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The authors demonstrate dual frequency switching in a cubic blue phase liquid crystal. The dual frequency blue phase was prepared by adding a strongly twisting chiral dopant to a dual-frequency nematic liquid crystal mixture. The crossover frequency appeared at few hundred kHz in the blue phase, and sub-millisecond response was obtained for dual-frequency operation, which was comparable to conventional voltage operation. This new class of material is advantageous over conventional blue phases in polarization-independent phase modulation devices, since a larger lattice deformation can be obtained.
© 2011 Optical Society of America
1. Introduction
Nano-structured liquid crystals are attracting attention as next generation display and optical materials. Blue phase liquid crystals (BPLCs) in which the LC molecules spontaneously form three-dimensional order with cubic symmetry are among the most studied, because of their useful properties such as macroscopic optical isotropy, field-induced birefringence and fast electro-optic response (≤ 1 ms) [1–3].
The fact that they are isotropic allows them to be used in polarization-independent devices [4]. When an electric field is applied in the direction of light propagation, the cubic lattice of BPs either becomes elongated or compressed depending on the sign of dielectric anisotropy, as shown in Fig. 1. For materials with positive dielectric anisotropy, the molecules tend to align parallel to the applied field causing elongation, whereas in negatively anisotropic materials, the molecules align perpendicular to the field, leading to compression. In either case, there is no phase retardation, because the deformation of the cubic lattice is symmetric around the direction of light propagation. Using this property, isotropic refractive index (RI) modulation of ∼ 10−3 can be achieved by applying electric fields of a few V/μm. However, the tuning range is still small for use in practical applications, and methods to enhance the RI modulation range need to be developed.
One of the approaches to enhance the RI modulation properties is to dope them with nanoparticles. The authors have previously shown that nanoparticles can stabilize the BP structure [5], and that field-induced transition into the birefringent cholesteric phase is inhibited in gold-nanoparticle-doped BP II, leading to an enhancement in the attainable isotropic RI modulation range [6]. Herein, we demonstrate another approach to enhance isotropic RI modulation, by using dual-frequency liquid crystals (DFLCs) [7, 8]. DFLCs generally possess positive dielectric anisotropy at low frequencies, but cross over to negative dielectric anisotropy above a certain crossover frequency fc. Thus, by switching the frequency from below to above the crossover frequency, the direction of molecular switching can be changed. This two-way driving of LC molecules has been utilized in nematic LCs to improve their switching speed [9], especially in devices where a large cell-gap is required, since the decay-time of a nematic LC increases proportionally to the square of the cell-gap. Because the reponse-time of BPs is already sufficiently fast, that is, faster than nematic LCs by more than a factor of 10, the merit of dual frequency operation of BPs lies not so much in faster switching, but rather in the fact that two-way deformation (compression and elongation) of the lattice becomes possible (Fig. 2). Because a larger deformation can be achieved compared to conventional BPs, a larger RI tuning range can be expected in this new class of LC material. In the following, we will describe how the DFBP was prepared, and then report its crossover frequency, Kerr-constant, and response speed.
2. Materials
The DFLC prepared for this study was a nematic LC mixture consisting of n-(4-methoxybenzylidene)-4-butylaniline (MBBA, 50wt%) and 4-pentylphenyl 2-chloro-4-(4-pentylbenzoyloxy)benzoate (EK11650, 50 wt%) [10]. MBBA possesses a negative dielectric anisotropy of Δɛ = −0.61, while EK11650 is a DFLC, with Δɛ = 6 at 100 Hz and Δɛ = −2 at 50 kHz. MBBA was added to lower the clearing point of EK11650, since it has a wide nematic range between 39.6 and 123.0 °C. Because BPs appear just below the isotropic clearing point, the DFBP would have to be driven at elevated temperatures, which is undesirable for dual frequency operation: the crossover frequency of DFLCs is known to increase exponentially with temperature, according to the following equation [9],
where E is the activation energy, kB is Boltzman’s constant and T is the temperature. If the crossover frequency is high, high-frequency signals must be applied to operate the device, inducing undesirable effects which deteriorate the LC device performance, such as dielectric heating and high energy consumption [9, 11]. The resultant mixture was found to have a lower clearing point of 72.3 °C (upon cooling), but still showed dielectric crossover, as can be seen in Fig. 3. As the temperature increased, the crossover frequency increased exponentially following Eq. (1) and had an activation energy of 850 meV.
Fig. 3 Frequency dependent dielectric anisotropy of the host nematic liquid crystal mixture at various temperatures.
