Computer Simulation of an Antiferroelectric Liquid Crystalline

Fujitsu Ltd., Nakase, Mihama-ku, Chiba-shi, Chiba 261, Japan, and Personal System Laboratory, Fujitsu Laboratories Ltd., 64 Nishiwaki, Ookubo, Aka...
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J. Phys. Chem. 1996, 100, 15207-15210

15207

Computer Simulation of an Antiferroelectric Liquid Crystalline Molecule: The Origin of Bent Structure Formation and the Molecular Packing Property of MHPOBC in Crystalline Phase H. Toriumi,*,† M. Yoshida,‡ M. Mikami,§,| M. Takeuchi,§ and A. Mochizuki⊥ Department of Chemistry, College of Arts and Sciences, The UniVersity of Tokyo, Komaba, Meguro-ku, Tokyo 153, Japan, Technical Research Institute, Toppan Printing Company, Sugito, Kita-katsushika-gun, Saitama 345, Japan, Research Center for Computational Science, Fujitsu Ltd., Nakase, Mihama-ku, Chiba-shi, Chiba 261, Japan, and Personal System Laboratory, Fujitsu Laboratories Ltd., 64 Nishiwaki, Ookubo, Akashi-shi, Hyogo 574, Japan ReceiVed: March 14, 1996; In Final Form: May 31, 1996X

Molecular orbital (MO) calculation and molecular dynamics (MD) simulation were carried out for an antiferroelectric liquid crystalline molecule, MHPOBC, to understand its conformational property and the origin of bent structure formation in crystalline phase. MO calculations performed for a chiral chain fragment of MHPOBC have determined the conformational state of each bond in the chiral chain. MD simulation, carried out for a system of 64 full MHPOBC molecules, has been able to reproduce the experimentally observed bent conformation and the molecular packing. The present study concludes that (1) the essential conformational feature of the chiral chain of MHPOBC is determined by intramolecular interactions, (2) MHPOBC can adopt two major conformations, i.e., linear and bent conformations, and (3) the bent conformation is selected in the crystalline phase as a consequence of intermolecular steric interactions.

Introduction MHPOBC ((S)-4-[(1-methylheptyloxy)carbonyl]phenyl 4′octyloxybiphenyl-4′-carboxylate: Figure 1) has extensively been studied as the first example of antiferroelectric liquid crystalline molecule.1 Among these studies, an X-ray crystallography carried out by Hori and Endo2 for a MHPOBC single crystal is particularly interesting, since it reveals a very unique and characteristic conformational property of the MHPOBC molecule. That is, the chiral chain of MHPOBC is oriented nearly perpendicular to the core moiety as illustrated in Figure 2, in contrast to our natural anticipation that the molecules forming smectic phases would adopt an elongated molecular shape to conform to the layered smectic structure. To understand the molecular origin of the bent structure formation, we carry out in this study molecular orbital (MO) and molecular dynamics (MD) calculations. The conformation of a chiral alkyl chain in ferroelectric and antiferroelectric liquid crystalline molecules is fundamentally different from that of simple alkyl chains in conventional nematic and/or smectic liquid crystals. Namely, the rotational state about skeletal C-C bonds is biased by the steric constraints imposed by substituting groups, and consequently the average orientation of the alkyl chain relative to the core moiety is modified. This “biased molecular shape” would affect the rotational and packing property of the molecule in liquid crystalline phases. Moreover, the conformational constraints imposed by chiral substituting groups may modify the orientation of the dipole moment located on an adjacent functional group, and this, in conjunction with the hindered molecular rotation, would determine the magnitude of spontaneous po* Corresponding author ([email protected]). † The University of Tokyo. ‡ Toppan Printing Co. § Research Center for Computational Science, Fujitsu Ltd. | Present address: National Institute of Materials and Chemical Research, 1-1 Higashi, Tsukuba-shi, Ibaraki 305, Japan. ⊥ Personal System Laboratory, Fujitsu Laboratories Ltd. X Abstract published in AdVance ACS Abstracts, August 1, 1996.

