The twist-bend phases: structure–property relationships, chirality and hydrogen-bonding

ABSTRACT This article will review some of our recent work concerning the relationships between molecular structure and the observation of the fascinating twist-bend nematic, NTB, phase. From a chemist’s perspective, understanding the molecular features influencing the formation and stabilisation of the NTB phase is of paramount importance, and allows for the design of new materials that have targeted properties. As such, recent work in Aberdeen has had the primary aim of enhancing our current understanding of these relationships in dimeric liquid crystals, through the synthesis and characterisation of a diverse range of materials, including a selection of supramolecular liquid crystals. A second aim has been to explore the intriguing question as to how the NTB phase, having spontaneous structural chirality, would respond at a microscopic level to the presence of intrinsic molecular chirality – the inclusion of chiral fragments in the dimers – and to obtain examples of the ‘chiral’ twist-bend nematic phase (N*TB) for comparative study alongside the conventional NTB phase. We also show that bent achiral molecules form heliconical smectic phases, as predicted by Dozov in his seminal 2001 work.


Introduction
The prediction [1,2] and subsequent experimental discovery [3] of the twist-bend nematic phase, N TB , is undeniably one of the most significant recent developments in the field of liquid crystals. Dubbed the 'structural link' between the conventional nematic, N, phase, and its chiral counterpart, N*, shown in Figure 1, in the N TB phase the director is tilted at constant angle θ and forms a heliconical superstructure of nanoscale periodicity, while the molecules retain a random distribution of their centres of mass [4,5]. The chiral helix is formed despite the constituent molecules being chemically achiral, and indeed, the N TB phase represents the first example of spontaneous chiral symmetry breaking in a fluid system with no spatial ordering. There exists an equal probability of the formation of either handedness of the helix and hence the N TB phase consists of doubly degenerate locally chiral domains of opposite handedness, giving a globally achiral phase. However, the presence of intrinsic molecular chirality removes this degeneracy and the chiral N TB phase is formed. Shortpitch heliconical smectic phases formed from achiral molecules were predicted together with the N TB phase, and examples of these have recently been reported [6,7].
The N TB phase was discovered through the comprehensive characterisation of the liquid crystal dimer 1,7-bis-4-(4-cyanobiphenyl) heptane, CB7CB, and its ability to exhibit this new phase was attributed to the bent shape of the molecule arising from the odd-membered spacer, resulting in an anomalously low bend elastic constant [3]. By far the greatest number of twist-bend nematogens reported are odd-membered liquid crystal dimers; however, the N TB phase has also been observed for rigid bent-core materials [8], a hybrid bent-corecalamitic dimer [9], trimers and tetramers [10][11][12][13], a hexamer [14], and main-chain polymers [15]. The common structural feature shared by these molecular architectures is curvature, not necessarily uniform, and it is now widely believed that this is a prerequisite to observe twist-bend nematic behaviour. This view has been reinforced by a generalised Maier-Saupe theory developed for rigid V-shaped molecules that has shown the twistbend nematic-nematic phase transition temperature to be highly sensitive to the molecular bend angle [16].
Motivated by the discovery of the N TB phase in CB7CB, much of our initial work focussed on revisiting a number of similar dimer series, originally synthesised some time ago as model compounds for polymers or as part of the still-ongoing quest to find the elusive thermotropic biaxial nematic phase [17][18][19][20]. Many of these materials had previously been reported to exhibit a smectic phase below the conventional nematic, assigned due to the former's polygonal and focal conic textures despite some unusual thermal behaviour. However, our studies were able to reassign a number of these designated smectic phases as N TB phases [21][22][23]. This early work culminated in a detailed structure-property investigation of the cyanobiphenyl-based series CBOnOCB, CBnCB and their intermediate CBnOCB [21], together with a comprehensive study on the latter series' hexyloxy member, CB6OCB [24]. This was subsequently selected as a candidate for further modification to explore the effects of structural changes on the incidence of the N TB phase and its properties. This particular structure was chosen because the methylene-ether link allows for the straightforward synthetic addition of different mesogenic units to the CB6O 'backbone' while maintaining the ideal molecular curvature required for an enantiotropic, stable twist-bend nematic phase. This compares to the corresponding ether-linked dimers, for which the increased linearity raises the melting point and lowers T NTBN such that the phases are typically highly monotropic and hence their study is difficult [21].
