Structural Analysis of a Banana-Liquid Crystal in ... - ACS Publications

†Department of Chemistry and Materials Science and ‡Department of Organic and Polymeric Materials, Graduate School of Science and Engineering, Tok...
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Structural Analysis of a Banana-Liquid Crystal in the B4 Phase by Solid-State NMR Kazuhiko Yamada,*,† Sungmin Kang,*,‡ Koji Takimoto,‡ Masaya Hattori,‡ Kei Shirata,‡ Susumu Kawauchi,‡ Kenzo Deguchi,§ Tadashi Shimizu,§ and Junji Watanabe‡ †

Department of Chemistry and Materials Science and ‡Department of Organic and Polymeric Materials, Graduate School of Science and Engineering, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8552, Japan § National Institute for Materials Science, Tsukuba, Ibaraki 305-0003, Japan S Supporting Information *

ABSTRACT: In this paper, we present a structural investigation of 1,3-phenylene bis[4-((4-10-decyloxyphenyl)iminomethyl)-benzoate], known as a banana-liquid crystal, in the B4 phase, which was performed by solid-state nuclear magnetic resonance (NMR) methodology combined with quantum chemical calculations. The present solid-state NMR measurements including 13C CPMAS, 2D TOSS-deTOSS, dipole-dephase, 1D and 2D EXSY, and MAS-j-HMQC provided accurate spectral assignments and unambiguous NMR parameters such as 13C chemical shift tensors, which were used for construction of the three-dimensional structure with the aid of density functional theory calculations. In the obtained molecular structure, two arms of the bent-core molecule are asymmetrically expanded such that the direction of the dipole moment is off alignment with respect to the middle line of the center benzene ring. It is this antisymmetric structure that is the origin of the twisted helical system in the B4 phase.

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INTRODUCTION It has been shown that molecules containing a bent rigid core, so-called banana molecules, exhibit spontaneous polarization and chirality in their smectic liquid crystal (LC) phases in spite of the fact that the molecule itself is achiral.1 The banana molecules in a 1.3-benzene bis[4-(4-n-alkoxyphenyliminomethyl) benzoate] (P-n-O-PIMB) homologous series, as illustrated in Figure 1a, have various characteristic physical properties in the LC phases, which are classified and designated as B-phases.2 It has been reported by Watanabe et al. that the 1.3-phenylene bis[4-(4-10-decyloxyphenyl)iminomethyl) benzoate] (P10OPIMB) molecule exhibits two types of B-phases: B2 and B4.3 The structural and physical properties of the B2 phase have been well investigated and understood.4 It is a smectic mesophase because its n-director is tilted normal to the layer, while its bent direction remains parallel to the layer, producing macroscopic polar order and chirality in addition to ferro- or antiferro-electric switching features. On the other hand, detailed physical properties of the B4 phase remain uncertain. One of the most interesting features in this smectic phase is the presence of transparency and visible blue color,3 from which the formation of the helical structure is deduced. So far, two models have been proposed to describe such helical structures: the twisted grain boundary (TGB)-like model3 and the helical nanofilament model.5 Although arguments for the packing systems continue, the presence of a twisted conformation in banana molecules is expected to be a © 2013 American Chemical Society

driving force for the formation of the helical structure in both models.3,5,6 Solid-state nuclear magnetic resonance (NMR) has been recently recognized as a powerful tool for investigating the physical properties of LCs in which valuable information, including molecular structures, orientation order, and molecular dynamics, can obtained unambiguously. So far, there have been several papers on solid-state NMR studies of banana LCs.7−12 Regarding the B2 phase, for example, Pelzl et al.7 have investigated the molecular conformation of a banana molecule possessing a chlorine substituent at the 4-position of the central benzene ring on the basis of analyses for the order parameters and the 13C chemical shielding (CS) tensor components. In their study, the effect of the chlorine substituents on the bending angles was discussed. Dong and co-workers8 have also reported that the molecular structures and dynamics of a bentcore mesogen 1,3-phenylene-bis 4-[4-(10-undecenyloxy)-benzoyloxy] benzoate (Pbis11BB) in the B2 and crystal phases are determined by solid-state 2H NMR and 13C cross-polarization magic-angle spinning (CPMAS) NMR, indicating that the banana molecule shows twisted conformations in these two phases and a symmetric structure in the isotropic phase. Kurosu et al.9 and Walba et al.10 have independently discussed the Received: March 5, 2013 Revised: May 8, 2013 Published: May 8, 2013 6830

