Phase behaviour of ester-linked cyanobiphenyl dimers and fluorinated analogues: the direct isotropic to twist-bend nematic phase transition

ABSTRACT Typically, the twist-bend nematic (NTB) phase appears below the temperature of the conventional nematic (N) phase. The direct formation of the NTB phase from the isotropic (Iso) phase is significantly rare. In this study, we discovered that certain ester-linked bent-shaped dimers exhibit a direct Iso–NTB phase transition. We synthesised two homologous series of ester-linked cyanobiphenyl-based dimers (COOn) and their fluorinated analogues (F-COOn) containing different numbers of carbon atoms (n) in the alkyl spacer chains (n = 3, 5, 7, 9, 11, and 13). The phase transitions of these dimers were investigated using polarised optical microscopy and differential scanning calorimetry. The long-spacer COOn (n = 7, 9, 11, and 13) exhibited the usual Iso–N–NTB phase sequence, whereas the short-spacer COOn (n = 3 and 5) showed the direct Iso–NTB phase transition. Lateral fluorination significantly reduced the phase-transition temperatures for F-COOn compared to COOn. The short-spacer F-COOn (n = 3 and 5) did not exhibit any liquid crystal phases. The F-COOn with longer spacers (n = 9, 11, and 13) displayed the Iso–N–NTB sequence, whereas F-COO7 showed the direct Iso–NTB transition. Additionally, we analysed a single-crystal structure of F-COO7 to investigate its molecular conformation and superimposition. GRAPHICAL ABSTRACT


Introduction
The nematic (N) phase is a non-layered fluidic liquid crystal (LC) phase that is considered to have a simpler phase structure than other layered or more structured phases such as the smectic (Sm), columnar, and cubic phases.However, the N phase can exhibit nanoscopic Sm-like molecular aggregation (or cluster formation) referred to as the cybotactic N (N Cyb ) phase [1].The presence of these molecular clusters can induce nanoscopic biaxiality, potentially leading to the formation of a thermotropic biaxial N phase [2][3][4][5].Moreover, the incorporation of chiral structures or the addition of chiral molecules (i.e.chiral dopants) results in finite nanoscopic helical twists, giving rise to cholesteric and doublecylindrical blue phases.In addition, a few N-associated phase variables have been identified in certain studies, such as, twist-bend N (N TB ) [6,7], splay-bend N [8][9][10], and polar and ferroelectric N phases [11][12][13][14][15][16].These N-related phases typically occur at temperatures lower than those of the conventional N phase.As a result, the diverse behaviour of the N phase and its associated LC phases has gained increasing attention in recent times.
Among the N-related phases noted above, the N TB phase has been intensively studied over the last decade.The potential of the N TB phase was initially predicted in theoretical studies [17][18][19], and it was later experimentally identified in bent LC dimers [6,7].In fact, certain unknown N (N X ) phases for bent-shaped molecules reported prior to the identification of the N TB phase could also be considered as examples of N TB phases [7,[20][21][22][23][24].The N TB phase is characterised by a heliconical director precession with an average pitch of tens of nanometres [25][26][27], which increases with rising temperature [28,29].The heliconical structures of the N TB phase exhibit optical textures and physical properties resembling those of the layered Sm phase rather than the conventional N phase [30][31][32][33][34][35], making the N TB phase a pseudolayered phase.However, further research is needed to fully elucidate the detailed structure of the N TB phase [36,37].
The direct appearance of a monotropic N TB phase from the Iso phase upon cooling is rare, and only a few studies have reported it, exhibiting the rare Iso-N TB phase sequence.The Iso-N TB phase transition has also been predicted and supported via molecular theories [79,80], for which relatively small interarm angles between long axes of the two arms in dimers (< ～ 130°) could be preferable.Archbold et al. first experimentally reported this transition in binary mixtures of a dimer with the usual Iso-N-N TB phase sequence and a chiral dopant (6-10 wt%) (Figure 1(a)) [81].In addition, five bent LC dimers have been reported to exhibit monotropic Iso-N TB phase transitions in their single-component systems (Figure 1(b)), including two imine-linked dimer homologues bearing a central propane spacer and terminal methoxy or ethoxy groups reported by Dawood et al. [82,83], propane-and ethylthio-linked cyanobiphenylbased dimers (CB3CB and CB2SCB, respectively) reported by our group [84,85], and a phosphine-bridged bent cyanobiphenyl dimer reported by Wang et al. [86].It is important to note that the single-component dimers with the direct Iso-N TB phase are limited to these five examples.Thus, understanding the structure-property relationships remains a challenging issue.
In this study, we analysed the phase-transition behaviour of ester-linked LC dimers and discovered that certain dimers exhibited the rare direct Iso-N TB phase transition.We synthesised two homologous series of ester-linked cyanobiphenyl-based dimers (COOn) and their fluorinated counterparts on the inner benzene rings (F-COOn).These dimers contained alkyl spacer chains with varying odd numbers of carbon atoms (n = 3, 5, 7, 9, 11, and 13) for a bent molecular shape (Figure 2).We examined their phase-transition behaviours using polarised optical microscopy (POM) and differential scanning calorimetry (DSC).Previous research reported non-mesogenic properties for nonfluorinated COOn homologues with n = 7, 9, and 11, with only their crystallisation temperatures upon cooling [54].Therefore, we reinvestigated these homologues and applied POM to supercooled Iso phase domains or droplets to determine their LC formation.Generally, the lateral fluorination of molecules lowers phase-transition Figure 1.LC dimers investigated in previous studies exhibiting the rare direct Iso-N TB phase transition based on (a) binary mixtures [81] and (b) single-component dimers from (top) imine-linked dimers [82,83], (centre) CB3CB [84] and CB2SCB [85], and (bottom) a phosphine-bridged dimer [86].

