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Optimized frequency regime for the electrohydrodynamic induction of a uniformly lying helix structure Yu-Lin Nian, Po-Chang Wu, and Wei Lee* College of Photonics, National Chiao Tung University, Guiren District, Tainan 71150, Taiwan *Corresponding author:
[email protected] Received July 22, 2016; revised September 7, 2016; accepted September 9, 2016; posted September 9, 2016 (Doc. ID 270761); published October 14, 2016 This study specifies the optimal frequency regime for the uniformly lying helix (ULH) alignment induced by the electrohydrodynamic (EHD) effect in a cholesteric liquid crystal with positive dielectric anisotropy. Based on the transport behavior of ionic charges in response to the externally applied ac electric field, four frequency regimes, divided by three critical frequencies (i.e., f L , f R , and f H ), are identified by means of dielectric spectroscopy. By discussing the voltage-dependent cholesteric textural changes in each frequency regime in terms of the voltageand frequency-dependent transmission spectra and optical textures, our results suggest that the designated frequency regime f L , f H , f R < f < f H , f L < f < f R , and f < f L ) for
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investigating the textural transition in a CLC cell under the application of external voltages in terms of the frequency dependence of ionic behavior. Subsequently, by selecting four frequencies individually lying within the designated frequency regimes, Fig. 2 illustrates textural changes of the R-CLC cell at various applied voltages V at a fixed temperature T of 40°C. In accordance with the results given in Fig. 1(a), values of f L , f R , and f H at T 40°C are 29, 118, and 498 Hz, respectively. The transport of ions in an electric field at frequencies higher than f H is restricted due to the fast reversal of field polarities so that the field-induced texture transition is primarily dominated by the dielectric coupling effect. For a typical planar-aligned CLC cell with positive dielectric anisotropy, the texture with the initial P state is electrically switched to the FC state by a moderate voltage and can be sustained in the homeotropic (H) state at a higher voltage. As evidenced in Fig. 2(a), the R-CLC cell exhibits FC textures with distinct colorful appearances at various V at a constant frequency (f 1 kHz > f H ), and it retains in the H state at V > 40 V (not shown in the figure). When the frequency condition of f < f H is satisfied, the cell driven by the voltage of V 9 V at various frequencies exhibits FC textures as well. This indicates that the voltage of 9 V is insufficient to energize the EHD effect and, thus, the molecular flow for the generation of the additional texture transition to the ULH state. Since the ionic effect governs the dielectric response of LC molecules and the strength of EHD flow under the external voltage, the voltage-induced FC textures with distinct domain sizes at various frequencies could be attributable to the transport behaviors of ions within the bulk of the cell as well as the weakened EHD effect. Noticeably, it can be identified from Figs. 2(b)–2(d) that additional textures—the ULH state and the dynamic scattering (DS) state—are sequentially observed between the FC and the H states in the voltage-increasing process at f 300, 70, and 5 Hz. Both the ULH and the DS textures are believed to be created by the low-frequency EHD effect. The ULH domain can be further attributed to the combination of molecular-flow-induced horizontal shear stress for helices and the dielectric torque between the LC and the electric field
Fig. 2. Electrically induced textural changes in the R-CLC cell at 40°C in the voltage ramp-up process at (a) f 1 kHz (f > f H ), (b) f 300 Hz (f R < f < f H ), (c) f 70 Hz (f L < f < f R ), and (d) f 5 Hz (f < f L ).