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Figure 1. (a) Molecular structure of P10-O-PIMB and the atomic labeling used in the present study. (b) View showing the flexible planes in P10-OPIMB. The molecule was conveniently divided into seven parts, and each plane was assumed to be rigid.

time, τ, was 2 ms, and phase-modulated Lee−Goldburg (PMLG) decoupling was applied during the delay time and t1 evolution time to remove proton−proton dipolar interactions. The 1H pulse width for PMLG was adjusted to 2.2 μs, and the MAS frequency was set to 10 kHz. For dipole-dephasing experiments, the dipole-dephasing time was gradually increased to 1 ms so that only the peaks arising from quaternary carbons remained. The 13C 2D exchange spectroscopy (EXSY) was performed at a MAS frequency of 15 kHz with various mixing times such as 1 ms, 100 ms, 1 s, and 2 s. The 1H and 13C π/2 pulse widths were 2.5 and 2.7 μs, respectively. In general, it might be rather difficult to directly obtain exchange rates from the 2D EXSY experiments. To extract the correlation time for the carbon exchange processes, 1D EXSY spectra16 were repeatedly measured with various mixing times from 100 ms to 10 s, providing the exchange rates. The 13C T1 effects and spin diffusion contributions were safely ignored in the exchange calculations, since the corresponding 13C T1 values were longer than approximately 40 s at room temperature. In the 2D TOSS reverse-TOSS experiments,17 MAS frequencies were set to 2.8, 3.4, and 4.0 kHz. A total of 256 t1 increments were collected. Offset frequencies of 100, 130, and 150 ppm were chosen with MAS frequencies of 2.8, 3.4, and 4.0 kHz, respectively. Spectral simulations for Herzfeld−Berger plots18 were performed with the HBA tool developed by Eichele.19 The error bar for each component was estimated to be ±5 ppm. Quantum Chemical Calculations. All the quantum chemical calculations on 13C CS tensors and structural optimizations were performed with the Gaussian 09 program package20 on the TSUBAME2.0 at Global Scientific Information and Computing Center at the Tokyo Institute of Technology. The gauge-induced atomic orbital approach21 was used for CS calculations. In NMR experiments, frequencies of NMR signals are observed relative to those of a reference compound, e.g., tetramethylsilane (TMS) for 13C NMR. Because the quantum chemical calculations give absolute CS values, σii, it is convenient to convert these values into chemical shift values relative to TMS, δii, by

molecular conformations for a Pn-O-PIMB series in the B2 and B4 phases by analyzing 13C CPMAS spectra observed at various temperatures. In particular, Walba et al.10 pointed out that there are a few doublet peaks in the 13C NMR spectra of the B4 phase and attempted to interpret the meaning of these doublets. To the best of our knowledge, however, threedimensional molecular structures of banana molecules in the B4 phase have not yet been reported in spite of their importance. In this paper, we present the three-dimensional molecular structure of P10-O-PIMB in the B4 phase, as determined by solid-state 13C NMR methods combined with quantum chemical calculations. The present investigation is the first step toward the understanding of the complete molecular packing system in the B4 phase.

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EXPERIMENTAL SECTION

Samples. The molecule used in the present study is P10-OPIMB. The synthetic route is described elsewhere.3 In the DSC thermogram, two sharp signals observed at 173.3 and 145.9 °C on the cooling trace correspond to the isotropic−B2 and B2− B4 phase transitions, respectively. Prior to the NMR measurements, the sample packed in an NMR MAS rotor was gradually heated to 220 °C (isotropic phase) and slowly cooled to room temperature inside the NMR spectrometer, and this procedure was repeated. We considered that the room-temperature phase of the molecule was the B4 phase. Solid-State NMR Measurements. 1H and 13C NMR experiments were carried out at 500.194 and 125.774 MHz, respectively, on a 11.7 T JEOL ECA 500 spectrometer using a 4 and/or 3.2 mm MAS probe at room temperature. Potassium bromide and adamantane were used for magic-angle adjustment and chemical referencing, respectively. Accumulations of 100− 300 were sufficient for most of the present NMR spectra. For 13 C CPMAS experiments, a standard ramped CP sequence was used with a mixing time of 5 ms and with high-power irradiation or two-pulse phase modulations13 for heteronuclear decoupling during the detection periods. The MAS frequencies were set to be 5−15 kHz, and the TOSS sequence14 was included prior to the detection periods in the cases of lower MAS frequencies. In MAS-j-HMQC experiments,15 the delay

