Abstract

Dual-frequency cholesteric liquid crystal (DFCLC) devices characteristically require high operation voltage, which hinders their further development in thin-film-transistor driving. Here we report on a lower-voltage switching method based on the thermodielectric effect. This technique entails applying a high-frequency voltage to occasion dielectric oscillation heating so to induce the increase in crossover frequency. The subsequent change in dielectric anisotropy of the DFCLC allows the switching, with a lower operation voltage, from the planar state to the focal conic or homeotropic state. The temperature rise incurred by the dielectric heating is described.

© 2013 Optical Society of America

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  1. A. B. Golovin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Fast switching dual-frequency liquid crystal optical retarder, driven by an amplitude and frequency modulated voltage,” Appl. Phys. Lett.83(19), 3864–3866 (2003).
    [CrossRef]
  2. P.-T. Lin, X. Liang, H. Ren, and S.-T. Wu, “Tunable diffraction grating using ultraviolet-light-induced spatial phase modulation in dual-frequency liquid crystal,” Appl. Phys. Lett.85(7), 1131–1133 (2004).
    [CrossRef]
  3. Y.-C. Hsiao, C.-Y. Wu, C.-H. Chen, V. Ya. Zyryanov, and W. Lee, “Electro-optical device based on photonic structure with a dual-frequency cholesteric liquid crystal,” Opt. Lett.36(14), 2632–2634 (2011).
    [CrossRef] [PubMed]
  4. Y.-C. Hsiao, C.-T. Hou, V. Ya. Zyryanov, and W. Lee, “Multichannel photonic devices based on tristable polymer-stabilized cholesteric textures,” Opt. Express19(24), 23952–23957 (2011).
    [CrossRef] [PubMed]
  5. Y.-C. Hsiao, Y.-H. Zou, I. V. Timofeev, V. Ya. Zyryanov, and W. Lee, “Spectral modulation of a bistable liquid-crystal photonic structure by the polarization effect,” Opt. Mater. Express3(6), 821–828 (2013).
    [CrossRef]
  6. M. Xu and D.-K. Yang, “Dual frequency cholesteric light shutters,” Appl. Phys. Lett.70(6), 720–722 (1997).
    [CrossRef]
  7. C.-Y. Huang, K.-Y. Fu, K.-Y. Lo, and M.-S. Tsai, “Bistable transflective cholesteric light shutters,” Opt. Express11(6), 560–565 (2003).
    [CrossRef] [PubMed]
  8. J. Ma, L. Shi, and D.-K. Yang, “Bistable polymer stabilized cholesteric texture light shutter,” Appl. Phys. Express3(2), 021702 (2010).
    [CrossRef]
  9. M. Xu and D.-K. Yang, “Electrooptical properties of dual-frequency cholesteric liquid crystal reflective display and drive scheme,” Jpn. J. Appl. Phys.38(3), 6827–6830 (1999).
    [CrossRef]
  10. F.-C. Lin and W. Lee, “Color-reflective dual-frequency cholesteric liquid crystal displays and their drive schemes,” Appl. Phys. Express4(11), 112201 (2011).
    [CrossRef]
  11. Y.-C. Hsiao, C.-Y. Tang, and W. Lee, “Fast-switching bistable cholesteric intensity modulator,” Opt. Express19(10), 9744–9749 (2011).
    [CrossRef] [PubMed]
  12. C.-H. Wen and S.-T. Wu, “Dielectric heating effects of dual-frequency liquid crystals,” Appl. Phys. Lett.86(23), 231104 (2005).
    [CrossRef]
  13. Y. Yin, S. V. Shiyanovskii, A. B. Golovin, and O. D. Lavrentovich, “Dielectric torque and orientation dynamics of liquid crystals with dielectric dispersion,” Phys. Rev. Lett.95(8), 087801 (2005).
    [CrossRef] [PubMed]
  14. Y. Yin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Electric heating effects in nematic liquid crystals,” J. Appl. Phys.100(2), 024906 (2006).
    [CrossRef]
  15. Y. Yin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Thermodielectric bistability in dual frequency nematic liquid crystal,” Phys. Rev. Lett.98(9), 097801 (2007).
    [CrossRef] [PubMed]
  16. M. Schadt, “Dielectric heating and relaxations in nematic liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.)66(1), 319–336 (1981).
    [CrossRef]
  17. H. K. Bücher, R. T. Klingbiel, and J. P. VanMeter, “Frequency‐addressed liquid crystal field effect,” Appl. Phys. Lett.25(4), 186–188 (1974).
    [CrossRef]
  18. H. Xianyu, S.-T. Wu, and C.-L. Lin, “Dual frequency liquid crystals: a review,” Liq. Cryst.36(6–7), 717–726 (2009).
    [CrossRef]
  19. C.-Y. Tang, S.-M. Huang, and W. Lee, “Dielectric relaxation dynamics in a dual-frequency nematic liquid crystal doped with C.I. Acid Red 2,” Dyes Pig.88(1), 1–6 (2011).
    [CrossRef]
  20. H.-H. Liu and W. Lee, “Time-varying ionic properties of a liquid-crystal cell,” Appl. Phys. Lett.97(2), 023510 (2010).
    [CrossRef]
  21. Y. A. Cengel, J. M. Cimbala, and R. H. Turner, Fundamentals of Thermal-Fluid Sciences, 4th ed. (McGraw-Hill, 2011).
  22. T. L. Bergman, A. S. Lavine, F. P. Incropera, and D. P. DeWitt, Fundamentals of Heat and Mass Transfer, 7th ed. (Wiley, New York, 2011).
  23. A. C. Metaxas, Foundations of Electroheat: A Unified Approach (Wiley, 1996).
  24. G. Solladié and R. G. Zimmermann, “Liquid crystals: A tool for studies on chirality,” Angew. Chem. Int. Ed. Engl.23(5), 348–362 (1984).
    [CrossRef]

