Open Access
Add to BibSonomy
Abstract
Electro-optical properties of polymer-stabilized sphere phase liquid crystal (PS-SPLC) switching devices are analyzed and validated experimentally. The experimental results show the voltage-dependent transmittance curves of PS-SPLC devices. A diffraction approach, called extended anomalous diffraction approach, is proposed to fit the experimental data. Good agreement between experiment and model is obtained. The scattering model provides practical guidance for the improvement of PS-SPLC displays performance and optimization.
© 2017 Optical Society of America
1. Introduction
Liquid crystal composites comprising of liquid crystal and polymer have attracted considerable interest for their wide range of applications in liquid crystal displays, phase modulators, and three-dimensional (3-D) tunable photonic crystals [1–4]. A typical example of liquid crystal composites is polymer dispersed liquid crystal (PDLC) formed with liquid crystal droplets dispersed in a matrix [5–7]. Conventional PDLC devices can be switched between scattering and transparent states with a slow switching time (>5 ms) owing to the large size of liquid crystal droplets. The switching time of nano-scale holographic (H)-PDLCs devices is of the order of submilliseconds [8–10]. Nonetheless, to drive liquid crystal molecules in such small droplets, a high switching electric field (>15 V/μm) is required to overcome the large anchoring energy of polymer [11]. Many efforts have been made to improve the switching electric field of H-PDLC devices. However, they are inevitable to lead to other issues, such as slow response time, poor stability, and low electric resistance.
Sphere phase liquid crystals (SPLCs) are usually observed in a very narrow temperature range between isotropic and blue phases or isotropic and chiral nematic phases. SPLCs are comprised of three-dimensional twist spheres (3-DTSs) induced by a chiral dopant, as illustrated in Fig. 1 [12, 13]. The coexistence of disclinations at an isotropic state stabilizes such three-dimensional periodic structures. The temperature range of the sphere phase can be broadened to more than 80 K through stabilization of the disclinations with amorphous polymer chains, to form so called polymer-stabilized (PS)-SPLCs. At the voltage-off state, a light beam passing through the PS-SPLC will be scattered owing to the mismatch of the refractive index 3-DTSs and the disclinations among them. The underlying physical mechanism of PS-SPLC is electrical-field-birefringence. As the applied electric field increases, the orientation of liquid crystal molecules will align with the electric field. The transmittance of the PS-SPLC device will increase gradually because of the decrease in the difference of the refractive index between the 3-DTSs and the disclinations. The PS-SPLC devices will show a transparent state until the induced birefringence reaches the saturation. Because of the small chiral pitch, PS-SPLC devices can be switched between scattering and transparent states with sub-millisecond response time, resulting in a wide range of applications in flexible display, light shutters and tunable photonic crystals. However, the electro-optical properties of PS-SPLC devices require further investigation. Furthermore, no numerical models exist for characterizing the electro-optical properties of PS-SPLC devices.
In this letter, we determine the electro-optical properties of PS-SPLC devices, and propose a numerical model, namely an extended anomalous diffraction approach (ADA), to describe voltage-dependent transmittance (VT) curves of PS-SPLC devices. On the basis of this extended ADA, we fitted the experimental data of the PS-SPLC devices. Good agreement between our numerical model and experimental results is found.
2. Materials and experimental setup
The PS-SPLC precursors was a mixture consisting of a nematic liquid crystal host HC-1015X (ne = 1.65, no = 1.50, Δε = 29, HCCH), chiral dopant R5011 (HTP = 100, HCCH), two kinds of photocurable monomers (C12A and RM257, HCCH), and photoinitiator IRG 184 (HCCH). The homogeneous precursors were sandwiched between two indium-tin-oxide (ITO) glass substrates without a surface alignment layer. To study the electro-optical performance of the PS-SPLC and validate our simulation model, Table 1 shows four samples with different cell gaps (d) and concentration of chiral dopant. The samples were all placed at the temperature controller at the cooling rate of 0.1 K/min and cured at sphere phase with 3 mWcm−2 UV light (365 nm) for 10 min. After UV exposure, PS-SPLC samples were formed.
Table 1. Recipes and cell gap of four samples.
Figure 2 depicts the experimental setup to measure the VT curves of our samples. The samples were irradiated vertically by a halogen lamp (DT-MINI-2-GS, Ocean Optics) and a photodiode connected to a spectrometer (USB 2000 + , Ocean Optics) with an optical fiber that was placed at a distance of 20 cm from the sample for signal reception. A square-wave voltage was amplified and then applied to the sample.
