f i i lSoft Active Materials

Zhigang Suo (锁志刚 )Harvard University

Where is Science Going in the 21st Century

1A Conference held on the occasion of the 25th Anniversary of the City University of Hong Kong

Hard Machines

2C-3PO R2-D2

Soft MachinesSoft Machines

A li J li O t

3

Angelina Jolie Octopus

octopus

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

S id h lSquid changes color

Chromatophores expands when muscles contractChromatophores expands when muscles contract.

5

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

Adaptive OpticsAdaptive Optics

M ti li d f ti•Many stimuli cause deformation.•Deformation affects optics.

6Wilbur, Jackman, Whitesides, Cheung, Lee, PrentissElastomeric opticsChem. Mater. 1996, 8, 1380-1385

Aschwanden, StemmerOptics letters 31, 2610 (2006)

gel = network + solvent

solvent

reversiblenetwork

gel

Solid-like: long polymers crosslink by strong bonds. Retain shapeLiquid like: polymers and solvent aggregate by weak bonds. Enable transport

7

DiaperDiaper

Sodium polyacrylateSodium polyacrylate

8

Mechanochemcial turbine

Aharon Katchalsky(1914-1972)

9Katchalsky, Eisenberg, Natutre 166, 267 (1950)Sussman, Katchalsky, Science 167, 45 (1970)

Gels regulate flow in plantsGels regulate flow in plants

Missy HolbrookMissy Holbrook

10Zwieniecki, Melcher, Holbrook,Hydrogel control of xylem hydraulic resistance in plants Science 291, 1095 (2001)

Self-regulating fluidicsg g

David Beebe

Responsive to

•pH•Salt

pPhysiological variables:

•Salt•Temperature•light

•Many stimuli cause deformation.

11

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

y•Deformation regulates flow.

Soft Active Materials (SAM)Soft Active Materials (SAM)

Soft: large deformation in response to small forces(e.g., rubbers, gels)

Active: large deformation in response to diverse stimuli(e.g., electric field, temperature, pH, salt)

Stimuli cause deformation. Deformation does something useful.

Stimuli SAMd f

Something useful

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pH, E, T, C… deforms optics, flow…

Dielectric elastomer

Reference State Current State

Dielectric Elastomer

L

A Φ

l

a Q+

Compliant Electrode

lQ−

13Pelrine, Kornbluh, Pei, Joseph High-speed electrically actuated elastomers with strain greater than 100%. Science 287, 836 (2000).

Parallel-plate capacitor P

batteryaΦ

lQ+

Q−electrode

vacuuml d

P force

electrode

lE

Φ=Electric field ED 0ε=

a

QD =Electric displacement field

ε0, permittivity of vacuum

14a

P=σstress field 2

02

1Eεσ = Maxwell stress

Field equations in vacuum, Maxwell (1873)

ii x

E∂Φ∂

−=0ε

qx

E

i

i =∂∂

Electrostatic field

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

−

∂= ijkkiji EEEEF δεε 0

0

∂ ijkkij

ji x 20

QP

ijkkijij EEEE δεεσ20

0 −=

Q−

20

2E

εσ =E

15

2Q+

PMaxwell stress

Include Maxwell stress in f b d dia free-body diagram

202

1 EεΦ

1

“Free-body” diagram

h ghρ ( ) 202

1 Egh εερ −=

2

21 Eε

16

Trouble with Maxwell stress in dielectrics

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

+ + + + + + + + +

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

+ + + + + + + + +

+-

Maxwell stress

±

a e s essElectrostriction2

33 2Eεσ −=

•In general, ε varies with deformation.

Our complaints:

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

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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 ”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

P Pii qEF =

+Q +Q

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

qEF19

ii qEF =

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

ll d t k th t th ti dreally 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

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much more complicated than the simple result we got for liquids.”

All troubles are gone if we use measurable quantities

Reference State

Φ

Current State

L

AΦ

l

a Q+

Q−

Pequilibrate elastomer and loads QlPF δδδ Φ+=

LA

Q

AL

lP

AL

F δδδ Φ+=divide by volume ( )ALFW /=

Nominal

Ll /=λ

APs /=

~DEsW~~δδλδ +=

LAALAL

name quantitiesaP /=σ

True

21

LE /~

Φ=

AQD /~=( )

λλ∂

∂=

DWs

~, ( )

D

DWE ~

~,~

∂∂

=λ

equations of statelE /Φ=

aQD /=

Construct a material model: ( )DW~

,λ

22

Dielectric constant is insensitive to stretchDielectric constant is insensitive to stretch

VHB 4910

23Kofod, Sommer-Larsen, Kornbluh, PelrineJournal of Intelligent Material Systems and Structures 14, 787 (2003).