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directors, whereas the formation of the DS texture arises from the turbulence via the increase in flow velocity at high voltages and, thus, the destabilization of LC directors. Note that the ULH structure can be partially generated in the cell at f 300 Hz (f R < f < f H ) and f 5 Hz (f < f L ) but is uniformly demonstrated at f 70 Hz (f L < f < f R ). This implies that a CLC cell with a well-aligned ULH structure exists when ac voltage is applied at a frequency within the f L < f < f R regime. Since the low-frequency EHD effect stems from the segregation of space charges and their interaction with the electric field, the ULH domains, as shown in Figs. 2(b)–2(d) with varying degrees of uniformities, can be elucidated in terms of fieldinduced movement of charges within a CLC cell as follows: In the frequency regime of f R < f < f H , electrical charges can cross only a part of cell thickness in that the ion-charging time constant is larger than the half-period of time of the applied ac electric field. Therefore, upon the application of a sufficiently high voltage at a frequency satisfying the condition of f R < f < f H to induce the EHD effect, nonuniform ULH domains would be generated through the molecular flow locally in the cell [Fig. 2(b)]. Comparatively in the regime of f L < f < f R , charge carriers can arrive at the electrodes before the end of a half-period of the field, and they can oscillate effectively in a period of time of the field. The effective spatial charge distribution enhances the EHD strength and more uniform ULH alignment is obtained through the expansion and coalition of ULH domains due to the increasing amount of molecular flow within the CLC bulk [Fig. 2(c)]. When f < f L , the ion-charging time becomes smaller than the half-period of time of the ac field, causing the accumulation of charges near the electrodes. The gradient in the ion distribution in the cell generates electrode double layers and the internal counteracting field, destabilizing the CLC molecules, particularly near the substrate surfaces. The EHD induced molecular flow by such a low-frequency voltage thus becomes weakened and is replaced by the turbulence, giving rise to the ULH and DS domains in the bulk of the cell [Fig. 2(d)]. The above-mentioned viewpoints for the explanation of low-frequency-voltage-induced textural transition in a CLC cell are further discussed with the following results. Figure 3 displays frequency-dependent transmission curves (f − T%) of the R-CLC cell at 40°C. In the case of V 10 V, the cell shows low transmittance (T% < 10%) in the frequency range between 1 and 700 Hz, connoting the preservation of the FC state, as shown in Fig. 3(a). This applied voltage seems too small to induce the EHD effect. By increasing V to 24 V, T% increases with decreasing frequency from 180 to 100 Hz, but falls when the frequency decreases further [Fig. 3(b)]. The positive and negative changes in light transmission with decreasing frequency manifest the FC-to-ULH and the ULHto-DS texture transitions, respectively. The optical texture of the cell driven by the voltage at 100 Hz corresponding to the maximum T% exhibits a well-aligned ULH state. Noticeably, this frequency satisfies the condition of f L 29 Hz < f < f R 118 Hz at 40°C. As the applied voltage gets higher (V 30 V), T% increases with decreasing frequency for f < 410 Hz, turning moderate in the frequency range from 190 to 40 Hz [Fig. 3(c)]. The transmittance (T% ∼ 50%) in this regime is lower than that (T% ∼ 70%) of the cell with the ULH
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Fig. 3. Frequency-dependent transmittance curves of the R-CLC cell driven by (a) 10, (b) 24, and (c) 30 V at 40°C. The probe beam for the measurement derives from a He–Ne laser operating at the wavelength of 632.8 nm. Accompanied are optical images at selected frequencies.
