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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 18 — Aug. 30, 2010
  • pp: 18886–18893
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30 to 50 ns liquid-crystal optical switches

M. W. Geis, T. M. Lyszczarz, R. M. Osgood, and B. R. Kimball  »View Author Affiliations


Optics Express, Vol. 18, Issue 18, pp. 18886-18893 (2010)
http://dx.doi.org/10.1364/OE.18.018886


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Abstract

The optical switching time of twisted-nematic liquid-crystal cells using the liquid crystals, 5CB (C5H11-Ph-Ph-CN), 5OCB(C5H11-O-Ph-Ph-CN) and PCH5 (C5H11-Cy-Ph-CN) have been characterized as a function of temperature, bias voltage and switching voltage, V. The transition time from 90% to 10% transmission scales as V-1.9 and is limited to 30 to 50 ns by the liquid-crystal breakdown electric field, ~100 V μm−1. The time from the initial switching voltage step to 90% transmission, delay time, decreases with increasing bias and switching voltage. For 5CB and 5OCB the delay time approaches a constant value at higher electric fields, >10 V μm−1. Both the transition and delay times decrease with increasing temperature. The minimum transition time at temperatures a few degrees below the nematic-isotropic temperature are 32, 32, and 44 ns and delay times are 44, 25 and 8 ns for 5CB, 5OCB, and PCH5 respectively.

© 2010 OSA

1. Introduction

Area, > 0.1 cm2, fast, < 1 μs, optical shutters have applications in recording images of laser and chemically driven explosions. Mechanical shutters have frame rates of up to 25x106 fps for 125 frames [1] and the simpler and more compact electronic shutters using a gated charge-coupled-device, CCD, array have frame rates of 2x106 fps for 50 frames [2

2. R. K. Reich, D. D. Rathman, D. M. O'Mara, D. J. Young, A. H. Loomis, R. M. Osgood, R. A. Murphy, M. Rose, R. Berger, B. M. Tyrrell, S. A. Watson, M. D. Ulibarri, T. Perry, F. Weber, and H. Robey, “Lincoln Laboratory high-speed solid-state imager technology,” Proc. SPIE 6279, 62791K (2007). [CrossRef]

]. This article reports on a simple twisted-nematic liquid-crystal shutter with demonstrated shutter times of 30 to 50 ns. This fast switching when combined with a CCD array could represent a third approach with superior properties [3

3. M. W. Geis, R. J. Molnar, G. W. Turner, T. M. Lyszczarz, R. M. Osgood, and B. R. Kimball, “30 to 50 ns liquid-crystal optical switches,” Proc. SPIE 7618, 76180J (2010). [CrossRef]

].

These liquid-crystal cells when used as optical shutters are characterized by two time constants, the switching time to rotate the liquid-crystal director under the application of an electric field and the recovery time after the electric field is removed. This article is concerned with just the switching time in the presence of an electric field. The recovery times are not extraordinary and are consistent with normal liquid crystal operation. This time is dependent upon several parameters: the character of the liquid crystal, the temperature, the switching electric field and the pretilt of the liquid crystal director [4

4. H. Takanashi, J. E. Maclennan, and N. A. Clark, “Sub 100 Nanosecond Pretilted Planar-to-Homeotropic Reorientation of Nematic Liquid Crystals under High Electric Field,” J. Appl. Phys. 37(5), 2587–2589 (1998). [CrossRef]

]. The pretilt in this report was controlled by the application of a bias voltage between 0 to 4 V. Using the comparatively small molecular weight liquid crystals 5CB (C5H11-Ph-Ph-CN), 5OCB(C5H11-O-Ph-Ph-CN) and PCH5 (C5H11-Cy-Ph-CN), the above parameters were varied to obtain the shortest practical switching times.

2. Experiment

The twisted-nematic liquid-crystal cells used with these experiments have an active area of 0.1 cm2 and gap thickness of either 5 or 10 μm. Details of lithography, etching and metallization are given elsewhere [3

3. M. W. Geis, R. J. Molnar, G. W. Turner, T. M. Lyszczarz, R. M. Osgood, and B. R. Kimball, “30 to 50 ns liquid-crystal optical switches,” Proc. SPIE 7618, 76180J (2010). [CrossRef]

]. The cell was designed to minimize its internal resistance and capacitance, having an RC time constant between 1.0 and 2.5 ns. Cells were often reused to characterize several liquid crystals under the same conditions. Each time the cell was reused it was disassembled, cleaned in acetone and in an oxygen plasma, rerubbed and filled with another liquid crystal in a vacuum of < 10 Pa and a few degrees above the nematic-isotropic temperature, TN-I. The cells eventually failed due to arcing during high voltage operation and were replaced with new cells. To the accuracy of our experiments results were consistent between cells.