2013 (1)

2011 (5)

2010 (2)

H.-H. Liu and W. Lee, “Time-varying ionic properties of a liquid-crystal cell,” Appl. Phys. Lett.97(2), 023510 (2010).
[CrossRef]

J. Ma, L. Shi, and D.-K. Yang, “Bistable polymer stabilized cholesteric texture light shutter,” Appl. Phys. Express3(2), 021702 (2010).
[CrossRef]

2009 (1)

H. Xianyu, S.-T. Wu, and C.-L. Lin, “Dual frequency liquid crystals: a review,” Liq. Cryst.36(6–7), 717–726 (2009).
[CrossRef]

2007 (1)

Y. Yin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Thermodielectric bistability in dual frequency nematic liquid crystal,” Phys. Rev. Lett.98(9), 097801 (2007).
[CrossRef] [PubMed]

2006 (1)

Y. Yin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Electric heating effects in nematic liquid crystals,” J. Appl. Phys.100(2), 024906 (2006).
[CrossRef]

2005 (2)

C.-H. Wen and S.-T. Wu, “Dielectric heating effects of dual-frequency liquid crystals,” Appl. Phys. Lett.86(23), 231104 (2005).
[CrossRef]

Y. Yin, S. V. Shiyanovskii, A. B. Golovin, and O. D. Lavrentovich, “Dielectric torque and orientation dynamics of liquid crystals with dielectric dispersion,” Phys. Rev. Lett.95(8), 087801 (2005).
[CrossRef] [PubMed]

2004 (1)

P.-T. Lin, X. Liang, H. Ren, and S.-T. Wu, “Tunable diffraction grating using ultraviolet-light-induced spatial phase modulation in dual-frequency liquid crystal,” Appl. Phys. Lett.85(7), 1131–1133 (2004).
[CrossRef]

2003 (2)

A. B. Golovin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Fast switching dual-frequency liquid crystal optical retarder, driven by an amplitude and frequency modulated voltage,” Appl. Phys. Lett.83(19), 3864–3866 (2003).
[CrossRef]

C.-Y. Huang, K.-Y. Fu, K.-Y. Lo, and M.-S. Tsai, “Bistable transflective cholesteric light shutters,” Opt. Express11(6), 560–565 (2003).
[CrossRef] [PubMed]

1999 (1)

