NEMATIC FLUCTUATIONS AS A PROBE OF THE PROPERTIES OF
LIQUID CRYSTAL ELASTOMERS
Martin Čopič
Irena Drevenšek-Olenik
Andrej Petelin
Boštjan Zalar
Outline
• Introduction to liquid crystal elastomers• Soft mode in semisoft LCE observed by light
scattering• Holographic diffraction gratings in light sensitive
LCE• Conclusions
LC elastomers are media that combine orientational ordering of liquid crystals with elasticity of rubber •Remarkable elastic and thermoelastic properties
In the nematic phase the shape of the coils is associated with anistropic random walk:
n||z^
Isotropic Gaussian chain: Anisotropic Gaussian chain:
nL20
2 r
head to tail distance
zy,x,i ,,02 nLL iefir
Lef,z > Lef,x = Lef,y
LC ELASTOMERS
Temperature dependence of deformation
Sample I (crosslinked in the isotropic phase)
Oriented samples
• Without some external influence samples are not oriented
• Nematic director can be oriented by applied strain• Preparation of oriented “monodomain” samples
(Finkelmann):– Partially crosslink– Stretch– Crosslink
• Freezes internal strain
region of soft elasticity
normal elastomer behaviour
Stretching of LC elastomer: for small elongations free energy f is constant because deformation energy is compensated by anisotropic reshaping of the coils. (no force is needed for stretching)(Golubović and Lubensky)
experiment H. Finkelmann et al.
SOFT ELASTICITY OF LC ELASTOMERS
Semi-soft elasticity
Why light scattering
• Mechanical properties have been extensively studied• In case of semi-soft elasticity the experiments on
dynamic elastic response are not conclusive– Is semi-soft theory correct
• Primary order parameter is nematic order Q• Nematic director fluctuations should be a good probe
of the dynamic properties of LC– Light scattering
• Deformation driven soft mode should exist
Previous dynamic light scattering (DLS) in LC elastomers
• First experiments – Schmidtke et al. (2000), Schonstein et al. (2001)
• Director fluctuations have no q dependence• Relaxation rate governed by internal strain
Samples
• Samples under study were a side-chain LCE with a siloxane-based polymer backbone with 3-but-3-enyl-bezoic acid 4-methoxy-phenylester as the mesogenic moiety, cross-linked with 3.5 mol% concentration of a trifunctional cross-linker 1,3,5-tris-undec-10-enoxy-benzene.
• Light sensitive samples contained 10% azo-benzene • Provided by Professor H. Finkelmann
Scattering geometry
Strain vs. T
Strain – stress curves
Fits are to results of Warner – Terentjev theory
Nematic relaxation rate vs. deformation
Sample N.Sample I is very similar
Relaxation rate vs. q^2 at critical deformation
The slope gives K/
r00
010
001
0l nnl )1(1 r
z
z
s
00
01
0
0
λ
Director fluctuations vs. strain in semi-soft LCE
Free energy
nematicFTrTrF .nn.λ.λδ.λ.l.λl T1T
0 2
1
2
1
• Take strain perpendicular to z
• eliminate z
• Expand to second order in shear and orientation• Eigenvalues of the quadratic form coefficients give relaxation rates of fluctuations
Parameter of semi-softnessa measure of internal strain
Relaxation rates of the fluctuations
• The fluctuations of n and shear are coupled• Assume a single effective viscosity cofficient • Two fluctuation modes exist with the relaxation rates
given by the eigenvalues of the inverse susceptibility matrix
• The slower mode is predominantly director motion, the faster one shear.
