High-Resolution 13C NMR Study of an Antiferroelectric Liquid Crystal

Toshihito Nakai, Hiroki Fujimori, Daisuke Kuwahara, and Seiichi Miyajima. The Journal of Physical Chemistry B ... Carlo Alberto Veracini , Marco Geppi...
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J. Phys. Chem. B 1999, 103, 406-416

ARTICLES High-Resolution 13C NMR Study of an Antiferroelectric Liquid Crystal: Verification of the Bent Chain Structure Toshihito Nakai,†,‡ Seiichi Miyajima,*,† Yoichi Takanishi,§ Shohei Yoshida,§ and Atsuo Fukuda| Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan, Department of Biotechnology, Tokyo UniVersity of Agriculture and Technology, Koganei 184-8588, Japan, Department of Organic and Polymeric Materials, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8552, Japan, and Department of Kansei Engineering, Shinshu UniVersity, Ueda 386-8567, Japan ReceiVed: July 13, 1998; In Final Form: October 14, 1998

A high-resolution 13C NMR study is reported on the antiferroelectric liquid crystal MHPOBC, 4-[(1methylheptyloxy)carbonyl]phenyl 4-[4-(octyloxy)biphenyl]carboxylate. The structures of the two alkyl chains, the chiral and achiral chains, are analyzed using isotropic shielding constants, cross polarization efficiency, and the field alignment-induced shifts. A comprehensive theoretical treatment for the alignment-induced shift is given. It is shown that the average direction of the chiral chain deviates from the molecular long axis by as much as 43° (bent chain structure), while that of the achiral chain extends along the molecular long axis. The relationships of this particular shape of the molecule with the emergence of the molecular biaxiality and with the onset of antiferroelectricity are discussed.

I. Introduction In 1989 Chandani et al. confirmed the antiferroelectricity in liquid crystal.1 This happened unexpectedly, in contrast to the case of ferroelectricity which was intended according to Meyer’s broken-symmetry approach.2 Therefore, the microscopic origin for this antiferroelectric dipolar ordering has been left as an important problem to be solved by both theoretical and experimental studies.3 The first antiferroelectric liquid crystalline compound was the one called MHPOBC, 4-[(1-methylheptyloxy)carbonyl]phenyl 4-[4-(octyloxy)biphenyl]carboxylate (Figure 1), in which permanent dipoles are located mainly on the two carbonyl groups and point approximately perpendicular to the molecular long axis. Studies of the optical transmittance spectrum for the bulk sample,1 ellipsoidally polarized light transmittance for free-standing film,4 defect structure observation,5 and also dielectric response6-9 revealed a remarkable microscopic structure for MHPOBC, i.e., compilation of smectic layers with the alternating tilt senses in the adjacent layers (Figure 2). It has long been believed in liquid-crystal science that the molecular long axes, on average, point similar directions for nearby molecules because of packing efficiency and anisotropic intermolecular forces as well as disordered layer structure for smectics. This situation has formed a firm theoretical basis for the elastic continuum description of the liquid-crystalline order, especially of the orientational director. To realize the molecular arrangement in Figure 2, there are a number of requirements for the microscopic interactions: (i) Rotation around the long molecular axis must be highly restricted so that the molecular dipole moments may not be †

Institute for Molecular Science. Tokyo University of Agriculture and Technology. § Tokyo Institute of Technology. | Shinshu University. ‡

Figure 1. Molecular structures of MHPOBC and TFMHPOBC. The carbon numbered as 23, indicated by an asterisk (*), is the chiral center. The methyl group with a carbon numbered as 30 for MHPOBC is replaced by a trifluoromethyl group in TFMHPOBC.

Figure 2. Schematic structural model for the antiferroelectric chiral smectic C (SCA*) phase with the alternating tilt sense for adjacent layers and the ordered arrangement of dipole moments.

averaged out and have residual components perpendicular to the layer normal. (ii) Layer structure must be rather distinct, meaning that the number density of molecules at the layer boundary is very low, in order to be free from serious alignment defect. (iii) There must be some interlayer interactions that stabilize antiparallel dipolar ordering between the molecules belonging to adjacent layers. The third requirement is a

10.1021/jp9829952 CCC: $18.00 © 1999 American Chemical Society Published on Web 01/05/1999

Study of an Antiferroelectric Liquid Crystal completely novel aspect in structures and intermolecular interactions in liquid crystals. To explain the microscopic origin for these interactions, a number of models have been proposed. Fukuda et al.3 proposed that the two molecules belonging to the adjacent layers form antiferroelectric pairs through direct dipole-dipole interactions. Miyachi et al.10 considered that dipoles gathering in the layer boundaries with a ferroelectric interaction interact antiferroelectrically across the layers (Px model, Figure 2). Takanishi et al.11 proposed a defect-induced macroscopic electric force acting between the layers. Prost and Bruinsma12,13 theoretically showed that fluctuating local spontaneous polarizations within each layer induce antiferroelectric coupling across the layers. While all these models emphasize the role of electric interactions, Nishiyama and Goodby14 showed that steric interactions between the chains may assist to form similar anticlinic layer stacking, even for apparently nonchiral molecules, if the molecules have split-tail chains. Recent theoretical calculation by Vanakaras et al.15 showed that an assembly of model molecules having two flexible tails in opposite ends condense in both synclinic and anticlinic layer orders. Direct dipole coupling models3,11 seemed to have serious difficulties in that they require unusually strong intermolecular dipole-dipole interactions acting across the layers. First, the potential barrier hindering the molecular rotation around its long axis does not seem to be high because of the rodlike shape of the molecule, so that the residual transverse dipole moment of the molecule is not very large if it is averaged over molecular rotation. Second, considering that the carbonyl groups which carry the largest dipole moments are located near or within the molecular core, the tail chain may obstruct the close intermolecular approach of the dipole moments across the layers. Then the intermolecular dipole-dipole interactions cannot be so strong as to induce interlayer dipolar ordering. An alternative microscopic model of the chain steric effect14 lacks general applicability. Hori and Endo16 showed by X-ray crystallographic analysis that in one of the crystalline modifications (a metastable phase at room temperature which is readily formed from organic solvent) of MHPOBC, the chiral chain is bent at the C(23) position while the achiral chain is straight (see Figure 1 for the numbering of the carbons). If this molecular structure (bentchain form) is adopted in the antiferroelectric liquid-crystalline phase, the most serious difficulties in the dipole-coupling model seem to be relieved: a bent shape is compatible with strong biaxiality of the molecule and consequently the large residual dipole moment. It also enables the carboxyl groups to come in close contact between the molecules across the layers. The attractive bent chiral chain structure, however, has not been verified experimentally in the liquid-crystalline states. We therefore started extensive 13C NMR investigations on the microscopic origin of antiferroelectricity. This paper, the first of a series, reports clear evidence that the two terminal chains, the achiral and chiral chains, are distinctly different in their structural and dynamical aspects; namely, in the liquid and all the liquid-crystalline states, the chiral chain is bent significantly from the molecular long axis while the achiral chain is not. The important role of this peculiar bent-chain structure on the emergence of the antiferroelectric order is discussed. Further experimental results and discussion on the molecular biaxiality and phase biaxiality and also the dynamical modes will be reported in the successive papers.