M. Xu and D.-K. Yang, “Electrooptical properties of dual-frequency cholesteric liquid crystal reflective display and drive scheme,” Jpn. J. Appl. Phys.38(3), 6827–6830 (1999).
[CrossRef]

1997 (1)

M. Xu and D.-K. Yang, “Dual frequency cholesteric light shutters,” Appl. Phys. Lett.70(6), 720–722 (1997).
[CrossRef]

1984 (1)

G. Solladié and R. G. Zimmermann, “Liquid crystals: A tool for studies on chirality,” Angew. Chem. Int. Ed. Engl.23(5), 348–362 (1984).
[CrossRef]

1981 (1)

M. Schadt, “Dielectric heating and relaxations in nematic liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.)66(1), 319–336 (1981).
[CrossRef]

1974 (1)

H. K. Bücher, R. T. Klingbiel, and J. P. VanMeter, “Frequency‐addressed liquid crystal field effect,” Appl. Phys. Lett.25(4), 186–188 (1974).
[CrossRef]

Bücher, H. K.

H. K. Bücher, R. T. Klingbiel, and J. P. VanMeter, “Frequency‐addressed liquid crystal field effect,” Appl. Phys. Lett.25(4), 186–188 (1974).
[CrossRef]

Chen, C.-H.

Fu, K.-Y.

Golovin, A. B.

Y. Yin, S. V. Shiyanovskii, A. B. Golovin, and O. D. Lavrentovich, “Dielectric torque and orientation dynamics of liquid crystals with dielectric dispersion,” Phys. Rev. Lett.95(8), 087801 (2005).
[CrossRef] [PubMed]

A. B. Golovin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Fast switching dual-frequency liquid crystal optical retarder, driven by an amplitude and frequency modulated voltage,” Appl. Phys. Lett.83(19), 3864–3866 (2003).
[CrossRef]

Hou, C.-T.

Hsiao, Y.-C.

Huang, C.-Y.

Huang, S.-M.

C.-Y. Tang, S.-M. Huang, and W. Lee, “Dielectric relaxation dynamics in a dual-frequency nematic liquid crystal doped with C.I. Acid Red 2,” Dyes Pig.88(1), 1–6 (2011).
[CrossRef]

Klingbiel, R. T.

H. K. Bücher, R. T. Klingbiel, and J. P. VanMeter, “Frequency‐addressed liquid crystal field effect,” Appl. Phys. Lett.25(4), 186–188 (1974).
[CrossRef]

Lavrentovich, O. D.

Y. Yin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Thermodielectric bistability in dual frequency nematic liquid crystal,” Phys. Rev. Lett.98(9), 097801 (2007).
[CrossRef] [PubMed]

Y. Yin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Electric heating effects in nematic liquid crystals,” J. Appl. Phys.100(2), 024906 (2006).
[CrossRef]

Y. Yin, S. V. Shiyanovskii, A. B. Golovin, and O. D. Lavrentovich, “Dielectric torque and orientation dynamics of liquid crystals with dielectric dispersion,” Phys. Rev. Lett.95(8), 087801 (2005).
[CrossRef] [PubMed]

A. B. Golovin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Fast switching dual-frequency liquid crystal optical retarder, driven by an amplitude and frequency modulated voltage,” Appl. Phys. Lett.83(19), 3864–3866 (2003).
[CrossRef]

Lee, W.

Liang, X.

P.-T. Lin, X. Liang, H. Ren, and S.-T. Wu, “Tunable diffraction grating using ultraviolet-light-induced spatial phase modulation in dual-frequency liquid crystal,” Appl. Phys. Lett.85(7), 1131–1133 (2004).
[CrossRef]

Lin, C.-L.

H. Xianyu, S.-T. Wu, and C.-L. Lin, “Dual frequency liquid crystals: a review,” Liq. Cryst.36(6–7), 717–726 (2009).
[CrossRef]

Lin, F.-C.

F.-C. Lin and W. Lee, “Color-reflective dual-frequency cholesteric liquid crystal displays and their drive schemes,” Appl. Phys. Express4(11), 112201 (2011).
[CrossRef]

Lin, P.-T.

