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Abstract
4-m-alkyl cyclohexane carboxylic acids and 4-n-alkylbenzoic acids were mixed to form hydrogen bonded liquid crystals (HBLCs), which exhibited a nematic phase at room temperature. Dielectric constants and three elastic constants of HBLC mixtures were investigated. Benzoic acid derivatives with some polar groups were added to the HBLC and the dielectric anisotropy was successfully enhanced. Considering the absorption loss of HBLCs in the terahertz wave region, the electro-optical properties of the homogeneous and twisted nematic cells were numerically evaluated using measured physical properties, and the transmitted polarization state was compared with that of conventional nematic LCs.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
Corrections
10 July 2023: A minor correction was made to the title.
1. Introduction
A nematic liquid crystal (NLC) has been extensively and intensively studied due to its distinctive properties and the importance of technologies for electro-optical applications mainly in LC displays. A large number of rod-like molecules which can form LCs have been synthesized, and hydrogen bonded LCs (HBLCs) have been reported as a new binary type of LC by Kato et al. [1–5]. HBLCs have attracted attention for both their fundamental aspects and various technological applications. Other groups have also reported that alkyl or alkyloxy benzoic acids form complementary hydrogen bonds with other acids to exhibit the N phase [6–19].
HBLCs have been studied mainly in terms of their phase diagrams, and less attention has been paid to optical tuning and switching by applying voltage to the HBLC cell. Only a few studies have been reported, including transmittance variations in twisted nematic (TN) cells [5] and homogeneously oriented cells [9,20]. Especially in Ref. 20, Ito et al. applied HBLCs to the phase shifter of a terahertz (THz) frequency range. LC devices are strong candidates for THz wave control devices, as well as visible light control devices, because of their tunability at low driving voltages and low power consumption. However, conventional LC materials generally exhibit large absorption anisotropy [21–28]. In contrast, the HBLC has been found to have almost no absorption anisotropy in the THz wave region [20,29,30].
To study the electro-optical properties of LC cells, numerical analyses of both the LC director distribution using continuum elasticity theory and the polarized light propagation using the Jones matrix method are powerful techniques. It is common to simulate the voltage-transmittance (V-T) curve in LC displays using these techniques. Physical properties of the LC material, elastic constants of splay (K11), twist (K22), and bend (K33), dielectric constants parallel and perpendicular to the director, and ordinary and extraordinary refractive indices are essential. However, there are only a few reports on these values for HBLC [13,14,18,31,32], and no data have been found for K22 and K33. In addition, those values were measured at around 100°C, as the nematic temperature range of those HBLCs is much higher than room temperature.
In this study, the physical properties of HBLCs necessary for the simulation of optical devices have been investigated at room temperature from the point of view of device application. Using the measured physical properties of the HBLCs, the electro-optical properties of the homogeneous and TN cells were numerically estimated in both the visible and THz wave ranges and compared with those of typical NLCs.
2. Materials and methods
2.1 Materials
Figure 1 shows chemical structures of (a) 4-m-alkyl Cyclohexane carboxylic acids (mCCA), (b) 4-n-alkylbenzoic acids (nBA), (c) 4-cyanobenzoic acid (4CNBA), (d) 3-cyanobenzoic acid (3CNBA) (e) 2-cyanobenzoic acid (2CNBA), (f) 4-fluorobenzoic acid (4FBA), (g) 3-fluorobenzoic acid (3FBA), (h) 2-fluorobenzoic acid (2FBA), (i) 4-chlorobenzoic acid (4ClBA), (j) 4-cyano-3-fluorobenzoic acid (4CN3FBA), (k) 4-chloro-3-fluorobenzoic acid (4Cl3FBA) used in this study. mCCA and nBA were purchased from LCC Co., Ltd. (Fujiyoshida, Japan) and benzoic acid derivatives attached to the polar groups were purchased from Tokyo Chemical Industry (Tokyo, Japan). The chemical structure of the HBLC dimer with 5BA and 4CNBA is shown in Fig. 1(l), which is similar to that of a typical positive dielectric NLC used in conventional LC devices. The mixture of 3CCA, 4CCA, and 5CCA (1:1:1 weight ratio) is available as CC-3 from LCC Co., Ltd. and it is in the N phase from 10 to 97°C. The other materials shown in Fig. 1(c) − 1(k) are in the crystal phase at room temperature.
