Twist-Grain-Boundary Structure in the B4 Phase of a Bent-Core Molecular System Identified
by Second Harmonic Generation Circular Dichroism Measurement
Fumito Araoka,1N. Y. Ha,2Yoshitaka Kinoshita,1Byougchoo Park,1,†J. W. Wu,2and Hideo Takezoe1,* 1Department of Organic and Polymeric Materials, Tokyo Institute of Technology,
2-12-1 O-okayama, Meguro-ku, Tokyo 152-8552, Japan
2Department of Physics, Ewha Womans University, Seoul 120-750, Korea
(Received 27 April 2004; published 7 April 2005)
Second harmonic generation circular dichroism (SHG CD) measurements are performed on the B4 phase of a bent-core molecular system. Numerical analysis of SHG CD incorporating magnetic-dipole as well as electric-dipole interaction shows that the B4 phase is in a twist-grain-boundary structure with the helical axis along the bent direction of the molecules. The result is extremely important in the sense that achiral molecules are spontaneously optically resolved, i.e., deracemization, the chiral domains of which give rise to huge chiral nonlinear optical effect.
DOI: 10.1103/PhysRevLett.94.137801 PACS numbers: 61.30.Eb, 61.30.Cz, 42.65.Ky, 42.70.Df
Bent-core molecular systems have opened a new era in liquid crystal science which is still filled with a myste-rious and attractive nature. Many recent studies are mo-tivated by two significant results for the achiral bent-core liquid crystal (LC) molecule 1, 3-benzene bis[4-(4-n-alkoxyphenyliminomethyl)benzonate] PnOPIMB by Watanabe et al., that is, (1) polar switching in the highest temperature smectic phase (B2 phase) [1], and (2) sponta-neous chiral formation in the room temperature phase (B4 phase) [2]. In fact, in the B2 phase, polarity is realized by close packing and symmetry breaking due to the tilt of bent-core molecules from the layer normal [3], so that the B2 phase also has a spontaneous chirality. In addition, many chiral phenomena have been reported such as en-hanced twisting power [4,5] and induced blue phase [6] by doping conventional chiral systems with achiral bent-core molecules.
The B4 phase is a very complicated glasslike state and exhibits no electric-field induced molecular reorientation. New insights into the structure could be obtained if the existing chirality was manifested as strong optical activity. While the B4 phase in thin LC cells exhibits a uniform and bluish colored microscope texture of small domains in transmission between crossed polarizers, optical segrega-tion could be easily recognized upon slight rotasegrega-tion of the analyzer from the crossed position. Recent reports on polarized Fourier-transform infrared spectrosopy [7,8] and NMR [2,9] suggest that the molecules in such domains have conformational chirality. However, such a strong optical activity in thin LC cells cannot be driven only by molecular conformational chirality but can also be due to macroscopic chirality such as helix formation. In fact, a twist-grain-boundary (TGB) structure has been suggested by x-ray diffraction [2,10] and freezed fraction transmis-sion electron microscopy [11] measurements, in which uniform smectic blocks twist through grain boundaries and form a helix along the smectic layer plane. But still,
it is not a complete model, because it would be intrinsically different from the usual TGB structure in conventional rod-core molecular systems [12]. Nevertheless, there is no doubt that the B4 phase is a novel version of a chiral aggregation form in achiral molecular systems.
In linear optics, chiral media are known for their optical activity effects, e.g., circular dichroism and optical rota-tion. These effects are well known and are due to magnetic-dipole contributions to the linear optical response. In addi-tion, chirality can also lead to important even-order non-linear optical (NLO) effects such as second harmonic generation (SHG). It is generally considered that even-ordered NLO effects, in the electric-dipole approximation (ED: eee process; two electric-dipole-transition processes at ! from a ground state to an excited state are followed by an electric-dipole-transition process at 2 ! for deexcita-tion), are forbidden in centrosymmetric systems, and hence SHG is often used as a convenient tool to investigate polar media. However, under certain conditions, higher order NLO effects through electric quadrupole (EQ: eeQ=Qee process) [13–15] or magnetic-dipole (MD: eem=mee pro-cess) [16 –18] interactions can be allowed. For example, SHG through a MD process can be of the same order of magnitude as that of the usual ED processes in chiral media [19]. Symmetry properties in such higher order processes are different, and can allow for significant contributions to SHG circular dichroism (CD) signals through NLO tenso-rial components different from those involved in ED pro-cess. Quantitative analysis of SHG CD through a MD process in chiral organic materials has already been per-formed by Persoons et al. [20 –25]. However, it is also true that the importance of the MD process was unambiguously recognized only in a few materials.
