1. NEMATIC FLUCTUATIONS AS A PROBE OF THE PROPERTIES OF LIQUID CRYSTAL ELASTOMERS Martin Čopič Irena Drevenšek-Olenik Andrej Petelin Boštjan Zalar

2. Outline Introduction to liquid crystal elastomers Soft mode in semisoft LCE observed by light scattering Holographic diffraction gratings in light sensitive LCE Conclusions

3. 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: head to tail distance L ef,z > L ef,x = L ef,y LC ELASTOMERS

4. Temperature dependence of deformation Sample I (crosslinked in the isotropic phase)

5. 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

6. 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

7. 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

8. 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

9. 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

10. Scattering geometry

11. Strain vs. T

12. Strain – stress curves Fits are to results of Warner – Terentjev theory

13. Nematic relaxation rate vs. deformation Sample N. Sample I is very similar

14. Relaxation rate vs. q^2 at critical deformation The slope gives K/ 

15. Director fluctuations vs. strain in semi-soft LCE Free energy 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-softness a measure of internal strain

16. 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.

17. Director mode relaxation rate Neglecting the nematic term the relaxation rate for the slow director mode can be very accurately approximated by At critical deformation the nematic elasticity becomes dominant and the relaxation rate depends on q

18. 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 Tr  [10 4 Pa]  [Pa s] K [10 -12 N] 60 1.88± 0.01 0.063 ±0.01 3.4 ± 0.4 440 ± 90 5.2 ± 1 70 1.620.0523.3120 ± 20 1 ± 0.2 75 1.410.0393.226 ± 8 1.2 ± 0.4 78 1.150.0172.810 ± 4 0.44 ± 0.2

19. Nematic elastic constant vs. order parameter

20. Stretching beyond critical point To prevent domain formation a bias shear was applied – relaxation rate no longer goes to zero

21. T dependence of relaxation rate in unstretched sample F=a(T-T c ) Q.Q+… a= 0.8x10 5 J/m 3 K Viscosity activation energy U=1.5 eV

22. June 1, 2010 April 24, 2009 LIGHT-SENSITIVE LIQUID CRYSTAL ELASTOMERS LIGHT-SENSITIVE photoisomerizable dyes (azobenzene derivatives) are added to the starting mixture

23. LCE Laser beam 1 Laser beam 2 trans cis Holographic recording of diffraction gratings

24. K g II n Recording Relaxation GRATING RECORDING/RELAXATION DYNAMICS

25. Promising materials for tunable diffractive optical elements. TUNABILITY OF THE GRATING PERIOD Stretching/retraction Heating

26. “Hidden” 2D grating

27. Hidden diffraction pattern Deformation and diffraction intensity on cooling from isotropic to nematic phase. Recording

28. GRATING DEPTH Angular dependence of diffraction efficiency Angular width of the peak K g  n d ef ~ 20  m

29. Simulated diffraction peak Simulated absorption profile of the cis conformers vs. irradiation times Calculated diffraction peaks vs. irradiation times

30. Grating depth and period vs. illumination

31. Relaxation of fluctuation rate and force after UV illumination (fixed length)

32. 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

33. Coworkers: Andrej Petelin Alenka Mertelj Irena Drevenšek Boštjan Zalar H. Finkelmann, Freiburg