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Liquid Crystal Institute. Determination of refractive indices of liquid crystal elastomer . Israel Lazo, Jeremy Neal and Peter Palffy-Muhoray Liquid Crystal Institute, Kent State University, Kent OH, 44242. Motivation and Objectives. Understand the physical properties of this new materials - PowerPoint PPT Presentation
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American Physical Society 2008 1
Liquid Crystal Institute
Israel Lazo, Jeremy Neal and Peter Palffy-MuhorayLiquid Crystal Institute, Kent State University, Kent OH, 44242
Determination of refractive indices of liquid crystal elastomer
American Physical Society 2008 2
Motivation and Objectives
Understand the physical properties of this new materials
Measure the individual refractive indices of a nematic liquid crystal elastomer
Determine how this refractive indices change as a function of strain
American Physical Society 2008 3
LC elastomer
O OO
O
Mesogen
O
CH3H
CH3
Si O
CH3
SiH
CH3
Si H
85
CH3
Backbone
CH2
O
CH2
O
Crosslinker
American Physical Society 2008 4
Refractive indices
E
k
nLC
E
k
n
no ne
Techniques:Brewster’s angle measurementInterferometry
LC elastomer
American Physical Society 2008 5
Brewster’s angle
2
222
21
21
222
21
21
sin1cos
sin1cos
ii
ii
nnnn
nnnn
R
Schematic diagram of the experimental setup for Brewster’s angle measurements
Holder
-polarizationi
He-Ne
Sample
Detector
n10 20 30 40 50 60 70
0.00
0.01
0.02
0.03
0.04
0.05
Incident angle
i (o)
Nor
mal
ized
refle
cted
sig
nal
Experiment Theory
B=57o
Brewster’s angle!
American Physical Society 2008 6
Brewster’s angle (Model)
BVn tan0
BHo
e nn 2
2
tan111
n
Samplex
z
E
Vertical configuration
n
Samplex
zE
Horizontal configuration
pv
American Physical Society 2008 7
n
Ei
2
Hi
2
ki
kt
Dt
Et
1
Elastomer’s surface
Er
cos)cos(cos
cos)cos(cos
2112
2112
nn
nnr
222
222
2222
cossincossin)(tan
oe
oe
nnnn
222
2222
cossin oe
oe
nn
nnn
2211 sinsin nn
Mathematical model
s
American Physical Society 2008 8
Results
Experimental results for Brewster’s angle technique
0 5 10 15 20 25 30
1.40
1.42
1.44
1.46
1.48
1.50
1.52
1.54
1.56
1.58
1.601.62
1.64
1.66
1.68
1.70
1.72
R
efra
ctiv
e In
dex
Strain (%)
ne
no
Sno 31
S 32
// S 32
// S 32
// S 32
// S 32
// S 32
// S 32
// Sne 32
S increases with strain
American Physical Society 2008 9
Interferometry
Schematic diagram of the experimental setup for conoscopic interferometer
M: Mirror
L: Lens
LSample
M
M
BP
He-Ne
nE
American Physical Society 2008 10
Interferometer
ii nnd 22
22 sincos12
222
2222
cossin oe
oe
nn
nnn
Phase shift
Special consideration must be taken when calculating ne
Ordinary refractive indexnon2
22
21
2
sin
tan
ei
eo
o
nnn
n
-1000 -500 0 500 10000.0
0.2
0.4
0.6
0.8
1.0
1.2
Position (a.u.)
Nor
mal
ized
Am
plitu
de
Intensity profile
American Physical Society 2008 11
Experimental results for Interferometer and Brewster’s angle techniques
0 5 10 15 20 25 30 35 40
1.401.421.441.461.481.501.521.541.561.581.601.621.641.661.681.701.721.74
Ref
ract
ive
Inde
x
Strain (%)
ne Interferometer
no Interferometer ne Brewster no Brewster
American Physical Society 2008 12
Conclusion
We have measured the ordinary and extraordinary refractive indices of a nematic liquid crystal elastomer using two different methods
Two methods are in a good agreement
To doConfirm and interpret the results.
American Physical Society 2008 13
0 500 1000 1500 2000 2500 3000 3500
0
50
100
150
200
250
300
Y A
xis
Title
X Axis Title
C
-1000 -500 0 500 1000-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Data: Sheet1_IModel: interference Equation: A*exp(-0.5*((x-xc)/w)^2)*B*cos(x^2*a/b)^2 Weighting:y No weighting Chi^2/DoF = 0.03788R^2 = 0.42984 A 0.72524 ±0w -414.23236 ±0xc 19.62006 ±0B 2153.78282 ±0a 0.00583 ±0.00024b 237.34718 ±9.94937
Y A
xis
Title
X Axis Title
I