Liquid Crystal Elastomer Dielectric Constant

MeasurementsJeremy NealP.Palffy-Muhoray

Ferroelectric Workshop – Kent State University Saturday, June 23, 2007

Liquid Crystal InstituteKent State UniversityKent, Ohio

Liquid Crystal Elastomers• liquid crystal + rubber

• LC nematic monodmain• synthesize here - need to characterize

LC mesogen

polymer backbone

cross-linker

Experiment 1

Variac

Ne Trans.ITO Glass

Elastomer

Elastomer is suspended on a string between two parallel pieces of ITOcoated glass. Elastomer aligns along sufficiently strong applied field.

Video of Experiment

0 2 4 6 8 10 12 140

20

40

60

80

100

120Angle vs. Time

Time (sec)

Ang

le (D

eg)

Experimental DataField On

Field Off

Overview

dd

dtdI 2

2 torqueenergy

I moment of inertia

Want to solve

:Depends on

dielectric constant components

k spring constantmaterial properties

Directly fromexperimental data

TheoryEnergy of elastomer:

2

20

20

12 2

112 2

12 2

V D E k

V E E k

V E P E k

2 20

2

12 2

12 2

V E P E k

V P E k

k - spring constantV -volume

susceptibility

P polarization

orientationally invariant

Theory

n̂m̂

ˆ ˆ

ˆ ˆ ˆ ˆ( )

loc

loc locll ll

locll

P E

E n E m

nn I nn E

�

�

In general:

nnIPNEnnPNE

PEE

appllapp

apploc

ˆˆˆˆ00

0

�

polarizabilitydensity

N depolarizing tensor

where

Theory

0 0

ˆ ˆ ˆ ˆll app ll appP PP E nn E I nn

�

appllllll EInnnnIP��

ˆˆˆˆ1

00

0

1a

0

ll llb

appll EInnnnbIaP�� ˆˆˆˆ

Make substitutions:

then

cont’d

Theory

Choose A & B such that

InnBIAnnbIa���

ˆˆˆˆ

)( baabB

ba

BA

1

appll EInnnnBIAP�� ˆˆˆˆ

aA 1

appll EnnBABIAP�

ˆˆ)()(

appll EInnnnbIaP�� ˆˆˆˆ

then

Theory

dd

dtdI 2

2

212 2V P E k

2 2 2 2

2 2 2

1cos2 2

1cos2 2

app ll app

ll app

V ga AE B A B E k

V B A B E k

2cos sinll appd B A B V E kd

torque

Recall

Thus

Want to solve

orientationally invariant

Theory

)(0

llll1 ,ll

llo

o

1

2

202 ( 1) cos sinll app

d dI B A B V E kdt d

11 ( 1)ll ll

A BN

( 1) ( 1)(1 ( 1) )(1 ( 1) )

ll ll

ll ll

N NB

N N

Need the following: ,

, ,

app

N N depolarizing factors

E electric field

I moment of inertiak or free parameters

Also

So

where

Depolarizing Factors

2 2 2 202 ( ) ( )( )( ), ,

a b c dsNs a s b s c s

a b c ellipse semi axes

101.9.22

a mmb mmc mm

10

1.9

.2

.0076.0922

.9002

llN NNN N

Assume depolarizing factors for an ellipse can be used:

Elastomer Properties

l

w

d

2 2

9 2

8 3

1 ( )12

1.29 10

3.28 10

I m d l

x kg m

V x m

2.003.8.43.386

l cmw mmd mmm g

Electric Field Measurement

VinVout

R1

R2

55.95 10appVE x m

1

2

98.5526,800

R MR

Voltage divider:(110) 15,206(140) 19,353

in

in

V VV V

Thus

Experiment 2

Elastomer is sandwiched between aluminum plates and capacitance is measured with bridge

Capacitance Bridge Elastomer

Al plates

spacers

Vout

CBCU

Theory & Results

Without elastomer:0 ,10 air airs s

tot

AACd d

0 ,20 0air airs s etot

AA ACd d d

Find3.88s

Using1.00059air

With elastomer:

Find3.38

Results

8

3.29

3.38

1.13 10 /k x N m

2

2

d dIdt d

LHS RHS

Using:

0 1 2 3 4 5 6 7 8

-6.0E-06

-4.0E-06

-2.0E-06

0.0E+00

2.0E-06

4.0E-06

6.0E-06

8.0E-06 Torque vs. Time

LHS

RHS

Time (sec)

Torq

ue (

N m

)

Possible Future Work• Remove shape effects:

OR

• Remove anisotropy effects:

• Repeat experiments in magnetic field

Conclusions

• Electric field response used to determine elastomer dielectric constant values

• Would like to do similar magnetic field measurements

• Still a work in progress