August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 Appendix A Measured Flexoelectric Coe?cients of Nematic Liquid Crystals N? andor ? Eber Institute for Solid State Physics and Optics Wigner Research Centre for Physics Hungarian Academy of Sciences P.O. Box 49, H-1525 Budapest, Hungary e-mail: eber@szfki.hu Since the discovery of ?exoelectricity1 in 1969 several direct and indirect methods for measuring the ?exoelectric coe?cients of nematic liquid crys- tals have been reported. These techniques, their advantages and drawbacks are discussed in detail in Chapters 2, 3 and 4 of this volume.2–4 Despite the diversity of the available methods, measurement of the ?exocoe?cients can still not be regarded as a routine task; e1 and e3 have been measured for a few compounds only. Unfortunately, sometimes even the data for a speci?c compound exhibit substantial deviations (di?erences in the magnitude or in the sign), depending on the experimental technique selected or even on the method of evaluation of the measured data sets. Comparison of data from various sources is encumbered by the fact that only a few techniques are capable of providing e1 or e3 directly; most meth- ods provide combinations of them, sometimes without information about their sign. Moreover, earlier papers give the ?exocoe?cients in CGS units (dyn1/2 ) instead of the SI ones (Cm?1 ) used nowadays (10?4 CGS units correspond to 3.33 * 10?12 Cm?1 ). To make the situation even more complicated, there exist two naming conventions for the ?exocoe?cients, which can be distinguished by looking at the de?nition of ?exoelectric polarization. According to the original de?nition of 1969 by Meyer1 P? = e1n(? · n) ? e3n * (? * n), (A.1) 249 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 250 N. ? Eber while the other convention, ?rst used by Patel and Meyer5 in 1987, also proposed by Rudquist and Lagerwall6 in 1997 and now suggested again by Meyer in the Introduction to the present book, uses Pf l = esn(? · n) + ebn * (? * n). (A.2) It can be seen that es = e1 but eb = ?e3; i.e. the two conventions di?er only in the sign of the bend ?exocoe?cient. Unfortunately, in some papers using the convention of Eq. (A.2) the ?exocoe?cients are still named e1 and e3 (instead of es and eb), which makes the sign of e3 ambiguous. In order to resolve these problems and help the comparison of data for the ?exocoe?cients on a wider scale than previous reviews,7,8 data available in the literature have been collected and are given in Tables A.1–A.9 in the same format. All values are in SI units and use the more widespread (original) naming convention corresponding to Eq. (A.1). The tables contain only an abbreviated name of each compound. The precise chemical names of the compounds are given in the relevant tables of Appendix B. In addition to the compounds listed in the tables, several other molecules have also been tested, however, only as a small concentration of dopants in some host nematic material. A linear extrapolation from these data might provide values for the ?exocoe?cients of the neat dopant; however, the ap- plicability of this procedure to many compounds is questionable (especially for bent-core molecules); therefore these data are not included in the tables. August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 Measured Flexoelectric Coe?cients for Nematics Liquid Crystals 251 Table A.1. Flexoelectric coe?cients of nematic liquid crystals using naming convention in Eq. (A.1): MBBA. Compound Flexoelectric coe?cient (Temperature) Alignment Method Reference MBBA |e3| ≈ 23.3 pC/ma (b ) homeotropic in-plane ?eld, induced bend, 9 interpretation of data from Ref. 10 MBBA e3 ≈ 1.2 pC/ma (? 22 ? C) homeotropic in-plane ?eld, induced bend 11 MBBA e3 ≈ 3.3 pC/ma (b ) homeotropic in-plane ?eld, induced bend, 12 reinterpretation of data in Refs. 10 and 11 MBBA e3 ≈ 17.3 ± 1.7 pC/ma (b ) homeotropic in-plane ?eld, conoscopy 13 MBBA |e3| ≈ 1.3 pC/m (25 ? C) homeotropic in-plane ?eld, induced bend 14 MBBA e1 ? e3 ≈ 3.3 ± 0.7 pC/ma (b) hybrid induced twist 15, 16 MBBA e1 ? e3 ≈ 14 ± 1 pC/m (30 ? C) hybrid in-plane ?eld, induced twist 7 MBBA |e1 ? e3| ≈ 17 pC/m (25 ? C) hybrid ?exodomains 17 MBBA e1 ? e3 = 6 pC/m (30 ? C) planar ?t of EC threshold 18 MBBA |e1 ? e3| ≈ 7 ± 0.15 pC/ma (b ) planar ?exodomains 19 MBBA e1 + e3 ≈ 10 pC/ma (b ) planar ?exoelectric oscillations 20 MBBA e1 + e3 ≈ 23.6 ± 4.6 pC/ma (35 ?C) homeotropic interdigitated electrodes, di?raction 21 MBBA e1 + e3 > 6.7 pC/ma (room) planar ?exodomains 22 MBBA e1 + e3 ≈ ?3.3 pC/ma (room) homeotropic in-plane ?eld, conoscopy 23, 16 MBBA e1 + e3 ≈ ?24.8 pC/ma (? 20? C) hybrid birefringence 24 MBBA e1 + e3 ≈ ?3.3 pC/ma (TNI ? 10? C) hybrid birefringence 24 MBBA e1 + e3 ≈ 0.17 pC/ma (b ) homeotropic oscillating pressure 25 MBBA e1 + e3 ≈ 0.5 pC/ma (b) homeotropic oscillating pressure 25 MBBA e1 + e3 ≈ ?15 pC/ma (b ) hybrid birefringence 26 MBBA e1 + e3 ≈ ?15 ± 2.3 pC/ma (b ) hybrid birefringence 27 MBBA e1 + e3 ≈ ?2.5 ± 0.2 pC/ma (room) hybrid pyroelectric 28 MBBA e1 + e3 ≈ ?2.5 ± 0.2 pC/ma (room) hybrid pyroelectric 29 MBBA e1 + e3 ≈ 40 pC/m (b ) homeotropic acoustic tilt 30 MBBA e1 + e3 ≈ 10 pC/ma (20 ? C) 72? tilt ellipsometry 31 MBBA e1 + e3 ≈ ?54 ± 1 pC/m (30 ? C) hybrid birefringence 7 MBBA e1 + e3 ≈ ?24 pC/m (room) hybrid pyroelectric, 32 reinterpretation of data in Ref. 28 MBBA e1 + e3 ≈ 88 pC/m (b ) hybrid birefringence, 33 reinterpretation of data in Ref. 24 MBBA e1 + e3 ≈ 1.6 ± 0.6 pC/m (b ) hybrid pyroelectric 34 MBBA e1 + e3 ≈ ?20 ± 5 pC/m (30 ? C) hybrid birefringence, 35 reinterpretation of data in Ref. 7 MBBA e1 + e3 = ?35 pC/m (30 ? C) planar ?t of EC threshold 18 a Converted from original data given in CGS units. b Temperature of measurement was not speci?ed. August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 252 N. ? Eber Table A.2. Flexoelectric coe?cients of nematic liquid crystals using naming convention in Eq. (A.1): cyanobiphenyls. Compound Flexoelectric coe?cient (Temperature) Alignment Method Reference 5CB e1 ≈ 5 pC/ma (room) hybrid pyroelectric 28 5CB e1 ≈ ?5 pC/ma (room) hybrid pyroelectric 29 5CB |e3| ≈ 40 pC/m (TNI ? 4 ? C) planar direct ?exing 36 5CB (e1 ? e3)/K2 ≈ 2.4 C/(Nm) (303 K) hybrid in-plane ?eld, induced twist 37 5CB (e1 + e3)/K3 ≈ 1.08 C/(Nm) (303 K) homeotropic quadrupolar ?eld, conoscopy 37 5CB e1 + e3 ≈ ?53 pC/m (25 ? C) hybrid pyroelectric 32 5CB e1 + e3 ≈ ?45.6 pC/m (25 ? C) hybrid pyroelectric 32 5CB e1 + e3 ≈ ?42 pC/m (25 ? C) hybrid pyroelectric 38 5CB e1 + e3 ≈ 30 pC/m (30 ? C) hybrid half-leaky guided mode 39 5CB e1 + e3 ≈ ?13 pC/m (room) hybrid pyroelectric 40 6CB (e1 ? e3)/K2 ≈ 2.51 C/(Nm) (301 K) hybrid in-plane ?eld, induced twist 37 7CB (e1 ? e3)/K2 ≈ 3.53 C/(Nm) (303 K) hybrid in-plane ?eld, induced twist 37 8CB e1 ? e3K ≈ 3.3 pC/ma (36.3 ? C) hybrid in-plane ?eld, induced twist 41, 16 8CB (e1 ? e3)/K ≈ 0.9 C/(Nm)a (36.3 ? C) hybrid in-plane ?eld, induced twist 41 8CB (e1 ? e3)/K ≈ 3.3 C/(Nm)a (36.3 ? C) hybrid in-plane ?eld, induced twist 41 8CB (e1 ? e3)/K2 ≈ 2.28 C/(Nm) (307 K) hybrid in-plane ?eld, induced twist 37 8CB e1 + e3 ≈ 480 pC/m (b ) homeotropic acoustic tilt 30 7OCBd (e1 ? e3)/K ≈ 1 C/(Nm)c (TNI ? 