S0022-3654(96)00790-3 CCC: $12.00

Figure 1. Structure and phase transition temperatures of MHPOBC.

Figure 2. Bent conformation of crystalline MHPOBC observed by X-ray crystallography (ref 2).

larization. Thus, the chiral chain conformation is intimately related to the origin of ferroelectricity and/or antiferroelectricity in liquid crystals; however the detailed conformational property of the chiral chain liquid crystalline molecules has not yet been clearly elucidated. In this study we carry out computer simulation for the antiferroelectric MHPOBC molecule. Our primary interest is to understand the fundamental conformational property of a chiral alkyl chain in ferro- and antiferroelectric liquid crystalline molecules. To accomplish this purpose, we perform (1) MO calculations for an R-substituted chiral chain fragment of MHPOBC to determine the conformational space available for each bond and (2) MD simulation for a set of full MHPOBC molecules to find their stable conformation and packing property in the crystalline state. The MO calculation suggests the formation of two possible conformations (i.e., linear and bent conformations). These two conformations, calculated for the chiral chain fragment of MHPOBC, are expected to be of general prototype structure that would commonly appear in all © 1996 American Chemical Society

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Figure 3. Chiral chain fragment of MHPOBC used in the MO calculations.

TABLE 1: Bond Lengths and Bond Angles Used in the MO Calculations of the Chiral Chain Fragment bond length/nm C-C (phenyl) C-C (alkyl) C-H C-O CdO

bond angle/deg 0.139 0.154 0.110 0.143 0.121

C1-C2-O1 C1-C2-O2 C2-O1-C3 C-C-C C-C-H

120.0 120.0 109.49 109.49 109.49

Figure 4. Rotamer distribution curve about the chiral chain χ2 bond of MHPOBC at T ) 298 K. P(χ2) is the probability density (arbitrary unit) of the torsion angle χ2: P(χ2) ) ∑χ1 ∑χ3 ∑χ4 ∑χ5 exp(-E/kBT).

ferro- and antiferroelectric liquid crystalline molecules with the R-substituted chiral alkyl chain. Comparison of the results of MO and MD calculations can separate intra- and intermolecular factors responsible for the determination of preferred molecular conformation of MHPOBC and indicates that the bent conformation is selected in the crystalline phase as a consequence of intermolecular interactions. Calculations (1) MO Calculations. The semiempirical molecular orbital calculation (MOPAC6, PM3)3 was carried out on a SGI IRIS workstation for the chiral chain fragment of MHPOBC shown in Figure 3. For simplicity, we assumed idealized geometry for phenyl groups (hexagonal) and for alkyl chains (tetrahedral) and fixed all bond lengths and bond angles to the values listed in Table 1. Conformational energy was calculated for 8 × 106 conformers with varying the torsion angles χ1-χ5 at every 15° interval, while maintaining the χ6-χ8 angles at the trans position according to the X-ray observation. As one might find in Figure 2, the chiral terminal chain would not reach the biphenyl group or beyond (even if it does, these conformers should have very high energies). Thus, the result obtained for the “small model molecule” introduced in Figure 3 should represent an intrinsic conformational property of an R-substituted chiral alkyl chain linked to the phenyl ring by the ester group. Consequently, this result should generally apply to all ferro- and antiferroelectric liquid crystalline molecules with the same chiral chain fragment. It may also be noted that the calculations using this small model molecule should reduce the computation time to a great extent. (2) MD Simulation. The molecular dynamics (MD) simulation was carried out for a system of 4 × 4 × 4 MHPOBC molecules under a periodic boundary condition using the Fujitsu MASPHYC program on a Fujitsu VP2600/10 UPX vectorcomputer (5 GFLOPS). Fujitsu MASPHYC is a multipurpose MD simulator for organic and inorganic materials, having a library of various potential functions. MASPHYC is especially advantageous to analyze the self-organizing systems such as liquid crystals, since it is designed to include large number of molecules (practically, no limitation is set for the number of molecules). The simulation was performed in a constant NTP ensemble: The temperature T was kept constant at 298 K by the Nose algorithm4 and the pressure P was kept constant at 1 atm by the Parrinello and Rahman algorithm.5 The initial configuration of the system was taken from the X-ray data in

