1

Soft Active Materials

Zhigang Suo

Harvard University

I. Dielectric Elastomers

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Hard Machines

C-3PO R2-D2

3

Soft Machines

Angelina Jolie Octopus

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octopus

Mäthger, Hanlon, Kuzirian – Marine Biological Laboratory, Woods Hole MA

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Squid changes color

Expand pigmented sacs by contracting muscles

Mathger, Denton, Marshall, Hanlon, J. R. Soc. Interface 6, S149 (2009)

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Elastomeric Optics

•Many stimuli cause deformation.•Deformation affects optics.

Wilbur, Jackman, Whitesides, Cheung, Lee, PrentissChem. Mater. 8, 1380 (1996)

Aschwanden, StemmerOptics letters 31, 2610 (2006)

George Whitesides

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reversible

elastomer = networkgel = network + solvent

solvent

networkgel

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Super absorbent diaper

Sodium polyacrylate

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

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)

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Swelling packers in oil wells

Cai, Lou, Ganguly, Robisson, SuoForces generated by a swelling elastomer subject to constraintJournal of Applied Physics, in press

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Gels regulate flow in plants

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

Missy Holbrook

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Self-regulating fluidics

Beebe, Moore, Bauer, Yu, Liu, Devadoss, Jo, Nature 404, 588 (2000)

David Beebe

•pH•Salt•Temperature•light

Responsive toPhysiological variables:

•Many stimuli cause deformation.•Deformation regulates flow.

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Soft Active Materials

Soft: capable of large and reversible deformation (rubbers, gels,…)

Active: response to diverse stimuli (electric field, temperature, pH, salt,…)

StimulipH, E, T, C…

SAM deforms

Functionsoptics, flow…

A stimulus causes deformation. Deformation provides a function.

Better life through deformation

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Dielectric elastomer

Compliant Electrode

Dielectric Elastomer

L

A

Reference State

l

a Q

Q

Current State

Pelrine, Kornbluh, Pei, Joseph High-speed electrically actuated elastomers with strain greater than 100%. Science 287, 836 (2000).

•Large strain•Noise-less•Cheap

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

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Roll to Roll ManufacturingDanfoss PolyPower

Roll coating of film

Metallise electrodes

Laminate metallised film

Roll actuators

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Parallel-plate capacitor P

P

lQ

Qbattery

force

electrode

vacuumelectrode

lE

aQ

D

aP

Electric field

Electric displacement field

stress field

a

ED 0

0, permittivity of vacuum

202

1E Maxwell stress

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+ + + + + + + + +

- - - - - - - - - - - - - - - - - - - - - - - -

+ + + + + + + + +

+-

Maxwell stressElectrostriction2

33 2E

Trouble with Maxwell stress in dielectrics

•In general, varies with deformation.•In general, E2 dependence has no special significance.•Wrong sign?

Our complaints:

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An atom in an electric field

e

Hydrogen atom

e

+ + + + + + + + +

- - - - - - - - - - - -

p

External electric field displaces positive and negative charges somewhat.•Polarization: Induce more charge on the electrodes.•Deformation: Distort the shape of the electron cloud.

p

battery

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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

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Field equations in vacuum, Maxwell (1873)

ijkkijj

i EEEEx

F 20

0

ii xE

0q

xE

i

i

A field of forces maintain equilibrium of a field of charges ii qEF

Electrostatic field

ijkkijij EEEE 20

0

Q

Q

20

2E

P

P

E

Maxwell stress

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Include Maxwell stress in force balance

h

202

1E

gh

2

2

1E

202

1Egh

“Free-body” diagram

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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

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Trouble with electric force in dielectrics

In a vacuum, external force is needed to maintain equilibrium of charges

+Q +Q

+Q +Q

In a solid dielectric,force between charges is NOT an operational concept

P Pii qEF

ii qEF

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The Feynman Lectures on PhysicsVolume 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.”

