1. C. C. Huang, Department of Physics, University of Minnesota Office: Phys. 335, Tel: 4-0861 Outline: 1.Introduction 2. Experimental results 3. Phenomenological model for the SmC* variant phases 4. Predictions of the model 5. New experimental results 6. Summary and questions Collaborators: D. Olson, X. F. Han, A. Cady, H. T. Nguyen,H. Orihara, J. W. Goodby, R. Pindak, W. Caliebe, P. Barios, and H. Gleeson Experimental and theoretical studies of the SmC* variant phases

2. Conventional molecular arrangements in the SmA and SmC phases DOBAMBC In 1975, R. B. Meyer et al., proposed and synthesized the following chiral compound that displays ferroelectric response in the SmC* phase. Spontaneous polarization is perpendicular to the tilt plane. SmC*

3. Two unique physical properties associated with the SmC* phase Sample: DOBAMBC, Tc : SmA-SmC* transition temperature Spontaneous polarization Saturation polarization  60  C/m 2 Helical pitch

4. Compounds with large spontaneous polarization In 1989, A. D. L. Chandani et al., (Jpn. J. Appl. Phys. Part 2 28, L1265) reported the discovery of antiferroelectric response from the following compound: MHPOBC Saturation polarization > 500  C/m 2.

5. Thermal studies of MHPOBC sample Refs: A. D. L. Chandani, et al., Jpn. J. Appl. Phys. 28, L1261 (89). K. Ema, et al., Phys. Rev. E 47, 1203 (93).

6. Chiral tilted smectic phases ? ? ?   x y z c

7. Sequence of SmC* variance phases and their preliminary properties By employing various electro-optical techniques to study these phases, the following properties have been obtained: Upon Cooling: SmC  * phase: uniaxial phase SmC* phase AF or SmC FI2 * phase: 4-layer structure SmC  * or SmC FI1 * phase: 3-layer structure SmC A * : 2-layer structure SmC A *SmC FI2 *SmC FI1 * Ref.: T. Matsumoto, et al., J. Mater. Chem. 9, 2051 (1999).

8. Why resonant x-ray diffraction?

9. Fluorescence spectrum from a 10OTBBB1M7 powder sample Sample: 10OTBBB1M7

10. Polarization-analyzed resonant x-ray results from SmC* variant phases Intensity (Counts/5 seconds) Qz/Qo SmC  * SmC FI2 * SmC FI1 * SmC A * Sample: 10OTBBB1M7         = 5 to 8 = 4 = 3 = 2 Ref: P. Mach et al., PRL 81, 1015 (98). proposed ruled out

11. X-ray scattering intensity in the vicinity of the resonant energy Sample: 10OTBBB1M7 Eo = 2474.8 eV In the SmC FI2 * phase

12. T = 82.51 °C Fitting parameters: d = 35.07Å  = 31.0° n e = 1.645 n o = 1.485  = 18° Ellipsometry results from the SmC FI2 * phase of MHDDOPTCOB proposedruled out Ref. : P. M. Johnson, et al. PRL 84, 4870 (2000). Employ a powerful ellipsometer specially designed by our research group

13. High-resolution resonant x-ray scattering results Sample: MHDDOPTCOB Ising Model: two equal intensity split peaks Clock Model: single peak Distorted Model: Split peaks with different intensity intensity ratio distortion angle separation size of helical pitch The measured distortion angle (   =15  ) in good agreement with our optical result which yielded   =18 . SmC FI2 * Ref: A. Cady et al., Phys. Rev. E (RC) 64, 05702 (2001)

14. Experimental Results Experimental advances by resonant x-ray diffraction and optical studies 1. SmC  *: incommensurate short-helical pitch with pitch size > 4 layers (1999) 2. SmC FI2 *: distorted 4-layer structure (2000, 2001) 3. SmC FI1 *: distorted 3-layer structure (2000) SmC   SmC FI2 *SmC FI1 *

15. 1. M. Yamashita and S. Miyazima, Ferroelectrics 48, 1, (1993). Ising-like structure 2. A. Roy and N.V. Madhusudana, Europhys. Lett. 36, 221 (1996). Uniform helical phases and a non-uniformly modulated phases 3. M. Skarabot et al., Phys. Rev. E 58, 575 (1998). Short helical pitch and bi-layer structures 4. S. Pikin et al., Liq. Cryst. 26, 1107 (1999). Short helical pitch structures 5. M. Cepic and B. Zeks, Phys.Rev. Lett. 87, 85501 (2001). Short helical pitch structures None of them predicts the stability of distorted 3- or 4-layer structures. Theoretical advances: phenomenological approach

16. Phenomenological model for the SmC* variant phases Chiral: the simplest chiral term is f 1 (  k x  k+1 ) Phenomenological model: one with a minimum number of expansion terms which yields all the observed SmC* variant phases and offers new predictions. The description of observed SmC* variant phases (ignore the long optical helical pitch): SmC*: ferroelectric phase SmC A *: antiferroelectric phase SmC FI1 *: distorted structure with a 3-layer unit cell SmC FI2 *: distorted structure with a 4-layer unit cell SmC  *: incommensurate nano-scale helical pitch structure with pitch size > 4 layers The molecular tilt in k-th layer can be described by  k =  (cos(  k ), sin(  k )). x y z  kk