Ideal dielectric elastomer

incompressibility

13λ

1321 =λλλ1

11

1λ2λ

( ) ( )λλλµλλ 3~

,,2

23

22

2121

DDW +−++=

Dielectric behavior is liquid-like, unaffected by deformation.

( ) ( )ε2

32

,, 32121

Elasticity Polarization

QD =

A

QD =~

~

λλD

D =

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

24

Zhao, Hong, Suo, Physical Review B 76, 134113 (2007)

a A 21λλ

Ideal dielectric elastomer 33Lλ

11Lλ Φ

33Lλ

11Lλ Φ2~D

22Lλ

Φ

Q22Lλ

Φ

Q( ) ( ) 22

21

22

22

122

2121 2

32

~,, −−−− +−++= λλ

ελλλλµλλ D

DW

I t f i l titi

2P 1P2P 1P

( )1

211

~,,

λλλ

∂∂

=DW

s( )

2

212

~,,

λλλ

∂∂

=DW

s

In terms of nominal quantities

In terms of true quantities

( ) 2222 Eελλλµσ −−= −− ( ) 2222 Eελλλµσ −−= −−

25

( )2111 Eελλλµσ = ( )2122 Eελλλµσ

How much can a dielectric elastomer be stretched?

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Two modes of failure

Φ

l

Q+

Q

Electromechanical instabilitySoft material

Q− l

El t i l b kdQ

Electrical breakdownHard material

polarizing thinningpolarizing

27Q

Φ

Q

Φ

A dilemmaA dilemma

•To deform appreciably without electrical breakdown, the elastomer must be soft.

•But a soft elastomer is susceptible to electromechanical instability.

How much can a dielectric elastomer be stretched?

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Electromechanical instability limits deformation of actuation

ΦQ+

Q

1λ

Q−1

λ

26.12 3/1 ≈=cλ

29Idea: Stark & GartonNature 176, 1225 (1955)

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

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

Pre-stretch i d f ti f t tiincreases deformation of actuation

33Lλ

11Lλ Φ

33Lλ

11Lλ Φ

22Lλ

Φ

Q22Lλ

Φ

Q

2P 1P2P 1P

30Experiment: Pelrine, Kornbluh, Pei, JosephScience 287, 836 (2000).

Theory: Zhao, SuoAPL 91, 061921 (2007)

Coexistent statesthinning

stiffening

ΦQ+ Φ

polarizingg

l

Q+

Q− Qthick thin

Φ

Top viewTop viewCross section

Coexistent states: flat and wrinkledObservation: Plante, Dubowsky, I t J S lid d St t 43 7727 (2006)

31Interpretation: Zhao, Hong, SuoPhysical Review B 76, 134113 (2007)

Int. J. Solids and Structures 43, 7727 (2006)

When stretched, a polymer stiffensy

n links

b

n links

Langevinreleased

nb

b

P

g

Gauss

λstretched

PP

n

λ

fully stretched

32bn

PP

fully stretched

Interpenetrating networks

•Short chains provide a safety net.•Long chains fill the space.

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Experiment: Ha, Yuan, Pei, PelrineAdv. Mater. 18, 887 (2006).

Theory: Suo, Zhu. Unpublished

Dielectric elastomer generatorDielectric elastomer generator

34Generate electricity from walking Generate electricity from waves

Pelrine, Kornbluh…

Maximal energy that can be converted b di l t i l tby a dielectric elastomer

E=0

EMI

6 J/g, Elastomer (theory)0.4 J/g, Elastomer (experiment)0.01 J/g ceramics

REMI

LT

EB

35

Koh, Zhao, Suo, Appl. Phys. Lett. 94, 262902 (2009)

Summary• Convergence of two worlds (soft biology, hard engineering).

• Soft active materials (SAMs) have many uses (soft robots, adaptive optics, self-regulating fluidics, oil recovery, energy harvesting, drug delivery, tissue regeneration, low-cost diagnosis…).

• Science of SAMs is interesting and challenging (Combining mechanics, electricity, and chemistry; large deformation, mass transport many modes of instability)mass transport, many modes of instability).

• The field is wide open (fabrication, computation, imagination).

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