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Does Introduction of a Bent Tail Stabilize Biaxiality and Lateral Switching Behavior of Smectic A Liquid Crystal Phases of Rodlike Molecules? Chiharu Koga, Michinari Kohri, Tatsuo Taniguchi, and Keiki Kishikawa J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.9b00589 • Publication Date (Web): 24 Apr 2019 Downloaded from http://pubs.acs.org on April 30, 2019
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Does Introduction of a Bent Tail Stabilize Biaxiality and Lateral Switching Behavior of Smectic A Liquid Crystal Phases of Rodlike Molecules? Chiharu Koga,† Michinari Kohri,† Tatsuo Taniguchi,† Keiki Kishikawa*,†,‡ †
Department of Applied Chemistry and Biotechnology, Graduate School of Science and
Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan ‡
Molecular Chirality Research Centre, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-
8522, Japan *Corresponding Author. E-mail:
[email protected], Phone: +81-43-290-3238.
ABSTRACT
By introducing an oleyl group at the end of the straight rod-like molecule, the effect of the tail shape on the liquid crystallinity, biaxiality, and lateral switching behavior of the smectic A phase was investigated. Three types of molecules possessing a fluorinated phenyl (pentafluorophenyl, 2,3,4-trifluorophenyl, or 2,3-difluorophenyl) group and a cis-octadec-9-enyl group were synthesized, and their liquid crystallinities were compared with the corresponding molecules with a straight alkyl (trans-octadec-9-enyl or n-octadecanyl) group. In switching experiments,
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the molecules with a bent terminal chain showed higher spontaneous polarization (Ps) values than those with a straight terminal chain. Further, the directional changes of the long molecular axes were suppressed for the molecules possessing a bent terminal chain. These results show that the introduction of a bent terminal chain is highly effective for stabilizing ferroelectric switching behaviors.
INTRODUCTION Uniaxial nematic (Nu) liquid crystal (LC) phases in which rod-like molecules only have one directional order are widely used in current LC displays (LCDs); the directions of the molecular long axes in these molecules are changed by an applied electric field in each of the LC switching cells (Figure 1a). Due to collision with the surrounding molecules, the switching movement of each molecule is not smooth, which suppresses a sufficient electro-response in LCDs. In this respect, recently, concern regarding biaxial nematic (Nb) and biaxial smectic A (SmAb) LC phases has increased.1-7 Nb and SmAb LC phases have a lateral directional order in addition to the directional order parallel to the molecular long axis. If each of the molecules has a lateral polarity, each molecule can respond to an applied electric field and switch its short axis directions around the molecular long axis (Figure 1b).1,2,8 The molecular rotational motion of these molecules is expected to be rapid compared with that of the Nu LC phases because of their smaller excluded volume during switching.1,2,9 Studies regarding switching in the Nb and SmAb LC phases are mostly limited to those of bentcore molecules,10-37 disc-like molecules,38-40 and mixtures of these molecules with rod-like molecules,41-47 which are known to be effective. However, these core shape-assisted approaches have the problem of low electro-responsiveness due to the large excluded volume during
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molecular rotation. On the other hand, we previously reported an interaction-assisted approach using a straight rod-like core, and our molecules showed a rapid switching response.48 However, our rod-like molecules had problems such as a high LC temperature range (102-178 ℃) and a low spontaneous polarization (Ps), which was approximately 80 nC∙cm-2 due to the low molecular ordering. Considering the application of biaxial LC molecules to LCDs, it is necessary that the molecules exhibit liquid crystallinity at a lower temperature and have a higher Ps value. In this paper, we describe the stabilization of biaxiality in SmA phases of rod-like molecules by introduction of a bent tail (= oleyl group) and realization of ferroelectrically switchable SmAb phases. To the best of our knowledge, few studies have been conducted that realize biaxiality by effectively using flexible bent terminal chains. We expected the bent tail to lower the LC temperature range and stabilize the molecular biaxiality to increase the Ps value.49,50
Figure 1. Schematic representation of the molecular motions for switching in (a) a uniaxial phase of axially polar molecules and (b) a biaxial phase of laterally polar molecules. The red arrows indicate the molecular dipoles.