Figure 5. Rotamer distribution curve P(χ3) for the chiral chain χ3 bond of MHPOBC.

ref 2, and the simulation was carried out up to 35 ps at 0.5 fs integration time steps. For the calculation of nonbonded interaction energies, the united-atom approximation was employed for the CH2 and CH3 groups, and the DREIDING force field parameters6 were used. The electrostatic interactions were calculated by the Ewald method7 using the electric charges optimized by molecular orbital (MOPAC ESP)8 calculations. Results (1) Molecular Conformation of MHPOBC. The conformer distribution curves calculated by MO and MD for the χ2-χ5 bonds in the chiral alkyl chain of MHPOBC are shown in Figures 4-7 together with the experimental X-ray data. The torsion angle χ1 (defining the phenyl-ring rotation relative to the ester plane) has only marginal influence on the alkyl chain conformation (χ2-χ5), and this will not be discussed in further detail. The χ2 rotamer distribution curve in Figure 4 calculated by MO shows a symmetric distribution around 180°. This structure corresponds to the one in which the asymmetric carbon atom C3* lies in the ester plane (see Figure 3). The experimental X-ray indicate that the same χ2 conformation is maintained in crystalline phase, while the MD simulation shows a slight shift of the χ2 angle to ∼150°. In Figure 5, all MO, MD, and X-ray results coincide with each other and indicate that the χ3 bond takes only one stable conformation at χ3 ≈ 225°. Originally, the O1-C3 bond has a 3-fold rotational potential in an unsubstituted linear alkyl chain. However, the introduction of the C10 methyl group destabilizes all these three conformers and restricts the χ3 rotation to the

MO and MD Simulation of Antiferroelectric MHPOBC

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Figure 8. Snapshot of initial and final configuration of the 64 MHPOBC molecules in the MD unit cell.

Figure 6. Rotamer distribution curve P(χ4) for the chiral chain χ4 bond of MHPOBC.

Figure 7. Rotamer distribution curve P(χ5) for the chiral chain χ5 bond of MHPOBC.

225° position. As shown in an inserted Newman projection, both C4 (alkyl) and C10 (methyl) groups are located at the most remote position from the ester C2(O2) group in this conformation. Introduction of the R-methyl group thus simplifies the rotational state about the χ3 bond. Since both χ2 and χ3 have only one rotamer, no major conformational transition should take place in this region. In contrast to this, the rotamer distribution curve about the χ4 bond becomes quite complicated when the R-methyl group is introduced. The P(χ4) curve in Figure 6 shows that the gauche conformer at χ4 ) 300° is destabilized because of C5C10 steric interactions and, at the compensation of this conformer, the population of the trans (165°) and the second gauche (75°) conformers increases. As we will see below, the trans χ4 rotamer results in an elongated, linear molecular conformation, which is generally believed to be the most favored structure of rodlike (calamitic) liquid crystalline molecules. Surprisingly, however, both MD and X-ray results indicate that MHPOBC in the crystalline phase assumes the χ4 gauche conformation, which leads to the bent molecular structure. Obviously, this selection of the gauche conformers is a consequence of intermolecular packing constraints imposed by neighboring molecules. The mechanism of the bent structure formation will be discussed again in a later section. Finally, we plot in Figure 7 the rotamer distribution curve for the C4-C5 bond (χ5). The P(χ5) curve shows a symmetric distribution of the trans and the two gauche conformers characteristic of the alkyl C-C bonds, and among these three

