Liquid Crystal Elastomer Liquid Crystal Elastomer Dielectric Constant Dielectric Constant

MeasurementsMeasurements

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

Liquid Crystal InstituteKent State UniversityKent, Ohio

Liquid Crystal InstituteKent State UniversityKent, Ohio

Liquid Crystal ElastomersLiquid Crystal Elastomers

• liquid crystal + rubber

• LC nematic monodmain

• synthesize here - need to characterize

LC mesogen

polymer backbone

cross-linker

Experiment 1Experiment 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 ExperimentVideo of Experiment

Experimental DataExperimental DataField On

Field Off

OverviewOverview

d

d

dt

dI

2

2torque

energy

I moment of inertia

Want to solve

:Depends on

dielectric constant components

k spring constant

material properties

Directly from

experimental data

TheoryTheoryEnergy of elastomer:

2

20

20

1

2 21

12 2

1

2 2

VD E k

VE E k

VE P E k

2 20

2

1

2 21

2 2

VE P E k

VP E k

k - spring constant

V -volume

susceptibility

P polarization

orientationally invariant

TheoryTheory

n̂m̂

ˆ ˆ

ˆ ˆ ˆ ˆ( )

loc

loc locll ll

locll

P E

E n E m

nn I nn E

�

��

In general:

nnIP

NEnnP

NE

PEE

appllapp

apploc

ˆˆˆˆ00

0

�

polarizability

density

N depolarizing tensor

where

TheoryTheoryTheoryTheory

0 0

ˆ ˆ ˆ ˆll app ll app

P PP E nn E I nn

����

appllllll EInnnnIP��

ˆˆˆˆ1

00

0

1a

0

ll llb

appll EInnnnbIaP��

ˆˆˆˆ

Make substitutions:

then

cont’d

TheoryTheory

Choose A & B such that

InnBIAnnbIa���

ˆˆˆˆ

)( baa

bB

baBA

1

appll EInnnnBIAP��

ˆˆˆˆ

aA

1

appll EnnBABIAP�

ˆˆ)()(

appll EInnnnbIaP��

ˆˆˆˆ

then

TheoryTheory

d

d

dt

dI

2

2

21

2 2

VP E k

2 2 2 2

2 2 2

1cos

2 21

cos2 2

app ll app

ll app

Vga AE B A B E k

VB A B E k

2cos sinll app

dB A B V E k

d

torque

Recall

Thus

Want to solve

orientationally invariant

TheoryTheory

)(0

llll1 ,ll

llo

o

1

2

202

( 1) cos sinll app

d dI B A B V E k

dt d

1

1 ( 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 inertia

k or free parameters

Also

So

where

Depolarizing FactorsDepolarizing Factors

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

, ,

a b c dsN

s a s b s c s

a b c ellipse semi axes

10

1.9

.22

a mm

b mm

c mm

10

1.9

.2

.0076

.0922

.9002

llN N

N

N N

Assume depolarizing factors for an ellipse can be used:

Elastomer PropertiesElastomer 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

2.00

3.8

.43

.386

l cm

w mm

d mm

m g

Electric Field MeasurementElectric Field Measurement

Vin

Vout

R1

R2

55.95 10appVE x m

1

2

98.55

26,800

R M

R

Voltage divider:(110) 15,206

(140) 19,353in

in

V V

V V

Thus

Experiment 2Experiment 2

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

Capacitance Bridge

Elastomer

Al plates

spacers

Vout

CBCU

Theory & ResultsTheory & Results

Without elastomer:0 ,10 air airs s

tot

AAC

d d

0 ,20 0air airs s etot

AA AC

d d d

Find3.88s

Using1.00059air

With elastomer:

Find3.38

ResultsResults

8

3.29

3.38

1.13 10 /k x N m

2

2

d dI

dt d

LHS RHS

Using:

Possible Future WorkPossible Future Work

• Remove shape effects:

OR

• Remove anisotropy effects:

• Repeat experiments in magnetic field

ConclusionsConclusions

• Electric field response used to determine elastomer dielectric constant values

• Would like to do similar magnetic field measurements

• Still a work in progress