J. Phys. Chem. B, Vol. 103, No. 3, 1999 407 II. Experimental Section The sample of R-MHPOBC with high optical purity was provided by Showa Shell Petroleum Co. and used without further purification. The phase sequence and the transition temperatures have been reported with various methods such as differential scanning,17,18 alternating current,19 relaxation,19,20 and adiabatic21 calorimetries, and they are in good agreement with one another. The isotropic liquid (I) phase transforms to the liquid-crystalline phase with successive phase transitions,21 I (421.73 K) f smectic A (SA) (396.51 K) f smectic CR* (SCR*) (395.29 K) f ferroelectric smectic C* (SC*) (393.64 K) f ferrielectric smectic Cγ* (SCγ*) (392.84 K) f antiferroelectric smectic C* (SCA*), and finally crystallizes. In the present NMR study, the subphases with narrow temperature widths (SCR* and SCγ*) were not distinguished because of limited accuracy and stability of the temperature control, and so the experimental results for the SA, SC*, and SCA* phases are reported in this paper. 13C NMR experiments were carried out with a JEOL GSX270 spectrometer at the Larmor frequency of 67.942 MHz, in the isotropic and liquid-crystalline phases, with the sample in both magic-angle-spinning (MAS) and the field-aligned conditions. In either experiment, the sample was evacuated for more than 10 h and sealed in a vacuum in a Pyrex tube after a freezepump-thaw cycle to remove humidity and oxygen. For MAS experiments, a 5 mm φ sealed Pyrex ampule was placed in a 7 mm φ zirconia rotor. Cross-polarization (CP) with a typical contact time of 1 ms was made from protons in the liquidcrystalline phases, unless otherwise stated. Comparison was also made between the spectra with and without CP to examine the CP efficiency. For spectral assignment, 13C NMR experiments were conducted for another antiferroelectric liquid crystal, R-TFMHPOBC, 4-[(1-trifluoromethylheptyloxy)carbonyl]phenyl 4-[4(octyloxy)biphenyl]carboxylate22 in which the lateral methyl group at the chiral C(23) position of MHPOBC was substituted by a trifluoromethyl group (Figure 1). Experimental results are analyzed for the chain carbons. Chemical shielding constants were measured relative to tetramethylsilane (TMS) with positive values on the less-shielded side. III. Results and Discussion III.1. MAS Spectra: Assignment and TemperatureDependence of Isotropic Shielding Constants. Figure 3 shows the aliphatic region of the 13C NMR spectra of MHPOBC (upper trace) and TFMHPOBC (lower trace) taken in I phase. The procedure used for spectral assignment is explained in Appendix I. In Figure 3 are shown the assignment and the relationship between the corresponding lines of the two compounds. Solid arrows indicate the fluorination-induced shift of the lines for chiral chain carbons, while the dashed lines indicate the achiral chain carbons. Table 1 summarizes the values of isotropic shielding constants and the fluorination-induced shifts. The 13C MAS spectra were recorded in the I, SA, SC*, and SCA* phases and are shown in Figure 4. As for the resonance frequency, i.e., the isotropic shielding constant, we detected no appreciable dependence on temperature for any of the 13C lines. Here we think about the validity of the bent-chain model. If the chiral chain assumes the most extended form along the molecular long axis in the isotropic phase and changes its conformation so that the chain may be bent at, e.g., the C(23) position in the SCA* phase, the change in the molecular structure must be detected by 13C MAS NMR spectroscopy: C(25) and C(30) would exhibit appreciable upfield shifts at a certain

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Figure 3. 1H-decoupled 13C NMR spectra in the isotropic liquid phase of MHPOBC (upper trace) and TFMHPOBC (lower trace) in the aliphatic carbon region. Fluorination-induced shifts are indicated by arrows: full arrows for the chiral chain carbons, and dashed arrows for the achiral chain carbons.

TABLE 1: 13C Spectral Assignments for MHPOBC and TFMHPOBC and Fluorination-Induced Chemical Shifts in the Isotropic Phasea carbon no. C(j)

MHPOBC (ppm)

TFMHPOBC (ppm)

fluorination-induced shifts (ppm)

C(1) C(2) C(3) C(4) C(5) C(6) C(7) C(8) C(23) C(24) C(25) C(26) C(27) C(28) C(29) C(30)

14.19 22.94 32.33 30.16 29.60 26.65 29.99 69.14 72.22 36.68 25.87 29.60 32.20 22.86 14.19 20.25

14.12 22.96 32.34 30.12 29.64 26.63 30.00 69.07 71.39 28.95 25.05 29.21 31.84 22.78 13.97 125

-0.07 +0.02 +0.01 -0.04 +0.04 -0.02 +0.01 -0.07 -0.83 -7.73 -0.82 -0.39 -0.36 -0.08 -0.22 +105

a The isotropic shielding constants are measured relative to tetramethylsilane with positive values for the less-shielded side. See Figure 1 for the numbering sequence of the carbon atoms.

Figure 4. Temperature and phase dependence of the 13C spectra for MHPOBC. Top trace represents the 1H-decoupled single-pulse spectrum in the I phase, while the others were taken with the CP/MAS method. For some of the resonance lines, the relative intensities change between SA and SC* phases, as indicated by double arrows.

temperature between I and SCA* phases because of a γ-gauche effect23 for C(25) and a steric methyl-carbonyl interaction for C(30). The experimental fact that neither C(25) nor C(30) exhibits temperature-dependent shifts means that the molecular shape does not change significantly throughout the phases studied. This result is in accordance with the recent report24

that molecular structures do not change with the phase changes or upon mixing with different optical isomers for some ferroelectric liquid crystals. Apart from the present study, a most understandable and tempting but, perhaps, oversimplified picture for the appearance of dipolar ordered phases may be as follows: the chiral chain is extended along the molecular long axis which is compatible with the uniaxial phase symmetry in the I, N, and SA phases but the chain is bent at the chiral position, and this change in molecular shape causes a significant increase in the hindering barrier against rotation. Then the molecular biaxiality and the transverse dipole moment comes up, and consequently the biaxial SC* or SCA* phases are realized. Our experimental finding proves the inappropriateness of the simplest model. The bent chain, if it exists in the SCA* phase, does not emerge on entering the SC* or SCA* phase but exists in all the phases studied. It is to be noted that we have not examined yet if the chain is bent or not. III.2. Cross-Polarization Efficiency. An interesting feature is noticed on the temperature dependence of the 13C spectra. By examining the spectra in Figure 4 carefully, we recognize that the relative intensities of the lines change depending on temperature. A significant finding is the reversal of the relative intensities between the lines corresponding to chiral and achiral chains. The reversal is clearly recognized between the lines C(6) and C(25) and between the overlapped lines C(4) + C(7) and C(5) + C(26), as indicated by double arrows in Figure 4. The reversal takes place at a temperature between 398 (SA) and 393 K (SC*). We now think about the origin of this phenomenon. The top trace in Figure 4 represents a 1H-decoupled single-pulse spectrum taken with a long-enough repetition period in I phase, and so the intensity is proportional to the number of carbons. The traces 2-5 were recorded by applying a 1H-13C crosspolarization (CP) sequence, and therefore, the intensity is modified by the efficiency of CP. To analyze the CP efficiency in a more quantitative manner, we measured the 13C MAS spectra by applying 1H-13C dipole decoupling without and with CP at each temperature. The results are depicted in Figure 5 for the SA (upper two traces) and SCA* (lower two traces) phases. The intensities are normalized to the biphenylene aromatic carbons for which CP efficiencies are believed to be independent of temperature, so that the intensities for individual lines obtained with CP compared with those without CP show the CP efficiency. In trace b of Figure 5, the arrows indicate the lines which exhibit significant loss in CP efficiency in the SA phase and are assigned to the lines containing the chiral chain carbons. In the lower temperature trace d (SCA* phases) of Figure 5, on the other hand, CP is effective enough for all the lines to a similar degree. It is clear that CP efficiency is almost inde-

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Figure 6. 13C spectra of the field-aligned sample of MHPOBC in SA, SC*, and SCA* phases.