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Figure 2. Molecular packing models in our concept: molecules in (a) the uniaxial SmA phase, (b) unstable biaxial SmA phase generated by the introduction of PFA-A interaction, (c) biaxial SmA phase stabilized by the introduction of both PFA-A interaction and bent chains, and (d) polarityswitchable biaxial SmA phase realized by introducing a lateral polarity (the red arrow indicates the molecular lateral dipole). In our concept (Figure 2), to realize ferroelectrically switchable SmAb phases of rod-like molecules, the molecules have the following two features; (1) the core has fluorinated benzoyl and biphenyl groups, and (2) the terminal chain is bent. The first feature is necessary to generate strong intermolecular perfluoroarene-arene (PFA-A) interactions51-74 that change the monoaxial SmA phase (Figure 2a) to the SmAb phase (Figure 2b). Regarding the second feature, the introduction of the bent terminal chain was expected to suppress the tight molecular packing to
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shift the LC temperature range to lower values49,50 and simultaneously stabilize the biaxiality and ferroelectricity due to the increase in the excluded volume of the spin and slide molecular movement (Figure 2c). The tri- and di-fluorinated benzoyl groups play an important role for generating a lateral polarity (Figure 2d),75-78 which is necessary for realizing the polarityswitchable SmAb phase. Based on our concept, we designed simple molecules F5-BB-C18(c), F3-BB-C18(c), and F2BB-C18(c) (Scheme 1) consisting of a fluorinated benzoyl group, a biphenyl moiety, and an oleyl group. Compound F0-BB-C18(c) with no fluorine atoms was synthesized to evaluate the influence of fluorine atoms on the liquid crystallinity. Further, compounds F5-BB-C18(t), F3BB-C18(t), and F2-BB-C18(t) with a trans-double bond and compounds F5-BB-C18(n), F3BB-C18(n), and F2-BB-C18(n) with a normal alkyl chain were synthesized to evaluate the influence of the geometries of the double bond and the existence of the double bond, respectively.
Scheme 1. Molecular structures of the compounds synthesized in this study.
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RESULTS AND DISCUSSIONS Compounds F5-BB-C18(c), F3-BB-C18(c), F2-BB-C18(c), F5-BB-C18(t), F3-BBC18(t), F2-BB-C18(t), F5-BB-C18(n), F3-BB-C18(n), and F2-BB-C18(n) were synthesized as follows (Figure S1). Oleyl alcohol ((Z)-octadec-9-en-1-ol), (E)-octadec-9en-1-ol,
and
1-octadecanol
were
brominated
by
carbon
triphenylphosphine to produce the corresponding alkyl bromides.
tetrabromide
and
Each of the alkyl
bromides obtained was reacted with 4,4’-biphenol to obtain 4-alkoxy-4’-hydroxybiphenyl. Condensation of the corresponding fluorinated benzoic acid with the monoalkylated biphenols produced the compounds. The phase transition behaviors are shown in Table 1 and their DSC charts are shown in Figures S2-S4. The phases were identified by polarized light optical microscopy (POM). The micrographs are shown in Figure 3. Compounds F5-BB-C18(c) and F3-BB-C18(c) exhibited the SmA phase (Figures 3a and 3b), and F2-BB-C18(c) exhibited the SmA and SmCA (Figure 3c) phases. In all these SmA phases, the homeotropic texture in POM appeared to be slightly clouded because of light scattering.(Figure S5) In SmCA phases, the molecules are tilt alternately in opposite directions from layer to layer. During the SmA-SmCA transition (Figure S6), the extinction brushes of the focal conic texture keeps their perpendicular and horizontal directions, though the homeotropic textures change from dark to schlieren textures. Further, two-brush defects are observed in its schlieren textures (Figure S7). These features are consistent with those of the SmCA phase.79,80 These mesophases were observed upon both heating and cooling. In contrast, compound F0-BBC18(c) exhibited the SmA (Figure3d) and SmCA phases only upon cooling. This result indicates that the introduction of the fluorine atoms greatly stabilizes the LC states.
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Table 1. Phase transition behaviors of the compoundsa
a
The transition temperatures (°C) and transition enthalpies (kcal mol−1) were determined by DSC (5 °C min−1) and are given above and below the arrows. Cr, SmA, SmCA, and Iso indicate the crystal, smectic A, smectic CA, and isotropic liquid phases, respectively. b The temperature was measured by POM because the temperature was not observed in the DSC experiment.