8 ? C) homeotropic cholesteric ?exoelectro-optic e?ect 42 8OCB e1 ? e3 ≈ ?16.7 pC/ma (77 ? ) hybrid in-plane ?eld, induced twist 41, 16 8OCB (e1 ? e3)/K ≈ ?4.7 C/(Nm)a (77 ? ) hybrid in-plane ?eld, induced twist 41 8OCB (e1 ? e3)/K ≈ 2.3 C/(Nm) (TNI ? 8 ? C) hybrid in-plane ?eld, induced twist 43 8OCB e1 + e3 ≈ 21.3 ± 5 pC/ma (73 ? C) homeotropic interdigitated electrodes, di?raction 21 8OCB e1 + e3 ≈ 4.7 pC/ma (TNI ? 7 ? C) homeotropic in-plane ?eld, conoscopy 23 8OCB e1 + e3 ≈ 7 ± 1.5 pC/m (75 ? C) hybrid pyroelectric 44 8OCB (e1 + e3)/K3 ≈ 0.29 C/(Nm) (343 K) homeotropic quadrupolar ?eld, conoscopy 37 5CT (e1 ? e3)/K2 ≈ 0.87 C/(Nm) (423 K) hybrid in-plane ?eld, induced twist 37 HBACPE e1 + e3 ≈ 270 pC/m (b ) homeotropic acoustic tilt 30 CBmix e1 + e3 ≈ 45 ± 22 pC/m (22 ? C) hybrid ?exoelectric o?set voltage 45 a Converted from original data given in CGS units. b Temperature of measurement was not speci?ed. c Original data were given using naming convention in Eq. (A.2). d Chiral dopant added for the measurement. August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 Measured Flexoelectric Coe?cients for Nematics Liquid Crystals 253 Table A.3. Flexoelectric coe?cients of nematic liquid crystals using naming convention in Eq. (A.1): cyclohexanes. Compound Flexoelectric coe?cient (Temperature) Alignment Method Reference PCH3 (e1 ? e3)/K2 ≈ 0.36 C/(Nm) (310 K) hybrid in-plane ?eld, induced twist 37 PCH3 (e1 + e3)/K3 ≈ 0.11 C/(Nm) (310 K) homeotropic quadrupolar ?eld, conoscopy 37 PCH4 (e1 ? e3)/K2 ≈ 1.55 C/(Nm) (311 K) hybrid in-plane ?eld, induced twist 37 PCH5 (e1 ? e3)/K2 ≈ 1.66 C/(Nm) (303 K) hybrid in-plane ?eld, induced twist 37 PCH5 (e1 + e3)/K3 ≈ 0.12 C/(Nm) (303 K) homeotropic quadrupolar ?eld, conoscopy 37 PCH7 (e1 ? e3)/K2 ≈ 1.2 C/(Nm) (303 K) hybrid in-plane ?eld, induced twist 37 PCH7 (e1 + e3)/K3 ≈ 0.23 C/(Nm) (303 K) homeotropic quadrupolar ?eld, conoscopy 37 CCH7 (e1 ? e3)/K2 ≈ ?1.29 C/(Nm) (343 K) hybrid in-plane ?eld, induced twist 37 CCH7 (e1 + e3)/K3 ≈ 0.51 C/(Nm) (343 K) homeotropic quadrupolar ?eld, conoscopy 37 CCH7 (e1 + e3)/S ≈ 36 pC/ma (0.93TNI ) hybrid AC ?eld, birefringence 46 MPPC (e1 ? e3)/K2 ≈ 0.52 C/(Nm) (323 K) hybrid in-plane ?eld, induced twist 37 EPPC (e1 ? e3)/K2 ≈ 0.28 C/(Nm) (323 K) hybrid in-plane ?eld, induced twist 37 PPPC (e1 ? e3)/K2 ≈ 2.97 C/(Nm) (310 K) hybrid in-plane ?eld, induced twist 37, 47 PCHmix e1 + e3 ≈ 48 ± 24 pC/m (22 ?C) hybrid ?exoelectric o?set voltage 45 Mix1 (e1 ? e3)/K2 ≈ 0.33 C/(Nm) (303 K) hybrid in-plane ?eld, induced twist 37, 47, 48 Mix1 (e1 + e3)/K3 ≈ ?0.60 C/(Nm) (303 K) homeotropic quadrupolar ?eld, conoscopy 37, 47, 48 aConverted from original data given in CGS units. August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 254 N. ? Eber Table A.4. Flexoelectric coe?cients of nematic liquid crystals using naming convention in Eq. (A.1): other calamitics. Compound Flexoelectric coe?cient (Temperature) Alignment Method Reference BHAOB e1 + e3 ≈ 16 pC/m (b ) homeotropic acoustic tilt 30 BMAOB |e1 ? e3| ≈ 5.7 pC/ma (25 ? C) planar ?exodomains 49 BMAOB |e1 ? e3| ≈ 5.7 pC/ma (b ) planar ?exodomains 50 BMAOB |e1 ? e3| ≈ 5.3 pC/m (29 ? C) planar ?exodomains 51 BMAOB |e1 ? e3| ≈ 12.3 ± 2 pC/ma (room) planar ?exodomains 52 BMAOB |e1 ? e3| ≈ 5.8 pC/ma (b ) hybrid ?exodomains 53 BBMBA e1 + e3 ≈ 8.3 pC/ma (TNA + 1 ? C) homeotropic interdigitated electrodes, di?raction 54 CBOOA |e1 + e3| ? 3 pC/ma (b ) homeotropic interdigitated electrodes, di?raction 54 ROCP-7037 (e1 ? e3)/K2 ≈ 4.36 C/(Nm) (319 K) hybrid in-plane ?eld, induced twist 37 ROCP-7037 (e1 + e3)/K3 ≈ 0.05 C/(Nm) (319 K) homeotropic quadrupolar ?eld, conoscopy 37 ROCP-7334 (e1 ? e3)/K2 ≈ 2.52 C/(Nm) (373 K) hybrid in-plane ?eld, induced twist 37 ROCP-7334 (e1 + e3)/K3 ≈ 0.16 C/(Nm) (373 K) homeotropic quadrupolar ?eld, conoscopy 37 HOT (e1 + e3)/K ≈ 2.7 C/(Nm)a (99.3 ? C) homeotropic interdigitated electrodes, di?raction 21 3PBClB (e1 + e3)/K ≈ 0.9 C/(Nm)a (48.9 ? C) homeotropic interdigitated electrodes, di?raction 21 NPOOB e1 + e3 ≈ 98 pC/m (b ) homeotropic acoustic tilt 30 8/7 e1 ? e3 = 2.9 pC/m (86 ? C) planar ?t of EC thresholds 55 8/7 e1 ? e3 = 1 pC/m (86 ? C) planar ?t of EC thresholds 56 8/7 e1 + e3 = ?59.5 pC/m (86 ? C) planar ?t of EC thresholds 55 8/7 e1 + e3 = ?20 pC/m (86 ? C) planar ?t of EC thresholds 56 unknown compound |e1 ? e3| = 4.4 pC/m (b ) planar domain walls 57 unknown compound e1 + e3 = 8 pC/m (b ) planar domain walls 57 DEmix e1 + e3 ≈ 46 ± 23 pC/m (22 ? C) hybrid ?exoelectric o?set voltage 45 PB |e1 ? e3| ≈ 6 pC/ma (25 ? C) planar ?exodomains 49 MixA e3 ≈ 0.3 pC/ma (b ) homeotropic oscillating pressure 58 a Converted from original data given in CGS units. b Temperature of measurement was not speci?ed. August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 Measured Flexoelectric Coe?cients for Nematics Liquid Crystals 255 Table A.5. Flexoelectric coe?cients of nematic liquid crystals using naming convention in Eq. (A.1): commercial mixtures. Compound Flexoelectric coe?cient (Temperature) Alignment Method Reference E7 (e1 ? e3)/K ≈ 0.9 C/(Nm)c (0.98TNI ) hybrid in-plane ?eld, induced twist 59 E7 e1 ? e3 ≈ -10.6 pC/m (b ) twisted in-plane ?eld, induced tilt, conoscopy 60 E7d e1 ? e3 ≈ 9.3 ± 0.3 pC/m (b ) twisted cholesteric ?exoelectro-optic e?ect 61 E7 e1 ? e3 ≈ 12.2 ± 1 pC/m (b ) twisted in-plane ?eld, induced tilt, conoscopy 60 E7 |e1 ? e3| ≈ 5 pC/m (57.6 ? C) 45? twist, 37? pretilt bistable polar switching 62 E7d e1 ? e3 ≈ 12.2 ± 1 pC/m (b ) twisted cholesteric ?exoelectro-optic e?ect 63 E7d e1 ? e3 ≈ 12.2 ± 0.8 pC/m (b ) hybrid cholesteric ?exoelectro-optic e?ect 64 E7d e1 ? e3 ≈ 12.2 ± 2 pC/m (b ) planar chiral Grandjean texture 64 E7 e1 + e3 ≈ 15 ± 2 pC/m (b ) hybrid fully leaky guided mode 65 E7 e1 + e3 ≈ 15 ± 3 pC/m (b ) hybrid fully leaky guided mode 66 E7 e1 + e3 ≈ 20 ± 5 pC/m (b ) homeotropic, grating di?raction 67 E7 e1 + e3 ≈ 600 pC/m (b ) homeotropic ZBD AC ?eld, birefringence 68 E7 e1 + e3 ≈ 40 ± 5 pC/m (? 20 ? C) homeotropic ZBD AC ?eld, birefringence 69 E7 e1 + e3 ≈ 14 ± 1 pC/m (b ) planar interferometry, interdigitated electrodes 70 E7 e1 + e3 ≈ 45 ± 22 pC/m (22 ? C) hybrid ?exoelectric o?set voltage 45 E7 e1 + e3 ≈ 35 ± 5 pC/m (b ) 180? twist, 35? pretilt birefringence 63 E7 e1 + e3 ≈ 14 ± 1 pC/m (b ) planar interferometry, interdigitated electrodes 71 E70Ad e1 ? e3 ≈ 3.5 ± 0.2 pC/m (b ) twisted cholesteric ?exoelectro-optic e?ect 61 E70A e1 + e3 ≈ 34 ± 17 pC/m (22 ?C) hybrid ?exoelectric o?set voltage 45 b Temperature of measurement was not speci?ed. c Original data were given using naming convention in Eq. (A.2). d Chiral dopant added for the measurement. August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 256 N. ? Eber Table A.6. Flexoelectric coe?cients of nematic liquid crystals using naming convention in Eq. (A.1): commercial mixtures. Compound Flexoelectric coe?cient (Temperature) Alignment Method Reference ZLI-4788-000 e1 + e3 ≈ 22 pC/mc (b ) hybrid fully leaky guided mode 72 ZLI-4788-000 e1 + e3 ≈ ?7 pC/mc (b ) hybrid fully leaky guided mode 72 ZLI-4792 (e1 ? e3)/K ≈ 0.6 C/(Nm)c (0.98TNI) hybrid in-plane ?eld, induced twist 59 ZLI-4792 |e1 + e3| ≤ 10 ± 1 pC/m (30 ? C) hybrid birefringence 7 ZLI-4792 e1 ? e3 ≈ ?15 ± 1 pC/m (30 ? C) hybrid in-plane ?eld, induced twist 7 TL-216d e1 ? e3 ≈ 1.45 ± 0.3 pC/m (b ) hybrid cholesteric ?exoelectro-optic e?ect 64 TL-216d e1 ? e3 ≈ 0.9 ± 0.3 pC/m (b ) planar