alignment driven by V 24 V at f 100 Hz. As seen in the optical images, the translucency of the cell driven at V 30 V in the frequency range (40 Hz < f < 190 Hz) results from the coexistence of the ULH and the DS domains [Fig. 3(c)]. On the basis of the f − T% curves and the corresponding optical images, Fig. 4 summarizes electrically driven CLC textures in the R-CLC cell at various frequencies. Again, the temperature for this measurement is fixed at 40°C so that the values of f L , f R , and f H are 29, 118, and 498 Hz, respectively. Let’s designate the onset voltages for the generation of the FC, the ULH, and the DS states as V FC , V ULH , and V DS , respectively. The R-CLC cell driven by V FC exhibits FC texture in all investigated frequencies. The promoted values of V FC in the regime of f < f L infer the reduction in effective voltage across the cell due to the accumulation of ions on the electrodes and,
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thus, the electrical double layers. While the cell for the condition of f > f H exhibits only the FC texture, an additional DS texture is observed for f R < f < f H . The value of V DS (∼32 V) is nearly independent of f in the range from 200 to 500 Hz. As f decreases to the regime f L < f < f R , low-frequency FC-toULH and ULH-to-DS texture transitions occur. Both V ULH and V DS decline with decreasing frequency, which is in good agreement with the frequency dependence of applied voltage for the onset of the EHD effect [23]. In the lowest frequency regime (f < f L ), direct FC-to-DS transition can take place, leaving the FC-to-ULH transition absent, contrary to the f L < f < f R case. The suppressed ULH formation in this lowfrequency regime is owing to severe adsorption of ionic charges on the electrodes, causing a high degree of destabilization of LC molecules near the substrates. Figure 4 indicates again that well-aligned ULH induced by the EHD effect can be accomplished in the CLC cell under a moderate ac applied voltage at an arbitrary frequency situated in the regime of f L < f < f R . Alternatively, Fig. 5 demonstrates some optical textures of the R-CLC cell at various temperatures, driven by a fixed voltage, 23 V at 70 Hz. Note that the voltage amplitude is high enough to induce the EHD effect in the cell at the investigated temperatures. Since f H , f R , and f L all increase with elevated T [see Fig. 1(b)], the frequency regimes are expected to shift to higher frequencies. Referring to the results as shown in Fig. 1(b), the applied frequency (f 70 Hz) here satisfies the frequency conditions of f > f H 66 Hz at T 10°C, f R 35 Hz < f < f H 142 Hz at T 20°C and f R 65 Hz < f < f H 284 Hz at 30°C, and f L 29 Hz < f < f R 118 Hz at T 40°C. It is worth mentioning that the voltage-induced textures showing FC state at T 10°C, the combination of FC and ULH domains at T 20°C and 30°C, and the well-aligned ULH state at T 40°C in the R-CLC cell can be fully interpreted by the aforementioned mechanism concerning the frequency dependence of ion transport on the strength of the EHD effect and the molecular flow. However, when f L < f < f R at T 50°C (f L 61 Hz, f R 236 Hz), the DS texture instead of the ULH one is generated under the application of the given voltage. (The temperature of T 50°C approaches to T c ∼ 60°C.) The enhanced turbulence and the strength of DS are likely the result of the additional thermohydrodynamic instability induced together with the EHD one [24]. To confirm that the optimized frequency regime (f L < f < f R ) is nonspecific for the generation of the EHDinduced ULH texture, we further investigated a counterpart
DS ULH FC
25 20 15
f < fL
fL< f < fR
fR< f < fH
10 10
100
Fig. 4. Frequency dependence of the onset voltages to the voltage formation of possible cholesteric textures in the R-CLC cell. The ambient temperature is 40°C.
Fig. 5. Voltage-induced optical textures of the R-CLC cell at (a) 10°C, (b) 20°C, (c) 30°C, (d) 40°C, and (e) 50°C. The applied ac voltage is 23 V at f 70 Hz.
