Sensitivity of the NTB phase formation to the molecular structure of imino-linked dimers

ABSTRACT Here we report on the synthesis and mesomorphic properties of a series of imino-linked dimeric molecules. In order to improve our understanding of the structure–NTB phase correlations, we have studied the impact of geometric and electronic factors arising from varying mesogenic units, different spacer lengths and from the ratio (n/m) between the lengths of terminal chains (n) and spacer (m). From the perspective of the molecular geometry, the results show that the stability of the NTB phase results from increasing effective molecular bending and with the broadening of the mesogenic unit, in particular near the spacer, and that the n/m ratio plays a substantial role in conjunction with the specific mesogenic unit. A computational study of the electronic properties shows that a broadening of the mesogenic core in the vicinity of the spacer is associated with an increased anisotropy of the electrostatic potential distribution. Within a given series of materials our study suggests that the incidence of the NTB phase and its thermal stability are governed by the synergy of specific geometrical factors and the anisotropy of the electrostatic potential distribution of the mesogenic core. GRAPHICAL ABSTRACT


Introduction
Liquid crystalline dimers, in which two mesogenic units are linked by a flexible spacer, are well known as a rich source of liquid crystalline phases, ranging from various new smectic [1][2][3] and columnar phases [4,5] to a recently observed new nematic phase displayed by a limited number of odd-membered dimers [6][7][8][9][10][11][12][13][14][15][16]. The new, lower temperature nematic phase has been assigned by Cestari et al. as a twist-bend nematic phase (N TB ), having an oblique helicoidal structure facilitated by a bent geometry of the achiral molecules [8]. Although the N TB phase had been proposed a decade ago by Dozov [17] and Memmer [18], just recently its periodic structure has been demonstrated for replicas of freeze fractured samples using transmission electron microscopy (FFTEM) [19,20]; however, an atomic force microscopy (AFM) study suggested that the periodic, submicron features can be attributed to crystallographic planes of a thin layer of a crystalline phase, easily formed during 'freezing' of the samples [21].
Investigations of structure-property relations for dimers have been primarily focused on the impact of the linkage group connecting the mesogenic unit with the flexible alkylene spacer. In early studies, the N TB phase was reported for symmetrical cyanobiphenylbased dimers, with methylene linkage but not for their ether-linked analogues [9]. The presence of the N TB phase was attributed to the greater extent of molecular bending of methylene-linked odd-membered dimers. Later, ether-linked fluorinated unsymmetrical dimers with a long spacer have been shown to exhibit the N TB phase [11,12]. It was suggested that a long spacer allows for the unfavourable angular constraints imposed by the ether-linking group to be nullified. Comparison of the hydrogen-bonded trimer having methylene and ether with one containing exclusively ether linkage groups showed that the N TB phase can be driven by hydrogen bonding but only in the complex in which molecular bending is accentuated by at least one methylene linkage group [12]. A molecular field theory based on symmetric V-shaped molecules predicts a strong sensitivity of the N TB phase formation to the molecular bending angle defined as the angle between the two mesogenic arms; as the angle becomes smaller the width of the N phase decreases and the N TB phase is progressively stabilised. [24] The theory predicts a first-order N TB -Iso transition when the angle between the mesogenic arms has reached 130°. Guided by this theory Dawood et al. [25] investigated the mesomorphic properties of ethoxybenzyloxybenzylidene dimers with various odd-numbered methylene groups in the spacers anticipating that the decrease in the spacer length will sufficiently increase the molecular curvature. Indeed, only for the homologue with a propane spacer was a direct Iso-N TB transition observed that is in line with the prediction. In addition experimental evidence of a direct Iso-N TB transition has been reported for the mixtures of nonane-1,9-diylbis(4,1-phenylene) bis(4-butoxybenzoate) containing 6-10 wt% of the chiral compound derived from dianhydro-D-glucitol [26].
