Phase Structure and Phase Transition Mechanism for Light-Induced

Mar 11, 2014 - 2 Experimental Section ... (PF) beamline BL-6A of the high-energy accelerator research organization (KEK), Tsukuba, Japan. ..... 9. Yon...
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Phase Structure and Phase Transition Mechanism for Light-Induced Ia3d Cubic Phase in 4′‑n‑Docosyloxy-3′-nitrobiphenyl-4-carboxlic acid/Ethyl 4‑(4′‑n‑docosyloxyphenylazo)benzoate Binary Mixture Ryo Hori,† Yohei Miwa,*,† Katsuhiro Yamamoto,‡ and Shoichi Kutsumizu† †

Department of Chemistry and Biomolecular Science, Faculty of Engineering, Gifu University, Yanagido, Gifu 501-1193, Japan Department of Life & Materials Engineering, Graduate School of Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan



S Supporting Information *

ABSTRACT: The light-induced smectic C (SmC) to bicontinuous cubic (Cubbi) phase transition was investigated using grazing-incidence X-ray diffraction (GI-XRD) and Fourier transform infrared (FT-IR) spectroscopy to elucidate the mechanism at the molecular level. The sample was a binary mixture of 4′-n-docosyloxy-3′-nitrobiphenyl-4-carboxylic acid with an azobenzene derivative having a similar structure. The GI-XRD analysis revealed that the lattice size of the lightinduced Cubbi phase almost coincides with the extrapolated value of the thermally induced one to the irradiation temperature. The FT-IR analysis also showed that the UV irradiation shifts the peak positions toward their extrapolated wavenumbers that would be displayed by the thermally induced Cubbi phase at the temperature. These results indicate that both the molecular state and periodic structure realized by the irradiation may be regarded as the “postulated” state and periodic structure of thermally induced Cubbi phase at the temperature. This leads to a conclusion that the trans−cis photoisomerization of the azobenzene derivatives in the mixture gives rise to destabilization of the SmC phase with layered structure, alternatively favoring the formation of the Cubbi phase with a twisted molecular arrangement. G′ ≈ 106 Pa), whereas the SmC phase with a 1D layered structure is optically anisotropic and relatively fluid (G′ ≈ 103 Pa).20,26 Although the morphologies and physical properties are largely different between the two LC phases, interestingly, the difference in the enthalpic state is usually quite small (typically a few kJ mol−1).19,24,29 This suggests that these LC phases are thermodynamically close to each other.7,24,28,29 Thus, a possibility is expected that the phase transition can be induced with small stimulation, such as externally driven comformational change of some constituent molecules. Recently, the authors first demonstrated the reversible switching between the SmC and Cubbi LC phases by UV/vis light irradiations for mixtures composed of ANBC-22 and ethyl 4-(4′-n-docosyloxyphenylazo)benzoate (AZO-22).30 The structures of the ANBC-22 and AZO-22 are shown in Chart 1. Examples of the trans−cis isomerization of the azobenzene unit under UV/vis irradiations are well-documented, and many possibilities have been suggested for the control of various LC organizations,31−35 including a few examples for the Cubbi

1. INTRODUCTION Thermotropic bicontinuous cubic (Cubbi) liquid crystals (LCs) have been the subject of intense attention in soft matter science.1−11 In the Cubbi LCs, two chemically incompatible moieties such as aromatic cores and alkyl tails are both continuous in three dimensions and one forms interwoven networks in harmony with cubic symmetry, although locally molecular diffusional motions are comparable to the normal liquid. In the early 1990s, the examples of thermotropic Cubbi LC phase were limited, but to date the number has been increasing largely, as one of the authors reviewed recently.10 In contrast to the lyotropic LC systems,2,12−15 however, why and how the single constituent molecules thermotropically selforganize into the Cubbi LCs having network structure is still a mystery. 4′-n-Alkoxy-3′-nitrobiphenyl-4-carboxlic acid (denoted as ANBC-n, where n denotes the number of carbon atoms in the alkoxy group) is a representative Cubbi-phase forming molecule;16−30 it forms two kinds of Cubbi phases, Ia3d and Im3m types, in addition to smectic C (SmC) LC phase, depending on the length of the alkyl tail and temperature.19,25,26 Because of the 3D symmetric structure, the Cubbi phase is optically isotropic and viscous (storage modulus © 2014 American Chemical Society