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All troubles are gone if we use measurable quantities

L

A

Reference State

P

l

a Q

Q

Current State

Ll /

APs /

LE /~

AQD /~

DEsW~~

equilibrate elastomer and loads

DW

s~

, D

DWE ~

~,~

equations of state

QlPF

LAQ

ALlP

ALF

divide by volume

name quantities

aP /

lE /

aQD /

ALFW /

Nominal

True

Suo, Zhao, Greene, J. Mech. Phys. Solids 56, 467 (2008)

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The nominal vs. the true

L

A

Reference State

P

l

a Q

Q

Current State

LE /~

AQD /~

)/( lE

)/( aQD

Battery does work DEALADLEQ~~~~

True electric field and true electric displacement are NOT work-conjugate

aEDlDElaDaElQ

Nominal electric field and nominal electric displacement are work-conjugate

Battery does work

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Dielectric constant is insensitive to stretch

Kofod, Sommer-Larsen, Kornbluh, Pelrine Journal of Intelligent Material Systems and Structures 14, 787 (2003).

VHB 4910

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2

~,

2DWDW stretch

Elasticity Polarization

Ideal dielectric elastomer

aQ

DAQ

D~

DD~

Dielectric behavior is liquid-like, unaffected by deformation.

For an ideal dielectric elastomer, electromechanical coupling is purely a geometric effect:

2

~~

,22D

WDW stretch

aA 1

incompressibility

1A

a

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Ideal dielectric elastomer

DW

s~

,

In terms of nominal quantities

In terms of true quantities

2

~~

,22D

WDW stretch

2~D

ddW

s stretch

2Ed

dWstretch

sDD~

ED

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Maxwell stress represented in three ways

Compliant Electrode

Dielectric Elastomer

L

A

Reference State

l

a Q

Q

Current State

2E 2E 2

21E

For incompressible material, the 3 states of stress give the same state of deformation

Uniaxial stress biaxial stress triaxial stress

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Stress-stretch curve

1

1

H

h

2hH Elastomer is incompressible

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Deformation of actuation

Q

Q

1

1

H

h

2E

2 EHEh

Equation of state

Maxwell stress

voltage

2 H

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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)

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l

Q

Q

Two modes of failure

Q

polarizing thinning

Q

polarizing

Electrical breakdownHard material

Pull-in instabilitySoft material

Stark & Garton, Nature 176, 1225 (1955)

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Electrical breakdown

2 HEhE BBB

Kofod, Plante…

B

To measure dielectric strength,one must suppress electromechanical instability by fixing stretch.

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Pull-in instability limits deformation of actuation

Calculation: Zhao & Suo Appl. Phys Lett. 91, 061921 (2007)

3.1c

Experiment: Pelrine, Kornbluh, Joseph, Sensors & Actuators A 64, 77 (1998)

c

Linear elastic model 1 Y

2 H

Xuanhe Zhao

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l

Q

Q

Interpretation: Zhao, Hong, SuoPhysical Review B 76, 134113 (2007)

Coexistent states: flat and wrinkledObservation: Plante, Dubowsky, Int. J. Solids and Structures 43, 7727 (2006)

Qthick thin

Top viewCross section

Coexistent states polarizing

thinning

stiffening

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Three types of behavior

Zhao and Suo, PRL 104, 178302 (2010).

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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)

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Interpenetrating networks

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

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When stretched, a polymer stiffens

nb

bn

b

n links

PP

PP

P

n

Langevin

Gauss

released

stretched

fully stretched

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2

1

2111

,E

W

2

2

2122

,E

W

sinhlog

tanhvkT

W

1

tanh1

n

2/123

22

21

1

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

Arruda-Boyce model

1321

n~lim

nvkT

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Change contour length of polymer chain

n = 5

50

500

kTv

H

B

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Effect of Prestress

n = 50

1

1

H h

P

Q

Q

P

4

2

HHP

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Desired stress-stretch curve

soft

hard

•Soft: enable deformation.•Hard: avert excessive deformation.