A comparative study of cyanobiphenyl dimers with methylene, ether and imino linkages implied that not only the curvature of the molecule but also the twist between the plane of mesogenic units and the plane common to the carbon atoms in the spacer contributes to the formation of the N TB phase [16]. Vanakaras et al. [27] have developed a theory for the molecular organisation of the low-temperature nematic phase. The model implies a strongly polar and chiral molecular ordering in the N TB phase, due to the existence of chiral molecular conformations caused by the torsion of the mesogenic units and the overall bent molecular shape. The transverse polar ordering is manifested by the helical twisting of the spontaneous polarisation direction about a unique helical axis. The theory anticipates a phase sequence Iso-N-N TB for molecules with relatively small molecular bending and large torsion and direct first-order Iso-N TB transition for molecules with large bending and small torsion.
Recent studies on various alkylene linked dimers with an emphasis on the impact of material polarity have shown that the N TB phase is suppressed in materials with either too strong a terminal dipole units or too low a polarisability associated with the terminal dipole unit [13,14]. Furthermore, it was found that by increasing the length-to-breadth ratio of the individual mesogenic units, the thermal stability of the N TB phase was increased for polar and decreased for apolar methylene-linked bimesogens. These results revealed that finding the relationship between the structure and the incidence of the N TB phase is not a simple task and requires far more structurally variant materials.
Our previous work on imino-linked dimers showed that the appearance of the N TB phase is rather scattered among various homologues [3,6,10]. Given the particular sensitivity of the N TB phase toward the overall molecular structure of the material, we performed detailed investigations on imino-linked dimers focusing our attention on the impact of various mesogenic units and the effective molecular curvature caused by different spacer lengths but also on the effect of the ratio (n/m) between the lengths of terminal chains (n) and spacer (m). For this study we prepared a series of novel symmetric dimers, incorporating salicyl, naphthyl and biphenyl groups as schematically presented in Figure 1, and for comparison we have included revised data of the previously reported imino-dimers containing the benzoyloxybenzyl (BB) [6] and benzoyloxysalicyl (BS) [3,10] mesogenic unit. Introduction of the salicyl moiety, which forms a sixmembered ring through hydrogen bonding or naphthyl groups broadens the mesogenic unit, while a biphenyl group extends its length. In addition to variations in geometry, utilisation of different aromatic groups leads to changes in the electron distribution within the mesogenic core what encourages us to investigate the electronic aspect influencing the incidence of the N TB phase. In order to facilitate the nematic behaviour, we studied only those dimers in which the length of the terminal chain is shorter than or approximately equal to the length of the spacer. Hence, dimers having terminal chains with n = 4, 6, and a spacer with m = 7, 9, were prepared and the effect of the spacer length and the ratio (n/m) with respect to the structural variation of the mesogenic unit were investigated and discussed in the context of the newly developed molecular field theory for the N TB phase [24].
DFT calculations were carried out on the monomers, representing each type of mesogenic core providing valuable information on the geometric and electronic aspects of the particular type of dimer. These results coupled with experimental data contribute to our understanding of the structure-N TB phase correlations that is a prerequisite for its prospects for applications in new liquid crystal device technologies.

General information
All the solvents were either puriss p.a. quality or distilled over appropriate drying reagents. All the other reagents were used as purchased from Aldrich. 1 H-(300 MHz) and 13 C-(75.5 MHz) NMR spectra were recorded on Bruker AV 300 or Bruker AV 600 instruments in CDCl 3 with SiMe 4 as an internal standard unless stated otherwise. Phase transition temperatures and textures were determined using an Olympus BX51 polarising microscope equipped with a Linkam TH600 hot stage and PR600 temperature controller. Enthalpies of transition were determined from thermograms recorded on Perkin-Elmer Diamond DSC, operated at scanning rates of 5°C min -1 . Two-dimensional XRD patterns of aligned samples (surface aligned on a glass plate on a temperature-controlled heating stage or aligned in a capillary with ⊘ 1 mm in a magnetic field in a temperature-controlled oven) were obtained using Ni filtered Cu K a radiation recorded by an area detector (VÅNTEC500, Bruker AXS). The data derived from the XRD patterns are presented in Table 1S (see Supplementary Information).

