1 Elastic dielectrics Zhigang Suo [email protected] Room 309, Pierce Hall Compliant Electrode...
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Transcript of 1 Elastic dielectrics Zhigang Suo [email protected] Room 309, Pierce Hall Compliant Electrode...
1
Elastic dielectrics
Zhigang [email protected] 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)