The measurement system consisted of a HeNe laser producing ~10 mW of 632 nm polarized light. The light passes through a liquid-crystal cell and into a polarizing-cube beam-splitter, which generates two light beams of opposite polarization. The intensity of each beam was monitored by a fast Si photodiode and recorded by a digital oscilloscope with a 2 ns rise time. Figure 1
Fig. 1 Experimental setup, HeNe laser, liquid-crystal cell, polarizing beam splitter, and two silicon photodiodes. On the left is the equivalent circuit for a 5-μm-gap cell. Below that, is the graph of the normalized output as a function of time from Si photodiode (A). The graph defines the delay, τD, and the transition, τT, times. The graph on the right shows waveform of the voltage step applied to the liquid-crystal cell. Below that graph is the normalized signal from Si photodiode (B) as a function of time.
shows the experimental step up.

2.1 Bias

If the director is parallel to the electrode surface, perpendicular to the applied switching electric field, then the initial torque on the director by the electric field is very small, resulting in a large τD before the cell switches. A variety of techniques have been used to generate a pretilted director including treatment of the liquid-crystal cell electrodes with specific polymers [5

5. H.-Y. Wu, C.-Y. Wang, C.-J. Lin, R.-P. Pan, S.-S. Lin, C.-D. Lee, and C.-S. Kou, “Mechanism in determining pretilt angle of liquid crystals aligned on fluorinated copolymer films,” J. Phys. D Appl. Phys. 42(15), 155303 (2009). [CrossRef]

], angled evaporation of SiO2 [6

6. M. Lu, K. H. Yang, T. Nakasogi, and S. J. Chey, “Homeotropic Alignment by Single Oblique Evaporation of SiO2 and Its Application to High Resolution Microdisplays,” SID Int. Symp. Digest Tech. Papers 31(1), 446–449 (2000). [CrossRef]

], or applying a bias voltage to the cell prior to the switching voltage [7

7. S. Lamarque-Forget, P. Martinot-Lagarde, and I. Dozov, “Technique for Local Pretilt Measurement in Nematic Liquid Crystals,” Jpn. J. Appl. Phys. 40(Part 2, No. 4A), L349–L351 (2001). [CrossRef]

]. This is consistent with the data in Figs. 2
Fig. 2 Normalized transmission as a function of time for several bias RMS AC voltages. The cell gap is 5 μm and is filled with 5CB at 30 °C. The switching voltage was 40 V.
and 3
Fig. 3 τD, τT and normalized optical transmission as a function of bias voltage for the same cell used in Fig. 2.
where τD decreases by an order of magnitude with an increase in bias voltage from 0 to 1 V. The same voltage increase only decreases the transition time, τT, by a factor of ~2. To obtain the shortest practical switching times the bias voltage was adjusted to reduce the transmission to ~90% of the maximum value for the data shown in Figs. 5
Fig. 5 Normalized light transmission with the application of a 800 V step on a cell similar to that used for Fig. 4.
through 11
Fig. 11 The same data as shown in Fig. 10 with the addition of the fastest switching time known to us in the literature [4]. The incomplete switching, from 0% to 80% for 5CB*, shown in ref 4, is not understood [15].
. Initially a DC bias voltage was used and this worked well for 5CB, but other liquid crystals proved to be more conductive and an AC bias had to be used. The increase in conductivity is a result of ion contamination in the liquid crystal. Under DC bias conditions these ions move in the liquid crystal and reduce the electric field of the bias voltage. The bias voltage can be increased to compensate the field reduction, but the required voltage becomes time dependent as more ions are generated and the experimental results are compromised when the DC bias voltage is more than a few volts. The ions cannot respond to an AC bias voltage at frequencies > 20 Hz. It was not feasible to repeat all the experiments with the same bias conditions so a DC bias was used for most of the 5CB data while an AC bias was used for most of the PCH5 data.

2.2 Quasi-static and high voltage DC pulse

Figures 4
Fig. 4 Normalized transmission and bias current as function of voltage for a 10-μm-thick 3-mm-diameter 5CB cell at 32.9 °C. The dotted line indicates negative current.
and 5 compare the liquid-crystal cell properties when switched by quasi-static DC voltage and a high voltage DC pulse. For the quasi-static measurement the voltage was ramped from 0 to 40 V and back at 0.32 V s−1 for a total time of 250 s. With a 40 V bias the transmitted beam is attenuated by 1000 with ~0.1 V hysteresis at 50% transmission between the voltage ramp increasing and decreasing in time.