Synthesis
The dimers having BS, NB, NS and BN mesogenic units were prepared in yields of 60-80% as described previously [3,10]. The biphenyl-based dimers were prepared by addition of a,ω-diamino alkane to the corresponding aldehyde following the synthetic path for NB and NS dimers, in good yields of 70-90%. The dimers were identified by 1 H and 13 C NMR spectroscopy (see Supplementary Information), while purity was established by elemental analysis (Tables 2S and 3S).

Mesogenic properties
Mesomorphic properties for the homologues series NB, BN and BPB are presented in Table 1 and for salicyl series BS, NS, BPS in Table 2, respectively. The homologues within each series have been arranged in decreasing n/m ratio. For comparative purpose the data of previously published BB_7-4 and BB_7-6 [6], BS_7-4 and BS_7-6 [3] and NS_7-8 [10] are also included in the tables.
Microscopy studies of the NB dimers revealed that the number and type of the liquid-crystalline phases depend significantly on the n/m ratio. Thus, the dimer NB_7-6, in which the lengths of terminal chains and spacer are almost equal, displays a single enantiotropic liquid crystalline phase. The liquid crystalline phase was characterised by the focal conic fan and schlieren-like texture with two and four brushes (see Figure 2(a)) that have already been observed in Cm represents the spacer with the number of methylene units m, Cn the terminal chain with the number of methylene units n, and MU the mesogenic unit. We refer to these compounds using the acronyms BB_m-n, BS_m-n, NB_m-n, NS_m-n, BN_m-n, BPB_m-n and BPS_m-n in which BB denotes benzoyloxybenzyl, BS benzoyloxysalicyl, NB naphthoyloxybenzyl, NS naphthoyloxysalicyl, BN benzoyloxynaphthyl, BPB biphenyloxybenzyl and BPS biphenlyloxysalicyl mesogenic unit.
intercalated SmC phases of non-symmetric [1,28,29] but also of a limited number of symmetric dimers [1,5,6,10,14]. Such intercalated tilted layer phases in which the mesogenic groups between adjacent layers are tilted in opposite direction can be interpreted by analogy to the B 6 structures of classical bent-core molecules ( Figure 2(a)) [30] as described for imino-linked dimers comprising benzyloxybenzyl-and naphthyl-  based mesogenic units [6,10]. They are called SmCc here for comparison with the intercalated phases of calamitic compounds and with the nomenclature used for such phases of odd-membered non-symmetric dimers in [1]. Similar textural characteristics were noticed for the low-temperature mesophase of the other three dimers within the same series. Contact preparation between the phases among the dimers of this series revealed that all of them display the same smectic phase. A decrease in the n/m ratio resulted in the appearance of the nematic phase. Hence, in addition to the intercalated smectic phase, an enantiotropic uniaxial nematic phase was observed for NB_9-6, NB_7-4 and NB_9-4 and also a monotropic N TB phase for NB_9-4. The uniaxial nematic phase was determined by its characteristic marble texture (see Figure 2(c)) The N-N TB transition is characterised by the fan-like texture (see Figure 2(b)) from which a polygonal texture and a characteristic striped structure developed. The X-ray investigations on samples of NB_7-4 and NB_9-4 aligned in a magnetic field show the patterns typical for a nematic phase forming clusters, a diffuse outer halo with its maxima on the equator of the pattern at d = 4.5 Å and a relatively strong inner scattering with maxima on the meridian of the pattern at d = 22 Å for NB_7-4 and 23.6 Å for NB_9-4 (see Figure 3(a), Figure S1). The inner halo condenses at the transition to the smectic phase to a sharp layer reflection at d = 22.2 and 23.5 Å for the two compounds, respectively, the maxima of the inner and outer scattering remaining on the meridian and the equator, respectively, but with a comparatively broad azimuthal distribution of the intensity (see Figure 3(c), Figure  S1). This is in keeping with an intercalated smectic C phase. Unfortunately the alignment of the sample was not good enough to estimate the tilt angle from the XRD data. The pattern of the intermediate N TB phase formed by NB_9-4 differs from that of the N phase mainly by a certain loss of orientational order (see Figure 3(b)) as frequently found at the N-N TB transition [16,19,31].