chiral Grandjean texture 64 TL-216 e1 ? e3 ≈ 0.4 ± 0.25 pC/m (b ) twisted in-plane ?eld, induced tilt, conoscopy 60 TL-216 e1 + e3 ≈ 1 pC/m (22 ? C) hybrid ?exoelectric o?set voltage 45 MDA-02-2419d e1 ? e3 ≈ 22 ± 1.5 pC/m (b ) hybrid cholesteric ?exoelectro-optic e?ect 64 MDA-02-2419d e1 ? e3 ≈ 28.2 ± 4 pC/m (b ) planar chiral Grandjean texture 64 MDA-02-2419 e1 + e3 ≈ 102 ± 51 pC/m (22 ? C) hybrid ?exoelectric o?set voltage 45 MDA-02-2419 e1 ? e3 ≈ 22 ± 1 pC/m (b ) twisted in-plane ?eld, induced tilt 64 MLC-7029 e1 + e3 ≈ ?7 ± 3.5 pC/m (22 ? C) hybrid ?exoelectric o?set voltage 45 MLC-6437-000d e1 ? e3 ≈ 3.2 pC/mc (0.9TNI ) homeotropic cholesteric ?exoelectro-optic e?ect 73 Phase4 e1 ? e3 = ?4.7 pC/m (20 ? C) planar ?t of EC thresholds 74 Phase4 e1 + e3 = ?31.5 pC/m (20 ? C) planar ?t of EC thresholds 74 Phase5 e1 ? e3 = ?2.9 pC/m (30 ? C) planar ?t of EC thresholds 18, 55 Phase5 e1 + e3 = ?50.1 pC/m (30 ? C) planar ?t of EC thresholds 18, 55 Phase5A e1 ? e3 = ?2.9 pC/m (30 ? C) planar ?t of EC thresholds 18, 55 Phase5A e1 + e3 = ?50.1 pC/m (30 ? C) planar ?t of EC thresholds 18, 55 b Temperature of measurement has not been speci?ed. c Original data were given using naming convention in Eq. (A.2). d Chiral dopant added for the measurement. August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 Measured Flexoelectric Coe?cients for Nematics Liquid Crystals 257 Table A.7. Flexoelectric coe?cients of nematic liquid crystals using naming convention in Eq. (A.1): bent-core compounds. Compound Flexoelectric coe?cient (Temperature) Alignment Method Reference ClPbis10BB |e3| ≈ 35000 pC/m (TNI ? 2 ?C) planar direct ?exing 36 ClPbis10BB e3 ≈ 40000 pC/m (TNI ? 4 ?C) planar ?exible electrode, interferometry 75 ClPbis10BB |e3| ≈ 15.8 pC/m (71.5 ?C) homeotropic in-plane ?eld, induced bend 76 ClPbis10BB |e1 ? e3| ≈ 6 pC/m (74 ?C) planar ?exodomains 76 ClPbis10BB |e1 ? e3| ≈ 11.2 pC/ma (75 ?C) hybrid ?exodomains 53 CNRbis12OBB e3 ≈ 3.9 ± 1 pC/m (120 ?C) homeotropic in-plane DC ?eld, induced bend 77 CNRbis12OBB |e3| ≈ 5.4 ± 0.4 pC/m (120 ?C) homeotropic in-plane AC+DC ?eld, induced bend 77 CNRbis12OBB |e1| ? 7.7 pC/m (120 ?C) homeotropic in-plane AC+DC ?eld, induced bend 77 BEPC |e1 ? e3| ≈ 5.95 pC/m (55 ?C) planar ?exodomains 78 BCCB e1 ≈ 17.6 pC/m (140 ?C) homeotropic surface polar instability 77 BCCB e3 ≈ 17.2 pC/m (140 ?C) homeotropic surface polar instability 77 C6band e1 ? e3 ≈ ?17.4 pC/m (TNI ? 11 ?C) homeotropic cholesteric ?exoelectro-optic e?ect 79 Azpac |e1 ? e3| ≈ 3.3 pC/m (100 ?C) planar ?exodomains 80 aConverted from original data given in CGS units. dChiral dopant added for the measurement. August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 258 N. ? Eber Table A.8. Flexoelectric coe?cients of nematic liquid crystals using naming convention in Eq. (A.1): bimesogens. Compound Flexoelectric coe?cient (Temperature) Alignment Method Reference 11Es5CBd e1 ? e3 ≈ ?10.4 pC/mc (b ) homeotropic cholesteric ?exoelectro-optic e?ect 81 11Es5CBd e1 ? e3 ≈ 10.4 pC/mc (b ) homeotropic cholesteric ?exoelectro-optic e?ect 82 5Es11CBd e1 ? e3 ≈ 9 ± 1 pC/mc (b ) homeotropic cholesteric ?exoelectro-optic e?ect 81 5Es11CBd e1 ? e3 ≈ 10.6 pC/mc (b ) homeotropic cholesteric ?exoelectro-optic e?ect 82 CBO8OCBd (e1 ? e3)/K ≈ 1.2 C/(Nm)c (TNI ? 22 ? C) homeotropic cholesteric ?exoelectro-optic e?ect 42 FFO5OCBd e1 ? e3 ≈ 20.4 pC/mc (0.84TNI ) homeotropic cholesteric ?exoelectro-optic e?ect 83 FFO6OCBd e1 ? e3 ≈ 12.6 pC/mc (0.84TNI ) homeotropic cholesteric ?exoelectro-optic e?ect 83 FFO7OCBd e1 ? e3 ≈ 20.6 pC/mc (0.84TNI ) homeotropic cholesteric ?exoelectro-optic e?ect 83 FFO8OCBd e1 ? e3 ≈ 14.6 pC/mc (0.84TNI ) homeotropic cholesteric ?exoelectro-optic e?ect 83 FFO9OCBd e1 ? e3 ≈ 19.8 pC/mc (0.84TNI ) homeotropic cholesteric ?exoelectro-optic e?ect 83 FFO10OCBd e1 ? e3 ≈ 15 pC/mc (0.84TNI ) homeotropic cholesteric ?exoelectro-optic e?ect 83 FFO11OCBd e1 ? e3 ≈ 21.2 pC/mc (0.84TNI ) homeotropic cholesteric ?exoelectro-optic e?ect 83 FFO12OCBd e1 ? e3 ≈ 13.2 pC/mc (0.84TNI ) homeotropic cholesteric ?exoelectro-optic e?ect 83 NSO9OFFd e1 ? e3 ≈ 20.4 pC/mc (0.84TNI ) homeotropic cholesteric ?exoelectro-optic e?ect 83 NSO9OphO9OCBd e1 ? e3 ≈ 11.6 pC/mc (0.91TNI ) homeotropic cholesteric ?exoelectro-optic e?ect 83 Mixture1d (e1 ? e3)/K ≈ 0.94 C/(Nm)c (b ) homeotropic cholesteric ?exoelectro-optic e?ect 84 Mixture2d (e1 ? e3)/K ≈ 1.74 C/(Nm)c (b ) homeotropic cholesteric ?exoelectro-optic e?ect 84 Mixture2d (e1 ? e3)/K ≈ 1.88 C/(Nm)c (0.84TNI ) homeotropic cholesteric ?exoelectro-optic e?ect 83 Mixture3d (e1 ? e3)/K ≈ 3.48 C/(Nm)c (0.84TNI ) homeotropic cholesteric ?exoelectro-optic e?ect 83 MixBimesd (e1 ? e3)/K ≈ 2 C/(Nm)c (TNI ? 22 ? C) homeotropic cholesteric ?exoelectro-optic e?ect 42 b Temperature of measurement was not speci?ed. c Original data were given using naming convention in Eq. (A.2). d Chiral dopant added for the measurement. August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 Measured Flexoelectric Coe?cients for Nematics Liquid Crystals 259 Table A.9. Flexoelectric coe?cients of chiral nematic liquid crystals using naming convention in Eq. (A.1). Compound Flexoelectric coe?cient (Temperature) Alignment Method Reference (S)-9PPP8dM e1 ? e3 ≈ 2 pC/mac (b) planar cholesteric ?exoelectro-optic e?ect 5 8OCB/CC |e1 ? e3| ≈ ?3 pC/m (57.6 ?C) planar Lehmann rotation 85 TM-216 (e1 ? e3)/K ≈ 0.12 C/(Nm) (b) homeotropic cholesteric ?exoelectro-optic e?ect 86 aConverted from original data given in CGS units. bTemperature of measurement was not speci?ed. cOriginal data were given using naming convention in Eq. (A.2). 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Abbreviation Chemical name BHAOB : n-butyl-n-heptanoil azoxy benzene BMAOB : 4-n-butyl-4 -methoxyazoxybenzene BBMBA : 4-butoxybenzal-4 -(β-methylbutyl)aniline CBOOA : 4-cyanobenzylidene-4 -octyloxyaniline MBBA : N-(4-metoxybenzylidene)-4 -butylaniline nCB : 4-alkyl-4 -cyanobiphenyl 5CB : 4-pentyl-4 -cyanobiphenyl 6CB : 4-hexyl-4 -cyanobiphenyl 7CB : 4-heptyl-4 -cyanobiphenyl 8CB : 4-octyl-4 -cyanobiphenyl 7OCB : 4-n-heptyloxy-4 -cyanobiphenyl 8OCB : 4-n-octyloxy-4 -cyanobiphenyl 5CT : 4 -pentyl-4 -cyano-4-terphenyl PCHn : 4-cyanophenyl-trans-4 -n-alkylcyclohexane PCH3 : 4-cyanophenyl-trans-4 -n-propylcyclohexane PCH4 : 4-cyanophenyl-trans-4 -n-butylcyclohexane PCH5 : 4-cyanophenyl-trans-4 -n-pentylcyclohexane PCH7 : 4-cyanophenyl-trans-4 -n-heptylcyclohexane CCHn : 4-alkyl-4 -cyanocyclohexylcyclohexanes CCH7 : 4-heptyl-4 -cyanocyclohexylcyclohexane MPPC : 4-methoxyphenyl trans-4-pentylcyclohexylcarboxylate EPPC : 4-ethoxyphenyl trans-4-pentylcyclohexylcarboxylate PPPC : 4-pentylphenyl trans-4-pentylcyclohexylcarboxylate PEC : 1-propyl-4(4-ethoxyphenyl)cyclohexane DE3 : 4 -cyanophenyl 4-propylcyclohexanecarboxylate DE5 : 4 -cyanophenyl 4-pentylcyclohexanecarboxylate DE7 : 4 -cyanophenyl 4-heptylcyclohexanecarboxylate ROCP-7037 : 5-heptyl-2-(4-cyanophenyl)pyrimidine ROCP-7334 : 5-(4-butylphenyl)-2-(4-cyanophenyl)pyrimidine 6OO8 : 4-n-octyloxy-phenyl-4-n-hexyloxybenzoate 8/7 : 4-n-octyloxy-phenyl-4-n -heptyloxy-benzoate BEPC : butyl p-(p-ethoxyphenoxycarbonyl)phenyl carbonate 267 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 268 Abbreviations Table B.1. Nematic compounds (continued). Abbreviation Chemical name HBACPE : n-heptyl benzonoic acid n-cyanobiphenyl ester NPOOB : 4-nytrophenyl-4-n-octyloxy benzoate HOT : 4,4 -dihexyloxytolan 3PBClB : 4,n-pentylphenyl-4,(pentylbenzoyloxy)-3-chloro benzoate MBB : 1,4-di-(4-butylbenzoyloxy)-2-methylbenzene CCa : cholesteryl chloride MHPOBCa : 4-(1-methylheptyloxycarbonyl)phenyl 4 -octyloxybiphenyl-4-carboxylate (S)-9PPP8dMa : S-4-n-nonyloxyphenyl-4 -(3 ,7 -dimethyloctyloxybenzoyloxy) benzoate a Chiral compound Table B.2. Bent-core nematic compounds. Abbreviation Chemical name ClPbis10BB : 4-chloro-1,3-phenylene bis 4-[4 -(9-decenyloxy) benzoyloxy] benzoate 10DClPBBC : 4,6-dichloro-1,3-phenylene bis[4-(9-decen-1-yloxy)-1,1 -biphenyl-4-carboxylate] 11DClPBBC : 4,6-dichloro-1,3-phenylene bis[4-(10-undecen-1-yloxy)-1,1-biphenyl-4-carboxylate] 10DClPBCP : 2,4-dichloro-5-[(4-decyloxy-1,1 -biphenyl)carbonyloxy]phenyl -4 -[(9-decene-1-yloxy)-1,1 -biphenyl]-4-carboxylate BC12 : 1,3-phenylene bis[4-(3-methylbenzoyloxy)] 4 - n-dodecylbiphenyl 4 -carboxylate CNRbis12OBB : 4-cyanoresorcinol bis[4-(4-n-dodecyloxybenzoyloxy) benzoate] C6ban : 4-cyano-1,3-phenylene bis [4-[4 -(hexyl) benzoyloxy] benzoate] Azpac : acetylacetonate derivative of the cyclopalladated 4,4-bis(hexyloxy) azoxybenzene Table B.3. Bimesogens. Abbreviation Chemical name BCCB : 4-((3-(4-(4-(decyloxy)benzoyloxy)benzoyloxy) phenylimino) methyl) -3-hydroxyphenyl 4-(6-(4 -cyanobiphenyl-4-yloxy)hexyloxy) benzoate 11Es5CB : 3-(10-Undecenyloxy)estra-1,3,5(10)-triene-17β-yl 5-(4 -cyanobiphenyl-4-yloxy)pentanoate 5Es11CB : 3-(4-Pentenyloxy)estra-1,3,5(10)-triene-17β-yl 10-(4 -cyanobiphenyl-4-yloxy)undecanoate FFOnOFF : α-(2 ,4-di?uorobiphenyl-4 -yloxy)-ω-(2 ,4-di?uorobiphenyl-4 -yloxy)alkanes FFO9OFF : α-(2 ,4-di?uorobiphenyl-4 -yloxy)-ω-(2 ,4-di?uorobiphenyl-4 -yloxy)nonane FFO11OFF : α-(2 ,4-di?uorobiphenyl-4 -yloxy)-ω-(2 ,4-di?uorobiphenyl-4 -yloxy)undecane FFEnEFF : α-(2 ,4-di?uorobiphenyl-4 -ester)-ω-(2 ,4-di?uorobiphenyl-4 -ester)alkanes FFE9EFF : α-(2 ,4-di?uorobiphenyl-4 -ester)-ω-(2 ,4-di?uorobiphenyl-4 -ester)nonane FFE11EFF : α-(2 ,4-di?uorobiphenyl-4 -ester)-ω-(2 ,4-di?uorobiphenyl-4 -ester)undecane August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 Abbreviations 269 Table B.3. Bimesogens (continued). Abbreviation Chemical name CBO8OCB : α-(4-cyanobiphenyl-4 -yloxy)-ω-(4-cyanobiphenyl-4 -yloxy)octane FFOnOCB : α-(2 ,4-di?uorobiphenyl-4 -yloxy)-ω-(4-cyanobiphenyl-4 -yloxy)alkanes FFO5OCB : α-(2 ,4-di?uorobiphenyl-4 -yloxy)-ω-(4-cyanobiphenyl-4 -yloxy)pentane FFO6OCB : α-(2 ,4-di?uorobiphenyl-4 -yloxy)-ω-(4-cyanobiphenyl-4 -yloxy)hexane FFO7OCB : α-(2 ,4-di?uorobiphenyl-4 -yloxy)-ω-(4-cyanobiphenyl-4 -yloxy)heptane FFO8OCB : α-(2 ,4-di?uorobiphenyl-4 -yloxy)-ω-(4-cyanobiphenyl-4 -yloxy)octane FFO9OCB : α-(2 ,4-di?uorobiphenyl-4 -yloxy)-ω-(4-cyanobiphenyl-4 -yloxy)nonane FFO10OCB : α-(2 ,4-di?uorobiphenyl-4 -yloxy)-ω-(4-cyanobiphenyl-4 -yloxy)decane FFO11OCB : α-(2 ,4-di?uorobiphenyl-4 -yloxy)-ω-(4-cyanobiphenyl-4 -yloxy)undecane FFO12OCB : α-(2 ,4-di?uorobiphenyl-4 -yloxy)-ω-(4-cyanobiphenyl-4 -yloxy)dodecane NSO9OFF : (E)-2,4 -di?uoro-4-((9-(4-(4-nitrostyryl)phenoxy)nonyl)oxy)-1,1 -biphenyl NSOnOphOnOCB : (E)-4 -((9-(3-((9-(4-(4-nitrostyryl)phenoxy)nonyl)oxy)phenoxy)nonyl)oxy)- [1,1 -biphenyl]-4-carbonitrile Table B.4. Mixtures. Abbreviation Composition 8OCB/CC : compensated cholesteric mixture of 8OCB (50%) and CC (50%) CBmix : mixture of 3CB (30%), 5CB (40%) and 7CB (30%) DEmix : mixture of DE3 (30%), DE5 (40%) and DE7 (30%) Mix1 : mixture of MBB (46%), PEC (50%) and 5CB (4%) MixA : mixture of azoxy compounds and 8CB PB : mixture of phenylbenzoates PCHmix : mixture of PCH3 (30%), PCH5 (40%) and PCH7 (30%) FFO9/11OFF : mixture of FFO9OFF (50%) and FFO11OFF (50%) Mixture3 : mixture of FFE9EFF (50%) and FFE11EFF (50%) Mixture1 : mixture of FFO9OFF (40%) and FFO11OFF (60%) Mixture2 : mixture of FFO9OFF (50%) and FFO11OFF (50%) MixBimes : mixture of substituted bimesogens, composition unspeci?ed E7 : commercial nematic mixture from Merck E70A : commercial nematic mixture from Merck MDA-02-2419 : commercial nematic mixture from Merck MLC-6437-000 : commercial nematic mixture from Merck MLC-7029 : commercial nematic mixture from Merck Phase4 : commercial nematic mixture from Merck Phase5 : commercial nematic mixture from Merck Phase5A : commercial nematic mixture from Merck TL-216 : commercial nematic mixture from Merck TM-216 : commercial thermochromic mixture from Merck ZLI-4788-000 : commercial nematic mixture from Merck ZLI-4792 : commercial nematic mixture from Merck August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 270 Abbreviations B.2. Common Abbreviations AC : Alternating current AFM : Atomic force microscopy BC : Bent-core BCLCE : Bent-core liquid crystalline elastomer BCN-LCE : Bent-core nematic swollen in a liquid crystal elastomer BLM : Black lipid membranes DC : Direct current EC : Electroconvection EHD : Electrohydrodynamic FLC : Ferroelectric liquid crystal HAN : Hybrid-aligned nematic HEK : Human embryonic kidney I : Isotropic IPS : In-plane switching ITO : Indium-tin-oxide LC : Liquid crystal LCD : Liquid crystal display LCE : Liquid crystalline elastomer N : Nematic ns-EC : Non-standard electroconvection OHC : Outer hair cell PVDF : Polyvinylidene ?uoride PZT : Pb-zirconate-titanate SAM : Self-assembled monolayer SAXS : Small-angle X-ray scattering s-EC : Standard electroconvection SEM : Scanning electron microscopy SmA : Smectic A SmC : Smectic C SSFLC : Surface-stabilized ferroelectric liquid crystal ST : Splay-twist STN : Supertwisted nematic TEM : Transmission electron microscopy TN : Twisted nematic TFT : Thin ?lm transistor ULH : Uniform lying helix UV : Ultraviolet VAN : Vertically aligned nematic WEM : Weak electrolyte model ZBD : Zenithal bistable device August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 Author Index Amos, R.M., 237 Apel, A., 62 Bailey, C., 66 Barberi, R., 232, 233 Barboy, B., 22 Beldon, S., 242 Blinov, L.M., 48 Bobylev, Yu.P., 105, 107 Bouligand, Y., 216 Boyd, G.D., 230, 231, 233 Breneman, K.D., 204 Brown, C.V., 38 Bryan-Brown, G., 242 Buka, ? A., 7, 36, 85, 101, 102 Care, C.M., 237 Carr, E.F., 36, 112 Castles, F., 228 ˇ Cepiˇ c, M., 7, 137, 157 de Gennes, P.G., 2, 65 Dequidt, A., 52 Derzhanski, A.I., 10, 22, 68, 86, 189 Deuling, H.J., 38 Dolphin, D., 2 Dozov, I., 45, 212 Durand, G., 47 ? Eber, N., 7, 61, 101, 249 Elston, S.J., 37 Ferrarini, A., 9, 27 Fodor-Csorba, K., vi, 80 Frank, F.C., 1–3 Freedericksz, V.K., 179 Gelbart, W.M., 22 Hamplov? a, V., vi Harden, J., 7, 61, 67, 72, 78, 86 Helfrich, W., 10, 22, 34, 36, 40, 68, 85–89, 112 Hinov, H.P., 109, 111, 125, 126 Indenbom, V.L., 140 J? akli, A., 7, 34, 36, 61, 66, 82, 229 Jones, C., 241 Jones, J.C., 237, 239, 240, 242, 243 Kischka, C., 50, 51 Kochowska, E., 113 Kramer, L., 102 Krekhov, A., 7, 101, 107–109, 117 Kumar, P., 85, 87 271 August 16, 2012 12:9 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 272 Author Index Lagerwall, S.T., 7, 35, 85, 211, 219, 250 Link, D.R., 64 Madhusudana, N.V., 7, 33, 47, 50, 81, 84 Marcerou, J.P., 4, 10, 22, 23, 35 Marinov, Y., 124, 125 Marinov, Y.G., 109 Matsunaga, Y., 62 May, M., 108, 128 Meyer, R.B., v, 1, 10, 11, 34, 37, 44, 53, 67, 68, 83, 86, 139, 180, 200, 214–217, 225, 249, 250 Mosbacher, J., 194 Mottram, N.J., 38 Osipov, M.A., 7, 9, 21, 