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containing S-5011 whose HTP has the same strength as that of but opposite handedness to R5011. Suggested by abovementioned results, three critical frequencies, f L 2.5 Hz, f R 10 Hz, and f H 29 Hz of the S-CLC cell, were first acquired at T 40°C, followed by the selection of f 5 Hz as the probe frequency for the condition of f L < f < f R . Our preliminary work indicated that none of the low-frequency texture transitions, such as the FC to ULH, ULH to DS, or FC to DS, can be induced in the S-CLC cell at voltages between 10 and 38 V. This implies that the ionic effect in the S-CLC cell is too weak to elicit the EHD effect as well as the molecular flow. Noticing that the critical frequencies are 1 order of magnitude smaller than those in R-CLC, we calculated the ion density n and diffusivity D in both the R-CLC and S-CLC cells by fitting their complex dielectric data in appropriate frequency ranges in accordance with the model established for the ionic behavior in LCs [18]. The deduced values for the S-CLC (n 1.35 × 1013 cm−3 , D 0.60 × 10−6 cm2 · s−1 ) are, respectively, 2.2 and 7.6 times smaller than those of the R-CLC cell (n 3.03 × 1013 cm−3 , D 4.57 × 10−6 cm2 · s−1 ). Previously, the ionic behaviors, including the ion density and the ion diffusivity, in an LC cell have been proven to be unstable, which can be magnified by temperature elevation [23] and ultraviolet (UV) exposure [25], or by preserving the cell over time [26]. Accordingly, the increase in the three critical frequencies (i.e., f L , f R , and f H ) would be expected when subjecting the cell to these stimuli. Here, UV exposure is applied to the S-CLC cell to enhance its ionic effect. Since the effect of UV exposure on the ionic behavior of the LC cell has been clarified previously [26], this study briefly shows the numerical difference in various ionic properties of the cell before and after UV exposure. We performed real-time measurement of the complex dielectric spectra of the cell during UV exposure, and Fig. 6(a) presents the ion density, diffusivity, and relaxation frequency of the S-CLC cell as a function of the UV exposure time. Clearly, both n and D reasonably grow over time, respectively, increasing from 1.35 × 1013 to 2.17 × 1013 cm−3 and 0.60 × 10−6 to 5.00 × 10−6 cm2 · s−1 after 20 mW · cm−2 UV exposure for 65 min when the final n and D values become comparable to those of the R-CLC. Furthermore, the relaxation frequency ascends from 10 to 117 Hz after 65 min UV exposure [Fig. 6(b)], and the three critical frequencies of the UV-irradiated S-CLC cell are boosted to f L 41 Hz, f R 117 Hz, and f H 313 Hz. Figure 7 shows voltage-dependent transmittance (V − T%) and optical images at specific voltages of the S-CLC cell. Prior to UV exposure, T% is lower than 15% in the voltage range between 9 and 35 V at f 5 Hz due to strong light scattering in the FC state. After performing UV irradiation for about 1 h, two additional voltage regimes can be identified at f 70 Hz, yielding superior transparency (T% ∼ 60%) in the ULH state between 20 and 30 V, as well as the translucency (T% ∼ 36%) in the wavelength-dependent light scattering state. Note that here f L 41 Hz < f 70 Hz < f R 117 Hz. Knowing that the strength of the ionic effect and applied voltage are nontrivial, one can conclude that the frequency range of f L < f < f R is expectedly deterministic for the formation of the EHD-induced ULH state in general. For the investigated EHD-induced ULH approach, it can be summarized from the abovementioned results that ions are regarded as an intermediary for the induction of the EHD
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Fig. 6. (a) Ion density and diffusivity and (b) relaxation frequency in the S-CLC cell under prolonged UV exposure at 365 nm. The radiance of the UV light is 20 mW · cm−2 .
Fig. 7. Comparisons of voltage-dependent transmittance and optical textures at specific voltages applied across the S-CLC cell thickness before and after UV exposure. The probe beam wavelength is 632.8 nm.
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effect by an externally applied voltage. A frequency condition of f L < f < f R optimal to obtain well-aligned ULH alignment is thus determined according to the transport behaviors of ions in response to the applied voltage. Note that the duration of the applied voltage required to form the ULH state and to switch it to the P or the FC state is too short to generate heat by the voltage-induced EHD or molecular perturbation. Once the ULH is generated and sustained by the voltage, the EHD flow as well as the ionic agitation can be suppressed by increasing the frequency of the applied voltage [16]. Consequently, being regarded as an optically stable state, the stability of the proposed ULH state in the current stage is expected to be independent of the strength of the ionic effect. A future prospect stemming from this work that is worth considering is to explore the relationship between the stability of the ULH state and the ionic behaviors.
