Liquid Crystal Elastomer Dielectric Constant Measurements
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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