Theoretical analyses of dipole moments and bent angles in H-bonded complexes

In order to analyze the variation of the polarities by insertion of single and double H-bonds in H-bonded complexes, the supramolecular dipole moments, electron cloud distributions, and bent angles were calculated by the molecular modelling, which would influence the polar switching behavior in covalent- and H-bonded bent-core structures with suitable bent-cores and flexible chains. Four simplified bent-core

Figure 2.12. Molecular electrostatic potential mapped on the electron density isosurface of 0.0004 au of the lowest energy structure for the four bent-core structures (a) S1, (b) I-A1, (c) IV1-A1, and (d) III1-B1.

structures, including H-bonded complexes I-A1, III1-B1, and IV1-A1, and covalent-bonded compound S1, bearing methoxyl groups at their terminuses were designed as shown in Figure 2.12, where the electron cloud distributions of these

X Y

Z

(a)

(b)

(c)

(d)

complexes I-A1, III1-B1, and IV1-A1 were reduced by the non-covalent aggregation of H-bonded electrons at benzoic acid positions. As shown in Table 2.9, the theoretical calculations of molecular modeling for covalent- and H-bonded bent-core structures with lowest energies (see supporting information) were simulated by Gaussian03 at B3LYP level with 6-31G(d) basis set. Regarding covalent-bonded compound S1, the projective low values of dipole moments along X and Z directions were equal to 1.394 and 0.172 Debyes, which were mutually offset due to the symmetric structure. However, a large value of -4.123 Debyes in direction Y was evaluated to contribute to the total dipole moment in the molecular polar direction.

Because of the symmetric skeleton in H-bonded complex I-A1, the similar results of the projective low values of dipole moments in X and Z dimensions were eliminated to 1.041 and -0.090 Debyes, and a very small value of 1.126 Debye was acquired in Y dimension due to the non-covalent electron aggregation of H-bonded sites. Hence, a much smaller total dipole moment of 1.53 Debye (along with the smallest polarity) was obtained in the simplified H-bonded complex I-A1, and thus to speculate the non-polar switching behavior for H-bonded symmetric trimers I-Am (with two H-bonds). In contrast to complex I-A1, the polar destruction was also obtained in Y direction (-2.971 Debyes) for complex IV1-A1 due to the non-covalent electron aggregation of H-bonded sites. However, the projective dipole contribution along X and Z directions (-3.418 and -0.022 Debyes, respectively) were revealed as a result of the asymmetric structure in complex IV1-A1. Therefore, the total dipole moment of 4.53 Debyes in complex IV1-A1 was achieved to suggest the polar switching behavior for H-bonded asymmetric dimers IVn-Am (with one H-bond). Comparing complexes I-A1 and IV1-A1, the polar switching behavior of H-bonded asymmetric dimers IVn-Am can be expected according to the visualization of the simplified model complex IV1-A1 with larger total dipole moments.

Table 2.9. Calculated Dipole Moments and Bent Angles of Optimized Covalent- and H-Bonded Bent-Core Structures at the B3LYP/6-31G(d) Level

Compound Bent angle (°)^a Axial Dipole moment (Debye)

X 1.394 conformational search using molecular mechanics force-field were used for full geometry optimization at the B3LYP/6-31G(d) level. ^a Bent angle (°) measured as the angle between the first, central and final benzene rings’ centers of the bent-core structures. The dipole moments of the lowest energy structure are given, and the calculated dipoles are in the range of 4.00-8.85 (S1), 0.21-1.94 (I-A1), 4.53-6.69 (IV1-A1), and 4.10-7.24 (III-B1) (see supporting information).

In the investigation of bent angle effect on the polar switching behavior of bent-core liquid crystals, the suitable bent angle for bent-core molecular configuartion is better close to 120° (or in the range of 110° to 130°).[3,29a,43d,58]

Usually, calamitic LC materials possessing bent-core configurations with bent angles larger than 130° or less than 110° will reveal normal mesophases without polar switching behavior, such as the smecitc C, smecitc A, and nematic phases. In

obtained in molecules S1 and IV1-A1, respectively, to support the existence of spontaneous polarization. However, the lower bent angle values (less than c.a.

100°) were achieved in complex III1-B1 due to the near central-site H-bonds, even if the sufficient total dipole moment values (c.a. 4.10 Debyes) were acquired. It would be speculated that the deficiency of polar switching behavior in H-bonded asymmetric dimers with single near-central H-bonded sites, such as complexes IIIn-Bm and IIIn-Cm, was owing to their small bent angles (less than c.a. 100°).

Overall, the asymmetric H-bonded molecular design as well as the suitable molecular bent angle is useful to enhance the total dipole moments and polarities in accordance with the theoretical analyses of molecular modelling, and the spontaneous polarization and switching behavior can not only be experimentally proven but also theoretically predicted in our study.

2.4. Conclusions

In summary, several series of novel banana-shaped liquid crystalline supramolecules consisting of H-bonded symmetric trimers (with two H-bonds) and asymmetric hetero-dimers (with one H-bond) were self-assembled by appropriate molar ratios of proton donors (H-donors) and acceptors (H-acceptors). The influences of H-bonded linking positions and aromatic ring numbers (in the rigid cores) as well as the chain lengths (in the flexible parts) on the mesomorphism and the switching behavior of the bent-core supramolecules were reported. Moreover, the voltage-dependent switching properties of spontaneous polarization (Ps) in the polar smectic C phase of the banana-shaped H-bonded complexes were observed. In the normal field-off state, except for the supramolecular structures with longer rigid cores or shorter flexible chains possessing the rectangular columnar (Col_r or B1) phase, the SmCAPA phase was revealed in most supramolecular asymmetric hetero-dimers (with

one H-bond), which was switched to the SmC_SP_F phase by applying electric fields. In addition, the SmA and nematic phases were observed in H-bonded asymmetric dimers with H-bonded sites close to the core center, but the polar smectic C phase was dominated for those with H-bonded sites apart from the core center. Compared with the fully covalent-bonded analogue, lower transition temperatures and lower threshold voltages were developed in H-bonded asymmetric dimers with the polar smectic C phase. The existence of polar switching behavior in the polar smectic C phase of asymmetric hetero-dimers (with one H-bond) related to the molecular configurations with higher dipole moments as well as the suitable bent angle was further demonstrated by the theoretical calculations of molecular modeling. Besides, the lack of polar switching behavior in supramolecular symmetric trimers (with two H-bonds), which exhibited the regular SmC phase with weak electrical stabilities, might be related to their configurations with smaller dipole moments. Finally, due to the low electrical stabilities of the H-bonded symmetric trimers (with two H-bonds), their supramolecular architectures with the polar smectic C phase may be preserved or created by the stabilization H-bonded structures through further auxiliary techniques (such as copolymerization and blending with covalent-bonded analogues) in the future studies. Finally, the spontaneous polarization and switching behavior of H-bonded banana-shaped LC materials are the first time experimentally proven and theoretically predicted in our study.

2.5. Electronic Supplementary Information