Received: December 31, 2013 Revised: March 8, 2014 Published: March 11, 2014 3743

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into ethyl 4′-hydroxybiphenyl-4-carboxylate, which was then reacted with 1-bromodocosane to produce ethyl 4′-ndocosyloxybiphenyl-4-carboxylate. The hydrolysis of this ethyl ester was the next step, followed by nitration, giving the final product of ANBC-22. The sample was purified by repeated recrystallizations from ethanol and confirmed to be fully pure by 1H NMR, thin layer chromatography, and elemental analysis. AZO-22 was prepared according to the method described by Ortega and co-workers (tetradecyloxy analogue of AZO-22) and Serrano and co-workers.30,47,48 The starting material, ethyl 4-aminobenzoate, was coupled with phenol into ethyl 4-(4′hydroxyphenylazo)benzoate by diazo coupling, which was then reacted with 1-bromodocosane to produce AZO-22. The sample was purified by repeated recrystallizations from acetone and confirmed to be fully pure by 1H NMR and thin layer chromatography. Preparation of Binary Mixtures. ANBC-22 and AZO-22 were first dissolved in tetrahydrofuran with the molar ratio of 80:20 (mol/mol), and then the solvent was removed at approximately 376 K. After that, the mixture was heated to about 500 K and then quenched to a room temperature and ground using an agate mortar into a fine powder before use. Homogeneity in the binary mixture was checked by differential scanning calorimetry (DSC), and agreement of the phase transition temperatures obtained was fairly good between three portions of the same mixture. 2-2. Measurements. Nuclear Magnetic Resonance. 1H NMR spectra were recorded on JEOL JNM-ECA600 (600 MHz) spectrometer. CDCl3 was used as solvent and tetramethylsilane as an internal standard. Differential Scanning Calorimetry. Phase transitions were determined by using a Seiko Denshi DSC-200 interfaced to a TA data station (SSC 5000 system) at a heating/cooling rate of 5 K min−1 under a dry N2 flow of 40 mL min−1. Transmission X-ray Diffraction. XRD patterns at elevated temperatures were obtained for powder samples using a Rigaku NANO-Viewer IP system, which was operated with a copper target at 45 kV and 60 mA. The Cu Kα radiation (wavelength λ = 0.15418 nm) was focused with a Confocal Max-Flux (CMF) mirror and collimated into the sample using a three-slit system. The sample was inserted into a drilled hole in a brass plate sealed with Kapton windows at both sides, which was placed in a heated cell with the temperature controlled to within ±0.1 K by a Rigaku Thermo Plus 2 system. The accuracy of the temperature was checked using a calibrated iron−constantan thermocouple. The scattered X-rays were recorded on a twodimensional imaging plate (IP). The intensities were radially integrated and averaged and redistributed when converting the pixel number into the corresponding scattering angle 2θ to produce a circularly averaged pattern. The 2θ values (or the reciprocal spacings) of the pattern were calibrated using standard materials (α-stearic acid and silver behenate at 298 K). Grazing-Incident X-ray Diffraction. GI-XRD measurements were carried out at the Photon Factory (PF) beamline BL-6A of the high-energy accelerator research organization (KEK), Tsukuba, Japan.30,46 The wavelength λ of the X-rays was 0.15 nm, and α-stearic acid and silver behenate was used as standard materials for the calibration. The sample-to-detector distance was ca. 650 mm. A set of aluminum foil strips was employed as semitransparent beam stops because the intensity of the specular reflection from the substrate is much stronger than the intensity of GI-XRD from the sample near the critical angle.

