American Physical Society 2008 1 Liquid Crystal Institute Israel Lazo, Jeremy Neal and Peter Palffy- Muhoray Liquid Crystal Institute, Kent State University, Kent OH, 44242 Determination of refractive indices of liquid crystal elastomer
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
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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
Israel
First of all understand...Regarding LCE what people usually do is determine the absolute birefringence of the sample, but so far nobody has measured the individual values of the ordinary and extraordinary refrective indices.We are interested not only in measuring this values in a NLCE but also we want to determine how this values change as the order in the sample is increased by applying a strain.
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LC elastomer
O OO
O
Mesogen
O
CH3H
CH3
Si O
CH3
SiH
CH3
Si H
85
CH3
Backbone
CH2
O
CH2
O
Crosslinker
Israel
Briefly LCE consists basically on 3 components: The LC of course, which provides the birefringence in the smaple, the backbone which is the polymer per se, and finally the crosslinker to attach this two components in the elastomer.If we have a monodmoain in the sample, this looks pretty much transparent and somthhing impoertant to note is that it preserves the high nirefringence given bu the LC as we can see in this pciture where the sample is between cross polarizers.
Since we are dealing with an anisotropic material, 2 different refractive indices are expected. If the electric field is oriented in such a way that is perpendicular to the nematic director the light will experince an ordinary refractive indexOn the other hand if the E is parallel to the director we will have the extraordinary refractive index.We want to measure this indices using two differet techniques, one based on reflection which is Brewster angle measurements, and the other based on transmission using a Mach zehnder interferometer.
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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!
Israel
Brewster abgle; As we know from theory for a pi polarization there's an angle at which the reflection is zero.By knowing this angle we can determine the refactive index of the sample.
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Brewster’s angle (Model)
BVn tan0
BHo
e nn 2
2
tan111
n
Samplex
z
E
Vertical configuration
n
Samplex
zE
Horizontal configuration
pv
Israel
In general we will have two configurations, the ordianry refractive index is determined in the same way we determine the refractive index in an isotropic material using Brewster angle technique. However this relation is not completely true for the extraordinary case. The reason is that when we have this configuration the electric field is not perpendicular anymore to the propagation vector k as light propagates through the sample.-------Doing the calculations we ended up with a very nice expression for the extraordinary refractive index which is a function of 2 variables that we can actually measure form the experiment.
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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
Israel
Here there's a cartoon showing the components of the electric field outside and inside the elastomer. In order to satisfy the boundary conditions for the tangential components of the electric field we need to consider the angle beta that the electric field separates away from the displacement vector.
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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
Israel
This graph shows the results that we got from the experiment. We can see that the extraordinary refractive index increases as a fucntion of the strain and on the contrary the ordianry refractive index is decreasing.This results are expected somehow if look at the theoretical expression for the refractice indices in a LC we can see that for the extraordinary index 'something' adds to the isotropic part of the dielectric permitivities and in a similar way for the ordinary case we can see that something substracts to the isotropic part.This something is a fucntion of the order parameter in the sample, and as we know the order parameter increases with the applied strain.
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Interferometry
Schematic diagram of the experimental setup for conoscopic interferometer
M: Mirror
L: Lens
LSample
M
M
BP
He-Ne
nE
Israel
In order to compare the previous results we implemet a second technique based on transmission. Here the light travels different distances as it goes through the sample.And again we have two differerent configutrations when the electric field is paralell or perpendicular to the director.
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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
Israel
We analize the intensity profile of the interference pattern. The phase shift between the reference beam and another inciding at an angle theta i on the sample is given by this expression. For the ordinary refractive index this expression doesnt require any other consideration and no = n2.However for the extraordinary index we need to consider that n2 is now the effective refractive index given by the properties of the LC
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Experimental results for Interferometer and Brewster’s angle techniques
A comparison of the results for both techniques is shown in this picture. where we can see that there's a good agreement between the two methods.However we have to say that we aould expect a larger change in ne with respect to no.
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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.
Israel
We have measured the individual values of the ordinary and extraordinary refractive indices of a LCE using two different techiniques.The results showed a good agreement between this techniques.And finally we still need to keep working on this to confirm and interpret our results.