δii = σ(TMS) − σii [ppm] 6831

(1)

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where σ(TMS) is the absolute CS constant for the 13C nucleus of TMS. This value depends on the specific theoretical method used, and in the present study, 183.2 and 183.7 ppm were used for the theoretical calculations at B3LYP22/6-31G(d,p) and 6311G(2df,2p) levels, respectively. Calculations for geometry optimization were performed at the B3YP/6-311G(2df,2p) level using the initial geometries deduced from the results of the solid-state NMR experiments, and the optimized structures were verified to have an equilibrium geometry by the Hessian index calculated from a vibrational analysis. For theoretical model calculations as given in Figure 6, the geometry optimization for P5-O-PIMB was carried out at the ωB97XD23/6-311G(d,p) level, followed by replacement of one lateral wing with a methoxyl group for reducing calculation costs.

contains an asymmetric structure, i.e., a twisted structure, (2) interconversion happens between two equivalent structures (chemical exchange) with respect to the NMR time scale, and (3) two magnetically inequivalent molecules exist. For reference, no doublet peaks were observed in the solution 13 C NMR spectra. Recently, Dong and co-workers8 reported that in both the crystal and B2 phases of Pbis11BB the doublet peaks originated from asymmetric lateral wings in the molecule. Their conclusion was reached because the doublet peaks appeared from the lateral rings and the carbon bonded to the ester group in the central ring, while singlet peaks for all the carbon sites were found in the central ring except for the abovementioned one. Walba et al.10 also extensively discussed the origin of the doublet peaks in the B4 phase of P9-O-PIMB; however, according to our understanding, no conclusion was reached. Previously, Kurosu et al.9 concluded that the doublet peak for the carbonyl carbons of the ester linkages was attributed to the presence of a twisted structure in the B4 phase, although only one doublet peak was observed owing to the slow MAS experiments in which most aromatic carbon peaks were overlapped by spinning side bands. Figure 3 shows

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RESULTS AND DISCUSSION Figure 2a shows a typical 13C CPMAS spectrum of P10-OPIMB. For clarity, only aromatic and alkoxy carbons are shown.

Figure 3. 13C 2D EXSY NMR spectrum of P10-O-PIMB in the B4 phase. For clarity, the aliphatic region is omitted.

Figure 2. (a) 13C CPMAS, (b) 1H−13C MAS-j-HMQC, and (c) dipole-dephasing NMR spectra of P10-O-PIMB in the B4 phase with some spectral assignments. The atomic labeling is given in Figure 1a.

the aromatic carbon region of the 2D 13C EXSY spectrum of P10-O-PIMB in the B4 phase acquired with a mixing time of 1.5 s. Clearly, there are two pairs of cross peaks between the aromatic carbons in the outer benzene ring (12/12′ and 13/ 13′) but no cross peaks for the doublets. Hence, the possibility of (2) is ruled out. From Figure 2, it is demonstrated that the doublet peaks originate from four quaternary (3, 5, 6, and 9) and Schiff’s base (10) carbon sites without undergoing chemical exchanges, and singlet peaks arise from the central carbon sites (1, 2, and 4), which is consistent with the results for the B2 phase structure by Dong and co-workers.8 Accordingly, the possibility of (3) is excluded and the doublet peaks arise from an antisymmetric structure, i.e., the possibility of (1). It is important to mention that no changes were observed in the 13C isotropic chemical shifts between stationary (in the B4 phase) and solution (isotropic state) NMR spectra, indicating the absence of alignment-induced shifts. In other words, no magnetic-field orientation was detected in the B4 phase. Furthermore, the 1H−13C CP processes, where magnetization transfer is achieved via dipole−dipole interactions, were found

