1. Introduction

The cholesteric liquid crystal (ChLC) is a liquid crystal phase in which the constituent molecules self-organize into a helical structure. The helical structure exhibits a so-called selective reflection (SR) band, which is a Bragg reflection band for circularly polarized light with the same handedness as the helix. The SR band spans over the wavelength region n_o × p –n_e × p, where n_o, n_e and p are the ordinary and extra-ordinary refractive indices and the helical pitch, respectively [1]. ChLCs are potentially applicable to electro-optic devices such as optical switches [2], lasers [3, 4] and displays [5], because the SR band is tunable by external stimuli [6–9]. However, they show a slow decay time typically of the order of several seconds [10], and the SR band becomes distorted upon removal of the electric field, hindering their use in electro-optic applications. The fabrication of polymer/ChLC (PChLC) composites by in situ polymerization of a mesogenic monomer and ChLC has proven to be effective in improving the response time of ChLCs. Depending on the size of pores in the composite, PChLCs show two response modes: the 'polymer-stabilized' response, in which the reflection band blue-shifts and the peak reflectance decreases with increasing electric field [11], and the 'deformation-free' response, in which only the long band-edge wavelength blue-shifts [12]. The 'deformation-free' mode appears in composites with nano-sized LC domains. Under an electric field, only the unpolymerized LC molecules confined in the nano-sized domains are reoriented along the electric field, but the helical structure is strongly fixed by the crosslinked polymer matrix. Therefore, the effective extra-ordinary refractive index of the nanocomposite is decreased, while the ordinary refractive index and helical pitch remain constant. Consequently, the 'deformation-free' PChLC nanocomposite shows a faster response time on the order of ~10 μs. The 'deformation-free' mode enables new functionalities to be achieved, such as tunable optical rotation and phase modulation [12, 13].

An important parameter of ChLC-based devices is their pitch, as it determines the spectral position of the SR band, and hence in most cases, the operating wavelength. However, the dependence of the electro-optic performance on the helical pitch has not been clarified in the PChLC composites. Gaining insight into the characteristics of PChLC composites is important for the future development of devices based on these materials. Here, the different behaviors of the helical pitch dependence in the threshold electric field between 'polymer-stabilized' and 'deformation-free' are investigated. Two different electro-optic response modes appear in the same PChLC precursor by changing the polymerization temperature [14]. Four PChLC precursors with different helical pitches are prepared, and polymerized in the ChLC phase at either 20 °C or −20 °C to fabricate composites showing the 'polymer-stabilized' and 'deformation-free' responses, respectively. Both samples showed a decrease in the threshold with increasing pitch, but reflecting the difference in the electro-optic response modes, the dependences were different, with the 'deformation-free' samples displaying a smaller dependence. The helical pitch dependence of the 'polymer-stabilized' nanocomposites is explained by the tilting of the helix, or Helfrich deformation. On the other hand, the helical pitch dependence of the low temperature polymerized nanocomposites is attributed to the Fredericks-transition-like response of the LC molecules confined in nano-sized LC domains.

2. Experimental procedure

The PChLC precursors with different helical pitches were prepared by mixing a photopolymerizable LC monomer (Merck, RM257, Δn = 0.179, Δε = −1.5), a nematic LC (Merck, MLC-6849-100, Δn = 0.1138, Δε = 11.3), a chiral dopant (Merck, ZLI-4572) and a photoinitiator (Ciba, Irgacure 819). The composition of each sample is listed in Table 1. The relative weight ratio of RM257 and MLC-6849-100 were fixed, while the concentration of ZLI-4572 was varied between 4.4 and 7.4 wt% in 1 wt% steps. The materials were dissolved in chloroform and left to evaporate for approximately 3 days. The helical pitches of the samples were measured using the Grandjean-Cano wedge method using home-made, planar alignment wedge cells with a wedge angle of ~0.04 ° [15]; the pitches obtained for samples with different polymerization temperatures (T_p) are also shown in Table 1.