Chart 1

phases.36,37 In most cases, accumulation of cis isomers decreases the order of the LC structure. This tendency is quite reasonable because the presence of cis isomers with a bent molecular shape must decrease the efficiency of the molecular packing and orientation. As a consequence, the isotropic liquid state is induced from the nematic (N)38 or smectic LC phases,39−41 and the pitch and color were modulated in the cholesteric phase,42 under UV irradiation. On the other hand, in our case, the generation of the cis isomers increases the phase dimensional order from the 1D SmC to the 3D Cubbi phases. In other words, the bent molecules of AZO-22 seems to stabilize the Cubbi phase. How does the AZO-22 work on the formation of the Cubbi phase? Moreover, how is the phase structure of the light-induced Cubbi phase related with that of the thermally induced one? These are not only curious but also an important key for universal understanding of the mechanism of the Cubbi phase formation. In the present paper, the mechanism of the light-induced phase transition in the ANBC-22/AZO-22 system was studied mainly by Fourier transform infrared (FT-IR) spectroscopic and grazing-incidence X-ray diffraction (GI-XRD) techniques. FT-IR is a powerful technique to reveal changes in intermolecular interactions and molecular geometry in LC molecules at phase transitions.21,43,44 In our previous work, changes in the conformational structure of the alkyl tail and interactions between the molecular cores were studied in detail for the ANBC-n at the phase transitions.21 In the present work, such information was obtained for the light-induced phase transition by FT-IR. Moreover, the lattice size and its temperature dependence for the light-induced Cubbi phase were investigated by GI-XRD.45,46 Interestingly, the lattice size of the light-induced Cubbi phase almost coincides with the extrapolated value obtained from the temperature dependence for the thermally induced Cubbi phase. This implies that the intermolecular interactions and periodic structures are similar between these two Cubbi phases having different origins (i.e., light-induced and thermally induced). Effects of the isomerization of the AZO-22 induced by UV irradiation on the SmC phase structure and the formation of the Cubbi phase are discussed.

2. EXPERIMENTAL SECTION 2-1. Sample Preparation. Materials. The starting materials were purchased from Kishida Chemical and Nacalai Tesque. The solvents were purchased from Kanto Chemical and Nacalai Tesque. All chemicals and solvents were reagent grade and used as received. Preparation of ANBC-22 and AZO-22. The preparation of ANBC-22 was reported previously.16,19,26,30 The starting material, 4′-hydroxybiphenyl-4-carboxylic acid, was esterified 3744

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The samples were mounted on a homemade z axis goniometer with TJA-550 temperature controller manufactured by AS ONE. The grazing angle (αi) of the X-rays between the X-rays and the sample surface was ∼0.174°. The ∼1.4 μm thick sample was mounted on the glass substrate. The glass substrates were first washed with a soap solution, and then soaked in a 1 mol % aqueous solution of KOH for 1h, followed by rinsing with water, and were finally soaked in 2-propanol and dried before use. The sample thickness was adjusted with a PET film spacer of a defined thickness (1.4 μm). UV irradiation (350−370 nm) was carried out using an ultrahigh-pressure mercury lamp [Ushio SX-UI501HQ (500 W)] with appropriate glass filters UVD-350 (AGC Techno Glass) and HAF-50S-30H (Sigma Optics). The UV intensity at the sample position was estimated at ∼25 mW cm−2. Fourier Transform Infrared Spectroscopy. Spectrum 400 FT-IR spectrometer manufactured by Perkin-Elmer was used for measurements. The temperature was controlled using Variable Temperature Cell with Specac 4000 temperature controller. The optical and digital resolutions were 2 and 0.25 cm−1, respectively. Triglycine sulfate (TGS) was used as a detector and more than 32 scans were typically integrated. An experimental spectrum was fitted using Gaussian function, and the wavenumber at the peak was determined. UV irradiation was carried out using the ultrahigh-pressure mercury lamp system, and the intensity at the sample position was estimated at ∼25 mW cm−2.

Figure 1. 2D-GI-XRD patterns for ANBC-22/AZO-22 binary mixture at 375 K: (a) before irradiation, (b) in 60 s after UV irradiation, and (c) in 60 s after termination of the irradiation. 1D-XRD profiles at qz = 0 for each state are shown in (d).

