Solid-State 13C NMR Study of Cholesteric Liquid Crystals - The

Article pubs.acs.org/JPCB

Solid-State

13

C NMR Study of Cholesteric Liquid Crystals

Kazuhiko Yamada,* Kazuhiro Marumo,‡ Sungmin Kang,‡ Kenzo Deguchi,§ Toshihito Nakai,∥ 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 ∥ JEOL RESONANCE Inc., 3-1-2 Musashino, Akishima, Tokyo 196-8558, Japan ABSTRACT: We investigated the structural behavior of cholesteric liquid crystals of 4-(hexyloxy)-4′-cyanobiphenyl (6OCB) in an 11.7 T magnetic field by solid-state 13C nuclear magnetic resonance. Five 6OCB cholesteric liquid crystal systems were prepared with 4-methoxyphenyl 3,4-Oisopropylidene-2,6-bis-O-(4-methylbenzoyl)-β-D-galactopyranoside (CR), in which 6OCB was doped with 0.51, 1.00, 2.34, 5.60, and 6.47 mol % CR, giving products with helical twisting powers (HTPs) of 0.28, 0.54, 1.27, 3.05, and 3.52 μm−1, respectively. Analyses of the alignment-induced shifts showed that the liquid crystals directors in pure 6OCB and 6OCB doped with 0.51 and 1.00 mol % CR become aligned with the 11.7 T magnetic field direction. However, 6OCB doped with 2.34, 5.60, and 6.47 mol % CR retained their cholesteric structures when the magnetic field was applied. The critical HTP value for resisting realignment by magnetic field was estimated to be approximately 1.27 μm−1. A biaxiality of the phase was partially considered during spectral simulations, although the molecular shape of 6OCB can be defined as cylinderical when it is rotating rapidly. Our current understanding is that the order parameters in the cholesteric structures are not uniform; i.e., the molecular directors already aligned almost perpendicular to the magnetic field are significantly perturbed by the external field.

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INTRODUCTION Cholesteric liquid crystals, in which the molecules are twisted perpendicular to the helical direction, the molecular axis being parallel to the director, are used in a number of optical applications such as liquid crystal displays and electronic paper.1,2One of the most important properties of cholesteric liquid crystals is that a specific wavelength can be selectively reflected by controlling the directions in which the molecules are oriented. In general, an external electric or magnetic field is used to control the cholesteric liquid crystal molecular directions, and it is important to understand the ways external fields affect the molecular arrangements and dynamics so that further developments can be made. There is a long history of research into the behavior of cholesteric liquid crystals in magnetic fields. In 1968, De Gennes3 reported a theoretical study of the structural behaviors of cholesteric liquid crystals in a variable magnetic field, and the usefulness of this theoretical treatment was later experimentally demonstrated by Meyer.4 These two pioneering studies formed the foundation of our understanding of the magnetic-field orientation of cholesteric liquid crystals. A cholesteric liquid crystal contains a helical structure in the absence of a magnetic field; however, applying a magnetic field can cause the liquid crystal molecules to be aligned parallel to the magnetic field, distorting the helical structure. The pitch of the helical structure may increase with the strength of the external field, and molecules © 2013 American Chemical Society

can become completely aligned at a critical magnetic-field intensity, forming a nematic structure. Solid-state nuclear magnetic resonance (NMR) spectroscopy is probably one of the most suitable analytical methods for investigating the orientation of liquid crystals in a magnetic field because it can be used to determine detailed molecular properties such as order parameters, molecular structures, and dynamical information on the local structures in a highly homogeneous magnetic field.5,6 A large number of studies of arrangement orders in nematic liquid crystals using solid-state NMR methods have been reported,5−8 but few fundamental NMR studies of cholesteric liquid crystals have been reported. In 1976, Collings and co-workers9 reported, for the first time, that orientational order parameters in a cholesteric liquid crystal could be determined by 19F NMR, and they found that the order parameters resembled those of nematic liquid crystals. Shivaprakash et al.10 also measured the 1H NMR derivative spectra of various cholesteric liquid crystals, although Collings11 commented on the accuracy of their experiments later. Doane and co-workers studied the self-diffusion and biaxiality of cholesteric liquid crystals using 2H NMR.12−14 Solid-state 13C NMR methods have great advantages in this research field over Received: August 30, 2013 Revised: October 31, 2013 Published: November 4, 2013 16325

