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We report that an asymmetric bent dimer, consisting of a rod mesogen and a cholesterol mesogen linked by a flexible spacer with 9 carbon atoms, was found to form blue phases with a record-wide temperature range. Moreover, highly stable, fast electro-optic switching is possible. In addition to the stable Kerr effect, the electrostriction effect was also observed.
© 2014 Optical Society of America
1. Introduction
The blue phase (BP) is one of unique liquid crystalline (LC) phases with three-dimensional superstructures stabilized by line defects and emerges below the isotropic (Iso) phase, generally in a very narrow temperature range. Hence, this phase has been discussed for a long period from a scientific point of view, in relation to the origin and the underlying molecular arrangement [1,2], but not from an application point of view. This has changed dramatically, since (i) BP was stabilized in a wide temperature range by partial polymerization [3], and (ii) BP-based display panels were demonstrated (Samsung electronics, 2008 SID, Los Angeles, USA) and subsequently display-oriented research was started [4,5]. These works have encouraged researches aiming practical display applications, which include fundamental ideas to stabilize BP both from experimental and theoretical standpoints. Owing to extensive studies, the concept for ideal molecular design to widen the BP temperature range became quite clear [6], i.e., a prerequisite for biaxial shape of molecules, such as bent- [7–17], T- [18–20], and U-shapes [21–23]. Particularly, bent-shaped molecules have been confirmed to have small bend elastic constants [12,24–27], and thus have been shown to be advantageous for stabilising BP [28,29]. Because of these facts and a pioneering work [7] showing that the doping calamitic chiral host systems with achiral bent-shaped molecules stabilizes BP, a lot of studies on BP using bent-shaped molecules have been conducted. However, most of the systems consist of achiral bent-shaped molecules and chiral dopant molecules.
Here, we report a novel molecular architecture bearing both a bent shape and a chiral center; asymmetric bent dimers composed of achiral rod and cholesterol mesogens [30]. These compounds exhibit wide BP temperature ranges of ~40 K on cooling. Despite the metastable character of the supercooled BP, stable electro-optic switching was observed due to the Kerr effect. A distinct electrostriction effect was also observed in addition to the Kerr effect.
2. A wide temperature-ranged cubic blue phase mediated by odd-even effect
The materials used in this study (Cn) were chiral asymmetric dimers consisting of cholesterol and N-benzylidene-p-toluidine units connected by a flexible alkyl spacer with n carbons in the spacer group (Fig. 1(a)) [30]. When n is odd, like in the major compound used (C9, n = 9), two mesogenic groups form a bent shape. The material has negative dielectric anisotropy; Δε changes from −0.33 to −0.86 monotonically with decreasing temperature in BP. We have already reported that these compounds show multiple nematic phases [30]; the chiral phases, cholesteric (Ch) and BP, at higher temperatures and an apparently uniaxial phase with bend-splay modulation (hereafter the Nx phase) at lower temperatures. The Nx phase is distinct from the NTB phase, which has attracted particular attention since the reports by Dozov [31] and Memmer [32]. Many works have been reported [33–37] including molecules with chiral mesogens [30,38], and even in the crystal phase [39]. The phase structure of the NTB phase is now well established as a short-pitch helix of about 10 nm [37], where each molecule tilts from the helical (director) axis and forms a helix with twist and bend deformation. According to high resolution differential scanning calorimetric (HR-DSC) studies [40,41] with a scan rate of 0.05 K/min, multiple intermediate (at least three) nematic phases are observable between BP and Nx (see left inset of Fig. 1(b)), as already reported in our previous paper for C15 [30].