Here we will describe a selection of recent projects which explore the exchange of the ether-linked cyanobiphenyl moiety of CB6OCB with a variety of mesogenic units, selected for reasons pertaining to the specific aim of the work, and these structures are illustrated in Figure 2.
The azobenzene moiety, Figure 2(a), undergoes photolytic isomerisation from its trans to cis form at certain wavelengths of light. This introduces the possibility of controlling molecular shape, and hence material phase behaviour and elastic properties, through external stimuli [25][26][27]. Benzylideneaniline units Figure 2(b,c) have historically been paired with cyanobiphenyl due to their respective electron rich and electron deficient natures, which result in a specific intermolecular attraction -possibly a quadropolar interaction -thought to drive the formation of intercalated smectic phases [19,28]. Local molecular intercalation was reported as a common feature of twist-bend nematogens, and hence this specific interaction appeared desirable. From a synthetic perspective, the imine link is a convenient and straightforward way to vary terminal alkyl and alkoxy groups to explore what happens when the terminal chain becomes longer than the hexyloxy spacer, assuming intercalation is no longer possible [23,29]. Moreover, those materials with long terminal chains have the potential to exhibit rare N TB -smectic phase transitions and, as we will see, heliconical smectic phases with unique structures. To extend the asymmetry of these dimers an additional phenyl benzoate was introduced to the benzylideneaniline moiety to give a threeringed mesogenic unit [6]. Use of a hydrogen-bond donor (such as benzoic acid, Figure 2(d)) or acceptor (e.g. stilbazole, Figure 2(e)) as the terminus of the mesogenic unit allows for an alternative construction of twistbend nematogens, in the form of bent-shaped supramolecular complexes [30][31][32][33]. Finally, we use a simple phenyl benzoate-based mesogenic unit (f) to attach a chiral terminal chain to our bent-dimer and explore the relationship between molecular and structural chirality in the context of the twist-bend nematic phase and its chiral counterpart, the chiral twist-bend nematic phase, N* TB [34].

Azobenzenes
The trans-to-cis isomerisation of the azobenzene unit is well documented in the literature [25] and, in the context of liquid crystals, results in a lowering of the nematic-isotropic transition temperature -readily explained by considering the more elongated molecular shape of the trans-isomer compared to that of the cis. This feature makes azobenzene-based compounds attractive candidates for use in applications such as liquid crystal displays, optical storage devices or nonlinear optics. To investigate the effect of trans-cis photoisomerisation on the primarily shapedriven N TB phase, we prepared a series of azobenzene dimers CB6OABX, with X = Me, OMe, Bu, OBu, CN and NO 2 ( Figure 3).
All these dimers were enantiotropic nematogens bar the methyl-terminated, which showed a monotropic nematic phase. Conversely, only the butoxy-terminated dimer exhibited an enantiotropic twist-bend nematic phase while the N TB phases shown by the other five were monotropic. Textures for these phases are shown in Figure 4(c). The enantiotropic N TB phase of CB6OABOBu allowed for its further investigation and for this material we demonstrated the first example of an isothermal, photochemically driven twist-bend nematic-nematic phase transition. UV irradiation reduced both T NI and T NTBN , with a more significant effect on the latter. This was attributed to changes in the relative concentrations of the trans-and cis-forms of the azobenzene moiety, confirmed by UV-vis spectroscopy, see Figure 4(d). Hence, increasing the concentration of cis conformations destabilises first the N TB phase in favour of a conventional nematic, then the nematic phase in favour of the isotropic phase. While the latter transition is expected, one might have thought the more strongly bent cis isomer would promote twist-bend behaviour, considering the dependence of the N TB phase on molecular bend. However, it is important to consider that while the trans isomer has a spatially uniform bend, governed by the geometry of the alkyl spacer, bend deformations in the cis isomer occur at two different locations: the spacer and the azobenzene moiety (Figure 4(b)). This causes a reverse in the bend polarity on moving from one end of the molecule to the other, creating a spatially variable bend. Such a bend appears incompatible with the local packing requirements of the twist-bend nematic phase, and hence it is destabilised. CB6OABOBu has been shown to exhibit a fast and giant photorheological effect, giving this material considerable applicability with the potential to achieve a whole new performance level for mechanically responsive organic materials [35].