dx.doi.org/10.1021/jp408683j | J. Phys. Chem. B 2013, 117, 16325−16335

The Journal of Physical Chemistry B

Article

The reaction mixture was refluxed for 24 h and then evaporated to dryness under reduced pressure. The residue was dissolved in chloroform and shaken with water in a separatory funnel. The chloroform layer was evaporated to dryness and the crude product was purified by column chromatography (with SiO2 stationary phase and a CHCl3 mobile phase) and recrystallized from methanol, giving a final yield of 52.3%. CR was purchased from Kanto Chemical Co., Inc. (Tokyo, Japan) and used without further purifications. NMR Measurements. 13 C NMR experiments were performed at 125.774 MHz on an 11.7 T JEOL ECA 500 spectrometer (JEOL, Tokyo, Japan) using a 4 mm magic-angle spinning (MAS) probe between 293 and 373 K. Potassium bromide and adamantane were used to adjust the magic angle and as a reference, respectively. Accumulations of 400−500 scans were sufficient to give most of the NMR spectra presented here. A standard ramped cross-polarization (CP) sequence was used with a mixing time of 1−5 ms and high-power irradiation to achieve heteronuclear decoupling during each detection period. The MAS frequencies were 10 kHz for all the CPMAS experiments. Dipole-dephasing experiments were performed using a gradually increased dipole-dephasing time, to 500 μs so that only peaks from quaternary carbons remained. 2D total sideband suppression (TOSS) reverse-TOSS experiments17 were performed using a MAS frequency set of 2.85 kHz and an offset frequency of 100 ppm. A total of 256 t1 increments were collected. Spectral simulations for Herzfeld−Berger plots18 were performed using the Herzfeld−Berger analysis program (HBA) tool developed by Eichele et al.19 The error bar for each component was estimated to be ±5 ppm. All of the spectral simulations and chemical shift calculations were performed using a program produced by us using MATLAB (Math Works, Inc., Natick, MA, USA).

NMR method that are typically available involving other nuclei, including giving unambiguous and detailed molecular information on the main chains of the liquid crystals. It is generally unnecessary to label a target sample with the 13C isotope for it to be studied by solid-state 13C NMR, which should allow this method to be widely applied in material sciences. Emsley and co-workers15 very recently used residual dipolar couplings between carbon atoms and protons to investigate the conformational changes in 1″,7″-bis(4-cyanobiphenyl-4′-yl)heptanes as it transformed from the achiral nematic to the chiral twistbend nematic phase. To the best of our knowledge, however, there have been very few solid-state studies of the relationship between the cholesteric liquid crystal structures and the strength of the applied magnetic field, despite the importance of this relationship. We performed solid-state 13C NMR study of the structural behaviors of the cholesteric liquid crystals of 4-(hexyloxy)-4′-cyanobiphenyl (6OCB) doped with 4methoxyphenyl 3,4-O-isopropylidene-2,6-bis-O-(4-methylbenzoyl)β-D-galactopyranoside (CR) in an 11.7 T magnetic field. The molecular structure of (a) 6OCB and (b) CR are shown in Figure 1. Instead of placing a single liquid crystal in a variable

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THEORETICAL BACKGROUND When a liquid crystal is aligned in a magnetic field, one of the most important NMR parameters is the alignment-induced shift (AIS) because chemical shifts may be different to those observed in CPMAS or solution NMR spectra. A number of studies about the analysis of AISs by solid-state NMR are reported.5,6 We believe that the theoretical treatment proposed by Miyajima and co-workers,20,21 in which several coordinate systems are defined and used to describe the molecular dynamics of a liquid crystal then sequentially transformed using Wigner rotation matrices, is the most straightforward procedure. Therefore, we followed that procedure, and a brief summary is given below. The chemical shift in the field-aligned molecule, δexp, is expressed as

Figure 1. Molecular structures of (a) 4′-(hexyloxy)-4′-cyanobiphenyl (6OCB) with the atomic labeling as used in this study and (b) 4-methoxyphenyl 3,4-O-isopropylidene-2,6-bis-O-(4-methylbenzoyl)β-D-galactopyranoside (CR).

magnetic field, we studied cholesteric liquid crystals with several pitches at a fixed magnetic field. Compound 6OCB was chosen because its molecular properties are well-known and it is easy to control the pitch of cholesteric liquid crystals of 6OCB by changing the dopant concentrations. The helical twisting power (HTP; in μm−1) is usually used to describe the strength of molecular twisting, and this parameter can be derived by the Cano-wedge method16 or polarization microscopy. We systematically synthesized and studied five cholesteric liquid crystals, 6OCB doped with 0.51, 1.00, 2.34, 5.60, and 6.47 mol % CR, which had HTPs of 0.28, 0.54, 1.27, 3.05, and 3.52 μm−1, respectively.