Fig. 1 (a) Molecular structure of an asymmetric dimer C9, where 9 denotes the number of carbon in a flexible spacer linking a rod and a cholesterol mesogenic groups. (b) HR-DSC data of C9. Upper and lower data correspond to heating and cooling processes, respectively. Note a wide temperature range of BPs of about 37 K on cooling. The existence of BPIII and cubic BP (BPcub) with platelet textures was identified by polarizing microscopy, although assignment of BPcub to BPI or BPII could not be made. On heating, the most temperature range between Nx and Iso are Ch phase. Inset (left) clearly shows sequential transitions in between the two nematic phases, as already reported for C15 [30]. Inset (right) exhibits three transition peaks corresponding to the transitions of Ch-BPI-BPII-BPIII. Arrows are the indicators of the temperature of each phase transition. (c) Texture obtained upon cooling in a planarly-treated cell with a surface agent AL1254. Right: BPIII appears right beneath the Iso phase and coexists with Iso; Left: BPIII transformed into BPcub at ~110.7°C.
In this work, we focus on BP observable in a wide temperature range on cooling. In the DSC scan of C9 shown in Fig. 1(b), the whole temperature range between the Iso phase and the Nx phase was occupied by BPs, BPIII and BPcub (BPII or BPI), covering 37 K. Although no detectable DSC peaks exist among BPs, texture observation (Fig. 1(c)) indicates the BPIII-BPcub transition occurring at 110.7 °C. Thus, most of the BP temperature range falls into BPcub. It is worth noting that also other homologues with odd n values (>3) exhibit BPcub over ~40 K, again only upon cooling, whereas those with even n values have no BPs but do exhibit the smectic phase as well as the cholesteric phase. This is the widest BP temperature range exhibited by a single compound, even compared with a binaphtyl derivative (~30 K) [21]. There are only a few eutectic LC mixtures composed of achiral or chiral hosts with chiral dopants that have slightly wider temperature ranges of BP; ~44 K [8], and ~38 K [22], compared with the present result. Note that the reported here BP temperature range observed in the present pure compound is comparable even to the BP temperature ranges in these mixtures composed of host and chiral dopants [8, 22]. In the material C9, BPs are also observable on heating, although the temperature range is much narrower, about 2 K, between the Ch and Iso phases.
3. Frequency-sensitive electric field effect in the cubic blue phase
As usual, BP was easily transformed into the Ch phase by shearing a sample (Fig. 2(a), left to middle). The distorted texture induced by shearing, i.e., unidirectionally stretched oily-streak defects, relaxed to a typical Ch texture (Fig. 2(a), right). The transformation from BP to Ch also occurred by applying an electric field (E-field) of low frequencies. Figure 2(b) (second left) displays one example of the changes in the texture by applying a rectangular voltage (10 Hz, 5 Vpp) at 85 °C. At such a low frequency, electrohydrodynamic convection took place and a turbulent state with random director distribution in the sample plane emerged. Once the transition to Ch was achieved, it was not possible to make the system transform back to BP neither thermally or electrically due to the metastability of the vanished BP. Instead, a well aligned Ch structure with its helix axis perpendicular to the surface could be achieved, leading to a transparent/reflective state with a few line defects known as oily streaks (Fig. 2(b), second right). The texture finally relaxed to a smoother state in 5 min after the field termination due to elastic reason (Fig. 2(b), right). In contrast, if a high-frequency (1 kHz) E-field was applied to BP in virgin cells, reflection color of BP slightly changed and returned back to the original color after turning off the field, without transforming to the Ch phase. Thus, two modes depending on the frequency of an applied E-field can be distinguished; transformation from BP to Ch at low frequencies and a stable electro-optic (EO) response within BP at high frequencies due to Kerr effect. Note the excellent stability of BP, i.e., the transformation to Ch was not observed by applying at least 167 Vpp/μm.
Fig. 2 Photomicrographs showing the BPcub-Ch transformation by (a) shearing and (b) E-field application. In (a), textures immediately after shearing (middle) and relaxing (right) are shown. The shearing direction is indicated by a double-headed arrow with “S”. In (b), textures showing the sequential process under field application are shown; 10 Hz E-field application, 1 kHz E-field application, and 5 min after field termination (from the second left to right). Blue arrows indicate that the turbulent and the reflective states can be reversely switched by dual-frequency driving. At 85 °C, the threshold voltage of the electrohydrodynamic convection occurred at 10 Hz and Freedericksz transition occurred at 1 kHz were 4.3 Vpp and 3.1 Vpp, respectively.