Recently, we demonstrated an electrogyration (EG) ef-fect in the B4 phase of the bent-core molecule [26]. The EG effect is an induced optical rotation effect, which is one of the linear electro-optical modulation effects through a PRL 94, 137801 (2005) P H Y S I C A L R E V I E W L E T T E R S 8 APRIL 2005week ending
MD process. This suggests the existence of a chiral NLO effect in the B4 phase. Detailed study of such a chiral NLO effect is significant and necessary to obtain structural information on the B4 phase. In this Letter, we will dem-onstrate a SHG CD measurement for the B4 phase, and present a distinct structural model by theoretical analysis. The sample used was a mixture of achiral (P8OPIMB, 85 wt %) and chiral (P8OPIMB6, 15 wt %) bent-core molecules, which has a phase sequence of Iso-B2-B3-B4. In general, P8OPIMB6works as a chiral dopant and raises up a ratio of () enantiomeric domains in the B4 phase [27,28]. The mixture was introduced into a sandwich shaped glass cell 8 m thick with a pair of indium tin oxide electrodes. To obtain sufficiently large domains, several temperature cycles between B2 and B4 phases were made under a rectangular electric field of 50 V peak-to-peak. After these treatments, we obtained suffi-ciently large () enantiomeric domains as well as () enantiomeric domains.
Experimental data for quantitative analysis were ob-tained by a quarter-wave plate rotation (QWR) method. The optical scheme of the measurement is shown in Fig. 1. By rotating the quarter-wave plate (QW) between two polarizers (P1 and P2), the input polarization of the fun-damental beam was continuously varied, and results were obtained as a function of rotation angle of the QW. For all measurements, 1064 nm light of an Nd:YAG laser was used as a fundamental beam and generated frequency doubled light at 532 nm was detected from the transmitted direction. Since an oblique geometry is required to analyze the chiral contribution, the incidence angle of the light was fixed at 45. The fundamental beam was focused to a 200 m diameter area on the sample cell.
Experimental results are plotted in Fig. 2 (filled circles) as a function of the angle between the optic axes of the QW and the sample domain. Here, four polarization combina-tions for the two polarizers (P1 and P2) are shown. For s input, 45 and 225 correspond to right-handed circular polarization (RCP), and 135 and 315 to left-handed circular polarization (LCP). The sign of each enantiomeric
domain designates the sign of its optical rotation direction. It is clear from the figure that for the same polarization combinations, plots in two different enantiomers are mirror images of each other. SHG CD is notably seen as an ob-vious difference between RCP and LCP. Particularly, the difference is remarkable for sin poutin Fig. 2(a) and 2(b);
namely, signals at 45and 225 which are corresponding to RCP fundamental light are larger than those at 135and 315corresponding to LCP for Fig. 2(a) and vice versa in Fig. 2(b). The same is true for the other polar-ization combinations. Defining the SHG CD intensity as ISHG CD 2ILCP IRCP=ILCP IRCP, we obtain
ISHG CD 0:35 and ISHG CD 0:39 for () and () domains, respectively. For the two enantiomeric domains, the SHG CD intensities are almost equal in magnitude but
QW z y x Es(ω) Ep(ω) Es(2ω) Ep(2ω) P1 P2 Sample 532nm 1064nm p s
FIG. 1. Optical scheme of the QWR measurement. Polarization of the incident beam is controlled by the first polarizer (P1) and a QW. Generated SH light is analyzed by the second polarizer (P2).
FIG. 2. Polar plots of experimental (filled circles) and theo-retical (solid curves) results of QWR measurement for (a) () domain and (b) () domain. Each polarization combination shows SHG CD between angles corresponding to LCP and RCP.
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opposite in sign. Hence, this suggests that the chiral con-tribution dominates the SHG in the B4 phase. It is also worth noting that these values are comparable with those estimated from reports on chiral organic films [20,25].
Now let us assume TGB structure models for the B4 phase, as illustrated in Fig. 3. The z and y axes were taken as parallel to the helical axis and normal to the substrates, respectively, and hence the z x plane was equivalent to the plane of the cell substrates. In this case, as mentioned in the report by Thisayukta et al., two different TGB struc-tures are expected because of the bent molecular shape; one has a helical axis parallel to the bent direction [z axis in Fig. 3(a)] of the molecules (mode A) and the other perpen-dicular to it (mode B) [10]. Based on the following simple consideration, however, we can conclude that only the first structure is possible: If we assume a point group C2for the bent-core molecule with a chiral conformation, the point groups of mode A and mode B are C1 and D1,
respec-tively. For D1symmetry, the only nonzero elements of the
nonlinear susceptibility, ijks, are those where i, j, and k are all different (for the eee, mee, and eem processes). This means that at least the signal for 0of sin soutmust be zero, since the signal should contain only ijks for i j k. However, the experimental result for sin sout clearly shows a strong signal at 0 (see Fig. 2). Thus, we can safely exclude the mode B from the choice.