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Figure 3. Polarized optical micrographs of (a) F5-BB-C18(c) at 116 ℃ (SmA), (b) F3-BBC18(c) at 104 ℃ (SmA), (c) F2-BB-C18(c) at 88 ℃ (SmCA), (d) F0-BB-C18(c) at 98 ℃ (SmA), (e) F5-BB-C18(t) at 100 ℃ (SmA), (f) F3-BB-C18(t) at 109 ℃ (SmA), (g) F2-BB-C18(t) at 84 ℃ (SmCA), (h) F5-BB-C18(n) at 111 ℃ (SmA), (i) F3-BB-C18(n) at 107 ℃ (SmA), and (j) F2-BB-C18(n) at 110 ℃ (SmA).
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To investigate the influence of the bent terminal chain on the liquid crystallinities, the phase transition behaviors of F5-BB- C18(t), F3-BB-C18(t), F2-BB-C18(t), F5-BB-C18(n), F3-BBC18(n), and F2-BB-C18(n) were compared with those of F5-BB-C18(c), F3-BB-C18(c), and F2-BB-C18(c).
Consequently, the corresponding derivatives showed the similar phase
transitions. F5-BB-C18(t), F3-BB-C18(t), F5-BB-C18(n), F3-BB-C18(n), and F2-BB-C18(n) exhibited a SmA phase (Figures 3e, 3f, 3h, 3i and 3j), and F2-BB-C18(t) showed a SmCA phase (Figure 3g). The orders of the Cr-SmA (or SmCA) transition temperatures are, from the lowest to the highest, F5-BB-C18(c) < F5-BB-C18(t) < F5-BB-C18(n) for the pentafluorobenzoate esters, F3-BB-C18(c) < F3-BB-C18(t) < F3-BB-C18(n) for the trifluorobenzoate esters, and F2-BBC18(c) < F2-BB-C18(t) < F2-BB-C18(n) for the difluorobenzoate esters. The orders of the compounds possessing the cis-octadecenyl, trans-octadecenyl, and n-octadecyl groups can be explained by the difference in the packing tightness of the terminal chains in the crystal states. In this respect, the bent terminal chain, the oleyl group, is the most effective for lowering the melting points of these series of LC compounds. On the other hand, the orders of the SmA-Iso transition temperatures are, from the lowest to the highest, F5-BB-C18(t) < F5-BB-C18(c) < F5BB-C18(n) for the pentafluorobenzoate esters and F3-BB-C18(t) < F3-BB-C18(c) < F3-BBC18(n) for the trifluorobenzoate esters. The order of the SmA-Iso transition temperature in the difluorobenzoate esters is, from the lowest to the highest, F2-BB-C18(c) < F2-BB-C18(t) < F2BB-C18(n). These results suggest that the compounds with the normal alkyl chain have the highest SmA-Iso transition temperatures of each series due to the tight packing structure in the LC phase. However, it is difficult to explain the order of the compounds possessing the cis- and trans-octadecenyl groups. These results may occur because the attractive electronic interactions between the cis-double bonds with weak polarities are stronger than those between the non-polar
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trans-double bonds, though the trans-alkenyl groups are assumed to stabilize the LC states more than the cis-alkenyl groups due to their tight packing.81 To investigate the molecular-packing structures in the LC phases of all the compounds, their one-dimensional and two-dimensional X-ray diffraction (1D-XRD and 2D-XRD) profiles were measured. XRD could not be performed on F0-BB-C18(c) and F2-BB-C18(n) due to their LC temperature ranges observed only on cooling. We attempted to measure the XRD profiles of the SmA phases of F0-BB-C18(c) and F2-BB-C18(n), but only their LC phases were not observed, because their recrystallization occurred. Figure 4 shows the 1D-XRD profiles of F5-BB-C18(c) (SmA), F3-BB-C18(c) (SmA), and F2-BB-C18(c) (SmCA). Three sharp peaks corresponding to d(100), d(200) and d(300) were observed at even intervals in all of these compounds, which are indicative of smectic phases. The broad peaks at 4.1 Å and 4.6 Å are derived from the distance between the cores and that between the molten alkyl chains, respectively. We carefully checked the bilayer periodicity about twice the d(100) in the XRD profiles, but no bilayer periodicity was observed.