δexp = −

1 PAS δ00 + 3

2 3

2

∑

δ2PAS m ⟨Dm0(PAS⇒LAB)⟩

m =−2

(1)

where δ is the irreducible spherical tensor in the principal axis system (PAS) and Dm0(PAS⇒ LAB) is the Wigner rotation matrix for the standard transformation from the PAS frame to the laboratory (LAB) frame.22 For a liquid crystal, it is more convenient to include four additional coordinate systems between the PAS and LAB frames, namely, a system for the moment of inertia of a fragment (FRAG), a system for the moment of inertia of a molecule (MOL), a system for the moment of inertia of a molecule as a rigid body (RIG), and a PAS

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EXPERIMENTAL SECTION Samples. Compound 6OCB was synthesized by dissolving 4-cyano-4′-hydroxybiphenyl (5.00 g, 25.6 mmol), potassium hydroxide (7.11 g, 51.2 mmol), and a catalytic amount of potassium iodide in a mixture of acetone (25 mL) and water (10 mL). A mixture of 1-bromohexane (5.05 g, 30.7 mmol) and acetone (10 mL) was added to the solution dropwise. 16326



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The transformation from the RIG to the DIR, which reflects the fluctuation of the molecular axis about the director, may be one of the most important information in the liquid crystals research. The relationships between the RIG and the DIR irreducible spherical tensors are expressed using order parameters, Sii, by

director frame (DIR) with the corresponding Euler angles for the coordinate transformations (Figure 2a).20,21

DIR RIG RIG δ20 = δ20 S00 + δ20 (S20 + S−20)

(4)

δ2DIR ±1 = 0

(5)

and δ2DIR ±2 =

1 RIG 1 RIG δ20 (S02 + S0 − 2) + δ22 (S22 + S2 − 2 + S−22 2 2 + S −2 − 2 )

(6)

where Figure 2. (a) Definitions of the coordinate systems used in this work with the corresponding Euler angles for the transformations. See the text for more detail. (b) Upper, 13C CS tensor directions in 6OCB, with respect to the local molecular structure, and lower, a principal axis moment of inertia system for fragment (FRAG).

S00 =

The three Euler angles used to characterize the coordinate transformation from the PAS to the FRAG are principally determined by the molecular electronic structure. Figure 2b shows the 13C CS tensor directions with respect to the local molecular frame of 6OCB and the FRAG frame. For C(ar)− C(ar) such as at carbon sites 2, 5, 6, and 9 in 6OCB, the δ11 component in the 13C CS tensor is parallel to the C−C bond and the δ33 component is perpendicular to the molecular plane. For C(ar)−H such as at sites 3, 4, 7, and 8, both δ11 and δ22 components lie on the molecular plane and the δ11 component is parallel to the CH bond. For CN such as at site 1, the δ33 component is parallel to the CN bond and the δ11 component is perpendicular to the molecular plane of the benzene ring. Therefore, the Euler angles (60°, 90°, 0°), (0°, 90°, 0°), and (0°, 0°, 0°) are obtained for C(ar)H, C(ar) C(ar), and CN, respectively. In the MOL, the long axis of the molecule is defined as zMOL, and the short axes are defined as xMOL and yMOL, respectively. These parameters can be estimated from the molecular structures or the shapes of a molecule. For 6OCB, it is expected that the directions of zMOL and zFRAG, the z axis in the FRAG, are the same so that βM = 0°. The transformation from the MOL to the RIG reflects the overall rotation of the molecule around its long axis. If the molecule rotates along the axis with more than 3-fold symmetry, indicating that it is regarded as being a uniaxial rigid body, then RIG δ20

=

δ20MOL

(7)

1 (S20 + S−20) = 2

2 ⟨cos 2ϕ sin 2 ϕ⟩ 3

(8)

1 (S02 + S0 − 2) = 2

2 ⟨sin 2 θ cos 2ψ ⟩ 3

(9)

and 1 (S22 + S2 − 2 + S−22 + S−2 − 2) 4 1 = ⟨cos 2ψ (1 + cos2 θ ) cos 2ψ 4 − 2 sin 2ϕ cos θ sin 2ψ ⟩

(10)

The brackets in the above equations imply time averaging. For reference, the order parameter expressions shown above are compared with well-known Maier−Saupe’s order parameters in eqs 11−14:23 S00 = Sz / z

(11)

1 (S20 + S−20) = 2

2 (Sx / z + Sy / z) 3

(12)

1 (S02 + S0 − 2) = 2

1 (Sz / x + Sz / y) 2

(13)

1 (S22 + S2 − 2 + S−22 + S−2 − 2) 4 1 = [(Sx / x + Sy / x) − (Sx / y + Sy / y)] 6

(2)

and RIG δ2RIG ± 1 = δ2 ± 2 = 0

1 ⟨3 cos 2θ − 1⟩ 2

(3)

(14)

The final transformation from the DIR to the LAB is characterized by the polar and azimuthal angles, αL and βL, respectively. For example, βL is the angle between the liquid crystal molecules director and the external magnetic-field direction. Considering all of the above, the chemical shift in the fieldaligned molecule, δexp, in eq 1 can be rewritten as20,21

In this study, the 6OCB molecule is regarded as a uniaxial rigid body, and therefore, biaxial properties of the molecule are ignored for this coordinate transformation, although the biaxiality of the phase expressed by eq 9 was additionally required for simulating 13C stationary NMR spectra for 6OCB doped with more than 2.34 mol % CR. This will be discussed in detail later. 16327



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Figure 3. Plots of helical twisting power (HTP) agianst the dopant concentrations in 6OCB.