At first glance, there were more carbon peaks than those expected from the molecular structure. Assignment of the 13C peaks could be successfully achieved by quantum chemical calculations, extrapolation of solution 13C NMR (data not shown), and conventional solid-state NMR techniques such as INEPT, MAS-j-HMQ, and dipole−dephasing (Figure 2b and c). Some of the results for the spectral assignments are given in Figure 2 (the atomic labeling is shown in Figure 1a). A total of six doublet peaks was found for alkoxy (a/a′), Schiff’s base (10/ 10′), aromatic (3/3′, 6/6′, and 9/9′), and carbonyl (5/5′) carbon sites. Note that, at this moment, the spectral assignments for the doublet peaks are arbitrary; e.g., one cannot assign the high-field peak of the carbonyl carbon (5′) to that of the left arm of P10-O-PIMB in Figure 1a. Chemical exchanges observed between the aromatic carbons in the outer benzene ring (12/12′ and 13/13′) will be discussed later. The following three possibilities can be considered as reasons for the presence of the doublet peaks: (1) the molecule 6832

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to be effective over a wide range of temperatures for the B4 phase. Therefore, the molecular properties of P10-O-PIMB in the B4 phase are more similar to those of polycrystalline samples than the molecular properties of smectic LCs with planar fluid layers. Solid-state 13C and 15N NMR spectroscopy has made a tremendous impact on structural analysis in materials sciences owing to the availability of advanced procedures for isotope enrichments.24 For example, 13C dipole−dipole interactions provide unambiguous information on atomic distances, by which a three-dimensional structure can be constructed successfully. In the present study, however, another procedure was applied, since no 13C isotope enrichment was carried out. The strategy for the present structural analysis is as follows: First, potentially flexible bonds were predicted from the molecular structure. Second, 13C CS tensors were extracted for these carbon sites, from which the possible conformations were deduced. Finally, quantum chemical calculations were carried out for all the possible conformations so that the most energetically stable one would be the final result. As illustrated in Figure 1b, the present molecule was conveniently divided into seven parts depending on the flexible bonds, and each plane was assumed to be rigid. In the figure, for example, the central ring was referred to as plane 0 and the next plane as plane I, and so on. Because a twisted structure is expected, the lateral wings must be distinguished, e.g., plane I and plane I′. Several solid-state NMR techniques for obtaining CS tensor components have been developed.25 The ideal technique for obtaining complete information on CS tensors is single-crystal NMR experiments. However, large single crystals suitable for NMR experiments are nearly impossible for the present sample. Alternatively, SASS experiments,26 where polycrystalline samples are generally used, are one of the best methods for the present study, but unfortunately, a special NMR instrument is required. Recently, multipulse MAS experiments, such as SUPER and RAI,27 which can recouple the chemical shift anisotropy to obtain powder patterns in the indirect dimension, have become popular because they are suitable for high spinning speeds of up to 15 kHz with a conventional MAS probe. In the present study, the 2D TOSS reverse-TOSS experiment17 was selected because the spectral resolution in the t1 direction is sufficient, and the method does not suffer from the intensity losses normally inherent in TOSS sequences. In fact, all the doublet peaks could be successfully separated, and each peak could be analyzed. Figure 4 shows the 2D 13C TOSS reverse-TOSS spectrum of P10-O-PIMB in the B4 phase acquired at the MAS frequency of 2.8 kHz. Both the f1 and f 2 projections are also given on the side and top, respectively. For clarity, the aliphatic carbon region is omitted. In the f1 dimension, only the isotropic chemical shifts are observed, while, in the f 2 dimension, both isotropic and sideband shifts are observed. A Herzfeld−Berger plot analysis18 can be applied to each cross section of the spectrum along the f 2 dimension, giving the three principal components of 13C CS tensors. In order to obtain reliable results, we carried out the 2D NMR experiments at three different MAS frequencies (2.8, 3.4, and 4.0 kHz), and the resulting values were averaged. Figure 5 shows the f 2 projections at 166.7 ppm of the two-dimensional spectrum in Figure 4 recorded with spinning speeds of (a) 2.8, (b) 3.4, and (c) 4.0 kHz (left) and the corresponding calculated spectra (right). The results for the 13C CS tensors for the doublet peaks in P10-O-PIMB are summarized in Table 1. Clearly, tensor analysis is more advantageous than simply