Fig. 1. Chemical structures of (a) mCCA, (b) nBA, (c)-(k) benzoic acid derivatives attached to polar groups, d (l) HBLC dimer.
2.2 LC physical property measurement
Two types of LC cells with homogeneous and 90° TN orientations were prepared by injecting the N phase HBLC into an empty cell purchased from EHC Co. Ltd (Hachioji, Japan). The precise cell gap d was measured by calculating the interference spectrum. The capacitance-voltage (C-V) curve of the cell was measured at 1 kHz using HP 4284 LCR meter. The conductivity of the investigated HBLCs was less than 10−11 S/cm. The real part of the dielectric constant was calculated from the ratio of the capacitance of the sample cell to that of the empty cell. The dielectric constant of the LC perpendicular to the molecular axis (${\varepsilon _ \bot }$) was measured by applying a voltage below the threshold, and that parallel to the axis (${\varepsilon _{/{/}}}$) was obtained by linear extrapolation to an infinite voltage as a function of 1/V. [33,34]. The voltage-transmittance (V-T) curve was measured using a laser diode (640 nm) between crossed polarizers. The polarizer axis was set at 45° to the LC director in the homogeneous cell and parallel to the LC director on either substrate in the TN cell. The frequency of the applied voltage was 1 kHz.
Figure 2 shows a definition of the LC director with tilt angle θ and twist angle $\phi $ in the LC cell. Wp_0 and Wp_d are the polar anchoring strengths and Wa_0 and Wa_d are the azimuthal anchoring strengths of each substrate. A total free energy per unit area F in the LC cell [35] is represented
Fig. 2. Definition of the LC director, n, and surface alignment conditions of the substrate in the LC cell.
The LC distributions of θ(z) and ϕ(z) in the cell were obtained by solving a set of Euler–Lagrange equations to minimize the total free energy of Eq. (1). The finite difference method was used to estimate θ(z) and ϕ(z). The LC layer was divided into d/1000 near the substrate and d/50 around the center of the cell to account for the anchoring strength in the difference method. The transmittance was calculated using the Jones matrix corresponding to each divided LC thin layer which can be approximated by a homogeneous medium [36]. In the homogeneous cell, K11 was first chosen to match the measured threshold voltage, and then K33, pretilt angle, polar anchoring strength, and refractive index anisotropy $\Delta n$ were adjusted to fit the theoretical C-V and V-T curves. K22 was further adjusted to fit the theoretical curves of the TN cell.
3. Results and discussion
3.1 physical properties of HBLCs
It is known that $\Delta n$ and $\Delta \varepsilon$ of bicyclohexane NLC are generally lower than those of biphenyl NLCs [37]. In fact, $\Delta n$ and $\Delta\varepsilon $ of CC-3 are respectively 0.052 and 0.16 (provided by LCC Co., Ltd.), and are too small to be applied to electro-optical devices. Therefore, nBA was mixed with CC-3 to increase anisotropy. Table 1 shows the HBLC homologous series with CC-3 and nBA (1:1 weight ratio). The HBLC mixture containing only CC-3 and 2BA exhibited the N phase at 25°C. Subsequently, 2BA (20 wt%) and nBA (30 wt%) were mixed with CC-3. In the series of mixtures, the HBLCs exhibited the N phase at 25°C except for 3BA.
Table 1. HBLC mixtures with CC-3 (mCCA) and nBA
Figure 3 shows the measured transmittance by applying a voltage to the homogeneous and TN cells using the HBLC mixture of CC-3 (50 wt%) and 2BA (50 wt%). Calculated curves were approximately fitted to the measured results by the appropriate selection of K11, K22, K33, $\Delta n$, pretilt angle, and polar anchoring strength. The estimated uncertainties of elastic constants, dielectric constants, and $\Delta n$ were ±1, ± 0.1, and ±0.002, respectively. Physical properties obtained in the homogeneous cell were almost the same as those obtained in the TN cell, as shown in Fig. 4. The pretilt angles were 0.5 − 1.0° and the polar anchoring strengths in each cell were 0.8 − 2.0 × 10−3 N/m, which are almost the same as those values using usual NLCs on the rubbed polyimide alignment surface (AL-1254 from JSR Corp. Japan). When the azimuthal anchoring strength was adjusted between 1 × 10−4 and 1 × 10−3 N/m in the TN cell, the changes in the calculated V-T curves were very small and did not affect the fitting results. Therefore, the azimuthal anchoring strength of 5 × 10−4 N/m was used to fit the measured V-T curve.