Figure 5. Comparison of the cross-polarization efficiency in the two smectic phases of MHPOBC. The figures show 1H-decoupled 13C MAS spectra in the (a) SA phase without CP, (b) SA phase with CP, (c) SCA* phase without CP, and (d) SCA* phase with CP. The intensities are normalized to the aromatic carbons. In b the lines belonging to the chiral chain are indicated by arrows to show significant loss in CP efficiency.

pendent of temperature for the achiral chain but is temperature dependent for the chiral chain: In the SA phase, the CP efficiency is poor for the chiral chain carbons but is achieved to an almost similar extent to that for the achiral chain in the SCA* phase. Considering that the 1H polarization is transferred to 13C spins mainly through intramolecular 1H-13C magnetic dipole interaction, it is clear that only the chiral chain experiences a largeamplitude motion in the uniaxial phase (SA) so that the interactions may be significantly reduced. For the achiral chain and aromatic core, the temperature-independent CP efficiency means that the interactions are not reduced significantly even in the high-temperature uniaxial phase (SA). Keeping in mind that the isotropic shielding constants are independent of the phases, and therefore the molecular structure is not much different in all the liquid-crystalline phases, it is most probable that the chiral chain is bent and the achiral chain is extended along the molecular long axis in all the phases studied. The bent chiral chain is probably subject to large amplitude precession in the SA phase to conform itself to the uniaxial symmetry of the phase, while in the SCA* phase this large amplitude motion is significantly biased and/or slows down and then the intramolecular 1H-13C magnetic dipole interaction is recovered. For the achiral chain, the rotational motion does not experience qualitative change between SA and SCA* phases. Following this model, the biased rotation of the chiral chain and the consequent growth of the molecular biaxiality would be mainly responsible for the onset of phase biaxiality and dipolar order in the SCA* phase. In the following subsections we treat the relationship between the bent angles of the chains and the NMR parameters in a more quantitative manner. In the course of this treatment, the effective symmetry of the molecule and the phase symmetry are also discussed. III.3. Shielding Constants for Oriented Samples. Fieldaligned MHPOBC was formed by cooling the sample slowly from the isotropic phase in a magnetic field of 6.3 T. The 13C NMR spectra for such a sample may exhibit a sharp single peak for each carbon since the 13C shielding anisotropy is averaged by the molecular rotation much faster than the magnitude of the anisotropy and the resultant effective principal axes of the

shielding tensor for each carbon become aligned over the whole sample. Figure 6 shows the spectra for field-oriented MHPOBC in the SA, SC*, and SCA* phases. The positions of the resonance lines exhibit no significant changes in these three phases, apart from small shifts attributed to changes of the orientational order parameters and the tilt angle. These observations confirm that the chain conformation is substantially invariable in all the liquid-crystalline states of MHPOBC, which is consistent with the conclusion drawn via analysis of the MAS spectra. In fact, a small tilt angle effect is recognized in the SC* and SCA* phases, and it is suggested that the optical-pitch axis lies along the external field, B0, and the director, n, inclines from the field direction by the tilt angle in these biaxial phases.25 In the following discussion we make a quantitative analysis of the field-oriented spectrum for the spectrum in SA phase and do not investigate the details of the tilt angle effect. The peak assignments in the spectra for field-aligned MHPOBC were made with the aid of the difference in CP efficiency in the SA phase, as revealed for the MAS spectra in the previous subsection; the carbons in the chiral chain are subject to a distinguishably low CP efficiency in this phase, in contrast with those in the achiral chain. Figure 7b and c illustrate the 13C NMR spectra for field-aligned MHPOBC in the SA phase observed without using CP and with using CP, respectively. In the figure are shown the most reasonable assignments determined by comparing these two spectra. The details of the assignment procedure are explained in Appendix II. In Figure 7 is also shown the spectrum of MHPOBC in the isotropic phase as well as the correlation of the resonance lines in this phase with those in the SA phase. The solid and dashed arrows correspond, as in Figure 3, to the chiral and achiral chain carbons, respectively. The alignment-induced shifts (AIS) for the individual carbons are summarized in Table 2. Obviously, the methylene carbons belonging to the achiral chain exhibit large upfield shifts of -2.7 to -7.2 ppm, whereas for the methylene carbons belonging to the chiral chain, the shifts are as small as +0.4 to -2.3 ppm. From the observed AIS for the methylene carbons, we can qualitatively deduce the following information on the chain structures of the MHPOBC molecule. First, the comparatively large upfield shifts for the achiral chain carbons are, as is wellknown,26 obtained because the most shielding (σ33) tensor axis, which is typically parallel to the chain direction,27 orients preferentially in the direction of the external magnetic field in the SA phase. Hence, the observations lead to the widely accepted picture for the liquid-crystal molecular structure that the chain is elongated along the molecular axis which aligns parallel to the magnetic field, as far as the achiral chain is concerned. On the other hand, the small shifts for the chiral chain are novel findings and may imply that this chain is away

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A00(j; j-PAS) ) -

1 [σ11(j) + σ22(j) + σ33(j)] ≡ x3 -x3σiso(j) (3)

A20(j; j-PAS) )

Figure 7. Spectral assignment for the 1H-decoupled 13C spectrum of field-oriented MHPOBC. (a) I phase, (b) SA phase without CP, and (c) SA phase with CP. The arrows in (c) indicate reduction of CP efficiency for the chiral chain carbons. The correlation between the isotropic spectrum and the oriented spectrum is shown between a and b with full arrows for the chiral chain carbons and dashed arrows for the achiral chain carbons.

from the molecular axis direction; suppose an extreme case that the σ33 axis makes an angle of 54.7° (i.e., the magic angle), then no alignment-induced shifts are expected. In the following theoretical treatment of AIS, we discuss the above inference rather quantitatively. III.4. Theoretical Treatment for the Alignment-Induced Shifts. The resonance frequency of the jth 13C nucleus of the methylene group (j ) 2-8 and 24-28) in the field-aligned MHPOBC molecule is given by

ν(j) ) -νC[1 - 〈σzz(j; LAB)〉]

(1)

where νC is the reference Larmor frequency of the nucleus and σzz(j; LAB) is the zz component of the magnetic shielding tensor of the jth carbon in the laboratory frame (LAB). The brackets 〈 〉 represent the time average with regard to various molecular motions, discussed later in detail. The time-averaged Cartesian tensor component 〈σzz(j; LAB)〉 may be expressed using the corresponding spherical tensor components Alm(j; LAB) and, furthermore, related with those in the principal axis system (PAS) of the shielding tensor Alm(j; j-PAS), using Wigner rotation matrixes28 13C