4. CONCLUSIONS A series of experiments have been conducted to investigate the ionic contribution to the low-frequency texture transitions in CLC cells. An optimized frequency regime has been identified for the generation of the EHD-induced ULH texture in the R-CLC with right-handed chirality and the S-CLC with lefthanded chirality by externally applied ac voltages. By means of the dielectric spectra and the deduced loss tangent, specific frequency regimes (i.e., f < f L , f L < f < f R , f R < f < f H , and f > f R ), separated by three critical frequencies f L , f R , and f H , were obtained, and the transport behavior of ion charges in response to the probe ac electric field for each frequency regime was explained. When the applied frequency of the voltage is lower than f H (i.e., f < f H ), the experimental results suggested that additional textures, including ULH and DS, can be obtained thanks to the transport of ions and, in turn, the EHD flow. Compared with the texture transitions in designated frequency regimes, the ULH alignment generated by applied ac voltages in f L < f < f R is quite uniform due to effective movements of electrical charges and less accumulation of ions on the electrodes. Accordingly, we provide a reliable pathway to determine the optimized frequency regime for the formation of a well-aligned ULH state in a CLC cell induced by an applied low-frequency ac voltage. Since the CLC with the ULH state has been proven potentially applicable in developing a variety of photonic devices, the contribution of this work is significant for obtaining a more uniform ULH alignment so as to promote the optical contrast of the proposed devices and their practical uses. Funding. Ministry of Science and Technology, Taiwan (MOST) (104-2112-M-009-008-MY3, 104-2811-M-009-051).
REFERENCES 1. 2.
3.
J. S. Patel and R. B. Meyer, “Flexoelectric electro-optics of a cholesteric liquid crystal,” Phys. Rev. Lett. 58, 1538–1540 (1987). D. J. Gardiner, S. M. Morris, P. J. W. Hands, F. Castles, M. M. Qasim, W.-S. Kim, S. S. Choi, T. D. Wilkinson, and H. J. Coles, “Spontaneous induction of the uniform lying helix alignment in bimesogenic liquid crystals for the flexoelectro-optic effect,” Appl. Phys. Lett. 100, 063501 (2012). B. I. Outram and S. J. Elston, “Spontaneous and stable uniform lying helix liquid-crystal alignment,” J. Appl. Phys. 113, 043103 (2013).
Nian et al. 4. Y. Inoue and H. Moritake, “Formation of a defect-free uniform lying helix in a thick cholesteric liquid crystal cell,” Appl. Phys. Express 8, 071701 (2015). 5. Y. Inoue and H. Moritake, “Discovery of a transiently separable high-speed response component in cholesteric liquid crystals with a uniform lying helix,” Appl. Phys. Express 8, 061701 (2015). 6. P. Rudquist, L. Komitov, and S. T. Lagerwall, “Volume-stabilized ULH structure for the flexoelectro-optic effect and the phaseshift effect in cholesterics,” Liq. Cryst. 24, 329–334 (1998). 7. R. M. Hyman, A. Lorenz, and T. D. Wilkinson, “Phase modulation using different orientations of a chiral nematic in liquid crystal over silicon devices,” Liq. Cryst. 43, 83–90 (2016). 8. H. Yoshida, Y. Inoue, T. Isomura, Y. Matsuhisa, A. Fujii, and M. Ozaki, “Position sensitive, continuous wavelength tunable laser based on photopolymerizable cholesteric liquid crystals with an in-plane helix alignment,” Appl. Phys. Lett. 94, 093306 (2009). 