To obtain the BP, a chiral dopant 2,5-bis[4′-(hexyloxy)-phenyl-4-carbonyl]-1,4;3,6-dianhydride-D-sorbitol (ISO(6OBA)2, 14 wt%) was added to the mixture. The phase sequence of the sample was investigated by observing the sample under a polarizing optical microscope while cooling the sample from 55 °C to 30 °C at a rate of −0.2 °C/min. The sample was found to possess the following phase sequence: Isotropic (49.4 °C) cubic BP (37.4 °C) Cholesteric. Since the selective reflection band existed in the ultraviolet region, the symmetry of the BP could not be determined. However, platelets were observed under a microscope, suggesting that the BP was cubic in symmetry.
3. Material Characterization
In a nematic DFLC, the crossover of dielectric anisotropy can be evaluated simply by measuring the capacitance of LC cells with planar and homeotropic alignment. However, in LCs with chirality, this method cannot be applied, since the molecules are not oriented uniformly inside the LC cell. Thus, we estimated the crossover frequency of our sample by measuring its electro-optic response at different temperatures. The sample was infiltrated in an 6.3 μm-thick LC cell with ITO electrodes, and its transmittance was monitored as the frequency of the applied electric field (square wave voltage, 6.4V/μm) was gradually varied. To improve accuracy of the measurements, sample heating caused by the high-frequency voltage was investigated by measuring the BP-cholesteric transition temperature at a cooling rate of −0.5 °C/min, while applying various frequencies. The results shown in Fig. 4 agree satisfactorily with the theoretical model [11], assuming a relaxation frequency of approximately 200 kHz. The results imply that observable heating starts to occur at several 10 kHz, exceeding 4 °C at 500 kHz.
Fig. 4 Change in BP-cholesteric transition temperature caused by application of high frequency fields.
Figure 5 (a) shows the frequency dependence of light transmittance in a cholesteric texture when the applied frequency was both increased and decreased. In both cases, a distinct crossover frequency, at which the transmittance suddenly changed, was observed. The change in transmittance is attributed to the change in texture from focal-conic which appears when the dielectric anisotropy is positive, to Grandjean which appears when the dielectric anisotropy is negative. The hysterisis observed in the electro-optic response is considered to be a result of the difference in the threshold field intensity which is required to change the alignment of the cholesteric phase. Figure 5 (b) shows the temperature dependence of the crossover frequency of the sample. The marker is placed at the average frequency of transmittance switching obtained for up-and-down frequency sweeping, and the bars indicate the actual values. Compared to the nematic host, the cholesteric sample had a slightly higher activation energy of approximately 1 eV. Since the only difference between the two materials is the presence of a chiral dopant, this is considered to be the cause for the increase in activation energy.
Fig. 5 (a) Frequency dependency of the transmittance of the cholesteric texture. (b) Temperature dependence of the crossover frequency.
The crossover frequency of the BP could not be determined in the same manner as in the cholesteric phase, because the texture of the BP hardly changed under the influence of a vertical electric field. To confirm dual frequency operation in the BP, an in-plane switching (IPS) LC cell was fabricated using chromium interdigitated electrodes with a gap of 10 μm. The substrates had no alignment layers, and the cell-gap was set to d = 8 μm using polyethylene terephthalate film spacers. The sample was placed on a polarizing optical microscope so that the electric field would be applied at an angle of 45° to the crossed polarizers, and electric field-induced birefringence was measured at various electric field frequencies and temperatures. To increase the sensitivity of measurement, a tint plate was inserted in the optical path of the microscope: the direction of the applied field was parallel to the fast axis of the tint plate. The response speeds for both voltage driving and frequency driving were also evaluated by measuring the change in tranmsittance of a semiconductor laser (λ = 635 nm) passing through the sample.
Figure 6 (a) shows the transmittance spectrum of the BP at 40.2 °C as a square wave voltage with various frequencies was applied. The spectrum without field corresponds to the spectrum of the tint plate. When a low-frequency field at 1 kHz was applied, the spectrum blue-shifted, and as the frequency was increased, the shift became smaller, until at one point it returned to the original position and continued to shift in the opposite direction (see spectrum for 500 kHz). Since the transmittance of a uniaxially anisotropic object placed between crossed polarizers is given by the following expression (assuming that the optical axis makes an angle of 45° to the polarizers),
where Δn is birefringence and λ is wavelength, the blue-shift of the spectrum corresponds to an decrease in retardation, which means that the refractive index increased in the direction parallel to the electric field. On the other hand, the red-shift obtained at 500 kHz corresponds to an increase in the refractive index perpendicular to the electric field. The relationship between the tint plate, direction of electric field and the change in refractive index is shown in Figs. 6 (b) and (c), which were taken concurrently with the transmittance measurements. Since the direction of refractive index modulation is inverted by changing the applied frequency, dual-frequency operation has been demonstrated for the first time in a BP.Fig. 6 (a) Transmittance of BP with tint plate, and (b) POM image with applied voltage of 1kHz (c) 500 kHz.