Table 1. Compositions and Helical Pitch Length of the Samples Used in This Study

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The mixtures were injected into 10 µm-thick, ITO-coated glass sandwich cells with planar alignment treatment (purchased from E. H. C Co.) in the isotropic phase (100 °C). The samples were cooled to the cholesteric phase (either 20 °C or −20 °C), and polymerized by irradiating UV light with a wavelength of 365 nm and a power of 200 mW/cm² for 1 hour. In general, irradiation of UV light from one side of the sample leads to a variation in polymer morphology in the depth direction of the cell, causing light reflectance to differ depending on the direction of light incidence [16–18]. Such effects were not observed in our samples, possibly due to the strong UV light intensity used. The reflection spectra were measured on a polarizing optical microscope using a fiber-optic spectrometer (Hamamatsu Photonics, PMA-11, fiber diameter ~1 mm) and a 10 × objective lens, as a square wave electric field with a frequency of 1 kHz was applied along the helical axis on the cell. A scanning electron microscopy (SEM) (Hitachi S-4300) was used to investigate the polymer morphologies of the PChLC nanocomposites. For SEM observation, the cell was opened and rinsed by super-critical CO₂ (Rexxam Co. Ltd., SCRD401) after the polymerization process.

3. Results and discussion

The electric-field-dependent reflectance spectra of the PChLC composites polymerized at 20° C are shown in Fig. 1(a). All nanocomposites showed a switching behavior typical of a 'polymer-stabilized' ChLC; with increasing electric field, the reflection band broadened and the peak reflectance decreased. This is explained by the tilting of the cholesteric helix. In general, the transition of pure ChLC from the planar to focal-conic state occurs through two different processes. One is through the appearance of the so-called oily streaks, which are bent cholesteric layers and the other is through the so-called Helfrich deformation, which is an undulation of the helical axis [19]. In the case of 'polymer-stabilized' ChLC, the nucleation of the oily streaks is suppressed by the polymer network [20]. Therefore, the electro-optic response of the PChLC composites polymerized at 20 °C is thought to be mainly affected by the Helfrich deformation. Theoretically, the Helfrich threshold, E_H, for the transition from the planar to the Helfrich state in a bulk ChLC is inversely proportional to the square root of the helical pitch length, p (E_H ∝ (p)^-1/2) [21]. To determine the threshold electric field to tilt the helix in the PChLC nanocomposites polymerized at 20 °C, we plot the electric field dependence of the normalized peak reflectance of the SR band (Fig. 1(b)) and find the electric field at which the normalized peak reflectance begins to decline; this corresponds to the cholesteric layers becoming undulated. The threshold electric field, E_th, is found by fitting the data below and above threshold with a line function and taking the point of intersection. As shown in Fig. 1(c), the threshold electric field increases with decreasing pitch in the 'polymer-stabilized' ChLCs. An analysis of the data using a power law equation E_th = Ap^-β yields a best fit for β = 0.57, which is close to the predicted value from Helfrich threshold. The results therefore suggest that the response of the 'polymer-stabilized' ChLCs is dominated by the Helfrich deformation of the helix.

 

Fig. 1 Dependence of the electro-optic switching on the helical pitch in the PChLC nanocomposites polymerized at 20 °C. (a) Electrical tuning of the SR band in the PChLC nanocomposites with different chiral dopant concentrations. (b) Normalized peak reflectance with respect to the applied electric field at different chiral dopant concentrations. (c) Helical pitch dependence of the threshold electric field. The red solid circles are measured results and red curve is the fitting curve. The blue dotted curve is the fitting curve of β = 0.5.

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Figure 2(a) shows the electro-optic response of the nanocomposites polymerized at −20 °C, and Fig. 2(b) shows the electric field dependence of the SR band position. The 'deformation-free' responses are observed, where only the long band-edge wavelength blue-shifts without showing a reduction in reflectance. Figure 2(c) shows the electric-field dependence of the normalized SR band-width on the helical pitch for the 'deformation-free' PChLC nanocomposites. The normalized SR band-width is defined as the relative band-width of the SR band compared to the width at zero field, and the threshold electric field is evaluated from the intersecting point of the two line functions describing the response below and above the threshold. Similar to the 'polymer-stabilized' samples, the threshold decreases with an increase in the helical pitch; however, a fit with the power function yields a smaller value for the exponent β of approximately 0.33 (Fig. 2(d)). The smaller value compared to that predicted from the Helfrich model implies that unlike the 'polymer-stabilized' samples, the electro-optic response in the 'deformation-free' PChLC nanocomposites is not dominated by the tilting of the helix but by another effect.