In each of the XRD profiles of F5-BB-C18(c) (SmA) and F3-BB-C18(c) (SmA)
(Figures 4a and 4b), a broad peak of about 11 Å, which includes both the repeat distance at which fluorinated and non-fluorinated benzene rings pile up and the repeat distance at which the two different benzene rings contact side by side, is observed. The 1D-XRD profiles of F5-BBC18(t), F3-BB-C18(t), F2-BB-C18(t), F5-BB-C18(n), and F3-BB-C18(n) are shown in Figure S8. Further, F2-BB-C18(c) and F2-BB-C18(t) exhibiting SmA-SmCA phase sequence showed the a slight change (about 1.5 Å) in the layer distance was observed at the SmA-SmCA transition.
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Figure 4. 1D-XRD profiles of (a) F5-BBC18(c) at 100 °C (SmA), (b) F3-BB-C18(c) at 110 °C (SmA), and (c) F2-BB-C18(c) at 86 °C (SmCA).
The XRD profile was
obtained at each temperature during heating process.
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Figure 5. 2D-XRD profiles of (a) F5-BB-C18(c) at 100 °C (SmA), (b) F3-BB-C18(c) at 135 °C (SmA), (c) F2-BB-C18(c) at 98 °C (SmA), and (d) F2-BB-C18(c) at 85 °C (SmCA, the broken lines indicate the direction of the center of the halo). The white arrows indicate the direction of the magnetic field. The layer normal and parallel directions are indicated by solid lines. The enlarged central part was added to the right of each XRD profile. The XRD profile was obtained at each temperature during heating process.
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Figure 5 shows the 2D-XRD profiles of F5-BB-C18(c), F3-BB-C18(c), and F2-BB-C18(c). Each of the samples in the Iso state in a glass capillary tube (diameter: 1.5 mm) was slowly cooled to the smectic phase to obtain a single crystal of the smectic phase under an applied magnetic field (3000 Gauss). The layer normal of the smectic crystals did not always coincide with the magnetic field direction due to the influence of the capillary glass surface. To facilitate the understanding of the packing structures, in each of the profiles, the layer normal and parallel directions are indicated with solid lines. For the F5-BB-C18(c) (Figure 5a), F3-BB-C18(c) (Figure 5b), and F2-BB-C18(c) (Figure 5c), two kinds of halos (11 and 4-4.5 Å) in the lateral direction of the molecule were observed at the equator of the profile, and their layer distances d(100) were observed on the meridian, indicating a SmA phase. From the scattering homeotropic textures in POM and these lateral repeat distances in XRD, it is assumed that these SmA phases locally have biaxiality, though the phases do not show dark schlieren textures like the SmAb phases reported.18,82-84 The directions of the molecular widths of F2-BB-C18(c) (Figure 5d) at a low LC temperature range were inclined to the equator line by 24º, indicating smectic SmCA phase. These XRD results agreed with the aforementioned POM results. The 2D-XRD profiles of F5-BB-C18(t) (SmA), F3-BB-C18(t) (SmA), F2-BB-C18(t) (SmCA), F5-BB-C18(n) (SmA), and F3-BB-C18(n) (SmA) are shown in Figure S9. The molecular packing structures of SmA and SmCA phases were postulated from the 1D- and 2D-XRD results, as shown in Figure 6. Figure 6a indicates the molecular model for F5-BBC18(c), F3-BB-C18(c), and F2-BB-C18(c). Figure 6b shows the molecular packing structure of the SmA phases. The cores have PFA-A interaction between the fluorinated and non-fluorinated benzene rings. In order not to lower the packing density, the bent alkyl chains interdigitate
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between the layers so as to direct their bending directions in one direction. Figure 6c indicates the structure of the SmCA phases. The cores are tilt alternately in opposite directions layer to layer. Because the interlayer distance and the molecular length were almost the same, these core parts were considered to have formed a layer by using the PFA-A interaction to self-organize the adjacent molecules anti-parallel each other.
Figure 6. Estimated molecular packing structures; (a) molecular model for F5-BB-C18(c), F3BB-C18(c) and F2-BB-C18(c), (b) front view of the SmA phase of F5-BB-C18(c), F3-BBC18(c), and F2-BB-C18(c) and (c) front and side views of the SmCA phase of F2-BB-C18(c).