The nature of the terminal group is clearly influential in determining the stability of both the N and N TB phases, as illustrated by the variation of T NI and T NTBN shown in Figure   Figure 2. Structures of nonsymmetric dimers discussed in this work. 4(e) [27]. The nitrile group ranks as the most efficient in stabilising both the N and N TB phases, while the butyl terminal chain is the least effective. The observed order may be accounted for in terms of subtle changes in the average molecular shape, steric factors, and the strength of the mixed mesogen interaction on varying the terminal group; however, this work reinforced the general view that there is not a clear and simple relationship between the electronic properties of the mesogenic units and T NI or T NTBN [36][37][38].
Additional structural modifications to our azobenzenebased dimers included exchange of the hexyloxy spacer with its diether analogue, oxypentyloxy (O5O), replacement of the cyanobiphenyl mesogen with methoxybiphenyl, and formation of symmetric azobenzenes-based dimers connected by the O5O spacer [27,39]. T NI is elevated and T NTBN reduced for the diether-linked dimers compared with the CB6OABX series, with the N TB phase seen only for the butyl and butoxy-terminated materials. These observations are attributed mainly to the influence of the spacer on molecular shape, a trend well documented for liquid crystal dimers [18,21,36,40] and completely in accord with the predictions of theoretical models [41,42]. In the symmetric materials, the N TB phase is lost and these are exclusively nematogenic, with the exception of the butyl-terminated dimer for which a conventional monolayer smectic A phase was observed [27].
Investigations into the photocontrolable azobenzene-based twist-bend nematogens remain ongoing, with intriguing aspects such as the effect of irradiation on the elastic constants and the possibility of lightcontrolled selective reflection in a chiral material yet to be fully addressed.

Benzylideneanilines
In addition to the N TB phase, Dozov's seminal 2001 work also predicted the existence of heliconical smectic phases formed from bent-shaped, achiral molecules [2]. This has been a particularly difficult prediction to verify as the majority of twist-bend nematic phases either crystallise or vitrify on further cooling and hence N TBsmectic phase transitions are only rarely observed. We sought to establish and understand how these bent molecules pack into smectic phases and the properties such phases exhibit. To this end, we prepared several dimer series combining the molecular curvature required to exhibit the N TB phase with selected structural features known to promote smectic phase behaviour, Figure 5(a-c). The cyanobiphenyl and Schiff's base moieties are known to exhibit a favourable specific interaction thought to drive smectic phase formation in mixtures of conventional low molar mass mesogens and in non-symmetric dimers. For this study, it was critical that the length of the terminal chain m could be readily varied given the role of microphase separation in smectic phase formation. The inclusion of phenyl benzoate in the benzylidieneaniline mesogenic unit to give the series shown in Figure 5(c) was to enhance intermolecular interactions between these units in order to further drive smectic behaviour.
CB6O.m dimers with m = 1-10 ( Figure 5(a)) show N and N TB phases, see Figure 6(a). X-ray diffraction measurements shown in Figure 6(b) revealed that for short chain lengths (m = 1-6) the local packing in both nematic phases is an intercalated arrangement; for intermediate chain lengths (m = 7-9) there exists a frustrated local structure, with competition between intercalated, monolayer and interdigitated arrangements, and for the longest chain length (m = 10) a new, bilayer arrangement is observed. This was the first time such a change in the local structure on increasing m had been seen in a dimer series exhibiting the N TB phase. Surprisingly, this has no apparent effect on the stability of either nematic phase, and T NTBN and T NI show a regular dependence on m (Figure 6(c)). Specifically, T NTBN and T NI decrease on increasing m and superimposed upon this is a weak odd-even effect in which the odd members show the higher values, typical behaviour for such dimer series. These results suggest that previous reports may have overstated the importance of local molecular intercalation in driving the formation of the N TB phase. A smectic mesophase with a lamellar bilayer arrangement (d = 2 l) is exclusive to the dimer with m = 10 and is discussed later.
Exchange of the alkyl terminal chain for an alkoxy chain gave the CB6O.Om series, Figure 5(b). N and N TB phases are again observed in all 10 dimers, and X-ray measurements found a somewhat similar local packing progression in the nematic phases on increasing m to that observed in the CB6O.m series. Thus, local molecular  intercalation is seen for short chain lengths, and frustration/monolayer packing for longer chains. Intercalated smectic phases are observed only in dimers with m = 3-5, and the higher temperature of these is suggested to be a new type of heliconical smectic phase, discussed later. The lack of smectic behaviour for longer terminal chain lengths suggests that intercalation has been destabilised, and the absence of a strong driving force for the formation of a monolayer smectic phase precludes its observation.