D(2) mn(j - PAS f LAB): 〈σzz(j; LAB)〉 ) -

1

x3 -

x∑ 2

A00(j; LAB) + 1

x

2

〈A20(j;LAB)〉 )

3

A00(j; j-PAS) +

x3

+2

3m)-2

A2m(j; j-PAS)〈D(2) m0(j-PAS f LAB)〉 (2)

The spherical tensor components in PAS may be rewritten using the principal values of the shielding tensor, σ11(j), σ22(j), and σ33(j), as28

x32[σ (j) - σ 33

iso(j)]

(4)

A2(1(j; j-PAS) ) 0

(5)

1 A2(2(j; j-PAS) ) [σ11(j) - σ22(j)] 2

(6)

where σiso(j), the isotropic shielding constant, is the average of the three principal values. In eq 2, we assumed that σ(j; j-PAS) is not affected by molecular motions. The quantity which is dependent on the details of molecular motion and ordering is the relative orientation of the three PAS axes with respect to the laboratory z-axis, and the orientational characteristics are described by Wigner rotation matrixes, Dm0(j-PAS f LAB). This assumption states that we treat the NMR line position problem as a problem of motional averaging. For the methylene carbons in MHPOBC, we take into account the following three modes of motions: (i) intramolecular segmental motions arising from the conformation changes of the alkyl chains; (ii) overall rotation of the molecule around its long axis; (iii) fluctuation of the molecular axis about the director. The transformation matrixes from j-PAS to LAB, which are to be averaged by these motions, are considered to comprise six successive transforms as schematically shown in Figure 8. Furthermore, we assume that the relevant transforms are independently averaged by specific modes of the motions. Namely, we treat the motions in an uncoupled model29 where the individual motions have no influence on one another. As a result, the motionally averaged matrix components are represented as

〈D(2) m0(j-PAS f LAB)〉 ) +2

+2

+2

+2

+2

∑ ∑ ∑ ∑ ∑

D(2) mn(j-PAS f j-SEG) × n)-2 p)-2 q)-2 r)-2 s)-2 (2) 〈D(2) np (j-SEG f f-CHAIN)〉Dpq (f-CHAIN f MOL) × (2) (2) 〈D(2) qr (MOL f RIG)〉〈Drs (RIG f DIR)〉Ds0 (DIR f LAB) (7) The right-hand side of eq 7 contains three bracketed quantities representing the respective motional averages. The quantities 〈D(2) np (j-SEG f f-CHAIN)〉 (f ) a or c for the achiral or chiral chain fragments) and 〈D(2) rs (RIG f DIR)〉, averaged by intramolecular segmental motions and the fluctuation of the molecular long axes about the director, respectively, yield the segmental order parameter tensors for the individual carbons and the overall order parameter tensor for the entire molecule. On the other hand, 〈D(2) qr (MOL f RIG)〉 reflects the overall rotation of the molecule around its long axis. In the following, we explicitly estimate the individual transformations involved in eq 7 and depicted in Figure 8, making several assumptions which restrict, more or less, the objects of interest but greatly simplify the theoretical treatment. First, we consider the transformation from j-PAS to j-SEG, the latter of which is the geometrical coordinate system of the jth methylene segment. If we define the zj-SEG axis parallel to the local C(j - 1) - C(j + 1) direction and the yj-SEG axis along the direction bisecting the H-C(j)-H angle, as shown in Figure 9, then j-SEG is typically coincident with j-PAS;

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Figure 9. Axes of the segmental frame of reference (SEG) for the jth methylene unit.

On the other hand, ϑj is the angle between these axes and is expected to fluctuate around zero. Provided that the chains are sufficiently flexible, we can assume no preferable orientations around the zj-SEG and zf-CHAIN axes; namely, the biaxiality of the motions around these axes is neglected. As a result, we obtain Figure 8. Frames of reference that describe the NMR parameters and the Wigner rotation matrixes for successive transformations.

TABLE 2: Alignment-Induced Shifts (AIS) of the 13C Lines of MHPOBC carbon no. C(j)

I phase (ppm)

SA phase (408 K) field-aligned (ppm)

AIS (ppm)

C(1) C(2) C(3) C(4) C(5) C(6) C(7) C(8) C(23) C(24) C(25) C(26) C(27) C(28) C(29) C(30)

14.19 22.94 32.33 30.16 29.60 26.65 29.99 69.14 72.22 36.68 25.87 29.60 32.20 22.86 14.19 20.25

11.8 20.2 26.7 23.0 22.5 20.2 23.0 62.5 45.8 36.2 26.3 27.3 30.8 22.0 13.2 20.2

-2.4 -2.7 -5.6 -7.2 -7.1 -6.5 -7.0 -6.6 -26.4 -0.5 +0.4 -2.3 -1.4 -0.9 -1.0 -0.1

namely, the principal 1, 2, and 3 axes of the shielding tensor of the jth carbon are parallel to the xj-SEG, yj-SEG, and zj-SEG axes, respectively. Consequently, the matrix components are given by

D(2) mn(j-PAS f j-SEG) ) δmn

(8)

Note that eq 8 does not hold for the carbons for which the deviation of the principal axis directions from the above typical directions is expected. For instance, we may exclude C(8), or the CH2O group, in the following treatment; in the presence of the adjacent oxygen atom, the direction of the σ33(8-PAS) axis is expected to deviate significantly from the O-C(7) direction. The unusualness of the shielding tensor is in fact suggested by the σiso(8) value, which is largely different from those for the other methylene groups, as listed in Table 2. Also, the deviation of the principal-axis directions may be probable for C(24) and C(25) because of the neighboring methine group in addition to the lateral methyl and carboxylic groups. We will later discuss the influences of such deviating principal-axis directions. The subsequent transformation from j-SEG to a-CHAIN or c-CHAIN reflects the intramolecular conformational motions, where a-CHAIN and c-CHAIN are the coordinate systems specifying the motionally averaged orientations of the achiral and chiral chains, respectively. If this transformation is represented by Euler angles (φjϑjψj), then φj and ψj characterize the fluctuations around the zj-SEG and zf-CHAIN axes, respectively.