3. RESULTS 3. 1. GI-XRD Measurements. The binary mixture containing 20 mol % of AZO-22 exhibits a phase sequence of Cr−SmC−Ia3d−Im3m−IL in the bulk state with increasing temperature (Figures S1 and S2 of the Supporting Information).30 This phase sequence was kept even for the thin sample with the thickness of ∼1.4 μm (Figure S3 of the Supporting Information). Moreover, the phase transition temperature, the value of lattice constant a, and its temperature dependence were identical between the bulk and thin samples (Figure S4 of the Supporting Information). Namely, effects of the decrease in the thickness were little on the phase behavior for the ANBC-22/AZO-22 binary mixture. Figure 1 shows the 2D GI-XRD patterns and their in-plane 1D profiles for the ANBC-22/AZO-22 binary mixture before, under, and after UV irradiations at 375 K cooled from 415 K. Without the UV irradiation, one arc corresponding to (001) reflection of the SmC phase was observed in the 2D GI-XRD pattern because 375 K is about 13 K below the Ia3d to SmC transition temperature on cooling (Figure 1a). The d of the SmC phase determined from the in-plane 1D profile is 5.48 nm (Figure 1d). In 60 s under the UV irradiation, the (001) reflection of the SmC phase vanished and spot-like diffractions appeared (Figure 1b); the two peaks in the in-plane 1D profile are assigned to (211) and (220) reflections of the Ia3d Cubbi phase, as shown in Figure 1d. Namely, the transition from SmC phase to Ia3d Cubbi phase was induced via the UV irradiation. On the other hand, the original diffraction from the SmC phase was recovered after the termination of the UV irradiation (Figure 1, panels c and d). In case of our previous GI-XRD experiment for the light-induced phase transition, it was found that some portion of the diffraction from the SmC phase remained even after UV irradiation for a long period such as 36 min.30 On the other hand, in the present work, the quick response of the light-induced phase transition has been

Figure 2. Relationship between lattice constants (a’s) for thermally induced and light-induced Cubbi phases. The a for the thermally induced one is linearly least-squares fitted. The vertical dotted line is the transition temperature from SmC to Cubbi phase determined by DSC.

achieved, owing to the optimization of the experimental conditions such as the UV intensity. In Figure 2, the lattice constant, a, for the light-induced Cubbi phase is plotted against temperature together with that for the thermally induced phase. The a for light-induced Cubbi phase, ∼12.8 nm, is distinctly larger than that for the thermally induced phase, ∼12.4 nm. Furthermore, if those values are compared at each irradiation temperature, the a for lightinduced Cubbi phase coincides fairly well with the extrapolated value from the temperature dependence of the a for the thermally induced Cubbi phase. 3. 2. FT-IR Measurements. FT-IR spectra for the ANBC22/AZO-22 binary mixture at 376 K with and without the UV irradiation are compared in Figure 3. The peaks at ∼2924 and 2853 cm−1 are assigned to asymmetric and symmetric stretching vibrations of C−H [νas(C−H)CH2 and νs(C− H)CH2] at the alkyl chain, respectively. The peaks at 1715, 1690, and 1609 cm−1 are assigned to stretching vibrations of 3745

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Figure 4. Temperature dependences of peak frequencies for (a) νs(C− H)CH2, (b) νas(C−H)CH2, (c) ν(CO)dimer, (d) ν(CO)monomer, and (e) ν(CC) without UV irradiation (green empty symbols) are shown. Frequencies before and after UV irradiation at 376 K are shown with red empty and filled symbols, respectively. Arrows indicate the direction of the peak shift. Red dashed lines are linearly leastsquares fits for the thermally induced Cubbi phase region.

Figure 3. FT-IR spectra of ANBC-22/AZO-22 binary mixture with (red) and without (blue) UV irradiation at 376 K. (a) Overall and magnified views for (b) νas(C−H)CH2, (c) νs(C−H)CH2, (d) ν(C O)monomer (weaker absorption) and ν(CO)dimer, and (e) ν(CC) are shown. The arrows indicate peak shift direction by UV irradiation. Dashed curves in (d) are fitted curves for ν(CO)monomer and ν(C O)dimer components with Gaussian function.