P.-T. Lin, X. Liang, H. Ren, and S.-T. Wu, “Tunable diffraction grating using ultraviolet-light-induced spatial phase modulation in dual-frequency liquid crystal,” Appl. Phys. Lett.85(7), 1131–1133 (2004).
[CrossRef]

Liu, H.-H.

H.-H. Liu and W. Lee, “Time-varying ionic properties of a liquid-crystal cell,” Appl. Phys. Lett.97(2), 023510 (2010).
[CrossRef]

Lo, K.-Y.

Ma, J.

J. Ma, L. Shi, and D.-K. Yang, “Bistable polymer stabilized cholesteric texture light shutter,” Appl. Phys. Express3(2), 021702 (2010).
[CrossRef]

Ren, H.

P.-T. Lin, X. Liang, H. Ren, and S.-T. Wu, “Tunable diffraction grating using ultraviolet-light-induced spatial phase modulation in dual-frequency liquid crystal,” Appl. Phys. Lett.85(7), 1131–1133 (2004).
[CrossRef]

Schadt, M.

M. Schadt, “Dielectric heating and relaxations in nematic liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.)66(1), 319–336 (1981).
[CrossRef]

Shi, L.

J. Ma, L. Shi, and D.-K. Yang, “Bistable polymer stabilized cholesteric texture light shutter,” Appl. Phys. Express3(2), 021702 (2010).
[CrossRef]

Shiyanovskii, S. V.

Y. Yin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Thermodielectric bistability in dual frequency nematic liquid crystal,” Phys. Rev. Lett.98(9), 097801 (2007).
[CrossRef] [PubMed]

Y. Yin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Electric heating effects in nematic liquid crystals,” J. Appl. Phys.100(2), 024906 (2006).
[CrossRef]

Y. Yin, S. V. Shiyanovskii, A. B. Golovin, and O. D. Lavrentovich, “Dielectric torque and orientation dynamics of liquid crystals with dielectric dispersion,” Phys. Rev. Lett.95(8), 087801 (2005).
[CrossRef] [PubMed]

A. B. Golovin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Fast switching dual-frequency liquid crystal optical retarder, driven by an amplitude and frequency modulated voltage,” Appl. Phys. Lett.83(19), 3864–3866 (2003).
[CrossRef]

Solladié, G.

G. Solladié and R. G. Zimmermann, “Liquid crystals: A tool for studies on chirality,” Angew. Chem. Int. Ed. Engl.23(5), 348–362 (1984).
[CrossRef]

Tang, C.-Y.

Y.-C. Hsiao, C.-Y. Tang, and W. Lee, “Fast-switching bistable cholesteric intensity modulator,” Opt. Express19(10), 9744–9749 (2011).
[CrossRef] [PubMed]

C.-Y. Tang, S.-M. Huang, and W. Lee, “Dielectric relaxation dynamics in a dual-frequency nematic liquid crystal doped with C.I. Acid Red 2,” Dyes Pig.88(1), 1–6 (2011).
[CrossRef]

Timofeev, I. V.

Tsai, M.-S.

VanMeter, J. P.

H. K. Bücher, R. T. Klingbiel, and J. P. VanMeter, “Frequency‐addressed liquid crystal field effect,” Appl. Phys. Lett.25(4), 186–188 (1974).
[CrossRef]

Wen, C.-H.

C.-H. Wen and S.-T. Wu, “Dielectric heating effects of dual-frequency liquid crystals,” Appl. Phys. Lett.86(23), 231104 (2005).
[CrossRef]

Wu, C.-Y.

Wu, S.-T.

H. Xianyu, S.-T. Wu, and C.-L. Lin, “Dual frequency liquid crystals: a review,” Liq. Cryst.36(6–7), 717–726 (2009).
[CrossRef]

C.-H. Wen and S.-T. Wu, “Dielectric heating effects of dual-frequency liquid crystals,” Appl. Phys. Lett.86(23), 231104 (2005).
[CrossRef]

P.-T. Lin, X. Liang, H. Ren, and S.-T. Wu, “Tunable diffraction grating using ultraviolet-light-induced spatial phase modulation in dual-frequency liquid crystal,” Appl. Phys. Lett.85(7), 1131–1133 (2004).
[CrossRef]

Xianyu, H.