Synthesis
The COOn and F-COOn series were synthesised as depicted in Schemes S1 and S2, respectively, and the procedures are also provided in the Supplementary Material.The molecular structures of the synthesised molecules were confirmed using 1 H, 13 C, and 19 F nuclear magnetic resonance spectroscopy on JEOL JNM-ECS400 and JNM-ECX500 spectrometers.

Phase transitions and identification
Phase characterisation was carried out using POM on an Olympus BX50 microscope equipped with a POM Linkam LK-600 PM hot stage for temperature control.The phase-transition temperatures and enthalpy changes (ΔH) were determined using DSC on a Shimadzu DSC-60 Plus instrument with a heating/cooling rate of 10°C min −1 , and nitrogen gas flowing at a rate of 50 mL min −1 .The phase-transition results for COOn and F-COOn are summarised in Tables 1 and 2, respectively.
To determine the LC phase in F-COO7, we prepared binary mixtures of F-COO7 and the previously studied CBCOO4CB which exhibits N and N TB phases [63].We combined these compounds at various ratios and dissolved the mixtures in dichloromethane at a concentration of 10 mg mL −1 .The solvent was then slowly evaporated under reduced pressure.Afterward, each dry mixture was heated to 150°C (the Iso phase temperature), and then cooled to room temperature to make mixtures homogeneous.Additionally, we examined the phase transitions by cooling the mixtures at a rate of 3°C min −1 from their Iso phase, using POM.

Single-crystal structural analysis
Single crystals of F-COO7 were prepared in a mixed solvent containing methanol and dichloromethane.Subsequently, single-crystal structural analysis was carried out based on the techniques detailed in our prior research [99].X-ray diffraction analysis was performed using a Rigaku FR-E+ SuperBright™ microfocus X-ray source and a Rigaku HyPix-600 detector, along with a multilayer mirror and monochromatic Mo-Kα radiation.The CrysAlisPro software was employed to collect scattering data.All calculations were conducted using the Olex2 crystallographic software package, while refinement procedures were implemented with the SHELXL software [100].