39, 86 Oswald, P., 52 Parry-Jones, L.A., 37 Patel, J.S., 214, 216, 217, 225, 250 Pershan, P.S., 41 Pesch, W., 7, 101 Petrov, A.G., 7, 10, 22, 37, 68, 69, 86, 177, 180–182, 184–186, 188–190, 192, 196, 203 Pikin, S.A., 105, 140 Prost, J., 4, 10, 22, 23, 35, 41 Raphael, R.M., 199, 200 Rudquist, P., 7, 35, 85, 211, 217, 219, 222, 226, 228, 250 Sachs, F., 184, 196 Salamon, P., 67 Schmidt, D., 40 Sokolov, V.S., 189 Spencer, T.J., 237 Straley, J.P., 10, 11, 19, 22 Strzelecky, L., 139 Takezoe, H., 85, 157 Taphouse, T.S., 47 Todorov, A.T., 69, 81, 189 T? oth-Katona, T., 7, 101, 113, 128 Turnbull, D., 1 Twieg, R., 80 Verduzco, R., 80 Vistin, L.K., 126 Vitkova, V., 203 Vojtylov? a, T., vi Vorl¨ ander, D., 62 Warrier, S.R., 50 Wiant, D., 126 ˇ Zekˇ s, B., 157 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 Subject Index actuator, 89, 177, 179 electromechanical, 205 alignment, 37, 56, 79, 91, 129, 155, 226–231, 233, 238, 247 coating, 122, 127 homeotropic, 33, 40, 41, 46, 47, 49, 50, 80, 85, 119, 251– 259 hybrid, 33, 213, 251–257 initial, 41, 103, 104, 117 molecular, 129 planar, 33, 46, 47, 49, 52, 77, 84, 251, 252, 254–257, 259 preferred, 111 process, 226 quality of, 226 surface, 79, 230–232 twisted, 255, 256 vertical, 50 ampli?er, 188 lock-in, 48, 49, 71, 76, 77, 92, 190, 191 patch clamp, 187, 188, 193 power, 76 analysis numerical, 48, 52, 55 rigorous, 47 tensorial, 179 theoretical, 42, 45, 57, 176, 190, 228, 239 anchoring, 57, 131 energy, 40, 42, 46, 49, 50, 55, 59, 131, 263 homeotropic, 40, 46, 111, 225, 227, 233, 237, 239, 241 planar, 46, 79, 111, 225, 227, 237, 243, 247 strength, 6, 43, 44, 46, 47, 58, 237, 239 strong, 6, 40, 48, 71, 110, 131 surface, 6, 40, 43, 85, 111, 231, 232, 247 weak, 6, 40, 43, 47, 110, 111, 232, 239 anisotropy, 185 conductivity, 36, 118, 133 dielectric, 32, 36, 39, 40, 44, 46, 47, 52, 124, 128, 212, 213, 216, 218, 227, 231, 236, 237, 242, 244, 266 negative, 36, 40, 48, 84, 111, 132 positive, 85, 102, 131, 134, 226, 242 elastic, 45 electric, 112, 114, 130 of polarizability, 5, 172 273 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 274 Subject Index of refractive index, 104 of susceptibility, 2, 6, 215 antiferroelectric, 63, 87, 176, 224, 245 liquid crystal, 96, 137, 138, 148, 150, 155, 157–159, 173– 176 properties, 148 antiferroelectricity, 93 approximation linear, 158 mean-?eld, 9, 18 molecular-?eld, 11, 12, 18, 24 one-elastic-constant, 44, 106, 108, 111, 224 Perkus–Yevic, 11 quasi-static, 111 van der Waals, 18 attraction, 82 Coulomb, 82 intermolecular, 12, 18, 19, 21, 22 steric, 11 van der Waals, 155 axis easy, 76 helical, 7, 35, 44, 50, 215–218, 225, 228 molecular, 25, 28, 143 long, 2, 12, 13, 19, 25, 62, 65, 68, 138–140, 145, 146, 157, 172 short, 12, 13, 19, 21, 138, 141 of cone, 4 optic, 7, 65, 215–220, 222–225, 228 polar, 65 preferred, 102, 106 roll, 114 rotation, 215 symmetry, 64, 214 twist, 214 bilayer, 95, 96, 178, 181, 183–186, 189, 206, 207, 209 curvature, 181 lipid, 69, 70, 82, 95, 96, 177, 178, 180, 182, 183, 206– 209 thickness, 181 biomembrane, 95, 97, 177, 178, 184–186, 201, 205, 206 boundary conditions, 6, 35, 36, 71, 72, 77, 97, 111, 120, 213, 214, 225, 237 asymmetric, 111, 131 cycling, 164 homeotropic, 71, 227 mechanical, 73, 75 periodic, 226 boundary treatment, 38 cell, 52, 72 area, 74, 197 biological, 178, 179, 183, 193– 195, 197, 199, 200, 208, 210 biology, 178, 198 centre of, 71, 72, 76 contact, 201 edge, 71, 75, 76 electromotile, 199 empty, 79 epithelial, 179 gap, 229, 239 geometry, 75, 78 homeotropic, 41, 80, 85 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 Subject Index 275 human embryonic kidney (HEK), 193, 194 hybrid, 70 hybrid-aligned nematic (HAN), 33, 45–47, 49, 50, 59, 84, 86, 88, 212, 243, 261– 265 interior, 196 leakage, 89 membrane, 178, 193, 194, 198, 199, 201, 202, 205, 207, 208 motility, 207 movement, 201 nematic, 57, 131, 132 normal, 228 outer hair (OHC), 7, 69, 95, 198–200, 208, 209 patch-clamped, 196, 197 Pi-, 50 planar-aligned, 38 plane, 228, 233, 234, 236, 238, 240 radius, 197 sandwich, 61, 71, 228 spherical, 196 substrate, 77 surface, 131, 225 symmetry, 72 thickness, 47, 117, 120, 121, 218, 228, 232, 243 TN-HAN, 243 twisted nematic (TN), 51, 124, 211, 212, 237, 243 zenithal bistable device (ZBD), 237, 238 charge, 69, 70, 72, 92, 112, 178, 184, 185, 189, 195, 204, 223 adsorbed, 48, 50 carrier, 103, 178 conservation, 111 density, 36, 50, 74, 111, 114 distribution, 4 e?ective, 30 elementary, 35, 53, 181 ?exoelectric, 5, 113, 119 free, 5, 70 induced, 82, 111 ionic, 5 relaxation, 112, 116 separation, 103, 201, 209, 213, 214 space, 5, 103 static, 82 surface, 36, 74, 186, 188, 195 total, 74 transfer, 207 transport, 191 cholesteric, 2, 7, 32, 35, 44, 56, 60, 81, 85, 97, 98, 111, 211, 213–218, 222, 223, 226, 228– 230, 244–246, 260, 266 cluster, 54, 67, 86–89 ferroelectric, 87 polar, 88 size, 87 smectic, 67, 87, 89, 99, 118 compression, 179, 186, 187, 190 modulus, 33, 43 computer simulation, 11, 12, 31 contribution bulk, 53, 172 charge, 195 cluster, 88 dielectric, 42, 46 dipolar, 14, 15, 23, 26, 29, 33, 42, 70, 87, 185, 195 elastic, 42, 105, 153, 154 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 276 Subject Index electrostatic, 147 ?exoelectric, 43, 113, 114, 146, 147, 167, 169, 171, 173 monopole, 185, 195, 196 piezoelectric, 147 polar, 20 polarization, 145 quadrupolar, 13–15, 23, 29, 39, 79, 87, 185, 186 surface, 49, 53 viscous, 42 converter current-to-voltage, 77 correlation, 7, 16, 26, 27, 53, 208 dipole–dipole, 9, 11, 12, 18, 24– 27, 30 direct, 16 interlayer, 161 intermolecular, 9, 10, 16, 24, 30 orientational, 30 steric, 18 correlation function auto, 203 direct, 9, 11, 12, 15–20, 24, 25 full, 15, 16 pair, 11, 12, 15, 16, 20, 24 coupling bilinear, 147, 159 chiral, 173 coe?cient, 202 conformational, 198 dielectric, 37, 41, 42, 46, 49, 81, 172 elastic, 173 electric, 191 electromechanical, 52, 81, 97 ferroelectric, 81 ?exoelectric, 35, 48, 51, 67, 98, 213, 216, 221, 231, 233, 237, 244, 245 linear, 81 quadratic, 216 quadrupolar, 155 crossover, 101, 114, 119, 120, 131 frequency, 114, 115 crystal, 10, 34, 67, 89, 94 dielectric, 89 ?exoelectric, 89 ionic, 30 piezoelectric, 2, 205 crystallite, 201 crystallization, 78 Curie's principle, 181, 214 current, 76, 77, 79, 187, 190–192, 223 AC, 71, 186 clamp, 187, 188, 192 density, 47, 92, 112 displacement, 96, 186, 187, 194, 207 ?exoelectric, 70, 71, 74, 76–80, 190, 191 generator, 77 induced, 92 leakage, 77 patch, 192, 193 photo, 201 polarization, 83 pressure-driven, 186 curvature cylindrical, 3 elasticity, 7, 195, 208 electricity, 57, 95, 98, 260 energy, 195 induced, 4, 5, 81, 82, 183, 216 local, 194 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 Subject Index 277 oscillation, 59, 187, 190, 262 radius of, 83, 84, 180–182, 188, 191, 196, 200 spherical, 82, 187, 197 strain, 83, 179 Debye screening layer, 122, 127 Debye screening length, 5, 35, 37, 185, 195, 196 defect, 1, 6, 7, 79, 125, 207, 208, 212, 230, 233, 237, 238, 241, 245, 247 deformation bend, 10, 68, 70, 71, 138, 180, 181, 214, 215, 235, 237, 238 director, 37 elastic, 215, 243 ?exoelectric, 57 gradient, 69 orientational, 10, 13, 16, 17, 180 oscillating, 70 pro?le, 71–73, 75 splay, 10, 68, 138, 180, 214, 235, 237, 238 splay-bend, 37, 85, 216, 221, 222 static, 70 twist, 45, 214, 219 degree of freedom, 