3. Results and discussion
Figure 3 shows the measured VT curves of our samples (λ = 0.6 um). At turn-off state, the scattering of sample 1 (d = 8 um) is stronger than that of sample 2 (d = 5 um), resulting in a high contrast ratio. However, a large applied voltage (> 80 V) needs to drive the liquid crystal molecules. To study the chiral dopant effect on the VT curve of the PS-SPLC, the VT curves of samples with different concentration of R5011 were measured, as shown in Fig. 3. When the concentration of the chiral dopant was increased from 4.6 to 4.8, the haze of the PS-SPLC became less and a higher applied voltage was required because of the reduced scattering cross section. The lowest applied voltage of the samples was more than 60 V, and the highest contrast ratio of the samples was less than 5:1. Thus, the electro-optical properties of these PS-SPLC devices do not meet the requirements of practical applications. A numerical model for the electric field and contrast ratio would help to optimize the performance of such devices.
Fig. 3 Fitting experimental data (λ = 0.6 um) using the scattering model. Dots are measured data and lines are fitting curves.
The anomalous diffraction approach is often used to determine the total droplet cross section of a PDLC [14–18]. At the voltage-off state, a PDLC scatter light strongly owing to the mismatch of the refractive index of liquid crystal droplets and that of the continuous polymer matrix covering liquid crystal droplets, as shown in Fig. 4(a). If the scattering centers were assumed to be optically transparent, in the absence of multiple scattering, the transmission T can be described as follows [19]:
where σs is the average scattering cross section for a collection of scattering centers, β is the number of droplets in the unit volume, and d is the liquid crystal mixture thickness. For large optically anisotropic droplets, the size of droplet, D, is of the order of a few tens of micrometers. Analytical formula for the total droplet cross section can be obtained based on the ADA:where σ0 = πD2/4 is the geometrical cross section of the liquid crystal domain, = (2π/λ)np, np is the refractive index of polymer, λ is the wavelength of incident light, no and ne are the ordinary and extraordinary refractive index of liquid crystal host, respectively. S(e) and P4s(e) are order parameters for different electric fields. where is the droplet director, u is the unit vector of the external electrical field, and are the second and fourth orders Legendre polynomial of the droplet director distribution. When an external field is applied to reorient liquid crystal among the 3-DTSs, the electric field causes the structural distortion and then induces the liquid crystal to align parallel to the field as the voltage increases. Here e stands for the reduced electric field as follows:where ξ is the average curvature radius with applied an electric field E, Δε and k are the dielectric anisotropy and a typical elastic constant of liquid crystal host, respectively, μ is a dimensionless factor, which describes the depolarization of the applied field, r stands for the average radius of the droplet.Fig. 4 Diagrammatic sketch of light scattering in (a) a polymer dispersed liquid crystal and (b) a polymer-stabilized sphere phase liquid crystal.
In the voltage-off state, the scattering of PS-SPLC results from mismatch of the refractive indices of 3-DTS and the disclinations are considered to be optical isotropic, as shown in Fig. 4(b); therefore, it is quite reasonable to assume that the average refractive index of disclinations remains constant [20]:
Here, the no and ne are the ordinary and extraordinary refractive index of the liquid crystal host. When the birefringence is small, Eq. (6) can be approximated by:If the birefringence of the disclinations remains constant, as for the polymer array of a PDLC, the VT curve of sample 1 could be fitted with Eq. (1), and with the use of ADA, as shown in Fig. 5. The fitting result shows that the trend of our experimental data could be explained with Eq. (1), however the ADA model showed poor fitting to the experimental data.Fig. 5 Measured VT curve of sample 1 and fittings with ADA and Extended ADA (μ = 0.3, k = 14 × 10−12 N, λ = 0.6 μm, β = 432, and D = 217 nm).
Unlike the polymer array of PDLC, the disclinations of PS-SPLC formed with the liquid crystals. The liquid crystals will be in response to external fields, as shown in Figs. 3(b) and 3(c). To accurately calculate the detailed molecular distribution of the liquid crystal within disclinations in response to external fields, both the Landau free energy and electric energy need to be considered, which complicates the analysis. Nevertheless, at the macroscopic scale the electro-optical properties can be calculated by a simple model based on the Kerr effect. When an electric field (E) is applied, birefringence is induced and the refractive index of the discliantions is related to E as [21]:
Here, λ is a reference wavelength, K is the Kerr constant of the disclination in the PS-SPLC. Considering the disclinations, we propose the following approach to obtain the total droplet cross section:We then used Eq. (1) to fit the experimental data leaving μ as an adjusting parameter. As shown in Fig. 5, the simulated results agreed well with the experimental data, when μ = 0.30. For convenience, we refer to this approach as an extended ADA.