The low leakage current, < 6 nA at 40 V, is characteristic of 5CB, but if the liquid crystal was exposed to laboratory air over a period of several months it became more conductive requiring an AC bias voltage. The low hysteresis, ~0.1 V, is a result of the low ion content in the liquid crystal. Hysteresis over a volt and leakage currents of several micro amps are common with more conductive liquid crystals, which require an AC bias voltage. Note the same reduction in transmission by ~1000 occurs for both the quasi-static and the DC pulse switching. The high voltage switching pulse results, as shown in Fig. 5, were independent of the liquid-crystal conductivity.

3. Simple model

τT of a twisted-nematic liquid-crystal cell for electric fields, >10 V μm−1, is approximated by Eq. (1) [8

8. I.-K. Huh and Y.-B. Kim, “Electro-optical Properties of Liquid Crystal Mixtures Containing Fluoroisothiocyanated Compounds,” Jpn. J. Appl. Phys. 41(Pt.1, No. 11 A), 6484–6485 (2002). [CrossRef]

]
τT=γε0ΔεE2,
(1)
where the switching electric field, E = V/d, is the switching voltage, V, across the cell divided by the cell gap, d, γ is the rotational viscosity, Δε is the change of the dielectric constant between the director perpendicular and parallel to the electric field, and ε0 is the vacuum permittivity, 8.85 x10−8 F μm−1.

For the purpose of comparing the measured τT with that calculated from Eq. (1), Δε [9

9. M. D. Simões, S. M. Simeão, A. de Campos, and A. J. Palangana, “Corresponding states of nematic birefringence: an order parameter universality,” Philos. Mag. 87(33), 5237–5247 (2007). [CrossRef]

,10

10. M. D. Simões, S. M. Simeão, S. M. Domiciano, and A. de Campos, “Nematic universality,” Phys. Lett. A 372(32), 5346–5351 (2008). [CrossRef]

] and γ [11

11. F.-J. Bock, H. Kneppe, and F. Schneider, “Rotational viscosity of nematic liquid crystals and their shear viscosity under flow alignment,” Liq. Cryst. 1(3), 239–251 (1986). [CrossRef]

] as a function of temperature were obtained from published data. Figure 6
Fig. 6 Normalized transmission through a 10-μm-thick 5CB cell as a function of time for several temperatures. A 900 V step was applied to the cell at Time = 0. 5CB was super cooled to 5 °C, 19 ° C below its crystallizing temperature, 24°C.
shows the transmission of a typical 5CB cell as a function of time for several temperatures, keeping all other parameters constant. From the data shown in Fig. 6, and other measurements, a comparison of the measured τ T to that calculated from Eq. (1) is shown in Fig. 7
fig. 7 Comparison of the measured τT for 5CB and 5OCB with Eq. (1) times a scalar constant of 0.8 as a function of temperature. TN-I is 35.3 °C for 5CB and 68 °C for 5OCB. The parameters used in Eq. (1) were obtained from references 9 to 11. εο = 8.85x108 F μm−1.
. At temperatures below 15 °C cells filled with 5CB exhibit an anomalous transmission tail. Because of this tail, data below 16 °C were not used in Fig. 7. We were not able to super cool the other liquid crystals to the same extent and they did not exhibit this anomalous transmission tail.

4. Results

A reasonable correlation between the calculated and measured switching times as a function of temperature for 5CB and 5OCB is shown Fig. 7. PCH5 exhibits a similar agreement. τD and τT were also characterized as a function of the switching electric field, E, from 4 to 90 V μm−1 by varying the switching voltage from 20 to 900 V, and the results are depicted in Figs. 1, 8
Fig. 8 Measured τD as a function of switching voltage. The liquid crystals were few degrees below their TN-I. The curves are a visual fit to the data using a power law and a constant. E is in V μm−1 and τD in ns for the equations in the figure .
11. τT monotonically decreases with increasing E, but τD approaches a constant value at high electric fields for 5CB and 5OCB. For 5CB the total switching time, the sum of τD and τT, is dominated by τD for E > 30 V μm−1. However, the τD for PCH5 continues to decrease with increasing E and its switching time is dominated by the τT for E approaching 100 V μm−1.