It is well documented for both conventional low molar mass and dimeric mesogens that replacement of an alkoxy terminal chain by an alkyl group results in a lowering of the melting and clearing points, as well as the other liquid crystal phase transition temperatures. A contributing factor to these reductions is the respective orientations of the terminal chains with respect to the mesogenic unit to which they are attached. Specifically, an all-trans alkyl chain protrudes at some angle from the plane of the unit, and hence disrupts the packing efficiency of the molecules (Figure 6(d)). In contrast, an alkoxy terminal chain lies more-or-less in the plane of the mesogenic moiety and enhances the shape anisotropy. This is indeed what we observe here, with the CB6O.m dimers having consistently lower melting, clearing and T NTBN temperatures than the corresponding member of the CB6O.Om series, see Figure 6(c). These lower transition temperatures may also account for the lack of intercalated smectic behaviour in CB6O.m dimers with short chains.
The phase behaviour of the CB6OBeIOm series with m = 1-10 ( Figure 5(c)) is illustrated in Figure 7(a) [6]. All 10 dimers were nematogenic, and those with short terminal chains exhibited the intercalated N TB phase. For m > 6, a sequence of up to four monolayerlamellar phases is seen below the N phase. Unique to homologues with m = 7 and 8 is a tilted, smectic C phase, the details of which are discussed in the next section. The lowest temperature smectic phase, common to all homologues, was identified as a hexatic-type phase, HexI, with unique multi-level chirality. AFM studies of the morphology of this phase revealed mesoscopic helical filaments with uniform twist over micron-size areas, see in Figure 7(b), resembling that of the B 4 phase but without an internal crystal structure [43,44].

The twist-bend smectic phases
Arguably the most exciting result to emerge from these studies is the discovery of new short-pitch, tilted smectic phases formed by achiral molecules, as were predicted by Dozov along with the N TB phase [2]. Such a phase was first seen in CB6OBeIO7 and CB6OBeIO8 preceded by non-tilted SmA and SmAb phases [6], and we termed this phase the twist-bend smectic C phase, SmC TB , proposing the structure illustrated in Figure 8(a). A variant of this phase, having apparent structural differences (discussed later), was subsequently observed in CB6O.10, formed directly from the N TB phase [7,23].
Although calorimetric studies of CB6O.10 clearly reveal the enthalpy change associated with the transition between the N TB and this phase, in optical studies the phase transition is not easy to detect. In planar aligned cells, the stripe texture of the N TB phase persists into the lower temperature SmC TB phase (Figure 8(b)) and in cells with homeotropic anchoring, both phases appear black and hence are optically uniaxial. This suggests that in both phases there is an averaging of molecular orientation in space due to the formation of the helix. Similar textural observations were made also for the CB6OBeIOm dimers. However, a lack of this optical uniaxiality need not discount the possibility of a SmC TB phase, and for a helical structure in which the molecular orientations are not fully averaged over the helix -ie. a 'distorted' clock structure -a schlieren texture may be observed. This is the case for CB6O.O5, for which resonant soft X-ray measurements in the SmC phase reveal a helicoidal structure despite its optical resemblance to a conventional SmC A phase [45]. This suggests the phase seen in CB6O.O5 may be a second structural variant of the SmC TB phase.