Altering the position of the naphthyl group within the mesogenic unit promotes the nematogenic behaviour. All of the dimers of the BN series show nematic phases. The compounds BN_7-6 and BN_9-6 display additionally a SmC C while BN_7-4 and BN_9-4 an N TB phase, respectively. As the 2D X-ray patterns of the two phases show the molecules of BN_9-6 reorient in the capillary at the N-SmC phase transition (see Figure 4(a,b), Figure S2). The molecular long axes are aligned parallel to the magnetic field in the nematic phase (i.e. parallel to the meridian of the 2D pattern, the maximum of the outer scattering is located on the equator), they tilt with respect to this direction in the smectic phase most probably because the smectic layers become surface aligned parallel to the walls of the capillary, their normal is parallel to the field and hence the layer reflections are found at the meridian, the outer scattering shows maxima above and below the equator, respectively from which a tilt of the molecules with respect to the layer normal of about 18°can be calculated (see Figure S2). The layer spacing amounts to 25.2 Å. Similar values would result for a smectic-cluster model of the nematic phase, the azimuthal distribution of the inner scattering at about 25 Å at the upper meridian reveals a tilt angle of about 16°for the molecules in the smectic clusters.
The patterns at different temperatures on cooling in the nematic state of BN_7-4 show no significant  difference (see Figure 4(c,d)). Compared with the N phases of compounds forming an SmC phase at lower temperatures, their inner scattering is less intense with respect to the outer scattering.
Replacing the naphthyl with the biphenyl group extends the mesogenic unit. A major effect of this structural change is a significant increase in the transition temperatures and a stabilisation of the smectic phase. The transitions above 240°C were accompanied by decomposition that precluded detailed X-ray investigation. The liquid-crystalline phases were determined by the characteristic textural features. The smectic phase was identified as SmC C phase by direct analogy with the textural behaviour displayed by the homologues of the series NB and BN and the nematic phase by its marble texture. According to microscopic examination, all four BPB dimers exhibited SmC C phases (see Figure 5). While the first two homologues showed a direct SmC C -Iso transition for the other two the presence of the SmC C and the nematic phase was established. Prevailing smectic organisation when the length of the terminal chains exceed half the length of the spacer is in agreement with the general behaviour of dimeric compounds [1].
The mesomorphic behaviour of the salicyl-type dimers presented in Table 2 revealed their very strong affinity towards the formation of the nematic phase regardless of the n/m ratio. In addition to the uniaxial nematic phase characterised by the marbled texture most of them displayed the twist-bend nematic phase. The observation of a polygonal texture from which a rope-like texture developed and the magnitude of the N-N TB entropy change are in agreement with this assignment. Mesogenic properties of the compound BS_7-6 have been published previously; [3] however, the low-temperature nematic phase was tentatively assigned as Ncol at the time based on direct analogy with the behaviour displayed by unsymmetrically di-substituted piperazines [32]. Recent studies of the rigid, bent-core mesogen UD68 which belongs to the group of unsymmetrically di-substituted piperazines confirmed that the low-temperature nematic phase is actually the N TB phase [22].
The results of the X-ray investigation on BS_7-6 resemble more closely those for compounds of the CB7CB type than that for the NB and BN series (see Figure 6, Figure S4), the inner scattering intensity being much weaker than the outer one. As for all compounds presented here the d value for the maximum of the inner scattering is within about 20 Å, shorter than half the molecular length in both nematic phases. If the scattering of the isotropic phase is subtracted from that of the nematic phases in the SAXD patterns of the compound a second very weak inner scattering can be seen at roughly half the 2θ value of the first one but in the same direction (see Figure 6(c-e)).