conformers the most favorable trans conformer is selected in the crystalline phase. This symmetric P(χ5) curve indicates that the steric constraints imposed by the R-methyl group no longer have any significant influence on the rotational state about the χ5 bond. The same result was obtained in a preliminary MO calculation for outer χ6-χ8 bonds, and this justifies the assumption we made in the present MO calculation that the χ6χ8 rotation can be fixed at the trans position. (2) MD Simulation of Molecular Packing. The experimentally observed molecular packing of MHPOBC in the crystalline phase has been reproduced by the MD simulation. More precisely, the initial crystalline structure is maintained over a reasonably long simulation period (35 ps or 70 000 steps, computation time 280 min). Snapshots of the initial and final configurations of the 64 MHPOBC molecules in a simulation cell are shown in Figure 8. Although small-amplitude conformational fluctuations are seen, essential conformational and packing features are well preserved even after 35 ps of equilibration. For critical evaluation of the MD results, we may have to point out the following observations. First, the unit-cell dimension was not properly reproduced, but its volume decreased approximately 6.2% after equilibration. Second, some the structure parameters (particularly those associated with aromatic core groups) showed certain deviation from the initial values. For example, the torsion angle of the biphenyl group was calculated to be (60° (with broad distribution around these values), although the initial angle was assumed to be 0° (coplanar conformation). These discrepancies, associated with either the core geometry or the core packing property, seem to arise from inappropirate setting of the force field parameters assumed for core atomic groups. In fact, we used “universal” force field parameters (i.e., the DREIDING parameters) without any further optimization. If we adjust, for example, the biphenyl 2-2′ interaction parameters so as to reproduce the experimentally observed coplanar structure, overall agreement between experiment and calculation would further be improved. Nevertheless, this inadequacy of the core interaction parameter does not affect the calculations of chiral chain conformation. As we have shown in Figures 4-7, the MD simulation can reproduce the experimental X-ray structure of the chiral alkyl chain in crystalline MHPOBC quite successfully. Discussion In this study we have shown that the MHPOBC molecule can adopt two major conformations. As illustrated in Figure 9, these two conformers have essentially the same structure except the rotational state about the χ4 bond. That is, when it assumes the gauche state (χ4 ) 75°), a bent conformation is formed, while when it is in the trans state (χ4 ) 165°), an elongated linear conformation results. Selection of the preferred conformation in the crystalline state is a consequence of intermolecular packing constraints, and MHPOBC chooses the one with the χ4 ) gauche conformation.

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Figure 9. Two major conformations of MHPOBC and the Newman projections of their χ4 bond predicted by MO calculations.

To continue the discussion, it may be helpful to summarize the results of MO and MD calculations obtained above. First, the χ2 and χ3 bonds have only one stable rotamer, and therefore no conformational transition can take place around these bonds. In other words, these bonds are “rigid”, and consequently the same conformation would be maintained regardless of the phase. Second, the most favored conformation of the alkyl χ5-χ8 bonds is the lowest energy trans conformation, and this conformation would also be preserved in all phases (although it is expected that gauche conformers may increase their population toward the chain end; this would have no major influence on the average molecular shape). Thus, the C3*C4 bond (χ4), which can assume either the trans or the gauche conformation (see Figure 6), is solely responsible for the determination of the overall molecular shape, and as we have seen above, the χ4 bond of MHPOBC in the crystalline phase assumes the gauche conformation (χ4 ) 75°) that leads to the bent structure. Integration of these results may suggest that the MHPOBC molecules in an antiferroelectric Sm*CA phase, which is the lowest temperature liquid crystalline phase located just above the crystalline phase, would also take on the bent conformation. However, the structure of phases in condensed systems such as liquid crystals, which may involve complex intermolecular interactions, cannot be simply determined by the quantity of state (e.g., temperature and pressure) but depends also on the thermodynamic process that the system has experienced. In fact, MHPOBC has a monotropic ()irreversible) polymorphism.2 The crystalline phase discussed in this paper, in which the bent structure has been observed, is a metastable phase. This metastable phase (I) transforms Via another metaphase (II) into a stable crystalline phase (III) in an irreversible fashion; that is the I and II phases do not appear when the stable III crystal is cooled. In addition, the powder X-ray observation indicates that the form III crystal has a longer layer spacing (37.1 Å) than the form I crystal (31.8 Å). These two observations together may indicate that the formation of the form III crystal involves not only the packing transition but also the conformational transition of the MHPOBC molecules. If this is the case, then we can suggest from the results of MO and MD calculations that the molecules in crystal III (and consequently those in the Sm*CA phase) might have the elongated, linear conformation instead of the bent conformtion found in crystal

