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., , , and ), are identified by means of dielectric spectroscopy. By discussing the voltage-dependent cholesteric textural changes in each frequency regime in terms of the voltage- and frequency-dependent transmission spectra and optical textures, our results suggest that the designated frequency regime , , where electrical charges can effectively oscillate in the bulk of the cell with less ion accumulation on the electrode surfaces, is most adequate for the generation of well-structured ULH via effective induction of the EHD flow by the external voltage. As a result, this study provides a pathway to determination of the optimal frequency regime for generating the EHD-induced ULH state prior to voltage treatment.
© 2016 Chinese Laser Press
The uniformly lying helix (ULH) structure with the helical axes aligned parallel to the substrate plane is a class of cholesteric textures typically obtained in a cholesteric liquid crystal (CLC) cell with a pitch length shorter than the wavelengths of visible light. Stemming from the discovery of the chiral-flexoelectric effect by Patel and Meyer , short-pitch CLCs with ULH alignment have received considerable attention for the development of fast-response optoelectronic elements through linear and temperature-independent electro-optical switching with submillisecond response time [1–5]. Other attractive applications of ULH-structured CLCs with electrically tunable birefringence have also been demonstrated as phase modulators [6,7] and tunable lasers  using the voltage-induced unwinding of ULH helices via the dielectric coupling effect. However, a CLC cell with either homogeneous or homeotropic surface alignment is preferably stabilized in the planar (P) or focal conic (FC) texture, meaning that the ULH can hardly be generated as a minimum-energy state in a simple cell geometry without external treatments. In considering practical uses of flexoelectric- and dielectric-switching-based CLC devices, a variety of technologies, including the combination of electric fields with mechanical or thermal treatment [1–5], the generation of the periodic anchoring conditions [9,10], and polymer network structures [11–14], have been developed to promote the uniformity and stability of ULH alignment and thus the optical contrast of proposed devices. Apart from the abovementioned electric-field treatments, another method utilizing the photoalignment technique has also been developed to yield photo-addressable CLC textures with lying helices for photonic applications .
Recently, an alternative approach involving the application of low-frequency voltage to a CLC with positive dielectric anisotropy has been illustrated for ULH formation via the electrohydrodynamic (EHD) effect . In comparison with the above-mentioned technologies, the EHD-induced ULH state as confirmed is optically stable and electrically switchable among the stable cholesteric textures. Such a stable ULH state together with the other well-known stable states (i.e., P and FC states) has been proposed for realizing tristable CLC devices and transreflective displays [17,18]. Nevertheless, the detailed mechanism of this EHD approach, involving the ionic contribution dictated by the critical voltage and frequency conditions, has remained unclear.
Previously, we studied the effect of transport behavior of mobile ions on the low-frequency textural transition between the FC and the ULH states in a CLC cell, and found that the ULH state can be obtained only when the applied frequency is lower than a critical value . Based on this finding, a series of experiments have been conducted in the present study to clarify the optimized frequency regime for the formation of the voltage-induced ULH alignment. The low-frequency regime where the complex dielectric function is dominated by space-charge polarization is identified by means of dielectric spectroscopy. The changes of cholesteric textures as a function of the applied ac voltage in this frequency regime are then discussed by measurements of voltage- and frequency-dependent transmission spectra, as well as by observations of optical textures.
Two CLC mixtures, designated R-CLC and S-CLC, were prepared by individually doping 2.55 wt. % right-handed (R5011, Merck) and 2.55 wt. % left-handed (S5011, Merck) enantiomers as chiral additives into the nematic LC host (E7, Daily Polymer), respectively. E7 is a eutectic nematic mixture exhibiting positive anisotropies in dielectric permittivity and electrical conductivity. The refractive indices of E7 are and at the wavelength of 589.3 nm and temperature of 20°C. Since the absolute values of helical twisting power (HTP) of R5011 and S5011 in E7 are identical (), the central wavelengths of the Bragg reflection in R-CLC and S-CLC are the same, approximately 550 nm. The two mixtures were separately injected into commercialized planar-aligned cells (Mesostate Co.) in isotropic phase by capillary action. Each cell has a cell gap of and an effective electrode area of . The clearing points () of the samples are approximately 60°C as confirmed by their birefringent textures.