4. Kerr effect in the cubic blue phase
The Kerr effect can be considered as a third-order nonlinear optical effect or a second-order EO effect, which is easily observed in polar liquids, such as nitrobenzene. The induced birefringence Δn is expressed by Δn = λKE2, where λ is the wavelength of unpolarized He-Ne laser used (λ = 632.8 nm) and K is the Kerr constant. BPs have cubic symmetries and are optically isotropic, and the birefringence Δn can be induced by applying an E-field due to reorientation of molecules. For the EO Kerr effect measurement, sample was sandwiched in a cell of 2 μm in thickness, which minimizes the E-field gradient in the cell, with in-plane comb electrodes with an electrode gap of 10 μm. To investigate its EO properties, we measured the optical transmittance from the material under crossed polarizers as a function of an applied electric field, and calculated the birefringence. A low-frequency E-field such as 10 Hz was shown to cause electrohydrodynamic convection (Fig. 2(b)), thus a rectangular high-frequency field of 1 kHz was applied. Since the experimentally observed Δn was proportional to E2 (see inset of Fig. 3(a)), at least in a low field region, the origin of induced birefringence was confirmed to be the Kerr effect. Large Kerr constants were observed, and increased with decreasing temperature attaining over 1.3 × 10−9 mV−2 (Fig. 3(a)). This value is relatively large among those in polymer-stabilized BPs [9,11,13,42,43]. Moreover, the Kerr constant seems to vary smoothly across the Iso-BP phase transition. The EO response in a cell with in-plane comb electrodes is stable and occurs repeatedly, as shown in Fig. 3(b). In the absence of an E-field, a dark but bluish texture was seen because of the Bragg reflections from the BP structure. We found that the hysteresis was less than 0.1 V, which was within the margin of uncertainty.
Fig. 3 Results on the Kerr effect measured under an E-field of 1 kHz. (a) Kerr constant as a function of temperature. Δn vs E2 showing the Kerr law is also shown in an inset. (b) Textures showing switching under an in-plane E-field application. Open red arrow is the field direction by comb electrodes. Dark bluish and yellowish colors are due to selective reflection and field-induced birefringence, respectively. (c) Rise (closed squares) and decay (open circles) times at various temperatures by applying 50 V across the electrode gap of 10 μm.
The response time of Kerr switching was measured at various temperatures by applying a pulsed wave with duration of 1 ms and height of 50 V across the electrode gap of 10 μm. The response time is defined as a time needed for the transmittance change between 10% and 90%. As shown in Fig. 3(c), the rise time was almost doubled compared with the decay time, being on an order of several hundreds of μs, but was still less than 1 ms even at the lowest temperature close to the BPcub-Nx transition. These response times are short compared with those in previous studies [10,19,20,44–49], except for a system showing very fast response (although the applied voltage was not shown) [42].
5. Electrostriction effect in the cubic blue phase
When a prolonged electric field was applied, a subsequent slow texture change occurred. Slow changes in reflection color with time and E-field strength, shown in Fig. 4(a), are due to the distortion of the crystallographic lattice of BP (electrostriction effect) [2,50–52]. The electrostriction measurements were made by observing reflection spectra from the BP textures under a square-wave AC field of 1 kHz applied across a 6-μm-thick sandwich cell for 5 min. By applying an E-field, the Bragg reflection peak blue shifted (from green to blue), but returned back to the original color within a few minutes after turning off the field (Fig. 4(a)). It should be stressed that BP remained stable without transforming to the Ch phase, at least under an E-field up to 167 Vpp/μm. Two EO origins, Kerr effect and electrostriction effect, are seen in reflection spectra (Fig. 4(b)). The first immediate reflectance decrease is mainly due to the Kerr effect. A subsequent slow peak shift originates from the electrostriction effect. It is known that the Kerr effect is coupled with the lattice distortion, which also quadratically depends on E. The Bragg reflection peak wavelength is plotted as a function of E in Fig. 4(c). The shrinkage of the cubic lattice of about 7% occurred under an application of 17 V/μm. The shrinkage was smaller compared with those found for low weight molecular systems; a strain over 15% under ~5 V/μm was observed previously [47,53–55].