Figure 10
Fig. 10 The best switching times for the liquid crystals tested. The electric fields were between 80 and 90 V μm−1 . The delay times and transition times are noted on the graph. The cell gap was 10 μm for 5CB and 5OCB and 5 μm for PCH5.
shows the best times obtained for the three liquid crystals tested. The very small τD for PCH5 is comparable to the rise time of the voltage pulse, 6 ns. The small delay time for PCH5 required a cell and switching circuit redesign. The cells, which were normally 10 μm thick, were changed to 5 μm allowing for a higher electric field with a smaller switching voltage. The lowered switching voltage allowed for a reduction in the switching circuit's output resistance and an overall reduction in the rise time of the voltage step.

5. Discussion

The application of very large electric fields on liquid-crystal cells demonstrates that the liquid-crystal τ T is dependent upon ratio of the rotational viscosity to the change in the dielectric constant, γ /Δε, vary as ~E-1.9, and is limited by the electric field break down ~100 V μm−1. Several groups have shown that the response times of liquid crystals are limited by several parameters including their dielectric relaxation time [14

14. M. Gu, Y. Yin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Effects of dielectric relaxation on the director dynamics of uniaxial nematic liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(6 Pt 1), 061702 (2007). [CrossRef]

]. Dielectric relaxation times of the liquid crystals a few degrees below TN-I are 15, 2.5, and 7-10 ns for 5CB, 5OCB and PCH5 respectively [12

12. S. Urban, B. Gestblom, W. Kuczyński, S. Pawlus, and A. Würflinger, “Nematic order parameter as determined from dielectric relaxation data and other methods,” Phys. Chem. Chem. Phys. 5(5), 924–928 (2003). [CrossRef]

,13

13. B. A. Belyaev, N. A. Drokin, V. F. Shabanov, and V. A. Baranova, “Dielectric Properties of Liquid Crystals of the Cyano Derivative Compounds with Different Fragments in the Molecular Core,” Phys. Solid State 46(3), 574–578 (2004). [CrossRef]

].

Fig. 9 Measured τT as a function of switching voltage. The liquid crystals were few degrees below their TN-I. The curves are a least square fit power law. E is in V μm−1 and τD in ns for the equations in the figure .

To the accuracy of these measurements τT is limited by the electric field breakdown of the liquid crystal cell and not by the dielectric relaxation time. τD for 5CB and 5OCB asymptotically approaches 40 and 20 ns respectively. However, the τD for PCH5 approaches no time limit even for fields of 80 V μm−1. Once the liquid crystal is switched a small voltage 2 to 5 V will keep it in the switched state. Although electric field approaching 100 V μm were used for these experiments, consistent reliable results were obtained for < 30 V μm, which limited the usable switching times to a few 100 ns.

To the best of our knowledge Gu et.al [14

14. M. Gu, Y. Yin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Effects of dielectric relaxation on the director dynamics of uniaxial nematic liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(6 Pt 1), 061702 (2007). [CrossRef]

]. and Takanashi et. al [3

3. M. W. Geis, R. J. Molnar, G. W. Turner, T. M. Lyszczarz, R. M. Osgood, and B. R. Kimball, “30 to 50 ns liquid-crystal optical switches,” Proc. SPIE 7618, 76180J (2010). [CrossRef]

] are the only published reports of nematic liquid-crystal cells with switching times < 100 ns. It is difficult to compare Gu’s experimental results with ours. However, we can make a direct comparison with Takanashi’s results as shown in Fig. 11. He uses a larger switching electric field, 120 V μm−1. The largest electric field that would give consistent results for our setup was 80-90 V μm−1. In spite of this, t D and t T reported here were smaller than Takanashi’s. This may be the result of Takanashi's more elegant approach to obtain pretilt with a rubbed polymer. The polymer reduces the electric field applied to the liquid crystal and might not have resulted in the optimum pretilt.

Ferroelectric liquid crystals are know to switch faster than nematic liquid crystal at low electric fields, 1 to 10 V μm. However, the switching time scales as one over the electric field, 1/E, for ferroelectric liquid crystals [16

16. N. A. Clark and S. T. Lagerwall, “Submicrosecond bistable electro-optic switching in liquid crystals,” Appl. Phys. Lett. 36(11), 899–901 (1980). [CrossRef]

] and as on over the electric field squares, 1/E2 for nematic liquid crystals. At large electric fields > 10 V μm the switching time of nematic liquid crystals is generally smaller than ferroelectric liquid crystals. However, the recovery time of nematic liquid crystals is usually milliseconds and not dependent on the electric field. The ferroelectric liquid crystals are bistable and must be switched back to their former state. Since this is driven by an electric field it can always be faster then the recover time of a nematic liquid crystal.