Fig. 3. Theoretical V-T curve fitted to measurement result in (a) homogeneous and (b) TN cell using HBLC mixture with CC-3 and 2BA.
Fig. 4. Add-even effects of alkyl carbon number on (a) elastic constant, (b) dielectric anisotropy, and (c) refractive index anisotropy in mCCA and nBA mixtures.
K11 and K33 clearly showed the odd-even effect of the alkyl carbon number n and K33/K11 decreased with n. Similar add-even effects have been reported for the n-cyanobipheny and n-phenylcyclohexane NLCs [38,39]. K22 slightly increased with n and the odd-even effect was not clearly observed. K22/K11 was about 0.3 − 0.5, which was small compared to the typical LCs of about 0.5 − 0.8. $\Delta\varepsilon $ was successfully increased about 4 − 5 times by the addition of nBA. $\Delta n$ was also increased by a factor of about 1.8.
To further increase the dielectric anisotropy, BA derivatives attached to the polar groups shown in Fig. 1(c) − 1(k) were added to the mixture of mCCA and nBA in which six acids were mixed in equal amounts (m = 3, 4, 5, n = 2, 4, 5, available as PC-29 from LCC). Table 2 shows the physical properties of the HBLC mixtures at 25°C. The concentration of BA derivatives in PC-29 was 5 wt%. All HBLC mixtures exhibited the N phase except for 2CNBA at 25°C. The ${\varepsilon _{/{/}}}$ of HBLC mixtures with the BA derivative whose polar group was at the para-position of the carboxylate group was higher than that of PC-29. On the other hand, no significant changes in the ${\varepsilon _ \bot }$ were observed. When 4CN3FBA was added, the largest $\Delta\varepsilon $, approximately 4 times higher than that of PC-29, was obtained. The effect of BA derivatives on the elastic constant and $\Delta n$ was small due to the low mixing concentration. For reference, the data of the typical NLCs of 5CB (4-cyano-4'-pentylbiphenyl) and 5PCH(4-(trans-4-pentylcyclohexyl)benzonitrile) are also shown in Table 2. Elastic constants of HBLC mixtures were higher than those of 5CB and 5PCH, resulting in a higher driving voltage in electro-optical devices.
Table 2. Physical properties of HBLC mixtures.
Figure 5(a) shows the dielectric anisotropy as a function of fluorobenzoic acid concentration. $\Delta\varepsilon $ increased with the concentration of 4FBA. Assuming that $\Delta\varepsilon $ increases proportionally to the concentration, $\Delta\varepsilon $ of the binary LC with fluorine polar and non-polar side-chain terminal groups is estimated to be about 3, which is a reasonable value compared to the fluorine-end type LCs [41]. In contrast, $\Delta\varepsilon $ decreased by adding 2FBA. 3FBA did not affect $\Delta\varepsilon $. Figure 5(b) shows the refractive index anisotropy as a function of fluorobenzoic acid concentration. When the mixture concentration was increased to 10 wt%, $\Delta n$ was about 0.11 and did not depend on the amount of fluorobenzoic acid. The $\Delta n$ value of fluorine-end-type LCs for display devices has been reported to be around 0.1. The addition of 15 wt% fluorobenzoic acid was attempted; however, the mixture exhibited a smectic phase at 25°C.
Fig. 5. (a) Dielectric anisotropy and (b) refractive index anisotropy as a function of fluorobenzoic acids concentration.