The key technique for identifying these heliconical smectic phases, and importantly, to distinguish between a conventional SmC A phase and a distorted-clock type smectic C TB phase, is resonant soft X-ray diffraction (RSoXS). This method reveals periodic structures related to orientational order and has in the past been used to study the structure of helical phases which have a uniform electron density but differ with respect to the orientation of the molecules, such as the N TB phase, the blue phases and subphases of the ferroelectric chiral smectic C* phase [46]. The twist-bend nematic phase, and indeed the SmC TB phases of CB6OBeIO7, CB6OBeIO8 and CB6O.O5, show simple RSoXS patterns containing a single signal associated with the helical pitch (which typically corresponds to just a few smectic layers). In contrast, RSoXS measurements of CB6O.10 revealed the potential complexity of a SmC TB -type phase, see Figure 8(c) [7]. The pattern consists of a large symmetrical splitting of the RSoXS signal and the simultaneous appearance of a weak harmonic signal, suggesting an additional nanoscale helical modulation is superimposed onto the basic, layered helical structure. Such an RSoXS pattern resembles that observed for the chiral smectic C subphase SmC FI2 *, seen in highly chiral systems in a temperature range between the anticlinic and synclinic forms of the smectic C* phase. In the SmC FI2 * phase, molecules in four consecutive layers form a distorted helix, represented by a clock model. The 'ideal' clock model (with the azimuthal angle between consecutive molecules φ = 90°) is shown in Figure 8(e) along with the distorted structure of SmC FI2* , for which φ ≠ 90°. The additional helical modulation arises due to interactions between the chiral molecules -the whole 4-molecule 'unit cell' is rotated by some angle with respect to the next. We therefore propose a similar structure for our SmC TB -type phase exhibited by CB6O.10, see Figure 8(e). However, our material is achiral. Therefore, if the structure of the phase does indeed resemble that of the SmC FI2 * phase, the interactions driving its formation must be different and are presumably related to the molecular bend and resulting low bend elastic constant of the material. It is also notable that the additional helical modulation in the SmC TB phase is on the nanoscale, while in the SmC FI2 * it is within the optical range.
Heliconical lamellar mesophases have also been observed in achiral, semi-rigid bent-core molecules with long terminal alkyl chains (C n H 2n+1 , where n = 12--22), either spontaneously formed on cooling from preceding smectic phases (n = 12-16) or induced by application of an electric field [8,47]. It is notable that these polar smectic phases have an even shorter pitch (<3 smectic layers) than our SmC TB -type phases [47]. (middle)) SmC FI2 * phase, with rotation between consecutive molecules ≠ 90° and very small rotation between layers (weak additional modulation) (bottom) proposed 'distorted' clock model of the SmC TB phase in CB6O.10, with an azimuthal rotation ≠ 90° and strong additional modulation, ie. the rotation between layers is significantly larger than in the SmC FI2 * phase.
It is clear that the investigations into these twist-bend smectic phases are still in their preliminary stages, and the preparation of a large number of new materials is required to elucidate structure-property relationships for this class of phases, and specifically to establish the molecular features that drive their subtly different microstructures. Moreover, it will be intriguing to discover whether the structural similarity of these phases to the ferroelectric SmC* subphases will be matched in their physical properties.

Chirality and the N TB phase
Mesophases exclusive to chiral liquid crystals arise because of molecular chirality -most commonly the presence of a chiral centre in a molecule but also through chiral axes or planes (axial chirality) -or are induced by the presence of a chiral dopant. Many of these chiral mesophases have a twisted or helical structure, for example, the chiral nematic N* or smectic C* phases, and hence have very different physicochemical properties compared to their achiral counterparts. The N TB phase was the first example of such a heliconical superstructure formed in the absence of intrinsic molecular chirality in a system with no spatial ordering. As this formation of chirality is spontaneous, the probability of either handedness of helix forming is equal; thus, the N TB phase consists of doubly degenerate locally chiral domains of opposite handedness and hence is a globally achiral phase. Our particularly intriguing research question was therefore how the N TB phase, having spontaneous structural chirality, would respond at a microscopic level to the presence of molecular chirality. Meyer extended the elastic instability model of the N TB phase to consider the effect of a chiral field introduced by chiral doping and predicted the removal of the double degeneracy of the chiral domains, with the new ground state of the N TB phase being those domains with the same handedness as the dopant [48]. With increasing chiral doping the conical angle in this favoured helical state increases, while that in the unfavoured helical state decreases, and eventually the more favoured handedness dominates. The helical pitch is predicted to be essentially unchanged. Chiral doping is therefore predicted to increase the stability of the N TB phase. Longa and Tomczyk used minimum coupling Landau-de Gennes theory to reveal the possibility of a polar, chiral N TB phase [49]. Only a handful of chiral nematic-twist-bend nematic transitions have been observed experimentally. These have included mixtures of twist-bend nematogens with a chiral dopant [11,50] as well as intrinsically chiral materials, with the latter being particularly rare and prior to our studies exclusive to cholesterol-based dimers [51].