Acknowledgements

References and Links

1.

http://www.cordin.com/index.html

2.

R. K. Reich, D. D. Rathman, D. M. O'Mara, D. J. Young, A. H. Loomis, R. M. Osgood, R. A. Murphy, M. Rose, R. Berger, B. M. Tyrrell, S. A. Watson, M. D. Ulibarri, T. Perry, F. Weber, and H. Robey, “Lincoln Laboratory high-speed solid-state imager technology,” Proc. SPIE 6279, 62791K (2007). [CrossRef]

3.

M. W. Geis, R. J. Molnar, G. W. Turner, T. M. Lyszczarz, R. M. Osgood, and B. R. Kimball, “30 to 50 ns liquid-crystal optical switches,” Proc. SPIE 7618, 76180J (2010). [CrossRef]

4.

H. Takanashi, J. E. Maclennan, and N. A. Clark, “Sub 100 Nanosecond Pretilted Planar-to-Homeotropic Reorientation of Nematic Liquid Crystals under High Electric Field,” J. Appl. Phys. 37(5), 2587–2589 (1998). [CrossRef]

5.

H.-Y. Wu, C.-Y. Wang, C.-J. Lin, R.-P. Pan, S.-S. Lin, C.-D. Lee, and C.-S. Kou, “Mechanism in determining pretilt angle of liquid crystals aligned on fluorinated copolymer films,” J. Phys. D Appl. Phys. 42(15), 155303 (2009). [CrossRef]

6.

M. Lu, K. H. Yang, T. Nakasogi, and S. J. Chey, “Homeotropic Alignment by Single Oblique Evaporation of SiO2 and Its Application to High Resolution Microdisplays,” SID Int. Symp. Digest Tech. Papers 31(1), 446–449 (2000). [CrossRef]

7.

S. Lamarque-Forget, P. Martinot-Lagarde, and I. Dozov, “Technique for Local Pretilt Measurement in Nematic Liquid Crystals,” Jpn. J. Appl. Phys. 40(Part 2, No. 4A), L349–L351 (2001). [CrossRef]

8.

I.-K. Huh and Y.-B. Kim, “Electro-optical Properties of Liquid Crystal Mixtures Containing Fluoroisothiocyanated Compounds,” Jpn. J. Appl. Phys. 41(Pt.1, No. 11 A), 6484–6485 (2002). [CrossRef]

9.

M. D. Simões, S. M. Simeão, A. de Campos, and A. J. Palangana, “Corresponding states of nematic birefringence: an order parameter universality,” Philos. Mag. 87(33), 5237–5247 (2007). [CrossRef]

10.

M. D. Simões, S. M. Simeão, S. M. Domiciano, and A. de Campos, “Nematic universality,” Phys. Lett. A 372(32), 5346–5351 (2008). [CrossRef]

11.

F.-J. Bock, H. Kneppe, and F. Schneider, “Rotational viscosity of nematic liquid crystals and their shear viscosity under flow alignment,” Liq. Cryst. 1(3), 239–251 (1986). [CrossRef]

12.

S. Urban, B. Gestblom, W. Kuczyński, S. Pawlus, and A. Würflinger, “Nematic order parameter as determined from dielectric relaxation data and other methods,” Phys. Chem. Chem. Phys. 5(5), 924–928 (2003). [CrossRef]

13.

B. A. Belyaev, N. A. Drokin, V. F. Shabanov, and V. A. Baranova, “Dielectric Properties of Liquid Crystals of the Cyano Derivative Compounds with Different Fragments in the Molecular Core,” Phys. Solid State 46(3), 574–578 (2004). [CrossRef]

14.

M. Gu, Y. Yin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Effects of dielectric relaxation on the director dynamics of uniaxial nematic liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(6 Pt 1), 061702 (2007). [CrossRef]

15.

Neal Clark, Liquid Crystal Group, Department of Physics, University of Colorado, Boulder, CO 80309–0390 (personal communication, 2009).

16.