(2) 〈D(2) np (j-SEG f f-CHAIN)〉 ) δn0〈d00 (ϑj)〉δp0

(9)

The assumption made here may not be valid for the methylene carbons neighboring the core unit of the molecule, such as C(7), C(24), and C(25), because the steric interactions with the core plane may not be negligible. We next consider the transformation from f-CHAIN to the principal-axis system of inertia of the whole molecule (MOL). If we use Euler angles (ξf ηfζf) for this transformation, the corresponding matrix components are written by (2) D(2) pq (f-CHAIN f MOL) ) exp(-ipξf)dpq (ηf)exp(-iqζf) (10)

The quantities ηa and ηc are the most important parameters in the present treatment and, respectively, represent the bent angles of the averaged directions of the achiral and chiral chains, za-CHAIN and zc-CHAIN, with respect to the principal axis of the smallest inertia of the molecule, zMOL, namely, the molecular long axis. It is the estimation for the angles ηa and ηc that is expected to verify the bent-chain model mentioned in the previous subsections. On the other hand, the other angles ξf and ζf give the phases of the chain rotation around the zf-CHAIN axis and of the molecular rotation around the zMOL axis, respectively. The angles ξf are averaged out, as demonstrated in eq 9, and so are the angles ζf, as we will show immediately below. Consequently, only d(2) pq (ηf) is effective in the transformation from f-CHAIN to MOL. The effect of the rotation of the liquid-crystal molecule around its principal axis of inertia is reflected in the subsequent transformation from MOL to RIG; RIG is defined to be the coordinate system of the molecule as a rigid body (MRB), where the details of the molecular structure are averaged out by the rotation. We introduce this idea so that one can incorporate the effective symmetry of the molecule into the theory explicitly. For simplicity, we take into account the rotation of MOL about its zMOL axis only, i.e., the uniaxial rotation of the molecule about its long axis is considered. Then the two axes zMOL and zRIG coincide, and therefore, the relationship, d(2) qr (0) ) δqr, greatly reduces the complexity of formalism. With this framework, the effective symmetry of the liquid-crystalline molecule is determined by the symmetry of the potential hindering the uniaxial rotation. If the rotation takes place at a hindering potential with symmetry higher than C3, the MRB is a symmetric top (uniaxial molecule), while if the potential symmetry is lower, the MRB is an asymmetric top (biaxial molecule). If we assume molecular uniaxiality, the matrix elements after motional

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averaging reduces to

〈D(2) qr (MOL f RIG)〉 ) δq0δr0

(11)

The molecular biaxiality neglected here could be potentially important in the subsequent biaxial ordering of the molecules over the bulk sample and, therefore, might play an essential role in characterizing ferroelectric or antiferroelectric phases and distinguishing them from ordinary paraelectric phases. However, in the present theoretical treatment, we intend to clarify the comprehensive molecular structures and dynamics common to all the phases of MHPOBC, omitting the molecular biaxiality. The idea of MRB is established after considering all the internal degrees of freedom so that it is a static concept except for the freedom with respect to translation. In the liquidcrystalline phases, the statistical distribution of the MRBs in space is characterized by the orientational order parameters. However, the fact that the narrow NMR lines are obtained for each of the carbons shows that the unique axes of MRB are also time dependent and averaged out in the time scale of the shielding anisotropy. The fluctuation considered here may be slower than those for the internal motions treated above. Here we assume that this fluctuation is characterized by the motion around a single director n (zDIR) and, moreover, possesses no preferable orientations around n. In other words, we neglect the biaxiality of the molecular assembly (phase biaxiality). This simplification may again be justified in discussing the approximate features common to all of the SA, SC*, and SCA* phases; logically speaking, there is no microscopic origin for the phase biaxiality after omitting the molecular biaxiality. By referring to the coordinate system specified by the director n as DIR and defining Euler angles for the transformation from RIG to DIR to be (φ,ϑ,ψ), we obtain (2) 〈D(2) rs (RIG f DIR)〉)〈exp(-irφ)dr0 (ϑ)〉δs0

(12)

Note that since the phase of the molecular rotation around the zRIG axis, φ, is averaged out, as shown in eq 11, the effective component in eq 12 is only 〈d(2) 00 (ϑ)〉. We finally consider the transformation from DIR to LAB. This transformation is characterized by the polar and azimuthal angles (ϑt, φt, where ϑt is the angle between n and the external magnetic field or the nonzero tilt angle existing in the SC* and SCA* phases. As shown below, we analyze the NMR spectrum of MHPOBC observed for the SA phase, and so we adopt ϑt ) 0. Thereby, the matrix components of the transformation are given by (2) (DIR f LAB) ) exp(-isφt) Ds0

(13)

The azimuthal angle φt is the phase of the fluctuational motion around n and does not appear in the final result because we neglected the biaxiality of the motion, as shown in eq 12. On the basis of the discussion for the individual transformations represented in eqs 8-13, we obtain a simple formalism for the entire transformation as (2) (2) (2) 〈D(2) m0(j-PAS f LAB)〉 ) δm0〈d00 (ϑj)〉d00 (ηf)〈d00 (ϑ)〉 )

δm0P2(cos ηf) SfjS00 (14) 〈d(2) 00 (ϑ)〉

is the overall order parameter expressing where S00 ≡ the fluctuation of the molecular long axis about n and Sfj ≡ 〈d(2) 00 (ϑj)〉 (f ) a or c) is the segmental order parameter of the jth carbon about the long axis of each of the average chain,

TABLE 3: Reduced Shifts, Cfj, and the Segmental Order Parameters, Sfj, for the Two Alkyl Chains of MHPOBCa j Caj Saj j Ccj Scj

2 (R) 0.3078 0.31

Achiral Chain 4 (γ) 5 (δ) 0.4690 0.4625 0.47 0.46

3 (β) 0.3648 0.36

28 (R) 0.1026 0.34

Chiral Chain 27 (β) 26 (γ) 0.0912 0.1498 0.30 0.49

6 () 0.4234 0.42

25 (δ) -0.0261 -0.09

7 (ζ) 0.4560 0.46 24 () 0.0326 0.11

a f Cj is defined as the alignment-induced shifts divided by the shielding anisotropy and the order parameter of the molecule as a whole, Cfj ≡ AIS(f,j)/∆σ(j)S00, and Sfj values were deduced by an optimization procedure shown by eq 18 in the text. The optimized bent angles are ηa ) 0° and ηc ) 43° for the achiral and chiral chains, respectively.

reflecting the conformational average at the site of this nucleus. Also, P2(cos ηf) in eq 14 is the second-rank Legendre polynomial having an argument involving the bent angle ηf of the achiral or chiral chain with respect to the molecular long axis. By substituting eqs 3-6 and 14 into eq 2, we obtain the expression for the alignment-induced shift (AIS) as

AIS(f,j) ≡ 〈σzz(j; LAB)〉 - σiso(j) ) ∆σ(j)P2(cos ηf)SfjS00

(15)

where ∆σ(j) ) σ33(j) - σiso(j) indicates the anisotropy of the shielding tensor in PAS at each carbon nucleus. Thus, we have established the formula for the alignment-induced shifts of liquid crystals, which allows quantitative analysis for the observed spectra. III.5. Numerical Analyses. The purpose of our discussion which follows is to estimate the bent angle ηf of each of the alkyl chains in the MHPOBC molecule by analyzing the observed alignment-induced shifts and thereby verify the bentchain model for this compound. To proceed, we first make a further assumption for the anisotropy parameter of the shielding tensor ∆σ(j): We use typical values of the principal components of the tensor, i.e. (σ11(j), σ22(j), σ33(j)) ) (54, 41, 16) ppm for the interior methylene carbons (j ) 3-7 and 24-27)27 and (37, 30, 15) ppm for the R-methylene carbons (j ) 2 and 28),30 so that ∆σ(j) ) -21 ppm for the former and -12 ppm for the latter. With regard to the overall order parameter S00 involved in eq 15, it is known to take a value of 0.7-0.8 in SA phases. Here we adopt the value of 0.73, which we evaluated from the alignment-induced shifts observed for some of the aromatic carbons in MHPOBC at the temperature of 408 K.31 We determined the principal components of their magnetic shielding tensors, necessary for the evaluation of S00, from the 13C MAS NMR spinning sideband analysis32,33 for this compound in the crystalline phase and then assumed the appropriate principal axis directions of the tensors,27 such that the most shielding axis is perpendicular to the aromatic-ring plane; the details of the analysis will be reported in our subsequent paper.31 Since ∆σ(j) and S00 have been estimated, we can evaluate the following reduced shifts from the experimental values of AIS(f,j):