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To investigate the ferroelectric switching behaviors of the molecules, electro-optic measurements were conducted. The samples were sandwiched between two glass plates that were coated with indium-tin-oxide (ITO) and polyimide (anti-parallel rubbing to align the molecules homogeneously). The size of the ITO area was 10 mm × 10 mm, and the cell gap was 5 μm. A triangular wave voltage was applied to the cell while the textures of the sample in the cell were observed by POM. Figure 7 shows the switching current response traces obtained in the LC phases of F5-BB-C18(c), F3-BB-C18(c), and F2-BB-C18(c) under the application of a triangular-wave electric field at 4 Hz (200 Vpp). The peak top voltage is not 0 V under applying the triangular wave voltage at 4 Hz, but each switching peak starts around 0 V. This means that the induced polarity is not be maintained after removal of the voltage. Therefore, we think that this switching should be distinguished from that of general ferroelectric LC phases. As shown in Figures 7a-c, switching current peaks were observed in the LC phases of F5-BB-C18(c), F3-BBC18(c), and F2-BB-C18(c). In addition, these samples responded to an approximately 10-15 Hz triangular voltage. Sharp peaks were observed for F5-BB-C18(c) and F3-BB-C18(c), but the peaks were broad for F2-BB-C18(c).
F5-BB-C18(c) has few lateral polarizations in the
pentafluorophenyl group; the ester groups are assumed to change their polar directions cooperatively under the application of a triangular wave voltage. Moreover, the Ps of F5-BBC18(c) was similar to that of F3-BB-C18(c) (Table 2). Therefore, presumably the sharp peaks of F5-BB-C18(c) and F3-BB-C18(c) are derived from the polarization reversal of the ester group, and the broad peaks of F2-BB-C18(c) are derived from the polarization reversal of both the ester and fluorinated phenyl groups. Accordingly, the PFA-A interaction in F3-BB-C18(c) is assumed to be so strong that the trifluorophenyl group cannot reverse. As shown in Table 2, the order of the Ps values are, from the lowest to highest, F5-BB-C18(n) < F5-BB-C18(t) < F5-BB-
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C18(c) for the pentafluorobenzoate esters, F3-BB-C18(n) < F3-BB-C18(t) < F3-BB-C18(c) for the trifluorobenzoate esters, and F2-BB-C18(t) < F2-BB-C18(c) for the difluorobenzoate esters. Since no switching peaks were observed in their Iso states (Figure S12), it is clear that the peaks are related to the smectic layer structures.
The orders of the compounds possessing n-
octadecanyl, trans-octadecenyl and cis-octadecenyl groups can be explained by the difference in the degree of intermolecular steric interaction between the terminal chains in the polarization reversal. Accordingly, the introduction of an oleyl group is most effective for generating high Ps values in these series of LC compounds.
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Figure 7. Switching current response traces obtained by applying a triangular-wave voltage; (a) F5-BB-C18(c) in the SmA phase (100 °C, 4 Hz, 200 Vpp), (b) F3-BB-C18(c) in the SmA phase (120 °C, 4 Hz, 200 Vpp) and (c) F2-BB-C18(c) in the SmA phase (95 °C, 4 Hz, 200 Vpp). Black arrows indicated the switching current peaks.
Table 2. Comparison of the Ps values of compounds possessing a (Z)-dodec-9-enyl, (E)dodec-9-enyl and dodecanyl groups Compound
Ps (nC∙cm-2)(temp(℃))
F5-BB-C18(c)
176 (100)
F3-BB-C18(c)
164 (120)
F2-BB-C18(c)
287 (95)
F0-BB-C18(c)
−a
F5-BB-C18(t)
119 (100)
F3-BB-C18(t)
135 (120)
F2-BB-C18(t)
166 (95)
F5-BB-C18(n)
20 (115)
F3-BB-C18(n)
78 (120)
F2-BB-C18(n)
−a
a
Not measurable due to the narrow liquid crystal range.