N. A. Clark and S. T. Lagerwall, “Submicrosecond bistable electro-optic switching in liquid crystals,” Appl. Phys. Lett. 36(11), 899–901 (1980). [CrossRef]

OCIS Codes
(160.3710) Materials : Liquid crystals
(230.3720) Optical devices : Liquid-crystal devices

ToC Category:
Optical Devices

History
Original Manuscript: June 25, 2010
Revised Manuscript: August 2, 2010
Manuscript Accepted: August 7, 2010
Published: August 19, 2010

Citation
M. W. Geis, T. M. Lyszczarz, R. M. Osgood, and B. R. Kimball, "30 to 50 ns liquid-crystal optical switches," Opt. Express 18, 18886-18893 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-18-18886


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References

  1. http://www.cordin.com/index.html
  2. R. K. Reich, D. D. Rathman, D. M. O'Mara, D. J. Young, A. H. Loomis, R. M. Osgood, R. A. Murphy, M. Rose, R. Berger, B. M. Tyrrell, S. A. Watson, M. D. Ulibarri, T. Perry, F. Weber, and H. Robey, “Lincoln Laboratory high-speed solid-state imager technology,” Proc. SPIE 6279, 62791K (2007). [CrossRef]
  3. M. W. Geis, R. J. Molnar, G. W. Turner, T. M. Lyszczarz, R. M. Osgood, and B. R. Kimball, “30 to 50 ns liquid-crystal optical switches,” Proc. SPIE 7618, 76180J (2010). [CrossRef]
  4. H. Takanashi, J. E. Maclennan, and N. A. Clark, “Sub 100 Nanosecond Pretilted Planar-to-Homeotropic Reorientation of Nematic Liquid Crystals under High Electric Field,” J. Appl. Phys. 37(5), 2587–2589 (1998). [CrossRef]
  5. H.-Y. Wu, C.-Y. Wang, C.-J. Lin, R.-P. Pan, S.-S. Lin, C.-D. Lee, and C.-S. Kou, “Mechanism in determining pretilt angle of liquid crystals aligned on fluorinated copolymer films,” J. Phys. D Appl. Phys. 42(15), 155303 (2009). [CrossRef]
  6. M. Lu, K. H. Yang, T. Nakasogi, and S. J. Chey, “Homeotropic Alignment by Single Oblique Evaporation of SiO2 and Its Application to High Resolution Microdisplays,” SID Int. Symp. Digest Tech. Papers 31(1), 446–449 (2000). [CrossRef]
  7. S. Lamarque-Forget, P. Martinot-Lagarde, and I. Dozov, “Technique for Local Pretilt Measurement in Nematic Liquid Crystals,” Jpn. J. Appl. Phys. 40(Part 2, No. 4A), L349–L351 (2001). [CrossRef]
  8. I.-K. Huh and Y.-B. Kim, “Electro-optical Properties of Liquid Crystal Mixtures Containing Fluoroisothiocyanated Compounds,” Jpn. J. Appl. Phys. 41(Pt.1, No. 11 A), 6484–6485 (2002). [CrossRef]
  9. M. D. Simões, S. M. Simeão, A. de Campos, and A. J. Palangana, “Corresponding states of nematic birefringence: an order parameter universality,” Philos. Mag. 87(33), 5237–5247 (2007). [CrossRef]
  10. M. D. Simões, S. M. Simeão, S. M. Domiciano, and A. de Campos, “Nematic universality,” Phys. Lett. A 372(32), 5346–5351 (2008). [CrossRef]
  11. F.-J. Bock, H. Kneppe, and F. Schneider, “Rotational viscosity of nematic liquid crystals and their shear viscosity under flow alignment,” Liq. Cryst. 1(3), 239–251 (1986). [CrossRef]
  12. S. Urban, B. Gestblom, W. Kuczyński, S. Pawlus, and A. Würflinger, “Nematic order parameter as determined from dielectric relaxation data and other methods,” Phys. Chem. Chem. Phys. 5(5), 924–928 (2003). [CrossRef]
  13. B. A. Belyaev, N. A. Drokin, V. F. Shabanov, and V. A. Baranova, “Dielectric Properties of Liquid Crystals of the Cyano Derivative Compounds with Different Fragments in the Molecular Core,” Phys. Solid State 46(3), 574–578 (2004). [CrossRef]
  14. M. Gu, Y. Yin, S. V. Shiyanovskii, and O. D. Lavrentovich, “Effects of dielectric relaxation on the director dynamics of uniaxial nematic liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(6 Pt 1), 061702 (2007). [CrossRef]
  15. Neal Clark, Liquid Crystal Group, Department of Physics, University of Colorado, Boulder, CO 80309–0390 (personal communication, 2009).
  16. N. A. Clark and S. T. Lagerwall, “Submicrosecond bistable electro-optic switching in liquid crystals,” Appl. Phys. Lett. 36(11), 899–901 (1980). [CrossRef]

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