The electro-optic effect in BPs is a Kerr effect in which the birefringence increases proportionally to the square of the electric field E, according to the equation Δn(E) = λKE2, where K is the Kerr constant. Figure 7 (a) shows the Kerr constant of the sample at different temperatures and frequencies, evaluated by fitting the transmittance spectrum according to Eq. (2) between 500 – 600 nm. Square wave electric fields up to 14 V/μm were applied for frequencies up to 100 kHz, and fields up to 7 V/μm were applied for frequencies above 100 kHz, while frequencies above 500 kHz were not applied since phase transition due to dielectric heating could not be prevented at such high frequencies. Special care was also taken to measure the spectra just seconds after the electric field was applied, to minimize heating effects. The Kerr constant was found to be both temperature and frequency dependent: at low temperatures, the Kerr constant decreased monotonically with frequency, but at high temperatures, the Kerr constant started small at 1 kHz but increased near 10 kHz, and decreased again at higher frequencies. The decrease in the Kerr constant with temperature at 1 kHz can be explained by the temperature dependence of the anisotropy of LC molecules, gradually approaching zero in the isotropic phase. The exact mechanism of the increase in the Kerr constant at 10 kHz at high temperatures is unknown at this time, although we suspect that field-induced phase transition may be playing a role. It is known that light transmittance in IPS-BP cells is actually non-uniform, because of field accumulation and corresponding phase-transition at the edge of the electrodes. [12] We have observed that at 10 kHz, the non-uniformity in the transmittance between the electrodes becomes pronounced, compared to other frequencies. Because of the bright edge regions, the transmittance, and thus the Kerr constant effectively seem to increase at this frequency. Experiments to determine whether the frequency dependence of non-uniform transmission is specific to this BP material is currently underway. Figure 7 (b) shows the temperature dependence of the crossover frequency in the BP, obtained by interpolating the data in Fig. 7 (a). As expected, sign inversion of the Kerr constant occurred at frequencies of a few 100 kHz, with the frequency increasing with temperature. The activation energy in the BP was approximately 1.1 eV and was similar to the value obtained in the cholesteric phase, which is easily understandable from the fact that the two materials are the same, but only differing in molecular order.
Fig. 7 (a) Frequency dependence of the Kerr Constant of the sample at various temperatures (b) Temperature dependence of the crossover frequency in BP.
The Kerr constant of this DFBP sample was not large because the dielectric anisotropy of the host was small, and the sample was being driven at high temperatures, which decreases the dielectric anisotropy even further. Improvement of the Kerr constant should be possible by developing new materials with large birefringence and dielectric anisotropy [13, 14]. However, there is another challenge here, since the crossover frequency must be kept as low as possible. One approach to overcome the problem of crossover frequency is to polymer-stabilize the system [15], since the operating temperature can be lowered by fixing the BP lattice.
Shown in Fig. 8 are temporal response curves obtained for both frequency and voltage operation of the DFBP. A square wave voltage of 13.4 V/μm was applied at 41.8 °C, and frequency-driving was performed by switching the applied square wave between 1 kHz and 300 kHz. The output signal for frequency-driving was slightly smaller than that for voltage-driving because the birefringence decreased as a result of dielectric heating caused by the application of a 300 kHz field. Importantly, however, sub-millisecond switching comparable to conventional voltage-driving was obtained. The response could be well described by the following dual exponential expression,
where the two time constants are attributed to the local reorientation of molecules in the BP lattice and lattice distortion (electrostriction), respectively. The short response time obtained shows the potential of these materials for electro-optic applications.4. Conclusion
Dual-frequency operation has been demonstrated in a blue phase liquid crystal. Sign inversion of the Kerr constant was confirmed at a few 100 kHz, and sub-millisecond electro-optic response comparable to the response for voltage operation was observed, showing the potential of these new class of BPs. Although the Kerr constant of the sample studied was small, DFBPs are advantageous over conventional BPs in RI tuning applications, since a greater lattice deformation can be achieved. Also, due to their fast response speed, these materials may be able to replace nematic DFLCs in certain applications, although the development of materials with large Kerr constants is necessary. Polymer-stabilization of these materials [15], which is currently underway, is an alternative approach for efficient operation, since the LC can be operated at lower temperatures, making the crossover frequency lower and dielectric anisotropy larger.
Acknowledgments
This work was supported by the New Energy and Industrial Technology Development Organization (NEDO) of Japan (Project Code P07026). H. Yoshida gratefully acknowledges support from the PRESTO Program of Japan Science and Technology Agency (JST).
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