Figure 4. 13C 2D TOSS reverse-TOSS NMR spectrum of P10-OPIMB in the B4 phase acquired at the MAS frequency of 2.8 kHz. For clarity, the aliphatic region is omitted.

considering the isotropic shifts. Xu et al.28 demonstrated that some of the 13C CS tensor components of 4,6-dichloro-1,3phenylenebis[4′-(9-decenyloxy)-1,1′-biphenyl] carboxylate (10DCIPBBC) were obtained for the crystal phase by 2D CP-SUPER experiments27b for unambiguous spectral assignments of the 13C NMR spectrum. For example, for the carbonyl and aromatic carbons of 10DCIPBBC, which correspond to 5/ 5′ and 3/3′ in the present molecule, respectively, their tensor components are reported as follows: for the former, δ11 = 242 ppm, δ22 = 133 ppm, and δ33 = 111 ppm; for the latter, δ11 = 217.2 ppm, δ22 = 145.2 ppm, and δ33 = 72.2 ppm. Apparently, our spectral assignment is consistent with those reported by Xu et al. Here we will discuss the possible conformations for each plane illustrated in Figure 1b using the obtained 13C CS tensor components and quantum chemical calculations. An analysis of the 13C CS tensors for the doublet peaks of alkoxy carbon sites (a/a′) is expected to be important for deducing torsion angles between planes II and III and between planes II′ and III′. It can be seen from Table 1 that the δ11 and δ22 components as well as the isotropic shifts are almost similar to each other, but a clear difference is found for the δ33 components. To understand such a difference, as shown in Figure 6a, we constructed a simple model of the banana molecule in which the torsion angle between planes II and III (θ) was artificially changed from 0 to 360° in steps of 30°, and quantum chemical calculations for the 13C CS tensors were performed at each step. In this model, the conformation in which the two planes are coplanar and carbon sites (a/a′) are located on the same side of the CN bond in plane II is defined as θ = 0°. Figure 7 indicates the dependence of (a) δ33 and (b) δ22 components on the torsion angles θ for the a/a′ carbons. It can be observed that both components somehow periodically vary according to the change in the torsion angle. The configuration of θ = 180° provides the largest value for the δ33 component, while the configuration of θ = 0° gives a value approximately 9 ppm smaller than that of θ = 180°. On the other hand, both configurations give almost the same values for δ22 components as well as δ11 components (data not shown). In addition, the δ33 component is experimentally reported to be 31 ppm for 1,4-diethoxybenzene29 in which the configuration between the benzene ring and the alkoxy chain30 is θ = 180° in 6833

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Figure 5. Experimental (left) and theoretical (right) NMR spectra of the f 2 projections at 166.7 ppm of the two-dimensional spectrum in Figure 4 at MAS frequencies: (a) 2.8 kHz, (b) 3.4 kHz, and (c) 4.0 kHz.

Table 1. Experimental 13C CS Tensors of the Doublet Peaks in P10-O-PIMBa,b carbon

d11

d22

d33

diso

3 3′ 5 5′ 6 6′ 9 9′ 10 10′ a a′

240 242 256 257 228 224 236 237 233 231 87 87

142 136 122 119 147 147 161 162 150 149 87 86

74 75 122 119 30 29 31 30 79 82 31 26

150.9 150.3 165.5 163.8 134.1 132.1 140.3 139.6 153.7 152.7 67.5 66.2

to one of the lateral wings. It should also be noted that the present theoretical calculations cannot perfectly reproduce the experimental data, but we assume that the trends obtained from the theoretical calculations, such as the periodic dependence of the torsion angles, are true. Overall, the possible conformations of θ are as follows: (plane II/III, plane II′/III′) = (0°, 180°) or (180°, 0°). As mentioned, there were chemical exchanges undergoing in the outer benzene rings, i.e., planes II and II′. It can be deduced from the molecular structure that the molecular motions involve π flip of the phenyl rings, which is generally observed in polymers and organic compounds.32 The fact that only singlet peaks were observed for carbons 11 and 14 also supports the above assignment. The present analysis of the 1D EXSY spectra suggests a rotation rate of the π flip on the order of 5−100 Hz for the molecule in the B4 phase at room temperature, which is in agreement with the results by Walba et al.10 As depicted in Figure 6b, cis and trans isomers must be considered for planes I and I′. Unfortunately, no significant differences within the experimental errors were observed for all the components of the 13C CS tensor for the doublet peaks 9/ 9′ and 10/10′, which could be responsible for the cis/trans configurations. To investigate the origin of these doublet peaks, we again constructed a theoretical model where the torsion angle ∠C8−C9−C10−N, ϕ, was varied from 0 to 360° in steps