 

Fig. 2 Dependence of the electro-optic switching on the helical pitch in the PChLC nanocomposites polymerized at −20 °C. (a) Electrical tuning of the SR band in the PChLC nanocomposites with different chiral dopant concentrations. (b) Electric field dependence of the SR band position in the PChLC nanocomposites with different chiral dopant concentrations. (c) Normalized SR band-width with respect to the applied electric field at different chiral dopant concentrations. (d) Helical pitch dependence of the threshold electric field. The red solid circles are measured results and red curve is the fitting curve. The blue dotted curve is the fitting curve of β = 0.5.

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The difference in the response mechanisms is also supported from the polarizing optical micrographs of the samples. Figure 3 shows the reflective polarizing optical micrographs of the PChLC composites with and without electric field. The PChLC composites polymerized at 20 °C showed distorted planar textures upon the application of an electric field, as shown in Fig. 3(a). On the other hand, the samples polymerized at −20 °C maintained the uniform planar cholesteric textures even under a high electric field of 20 V/μm (Fig. 3(b)), i.e., the macroscopic helical structure was retained. The polarizing optical micrographs suggest that the electro-optic response mechanism of the samples polymerized at 20 °C and −20 °C is different.

 

Fig. 3 Polarizing optical micrographs of the PChLC nanocomposites with different chiral dopant concentrations. (a) Samples polymerized at 20 °C. (b) Samples polymerized at −20 °C.

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In our previous study, the threshold electric field increased with decreasing the domain size, despite having approximately the same pitch lengths [12]. The change in LC domain size caused by a change in pitch, if it exists, could be one of the causes for the change in threshold. Figure 4 shows the morphologies of the polymer networks in the PChLC composites, after rinsing out the unpolymerized LC molecules by super-critical CO₂. Figure 5 shows the dependence of the void size on the chiral dopant concentration, obtained by analyzing the images in Fig. 4. The void sizes were defined as the diameter of the polymer-free regions enclosed by the polymer strands and evaluated from the SEM images. The void sizes in Fig. 4(a) and Fig. 4(b) were averaged over 20 voids and 50 voids, respectively. The sizes of voids, which correspond to the LC domains, depends strongly on the polymerization temperature [22]: the samples polymerized at 20 °C have pore sizes of approximately 295 nm, while the samples polymerized at −20 °C have pore sizes of approximately 40 nm. On the other hand, the effect of the helical pitch on the domain size is hardly detectable. The decrease in the domain size depending on the polymerization temperature can be attributed to the increased viscosity at lower temperature, suppressing polymerization-induced phase separation of the polymer and LC [14]. The difference in LC domain sizes causes the different reorientation mechanisms between the composites polymerized at 20 °C and −20 °C. However, the small dependence of the domain size on the helical pitch implies that the LC domain size is not a major cause of the difference in the thresholds.

 

Fig. 4 Chiral dopant concentration dependence of the polymer network morphologies in the PChLC nanocomposites (a) polymerized at 20 °C. (b) polymerized at −20 °C.

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Fig. 5 Chiral dopant concentration dependence of void-size distribution in the PChLC nanocomposites polymerized at 20 °C and −20 °C.

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In a previous study, we discussed that nematic LC molecules confined in nano-sized domains exhibit an improved response time because of the effective decrease in the confined volume [23]. The previous discussion was limited to the nematic phase and did not consider the effect of twist that is present in the ChLC. To extend our discussion to the ChLC case, we consider the Fredericks transition of twisted nematic LC molecules confined between two anchoring walls with a correlation length of ξ (Fig. 6). The non-polymerized LC molecules confined in nano-sized polymer walls are regarded as the twisted nematic LC molecules. For a ChLC with pitch, p, the total twist angle, Φ, in the domain is given by

 

Fig. 6 Schematics of possible driving mechanism of the PChLC nanocomposite having small domains.

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4. Conclusion

In this paper, the helical pitch dependence of the threshold electric field in low monomer concentration PChLC nanocomposites was investigated. The polymerization temperature changes the electro-optic switching response of the PChLC nanocomposites from a 'polymer-stabilized' response (room temperature polymerization) to a 'deformation-free' response (low-temperature polymerization). The thresholds of the nanocomposites increased as the pitch shortened for both response modes, but the dependence was smaller in the 'deformation-free' sample, reflecting the difference in the driving mechanisms. The properties of PChLCs revealed here should aid the application of these materials in tunable electro-optic devices, such as phase modulators and tunable filters.