9. L. Komitov, G. P. B. Brown, E. L. Wood, and A. B. J. Smout, “Alignment of cholesteric liquid crystals using periodic anchoring,” J. Appl. Phys. 86, 3508–3511 (1999). 10. G. Hegde and L. Komitov, “Periodic anchoring condition for alignment of a short pitch cholesteric liquid crystal in uniform lying helix texture,” Appl. Phys. Lett. 96, 113503 (2010). 11. S. H. Kim, L.-C. Chien, and L. Komitov, “Short pitch cholesteric electro-optical device stabilized by nonuniform polymer network,” Appl. Phys. Lett. 86, 161118 (2005). 12. B. J. Broughton, M. J. Clarke, S. M. Morris, A. E. Blatch, and H. J. Coles, “Effect of polymer concentration on stabilized large-tiltangle flexoelectro-optic switching,” J. Appl. Phys. 99, 023511 (2006). 13. A. Varanytsia and L.-C. Chien, “Bimesogen-enhanced flexoelectrooptic behavior of polymer stabilized cholesteric liquid crystal,” J. Appl. Phys. 119, 014502 (2016). 14. C. C. Tartan, P. S. S. Martin, J. Booth, S. M. Morris, and S. J. Elston, “Localised polymer networks in chiral nematic liquid crystals for high speed photonic switching,” J. Appl. Phys. 119, 183106 (2016). 15. L.-L. Ma, S.-S. Li, W.-S. Li, W. Ji, B. Luo, Z.-G. Zheng, Z.-P. Cai, V. Ghigrinov, Y.-Q. Lu, W. Hu, and L.-J. Chen, “Rationally designed dynamic superstructures enabled by photoaligning cholesteric liquid crystals,” Adv. Opt. Mater. 3, 1691–1696 (2015). 16. C.-T. Wang, W.-Y. Wang, and T.-H. Lin, “A stable and switchable uniform lying helix structure in cholesteric liquid crystals,” Appl. Phys. Lett. 99, 041108 (2011). 17. C.-T. Wang and T.-H. Lin, “Vertically integrated transflective liquid crystal display using multi-stable cholesteric liquid crystal film,” J. Disp. Technol. 8, 613–616 (2012). 18. S.-H. Joo, J.-K. Kima, H. Kim, K.-C. Shin, H. Kim, and J.-K. Song, “Tri-stable polarization switching of fluorescent light using photo-luminescent cholesteric liquid crystals,” Mol. Cryst. Liq. Cryst. 601, 29–35 (2014). 19. P.-C. Wu, L. N. Lisetski, and W. Lee, “Suppressed ionic effect and low-frequency texture transitions in a cholesteric liquid crystal doped with graphene nanoplatelets,” Opt. Express 23, 11195– 11204 (2015). 20. P.-C. Wu and W. Lee, “Phase and dielectric behaviors of a polymorphic liquid crystal doped with graphene nanoplatelets,” Appl. Phys. Lett. 102, 162904 (2013). 21. R. J. Klein, S. Zhang, S. Dou, B. H. Jones, R. H. Colby, and J. Runt, “Modeling electrode polarization in dielectric spectroscopy: Ion mobility and mobile ion concentration of single-ion polymer electrolytes,” J. Chem. Phys. 124, 144903 (2006). 22. B.-R. Jian, C.-Y. Tang, and W. Lee, “Temperature-dependent electrical properties of dilute suspensions of carbon nanotubes in nematic liquid crystals,” Carbon 49, 910–914 (2011). 23. Orsay Liquid Crystal Group, “Hydrodynamic instabilities in nematic liquids under ac electric fields,” Phys. Rev. Lett. 25, 1642–1643 (1970). 24. O. S. Tarasov, A. P. Krekhov, and L. Kramer, “Dynamics of cholesteric structures in an electric field,” Phys. Rev. E 68, 031708 (2003). 25. P.-C. Wu, S.-Y. Yang, and W. Lee, “Recovery of UV-degraded electrical properties of nematic liquid crystals doped with TiO2 nanoparticles,” J. Mol. Liq. 218, 150–155 (2016). 26. H.-H. Liu and W. Lee, “Time-varying ionic properties of a liquidcrystal cell,” Appl. Phys. Lett. 97, 023510 (2010).