3.2 Electro-optical properties
Figure 6(a) shows V-T curves calculated in homogeneous cells between crossed polarizers using the parameters shown in Table 2. The wavelength was 640 nm. The cell thickness was determined so that the phase retardation $\Delta\varGamma \; ({ = 2\mathrm{\pi}\Delta nd/\lambda } )$ was 2π. The threshold voltage of PC-29 was 5.1 V, which was approximately 6 times higher than that of 5CB. It was reduced to 2.7 V by adding 4CN3FBA at 5 wt%. The $\Delta\varGamma $ decreased from 2π to nearly 0 by the LC reorientation with voltage. Therefore, the transmittance reaches 100% at $\Delta\varGamma $ of π where the LC cell acts as a λ/2 plate. Figure 6(b) shows calculated V-T curves in 90° TN cells between crossed polarizers. The cell thickness was set to satisfy the 1st Mauguin minimum condition, that is $d = \sqrt 3 \lambda /\Delta n$. In the visible light range, the LCs exhibit no absorption loss, therefore the polarization of the incident light rotates perfectly at 90° and the transmittance is 100% in the absence of the applied voltage. The transmittance decreased with the applied voltage and became less than 0.1% at 7 V when the HBLC of PC-29 + 4CN3FBA was used.
Fig. 6. V-T curves in (a) homogeneous cells and (b) TN cells between crossed polarizers. The wavelength is 640 nm.
In the THz range, the LC exhibits absorption loss. Common NLCs have a negative dichroism [26,42–44], while the HBLC of PC-29 has been reported to have no dichroism [20]. When the incident light is normal to the substrate, the absorption coefficient α and $\Delta n $ of the LC are represented as a function of tilt angle θ
Figure 7 shows V-T curves of the homogeneous cell in the THz range. The transmittance was calculated using the absorption coefficients shown in Table 3 and the other physical properties shown in Table 2. The incident light was polarized parallel to the LC director. At THz frequencies, the cell thickness must be larger than 100 µm to obtain suitable cell performance. When the cell thickness was 500 µm, the transmittances of 5CB and 5PCH cells without voltage were 58.0% and 51.9%, respectively, and decreased with voltage, as shown in Fig. 7(a). On the other hand, the transmittance of PC-29 cell was constant at 15.7%.
Fig. 7. V-T curves of the extraordinary THz wave in homogeneous cells. The cell thickness is (a) 500 µm and (b) is set to be the retardation of 2π.
Table 3. Refractive index and absorption coefficient of LCs in THz wave.
Figure 7(b) shows the calculated V-T curves when each cell thickness is set to be the $\Delta\varGamma $ of 2π. Each cell thickness used was 1250 µm at 2 THz for 5CB, 1875µm at 2 THz for 5PCH, and 706 µm at 2.5 THz for PC-29. Nose and coworkers have reported that $\Delta n$ of usual NLCs at millimeter-wave and THz regions was smaller than that at the visible light [47]; 5CB and 5PCH as well (see Tables 1 and 3). On the other hand, it has been reported that $\Delta n$ of HBLCs at 50 GHz was larger than that at the visible light [48]. Therefore, the absorption loss was suppressed in the PC-29 cell and the transmittance was higher than those of the 5CB and 5PCH cells under the high voltage application due to the thinner cell thickness and no dichroism.
Figure 8(a) shows calculated V-T curves in homogeneous between crossed polarizers. Since the transmittance was dominated by the value of $\Delta n$, here the unmeasured ${n_\textrm{o}}\; \textrm{and}\; {n_\textrm{e}}$ were set to 1.5 and 1.67, respectively. The cell thickness was determined so that the $\Delta\varGamma$ became 2π. The transmittance was 0% in the PC29 cell in the absence of voltage, because the output light was linearly polarized at 45° as shown in Fig. 8(c). The maximum transmittance was 7.3% at 8.2 V where the $\Delta\varGamma$ was reduced to π, and the output light was linearly polarized at −45°, as shown in Fig. 8(d). When the voltage of 13.7 V was applied, the $\Delta\varGamma$ became π/2 and the output light was right-handed circularly polarized, as shown in Fig. 8(e). At a voltage of 6.4 V, the $\Delta\varGamma$ was 3π/4, resulting in left-handed circular polarization. Assuming that the absorption coefficient of PC-29 + 4CN3FBA is the same as that of PC-29 due to the low concentration of 4CN3FBA, the polarization control is performed at about half the applied voltage.
