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