Phase behaviour of COOn
Table 1 presents the phase-transition temperatures and associated enthalpy changes of COOn.Upon heating, none of the COOn samples exhibited a mesophase, and most of them tended to crystallise from the Iso phases upon cooling, as evident from the POM and DSC results, which is consistent with a previous study on COOn (n = 7, 9, and 11) [54].To investigate LC formation in this study, we performed POM observations in the supercooled Iso phase domains of the COOn samples that did not crystallise during cooling.This led to the discovery of monotropic N TB phase formation in all the COOn homologues.Meanwhile, no typical N-phase textures such as marble or schlieren textures were observed during this phase transition.These optical textures are analogues to the direct Iso-N TB phase transition of CB2SCB [84] and CB3CB [85].In addition, COO5 showed small blocky textures as shown in Figure S2.COO3 also exhibited similar indistinctive textures directly from the Iso phase, with a strong crystallisation tendency.This could also be the N TB phase (Figure S1).The phase-transition temperatures at the Iso-N, N-N TB , and Iso-N TB phase transitions (T IN , T NNTB , and T INTB , respectively) during cooling are plotted in Figure 5 as functions of n for COOn.Generally, decreasing the alkyl-chain spacer length enhances the effective molecular curvature (or biaxiality) of the bent-dimer homologous series [82,83], which in turn lowers T IN and reduces the N-phase temperature range for shortspacer homologues.Given the narrow temperature ranges of the N phases for COOn with n = 7, 9, 11, and 13, which diminished as n decreased from 13 to 7, the intermediate N phase was found to disappear for COOn (n = 3 and 5).This led to the direct formation of the N TB phase from the Iso phase, as previously reported in our studies on asymmetric methylene-and thioetherlinked homologues (CBnSCB) [84] and symmetric methylene-linked cyanobiphenyl dimer homologues (CBnCB) [85].In these studies, the shortest CB2SCB and CB3CB homologues exhibited the direct Iso-N TB phase transition, while the other longer-spacer homologues followed the typical Iso-N-N TB phase transition.Since the observations were made in supercooled  samples or regions during cooling, all the T IN , T NNTB , and T INTB values for all the COOn homologues were lower than T Cr (Table 1).

Phase behaviour of F-COOn
The phase-transition findings for the fluorinated F-COOn homologues are tabulated in Table 2.As with the COOn series, no LC phases were detected in the F-COOn samples during heating.The short-spacer F-COOn homologues (n = 3 and 5) did not exhibit LC phase formation upon cooling.However, the presence of LC phases in these homologues cannot be entirely ruled out, given the challenge in observing LC optical textures in supercooled regions.In contrast, monotropic LC phases were identified in the long-spacer F-COOn homologues (n = 7, 9, 11, and 13).Specifically, the F-COOn homologues with n = 9, 11, and 13 displayed both N and N TB phases, conforming to the typical Iso-N-N TB phase sequence.The optical textures of the N phases for F-COOn homologues with n = 9, 11, and 13 transitioned to blocky textures characteristic of the N TB phase at 44, 52, and 56°C, respectively.Notably, F-COO7 exhibited the rare direct Iso-N TB phase transition at 27.6°C although the non-fluorinated COO7 followed the typical Iso-N-N TB phase transition.This indicates that lateral fluorination is responsible for this unique transition, as the direct Iso-N TB phase transition is not present in the non-fluorinated analogue.Moreover, this direct Iso-N TB phase transition of F-COO7 can be explained considering the narrow temperature ranges of the upper N phases of both COO7 and F-COOn (n = 9, 11, and 13).The temperature range of the N phase of nonfluorinated COO7 is considerably narrow (in the range of approximately 2°C).Lateral fluorination generally reduces T IN (or T NI upon heating) [87][88][89][90][91][92][93][94][95][96][97][98], often contributing to a decrease in the N-phase temperature.Thus, the lateral fluorination disturbs or diminishes the formation of the N phase of F-COO7, leading to the direct Iso-N TB phase transition.Additionally, the effects of different spacer lengths on the phase-transition temperatures of bent LC dimer homologues were also considered, as discussed in the previous section on COOn.The T IN , T NNTB , and T INTB values upon cooling are plotted in Figure 7 as functions of n for F-COOn.It was observed that the N-phase temperature ranges of the long-spacer F-COOn homologues (n = 9, 11, and 13) were also narrow (below 10°C) and decreased with decreasing n because of the increase in the effective molecular curvature or biaxiality [82,83].Hence, for n = 7, the conventional N phase disappeared, and the N TB phase was formed directly from the Iso phase (Figure 7).
The DSC curves of F-COO7 were analysed upon cooling at different rates, and the results are presented in Figure 8.At a low cooling rate of 3°C min −1 , a broad crystallisation peak was observed.However, increasing the cooling rate prevented crystallisation and resulted in another exothermic peak at approximately 28°C, corresponding to the I-N TB phase transition.It is interesting to note that the N TB phase was subjected to vitrification at approximately 10°C.These results demonstrate that lateral fluorination renders F-COO7 vitrifiable.