179, 201, 202, 205 density functional, 11, 15, 18, 24, 32 dimer, 11, 23, 31, 53, 85 molecular, 30 dipole, 25, 69, 87, 172, 183–185, 191, 216 antiparallel, 23 density, 4 electric, 9–12, 15, 24, 27, 34, 62 lateral, 53, 54 localized, 30 longitudinal, 9–11, 23, 34, 50 molecular, 10–14, 17, 19, 23, 24, 26, 29, 42, 68, 145 moment, 4, 34, 42, 53, 54, 68, 87, 103, 138, 140, 185, 186, 188, 229 permanent, 10, 13, 14, 27, 29, 55, 103 shape, 34 steric, 10, 12, 15, 19, 20, 24, 25, 27 transverse, 4, 9–11, 23, 24, 27, 54 director gradient, 13, 17, 18, 68, 76, 86 displacement, 71, 72, 75–77, 79, 82, 191, 194–197, 199, 203, 204, 210 amplitude, 77, 79, 204 electric, 37, 46, 102 display, 6, 36, 96, 211, 214, 219, 229, 230, 234, 240–242, 244, 246, 247 active matrix, 223, 229 Binem, 231 bistable, 214, 231, 240 ferroelectric liquid crystal, 214, 247 in-plane switching (IPS), 214 liquid crystal (LCD), 36, 37, 56, 135, 230, 245, 247 memory, 213 mode, 211, 212, 242 nematic, 212, 230 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 278 Subject Index surface-stabilized ferroelectric liquid crystal (SSFLC), 240 twisted nematic (TN), 242 zenithal bistable (ZBD), 35, 211, 212, 214, 233, 235– 240, 242, 243, 247, 264, 270 dissipative, 101, 105, 119 distortion angle, 38, 45 bend, 2, 3, 36, 44, 83, 85, 105 ?eld-induced, 38, 41, 213, 216 ?exoelectric, 42 mechanical, 81 of director ?eld, 3, 4, 34, 36, 37, 39–41, 44, 55, 84, 85, 103, 105–107, 109, 110, 127, 216 orientational, 81, 213 oscillatory, 36 out-of-plane, 103 pro?le, 38, 45 splay, 2–4, 36, 44, 50, 102, 105 splay-bend, 33, 35, 36, 38, 45, 55, 84, 213, 217 static, 36 twist, 51 distortion-free, 234 distribution function orientational, 13–16, 28, 29 domain, 6, 90, 132, 135, 186, 241 chiral, 93 ?exoelectric, 31, 58, 59, 101, 103–112, 116, 117, 119– 132, 135, 198, 200, 251, 254, 257, 261, 263 longitudinal, 131, 135, 263 elastic, 49, 89, 202, 206 constant, 22, 31, 34, 37, 38, 42, 43, 46, 49, 51, 52, 55, 56, 68, 102, 103, 105, 107, 109, 124, 134, 155, 171, 222 e?ect, 95, 206 modulus, 179, 183, 200 properties, 38, 118, 148, 154, 245 elasticity, 1, 47, 56–58, 71, 96, 155, 206, 222 anharmonic, 43 anisotropic, 107, 108, 131, 263 ?rst-order, 224 isotropic, 106 rubber, 90 stretching, 197 elastomer, 10, 67, 69, 90–92, 95 liquid crystalline (LCE), 62, 89–91, 96, 99, 270 bent-core (BCLCE), 61, 90–92, 99, 270 swollen, 90, 91, 96, 270 electro-optic applications, 212 behaviour, 131 data, 55 device, 211, 212, 234 e?ect, 7, 32, 35, 37, 38, 57, 59, 81, 98, 134, 212–214, 218, 229, 231, 244, 245, 260, 266 experiment, 33, 40 geometry, 242 method, 78 performance, 226 properties, 58, 93, 96 response, 36, 40, 47, 227 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 Subject Index 279 signal, 43 technique, 38, 41, 55, 59 electro-optical e?ect, 260, 262 electro-optics, 32, 56, 98, 218, 223, 260, 261 electroconvection (EC), 101, 104, 105, 111–117, 119, 120, 122, 125–127, 130–133, 135, 261, 263, 270 conductive, 114, 115, 120–122 dielectric, 114, 115, 118, 121, 123 non-standard (ns-EC), 101, 104, 113, 117–119, 126, 130, 132, 133, 263, 270 standard, 101, 109, 113, 114, 117, 118, 125, 132 electrode area, 71, 74, 83 ?exible, 71, 79 gap, 76, 228 interdigitated, 33, 41, 43, 54, 228, 230 spacing, 41 electromechanical activity, 193 e?ect, 60, 97 model, 95 technique, 86 transduction, 208 energy, 37, 44, 51, 83, 155, 203, 241 barrier, 160, 233 bending, 83 conservation, 86, 208 conversion, 87, 89, 90, 92, 201 density, 2, 6, 37, 39, 45, 105, 147, 154, 213, 218 elastic, 2, 154, 216, 227, 233, 234 electric, 86, 198, 201, 217 electrostatic, 37, 169 ?exoelectric, 6, 83 free, 2, 6, 15, 16, 19, 24, 36, 38, 102, 103, 105, 106, 140, 142–147, 153–157, 159, 160, 162, 165–167, 171, 204, 213, 218–220, 233, 241 interaction, 21, 22, 25, 32, 34 internal, 19 mechanical, 86, 198 optical, 201 surface, 58 thermal, 68 transformation, 198, 201 entropy, 62 orientational, 19 packing, 19 equation coupled, 47 Debye, 221 di?erential, 71, 237 electrohydrodynamic, 104, 124 electromechanical, 204 Euler–Lagrange, 39, 43, 46 Helmholtz, 182 integral, 17 linear, 109 Lippmann, 194 Navier–Stokes, 103 nemato-electrohydrodynamic, 114, 117, 122, 123, 128 non-linear, 47 Ornstein–Zernike, 15 phenomenological, 182 transcendental, 107 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 280 Subject Index equilibrium, 21, 38, 48, 102, 105, 109, 119, 197, 206, 216, 220, 232 equivalent circuit, 77, 127, 187, 188 excitation, 2, 132 ?exoelectric, 214 mechanical, 77, 86 pulse, 177, 178, 191, 194 sine, 177, 190, 193 expansion, 12, 17, 20, 25 gradient, 17, 28 Landau, 142–144 periodical, 95, 206 Taylor, 16 ferrielectric properties, 152 ferroelectric, 67, 87, 89, 92, 97, 99, 150, 151, 224, 236, 246 liquid, 34 liquid crystal (FLC), 81, 92, 96, 137–140, 173–175, 213, 231, 245 ferroelectricity, 69, 96, 175 ?eld AC, 48, 50, 52, 225 DC, 38, 40, 43–48, 50–53 director, 33, 35, 36, 38, 45, 51, 180, 200, 213, 214, 216, 222, 233–235 gradient, 39, 40, 42, 46, 49, 53, 69 high, 40, 57, 224, 228 in-plane, 35 internal, 37, 85, 88 intramembrane, 188 intrinsic, 50 lateral, 228 lines, 228 magnetic, 35, 37, 102, 215, 245 molecular, 39 strength, 6, 228 transmembrane, 195 van der Waals, 155, 163 zero, 195, 241 ?exoelectricity, 1–12, 14–17, 19, 20, 22, 23, 27, 30–33, 35–39, 41–44, 46, 47, 49, 51, 52, 55– 62, 66–69, 76, 81–84, 88, 89, 91, 95–99, 101–105, 107, 112–115, 118, 125, 129–132, 135, 137, 138, 144, 145, 148, 149, 153, 154, 157, 159, 162, 163, 167, 169, 171–173, 176–181, 183– 186, 193–195, 198, 201, 203, 204, 206, 207, 209, 211–214, 216, 233, 237, 244, 245, 260– 266 converse, 61, 62, 67, 69, 81–84, 86, 88, 89, 96–99, 177, 178, 182, 183, 186, 189, 193–195, 198–200, 207, 213, 216, 265 dipolar, 9, 10, 12, 14, 23, 68 direct, 71, 81, 83, 84, 88, 89, 177, 182, 183, 189–191, 198, 207, 211, 213, 264 giant, 7, 56, 61, 62, 67, 70, 76, 82, 83, 85–90, 92, 94, 99, 246, 262 quadrupolar, 9, 12, 14, 23, 186 ?exoelectro-optic device, 211, 221, 246 e?ect, 14, 23, 35, 40, 46, 59, 85, 86, 99, 212, 214, 215, 218, 220, 223, 225, 227– 229, 245, 262, 265 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 Subject Index 281 geometry, 229 properties, 56 ?exoelectro-optics, 33, 97, 131, 244, 260 ?ow, 79, 103, 104, 111, 112, 125 ?uctuation, 201–203, 206, 209, 216 force, 194, 195, 197 attractive, 155 Coulomb, 103 elastic, 11 external, 146 ?exoelectric, 201 generation, 197 Freedericksz state, 103, 104, 107, 109 stripe, 107, 108 transition, 37, 43, 45, 51, 57, 102, 103, 110, 119, 129, 130 gradient, 10, 12–14, 40, 43, 49, 68, 131, 237, 265 spatial, 4, 35, 38, 40, 52 handedness, 63, 145, 148, 158, 163, 168 harmonic, 76, 133 ?rst, 48, 49, 187, 190, 191 second, 49, 93, 187 helix, 2, 52, 92, 98, 176, 215, 216, 224–226, 228, 244, 264 inversion, 52 lying, 226–228, 230 standing, 212, 227–230 uniform lying (ULH), 225, 226, 228, 229, 245, 270 uniform standing, 56 instability, 36, 40, 118, 120–122, 126, 131, 133, 134, 174, 224 electrohydrodynamic (EHD), 33, 35, 36, 44, 56, 112, 130, 132–134, 263 ?exoelectric, 45, 59, 85, 131, 261 pattern-forming, 111, 123, 124, 128, 129 periodic, 45 piezoelectric, 58, 129 polar, 40, 57 secondary, 119 twist, 59 interaction, 4, 5, 30, 42, 69, 88, 138, 144, 148, 149, 153, 155, 157–164, 167, 171, 205 achiral, 158–160, 162–164 anisotropic, 22 attraction, 19–22, 24, 25 