Cfj ≡

AIS(f,j) P (cos ηf)Sfj ∆σ(j)S00 2

(16)

and are tabulated in Table 3. The values of Cfj for the chiral chain are significantly smaller than those for the achiral chain. A problem is that the unknown variables in eq 16, Sfj and ηf,

Study of an Antiferroelectric Liquid Crystal

J. Phys. Chem. B, Vol. 103, No. 3, 1999 413

Figure 10. Segmental order parameters Sjf vs possible bent angles ηf for some of the methylene carbons belonging to (a) achiral and (b) chiral chains in the SA phase at 408 K.

are not determined separately from the single known variables Cfj. However, possible ranges of the bent angles ηf can be limited from the ranges of the values of Sfj ≡ 〈d(2) 00 (ϑj)〉 ) 〈P2(cos ϑj)〉. Namely, by putting the maximum Cfj values, Ca4 ) 0.469 and Cc26 ) 0.150, into the inequalities

Cfj 1 e1 - e Sfj ) 2 1 (3 cos2 ηf - 1) 2

(17)

we obtain 0° e ηa e 37° for the achiral chain and 0° e ηc e 49° or 69° e ηc e 90° for the chiral chain. In Figure 10 are depicted the graphs of the segmental order parameters Sfj for some of the methylene carbons vs the possible bent angles ηf. As clearly demonstrated in Figure 10, we can speculate that if the chiral chain as well as the achiral chain is not bent much, i.e. ηc ≈ ηa ≈ 0°, the segmental order parameters for the chiral chain carbons should be prominently smaller than those for the achiral chain carbons. In other words, we should permit the conformations of the chiral chain to be unreasonably random and extremely different from those of the achiral chain. We now take a standpoint that the apparent significant difference in Caj and Ccj does not come from the unrealistic difference in conformational motions but from the difference in bent angles, ηa and ηc. Along this line, we can proceed further to a quantitative discussion by assuming that three pairs of the methylene carbons, namely, R-methylenes of C(2) and C(28), β-methylenes of C(3) and C(27), and γ-methylenes of C(4) and C(26), should, respectively, have the similar segmental order parameters around each average chain axis. That is to say, we evaluate the bent angles as those minimizing the following function:

1 RMS(ηa,ηc) ) {[Sa2(ηa) - Sc28(ηc)]2 + 3 [Sa3(ηa) - Sc27(ηc)]2 + [Sa4(ηa) - Sc26(ηc)]2}1/2 (18) As a result of iterative calculations, we found the optimal bent angles ηa ) 0° and ηc ) 43°, with RMS ) 0.025. Thus, we can conclude that, in the MHPOBC molecule of the present interest, only the chiral chain is remarkably bent with respect to the molecular long axis whereas the achiral chain extends along the molecular long axis, provided that randomness of the local conformations is similar for the two chains. Figure 11 illustrates the schematic molecular structure derived from the present analysis. Table 3 shows a series of segmental order parameters deduced for the individual methylene carbons, corresponding to the above optimal bent angles, and the results for R, β, and γ methylenes

Figure 11. Schematic molecular structure of MHPOBC in the liquid and liquids crystalline states. The average direction of the chiral chain is bent as much as 43° from the long molecular axis.

Figure 12. Segmental order parameters for the R, β, and γ methylenes in the SA phase (408 K). The solid and open circles represent the values for chiral and achiral chain carbons, respectively.

are shown in Figure 12. We can roughly state that among R-, β-, and γ-methylene groups, more terminal ones have smaller segmental order parameters, and this implies that more terminal groups change their conformations more randomly. Even (R and γ)-odd (β) oscillations are also recognized. On the other hand, in Table 3, the segmental order parameters determined for C(24) and C(25) are unreasonably small in comparison with the others, despite the relatively less flexibility that is naturally expected. This inconsistency may be understood from the impropriety of the following two assumptions made in the above formulation of the alignment-induced shifts. One assumption is that the anisotropy parameters ∆σ(j) ) -21 ppm and their most shielding directions are parallel to the chain axis, which is not the case for these carbons. This may occur if the chain conformations (as time averages) are gauche around the O-C(23) and C(23)-C(24) bonds; the γ-gauche effects, wellknown for the isotropic magnetic shielding,23 exhibit themselves

414 J. Phys. Chem. B, Vol. 103, No. 3, 1999 on the principal components and directions of the anisotropic shielding tensors more prominently.34 Such gauche-like conformations, in turn, suggest that the chiral chain is bent around these bond positions. To overcome possible uncertainty originating from the conformation-induced change in shielding tensors and to determine the more accurate segmental order parameters for C(24) and C(25), we can make use of the quadrupolar splittings of 2H nuclei for deuterated MHPOBC samples. The subject is under investigation. The other assumption considered to be invalid for C(24) and C(25) is that there is no preferable direction of the segmental motion perpendicular to the zj-SEG axis. As mentioned above, the methylene carbons neighboring the core unit of the liquidcrystal molecule may be less mobile so that the biaxiality of their motions is probably not negligible. In such a case, we should consider five independent components of the segmental f order parameter tensor 〈exp(inφj)d(2) n0 (ϑj)〉 ) Sj,n (n ) 0, (1, (2) (2), instead of a single parameter 〈d00 (ϑj)〉 ) Sfj. For simplicity, however, we will not enter into further discussion using Sfj,n. For the reasons stated here and above, the values of the segmental order parameters for C(24) and C(25), listed in Table 3, may be fictitious. Finally, we mention that inclusion of the data for C(24) and C(25) in optimizing the bent angles does not affect the conclusion significantly. Even if we took into account these carbons by submitting to the two failed assumptions, the bent angles would be optimized at ηa ) 0° and ηc ) 41-44°. The uncertainty in estimating the bent angle comes from ambiguity in assigning the corresponding carbons to be compared, such as C(5) and C(25) and/or C(6) and C(25), since the chain structures are different between achiral and chiral chains. Thus, the speculation regarding the bent conformation model which we qualitatively stated in sections III.2 and III.3 has quantitatively been concluded: The chiral chain in the MHPOBC molecule is bent by as much as 43° with respect to the molecular long axis, whereas the achiral chain extends along the molecular long axis. III.6. Bent Chiral Chain: Its Role in the Origin of Antiferroelectricity. We have shown clear evidence for the bent chiral chain structure in MHPOBC. Recently, this model was supported by systematic X-ray analysis in the liquid-crystalline phases and molecular mechanics calculations for a series of compounds35 and also by the polarized infrared absorbance study.36 This particular molecular structure brings about two features which are considered essential in electric dipolar ordering. First, the structure, as in Figure 11, is rather far from the rodlike shape which is commonly accepted in classical liquid crystals. In the classical systems, the rotation about the molecular long axis results in MRB of almost cylindrical symmetry, so even if it condenses into the biaxial phase such as SC, the molecular biaxiality is considered small. In MHPOBC, on the other hand, the bent chiral chain causes strong steric hindrance against rotation. In the SA phase, the chiral chain precesses about the molecular long axis to conform the molecular symmetry to the phase symmetry. However, even in the SA phase, the rotational potential may possibly be biased and the molecular biaxiality and, consequently, the residual transverse dipole moment may come up. If it is the case, it is natural to expect the growth of the transverse dipole moment at lower temperature and finally the occurrence of the ordering transition. A second feature is that this molecular structure makes it possible for the molecules belonging to the adjacent layers to come in close contact. This feature enables the unusually strong