Replacement of the phenyl with the naphthyl group resulted in the occurrence of the N TB phase in all homologues of this series. For the homologues NS_9-6 and NS_9-4 the presence of the monotropic N TB phase was determined by the obvious and sharp change in the optical texture that occurs at a well-defined temperature. X-ray diffraction was performed on NS_7-6 and NS_7-4. The nematic phases of both compounds show a similar behaviour like those of BS_7-6 in the magnetic field ( Figure S3) with d values for the maxima of the inner scattering of about 21 Å, the only significant change in the 2D XRD patterns at the N-N TB phase transition being the loss of director alignment. The SAXD results for BS_7-6 and a comparison with the WAXD patterns of NS_7-8 [10] showing two inner scatterings in both nematic phases lead us to have a closer look at the small-angle region of the three homologues with m = 7. Unfortunately the isotropic phase could only be investigated in case of NS_7-8 with our equipment, so the innermost scattering can be hardly seen in the patterns of NS_7-6 and NS_7-4 (see Figure S3). However, the theta scans for the three compounds show, that the innermost scattering becomes more pronounced with increasing n/m (see Figure 7). These two maxima of the inner scattering have been found previously for the nematic phases of several dimers, for instance a chiral dimer published by Gorecka et al. [33] shows the two inner intensity maxima in both nematic phases, also, the innermost being much stronger as for the symmetric compounds presented here, whereas in case of the fluorinated symmetric dimer described by Tamba, Salili et al. [34] the intensity ratio of the two maxima is comparable to that for NS_7-8. [10] In their recent report on the Nx phase in mixtures Ramou et al. [31] discuss possible molecular arrangements based on XRD measurements on the symmetric cyanobiphenyl dimer with a C 9 spacer (abbreviated CBC9CB there), which closely resemble our scattering patterns of, e.g. BS_7-6, but we do not have a unique and consistent model giving these XRD patterns, yet. We hope that further discussions and investigations on these examples of the N TB phase can help to clarify the nature of this phase. Among all of the salicyl dimers only the biphenyl containing dimers BPS_7-6 and BPS_9-6, exhibited an intercalated smectic phase in addition to the nematic one. Due to the very high isotropisation temperature, the transition is accompanied by decomposition. The liquid crystalline phases were identified by direct analogy with the optical texture displayed by the imino-linked dimers for which the intercalated smectic and the N TB phase were established.

Structure-property relations
In general the results revealed that the appearance of the N TB phase in the given series of imino-linked dimers depends not only on the extent of bending resulting from different spacer lengths but also on the mesogenic core structure as well as on the ratio between the lengths of the terminal chain and spacers (n/m). Previously reported BB_7-4,[6] exhibits a monotropic N TB phase. Replacement of the phenyl ring near the linkage group with a naphthyl moiety (BN_7-4) not only elongates the mesogenic core but also increases its breadth and consequently the N-Iso transition temperature is considerably increased and a mesogen results with a large nematic range of more than 60 K and with an enantiotropic N TB phase. Altering the position of the naphthyl group in NB_7-4 causes a significant reduction of the nematic temperature range (to 38 K) and a formation of the smectic phase at the expense of the N TB phase. According to the model of Ferrarini et al. [35] a decrease in the values of ΔS NI /R can be attributed to an increasing molecular biaxiality, which results from the difference in the bond angle between the para-axis of the mesogen and the first bond in the spacer. The value ΔS NI /R for BN_7-4 (ΔS NI /R = 0.17) is smaller than for NB_7-4 (ΔS NI /R = 0.22) suggesting that the bending is less pronounced for the latter although a contribution of various degrees of organisation in the isotropic phase prior to the Iso-N transition, as observed for BB_7-4, [16] cannot be excluded. In relation to the theory of Greco et al. [24] that predicts stabilisation of the N TB phase with decreasing molecular bending angle and range of the N phase, the dimers of the BN and NB series show anomalous behaviour. Comparison of ΔS NI / R within the BN and NB series shows that their values increase with increasing number of methylene units in the spacer. Based on the continuous model [36]] this implicates a higher bending for the homologues with seven methylene units in the spacer and yet the dimer NB_9-4 exhibits the N TB phase while NB_7-4 does not. In addition, the temperature range of the nematic phase is higher for NB_9-4 (ΔT = 42 K) than for NB_7-4 (ΔT = 38 K). A comparison of the mesomorphic properties of all members of the NB series revealed that decreasing the spacer length promotes smectic over nematic behaviour.