H. Xianyu, S.-T. Wu, and C.-L. Lin, “Dual frequency liquid crystals: a review,” Liq. Cryst.36(6–7), 717–726 (2009).
[CrossRef]

Xu, M.

M. Xu and D.-K. Yang, “Electrooptical properties of dual-frequency cholesteric liquid crystal reflective display and drive scheme,” Jpn. J. Appl. Phys.38(3), 6827–6830 (1999).
[CrossRef]

M. Xu and D.-K. Yang, “Dual frequency cholesteric light shutters,” Appl. Phys. Lett.70(6), 720–722 (1997).
[CrossRef]

Yang, D.-K.

J. Ma, L. Shi, and D.-K. Yang, “Bistable polymer stabilized cholesteric texture light shutter,” Appl. Phys. Express3(2), 021702 (2010).
[CrossRef]

M. Xu and D.-K. Yang, “Electrooptical properties of dual-frequency cholesteric liquid crystal reflective display and drive scheme,” Jpn. J. Appl. Phys.38(3), 6827–6830 (1999).
[CrossRef]

M. Xu and D.-K. Yang, “Dual frequency cholesteric light shutters,” Appl. Phys. Lett.70(6), 720–722 (1997).
[CrossRef]

Yin, Y.

Y. Yin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Thermodielectric bistability in dual frequency nematic liquid crystal,” Phys. Rev. Lett.98(9), 097801 (2007).
[CrossRef] [PubMed]

Y. Yin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Electric heating effects in nematic liquid crystals,” J. Appl. Phys.100(2), 024906 (2006).
[CrossRef]

Y. Yin, S. V. Shiyanovskii, A. B. Golovin, and O. D. Lavrentovich, “Dielectric torque and orientation dynamics of liquid crystals with dielectric dispersion,” Phys. Rev. Lett.95(8), 087801 (2005).
[CrossRef] [PubMed]

Zimmermann, R. G.

G. Solladié and R. G. Zimmermann, “Liquid crystals: A tool for studies on chirality,” Angew. Chem. Int. Ed. Engl.23(5), 348–362 (1984).
[CrossRef]

Zou, Y.-H.

Zyryanov, V. Ya.

Angew. Chem. Int. Ed. Engl. (1)

G. Solladié and R. G. Zimmermann, “Liquid crystals: A tool for studies on chirality,” Angew. Chem. Int. Ed. Engl.23(5), 348–362 (1984).
[CrossRef]

Appl. Phys. Express (2)

J. Ma, L. Shi, and D.-K. Yang, “Bistable polymer stabilized cholesteric texture light shutter,” Appl. Phys. Express3(2), 021702 (2010).
[CrossRef]

F.-C. Lin and W. Lee, “Color-reflective dual-frequency cholesteric liquid crystal displays and their drive schemes,” Appl. Phys. Express4(11), 112201 (2011).
[CrossRef]

Appl. Phys. Lett. (6)

C.-H. Wen and S.-T. Wu, “Dielectric heating effects of dual-frequency liquid crystals,” Appl. Phys. Lett.86(23), 231104 (2005).
[CrossRef]

A. B. Golovin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Fast switching dual-frequency liquid crystal optical retarder, driven by an amplitude and frequency modulated voltage,” Appl. Phys. Lett.83(19), 3864–3866 (2003).
[CrossRef]

P.-T. Lin, X. Liang, H. Ren, and S.-T. Wu, “Tunable diffraction grating using ultraviolet-light-induced spatial phase modulation in dual-frequency liquid crystal,” Appl. Phys. Lett.85(7), 1131–1133 (2004).
[CrossRef]

H. K. Bücher, R. T. Klingbiel, and J. P. VanMeter, “Frequency‐addressed liquid crystal field effect,” Appl. Phys. Lett.25(4), 186–188 (1974).
[CrossRef]

H.-H. Liu and W. Lee, “Time-varying ionic properties of a liquid-crystal cell,” Appl. Phys. Lett.97(2), 023510 (2010).
[CrossRef]