Toriumi et al. I. This speculation is consistent with the fact that the form III crystal formed by elongated MHPOBC molecules (the most favorable conformer in Figure 6) does not transform back to the form I crystal of the bent MHPOBC molecules. Moreover, an independent deuterium NMR study9 carried out for a ferroelectric liquid crystalline molecule (with a chiral alkyloxy chain instead of the alkyl ester chain in MHPOBC) has shown that this chiral alkyloxy chain assumes an elongated all-trans conformation in smectic liquid crystalline phases. All these observations together indicate that the MHPOBC molecule and other ferroelectric compounds with the R-substituted chiral chain should take on the elongated molecular conformation in liquid crystalline phases, while the origin of the formation of the bent MHPOBC structure in a metastable crystalline phase (I) should be attributed to intermolecular steric constraints. No single-crystal X-ray data are reported for the form III crystal, nor can we observe the molecular packing and conformation in bulk liquid crystalline phases directly. At the present stage, computer simulation is the only available technique with which we can visualize the structure and packing of molecules in fluid liquid crystalline phases. The problem discussed in this study, i.e., the origin of supramolecular organization in crystalline and liquid crystalline phases, is a good example for which computer simulation can demonstrate its potential predictive powder. We still need to carry out MD simulations at different temperatures and in different phases to draw more definitive conclusion, since the bent conformation has been anticipated to play a certain important role in determining the physical property of Sm*CA liquid crystalline phases.10,11 It is particularly interesting to explore the possibility of the formation of crystalline and/or liquid crystalline phases consisting of elongated, linear MHPOBC molecules. This computer experiment should reinforce our prediction of the formation of an elongated MHPOBC conformation in antiferrolectric liquid crystalline phases. A MD simulation along this direction is now in progress. Acknowledgment. This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture, Japan. References and Notes (1) Chandani, A. D. L.; Gorecka, E.; Ouchi, Y.; Takezoe, H.; Fukuda, A. Jpn. J. Appl. Phys. 1989, 28, L1265. (2) Hori, K.; Endo, K. Bull. Chem. Soc. Jpn. 1993, 66, 46. (3) Stewart, J. J. J. Comput. Chem. 1989, 10, 209, 210. (4) Nose, S. Mol. Phys. 1984, 52, 255; J. Chem. Phys. 1984, 81, 511. (5) Parrinello, M.; Rahman, A. Phys. ReV. Lett. 1980, 45, 1196; J. Appl. Phys. 1981, 52, 7182. (6) Mayo, S. L.; Olafson, B. D.; Goddard, W. A., III. J. Phys. Chem. 1990, 94, 8897. (7) Ewald, P. P. Ann. Phys. 1921, 64, 253. (8) Bester, B. H.; Uerg, K. M., Jr.; Kollman, P. A. J. Comput. Chem. 1990, 11, 431. (9) Toriumi, H.; Yoshida, M.; Kusumoto, T.; Kumaraswamy, G.; Hiyama, T.; Samulski, E. T.; Poon, C.-D. To be published. (10) Miyachi, K.; Matsushima, J.; Takanishi, Y.; Ishikawa, K.; Takezoe, H.; Fukuda, A. Phys. ReV. E 1995, 52, R2153. (11) Ouchi, Y.; Yoshioka, Y.; Ishii, H.; Seki, K.; Kitamura, M.; Noyori, R.; Takanishi, Y.; Nishiyama, I. J. Mater. Chem. 1995, 5, 2297.

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