In the BN series dimer BN_7-4 displays an enantiotropic N TB phase and BN_9-4 a monotropic one. Considering variations in the bending angle, the behaviour is in agreement with the prediction. [24] However, the stabilisation of the N TB phase is accompanied by an increased range of the N phase following the same trend observed for the NB series.
Elongation of the mesogenic unit by incorporation of the biphenyl group (BPB_7-4) resulted in a further increase of the transition temperatures, facilitation of the smectic organisation and destabilisation of the nematic phases. This behaviour can be explained in the context of the molecular length-to-breadth ratio and is consistent with the hypothesis that on increasing the aspect ratio of the mesogenic core, the tendency to form smectic phases dominates. [14] Introduction of the hydroxy group in ortho position towards the imino linkage leads, through hydrogen bonding, to the formation of an additional six-membered ring that reduces the flexibility of the molecule and increases the breadth near the spacer. This change in the structure promotes the formation of the N TB phase for the BPS homologues with n/m ≤ 0.6. In contrast to the corresponding NB homologues, the stability of the N TB phase increases in the BPS dimers with the decreasing temperature range of the nematic phase. The significance of an increased breadth near the spacer can also be traced in the behaviour of the BS and NS series. Compounds of both series are prone to form nematic phases. Reinvestigation of the BS series in the light of new developments showed that only homologues with comparable lengths of chain and spacer exhibit the N TB phase. This behaviour is rather surprising since currently, among the dimers with terminal chains, the N TB phase was only observed for those having a chain length significantly smaller than the spacer (n/m ≤ 0.6). [9,14] Further, a comparison of BS_7-4 and BPS_7-4 with n/m = 0.6 implies that increasing the aspect ratio of the mesogenic core promotes the formation of the N TB phase. This was observed for the methylene-linked dimers having terminal polar groups; [13] however, the behaviour of the corresponding homologues with n/m = 0.9 (BS_7-6 and BPS_7-6) suggests the opposite conclusion. The reduction of the aspect ratio by inserting a naphthyl moiety in the outer part of the mesogenic core is manifested by nematic polymorphism exhibited by all of the homologues of the NS series. Correlation between corresponding homologues with C 7 and C 9 spacers shows that the stability of the N TB phase grows with increased effective molecular bending and that it is accompanied by a reduction of the temperature range of the nematic phase, consistent with the theoretical model. [24] Also, the width of the nematic phase decreases with increasing n/m ratio and DT between N TB -N transition and melting point changes in a way that N TB becomes enantiotropic. The results revealed that a hydroxy group in the ortho position towards the imino linkage promotes nematic behaviour including the formation of the N TB phase.