Molecular chirality is most easily introduced to a liquid crystal dimer by the addition of a methyl branch to a carbon atom in a terminal chain. It became apparent in earlier work, however, that such branching destabilises nematic behaviour, by disrupting the interactions between the mesogenic units [36]. Thus, our design strategy for new chiral dimers was to begin with a liquid crystal dimer confirmed to exhibit the N TB phase, 4-butoxyphenyl 4-{[6-(4ʹ-cyano[1,1ʹ-biphenyl] -4-yl)hexyl]oxy}-benzoate, CB6OPEPO4 [36], and extend one of the mesogenic units by the addition of a phenyl benzoate fragment, with the aim of raising the liquid crystal transition temperatures such that the subsequent addition of the branch would not remove N TB behaviour. This approach proved successful and we recently reported the first example of the chiral twist-bend nematic phase, N* TB , below the N* phase in a material with a single chiral centre, (S)-CB6OPEPƎPO(2-Me)4, Figure 9 [34]. Moreover, we made the first direct comparison between the conventional N TB and its chiral equivalent, the N* TB phase, through the synthesis of the racemic version of CB6OPEPƎP(2-Me)4, which exhibits an N TB -N transition.
The N* TB phase exhibits optical textures with lower birefringence than those observed for the achiral N TB phase, suggesting an additional mechanism of averaging the molecular orientations. Textural features include stripes/'ropes', as seen in the N TB phase formed by achiral molecules, but also several unique patterns, the origins of which are unclear. These include 'jagged' stripe textures, uniform areas with a faint 'diamond-like' pattern and chain-like defects, see Figure 10(a). A particularly intriguing observation is that although T N*I ≈ T NI , the N* TB phase is consistently seen at a higher temperature than N TB when comparing the chiral and racemic versions of CB6OPEPƎP(2-Me)4 in mixtures with CB6OCB, see Figure 10(b), and currently the largest observed difference is ~10°C [52]. This is in accord with Meyer's elastic instability model [48], and indeed suggests that the double degeneracy of the helical twist sense in the N* TB phase is removed by the intrinsic molecular chirality and the favoured twist sense becomes more stable. This may be a consequence of differences in the mechanism in forming the heliconical structure of the N(*) TB phase, and depends on the structure of the preceding phase. A second curiosity is the formation of a square lattice pattern in the N* phase over a temperature range of several degrees above, before disappearing prior to, the N* TB -N* phase transition, see Figure 10(c). A similar phenomenon had been reported for chirality-doped bent-core materials and may be attributed to a non-monotonic dependence of the bend elastic constant [53].
There is considerable application potential for materials combining the properties of the chiral and twistbend nematic phases. An electrically tunable helical pitch may be used in, for example, tunable lasers or energy-saving smart-windows. It has been demonstrated in a proof-of-concept study that mixtures containing chirally doped nematogens with a sufficiently low bend elastic constant (ie. twist-bend nematogens) do indeed possess an electrically tunable pitch in their cholesteric phase [54,55]. However, use of such mixtures in liquid crystal applications can introduce numerous problems including phase separation of the mixture components and incompatibility issues, and thus it would be desirable to use a less complex mixture, or indeed, a single component capable of exhibiting both the N* and N* TB phases.

Hydrogen-bonding and the N TB phase
The majority of twist-bend nematogens are covalently bonded oligomeric or bent-core materials, but we have also reported the observation of both the N TB and the N* TB phases in supramolecular liquid crystals (SLCs), specifically, bent-shaped complexes created through hydrogen bonding (H-bonding). The preparation of supramolecular mesogens via H-bonding is a flexible and efficient alternative to covalent bonding, and a convenient way of adding functionality to a molecule in an effective and controllable manner. Moreover, it is useful for introducing chirality to a system as it avoids the risk of partial racemisation during the synthetic process. H-bonding emerged as a means of constructing liquid crystal systems in the early 1950 s, with one of the earliest reports detailing the phase behaviour of the n-alkoxybenzoic acids (nOBAs) [56]. Their mesogenic behaviour was attributed to the formation of calamiticlike, symmetric homomeric complexes of two equivalent benzoic acid fragments with a supramolecular core formed via hydrogen bonding. We extended this approach, reporting the formation of the first supramolecular twist-bend nematogen, CB6OBA, in which two acid dimers hydrogen-bond to form a bent supramolecular trimer, see Figure 11 [31].
The first heterodimeric rod-like complexes formed via hydrogen bonding between unlike hydrogen-bond donors and acceptors -for example, benzoic acid and pyridylbased fragments -were described by Kato and Frechet in the late 1980s [30]. In 2018, we reported the first example of spontaneous chiral symmetry breaking through the mixing of achiral components; specifically, the induction of the N TB phase through molecular recognition in mixtures containing unlike H-bond donors and acceptors: the nOBAs (n = 4,5) and 1OB6OS, respectively, Figure 12 [57].