To validate the extended ADA, we tried to fit the experimental VT curves of samples 2, 3, and 4. The extended ADA simulated results fitted the experimental data well, as shown in Fig. 3. The value of μ for samples 2, 3, and 4 obtained through the fitting parameter were 0.19, 0.3, and 0.19, respectively. The results show that μ mainly depends on the cell gap. However, the ratio of the cell gap, 8/5, was slightly larger than that of μ, 0.3/0.19. This difference could be attributed to two factors: (1) a portion of the LC was embedded in the polymer, and some SPLCs were strongly anchored by the nanostructured 3-DTS boundaries and could not show a response to the E, and (2) polymer located in disclination did not show a response to the E.
Hysteresis is a key issue that affects the properties of LC devices and it should be addressed before the wide application of PS-SPLC. To investigated the hysteresis of our device, the device was driven by switching the applied voltage upward to Von and then downwards to zero, as shown in Fig. 6(b). The VT curve measured during the reverse scan did not match well with that of the forward scan, resulting in hysteresis. The large hysteresis appeared because of SPLC molecules and polymer chain were deformed by the large applied electric field. To suppress the hysteresis of the PS-SPLC device, a stronger the polymer system should be used that is distorted less than the large electric field [22–27].
4. Conclusion
In conclusion, the electro-optical properties of a PS-SPLC device are investigated. The haze of PS-SPLC device decreased when the cell gap was decreased or the concentration of chiral dopant was increased. A conventional ADA, used to predict the electro-optical properties of PDLC, did not accurately describe the VT curves of PS-SPLC devices. To explain this phenomenon, an extended ADA model is proposed here, which fit well with the VT curves of our devices. Our scattering model provides practical guidance for improving the performance of PS-SPLC material and optimizing devices.
Funding
National Natural Science Foundation of China (NSFC) (11504080); National Science Foundation of Hebei province of China (A2017202004, A2015202343); Key Subject Construction Project of Hebei Province University.
References and links
1. W. M. Gibbons, P. J. Shannon, S. T. Sun, and B. J. Swetlin, “Surface-mediated alignment of nematic liquid crystals with polarized laser light,” Nature 351(6321), 49–50 (1991). [CrossRef]
2. D. K. Yang, L. C. Chien, and J. W. Doane, “Cholesteric liquid crystal/polymer dispersion for haze-free light shutters,” Appl. Phys. Lett. 60(25), 3102–3104 (1992). [CrossRef]
3. Z. Zheng, L. Yao, R. Zhang, Z. Zou, Y. Liu, Y. G. Liu, and L. Xuan, “Thermo-stability of acrylate based holographic polymer dispersed liquid crystal gratings,” J. Phys. D Appl. Phys. 42(11), 115504 (2009). [CrossRef]
4. B. Liu, Z. Zheng, X. Chen, and D. Shen, “Low-voltage-modulated laser based on dye-doped polymer stabilized cholesteric liquid crystal,” Opt. Mater. Express 3(4), 519–526 (2013). [CrossRef]
5. Y. H. Fan, Y. H. Lin, H. W. Ren, S. Gauza, and S. T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004). [CrossRef]