Experimental errors for tensor components were estimated to be ±5 ppm. bThe isotropic shifts were obtained from the 1D CP MAS spectrum.

a

the present definition. Moreover, it can be seen from X-ray diffraction studies of similar organic compounds31 that the most stable configuration is either θ = 0° or θ = 180°. Therefore, low-field (a) and high-field (a′) carbon sites could be reasonably assigned to the configurations of θ = 180° and θ = 0°, respectively. Unfortunately, each peak cannot be assigned 6834

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Figure 8. (a) δ33 components and (b) isotropic shifts of calculated 13C CS tensors for 9/9′ and 10/10′ carbon sites in the theoretical model depicted in Figure 6b versus the torsion angle ϕ.

Figure 6. Three theoretical models used in the present study. See details in the text.

kcal/mol). Hence, in the current understanding, those doublet peaks did not arise from the cis−trans isomers but are attributed to the fact that the molecular plane is distorted slightly. Because of the small differences in these 13C CS tensor components, it can be anticipated that such a distortion is relatively small so that we still assume that planes I and I′ are coplanar nearly. Thus, at this moment, the possible conformations of this isomer are expected as follows: (plane I, plane I′) = (cis, cis), (trans, trans), (cis, trans), or (trans, cis). The molecular conformations for the central mesogen moiety of the banana molecules have been previously discussed in detail.33 Next, we define the torsion angle between planes 0 and I as φ (Figure 6c). In this side view, the angle φ increases in an anticlockwise manner from the coplanar position, where the direction of CO (C5 → O) is parallel to that of the C4 → C1 vector, when the CO bond side (lateral wing) is placed to the fore. Using ab initio calculations and solution 2H NMR experiments, Domenici et al.33b demonstrated that the ester group and the inner phenyl rings of the lateral wing (C6C9) favored lying in the same plane, implying that the bonds between OC5 and C5C6 were not flexible. Moreover, the core moiety of the banana molecules showed high flexibility in terms of φ, and it was considered that the conformations might be influenced by subtle intermolecular interactions. Imase et al.33a also reported a conformational analysis of the central mesogenic moiety using density functional theory calculations, in which the φ rotation was relatively free, but the energies were minimum at φ = 49.4 and 130.6°. In their study, the following seven conformers of the mesogen unit, abbreviated as BD, were proposed and analyzed in terms of their energies and 13C isotropic chemical shifts: BD1 (300°, 300°), BD2 (60°, 300°), BD3 (120°, 120°), BD4 (240°, 240°), BD5 (60°, 120°), BD6 (120°, 300°), and BD7 (0°, 0°). The angles in parentheses are those defined in Figure

Figure 7. (a) δ33 and (b) δ22 components of calculated 13C CS tensors for a/a′ carbons in the theoretical model depicted in Figure 6a versus the torsion angle θ.

of 30°, and NMR calculations were carried out for the 13C CS tensors at each step. As illustrated in Figure 6b, when ϕ is 0 and 180°, the corresponding configurations were defined as cis and trans, respectively. Figure 8 displays the dependence of (a) δ33 components and (b) isotropic shifts on the torsion angles ϕ for carbons 9 and 10. The present theoretical results demonstrate that there was almost no difference in the chemical shifts between cis and trans configurations, but the rotational barrier for the bond between carbons 9 and 10 was relatively low (7 6835