Director mode relaxation rate
• Neglecting the nematic term the relaxation rate for the slow director mode can be very accurately approximated by
22
2
122
31
c
c
rr
rr
2
2
2
122
1zq
K
rr
r
• At critical deformation the nematic elasticity becomes dominant and the relaxation rate depends on q
Values of parameters
• Deformation vs. T gives r
• From critical deformation -
• Slope of the strain – force -
• Relaxation rate at no deformation – viscosity
• Dependence on q at critical deformation - K
T r [104Pa]
[Pa s]
K[10-12N]
60 1.88± 0.01
0.063 ±0.01
3.4 ± 0.4
440 ± 90
5.2 ± 1
70 1.62 0.052 3.3 120 ± 20
1 ± 0.2
75 1.41 0.039 3.2 26 ± 8 1.2 ± 0.4
78 1.15 0.017 2.8 10 ± 4 0.44 ± 0.2
Nematic elastic constant vs. order parameter
Stretching beyond critical point
To prevent domain formation a bias shear was applied – relaxation rate no longer goes to zero
T dependence of relaxation rate in unstretched sample
F=a(T-Tc ) Q.Q+…
a= 0.8x105 J/m3K
Viscosity activation energy
U=1.5 eV
June 1, 2010April 24, 2009
LIGHT-SENSITIVELIGHT-SENSITIVELIQUID CRYSTAL ELASTOMERSLIQUID CRYSTAL ELASTOMERS
LIGHT-SENSITIVELIGHT-SENSITIVELIQUID CRYSTAL ELASTOMERSLIQUID CRYSTAL ELASTOMERS
•photoisomerizable dyes (azobenzene derivatives) are added to the starting mixture
LCELaser beam 1
Laser beam 2
trans
cis
Holographic recording of diffraction gratings
0 200 400 600 800 1000 1200 1400 1600
0.1
1
10
0 2 4 6 80
5
10
15
20
25
Inte
nsi
ty (
arb
. un
its)
Time (min)
Kg II nRecordingRelaxation
GRATING RECORDING/RELAXATION DYNAMICSGRATING RECORDING/RELAXATION DYNAMICSGRATING RECORDING/RELAXATION DYNAMICSGRATING RECORDING/RELAXATION DYNAMICS
0 50 100 150 200 250 300
2.3
2.4
2.5
2.6 Expansion Contraction
Gra
tin
g p
erio
d (m
)
Strain (m)
Promising materials for tunable diffractive optical elements.
20 30 40 50 60 70 80
1.8
2.0
2.2
2.4
Gra
tin
g p
erio
d (m
)
Temperature (oC)
0.0
0.3
0.6
0.9
1.2
Dif
frac
tio
n e
ffic
ien
cy (
%)
TUNABILITY OF THE GRATING PERIODTUNABILITY OF THE GRATING PERIODTUNABILITY OF THE GRATING PERIODTUNABILITY OF THE GRATING PERIOD
Stretching/retraction
Heating
“Hidden” 2D grating
Hidden diffraction pattern
70 72 74 76 78 80 82 84 86
0.90
0.95
1.00
1.05
1.10
1.15
1.20
D/D
0
Temperature (oC)
Longitudinal Transversal
0
10
20
30
40
50
60
Diffractio
n (a.u
.)
Diffraction
Deformation and diffraction intensity on cooling from isotropic to nematic phase.
Recording
GRATING DEPTHGRATING DEPTHGRATING DEPTHGRATING DEPTHAngular dependence of diffraction efficiency
Angular width of the peak
Kg n
def ~ 20 m
Simulated diffraction peak
Simulated absorption profileof the cis conformers vs. irradiationtimes
Calculated diffraction peaks vs. irradiation times
Grating depth and period vs. illumination
-40 -30 -20 -10 00
1
2
3ExpectedBragg angle
Recording time 2 s 100 s
Diff
ract
ed
In
ten
sity
(a
rb.
un
its)
Incident angle (deg)
Relaxation of fluctuation rate and force after UV illumination (fixed length)
Conclusions
• Temperature tunable diffraction gratings in light sensitive LCE can be made
• We obtain the depth of the optical recording and isomerization rates
• Diffraction pattern can be used to probe the strain field and nematic order
• We observe a dynamic soft mode leading to semi-soft elasticity
• The experimental data is well described by the semi-soft nematic rubber theory
• All the parameters of the semi-soft theory can be obtained
Coworkers:
Andrej PetelinAlenka MerteljIrena DrevenšekBoštjan Zalar
H. Finkelmann, Freiburg
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