The temperature of all CLC cells was controlled by a temperature controller (TEC Controller CDSI5008RRA). The complex dielectric spectra in the frequency range from 1 to were obtained using an LCR meter (HIOKI 3522-50). To reduce noise originating from environmental signals and to avoid contribution to the reorientation of liquid crystal (LC) molecules, the probe voltage was optimized at 0.3 V for dielectric measurements. The change in CLC texture as a function of the applied ac voltage, supplied by an arbitrary function generator (Tektronix AFG-3022B) along with an amplifier (TREK Model 603), was monitored by the corresponding optical image using a polarizing optical microscope (Olympus BX51). Here, the FC and the ULH textures are distinguished according to the alignment uniformity. While the optical image of the FC state displays nonuniform multisized domains intermediated with defects, the ULH exhibits uniform color appearance attributable to the birefringence effect under crossed polarizers. Sequentially, the alignment revealing the coexistence of nonuniform- and uniform-color domains intermediated by defects can further be defined as the alignment. Moreover, the voltage- () and frequency-dependent transmission () curves were acquired by placing a CLC cell between a He–Ne laser source operating at 632.8 nm and a photodetector. No polarizer was employed in the measurement of transmission spectra.
3. RESULTS AND DISCUSSION
Figure 1(a) depicts an example of the frequency dependence of the complex dielectric function and the loss tangent tan of an R-CLC cell in the frequency range between 1 and at 40°C. The complex dielectric function can be expressed as , where and are the real and imaginary parts of the dielectric function, respectively. The dielectric loss tangent defined as tan represents a dissipation factor of electromagnetic energy in a dielectric medium. According to the transport behavior of mobile ions under the application of a probe ac electric field, the complex dielectric spectra shown in Fig. 1(a) can be divided into three frequency regions, separated by two critical frequencies designated and , where the and curves intersect each other. In region III (), is independent of the frequency due to the constant dielectric contribution from the orientational ordering of LC molecules as well as the immobilization of ions under the application of a probe voltage at such high frequencies. In contrast, variations in and as and , respectively, in region II () are undoubtedly attributable to the relaxation behavior of the electrode and space-charge polarizations . The complex dielectric spectrum of a cell in this frequency region is thus meaningful to clarify the transport behavior of electrical charges in response to the probe voltage. Moreover, the relaxation behavior of tan in frequency region II originates from the space-charge polarization as well. The relaxation frequency , which corresponds to the maximum value of tan , is useful to characterize the relaxation time of ions defined as the sum of ion charging and discharging times. As the frequency decreases below () in region I, the speed for the inversion of electrical polarity becomes smaller than the drift velocity of ions, permitting an increasing amount of ions to accumulate near the electrodes. The resulting gradient in ionic density and generation of electrical double layers near the electrodes lead to the induction of coulombic repulsions and, in turn, the reduction in effective electric field across the cell, incurring a decrease in in the low-frequency region . Furthermore, Fig. 1(b) shows the temperature () dependence of , , and of the R-CLC cell. These specific frequencies increase with increasing , following the Arrhenius law. This, suggesting the shift of the and tan curves to higher frequencies, has been well explained by the promotion of ion transport at higher temperatures or by increasing charge carriers contributing to electric conduction in the cell . Obviously, here the three critical frequencies (i.e., , , and ) can be determined by the dielectric measurement; they define four frequency regimes (i.e., , , , and ) for 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 at a fixed temperature of 40°C. In accordance with the results given in Fig. 1(a), values of , , and at are 29, 118, and 498 Hz, respectively. The transport of ions in an electric field at frequencies higher than 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 at a constant frequency (), and it retains in the H state at (not shown in the figure). When the frequency condition of is satisfied, the cell driven by the voltage of 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 , 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 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 () and () but is uniformly demonstrated at (). This implies that a CLC cell with a well-aligned ULH structure exists when ac voltage is applied at a frequency within the 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 field-induced movement of charges within a CLC cell as follows: In the frequency regime of , 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 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 , 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 , 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 () of the R-CLC cell at 40°C. In the case of , the cell shows low transmittance () 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 to 24 V, 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 ULH-to-DS texture transitions, respectively. The optical texture of the cell driven by the voltage at 100 Hz corresponding to the maximum exhibits a well-aligned ULH state. Noticeably, this frequency satisfies the condition of at 40°C. As the applied voltage gets higher (), increases with decreasing frequency for , turning moderate in the frequency range from 190 to 40 Hz [Fig. 3(c)]. The transmittance () in this regime is lower than that () of the cell with the ULH alignment driven by at . As seen in the optical images, the translucency of the cell driven at in the frequency range () results from the coexistence of the ULH and the DS domains [Fig. 3(c)].
