NEMATIC FLUCTUATIONS AS A PROBE OF THE PROPERTIES OF LIQUID CRYSTAL ELASTOMERS

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 • LC elastomers are media that combine orientational ordering of liquid crystals with elasticity of rubber • Remarkable elastic and thermoelastic properties ^ n||z In the nematic phase the shape of the coils is associated with anistropic random walk: Anisotropic Gaussian chain: Isotropic Gaussian chain: Lef,z > Lef,x = Lef,y head to tail distance

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. SOFT ELASTICITY OF LC ELASTOMERS 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) normal elastomer behaviour region of soft elasticity Semi-soft elasticity experiment H. Finkelmann et al.

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 Parameter of semi-softnessa measure of internal strain 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

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

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-Tc ) Q.Q+… a= 0.8x105 J/m3K Viscosity activation energy U=1.5 eV

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

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

24. GRATING RECORDING/RELAXATION DYNAMICS Recording Relaxation Kg II n

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

26. “Hidden” 2D grating

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

28. GRATING DEPTH Angular dependence of diffraction efficiency Kg n Angular width of the peak def ~ 20 m

29. Simulated diffraction peak Simulated absorption profileof 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