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experimental values for the δ22 components differ. Therefore, the possible models for the conformations of the connection between planes 0 and I and between planes 0 and I′ are as follows: (plane 0/I, plane 0/I′) = (60°, 300°), (60°, 120°), or (120°, 300°). So far, we have discussed possible conformations for each component. The final step is to build each component for forming the total structure, carry out the structural optimizations, and calculate the energies for all the possible combinations. We have assumed that the most stable structure is the one in the B4 phase. First, we briefly summarize all the results. We suggested three possibilities for φ in the ester linkages; (plane 0/I, plane 0/I′) = (60°, 300°), (60°, 120°), or (120°, 300°). The cis−trans isomers in plane I and I′ gave four possibilities: (plane I, plane I′) = (cis, cis), (trans, trans), (cis, trans), or (trans, cis). For plane II/II′, molecular motions of π flip of the phenyl ring were observed for both wings, but they were not included in the structural calculations. There were two possibilities for θ for the connections between the outer benzene ring and alkoxy groups: (plane II/III, plane II′/III′) = (0°, 180°) or (180°, 0°). As pointed out by Walba et al.,9 however, it might be possible that the relative abundance for each conformation was not 50% from the peak at 67 ppm in Figure 2a and several doublet peaks in Figure 2c. Hence, it was appropriate to consider and add two additional possibilities for θ: (plane II/III, plane II′/III′) = (0°, 0°) and (180°, 180°). Overall, 48 possible conformations were proposed for the final molecular structure of P10-O-PIMB in the B4 phase, starting from which we performed geometry optimizations. We confirmed that, in all the calculated structures, the initial conformations were maintained during the optimization process, e.g., cis isomers were not converted to trans isomer. For reference, the conformations for (plane 0/I, plane 0/I′) = (120°, 120°), which were ruled out by the present study, were also calculated. All the results are summarized in Table 2, and the energy is expressed as a relative energy with respect to that of the structure with (plane 0/I, plane 0/I′) = (120°, 120°), (plane I, plane I′) = (cis, trans), and (plane II/III, plane II′/ III′) = (0°, 180°). Some conformations gave imaginary frequencies, which are expressed by a dashed line in the

6c; one angle corresponds to the right side and the other to the left side in the lateral wings. Note that the enantiomer was ignored. Obviously, BD1−4 and BD7 were symmetric structures, while BD5 and BD6 were asymmetric ones; thus, we concluded that the lowest energy model, which was also consistent with the previous 13C NMR results,34 was BD5. For the present compound, the doublet peaks for 3/3′, 5/5′, and 6/6′ carbon sites are expected to be influenced by the changes in φ. Unfortunately, however, a statistical difference within the experimental errors is only observed for the δ22 components of C3/3′. To evaluate such a difference, once again, we constructed a theoretical model where the torsion angle ∠C5−O−C3−C2, φ, was varied and NMR calculations were carried out. The results are given in Figure 9, and it is

Figure 9. (a) δ22 components of calculated 13C CS tensors for 3/3′ carbon sites in the theoretical model depicted in Figure 6c versus the torsion angle φ.

observed that the δ22 components are sensitive to changes in φ. Because no literature values were available for the 13C CS tensors and X-ray structures for similar compounds, it was difficult to determine unambiguous values of φ from the δ22 components. Thus, we assumed that the previous results by Imase et al.33a were true; that is, the possible values of φ were 60, 120, 240, or 300°. From Figure 9, it is seen that the δ22 components are different for the values of φ = 60, 120, 240, and 300°, indicating that φ must differ in the lateral wings, since the

Table 2. Relative Energies for Possible Conformations of P10-O-PIMB (plane 0/I, plane 0/I′) (plane I/plane I′), (plane II/III/plane II′/III′) (cis/cis), (180°, 180°) (cis/cis), (180°, 0°) (cis/cis), (0°, 180°) (cis/cis), (0°, 0°) (cis/trans), (180°, 180°) (cis/trans), (180°, 0°) (cis/trans), (0°, 180°) (cis/trans), (0°, 0°) (trans/cis), (180°, 180°) (trans/cis), (180°, 0°) (trans/cis), (0°, 180°) (trans/cis), (0°, 0°) (trans/trans), (180°, 180°) (trans/trans), (180°, 0°) (trans/trans), (0°, 180°) (trans/trans), (0°, 0°) a

(60°, 120°) 0.01

0.17 0.06 0.05 0.09 0.05 0.02 0.17 0.09 0.13 0.01 0.11 −0.02 0.12

(120°, 300°)

(60°, 300°)

(120°, 120°)

0.26 0.37 0.37 0.43 0.24 0.30 0.38 0.39

0.33 0.43 0.38 0.53 0.28 0.28 0.40 0.24 0.28 0.41 0.35 0.43

0.14 0.10 0.10 0.10 0.09 0.04 0.00a 0.06 0.09 0.00 0.04 0.06 −0.01 0.09 0.09 0.14