On the basis of the 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 , , and 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 , , and , respectively. The R-CLC cell driven by exhibits FC texture in all investigated frequencies. The promoted values of in the regime of infer the reduction in effective voltage across the cell due to the accumulation of ions on the electrodes and, thus, the electrical double layers. While the cell for the condition of exhibits only the FC texture, an additional DS texture is observed for . The value of () is nearly independent of in the range from 200 to 500 Hz. As decreases to the regime , low-frequency FC-to-ULH and ULH-to-DS texture transitions occur. Both and decline with decreasing frequency, which is in good agreement with the frequency dependence of applied voltage for the onset of the EHD effect . In the lowest frequency regime (), direct FC-to-DS transition can take place, leaving the FC-to-ULH transition absent, contrary to the case. The suppressed ULH formation in this low-frequency 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 .
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 , , and all increase with elevated [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 () here satisfies the frequency conditions of at , at and at 30°C, and at . It is worth mentioning that the voltage-induced textures showing FC state at , the combination of FC and ULH domains at and 30°C, and the well-aligned ULH state at 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 at (, ), the DS texture instead of the ULH one is generated under the application of the given voltage. (The temperature of approaches to .) The enhanced turbulence and the strength of DS are likely the result of the additional thermohydrodynamic instability induced together with the EHD one .
To confirm that the optimized frequency regime () is nonspecific for the generation of the EHD-induced ULH texture, we further investigated a counterpart containing S-5011 whose HTP has the same strength as that of but opposite handedness to R5011. Suggested by above-mentioned results, three critical frequencies, , , and of the S-CLC cell, were first acquired at , followed by the selection of as the probe frequency for the condition of . 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 and diffusivity 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 . The deduced values for the S-CLC (, ) are, respectively, 2.2 and 7.6 times smaller than those of the R-CLC cell (, ).
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  and ultraviolet (UV) exposure , or by preserving the cell over time . Accordingly, the increase in the three critical frequencies (i.e., , , and ) 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 , 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 and reasonably grow over time, respectively, increasing from to and to after UV exposure for 65 min when the final and 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 , , and . Figure 7 shows voltage-dependent transmittance () and optical images at specific voltages of the S-CLC cell. Prior to UV exposure, is lower than 15% in the voltage range between 9 and 35 V at 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 , yielding superior transparency () in the ULH state between 20 and 30 V, as well as the translucency () in the wavelength-dependent light scattering state. Note that here . Knowing that the strength of the ionic effect and applied voltage are nontrivial, one can conclude that the frequency range of 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 effect by an externally applied voltage. A frequency condition of 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 . 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.
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 left-handed chirality by externally applied ac voltages. By means of the dielectric spectra and the deduced loss tangent, specific frequency regimes (i.e., , , , and ), separated by three critical frequencies , , and , 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 (i.e., ), 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 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.
Ministry of Science and Technology, Taiwan (MOST) (104-2112-M-009-008-MY3, 104-2811-M-009-051).
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