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Figure 8. Change of textures in POM before and after voltage application; (a)(b) F5-BB-C18(c) (100 °C, 4 Hz, 200 Vpp), (c)(d) F5-BB-C18(t) (100 °C, 4 Hz, 200 Vpp), and (e)(f) F5-BB-C18(n) (115 °C, 4 Hz, 200 Vpp). Furthermore, the electro-responsive behaviors of pentafluorobenzoyl esters F5-BB-C18(c), F5-BB-C18(t), and F5-BB-C18(n) in the SmA phase were observed by POM under applying the triangular-wave voltage (Figure 8). In F5-BB-C18(c) (Figures 8a (0 V) and 8b (+100 V)), although the brightness slightly changes, the homogeneous texture remains during the voltage application. This result means that each molecule changed its molecular short axis direction around the molecular long axis under the applied electric field (Figure 9a).85 It is thought that this change in brightness includes those due to increase and decrease in orientation order. In comparison with this result, the textures of F5-BB-C18(t) and F5-BB-C18(n) (Figures 8c, 8d, 8e, and 8f) became dark from the application of the voltage (0 V→+100 V) and after removal of the
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voltage (+100 V→0V) their textures appeared again; each molecule changed the direction of its molecular long axis due to the applied electric field (Figure 9b). It is thought that the direction of the molecule has changed due to the influence of the dielectric anisotropy and the molecular dipole to the applied electric field. The DFT calculation (B3LYP6-31G(d)) showed that all these molecules had similar core shape and molecular dipole direction (Figure S13).
However, the
oleyl group suppresses the directional change of the molecular long axis during the switching process. Accordingly, it is clear that the introduction of an oleyl group stabilizes the lateral switching behavior.
Figure 9. Schematic representation of molecular movements under the application of the triangular wave voltage; (a) directional change of the molecular short axes of the F5-BB-C18(c)
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molecules around their long axes and (b) directional change of molecular long axes of F5-BBC18(t) and F5-BB-C18(n) around their short axes. CONCLUSIONS We synthesized rod-like LC compounds possessing a fluorinated benzoyl group and an alkyl chain and confirmed their ferroelectric switching behaviors. In this study, we found that the introduction of a bent terminal chain was effective not only for lowering the LC temperature ranges but also for increasing the Ps values in switching. These results are surprising because these long alkyl groups are highly flexible compared to the mesogenic cores in the LC temperature ranges. We believe that these results make an important contribution to the study of LC science and the design of LC molecules.
ASSOCIATED CONTENT Supporting Information Figure S1 presents the synthetic routes of the compounds. Their synthetic procedures and spectral data are described. Figures S2-S4 presents their DSC charts. Figure S5 shows microphotographs of slightly clouded homeotropic textures of the SmA phases. Figures S6 and S7 present microphotographs of F2-BB-C18(c) in SmCA phase. Figure S8 shows 1D-XRD profiles of F5-BB-C18(t) (SmA), F3-BB-C18(t) (SmA), F2-BB-C18(t) (SmCA), F5-BB-C18(n) (SmA), and F3-BB-C18(n) (SmA). Figure S9 shows the 2D-XRD profiles of F5-BB-C18(t) (SmA), F3-BB-C18(t) (SmA), F2-BB-C18(t) (SmCA), F5-BB-C18(n) (SmA), and F3-BB-C18(n) (SmA). Figure S10 shows 2D-XRD profiles of F5-BB-C18(t) (SmA), F3-BB-C18(t) (SmA), F2BB-C18(t) (SmCA), F5-BB-C18(n) (SmA) and F3-BB-C18(n) (SmA). Figure S11 shows azimuthal plots of F2-BB-C18(c) (SmCA) and F2-BB-C18(t) (SmCA). Figure S12 shows
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switching current response trace in the Iso state of F5-BB-C18(c) at 140 °C, 4 Hz, 200 Vpp. Figure S13 presents the most stable conformers of F5-BB-C18(c), F3-BB-C18(c), F2-BBC18(c), F5-BB-C18(t), F3-BB-C18(t), F2-BB-C18(t), F5-BB-C18(n), F3-BB-C18(n), and F2BB-C18(n) obtained by DFT (B3LYP6-31G(d)) calculation.
AUTHOR INFORMATION Corresponding Author *E-mail:
[email protected] ORCID identifier 0000-0002-7539-568X Notes There are no conflicts to declare. The manuscript was written through contributions of all authors.
ACKOWLEDGEMENTS This work was financially supported by Japan Society for the Promotion of Science KAKENHI Grant Numbers 17H03035, 25288088. We thank Dr. H. Ozaki who saved KK’s life by an operation for brain hemorrhage five years ago.
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