17. Various interlayer coupling terms A) n.n. coupling term: a 1 (  k.  k+1 ) a 1 < 0  ferroelectric coupling a 1 > 0  anti-ferroelectric coupling B) 3-layer unit cell: requires 3 rd n.n. coupling term: a 3 (  k.  k+3 ) and a 3 < 0 C) Thus the free energy expansion can be written as: G =  [a 1 (  k.  k+1 ) + a 2 (  k.  k+2 ) + a 3 (  k.  k+3 ) + f 1 (  k x  k+1 )] D) Do we need 4 th n.n. coupling term to describe SmC FI2 * with a 4-layer unit cell? The key feature for SmC FI2 * is that n.n.n. orientation is anti-clinic. Thus this requires that a 2 > 0 as well as both a 1 and a 3 are not too large. Simulation results: f 1  0, leads to simple helical structures and no well-defined phases with 3- or 4-layer unit cell and is similar to Cepic’s approach. k

18. One crucial additional term: b(  k.  k+1 ) 2 Thus: G =  [a 1 (  k.  k+1 ) + a 2 (  k.  k+2 ) + a 3 (  k.  k+3 ) + f 1 (  k x  k+1 ) + b(  k.  k+1 ) 2 ] b > 0 bi-layer model which has been considered previously b < 0 stable 3- and 4- layer distorted unit cell. We are mainly interested in minimizing the free energy G for various molecular azimuthal orientation with a given set of coefficients: a 1, a 2, a 3, f 1, and b. It is expected that a 1 and a 2 are the two most important ones. Thus for a given set of parameters (a 3, f 1, and b), we have identified the following phase diagram as a function of a 1 and a 2. The final free energy which yields the all the observed phases k

19. Phase diagram generated by the phenomenological model a 3 = -0.07K, f 1 = 0.12 K b  2 = -0.2K a 2 < 0 n.n.n. synclinic a 1 < 0 SmC* a 1 > 0 SmC A * a 1  0, a 2  0 and a 3 < 0 SmC d3 * a 2 > 0 n.n.n. anticlinic small a 1 SmC d4 * a 2  - a 1 SmC  1 * a 2  a 1 SmC  2 * SmC d3 * and SmC d4 *: 3- and 4- layer distorted structure. SmC  1 * and SmC  2 *: INHP structure with pitch > 4 and < 4 layers Ref: D. A. Olson, X. F. Han, A. Cady, and C. C. Huang, PRE 66, 021702 (2002).

20. Pitch evolution along two different paths Pitch length (layers) a) pitch versus a 2 along the path 1 for the SmC  1 *-SmC* transition. b) pitch versus a 1 along the path 2 for the SmC  1 *-SmC d4 *- SmC  2 * transition. SmC  1 * SmC* SmC  1 * SmC  2 * SmC d  *

21. Optical rotatory power vs. temperature from two compounds 10OTBBB1M7 11OTBBB1M7 pitch inversion no pitch inversion within the SmC FI2 * phase window Ref: F. Beaubois, et al., Eur. Phys. J. E 3, 273 (2000).

22. The distortion angle (  ) in 4- and 3-layer distorted phases a 3 = -0.07K, f 1 = 0.12 K b  2 = -0.2K In the SmC d4 *,    arcsin(- f 1 /(2 b  2 ))  if pitch length is large.

23. a) The helical pitch of 10OTBBB1M7 decreases monotonically on cooling through the SmC  * phase as measured using resonant x-ray diffraction by P. Mach et al., Phys. Rev. E 60, 6793 (1999). b) A much different helical pitch evolution in MHR49 as measured using resonant x-ray diffraction by L. S. Hirst et al., Phys. Rev. E 65, 041705 (2002). Temperature variation of pitch (> 4 layers) from two compounds

24. Pitch evolution in MHPOCBC SmC A * SmC  * A new SmC  * phase with pitch < 4 layers is experimental found by an optical probe! Layer thickness  3nm Laser wavelength = 630nm. Ref. A. Cady et al., PRL 91, 125502 (2003).

25. Summary 1. Our phenomenological model with five expansion terms has given theoretical support to the existence of the SmC d3 * and SmC d4 * with 3- and 4- layer distorted structures. Question Can the SmC d3 * and SmC d4 * fully describe the corresponding SmC FI1 * and SmC FI2 * phases? More research work needs to be done to answer the question. At least, the predicted helical pitch inversion in the SmC FI2 * phase has been observed in one liquid crystal compound. 2. The model also predicts the existence of the SmC  2 * phase with pitch less than four layers. Experimentally we have shown the existence of such a phase. Question Some critical properties of the SmC  2 * phase have to be experimentally tested. Related work is in progress. 3. The proposed model may not be the complete one. On the other hand, it contains the minimum number of terms to yield the stability of all observed SmC* variant phases. Definitely, it will form the starting point for the future theoretical modeling for the SmC* variant phases.

26. Phase sequences upon cooling SmA –SmC  1 *-SmC*-SmC FI2 *-SmC FI1 *-SmC A *

27. Additional questions 1.With liquid-like molecular arrangements within each layer, what are the physical origins of the next-nearest-neighbor and the 3 rd nearest neighbor interactions, required for this phenomenological model? Recently, M. B. Hamaneh and P. L. Taylor (PRL, in press) have offered one plausible explanation. 2. At least, two theoretical models have predicted the stability of a phase with the six-layer structure. So far, there is no experimental support of such a six-layer structure. Can a phase with the six-layer structure be stable in our simple model? a 2 (  k.  k+2 ) + b (  k.  k+1 ) 2 four- layer structure a 3 (  k.  k+3 ) + b (  k.  k+1 ) 2 ? Research work is supported by NSF, PRF, and DOE through BNL