attractive, 160 bilinear, 158, 160, 162, 163 biquadratic, 160, 164 chiral, 142–144, 155, 158, 160, 163, 164 competing, 159, 167 dipole–dipole, 24, 25 direct, 158–160, 163, 167 e?ective, 159 elastic, 142, 143 electrostatic, 34, 176 energy, 20 ?exoelectric, 44, 153, 154, 157, 164, 171, 209 indirect, 157, 159, 160, 162, 163, 167, 173 interfacial, 58 interlayer, 137, 157, 159, 161, 162, 166, 173, 175, 176 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 282 Subject Index intermolecular, 10, 11, 15, 22, 25, 30, 32, 143, 153 intralayer, 155, 159, 171 multipole, 20 pair, 21 piezoelectric, 164 polar, 156, 158, 159, 162 polarization, 148, 160 potential, 19–21, 24, 25, 27, 30 steric, 159, 160, 209 surface, 27, 30 synclinic, 160 van der Waals, 159, 160 interface, 35, 38 aqueous, 184 chevron, 240 nematic-isotropic, 38 water/air, 185 water/oil, 185 interferometer, 43, 82 interferometry, 58, 187, 189, 207, 255, 265 interpretation dipolar, 14 microscopic, 8, 10, 30, 56, 129 molecular, 31 ion, 38, 41, 46, 47, 53, 91, 96, 118, 127, 178, 186, 209, 236 adsorption, 40, 55 channel, 96, 202, 207, 209 density, 47 distribution, 47 motion, 48, 53 transport, 179, 201 ionic, 127, 231, 264 concentration, 196 conditions, 183, 189 contamination, 36, 57 impurity, 33, 35, 36, 42, 50, 55 migration, 43 motion, 49 screening, 36, 37, 70, 91 strength, 194–196 transport, 209 Lagrange multiplier, 16 laser, 193, 262 beam, 43, 47, 48, 51, 226 He-Ne, 43, 47 tweezers, 179 ultraviolet (UV), 226 layer, 70, 176 alignment, 231 chirality, 63, 64, 93 compression, 43, 145 displacement, 43 distant, 137, 149, 153, 157–159, 164, 167, 171, 173 double, 185 interacting, 154, 157, 158, 160, 162–164 isolated, 142 modulation, 66 monomolecular, 206 nearest, 158, 159, 162, 163, 171 neighbouring, 63, 140, 142, 143, 146, 149–151, 153–156, 158–165, 167–169, 172 nematic, 5, 57, 58, 102, 106, 111, 117, 126, 127, 131 next nearest, 155, 159, 162, 163, 168 normal, 62–65, 137, 139, 141, 142, 144, 145, 149, 167, 168, 172 photoresist, 241 plane, 103 polar, 62, 63, 87, 88, 139, 155 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 Subject Index 283 resin, 241 smectic, 137, 139 spacing, 225 structure, 245 thickness, 71, 143, 145, 154, 170 Lifshitz frequency, 112, 117, 120, 122, 125 light polarization, 46, 84, 85 lipid, 81, 178, 180, 183–185, 189, 205, 207 Lippmann e?ect, 194 lyotropic, 69, 70, 95, 96, 177, 178, 181, 183, 205 macromolecule, 178 mechanism Carr–Helfrich, 36, 127 dipolar, 12, 68, 69 ?exoelectric, 198 isotropic, 118 latching, 237 linear, 81 miscoscopic, 10 molecular, 181, 183 polar, 237 quadratic, 81 quadrupolar, 10, 12, 14, 68, 69, 86 sensory, 69 surface polarization, 118, 126 mechano-electric behaviour, 194 e?ect, 179 phenomenon, 179 mechano-electricity, 178, 198, 207 membrane, 70, 95, 96, 177, 179, 180, 182–188, 190, 191, 193– 203, 205–209 area, 197 astrocyte, 193 biological, 7, 70, 197, 205–207, 209 black lipid (BLM), 69, 82, 95, 187, 201, 207, 270 charged, 194 chemistry, 202 clamped, 190, 209 composite, 69, 95 contact, 177 curvature, 179, 180, 184, 186– 188, 190, 191, 198, 200– 202, 205 curved, 181, 185, 186, 188 displacement, 194, 204, 208 elasticity, 209 electrodynamics, 201 ?exoelectricity, 181, 200, 209 function, 200 interface, 185, 186 lipid, 81, 95, 96, 177, 184, 186, 189, 204, 206, 207, 209 living, 97, 184, 198, 206 machine, 202, 205, 209 mechanics, 201 mitochondrial, 179, 186, 198 model, 97, 177, 179, 190, 198, 206, 207 native, 177–179, 190, 191, 193, 194, 197, 201, 202, 207 natural, 201 nerve, 203, 204 normal, 180 patched, 190 photoactive, 201 polarization, 180, 185, 198 potential, 202, 204 purple, 186, 206 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 284 Subject Index surface, 180, 185, 196 tension, 194, 196, 197, 202, 204 thickness, 185, 191 thylakoid, 179 transport, 177 voltage, 196 mesophase, 62, 174, 175, 208 microscope, 118, 199, 237 microscopic, 5, 11, 12, 30, 68, 86, 103, 145, 199 microscopy, 79 atomic force (AFM), 177–179, 193–197, 208, 270 confocal, 178, 179, 195–197 electron, 199 phase contrast, 197 scanning electron (SEM), 237, 240, 242, 270 transmission electron (TEM), 88, 270 mixture, 49, 52, 56, 60, 79, 81, 84, 88, 94, 98, 124, 262, 269 binary, 56, 129 cholesteric, 60, 97 commercial, 43, 48, 53 multicomponent, 53 nematic, 36, 53, 60, 98, 133, 135, 263, 265 racemic, 63 model continuum, 59, 262 Danielli–Dawson, 186 discrete, 138, 153 distribution, 183 electrodi?usion, 133 ?exoelectric, 96, 205, 209 ?uid-mosaic, 185, 205 hydrodynamic, 133 micromechanical, 200 molecular, 12, 18 nanomechanical, 199 numerical, 237 one-dimensional, 237 phenomenological, 137, 140, 153 piezoelectric, 208 standard, 104, 105, 112–114, 117–119, 125, 178 structural, 67 structure-function unitization, 178, 186, 205 theoretical, 31, 96, 138, 176 weak electrolyte, 118, 270 molecular aspects, 96 conformation, 29 di?usion, 161 dimension, 53, 68 dimensions, 34 end, 40 environment, 139 ?exibility, 11 fragment, 30 frame, 28, 29 length, 35 model, 9, 10, 54 origin, 4, 10 packing, 62 parameters, 9 plane, 62–65 properties, 5, 34, 36, 39 shape, 4, 7, 9–12, 18–22, 27, 31, 53, 62, 66, 68, 94, 145, 146, 155, 174, 181 size, 28 surface, 27–29 topology, 174 weight, 68 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 Subject Index 285 molecule achiral, 92, 93, 133, 175 asymmetric, 10 banana-shaped, 4, 10, 34, 36, 68, 92, 93, 145, 175 bent-core, 7, 11, 25, 53–56, 60– 64, 66–70, 84, 86–88, 94, 98, 133, 250, 260, 262, 265 bent-shaped, 53, 68, 93, 146 biaxial, 13 calamitic, 84, 88, 133 chiral, 69, 70, 137, 139, 140, 143, 144, 155, 163 cone-shaped, 4, 10, 11 discotic, 62 mesogenic, 11, 21, 22, 27, 34, 53 nematogenic, 32, 40, 103 non-aromatic, 50, 54, 55 nonchiral, 93 pear-shaped, 31, 68, 81 polar, 24, 26, 27, 172 rod-like, 2, 35, 36, 53, 54, 56, 60, 90, 94, 98, 178, 262 swallow-tailed, 53, 124 symmetric, 4, 20, 62, 69 tilted, 143, 145, 149 V-shaped, 56 wedge-like, 60, 135, 263 monolayer, 184–186, 195, 207, 226, 270 multi-layer, 7, 159 nematic, 2, 3, 9–12, 15, 16, 22– 24, 26–38, 41, 42, 44, 46–48, 50, 52, 53, 56–60, 66–68, 70–72, 74, 85, 86, 95, 96, 98, 101–105, 108, 110, 111, 113, 114, 117– 121, 123–135, 200, 206, 244, 246, 249, 250, 260–265 aligned, 34 banana, 77 bent-core, 56, 61, 66, 67, 70, 76, 79–82, 84–91, 94, 97, 98, 118, 126, 133, 134, 246, 262, 265 calamitic, 68, 70, 78–80, 82–86, 89, 117, 119, 126 chiral, 51, 56, 99, 245, 262, 265 discotic, 107 drop, 35 homeotropic, 133 host, 53 hybrid-aligned (HAN), 84, 98, 111, 131, 236, 238, 261 lyotropic, 181 material, 14, 23, 27, 104 matrix, 87–89 metallo-organic, 124 non-chiral, 51 ordered, 35 planar, 106, 119, 129 polymer, 129, 130 range, 54, 91 rod-like, 107 supertwisted (STN), 135, 231, 242, 270 twisted (TN), 50, 135, 238, 264, 270 vertically aligned (VAN), 270 wedge-shaped, 60 non-equilibrium, 104, 111 order, 146, 151 chiral, 93 electricity, 38, 57 ?rst, 2, 17, 78, 195 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 286 Subject Index ?uid, 66 higher, 17, 142 long-range, 139 lowest, 75, 145 nematic, 55, 67, 140 orientational, 25, 35, 37, 42, 139 second, 2, 25 smectic, 61, 94, 140, 159, 161 order parameter, 31, 38, 39, 54, 137, 141, 143, 144, 153, 154, 159, 176 improper, 147 nematic, 13, 14, 21, 49 orientational, 13, 39 polarization, 142, 147 proper, 147 secondary, 144 tensor, 38 tilt, 141, 142, 