Ear lobe

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Design materials for desirable stress-stretch curve

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2

1

2111

,E

W

2

2

2122

,E

W

sinhlog

tanh20vkT

W

1

tanh1

n

2/123

22

21

0

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

1321

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Zhao and Suo, PRL 104, 178302 (2010).

Dielectric gel

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Energy harvesting

Generate electricity from walking Generate electricity from waves

Pelrine, Kornbluh…

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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, Elastomer1 mJ/g ceramics

•Cheap•Reliable

Adrian Koh

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VHB and Natural Rubber

Koh, Keplinger , Li, Bauer, Suo, submitted (2010)

(a) (b)

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VHB and Natural Rubber

Koh, Keplinger , Lii, Bauer, Suo, submitted (2010)

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Generator X

Koh, Keplinger , Lii, Bauer, Suo, submitted (2010)

0.3MPa

MPa024.0

RubberNatural2

EBE

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+ + + + + + + + +

- - - - - - - - - - - - - - - - - - - - - - - -

+ + + + + + + + +

+-

Maxwell stressElectrostriction2

33 2E

Electrostriction

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Non-ideal dielectric elastomer

31 321 c

Die

lect

ric

con

stan

t

Area ratio

Wissler, Mazza, Sens. Actuators, A 138, 384 (2007).

deformation affects dielectric constant

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Quasi-linear dielectric elastomer

Zhao, Suo, JAP 104, 123530 (2008)

2~

,2D

WDW stretch

DW

s~

,

22

2

~

ddD

ddW

s stretch

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A field of markers: stretch

Reference state Current state

X x(X, t)

K

iiK X

txF

,X

X+dX x(X+dX, t)

L lLl

K

ii

dXtxtdx ,, XXX

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A field of batteries: electric field

t,X

X

x(X, t)

X+dXx(X+dX, t)

td ,XX

ground

Reference state Current state

L l LE

~

KdX

ttd ,, XXX

K

K Xt

E

,~ X

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3D inhomogeneous field

dAdVqdAxTdVxtx

BWdV iiii

i

2

2

P

Q

l

Need to specify a material model

DF~

,W DW~

,

KKiKiK DEFsW~~~

, DF

iK

iK FW

s

DF~

, K

KD

WE ~

~,~

DF

Condition of thermodynamic equilibrium

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PDEs

K

iiK X

txF

,X

KK X

tE

,~ X

iK

iK FW

s

DF~

, K

KD

WE ~

~,~

DF

Suo, Zhao, Greene, J. Mech. Phys. Solids 56, 467 (2008)

2

2 ,,

,t

txtB

Xts i

iK

iK

XX

X tqX

tD

K

K ,,

~X

X

Toupin (1956), Eringen (1963), Tiersten (1971), Goulbourne, Mockensturm and Frecker (2005), Dorfmann & Ogden (2005), McMeeking & Landis (2005)…

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dATdVtx

BdVXF

Wiii

ii

K

i

iK

2

2ˆ

Conditions of thermodynamic equilibrium

dAdVqdVXE

W

KK

~ˆ

Finite element method

KKEDWW~~~

,ˆ EF

Solve for txi ,X t,X

Legendre transformation

K

iiK X

txF

,X

KK X

tE

,~ X

Zhao, ABAQUS user-supplied subroutine, http://imechanica.org/node/4234

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States of equilibrium

L

Simple Layer

A

BP

Ring

P

R

Sphere

Zhao and Suo, APL 93, 251902 (2008)

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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

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Programmable deformation

Design:Kofod, Wirges, Paajanen, BauerAPL 90, 081916 (2007)

Simulation:Zhao, SuoAPL 93, 251902 (2008)

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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).

StimulipH, E, T, C…

SAM deforms

Functionsoptics, flow…