Phase characterisation of F-COO7
The optical textures of F-COO7, which were formed directly from the Iso phase, were ambiguous and contained small domains, as shown in Figure 10(a,b).Striped textures containing small focal conic domains grew via annealing at a temperature slightly below that of the Iso phase or cooling at a low rate of 0.1°C min −1 from the Iso phase, as shown in Figure 10(c,d).This indicates the layered or pseudo-layered nature of the observed mesophase.The observed optical textures were similar to those of the N TB phase of CB2SCB, which was also formed directly from the Iso phase [84].
We performed POM using a contact preparation test on F-COO7 and a structurally similar reference, specifically the CBCOO4SCB dimer.This dimer displays a thermal phase sequence with decreasing temperature as follows: Iso (68.7°C)N (52.3°C)N TB (20.7°C)Glassy N TB [63].F-COO7 and CBCOO4SCB samples were positioned on the right and left sides in two glass plates, respectively, as depicted in Figure 11.In Figure 11(a), the birefringent texture on the left and the dark region on the right correspond to the N phase of CBCOO4SCB and the Iso phase of F-COO7, respectively.As the temperature decreased, the N phase on the left transitioned to the N TB phase, as demonstrated in Figure 11(b,c).Following this, the N TB phase texture began to propagate into the F-COO7-rich Iso phase dark region on the right, as illustrated in Figure 11(c,d).This occurred at temperatures above approximately 40°C, which is higher than the Iso-to-LC phase transition temperature of pure F-COO7 (approximately 28°C).In terms of optical textures, smaller domains started to emerge from the centre towards the right side, as shown in Figure 11(c,d).The continuous appearance of these domains indicates that the LC phase of F-COO7 is miscible with the N TB phase of CBCOO4SCB.
We determined the phase sequences of binary mixtures of F-COO7 and CBCOO4SCB using POM.The phase-transition temperatures of the binary mixtures upon cooling are plotted in Figure 12 as a function of the molar fraction of CBCOO4SCB.It is evident that decreasing the proportion of CBCOO4SCB in the mixture (or increasing that of F-COO7) resulted in a greater decrease in T IN than in T NNTB .Therefore, the temperature range of the N phases of the binary mixtures became narrower with decreasing concentrations of CBCOO4SCB, disappearing at approximately 50 mol%.Near this concentration, the blocky texture characterising the N TB phase was directly formed from the Iso phase, providing further evidence for the direct Iso-N TB phase transition of F-COO7.The values of T NNTB of CBCOO4SCB (approximately 52°C) and T INTB of F-COO7 (approximately 28°C) in the plot in Figure 12 were connected continuously by an upward curve.