Comparison of ΔS NI /R of BS_5-6 and BS_7-6 with those of BB_5-2 (abbreviated 2O.5.O2 there, ΔS NI / R = 0.06) and BB_7-2 (abbreviated 2O.7.O2 there, ΔS NI /R = 0.11) reported by Dawood et al. [25] and these of the dimers of the NS series with those of the BN series suggest that broadening near the spacer as a result of the formation of an additional six-membered ring through hydrogen bonding does not increase the effective bending. Figure 8 shows the space-filling models of the calculated energy minimum structures for BB_7-4 vs. BS_7-4 and BN_7-4 vs. NS_7-4 revealing that all four types of dimers have similar curvature, imposed by the same linkage group. These results suggest that the change in electronic properties caused by the presence of a hydroxy group might assist in stabilising the N TB phase. This prompted us to investigate electrostatic factors that might contribute to the formation of the NTB phase. Figure 8 presents the space-filling models of the calculated minimum-energy structures for BB_7-4, BS_7-4, BN_7-4, NS_7-4.
Since several recent studies [13,14,16] reported a negligible effect of the dipole, we focus our attention on the electrostatic potential distributions. Computational analysis was performed using the density functional theory [37] with the B3LYP functional and the 6-31G(d,p) basis set on the monomers representing each type of mesogenic core.
Inspection of the electrostatic potential isosurfaces for the most stable conformers related to the particular class of dimers, presented in Figure 9 (see Table S4), reveals an anisotropic distribution of the electron density across the mesogenic unit. For mesogenic cores BB, NB, BPB and BN the highest accumulation of electron density is observed on the carboxylate group. Comparison of BB, NB and BPB shows that a replacement of the terminal phenyl with naphthyl and biphenyl increases the electron density of the mesogenic core. Increased delocalisation of the electrons reduces the electron density on the carboxylate group and so diminishes the anisotropy of the electrostatic potential distribution across the mesogenic core.
In the compounds with a salicyl moiety, the highest accumulation of electron density is moved toward the hydroxyl group. Due to the rather high value of the negative electrostatic potential on the hydroxyl group, the extent of the anisotropy of the electrostatic potential distribution is higher than that for the corresponding BB, NB and BPB. These results show that broadening near the spacer is associated with a higher extent in the anisotropy of the electrostatic potential distribution.
In relation to the observed mesomorphic properties, it appears that an increased magnitude of the anisotropy promotes the formation of the N TB phase. This is particularly pronounced for the dimers containing BPS and NS cores or BPB and NB moieties, respectively. In addition, the larger anisotropy calculated for BN than for NB might explain the difference in the nematic behaviour between dimers of those two series. Thus the analysis of electrostatic potential isosurfaces combined with experimental data suggests that the incidence of the N TB phase is facilitated by the anisotropy of the electrostatic potential distribution in the mesogenic core.

Conclusion
Here we have described the synthesis and the mesomorphic properties of a series of imino-linked dimeric molecules in order to improve our understanding of the structure-N TB phase correlations. The study has focused on the impact of various mesogenic units and effective molecular curvature caused by different spacer lengths but also on the effect of the (n/m) ratio. The results presented here show that the incidence of the N TB phase and its thermal stability are highly sensitive to changes in the molecular structure. Generally, the stability of the N TB phase is enhanced with increasing effective molecular curvature arising from a smaller number of methylene units in the spacer. Correlation of the mesomorphic properties of dimers containing various mesogenic cores suggests that broadening of the mesogenic unit, in particular near the spacer, promotes the formation of the N TB phase. Computational studies showed that broadening of the mesogenic core near the spacer is associated with an increased anisotropy of the electrostatic potential distribution. Observation of the N TB phase for the dimers having both a chain length significantly smaller than the spacer and comparable lengths of chain and spacer points to the importance of the n/m ratio in conjunction with the specific mesogenic unit. Overall our studies suggest that within a given series of materials the formation of the N TB phase is imposed by the synergy of specific geometrical factors and the anisotropy of the electrostatic potential distribution of the mesogenic core, but they also revealed a new puzzling issue. The homologues of the BS and NS series with a comparable length of the chains and the spacer form the N TB phase characterised by two maxima in the small angle region of the XRD patterns, the first could correspond to the full and the second, stronger one to half the molecular length. Whether these intriguing results represent special cases of the N TB phase and how they fit into the current model of the N TB phase have yet to be clarified.