Rack-gear structures in columnar liquid crystal phases of trialkoxybenzyl pentafluorobenzoates and their influences on intercolumnar interdigitation and macroscopic morphologies

ABSTRACT In this study, 3,4,5-trialkoxybenzyl pentafluorbenzoates with alkyl chains of various lengths were synthesised, and the phase transition behaviours, liquid crystallinities, and molecular packing structures of their columnar phases were investigated. The results showed that discs comprising two half-discoid molecules stack up to form columns with rack-gear structures, generating columnar liquid crystal phases. From powder and single crystal X-ray diffraction investigation, the mechanism of the self-assembly of molecules into columns and their intercolumnar interdigitation was postulated. Furthermore, it was revealed that the combination of alkyl groups of the benzyl groups was closely related to the type of columnar liquid crystal phases generated and the macroscopic morphologies of the liquid crystal domains. GRAPHICAL ABSTRACT


Introduction
Columnar liquid crystal (LC) phases have been used for molecular self-organisation, in which disc-shaped molecules having alkyl chains stack to form columnar structures [1][2][3][4][5][6][7][8][9][10]. The intermolecular interactions that interact in those phases are classified as intracolumnar and intercolumnar interactions. Generally, intracolumnar interactions are considered to be important for generation of the columnar LC phases. However, intercolumnar interactions also strongly influence the liquid crystallinity, and especially interactions due to the interdigitation of alkyl chains (or other flexible terminal moieties) between the columns play an important role in stabilising columnar LC phases. Yu et al. showed that the peripheral chains in the columns of C 3 -symmetric star-shaped LC compounds interdigitate between neighbouring columns to fill the free space between the three arms of the molecules [11]. Cristiano et al. reported that in tris [1,2,4]triazolo [1,3,5]triazine compounds exhibiting columnar LC phases, the interdigitation of the outer chains between neighbouring columns is crucial for generating a columnar LC phase [12]. Funahashi et al. reported that the cyclotetrasiloxane rings at the terminal of the alkyl chains in disc molecules interdigitate into neighbouring columns and that their interaction promotes the formation of a columnar mesomorphic structure [13]. Ong et al. reported that intercolumnar interdigitation of the alkoxy chains in LC dibenzo[a,c]phenazine compounds significantly affects their liquid crystallinities [14]. Furthermore, the importance of interdigitation between helical columnar structures has been emphasised. Park et al. reported an interdigitated 3D arrangement between the helical columns of C 3 -symmetric propeller-like molecules [15]. Roche et al. stated that an effective interdigitation can promote intercolumnar positional correlation [16]. Although the above reports mentioned the importance of intercolumnar interdigitation, there are few studies on the effective utilisation of interdigitation in controlling the positional correlation and liquid crystallinity of columnar LC phases. Figure 1 shows the relationship between the disc type and interdigitation form. The A-type disc molecules ( Figure 1a) are fully surrounded by alkyl chain stacks to generate a column via core-core interactions ( Figure 1b). In this case, no large intercolumnar interdigitation occurs because the disc is fully surrounded by the alkyl chain layer (Figure 1c). On the other hand, stacking of the B-type ( Figure 1d) and C-type ( Figure 1g) disc molecules that are partially surrounded by alkyl chains generates a 'rack gear'-like structure at the peripheral part of the column (Figure 1e,h). As shown in Figure 1f,i, the alkyl chains in these columns interdigitate with one another, and a columnar LC phase is stabilised by interdigitation, which enhances the intercolumnar van der Waals interactions and fills the free space. In our previous study, we observed intercolumnar interdigitation of B-type disc molecules [17]. The molecules generated rack-gear columnar structures, and the columns were interdigitated one-directionally. However, to the best of our knowledge, C-type disc molecules that generate two-directional interdigitation have not been reported.
In this study, we investigated the self-organisation of C-type discs formed by the dimerisation of half-discoid molecules. As shown in Scheme 1, 12 benzyl pentafluorobenzoates (Bz(l-m-n)PFB) (l, m and n in each compound name indicate the carbon atom numbers of the 3, 4, and 5-alkoxy groups of the benzyl groups, respectively) were prepared, and the packing structures were investigated by polarised-light optical microscopy (POM), single-crystal X-ray diffraction (XRD), differential scanning calorimetry (DSC) and powder XRD analysis. In 2007, our POM observations showed that Bz (8-8-8)PFB exhibits columnar phases with curved tapelike textures. Although this texture suggests a highly Figure 1. (Colour online) Stacking and intercolumnar interdigitation in three types of alkylated disc molecules. A-type discs: (a) discs with alkyl groups on the entire circumference, (b) stacking of A-type discs and (c) non-interdigitated columns. B-type disc: (d) disc with alkyl groups on half the circumference, (e) stacking of B-type discs with a generating rack-gear structure and (f) one-directionally (1D) interdigitated columns. C-type disc: (g) disc with alkyl groups on the opposite side of the circumference, (h) stacking of C-type discs with a generating rack-gear structure and (i) two-directionally (2D) interdigitated columns. ordered columnar phase, we did not systematically investigate the detailed molecular packing structure [18].