Crystal structural analysis of F-COO7
In the final stage of our analysis, we examined the singlecrystal structure of F-COO7.The obtained crystal data were uploaded to the Cambridge Crystallographic Data Centre (CCDC) database (CCDC number 2,149,667).Table 3 presents the extracted crystallographic data,  while Figure 13 displays the single-molecule forms and molecular packing.As depicted in Figure 13(a), two independent molecular forms were observed in the crystal structure.The central alkyl-chain spacers adopted an all-trans conformation, with the two cyanobiphenyl arms in each form nearly lying in the same plane.The C(Ph)-C-O bond angles were 113.2° for C10-C14-O2, 110.9° for C24-C28-O4, 112.0° for C45-C49-O6, and 111.8° for C59-C63-O8.These bond angles of COO esters were similar to those of C-CH 2 -C (approximately 110°) and smaller than those of C-O-C (approximately 118°).Further, the interarm angles between the long axes of the two cyanobiphenyl arms in each dimer were assumed to be around 92° and 96°, which are similar to a value  estimated from an optimised structure of ester-linked dimers [54].This indicates that in the case where only the trans conformation is included in the central alkyl chain, the interarm angles likely depend on the type of linkage between the arm and central spacer.In addition, the obtained values are within the range of those predicted theoretically for the direct I-N TB phase transition [79,80].Indeed, the observed molecular forms of F-COO7 appeared to be superficially more bent than those observed in the single-crystal structures of CBO7OCB [101] and CB9CB [102], which exhibited the typical Iso-N-N TB phase sequence [70].Figure 13(b,c) show the dimers laterally superimposed and occupying free space in a manner similar to bend deformation in the    LC phase.However, in the crystal phase, the cyanobiphenyl arms did not superimpose antiparallelly, and no specific interatomic contacts were observed around the F atoms.
Most previously reported dimers that exhibit the direct Iso-N TB phase transition have short central spacers, such as the three-atom-based spacers shown in Figure 1(b) [82][83][84][85], whereas their longer-chain homologues exhibit the typical Iso-N-N TB phase transition [84,85].Shortening the spacer chains should increase the effective molecular curvature (or biaxiality) and rigidity of the bent-dimer homologues.However, one exception was observed in a longer-spacer based phosphine-bridged dimer with the direct Iso-N TB phase transition, which showed a folded U-shape on its optimised single conformer, indicating a more bent form [86].In such case, molecules are more likely to pack laterally to fill free space, as shown in Figure 13(c) for F-COO7, which may result in increased steric restraint of molecular motion and may be disadvantageous for forming the conventional N phase.
Furthermore, the rotational energy of the Ar-C(=O) bond in the ester can be high, indicating the rigidity of the COO-linked dimers [34].Therefore, the ester-linked COOn and F-COOn dimers investigated in this study could be considered more rigid than other cyanobiphenyl dimers with the Iso-N-N TB phase sequence.Thus, in addition to appropriate molecular curvature, the direct N TB phase formation of certain COOn and F-COOn dimers may be attributed to their lower flexibility compared to other homologues and analogues.

Conclusions
We synthesised two homologous series of LC dimers based on cyanobiphenyl, linked by ester groups (denoted as COOn), and their fluorinated counterparts with fluorine substitution on two inner benzene rings (denoted as F-COOn), where n = 3, 5, 7, 9, 11, and 13.Among them, the longer-chain COOn molecules (n = 7, 9, 11, and 13) exhibited the typical Iso-N-N TB phase sequence with narrow N phase temperature ranges, whereas the short-spacer COOn molecules (n = 3 and 5) exhibited direct Iso-N TB phase transitions.This suggests that reducing the length of the alkyl spacers led to direct Iso-N TB phase transitions in the COOn homologous series with n = 3 and 5. Additionally, fluorination significantly lowered the phase-transition temperatures of F-COOn compared to COOn molecules with the same n.Furthermore, the short-spacer F-COOn molecules (n = 3 and 5) did not exhibit LC phases, whereas the long-spacer F-COOn molecules (n = 9, 11, and 13) showed the typical Iso-N-N TB phase.Interestingly, F-COO7 displayed a direct Iso-N TB phase transition.Considering that the N phase of non-fluorinated COO7 has a narrow temperature range (approximately 2°C) and exhibits the typical Iso-N-N TB phase, we propose that lateral fluorination destabilises and diminishes the N phase formation of F-COO7, resulting in the direct Iso-N TB phase sequence.Moreover, reducing the length of alkyl spacers also narrows the temperature ranges of the N phase for long-spacer F-COOn molecules (n = 9, 11, and 13), giving rise to the direct Iso-N TB phase transition for F-COO7.The single-crystal structure of F-COO7 reveals a more bent molecular geometry compared to typical dimers, leading us to hypothesise that molecular curvature and rigidity may also play a crucial role in the direct formation of the N TB phase from the Iso phase.Our results offer guidance for the molecular design of LC dimers using ester linkage and lateral substitution to exhibit the direct Iso-N TB sequence.Future studies on the effects of fluorination on phase behaviour and the N TB phase of various cyanobiphenyl-based LC dimers will be reported elsewhere.