4. DISCUSSIONS 4. 1. Structure of Light-Induced Ia3d Cubbi Phase. The ANBC-22/AZO-22 binary mixture shows the SmC and Ia3d Cubbi phases in the temperature ranges of 337−388 K and 388−409 K, respectively, on the cooling process (Figure S1 of the Supporting Information). However, as shown in Figure 1, even at 375 K, at which the SmC is thermally stable, the Ia3d Cubbi phase was induced via UV irradiation. Moreover, the phase transition was reversibly controllable by UV irradiation. Does the light-induced Cubbi phase have the same phase structure with the thermally induced one? In this section, how the structures are different between the light- and thermally induced Ia3d Cubbi phases is discussed. In the case of the thermotropic LC systems composed of rodlike molecules, the Cubbi phase is considered to be induced by the balance between interactions for molecular cores and lateral thermal expansion of alkyl tail.22,26,27,49−52 Namely, stacking interactions between molecular cores, such as a dipole−dipole interaction for nitro groups, hold the side-byside parallel packing of LC molecules. On the other hand, the thermal expansion of the alkyl tails disturbs the side-by-side packing and destabilizes layered structure in the smectic phase as illustrated in Figure 5a. In the Cubbi phase, the arrangement of the constituent molecules is twisted with each other as a consequence of the competition of these effects.50−52 Here, the lattice constant, a, is a measure of the twisted molecular arrangement in the Cubbi phases. That is, if the alkyl tail is largely expanded, the extent of twisted arrangement of neighboring molecules would be larger; thus, a unit lattice of the Cubbi phase should be built up with smaller number of molecules and the a reduces.51 As shown in Figure 2, the a for the light-induced Ia3d Cubbi phase, ∼12.8 nm, is larger than

isolated carbonyl CO [ν(CO)monomer], hydrogen-bonded carbonyl CO [ν(CO)dimer], and phenyl ring CC [ν(CC)], respectively.21 The frequencies for the νas(C− H)CH2, ν s(C−H)CH2, ν(CO) monomer, and ν(CO)dimer increased under the UV irradiation, while the frequency of the ν(CC) decreased. It is well-known that the higher frequency shifts of the νas(C−H)CH2 and νs(C−H)CH2 reflect the disordering of chain packing and the introduction of gauche conformers on the alkyl chains.21,43,44 The increase in the frequencies of the ν(CO)monomer and ν(CO)dimer indicate reduction of intermolecular interactions of the carbonyl group. In particular, the increase in the frequency of the ν(CO)dimer suggests weakening of the intermolecular hydrogen bonding. On the other hand, the decrease in frequency of the ν(CC) may indicate an increase in the π−π stacking interaction between neighboring molecules. In Figure 4, the temperature dependences of the frequencies for the five peaks without UV irradiation are shown. The frequencies for the νas(C−H)CH2, νs(C−H)CH2, ν(CO) monomer, and ν(CO) dimer peaks increase with an increase in temperature and show a steplike increase at the SmC−Ia3d transition, whereas the ν(CC) peak shows the opposite behavior. The data points above the SmC−Ia3d transition temperature are linearly least-squares fitted and extrapolated to lower temperatures including 376 K. The frequencies for the νas(C−H)CH2, νs(C−H)CH2, ν(C O)monomer, and ν(CC) peaks in the light-induced Ia3d Cubbi phase at 376 K show good agreement with those extrapolated values as shown in Figure 4 (panels a, b, d, and e, respectively). On the other hand, in Figure 4c, the frequency for the ν(C O)dimer peak in the light-induced Ia3d Cubbi phase shows slightly lower value compared to the extrapolated one. 3746

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the AZO-22 into the cis isomers, the bent molecules destabilize the layered structure of the SmC phase because of the drawback for the dense side-by-side packing. On the other hand, the Cubbi phase is considered to be more favorable for this situation by taking the twisted molecular arrangement, as shown in Figure 5b. We believe that this is the trigger of the light-induced SmC to Cubbi phase transition. Namely, it is not that the trans− cis photoisomerization of AZO-22 in the mixture directly contributes to the stabilization of the Cubbi phase but that the increase in the cis isomer destabilizes the planar structure of the SmC phase, leading to the formation of the Cubbi phase at the SmC phase temperature. At this point, it may be said that the molecular mechanism is quite similar to that accepted for most of the light-induced phase transitions in the azobenzene/LC mixtures.33,38,39 In the present paper, we have focused the effects of the trans−cis photoisomerization of the AZO-22 on the transition from the SmC to the Ia3d Cubbi transition at which planar molecular arrangement transforms to a twisted one. On the other hand, this system shows a transition between different types of Cubbi phases, Ia3d and Im3m, on varying temperature as shown in Figure S1 of the Supporting Information. In this case, the molecular arrangements in both Cubbi phases are twisted, even though the degree of the twist may be different in these phases. We are considering that the effect of the photoisomerization of the AZO-22 on this transition is of much interest. Probably this may be a more complex subject, but such information is crucial for further understanding the mechanism of the formation of the Cubbi phases, especially of factors discriminating between those Cubbi phases. The project is currently in progress.