Fig. 8. (a) V-T curves of THz wave in the homogeneous cell between crossed polarizers (ϕp = 45°, ϕA = −45°). (b) The polarization state of the incident terahertz wave. (c)−(e) Polarization state variation of the transmitted terahertz wave in homogeneous cells by applying a voltage.
In the 5CB cell, the transmittance was 1.8% at a voltage of 0 V, because the polarization angle is 21.6°, even when the output light was linearly polarized, as shown in Fig. 8(a) and 8(f). The peak transmittance of 5.5% was obtained at 1.3 V. Here, the $\Delta\varGamma$ was 1.13π and the output wave was elliptically polarized as shown in Fig. 8(g). Output polarization states at the $\Delta\varGamma$ of π and π/2 are shown in Fig. 8(h) and 8(i). In the 5PCH cell, the absorption loss of the ordinary wave was so large that the transmittance decreased monotonically with voltage.
Figure 9 shows calculated V-T curves in 90° TN cells between crossed polarizers. Each cell thickness used in the calculation was 1083 µm at 2 THz for 5CB, 1624 µm at 2 THz for 5PCH, and 611 µm at 2.5 THz for PC-29 to satisfy the 1st Mauguin minimum condition. In the PC-29 cell, the polarization direction of the incident light was completely rotated at 90° and the transmittance was 10.4% whether the polarization direction was parallel (ϕp = 0°) or perpendicular (ϕp = 90°) to the LC direction of the entrance side of the substrate. At a voltage above 13 V, the optical rotation function was lost and the transmittance was close to 0%. When the cell was placed between parallel polarizers, the transmittance changed from 0% to 10.4% by applying a voltage.
Fig. 9. (a) V-T curves of THz wave in the TN cell between crossed polarizers. (b)−(e) Polarization states of the transmitted wave in the TN cell at 0 V.
In the 5CB and 5PCH TN cells, the transmittance and the polarization state depended on the polarization direction of the incident light due to the dichroism of the LCs. The output wave showed elliptical polarization as shown in Fig. 8(d) − 8(g) without applied voltage. The transmission of the incident wave at ϕp = 90° was less than half of that at ϕp = 0° due to the larger absorption loss of the ordinary wave. When 2.2 V was applied to the 5CB cell, the optical rotation function was lost and the transmittance after passing through the analyzer was almost 0%. Without analyzer, the transmittances of the incident light of ϕp = 0° and 90° were 20.8% and 6.2% at 0 V, and both transmittances decreased to about 5.2% at 5 V.
The thick LC layer results in poor orientation uniformity, long decay time, and light scattering. In the homogeneous LC cell, C.-F. Hsieh and R.-P. Pan have reported 858 and 570 thick cells as a phase shifter [49]. R. Ito, et al. have also controlled the phase of the 800 µm thick HBLC cell [20,29,30]. A good agreement between calculated and experimental results have been obtained in those studies. For decay time and light scattering, some methods using composite systems with polymers have been proposed to solve these the problems [50–52]. Considering the light scattering effect, it might be possible to incorporate the turbidity of LCs into transmission simulations [34,53] as well as the absorption coefficient, which is an issue for the future.
4. Conclusions
In summary, the physical properties of the HBLCs in the N phase have been investigated at room temperature. The odd-even effect of the alkyl carbon number of nBA on the elastic constants was similar to that of n-cyanobipheny and n-phenylcyclohexane NLCs. The addition of BA derivatives attached to polar groups increased the dielectric anisotropy of the mCCA and nBA mixture, which reduced the driving voltage. Using measured physical properties, the electro-optical properties of the homogeneous and TN cells with HBLCs were calculated. The potential of dichroism-free HBLC as an optical material for terahertz devices was demonstrated in comparison to those using dichroic LC materials.
Acknowledgments
The author likes to thank Hikari Kaneko, Minami Shibata, Kanta Saga, and Yukiya Suga for their support in the experiments.
Disclosures
The author declares no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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