Identification of the phase transition behaviours of Bz(l-m-n)PFB
Their phase transition behaviours were identified using POM, DSC (Figures S2), and powder XRD data ( Figures  S3-S5). Table 1 presents their phase transition behaviours. In Table 1, the total number of carbon atoms of the alkoxy groups in a molecule, C n = l + m + n, is indicated, and the compounds are listed in ascending order of C n . Compound Bz(6-6-6)PFB (C n = 18) did not exhibit any LC phase. In compounds with C n = 19−25, rectangular columnar (Col r ), oblique columnar (Col ob ) and hexagonal columnar (Col h ) phases could be observed as LC phases. In contrast, compounds with C n = 26 − 36 exhibited only a Col h phase as LC phase. This suggests that the total alkyl volume in a molecule plays an important role with respect to whether Col h or Col r (or Col ob ) phase is generated. For all these LC compounds, the transition temperatures between the columnar phase and the isotropic liquid state were similar: 41−46°C on heating (36−42°C on cooling). This is explained by the features of the perfluoroarenearene (PFA -A) interaction [22][23][24][25][26][27], mainly comprising van der Waals (VDW) forces, which only operate at short atomic distances in pentafluorophenyl and trialkoxyphenyl groups. Although the PFA -A interaction is estimated to be in the range of 3.7 − 5.6 kcal/mol and is known to be one of the strongest interactions in LC molecules [28][29][30][31], the strength of the VDW force is proportional to 1/r 6 (r: inter-centroid distance between the two benzene rings). In these molecules, at temperatures above 50°C, it is assumed that the intermolecular distance between the benzene π-faces of the perfluorophenyl and trialkoxyphenyl groups is no longer short because of their intense molecular motion. As the PFA -A interaction is utilised to generate highly ordered structures in nematic, smectic [32][33][34][35] and columnar [36,37] LC phases, the formation of higher-order structures is also expected in these compounds. measurements clarified their liquid crystallinity, indicating a broad peak attributable to the molten alkyl chains. Figure 3a, b show the textures of the Col r and Col h phases of Bz(7-7-7)PFB in which both curved tape-like and fan-shaped textures can be observed. Figure 3c,d show the textures of the Col r and Col h phases of Bz (8-8-8)PFB; these are similar to those of the phases of Bz(7-7-7)PFB. In these compounds, it is difficult to distinguish the Col r phase from the Col h phase from the POM observations. What is surprising is that these textures are quite different from the aforementioned linear tape textures of Bz(7-8-7)PFB and Bz(8-7-8)  Figure 4 shows the textures of Bz(9-8-9)PFB, Bz (9-9-9)PFB, Bz(9-8-9)PFB, Bz(10-10-10)PFB and Bz (12-12-12)PFB (C n = l + m + n ≥ 26). These compounds showed the typical textures of Col h phases, in which fanshaped textures can be mainly observed.  d(600) peaks, the phase is identified to be a Col r phase. Furthermore, two peaks at 2θ = 24.67° (3.70 Å) and 25.03° (3.65 Å) can be observed in the Col r phase, indicating two types of stacking distances between the perfluorophenyl and trialkoxyphenyl groups, which are characteristic peaks for these Col r phases in this study. The phases of the other compounds could be identified from their diffraction peaks; Figures S3-S5 show the XRD results. Compounds Bz(6-7-6)PFB, Bz(8-7-8)PFB and Bz (9-7-9)PFB showed only the Col r phase. The XRD profiles of the Col r phases had two types of stacking distances in the range of approximately 3.6-3.7 Å. Bz (6-8-6)PFB showed two Col ob phases, and Bz(7-8-7) PFB showed two Col r phases. Bz(9-8-9)PFB, Bz (9-9-9)PFB, Bz(10-10-10)PFB and Bz(12-12-12)PFB were assigned to the Col h phase. Both the Col h and Col r phases had a broad halo at approximately 4.5 Å, corresponding to the molten alkyl chains. The number of molecules in the lattice unit (Z) was 1.9 − 2.0 in the Col h phase and 3.5 − 3.7 in the Col r and Col ob phases, implying that each disc unit comprised two molecules. Figure 5c,d show the electron density maps (EDMs) of Table 1. Phase transition behaviours of Bz(l-m-n)PFB .a. a C n : total number of carbon atoms in three alkyl groups (C n = l + m + n). Cr, Cr(1) and Cr (2)

Bz(7-7-7)PFB in the Col h (42 °C) and Col r (29 °C)
phases [38]. In both the phases, the core and alkyl areas are indicated in purple and green, respectively.
The core shape in the Col h phase is a hexagon with rounded corners, whereas that in the Col r phase is a skewed hexagon with rounded corners.