Table 2 .
Values of T m upon heating, T IN , T INTB , T NNTB , and T c upon cooling, and the enthalpy changes ΔH m and ΔH c at T m and T c , respectively, for F-COOn determined by DSC and POM.
7 57.0 a Determined by POM.The I-N and N-N TB phase-transition peaks upon cooling of n = 11 overlapped with the crystallisation peak.Hence, the T IN and T NNTB values of n = 11 were also determined by POM.b Small ΔH c is because F-COO7 is mainly vitrified at approximately 10°C as shown in DSC curve (Figure 7) upon cooling.

Figure 2 .
Figure 2. Molecular structures of the (a) COOn and (b) F-COOn homologues synthesised in this study.
Specifically, the long-spacer COOn homologues (n = 7, 9, 11, and 13) exhibited the N TB phase below the temperature of the N phase, indicating the typical Iso-N-N TB phase sequence.The optical textures of the N phase of the COOn homologues with n = 7, 9, 11, and 13 transitioned to blocky textures, which are typical of the N TB phase, at approximately 74, 79, 82, and 82°C, respectively.The optical textures of the N and N TB phases of COO7 are shown in Figure 3(a,b), while those of the COOn homologues with n = 9, 11, and 13 are presented in Figures S3-S5, respectively, in the Supplementary Material.Remarkably, short-spacer COOn samples with n = 3 and 5 formed the N TB phase at approximately 50 and 55°C, respectively, directly from the Iso phase, demonstrating the uncommon Iso-N TB phase sequence.Birefringent textures appeared in the Iso phase droplets of COO5 (Figure 4(a)) and grew for unclear fan-and focal-conic-like domains, as shown in Figure 4(b-).

Figure 4 .
Figure 4. (Colour online) Optical textures in the direct Iso-N TB phase transition of COO5 kept at 54.6°C, at which temperature the transition started in the present observation.

Figure 6
presents the optical textures of the N and N TB phases of F-COO9, while Figures S6 and S7 in the Supplementary Material show those of F-COOn homologues with n = 11 and 13.

Figure 5 .
Figure 5. (Colour online) T IN , T NNTB , and T INTB values upon cooling of COOn plotted as a function of n.T m and T c values upon heating and cooling, respectively, are omitted, for clarity.

Figure 9
Figure 9 shows the melting temperature (T m ) values upon heating and T IN , T NNTB , and T INTB values upon cooling plotted as functions of n for COOn and F-COOn.It is evident that all the phase-transition temperatures of the F-COOn homologues were significantly lower than those of COOn because of lateral fluorination.

Figure 7 .
Figure 7. (Colour online) T IN , T NNTB , and T INTB values of F-COOn plotted as a function of n.

Figure 9 .
Figure 9. (Colour online) (a) T m, (b) T IN , (c) T NNTB , and (d) T INTB values of COOn and F-COOn plotted as a function of n.

Figure 10 .
Figure 10.(Colour online) Optical textures of F-COO7 during (a, b) cooling at a rate of 10°C min −1 and (c-e) annealing at the starting temperature of the LC phase (32°C).

Figure 11 .
Figure 11.(Colour online) POM images of the contact preparation of F-COO7 and CBCOO4SCB.(a) Iso phase of the F-COO7-rich region (right side) and N phase of CBCOO4SCB (left side) at 53.6°C, (b) Iso phase of the COO7-rich region and N TB phase of CBCOO4SCB at 50.6°C, and (c, d) gradual growth of optical textures from the N TB phase of the CBCOO4SCB-rich region to the F-COO7-rich region (at 38.9 and 33.4°C, respectively).

Figure 12 .
Figure 12. (Colour online) Phase-transition temperatures of binary mixtures of F-COO7 and CBCOO4SCB upon cooling as a function of molar fraction of CBCOO4SCB.

Figure 13 .
Figure 13.(Colour online) (a) Two independent molecular forms, (b) molecular packing of the single-crystal structure of F-COO7 in a unit cell and along the b-axis, and (c) extracted molecular packing in a plane.

Table 1 .
Values of T m upon heating, T IN , T NNTB , T INTB , and T c upon cooling, and the enthalpy changes ΔH m and ΔH c at T m and T c , respectively, for COOn determined by DSC and POM.
a Determined by POM.