We later extended this study to include more members of the nOBA series (n = 1-10) and a second H-bond acceptor, CB6OS, to create two homologous series of new supramolecular liquid crystals, see Table 1 [32,33]. By analogy with the covalently assembled systems discussed earlier, extending the terminal chain attached to the hydrogen-bond donor aimed to drive the formation of smectic phases.
Several members of the 1OB6OS:nOBA and CB6OS: nOBA series show N TB phases over a broad temperature range despite the H-bond acceptor not being liquid crystalline and the donor exhibiting only the conventional N phase. Those with short values of n exhibit N and N TB phases and for longer chains the N TB phase is lost and a series of up to four smectic phases is seen below the N phase. In the CB6OBA:nOS mixtures (where nOS are short, non-mesogenic stilbazole-based materials, see Table 1), considered to be the 'reverse' of the CB6OS: nOBA complexes, the N TB phase is exhibited up to n = 7, whereas mixtures with n > 7 again show a Sm-N transition. Selected mixtures also exhibited N TB -smectic transitions, for example, CB6OBA:nOS with n = 4-7 cooled from the N TB phase into a SmC phase, although unfortunately, the monotropic nature of this phase precluded study by RSoXS. This is true also for CB6OS:nOS mixtures with n = 7-10 which exhibit an SmC-SmA transition.
Temperature-dependent FT-IR spectroscopy confirmed the presence of strong hydrogen bonding in the mixtures and revealed the existence of a complex equilibrium between various species, Figure 13(a) [32,58]. The amounts of the various H-bonded species present and how these shift on cooling from the   isotropic liquid through the liquid crystal phases were measured semi-qualitatively by the deconvolution of the complex C = O stretching region (1650-1740 cm −1 ) into six Gaussian peaks representing the different individual contributions of each species to the overall band shape, see Figure 13(b) [59,60]. The bent-shaped heterocomplex formed between the unlike benzoic acid and stilbazole fragments is the dominant species in the observed mesophases, but various homomeric acid dimers are also present in significant amounts and thus may play a role in the stabilisation of these phases [32,57].
In general, we find that the behaviour of these supramolecular liquid crystals is reminiscent of that of their covalently bonded analogues. Similar to the CB6O.(O) m series discussed earlier, X-ray diffraction studies revealed a progression of the local molecular packing from intercalated, to frustrated, to monolayer with no effect on the stability of either nematic phase, further evidence that intercalation is not key in forming the N TB phase. Smectic phases are favoured by long terminal chains, a common observation in non-symmetric liquid crystal dimers, and indeed this is also seen for the CB6OBeIOm series. Birefringence measurements strongly resemble those for CB6OCB: namely, a departure from critical dependence several degrees above T NTBN caused by the instantaneous formation of local heliconical states and a decrease in birefringence at T NTBN as a consequence of the tilting and averaging of the molecular positions around the helical axis.
Additional studies on H-bonded materials have included the supramolecular trimers CB6OBA:CB6OS and CB6OBA:1OB6OS, which exhibit N and N TB phases. These are the first H-bonded trimers consisting of unlike donor and acceptor fragments which exhibit N TB behaviour [32].

Summary
Summarising, it is evident that our investigations into relationships between molecular structure and the incidence of the twist-bend nematic phase have revealed many unique and unprecedented features. Particularly notable observations include the first twist-bend nematic-nematic transition controlled by light, the first example of spontaneous symmetry breaking driven by molecular recognition, and the first series of twist-bend nematogens to show a change in local packing structure from intercalated to bilayer. In addition, we have reported the first dimers to exhibit short-pitch heliconical smectic phases -the SmC TB phases -and new examples of the chiral twist-bend nematic phase, N* TB , in both covalently and hydrogen-bonded materials. In general, these projects have reaffirmed previous conclusions that the main structural feature required for the observation of the twist-bend phases is molecular curvature; while the dimeric structure need not be symmetric, the bend must be spatially uniform. However, with some of our dimers exhibiting monolayer, partially-and fully-bilayer N TB phases, we have shown that local molecular intercalation does not appear to be as important a feature in driving its formation as previously thought.
While our understanding of the N TB phase has progressed significantly over the past decade, it is clear that each advance introduces many new questions and there remains much to discover about these fascinating twistbend phases.