Figure 5. Schematic description of SmC−Ia3d Cubbi phase transitions with different driving forces, (a) thermally induced and (b) lightinduced transitions.

that for thermally induced one, ∼12.4 nm. This indicates that the extent of twisted arrangement of neighboring molecules in the thermally induced Cubbi phase is larger than that in the light-induced one. Interestingly, if we compare those at a given temperature, the a value for the light-induced Ia3d Cubbi phase is almost equivalent to the extrapolated value from the temperature dependence of the a for the thermally induced Ia3d Cubbi phase. In other words, the trans−cis photoisomerization of the AZO-22 induces a “postulated” state of thermally induced Ia3d Cubbi phase that is not thermally stable over the SmC phase at those temperatures without the UV irradiation. The FT-IR results support the formation of the “postulated” Ia3d Cubbi phase from the view of the intermolecular interactions. As shown in Figure 4, the FT-IR peaks assigned to the νas(C−H)CH2, νs(C−H)CH2, ν(CO)monomer, ν(C O)dimer, and ν(CC) vibrations distinctly shifted under UV irradiation. The frequencies of four peaks other than the ν(C O)dimer peak at 376 K are in good agreement with those values extrapolated from the temperature dependence in the range of 388−416 K for the thermally induced Ia3d Cubbi phase. One might expect a decrease in the stacking interactions between molecular cores because the photoisomerization of the AZO-22 could expand the distance between the molecular cores. However, the result clearly indicates that the interactions between the molecular cores in the light-induced Ia3d Cubbi phase are comparable to those in the “postulated” thermally induced Ia3d Cubbi phase at the irradiation temperature, 376 K. On the other hand, the ν(CO)dimer peak in the light-induced Ia3d Cubbi phase shows slightly lower wavenumbers compared to the extrapolated values at 376 K. This may indicate that the dimerized carboxylic acid is less affected by the photoisomerization of the AZO-22 because the ANBC-22 forms the hydrogen bond with each other and does not with the AZO-22. 4. 2. Effect of Isomerization of AZO-22 on LightInduced SmC−Ia3d Transition. As illustrated in Figure 5, the smectic phase is stable for dense side-by-side packing of rodlike molecules having strong stacking interactions. In the case of the ANBC-22/AZO-22 binary mixture, the second component AZO-22 takes the trans form of a nearly rod shape in the SmC phase. When the UV irradiation changes some of

5. CONCLUSION We have revealed the change in the molecular state and selfaggregation structure of the ANBC-22/AZO-22 binary mixture during the light-induced SmC to Cubbi phase transition by using GI-XRD and FT-IR. The lattice size a (∼12.8 nm) for the light-induced Cubbi phase at 376 K is in good agreement with the extrapolated value to the temperature of thermally induced Cubbi phase; the thermally induced one is observed above 388 K without UV irradiation. In addition, the UV irradiation shifted the IR peak positions toward the wavenumbers that would be displayed by the thermally induced Cubbi phase at the temperature. These two results indicate that both the molecular state and periodic structure of light-induced Cubbi phase may be regarded as the “postulated” state and structure of thermally induced Cubbi phase at the irradiation temperature; without UV irradiation the latter phase is not thermally stable over the SmC phase at the temperature. Thus, the conclusion derived is that the light-induced Cubbi phase has the same aggregation structure as the thermally induced Cubbi phase but via another driving force: the trans−cis photoisomerization of AZO-22 in the mixture destabilizes the layered structure of the SmC phase, alternatively favoring the formation of the Cubbi phase.



ASSOCIATED CONTENT

S Supporting Information *

Sample preparation, DSC thermograms, transmission XRD patterns, two-dimensional GI-XRD patterns, plots of lattice parameters. This material is available free of charge via the Internet at http://pubs.acs.org. 3747

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS This work was supported in part by Grant-in-Aid for Scientific Research (C) 25410091 from the Japan Society for the Promotion of Science (JSPS). Beam time at PF-KEK provided by Programs 2011G029, 2012G673, 2013G144, and 2013G687 is also acknowledged.



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