Table 1. Phase Transition Temperatures for 6OCB and 6OCB Doped with CR and the Helical Twisting Power (HPT) compound 6OCB 6OCB 6OCB 6OCB 6OCB 6OCB

+ + + + +

CR(0.51 CR(1.00 CR(2.34 CR(5.60 CR(6.47

δexp = δiso +

mol mol mol mol mol

isotropic to nematic

nematic to crystal

HTP/ μm−1

351 348 346 340 329 323

308 308 308 308 303 303

0.28 0.54 1.27 3.05 3.52

%) %) %) %) %)

2 MOL δ20 S00P2(cos βL ) 3

Figure 4. 13C CPMAS NMR spectra acquired at 293 K of (a) 6OCB and (b) 6OCB doped with 5.60 mol % CR.

1 MOL δ20 (S02 + S0 − 2) sin 2 βL 2 2 MOL + δ22 ⟨cos 2(αR + γR )⟩(S20 + S−20)P2(cos θL) 3 1 + δ20MOL⟨cos 2(αR + γR )⟩(S22 + S−22 + S−22 2 +

+ S−2 − 2) sin 2 βL

(15)

where P2(cos βL ) =

1 (3 cos2 βL − 1) 2

(16)

and MOL PASS PASS δ2p = {δ20 D00(αF ,βF ,γF) + δ22 [D20(αF ,βF ,γF)

+ D−20(αF ,βF ,γF)]} × D0p(αM ,γM ,γM)

(17)

Equation 15 can be simplified for the uniaxial molecules to δexp = δiso +

{(δ

33

− δiso)P2(cos βF) +

× cos 2αF sin 2 βF

1 (δ11 − δ22) 2

} × ⟨P (cos β )⟩S P (cos β ) 2

M

00 2

F

(18)

Figure 5. (a) Magnified view of 13C CPMAS NMR spectra and (b) dipole-dephasing NMR spectra of 6OCB at 293 K with spectral assignments. The atomic labeling is given in Figure 1.

The order parameter, S00, can be obtained for each carbon site if the AIS value (i.e., δexp − δiso), the three principal 13C CS 16328



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Figure 6. (a) 2D 13C Toss reverse-Toss spectrum of 6OCB in the crystal phase acquired at the MAS frequency of 2.85 kHz and (b) f 2 projections at 161.2 ppm of the two-dimensional spectrum (left) and the corresponding calculated spectra (right).

tensor values, βM (which may be estimated from the molecular structure), and βL are given.

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the 6OCB 13C CPMAS NMR spectrum. Several doublet peaks were also observed in the NMR spectra of the crystal phases, and these were caused by the presence of two crystallographically different molecules in each unit cell, which was demonstrated in an X-ray diffraction study of 6OCB.24 The average 13C isotropic chemical shifts and chemical shielding tensors for these doublet peaks are used in the later discussion. We will present the spectral assignment for 6OCB in the crystal and liquid crystal phases including molecular dynamics. Then, we will discuss the structural behaviors of the cholesteric liquid crystals in a strong magnetic field in detail. Spectral Assignments and Determination of Order Parameters for 6OCB. For simplicity, we will focus on the aromatic regions of 6OCB. Figure 5a shows a magnified 13C CPMAS spectrum, and Figure 5b shows dipole−dephasing NMR spectrum of 6OCB in the crystal phase. The 13C peaks were successfully assigned using quantum chemical calculations and extrapolating from solution 13C NMR spectra (data not shown), and the spectral assignments are shown in Figure 5 (the atomic labeling is shown in Figure 1a). Four doublet peaks were found for quaternary carbon atoms that may have flexible bonds, and the average chemical shifts were used for these