6. P. S. Drzaic, Liquid Crystal Dispersions (World Scientific, 1995).
7. Y. H. Lin, H. Ren, and S. T. Wu, “High contrast polymer-dispersed liquid crystal in a 90° twisted cell,” Appl. Phys. Lett. 84(20), 4083–4085 (2004). [CrossRef]
8. Z. Zheng, L. Zhou, D. Shen, and L. Xuan, “Holographic polymer-dispersed liquid crystal grating with low scattering losses,” Liq. Cryst. 39(3), 387–391 (2012). [CrossRef]
9. D. Rudhardt, A. Fernandez-Nieves, D. R. Link, and D. A. Weitz, “Phase switching of ordered arrays of liquid crystal emulsions,” Appl. Phys. Lett. 82(16), 2610–2612 (2003). [CrossRef]
10. T. J. Bunning, L. V. Natarajan, V. P. Tondiglia, and R. L. Sutherland, “Holographic polymer-dispersed liquid crystals,” Annu. Rev. Mater. Sci. 30(1), 83–115 (2000). [CrossRef]
11. M. D. Sarkar, J. Qi, and G. P. Crawford, “Influence of partial matrix fluorination on morphology and performance of HPDLC transmission gratings,” Polymer (Guildf.) 43(26), 7335–7344 (2002). [CrossRef]
12. J. L. Zhu, S. B. Ni, C. P. Chen, D. Q. Wu, X. L. Song, C. Y. Chen, J. G. Lu, Y. K. Su, and H. P. Shieh, “Chiral-induced self-assembly sphere phase liquid crystal with fast switching time,” Appl. Phys. Lett. 104(9), 091116 (2014). [CrossRef]
13. J. L. Zhu, W. H. Li, Y. B. Sun, J. G. Lu, X. L. Song, C. Y. Chen, Z. D. Zhang, and Y. K. Su, “Random laser emission in a sphere-phase liquid crystal,” Appl. Phys. Lett. 106(19), 191903 (2015). [CrossRef]
14. J. W. Doane, N. A. Vaz, B. G. Wu, and S. Žumer, “Field controlled light scattering from nematic microdroplets,” Appl. Phys. Lett. 48(4), 269–271 (1986). [CrossRef]
15. J. R. Kelly and P. Palffy-Muhoray, “The optical response of polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 243(1), 11–29 (1994). [CrossRef]
16. V. A. Loiko, A. V. Konkolovich, and A. A. Miskevich, “Order parameter of elongated liquid crystal droplets: The method of retrieval by the coherent transmittance data,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3), 031704 (2006). [CrossRef] [PubMed]
17. S. Zǔmer, “Light scattering from nematic droplets: Anomalous-diffraction approach,” Phys. Rev. A Gen. Phys. 37(10), 4006–4015 (1988). [CrossRef] [PubMed]
18. J. B. Whitehead Jr, S. Zumer, and J. W. Doane, “Light scattering from a dispersion of aligned nematic droplets,” J. Appl. Phys. 73(3), 1057–1065 (1993). [CrossRef]
19. L. Méchernène, L. Benkhaled, D. Benaissa, and U. Maschke, “Studies of optical transmission properties of electron beam cured polymer/liquid crystal systems,” Opt. Mater. 31(4), 632–639 (2009). [CrossRef]
20. J. Yan, H. C. Cheng, S. Gauza, Y. Li, M. Jiao, L. Rao, and S. T. Wu, “Extended Kerr effect of polymer-stabilized blue-phase liquid crystals,” Appl. Phys. Lett. 96(7), 071105 (2010). [CrossRef]
21. Z. Ge, S. Gauza, M. Jiao, H. Xianyu, and S. T. Wu, “Electro-optics of polymer-stabilized blue phase liquid crystal displays,” Appl. Phys. Lett. 94(10), 101104 (2009). [CrossRef]
22. J. L. Zhu, S. B. Ni, C. P. Chen, X. L. Song, C. Y. Chen, J. G. Lu, and Y. K. Su, “The influence of polymer system on polymer-stabilized blue phase liquid crystals,” Liq. Cryst. 41(6), 891–896 (2014). [CrossRef]
23. Y. H. Lee, F. Gou, F. Peng, and S. T. Wu, “Hysteresis-free and submillisecond-response polymer network liquid crystal,” Opt. Express 24(13), 14793–14800 (2016). [CrossRef] [PubMed]
24. H. S. Chen, Y. H. Lin, C. H. Wu, M. Chen, and H. K. Hsu, “Hysteresis-free polymer-stabilized blue phase liquid crystals using thermal recycles,” Opt. Mater. Express 2(8), 1149–1155 (2012). [CrossRef]
25. H. C. Cheng, J. Yan, T. Ishinabe, and S. T. Wu, “Vertical field switching for blue-phase liquid crystal devices,” Appl. Phys. Lett. 98(26), 261102 (2011). [CrossRef]
26. Y. H. Kim, S. T. Hur, C. S. Park, K. W. Park, S. W. Choi, S. W. Kang, and H. R. Kim, “A vertical-field-driven polymer-stabilized blue phase liquid crystal mode to obtain a higher transmittance and lower driving voltage,” Opt. Express 19(18), 17427–17438 (2011). [CrossRef] [PubMed]
27. J. Yan and S. T. Wu, “Effect of polymer concentration and composition on blue-phase liquid crystals,” J. Disp. Technol. 7(9), 490–493 (2011). [CrossRef]