M. Xu and D.-K. Yang, “Dual frequency cholesteric light shutters,” Appl. Phys. Lett.70(6), 720–722 (1997).
[CrossRef]

Dyes Pig. (1)

C.-Y. Tang, S.-M. Huang, and W. Lee, “Dielectric relaxation dynamics in a dual-frequency nematic liquid crystal doped with C.I. Acid Red 2,” Dyes Pig.88(1), 1–6 (2011).
[CrossRef]

J. Appl. Phys. (1)

Y. Yin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Electric heating effects in nematic liquid crystals,” J. Appl. Phys.100(2), 024906 (2006).
[CrossRef]

Jpn. J. Appl. Phys. (1)

M. Xu and D.-K. Yang, “Electrooptical properties of dual-frequency cholesteric liquid crystal reflective display and drive scheme,” Jpn. J. Appl. Phys.38(3), 6827–6830 (1999).
[CrossRef]

Liq. Cryst. (1)

H. Xianyu, S.-T. Wu, and C.-L. Lin, “Dual frequency liquid crystals: a review,” Liq. Cryst.36(6–7), 717–726 (2009).
[CrossRef]

Mol. Cryst. Liq. Cryst. (Phila. Pa.) (1)

M. Schadt, “Dielectric heating and relaxations in nematic liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.)66(1), 319–336 (1981).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Opt. Mater. Express (1)

Phys. Rev. Lett. (2)

Y. Yin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Thermodielectric bistability in dual frequency nematic liquid crystal,” Phys. Rev. Lett.98(9), 097801 (2007).
[CrossRef] [PubMed]

Y. Yin, S. V. Shiyanovskii, A. B. Golovin, and O. D. Lavrentovich, “Dielectric torque and orientation dynamics of liquid crystals with dielectric dispersion,” Phys. Rev. Lett.95(8), 087801 (2005).
[CrossRef] [PubMed]

Other (3)

Y. A. Cengel, J. M. Cimbala, and R. H. Turner, Fundamentals of Thermal-Fluid Sciences, 4th ed. (McGraw-Hill, 2011).

T. L. Bergman, A. S. Lavine, F. P. Incropera, and D. P. DeWitt, Fundamentals of Heat and Mass Transfer, 7th ed. (Wiley, New York, 2011).

A. C. Metaxas, Foundations of Electroheat: A Unified Approach (Wiley, 1996).

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Figures (5)

Fig. 1
Fig. 1

Schematic of three CLC configurations and comparative drive methods to switch the DFCLC to the optically stable FC or voltage-sustained H state from the optically stable P state.

Fig. 2
Fig. 2

Dielectric dispersion of a DFCLC sample consisting of 5 wt% CD at 300 K.

Fig. 3
Fig. 3

Imaginary-part dielectric constant at 100 kHz as a function of the CD concentration. The straight line is the best fit to the experimental data represented by the symbol.

Fig. 4
Fig. 4

Voltage (100 kHz)-dependent dielectric heating in DFCLC with various CD concentrations. The symbols show the experimental results and the curves are derived theoretically from the approximation given by Eq. (5).

Fig. 5
Fig. 5

Voltage-dependent transmittance at operation frequencies of (a) 1 kHz and (b) 100 kHz. Inset: the photograph of the DFCLC cell showing the transition process with various zones separately in the P state (yellow), FC state (gray) and H state (dark) under crossed polarizers.

Tables (1)

Tables Icon

Table 1 Transition Times from the Planar State to the Homeotropic State in DFCLCs with Various Chiral-Dopant Concentrations at 15 Vrms at Three Different Frequencies

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

f c = A 0 exp( E a k B T ),
Q out =hA( T s T 0 ),
T T 0 = ( 1 + Bi )( T s T 0 ),
P=ω ε 0 ε (ω) E 2 = 2πf ε 0 ε (ω) V rms 2 d 2 ,
ε (c)=α+βc,
T= T 0 + πf( 1+Bi )A( α+βc ) V rms 2 hd T 0 +γ f c V rms 2 ,
p= 1 βcr ,

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