1

Elastic dielectrics

Zhigang Suosuo@seas.harvard.eduRoom 309, Pierce Hall

Compliant Electrode

Dielectric ElastomerA

Reference State

l

a Q

Q

Current State

Battery

2

Dielectric elastomer actuators

Kofod, Wirges, Paajanen, BauerAPL 90, 081916, 2007

•Large deformation•Compact•Lightweight•Low cost•Low-temperature fabrication

3

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

laQ

0

Q

4

An atom in an electric field

e

Hydrogen atom

e

+ + + + + + + + +

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

p

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

p

battery

5

A dipole in an electric field

Polar molecules

+ + + + + + + + +

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

External electric field reorients dipoles.•Polarization: Induce more change on the electrodes.•Deformation: Distort the shape of the sample.

battery

6

+ + + + + + + + +

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

+ + + + + + + + +

+-

Maxwell stressElectrostriction2

2E

thinning or thickening?

Cheng, Zhang, MRS Bulletin 33, 183 (2008).

Subject to an electric field, many polymers thin, but many ceramics thicken.

7

DW

s~,

D

DWE ~

~,~

Equations of state

Thermodynamics of elastic dielectrics

L

A

Reference State

P

l

a Q

Q

Current StateLl /

APs /

LE /~

AQD /~

QlPF

DEsW~~

LAQ

ALlP

ALF

For elastic dielectrics, work fully converts to free energy:

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

Free-energy density

8

2

,~,,

2

2121

DWDW s

32

, 23

22

2121 sW

Ideal dielectric elastomers

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

a

QD

A

QD ~

21

~

D

D

213 /1

Dielectric behavior is liquid-like, unaffected by deformation.

Ideal electromechanical coupling is purely a geometric effect:

Choose a free energy of stretching. For example, neo-Hookean law:

incompressibility

2P 1P

22L

33L

11L

Q

2P 1P

22L

33L

11L

Q

22

31

22

23

111

211

~~,

DDWs

21

32

22

13

222

212

~~,,

DDW

s

22

21

21

~

~

~,,~

D

D

DWE

9

Dielectric constant is insensitive to stretch

Kofod, Sommer-Larsen, Kornbluh, Pelrine Journal of Intelligent Material Systems and Structures 14, 787-793 (2003).

10

l

Q

Q

Stark & Garton, Nature 176, 1225 (1955)

Theory of pull-in instability

3/12~

1

D

Q

l

3/22~

1~

/

~

DDE

mVmF

mNEc /10

/10

/10~~

~ 810

6

Zhao, Suo, APL 91, 061921 (2007)

22

12~

322

~,

DDW

0

~,

DW

s D

DWE ~

~,~

63.0cQ

polarizing thinning

11

Pre-stretch increases actuation strain

2P 1P

22L

33L

11L

Q

2P 1P

22L

33L

11L

Q

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

Theory: Zhao, SuoAPL 91, 061921 (2007)

12

l

Q

Q

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

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

Qthick thin

Top viewCross section

Coexistent states polarizing

thinning

stiffening