To describe the SH signal as a function of rotation angle of QW, we take a simple notation proposed by Persoons et al. [20 –25] using p-polarized (Ep) and s-polarized (Es) field components for incident angle as,
E2! / fE2
p! gE2s! hEp!Es! fF gG hH; (1) where the factors, F E2
0sin2 icos22, G E2
0sin2cos21 i2, and H E20sin cos
1 isin2 icos2, represent complex-formalized
fields of fundamental wave. And the other three factors f, g, and h are effective nonlinear susceptibilities for the field factors F, G, and H, respectively.
Assuming a MD (eem and mee) process induced by chirality, the independent tensorial components of the non-linear susceptibility for the C1group are restricted to only
15, eee
zzz, eeezxx eeezyy, eeexxz eeexzx eeeyyz eeeyzy and eeexyz eeexzy eeeyxz eeeyzx for the eee process, eem
zzz , eemzxx eemzyy, eemxxz eemyyz, eemxzx eemyzy, eemxyz eem
yxz, eemzxy eemzyx, and eemxzy eemyzx for the eem process, and meezzz , meezxx meezyy, meexxz meexzx mee
yyz meeyzy, and meexyz meexzy meeyxz meeyzx for the mee process. Then, f, g, and h for the s- and p-polarized SH field in transmission are
fTs 2eeexyzsin cos eemxzx cos 2mee
xxz meezxxsin2 cos meezzz cos3 gTs eemxxz meezxx cos
hTs 2eeexxzcos eemxyz eemxzy 2meexyz sin cos fTp 2eee
xxz eeezxxsin2 cos eeezzzcos3 eem
zxy eemxzy 2meexyz sin cos gTp eee
zxxcos eemzxy eemxyz sin cos
hTp 2eeexyzsin cos eemxxz eemxzxsin2 cos eem
zzz eemzxxcos3 2meexxz cos: (2) According to the perturbation theory, all of the nonlinear susceptibility elements are complex. In nonresonant con-ditions, however, the imaginary part of eeeis sufficiently small and negligible. On the other hand, those of eemand meeare pure imaginary under nonresonant conditions. In the present experimental conditions, the SH wavelength (532 nm) is far from the absorption band (around 370 nm), so that the nonresonant condition can be safely assumed for the calculation.
The solid curves in Fig. 2 are the best fit to all the experimental results using mode A. Here, for the chiral components, the same absolute values with opposite signs were used for two chiral domains. Obviously, the agree-ment is satisfactory. Again, a mirror relation is confirmed in the patterns of two enantiomers for the same polarization combinations, which is theoretical proof of an existence of a chiral NLO effect. At the same time, the agreement strongly supports our TGB model.
The estimated relative values of independent compo-nents of the nonlinear susceptibility are listed in Table I. Surprisingly, one of chiral components, eem
xxz, reaches al-most half of the maximum component eee
zzz together with achiral components such as mee
xyz and eemxzy. It should be noted that these MD contributions in the present achiral system are comparable to that in chiral conjugated poly-mers [22]. Thus, it is concluded that the chiral NLO phenomena in the B4 phase are mainly attributed to MD processes induced by chirality. This fact is consistent with our previous study on the electrogyration effect.
In conclusion, we have successfully analyzed SHG CD in the B4 phase by means of a QWR method. As a definite (a) Mode A
(b) Mode B
z axis
FIG. 3. Expected TGB structures in the B4 phase with helical axes; (a) parallel and (b) perpendicular to the bent direction of the molecules. Each broken line indicates a helical axis and is parallel to the z axis.
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model of the B4 phase, a TGB structure having its helical axis along the bent direction was proved. In such a chiral structure, magnetic transition processes can play an im-portant role and are comparable with those in chiral poly-mer systems. Finally, we should emphasize that the present huge chiral NLO effect is observed in a system consisting of achiral molecules.
The authors acknowledge Professor Thierry Verbiest in University of Leuven for careful reading and useful com-ments. This work is partly supported by a grant-in-aid for Scientific Research on Priority Area (B) (12129202), 21st century COE program by the Ministry of Education, Science, Sports, and Culture of Japan, and the q-PSI pro-gram at Hanyang University through KOSEF of the Republic of Korea.
*Email address: htakezoe@o.cc.titech.ac.jp
Electronic address: http://www.op.titech.ac.jp/gs/takezoe/ index.html
†Present address: Department of Electrophysics,
Kwangwoon University, Seoul 139-701, Korea.
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TABLE I. Relative values of the nonlinear susceptibilities determined by QWR, normalized with respect to Reeee
zzz
1:000. Double signs are in the same order; the upper ones apply to the () domain and the lower tothe () domain.
Achiral components Chiral components
eee eee zzz 1:000 eeexyz 0:022 eee xxz 0:035 eee zxx 0:052 eem eem
xyz 0:290i eemzzz 0:039i
eem
xzy 0:450i eemzxx 0:216i
eem
zxy 0:281i eemxxz 0:433i
eem
xzx 0:186i
mee mee
xyz 0:442i meezzz 0:229i
mee
zxx 0:009i
mee
xxz 0:022i
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