transport, instability). The field is wide open (stimuli, SAMs, functions). Stimuli pH, E, T, C… SAM deforms Functions optics, flow…