RESULTS AND DISCUSSION

The HTP is very often used to express the strength of a cholesteric liquid crystal. It is desirable to develop materials that have higher HTPs and that are compatible with liquid crystal molecules as host. The HTP is plotted against dopant concentration in Figure 3, and the slope of the line was 54.4 μm−1 mol−1 (which is the change in HTP with dopant concentration), from which one can find the HTP for any other concentration. The phase transition temperatures for 6OCB and 6OCB doped with CR at 0.51, 1.00, 2.34, 5.60, and 6.47 mol % were determined by differential scanning calorimetry and/or polarization microscopy, and the results are summarized in Table 1, together with the corresponding HTP values. Figure 4 shows 13C CPMAS NMR spectra, acquired at 293 K, of (a) 6OCB and (b) 6OCB doped with 5.60 mol % CR. On rough inspection, there were no differences in the peak positions and numbers of peaks in the two NMR spectra. The dopant NMR peaks can, therefore, be neglected because they are present in such small amounts that they do not affect 16329



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doublet peaks. The C−H carbon sites (4 and 7) had almost identical peak positions, so they were treated together, without distinction. Figure 6a shows the 2D 13C Toss reverse-Toss spectrum of 6OCB in the crystal phase acquired at a MAS frequency of 2.85 kHz. The f1 and f 2 projections are also given, at the side and top, respectively. The aliphatic carbon region is omitted to aid clarity. Only the isotropic chemical shifts were observed in the f1 dimension, whereas both isotropic and sideband shifts were observed in the f 2 dimension. A Herzfeld−Berger plot analysis15 was applied to each cross-section of the spectrum along the f 2 dimension, resulting in the three principal components of the 13C CS tensors. For example, Figure 6b showed f 2 projections at 161.2 ppm in the two-dimensional spectrum (left) and the corresponding calculated spectra (right). The 13C CS tensor results for the aromatic carbons in 6OCB are summarized in Table 2, together with the isotropic chemical shifts. Each component for the 13C CS tensor doublet peaks was averaged. Table 2. Experimental 13C CS Tensors for 6OCB Obtained by 2D Toss Reverse-Toss at 293 K and the Order Parameters at 318, 338, and 348 K S00 site

δiso

δ11

δ22

δ33

318

338

348

2 8 1 4/7 6 3 5 9 av

111.8 118.4 120.3 128 130.8 133.5 144.5 160.1

196 199 225 218 218 230 231 240

114 130 196 143 149 139 178 171

26 27 −60 24 26 31 24 71

0.80 0.77 0.76 0.70 0.69 0.99 0.74 0.70 0.77

0.67 0.64 0.63 0.59 0.58 0.87 0.62 0.60 0.65

0.50 0.47 0.48 0.45 0.44 0.67 0.48 0.46 0.49

Figure 7 shows the 13C CP stationary NMR spectra of 6OCB acquired at (a) 348 K, (b) 338 K, and (c) 318 K. It should be emphasized that the sample was not rotated when these spectra were recorded (unlike for the standard MAS spectra shown in Figure 5), but sharp signals appeared in the NMR spectra, showing that the 6OCB molecules were aligned with the magnetic field. AIS was obtained; i.e., the chemical shifts for the aromatic regions were observed from 130 to 220 ppm (see Figure 5 for comparison). As well as using literature sources of spectral assignments for 4-n-pentyl-4′-cyanobiphenyl (5CB),7 AIS spectral assignments were achieved from the following observations. The AIS values for the quaternary carbon sites (2, 5, 6, and 9) were larger than the AIS values for the C(ar)−H sites (3, 4, 7, and 8).25 The signal intensities were expected to be two times higher for the latter than for the former. The chemical shifts for the nitrile carbon site (1) moved downfield with increasing temperature, whereas the chemical shifts for the other sites (2−9) moved upfield.25 The spectral assignment results are given in Figure 7. A doublet peak split by less than 2 ppm was observed for the C(ar)− H sites (4 and 7), but their values were averaged and treated as one peak because of the difficulties in maintaining a distinction between them. It can safely be assumed that the long axis of the molecule is parallel to the magnetic-field diretion, βL = 0, and biaxiality properties of the molecule are neglected. The well-known Maier−Saupe order parameter, S00, can be obtained for each carbon site using eq 18, and the results for the order parameters at 318, 338, and 348 K are summarized in Table 1.

Figure 7. 13C CP stationary NMR spectra of 6OCB, acquired at (a) 348, (b) 338, and (c) 318 K. The sample was not rotated in the MAS probe. Spectral assignments are given in the figure.