Nakai et al. dipole interactions among the molecules and is also an important requirement for the antiferroelectric dipolar ordering. Recent X-ray structure analyses37,38 reported that the bent chiral chain is often observed in the crystalline states of the molecules which exhibit antiferroelectric chiral smectic phases. This finding also supports the above idea that the bent chiral chain plays an essential role in dipolar ordering, especially the antiferroelectric ordering in liquid crystal. Acknowledgment. We thank Daisuke Kuwahara and Hiroki Fujimori for experimental assistance. This work was supported partly by a Grant-in-Aid for Scientific Research (Specially Promoted Research No. 06102005) from the Ministry of Education, Science, Sports, and Culture of Japan and the Joint Studies Program (1995-96) of IMS. Appendix I: Spectral Assignment for MAS Samples The MAS spectral lines of MHPOBC and TFMHPOBC were assigned as shown in Figure 3 and Table 1 by the following procedure. Spectral assignment was made first by referring to the literature data on related aliphatic materials such as alkanes:39 There are rather established empirical rules such as (i) methyl groups usually appear at ca. 14 ppm, (ii) R-methylene next to methyl at ca. 23 ppm, (iii) β-methylene at ca. 32 ppm, and (iv) interior methylenes at 26-30 ppm. The closely located pair at 14 ppm was thus assigned to C(1) and C(29). Similarly, the pair at 23 ppm were assigned to C(2) and C(28) and the pair at 32 ppm to C(3) and C(27). The closely located pairs exist because MHPOBC has two terminal chains which exhibit similar shielding values. A methylfluorination effect was usefully applied to assign these lines. Namely, one of the two lines in each of the closely located pairs exhibited a significant fluorination effect, and this line was assigned to the chiral chain carbon. C(29), C(28), and C(27) were thus distinguished from C(1), C(2), and C(3), respectively. Before proceeding to the assignment of the interior carbons, the fluorination effect around the chiral part was examined: C(23), C(24), and C(30) are expected to exhibit the most significant fluorination effect because of their close location to the fluorine atoms. Generally, fluorination has two different effects on the 13C shieldings. One is the diamagnetic effect which comes from the higher electron density of the CF3 group than CH3. On the other hand, the strongly electronegative nature of fluorine withdraws the electrons from the nearby bond orbitals and results in a paramagnetic contribution to shielding. Usually the carbon directly attached to fluorine experiences a strong paramagnetic effect while the carbons located farther from CF3 experience small diamagnetic effect. The literature says that for toluene the methyl line at 21.4 ppm shifts to 124.5 ppm in trifluoromethylbenzene (the methyltrifluorinated toluene, represented by TFMB hereafter). On the other hand, the ring carbon (at 137.7 ppm in toluene) next to a methyl group shifts to 131.1 ppm in TFMB. The large paramagnetic shift of 103.1 ppm for methyl carbon and a relatively small diamagnetic shift of -6.6 ppm for the next-tomethyl carbon were thus observed. It is thus expected that C(30) shows a paramagnetic shift as large as ca. 100 ppm, while C(23) shows only a few parts per million diamagnetic shift. It is also a key feature that the methyl and the next-to-methyl carbons in TFMB exhibited 19F-13C quartets of 272 and 32 Hz, respectively, because of the indirect spin-spin (J) coupling. They correspond to 4 and 0.5 ppm at the Larmor frequency (67.942 MHz) of the present experiment. We found a significant

Study of an Antiferroelectric Liquid Crystal quartet of J ) 270 Hz at 125 ppm and assigned it to C(30) in TFMHPOBC, and the peak at 20.25 ppm in MHPOBC which apparently “disappeared” from Figure 3 by fluorination was assigned to C(30) in MHPOBC. The fluorination shift is thus 105 ppm for C(30) and is consistent with the known results for toluene and TFMB. Another significant 1:3:3:1 quartet was found at 71.39 ppm with J ) 30 Hz in TFMHPOBC. This was ascribed to C(23), and the fluorination shift is found to be only -0.83 ppm. Both J and the shift are in accordance with the results for toluene and TFMB. Another peak of MHPOBC that exhibits a significant fluorination shift is the one at 36.68 ppm, which is ascribable to C(24). It is a problem to locate in the lower trace of Figure 3, the counterpart for TFMHPOBC. The spectra in Figure 3 were taken under the condition of proton decoupling at nearly the center of the methylene resonances. Therefore, the methyl protons are less intense because of off-resonance decoupling. In addition to this, one finds in the lower trace of Figure 3 that the line at 28.95 ppm is less intense than the other methylenes, and it is assigned to C(24). The reduced intensity is ascribable partly to an off-resonance effect of the proton and also partly to the indirect coupling with fluorines, though the split feature is undetectable due to a resolution limit. By this procedure the fluorination effect is as large as -7.73 ppm for C(24). Actually, this value is unexpectedly large and suggests that the local molecular structure around the chiral center of TFMHPOBC is slightly different from that of MHPOBC because of the steric effect caused by the bulky trifluoromethyl group. Now the assignments of the interior methylenes, C(4), C(5), C(6), C(7), C(25), and C(26), are made. The problem remains of how to assign the peaks between 25 and 31 ppm for both MHPOBC and TFMHPOBC in Figure 3. MHPOBC exhibits five peaks in this region. Since the peak at 29.60 ppm is doubly intense, the expected six peaks are all present. The most shielded peak at 25.87 ppm exhibits a significant diamagnetic shift to 25.05 ppm in TFMHPOBC, and therefore, the peak comes from the chiral chain. One more chiral chain carbon must be identified next. One finds in Figure 4 that the doubly intense peak at 29.60 ppm shows less efficiency of cross-polarization (CP) in the SA phase, which is similar to the peak at 25.87 ppm. These peaks are, therefore, assigned to chiral chain carbons. To determine which of the above two peaks are assigned to either C(25) or C(26), an empirical rule39 is applied. A methylene at the third neighbor to oxygen (which means C(25)) has a shielding constant of ca. 26 ppm, while the fourth methylene (which means C(26)) is located at ca. 29 ppm. Thus, the assignment for MHPOBC is C(25) at 25.87 ppm and C(26) at 29.60 ppm. The lines of TFMHPOBC were also assigned by considering the fluorination-induced shift and CP efficiency: the result is given in Figure 3 and Table 1. To locate the achiral chain carbons, C(4), C(5), C(6), and C(7), published data for a number of alkoxy chains of carboxylic acid esters were referred. The typical σiso values are 65 ppm for C(8), 29 ppm for C(7), 26 ppm for C(6), 28.7 ppm for C(5), 29.8-30.0 ppm for C(4), 32 ppm for C(3), 22.7 ppm for C(2), and 14 ppm for C(1). One finds that experimental values of σiso for MHPOBC are generally larger because of an aromatic effect, but the general trend along the chain must be similar. The most delicate problem was how to assign the closely located three peaks around 30 ppm. C(4), C(5), and C(7) were assigned according to the order of the literature data. The assignment of all the chain carbons was accomplished with the procedure described above. The result summarized in Table 1 shows that the fluorination shift is within -0.07 and