0.26 0.13 0.18 0.16 0.21

0.29 0.25

The total energy was −1420082.8 kcal/mol, and was set to be zero. 6836

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angles of the ester linkages, φ. From Table 2, it is seen that the energies for structures containing (plane 0/I, plane 0/I′) = (60°, 120°) tend to be smaller than those with (plane 0/I, plane 0/I′) = (120°, 300°) and (60°, 300°). It is also seen that conformational changes in the lateral wings, i.e., cis−trans isomerization and changes in the torsion angles, barely affect the total energy. Because conventional 13C CP MAS experiments hardly allow quantitative determination, there may be cases where multiple structures are mixed on the basis of (plane 0/I, plane 0/I′) = (60°, 120°).

table. It is interesting that the conformation with the lowest energy, the final molecular structure of P10-O-PIMB in the B4 phase, is the asymmetric structure with (plane 0/I, plane 0/I′) = (60°, 120°), (plane I, plane I′) = (trans, trans), and (plane II/ III, plane II′/III′) = (0°, 180°). In Figure 10, (a) side and (b)

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CONCLUSION We have investigated the molecular structure of P10-O-PIMB, one of the classic banana-LCs, in the B4 phase, obtained by solid-state 13C NMR experiments combined with quantum chemical calculations. Six doublet peaks were observed in the 13 C CPMAS spectrum in the B4 phase, and five of them were assigned as quaternary carbons, suggesting that this molecule has an antisymmetric structure. Using the 2D TOSS reverseTOSS experiment, the 13C CS tensors for each doublet peak were obtained, from which possible conformations for the local structure were discussed with the aid of quantum chemical calculations. The total structure was constructed by building each conformation, and using such structures as an initial geometry, optimization geometries were extensively carried out for all the candidates. We have obtained a final molecular structure having the lowest energy in which the two arms of the bent-core structure are found to be expanded asymmetrically. It was postulated that such an asymmetric structure is the origin of the twisted helical system in the B4 phase.

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Figure 10. (a) Side and (b) top views of the molecular structure of P10-O-PIMB in the B4 phase. The direction of the dipole moment is expressed by an arrow.

ASSOCIATED CONTENT

S Supporting Information *

Complete ref 20. This material is available free of charge via the Internet at http://pubs.acs.org.

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top views of the structure are illustrated. The lateral wings spread and the maximum molecular length, a distance between the ends of the lateral wings, is calculated to be 39.3 Å. The torsion angles ∠C2−C3−O−C5 and ∠C2−C3′−O−C5′ are found to be 116.3 and 121.4°, respectively. Moreover, the bond angles ∠O−C3−C4 and ∠O−C3′−C4 are 116.3 and 121.4°, respectively. Thus, the two arms of the bent-core structure are asymmetrically expanded. In the side-view figure, the direction of the dipole moment of this molecule is expressed by an arrow, which is off alignment with respect to the middle line of the center benzene ring. To the best of our knowledge, this is the first report of the detailed molecular structure of classic banana LCs in the B4 phase. Hough et al.5 inferred that the flat layers composed of symmetric molecular structures were not at a thermodynamic minimum and the structures in the layers should bend to decrease the total energy. We believe that this antisymmetric structure is the origin of the twisted helical system in the B4 phase, and further investigations on packing systems are in progress in our laboratory. Finally, it is important to point out that the energy differences among the calculated structures in Table 2 are relatively small. For example, the difference between the lowest value and the second lowest one is only 0.03 kcal/mol. This suggests that the final conformation in the B4 phase is readily influenced by external environments, such as the rate of phase transition into the B4 phase and thermal history. Apparently, the total energy for the banana molecule largely depends on the

AUTHOR INFORMATION

Corresponding Author

*Phone: +81-3-5734-3602 (K.Y.); +81-3-5734-3641 (S.K.). Fax: +81-3-5734-2888 (K.Y.); +81-3-5734-2888 (S.K.). E-mail: [email protected] (K.Y.); [email protected]. ac.jp (S.K.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was financially supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Grant-in-Aid for Young Scientists (B) (22750009).

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REFERENCES

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