Magnetic Orientations of 6OCB Doped with CR. In general, an external magnetic field will cause the structures of molecules such as 6OCB to align with their helical axes perpendicular to the field. Increasing the strength of the magnetic field will cause the helical structure to be distorted so that its pitch increases gradually. Above the critical strength of the magnetic field, the liquid crystal will be converted into a nematic liquid structure aligned with the magnetic field. We used a fixed magnetic field (11.7 T) in this study, and the HTP values varied from 0.28 to 3.52 μm−1. We expected that cholesteric liquid crystals may have been converted into nematic liquid crystals below a critical HTP value, and vice versa. Figure 8 shows the 13C CP stationary NMR spectra of 6OCB doped with 0.51 mol % CR, acquired at (a) 338, (b) 333, (c) 328, (d) 318, and (e) 308 K. The sharp signals make it obvious that the cholesteric liquid crystals were converted into nematic liquid crystals and were aligned with the magnetic field. Similarly to 6OCB, an order parameter could be obtained for each carbon site using eq 18 and the observed AIS values. Plots of the averaged order parameters for undoped 6OCB (points marked □) and for 6OCB doped with 0.51 mol % CR (points marked ○) against temperatures are shown in Figure 9. The data points in the figure were best-fitted using 16330



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Figure 9. Plots of the order parameters against the observed temperature for 6OCB (□) and 6OCB doped with 0.51 mol % CR (○).

crystals by our group.26,27 Both order parameters appeared to decrease with temperature, and they obeyed the above equation. No difference in magnetic orientation was found between the 6OCB with or without low dopant concentrations. Figure 10 shows 13C CP stationary NMR spectra of 6OCB doped in 1.00 mol % CR acquired at (a) 333, (b) 328, (c) 323, and (d) 318 K. Although some line broadening and baseline distortion were observed, it was actually clear that the cholesteric liquid crystals were aligned with the magnetic field. Interestingly, however, completely different line shapes were found for 6OCB with 6.47 mol % CR, which gave the highest value of HTPs in the present study, at (a) 318, (b) 313, and (c) 308 K (Figure 11). The line-shapes dramatically varied with temperature at the same dopant concentrations. It is important to point out that higher HTPs are observed at lower temperatures because the effect of dopant is positive at larger S00. Thus, the NMR spectrum at 308 K in which one broad peak was found at ca. 132 ppm in the aromatic region, had the highest HTP in this study. As the HTP decreased, a small shoulder peak appeared at ca. 120 ppm, and two peaks became slightly narrower. It is reasonable to assume that the line shapes shown in Figure 11 reflect the presence of helical structures in cholesteric liquid crystals even in the strong magnetic field, and it can safely be assumed that the helical structure directions were perpendicular to the magnetic field, as proposed by Meyer.4 At first, eq 18, in which uniaxial rotation is assumed, was used to simulate the line shapes in Figure 11. According to the field effect on cholesetric liquid crystals, in which, macroscopically, cholesteric liquid crystals are spontaneously twisted nematics,4 eq 18 was integrated in terms of βL, which should have provided the pseudo line shapes of helical structures in the magnetic field. However, it was very difficult or nearly impossible to reasonably reproduce the experimental line shape with our analysis. Therefore, the concept of biaxiality for the phase was introduced; i.e., eq 15 was used and integrated in terms of βL for the spectral simulations, despite no biaxial properties being shown in the 6OCB molecular shape. The upper trace in Figure 12 shows a magnified view of the experimental 13C CP stationary NMR spectra of 6OCB doped with 6.47 mol % CR at (a) 308 and (b) 318 K and the lower trace shows the corresponding best-fitted calculated line shape using eq 15. The order parameters, S00, were assumed to be the same in the spectral simulations as in 6OCB doped with 0.51 mol % CR at the same temperature, and the order parameters of (1/2)(S02 + S0−2) were varied until each

Figure 8. 13C CP stationary NMR spectra of 6OCB doped with 0.51 mol % CR, acquired at (a) 338, (b) 333, (c) 328, (d) 318, and (e) 308 K. a ⎛ T ⎞⎟ S = S0 ⎜1 − ⎝ T* ⎠

(19)

The value of a was found to be 0.13 for both systems, which is consistent with the previous observations for nematic liquid 16331



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Figure 11. 13C CP stationary NMR spectra of 6OCB doped with 6.47 mol % CR, acquired at (a) 318, (b) 313, and (c) 308 K.

in the coordinate transformation from the RIG to the DIR by introducing the following order parameters: (1/2)(S02 + S0−2), (1/2)(S20 + S−20), and (1/4)(S22 + S−22 + S−22 + S−2−2), and this led to the rotating molecule being defined as cylindrical or rugby-ball shapes with biaxial rotation properties with respect to the directors. A simple physical interpretation of this, based on our current understanding, follows. Let us consider that the directors are expressed as unit vectors (zero-origin) and lie on the y−z plane as a projection view, in which the z-axis is the magnetic -field direction and the x-axis is the helical structure direction. Molecule directions along the z-axis imply that directions parallel or nearly parallel to the magnetic field may not be strongly influenced by the external magnetic field. We would expect that such order parameters would be similar to those observed in nematic structures aligned with the magnetic field. However, molecular directors along the y-axis that correspond with the directions perpendicular or nearly perpendicular to the magnetic fields may be greatly disturbed by the