J. Phys. Chem. B, Vol. 103, No. 3, 1999 415 +0.04 ppm for the achiral chain carbons, C(1)-C(8), while the chiral chain carbons, C(23)-C(29), exhibit a diamagnetic shift between -0.08 and -7.73 ppm. An exceptionally large paramagnetic shift amounting to 105 ppm was observed for the methyl carbon C(30) upon which fluorine atoms are attached directly. Appendix II: Spectral Assignment for Oriented Samples The strongly first-order I-SA phase transition of MHPOBC prevents one from following the lines through the transition. Cross-polarization (CP) efficiency was, therefore, applied for spectral assignment of the oriented samples. CP efficiency reflects the magnitude of 1H-13C dipole interaction for the individual carbon and is determined mainly by the extent of motional averaging of the interaction. We learned from Figure 5 and the discussion in section III.2 that the carbons belonging to the chiral chain exhibit significantly less CP efficiency compared with that of the achiral chain carbons. The MAS experiment imposes artificial averaging of the dipole interaction in addition to the pristine averaging caused by molecular motion in a liquid crystal. Therefore, the CP efficiency is generally improved in the experiment of the oriented sample. However, if we compare the CP efficiency between chiral and achiral chain carbons, the difference remains. We thus expect to apply the difference in CP efficiency for the line assignment of the oriented sample. In Figure 7 the peaks for which the intensities are diminished by cross-polarization are indicated by arrows. In Figure 7a one finds that the methyl carbons are located in the most shielded region of the isotropic spectrum. It is also generally known that the chemical shift anisotropy, ∆σ(j) ) σ33(j) - σiso(j), is small for methyl carbons, and so the methyl carbons will also be found in the most shielded region in the oriented spectra. Figure 7b and c show clearly that the split peaks at 11.8 and 13.2 ppm are assigned to the methyl carbons. Following the discussion on CP efficiency in section III.2, the peak at 11.8 ppm with a high CP efficiency was assigned to C(1) and the peak at 13.2 ppm with a low CP efficiency to C(29). The least shielded peak in Figure 7b and c at 36.2 ppm is assigned to C(24) because it is well separated from others. From the assignments of C(1), C(29), and C(24), one finds that the carbons belonging to the chiral chain exhibit a very small alignment-induced shift (AIS) compared with the achiral chain carbons. Complex peaks between 20 and 35 ppm contain the rest of the lines, namely, C(2), C(3), C(4), C(5), C(6), and C(7), six lines from the achiral chain, and C(25), C(26), C(27), C(28), and C(30), five lines from the chiral chain. Assignment of the latter was made first. Four lines are found with less CP efficiency at 30.8, 27.3, 26.3, and 22.0 ppm. One peak seemed to be lacking. However, considering that the AIS is generally small for methyl carbons, it is most natural to think that the C(30) line is not contained in the above four, and an intense peak at 20.2 ppm contains the remaining methyl line in it. Keeping in mind that all five peaks belong to the same (chiral) chain, AIS do not differ too much so that the peaks are assigned in the order of the isotropic spectrum. The assignments are C(27) at 30.8 ppm, C(26) at 27.3 ppm, C(25) at 26.3 ppm, C(28) at 22.0 ppm, and C(30) at 20.2 ppm. The lines with high CP efficiency are assigned next. A peak of single intensity at 26.7 ppm, two peaks of double intensity at 23.0 and 20.2 ppm, and a shoulder at 22.5 ppm are ascribed to the expected six lines. Here again, the lines belonging to the

416 J. Phys. Chem. B, Vol. 103, No. 3, 1999 same (achiral) chain are assumed to exhibit AIS not too much different from one another, and the peaks are assigned in the order of the isotropic spectrum: C(3) at 26.7 ppm, C(4) and C(7) overlapped at 23.0 ppm, C(5) at 22.5 ppm, and C(6) and C(2) overlapped at 20.2 ppm. The above procedure resulted in significantly less AIS for chiral chain carbons than achiral chain carbons, consistent with the results for C(1), C(29), and C(24) explained before. Therefore, the present assignment has been proved totally consistent and probable. This result is summarized in Table 2. References and Notes (1) Chandani, A. D. L.; Gorecka, E.; Ouchi, Y.; Takezoe, H.; Fukuda, A. Jpn. J. Appl. Phys. 1989, 28, L1265. (2) Mayer, R. B.; Liebert, L.; Strzelecki, L.; Keller, P. J. Phys. (Fr.) 1975, 36, L69. (3) Fukuda, A.; Takanishi, Y.; Isozaki, T.; Ishikawa, K.; Takezoe, H. J. Mater. Chem. 1994, 4, 997. (4) Bahr, C. H.; Fliegner, D. Phys. ReV. Lett. 1993, 70, 1842. (5) Takanishi, Y.; Takezoe, H.; Fukuda, A.; Watanabe, J. Phys. ReV. B 1992, 45, 7684. (6) Chandani, A. D. L.; Hagiwara, T.; Suzuki, Y.; Ouchi, Y.; Takezoe, H.; Fukuda, A. Jpn. J. Appl. Phys. 1988, 27, L729. (7) Hiraoka, K.; Taguchi, A.; Ouchi, Y.; Takezoe, H.; Fukuda, A. Jpn. J. Appl. Phys. 1990, 29, L103. (8) Lee, J.; Chandani, A. D. L.; Itoh, K.; Ouchi, Y.; Takezoe, H.; Fukuda, A. Jpn. J. Appl. Phys. 1990, 29, 1122. (9) Orihara, H.; Fujikawa, T.; Ishibashi, Y.; Yamada, Y.; Yamamoto, N.; Mori, K.; Nakamura, K.; Suzuki, Y.; Hagiwara, T.; Kawamura, I. Jpn. J. Appl. Phys. 1990, 29, L333. (10) Miyachi, D.; Matsushima, J.; Takanishi, Y.; Ishikawa, K.; Takezoe, H.; Fukuda, A. Phys. ReV. E 1995, 52, R2153. (11) Takanishi, Y.; Hiraoka, K.; Agrawal, V.; Takezoe, H.; Fukuda, A.; Matsushita, M. Jpn. J. Appl. Phys. 1991, 30, 2023. (12) Prost, J.; Bruinsma, R. Ferroelectrics 1993, 148, 25. (13) Bruinsma, T.; Prost, J. J. Phys. (Fr.) 1994, 4, 1209. (14) Nishiyama, I.; Goodby, J. W. J. Mater. Chem. 1992, 2, 1015. (15) Vanakaras, A. E.; Photinos, D. J.; Samulski, E. T. Phys. ReV. E 1998, 57, R4875. (16) Hori, K.; Endo, K. Bull. Chem. Soc. Jpn. 1993, 66, 46.

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