153, 154, 156, 159, 168, 169 ordering, 7, 10, 13, 138 anticlinic, 160 antiferroelectric, 156, 160, 162 antiparallel, 163 cholesteric, 30 dipolar, 10 ferroelectric, 162 molecular, 7 orientational, 178 parallel, 162 smectic, 133 orientation anticlinic, 162 antiparallel, 34, 158, 160 homeotropic, 76, 118, 119 imperfect, 78 initial, 40, 110, 118 molecular, 70, 139, 145, 157 out-of-plane, 160 parallel, 142, 158, 160 perpendicular, 160, 164 planar, 76 preferred, 126 surface, 57 tilt, 168 uniaxial, 69 uniform, 34, 45 pattern, 101, 102, 104, 109, 111, 113, 114, 119, 120, 124–128, 135, 200, 204 cellular, 119 convective, 118, 133 di?raction, 122 double-tiered, 178, 186 electroconvection, 101, 103– 105, 109, 110, 112, 117, 119, 120, 124–128, 132, 134 equilibrium, 103 etched, 43 ?exoelectric, 111, 125, 131 formation, 7, 56, 58, 98, 101, 103, 127, 129, 130, 132, 133, 260 fringe, 43 grid, 112 longitudinal, 103, 130, 265 periodic, 130 perpendicular, 112 roll, 112, 119, 120 square, 114 stripe, 7, 103, 104, 111, 131 subharmonic, 113, 114, 132 transient, 104, 130 transversal, 130, 265 pH gradient, 202, 203 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 Subject Index 287 phase antiferroelectric, 63, 93, 137, 138, 150–152, 175 B7, 66 columnar, 66, 181 crystal, 83 diagram, 175, 176 distorted, 11, 13, 14 ferroelectric, 63, 69, 93, 137, 149 four-layer, 137, 149 glassy, 91 grating, 41, 42, 58, 265 hexagonal, 181 homogeneous, 12, 13 isotropic, 58, 78, 79, 82, 83, 91, 118, 131 lamellar, 178, 179, 181, 183 leaning, 64 lyotropic, 95, 178, 181, 206 nematic, 2, 10–16, 18, 19, 23, 26, 27, 32, 56, 61, 67, 83, 86, 91, 92, 94, 99, 118, 131, 133, 245, 262, 263 uniaxial, 13 re-entrant, 152 sequence, 79, 80, 149, 152, 153, 176 six-layer, 137, 149, 152 smectic, 7, 12, 31, 63, 93, 94, 139, 175, 176, 263 chiral, 175 ferrielectric, 138, 151, 176 ferroelectric, 138 modulated, 66 orthogonal, 139, 148, 151, 174 tilted, 12, 137, 140, 142, 148, 149, 151, 174 structure, 138, 149, 155, 167, 169–171 tetrahedric, 134 three-layer, 137, 149 tilted, 173 transition, 90, 102, 104, 143, 144, 147, 148, 204 two-layer, 149 undistorted, 13, 16 phase angle, 49, 50, 143 phase di?erence, 142, 143, 151– 153, 156, 157, 164–166, 168– 170 phase transition isotropic-cholesteric, 244 isotropic-nematic, 22, 32, 42, 53, 78, 83, 90, 91 nematic-to-smectic, 42, 54, 133 phospholipid, 95, 190, 206, 207 photoelectric, 202 e?ect, 201, 209 photoelectricity, 202 photo?exoelectricity, 97, 202 photopotential, 202, 203 piezoelectric, 89, 199, 209 coe?cient, 163 component, 167 composite, 99 e?ect, 8, 30, 55, 69, 94, 95, 97, 99, 129, 145, 160, 163, 176, 205, 260, 261 properties, 30, 95, 179, 203 piezoelectricity, 2, 30, 34, 55, 81, 95, 97, 103, 145, 148, 176, 179, 183, 186, 199, 200, 260, 261 piezoelectrics, 180 pitch, 148, 149, 151, 175, 176, 217, 223, 224, 226, 227, 232, 241, 242 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 288 Subject Index helical, 35, 85, 152, 173, 214, 218, 219 long, 51 modulation, 148 short, 7, 35, 151, 211, 216, 218, 228 polarity, 48, 63, 82, 216, 232, 235, 236 dependent, 35, 40, 57, 82, 231 independent, 82 shape, 9, 19, 34, 37 polarization bulk, 180, 183, 211, 239 curvature-induced, 3, 5, 179, 181, 182, 201, 216 density, 213 distortion-induced, 34, 36 electric, 34, 63, 180, 237 ferroelectric, 62, 161 ?exoelectric, 4, 14, 18, 29, 34– 39, 42, 45, 47, 50–53, 58, 68, 70, 71, 74, 84, 85, 88, 99, 103, 105, 113, 114, 117, 119, 122, 128, 137– 140, 146, 159, 161, 162, 167–173, 181, 182, 186, 187, 191, 198, 211–213, 217, 223, 224, 231, 232, 235, 236, 238, 261–263, 265 induced, 215, 223 layer, 62–65, 139, 167, 169, 171 longitudinal, 168–171, 173 macroscopic, 10–13, 34, 62 net, 4, 68, 140 order-electric, 38 orientation, 34 piezoelectric, 145, 147, 156, 161, 162, 167–169, 172 properties, 31 reversal, 140 spontaneous, 2, 175 surface, 40, 42, 48, 50, 53, 55, 59, 134, 172, 180, 261– 264 thermal, 30 polarizer, 52, 117, 218, 220, 228, 236, 243 crossed, 46, 49, 51, 52, 117, 118, 212, 213, 218, 228, 236, 243 potential action, 203, 204, 209, 210 chemical, 15 di?erence, 188 electric, 43, 83, 182, 184, 197 Gay–Berne, 11 holding, 188, 191, 193, 194, 196 intermolecular, 19 mean-?eld, 27, 28 redox, 46 resting, 204 surface, 27, 28, 110, 184, 185, 188, 195 pressure, 187, 190, 192, 193, 203, 204 clamp, 187, 192 di?erence, 187 gradient, 102, 186 oscillating, 70, 186, 190, 191 pulsed, 187, 191, 193 protein, 178, 180, 183, 185, 186, 198–201, 205, 207 quadrupole, 13, 29, 183 density, 4, 10, 12–14, 35 molecular, 10, 13, 29, 69 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 Subject Index 289 moment, 13, 15, 42, 54, 55, 69, 87, 103, 155, 185 refractive index, 46–49, 51, 52, 55, 172, 244 relaxation, 193, 220, 227, 232, 239 dielectric, 42, 67 frequency, 42 time, 112, 114, 116, 128, 238 reorientation, 48, 131 repulsion intermolecular, 12, 22 steric, 11, 18, 22 response antiferroelectric, 87 ferroelectric, 87, 94 ?exoelectric, 86, 246 sensor, 89, 177, 179, 202 electromechanical, 205 mechanoelectric, 209 shear, 2, 102, 225, 226 smectic, 263 layer, 62, 65, 66, 141, 167 strain, 2, 67, 68, 179, 213, 227 gradient, 67, 89, 92, 99 stress, 67, 102, 198, 204 stripe longitudinal, 105 structure antiferroelectric, 62, 87, 162 complex, 138, 155, 169, 172, 173 curvature, 5, 6 director, 127 dissipative, 101, 103, 111 equilibrium, 101, 104, 105 ferroelectric, 62, 162 grating, 212, 239, 241, 242, 247 helical, 35, 85, 225–230, 245 microscopic, 148 modulated, 93, 137, 143, 144, 151, 152 molecular, 1, 2, 4, 5, 7, 10, 14, 15, 27, 30, 64, 80, 92, 143, 183, 245 chiral, 143 multi-layer, 137 periodic, 44, 108, 131 twisted, 131, 133 uniaxial, 2 subphase, 64, 65, 176 surface layer, 59, 172 zenithal bistable device (ZBD), 237–239, 242 switching, 6, 7, 59, 193, 211, 212, 214, 218, 221, 223, 224, 227, 229, 230, 236–240, 245, 246, 264, 265 antiferroelectric, 62 bistable, 246 electro-optic, 241, 246 electroclinic, 224 ferroelectric, 62, 213 ?exoelectric, 131, 247, 262, 265 in-plane (IPS), 212, 218, 220, 229 o?, 193 on, 192, 193 polar, 236 speed, 223, 229 time, 36, 222, 238 texture, 1, 7, 31, 58, 98, 226, 227, 244, 245, 260 ?ngerprint, 223 Grandjean, 226, 264 August 7, 2012 12:32 World Scienti?c Review Volume - 9in x 6in Catherine P812 Flexoelectricity/Chp. 7 290 Subject Index theory density functional, 11, 15, 31 linear response, 12 mean-?eld, 9, 11, 12, 27 molecular, 9, 11, 12, 23, 30, 32 molecular-statistical, 9, 10, 14, 15, 22, 27 statistical, 10, 30 threshold electroconvection, 104, 125, 254 ?eld, 6, 37, 38, 40, 44, 50, 89, 102, 103, 105, 106, 236 Freedericksz, 35, 52, 103 latching, 237–239, 241 voltage, 44, 85, 106, 111, 112, 114, 117, 118, 120, 123, 125, 127, 135 torque balance, 38, 40, 48, 49, 102, 106, 109 bulk, 40, 42, 46 dielectric, 38, 85, 102, 124, 213, 214, 220, 236 elastic, 38, 102, 104, 124, 195 electric, 102–104, 107, 114, 119 ?exoelectric, 38–40, 42, 43, 46, 48, 49, 53, 103, 105–107, 113, 119, 124, 197, 220 net, 38 surface, 42, 46, 48, 49, 195 viscous, 38, 104, 111, 113, 119, 124 transition conformational, 96 continuous, 142 discontinuous, 142 equilibrium, 103 temperature, 90, 148, 156, 157, 173 vesicle lipid, 202, 203 viscosity, 118, 220, 229 coe?cient, 124 isotropic, 112 orientational, 134 rotational, 43, 49, 52, 55, 112, 223 X-ray, 67, 87, 143, 152, 153, 175, 176, 270