Figure 10. 13C CP stationary NMR spectra of 6OCB doped with 1.00 mol % CR, acquired at (a) 333, (b) 328, (c) 323, and (d) 318 K.

calculated spectrum reproduced the experimental spectrum. The best-fitted averaged order parameters were found to be 0.26 and 0.47 at 308 and 318 K, respectively. The biaxial properties were required to reproduce the experimental NMR spectra of 6OCB with 6.47 mol % CR. Provided that the molecular shape was not approximately cylindrical when it rotated rapidly, the irreducible spherical tensors after the transformation from the MOL to the RIG would become (instead of eq 3), MOL δ2RIG ± 2 = δ 22 ⟨cos 2(αR + γR )⟩

(20)

The parameter ⟨cos 2(αR + γR)⟩ is known as the biaxiality of the molecule.25 This parameter was set to zero in the spectral simulation above. As an alternative, the biaxiality was included 16332



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Figure 13. 13C CP stationary NMR spectra of 6OCB doped with 5.60 mol % CR, acquired at (a) 328, (b) 325, and (c) 318 K.

shows the 13C CP stationary NMR spectra of 6OCB doped with 2.34 mol % CR acquired at (a) 338, (b) 328, (c) 318, and (d) 313 K. It can be seen that the line shape was almost the same at 338 K as those of 6OCB doped with 5.60 mol % CR at all temperatures and of 6OCB doped with 6.47 mol % CR at 318 K. At 313 K, however, 6OCB doped with 2.34 mol % CR gave a different line shape, and small peaks or shoulders were found at 120, 146, and 155 ppm. Unfortunately, however, we could not reproduce the experimental NMR spectrum at 313 K in the present spectral simulations. One possible reason for the different shape is that the 6OCB and/or the dopant started to crystallize, and this is accompanied by the line widths also becoming wider in the aliphatic region and by the continuity of the line shapes being lost (the line shape for 6OCB with 6.47 mol % CR at 318 K was almost the same as that with 5.60 mol % CR at 318 K, but the line shape for 6OCB with 5.60 mol % CR at 325 K was not the same as that with 2.34 mol % CR at 313 K but was the same as that for 6OCB with 2.34 mol % CR at 338 K). Similarly, some baseline distortions observed in Figure 10, in which the line widths in the aliphatic region became wider, may be related to the crystallization of 6OCB and/or the dopant. It is important to remember that the helical cholesteric liquid crystal structure is distorted and the pitch may increase with field strength when cholesteric liquid crystals are placed in a magnetic field. There is complete alignment, like in a nematic liquid crystal, at the critical magnetic-field intensity. Inversely, there is a critical HTP value at a fixed external magnetic field. In this study, the situation changed at an HTP of 1.27 μm−1. Although the data are not shown, 6OCB doped with a dopant

Figure 12. Magnified view of (upper trace) experimental 13C CP stationary NMR spectrum of 6OCB doped with 6.47 mol % CR at (a) 308 and (b) 318 K and (lower trace) the best-fitted calculated lineshape using eq 15.

external field. We believe that this is the origin of the biaxial properties of cylindrical molecules of cholesteric liquid crystals in strong magnetic fields. A decrease in the HTPs results in a lack of constraints on molecular packing. Therefore, the biaxiality of the phase will be expected to be higher with increasing temperature. This may be the reason for the line shapes for 6OCB doped with 6.47 mol % CR dramatically vary between 308 and 318 K. In fact, the biaxiality order parameter was higher at 318 K than at 308 K. Figure 13 shows the 13C CP stationary NMR spectra of 6OCB doped with 5.60 mol % CR acquired at (a) 328, (b) 325, and (c) 318 K. There were two peaks in the aromatic region in each of the spectra, one main peak at ca. 132 ppm and a small peak at ca. 120 ppm. It can be seen that the line shapes became slightly narrower with increasing temperature, which may be reflected by changes in the order parameter, S00. Figure 14 16333



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our experimental conditions. Biaxial properties were partially introduced to simulate the 13C CP stationary NMR spectra of the cholesteric structures, although the molecule was defined as cylindrical in the RIG. This is probably because the order parameters are not uniform, and molecules are strongly disturbed by the external field when the directors are nearly perpendicular to the magnetic fields. Further investigation is required to determine the molecular behaviors of cholesteric liquid crystals in strong magnetic fields, and we successfully demonstrated that solid-state 13C NMR is very useful for such investigations.

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AUTHOR INFORMATION

Corresponding Author

*K. Yamada: phone, +81-3-5734-3602; fax, +81-3-5734-2888; e-mail, [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was financially supported by a Ministry of Education, Culture, Sports, Science and Technology (MEXT), Grant-in-Aid for Young Scientists (B) (22750009). We also thank anonymous reviewers for helpful comments.