Single-crystal XRD study of Bz(3-3-3)PFB
To estimate the LC packing structures of Bz(l-m-n)PFB, a single-crystal XRD of Bz(3-3-3)PFB was performed. The crystal lattice parameters, a = 7.2129 Å, b = 18.4973 Å, c = 19.563 Å, α = 63.952°, β = 88.4340°, and γg = 87.0240° (space group: P-1, triclinic, Z: 2) were obtained. Although Bz(3-3-3)PFB has no LC phase, it is assumed that its crystal structure provides important information about the selforganisation of Bz(l-m-n)PFB molecules. Figure 6a shows nine columns indicated using a space-filled model, and the core part of the column is surrounded by a yellow square. The column axes are parallel to the a-axis. The interdigitation directions are indicated by black double arrows. Figure 6b,c show the side and top views of a column comprising eight dimers. Figure 6d shows two dimers stacked along the a-axis. The two dimers in the stack are oriented 90° from each other. The tetramer, comprising two stacked dimers, has four π-π stacking parts (A, B, C and D). These stacked benzene rings generate two types of distances (3.46 Å and 3.50 Å) for the π-π stacked benzene rings at A (or D) and B (or C) parts, respectively. Figure 7a shows the 3 × 3 columns in which the two sets of three columns along the c-axis and b-axis are marked by green and blue rectangles. The three columns in Figure 7b,c are indicated in blue, orange and green to clarify the outlines of the neighbouring columns. Interdigitation of the rack-gear structures can be observed between the neighbouring columns along both the b-and c-axes.

Estimation of the molecular packing structures
The self-organisation of Bz(l-m-n)PFB molecules was estimated as follows ( Figure 8): The two monomers generate a disc-shaped dimer via intermolecular dipoledipole interactions. During the process of column formation, a dimer stacks on top of another dimer while changing its direction by 90° due to intermolecular PFA -A interactions and intermolecular steric repulsion between the alkyl groups. This column has a rackgear structure in four directions around it. In Bz(l-m-n) PFB with C n = 26 − 36, directional intercolumnar interdigitation hardly occurs because of the flexible movement of the long terminal chains, which allows smooth rotational movement of the column about the column axis. The rotational movement makes the column isotropic in the direction vertical to the column axis, resulting in the generation of a Col h phase. In Bz(l-m-n) PFB with C n ≤25, intercolumnar interdigitation occurs between the rack-gear structures because of the low flexibility of the shorter terminal chains. This strongly suppresses column rotation about the column axis, and the compound produces a Col r phase, which has anisotropy in the vertical direction of the column axis. The highly ordered molecular packing structure generated by intercolumnar interdigitation affects the growth of the macroscopic LC domains, and linear tape-like textures that are reminiscent of platelet crystals can be seen in the POM observations.
Notably, Bz(7-7-7)PFB and Bz(8-8-8)PFB, despite C n ≤25, exhibited a Col h phase above their Col r phases. Their tetramers have largely perfect circular shapes because the 3-, 4-and 5-positions of the benzyl group have alkoxy groups of the same length (l = m = n). Figure 9a shows the top view of the Bz(7-7-7)PFB tetramer. The tetramer largely fits the green circle with a diameter of 36 Å, and the column model has an even surface at the edge of each alkyl part (grey fin-like part). The even surfaces on the column allow the rotational movement of the columns about the column axis at the higher temperature in the columnar LC temperature range, resulting in the generation of the Col h phase.
For the other compounds Bz(l-m-n)PFB with C n ≤25, the alkoxy group at the 4-position is different from those at the 3-and 5-positions (l = n ≠ m), and the tetramer shape is not a perfect circle because of the different lengths of the alkyl chains. The shape of the trialkoxyphenyl group suppresses the rotational movement of the column to generate Col r or Col ob phases over the entire LC temperature range. As shown in Figure 9b,c, the top views of Bz(6-7-6) PFB and Bz(9-7-9)PFB tetramers do not fit the circle with a diameter of 36 Å because the alkoxyl groups at the 3,5-positions are shorter and longer than the heptyloxy group at the 4-position, respectively, and their column models have an uneven surface at the edge of each grey fin (= three alkoxy groups of the benzyl group). Accordingly, the columns cannot rotate smoothly about the column axis. The difference in the smoothness of column rotation is assumed to be responsible not only for the type of columnar LC phases, but also for the shape of the macroscopic domains. Accordingly, it is assumed that compounds Bz(7-7-7)PFB and Bz(8-8-8)PFB with smooth column rotation show fan-like and curved tape-like textures (Figure 9d), whereas compounds

Conclusions
We demonstrated that the interdigitation of columns with rack-gear structures can generate highly ordered molecular packing structures in columnar LC phases. This study provides new insights into the effects of the length and balance of the alkyl chains in a molecule on the columnar packing structure and macroscopic domain growth. Although columnar LC phases generally give rise to curved or fan-shaped textures, we succeeded in growing the domains linearly. We believe that these results will be useful for tuning the anisotropy of domain growth in the design of functional materials with columnar LC phases.