Fig. 4 Results showing the electrostriction effect measured under an E-field of 1 kHz. (a) Texture changes in a 6-μm-thick cell under sequential application of an E-field, termination, and relaxation. Reflection color changes by E-field application and returns back to the original color in some minutes after termination. Cracks seen in platelets suggest some lattice distortions. (b) Time evolution of reflection spectra under 100 Vpp to a 6-μm-thick cell. (c) Bragg reflection peak against E. Inset reveals the strain u defined by the Bragg reflection peak shift rate, |λ(E) - λ(0)|/λ(0), as a function of E2. Note the existence of two field regions showing different slopes. Here we only use the slope at the low field region to determine the electrostriction coefficient.
Two features should be noted in the present data; (i) the existence of two distinct E-field regions with different slopes, and (ii) very slow response time. We can point out one similar example related to (i). In [8] the authors showed E-dependence of the Bragg peak, and attributed the linear dependence region at high E to the electrostriction effect. However, the electrostriction behavior should be described by E2-dependence. By replotting the data of [8] as a function of E2, we recognized the two distinct E2-dependent regions, in which the higher E-field region has a steeper slope in contrast to our result. We can speculate two possibilities; E-field-induced phase transition to another BP [56] or E-field-induced lattice reorientation (change of diffraction planes) [51,52,57]. In fact, the cracks were observed in platelets upon an E-field application (Fig. 4(a)), as observed in the BP composed of azo molecules by photoisomerization [58], suggesting lattice distortion and rearrangement. The detailed symmetry argument by using the Kossel diagram is definitely necessary and will be our future program. As for (ii), quite slow responses (s or min) were reported in some old reports [53,57,59], but fast responses (ms range) in most previous studies [8,48,49,60], although the response time of the electrostriction effect is slower than that in Kerr effect anyway.
Finally, we estimated the electrostriction coefficient, which is an indicator of how deformable BP lattices are against the applied E-field, in C9 as well as C7 homologue (for comparison) to see the effect of the dimer spacer length. Without considering tensor components of the electrostriction coefficient, the free energy under an E-field can be simply written by using a strain u imposed on a crystallographic lattice as [2], under the assumption of sufficiently small E and u. Here, , and K is a measure of elasticity. By differentiating F with respect to u we obtain, where R is the electrostriction coefficient. By this relation, R values for C7 and C9 in the low field region were determined as 2.20 × 10−16 m2V−2 and 1.02 × 10−16 m2V−2 from the slope of fitting curves shown in the inset of Fig. 4(c), respectively, which are one or two orders of magnitude smaller than those reported previously; typically in the range of 10−15~10−14 m2V−2 [2,51,55]. Moreover, this result provides further insight on the molecular design: dimers with a shorter spacer have a larger electrostriction coefficient, indicating a shorter spacer makes the deformation of BP lattice relatively easier probably because of higher local ordering [61].
6. Conclusions
We found that asymmetric bent dimers consisting of a rod mesogen and a cholesterol mesogen form BPs with a record-wide temperature range among single chiral molecular systems. Moreover, highly stable, fast electro-optic switching is possible, unless a low-frequency E-field is applied. In addition to the stable Kerr effect, the electrostriction effect was also observed. Although the Kerr constant is relatively high, the electrostriction coefficient is one or two orders of magnitude smaller compared with previously reported values. Probably partly because of this, the observed dynamics of the electrostriction were quite slow. Fast and stable Kerr responses together with slow and small electrostriction responses are ideal for display application. It should be noticed that the polymer-stabilized BP does not show the electrostriction. Thus, for E-field dependent photonic devices, the polymer stabilization technique cannot be used and some other stabilization methods are required [54]. In this respect, the present compounds are also valuable and intriguing, since they have small but tunable (by spacer length) electrostriction effect and show very stable EO response.
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