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REFERENCES

(1) de Gennes, P. G.; Prost, J. The Physics of Liquid Crystals; Clarendon Press: Oxford, 1993. (2) Collings, P. J.; Hird, M. Introduction to Liquid Crystals; Taylor & Francis: Bristol, PA, 1997. (3) De Gennes, P. G. Calcul De La Distorsion D’une Structure Cholesterique Par Un Champ Magnetique. Solid State Commun. 1968, 6, 163−165. (4) Meyer, R. B. Effects of Electric and Magnetic Fields on the Structure of Cholesteric Liquid Crystals. Appl. Phys. Lett. 1968, 12, 281−282. (5) Emsley, J. W., Ed. NMR of Liquid Crystals; Reidel: Dordrecht, The Netherlands, 1985. (6) Dong, R. Y. Nuclear Magnetic Resonance of Liquid Crystals; Springer: New York, 1994. (7) Emsley, J. W. In Encyclopedia of Nuclear Magnetic Resonance; Grant, D. M., Harris, R. K., Eds.; John Wiley & Sons: Chichester, U.K., 1996; Vol. 4, pp 2788−2799. (8) Dong, R. Y. Advances in NMR Studies of Liquid Crystals. Annu. Rep. NMR Spectrosc. 2004, 53, 67−155. (9) Collings, P. J.; McKee, T. J.; McColl, J. R. Nuclear Magnetic Resonance Spectroscopy in Cholesteric Liquid Crystals. I. Orientational Order Parameter Measurements. J. Chem. Phys. 1976, 65, 3520− 3525. (10) Shivaprakash, N. C.; Shashidhara Prasad, J. Nuclear Magnetic Resonance Spectroscopy in Cholesteric Liquid Crystals. I. Orientaional Order Parameter measuremsts. J. Chem. Phys. 1982, 76, 866−871. (11) Collongs, P. J. Comment on “Nuclear Magnetic Resonance Spectroscopy in Cholesteric Liquid Crystals. I”. Orientaional Order Parameter Measurements. J. Chem. Phys. 1983, 79, 3605−3606. (12) Vaz, N. A. P.; Chidichimo, G.; Yaniv, Z.; Doane, J. W. Space Modulation of Self-Diffusion in the Cholesteric Phase Distorted by a Magnetic Field. Phys. Rev. A At. Mol. Opt. 1982, 26, 637−643. (13) Yaniv, Z.; Chidichimo, G.; Doane, J. W. Deuterium NMR Spectra of the Cholesteric and Blue Phases: A Study of Biaxiality. Phys. Rev. A At. Mol. Opt. 1983, 28, 3012−3019. (14) Blinc, R.; Marin, B.; Pirs, J.; Doane, J. W. Time-Resolved NMR Study of Self-Diffusion in the Cholesteric Phase. Phys. Rev. Lett. 1985, 54, 438−440. (15) Emsley, J. W.; Lelli, M.; Lesage, A.; Luckhurst, G. R. A Comparison of the Conformational Distributions of the Achiral

Figure 14. 13C CP stationary NMR spectra of 6OCB doped with 2.34 mol % CR, acquired at (a) 338, (b) 328, (c) 318, and (d) 313 K.

similar to CR (4-methoxyphenyl 2,6-di-O-acetyl-3,4-O-isopropylidene-β-D-galactopyranoside, at 4.89 mol %) also gave an HTP of 1.27 μm−1,28 when the magnetic orientation was observed at 11.7 T. The critical HTP for cholesteric liquid crystals of 6OCB at 11.7 T is, therefore, estimated to be around 1.27 μm−1.

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CONCLUSIONS We investigated the dynamic behaviors of cholesteric liquid crystals of 6OCB with CR in a strong magnetic field in solidstate 13C NMR experiments. Five cholesteric liquid crystals were prepared and their HTPs were from 0.28 to 3.52 μm−1. Sharp signals were observed in the 13C CP stationary NMR spectra of 6OCB in the nematic liquid crystal phase, indicating that the director was parallel with the magnetic field. 2D TOSS reverse-TOSS experiments in the crystal phase allowed the 13C CS tensors to be derived for the aromatic carbon sites, and the AIS to be obtained, from which the order parameters of S00 were found for each carbon in the nematic liquid crystal phases. The directors for 6OCB doped with CR at 0.51 and 1.00 mol % were found to be aligned with the magnetic fields. However, cholesteric structures were preserved for 6OCB doped with CR at 2.34, 5.60, and 6.47 mol % even in a magnetic field. The critical HTP was found to be approximately 1.27 μm−1 under 16334



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Solid-State 13C NMR Study of Cholesteric Liquid Crystals - The

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