A Ten-Year Perspective on Twist-Bend Nematic Materials

The discovery of the twist-bend nematic phase (NTB) is a milestone within the field of liquid crystals. The NTB phase has a helical structure, with a repeat length of a few nanometres, and is therefore chiral, even when formed by achiral molecules. The discovery and rush to understand the rich physics of the NTB phase has provided a fresh impetus to the design and characterisation of dimeric and oligomeric liquid crystalline materials. Now, ten years after the discovery of the NTB phase, we review developments in this area, focusing on how molecular features relate to the incidence of this phase, noting the progression from simple symmetrical dimeric materials towards complex oligomers, non-covalently bonded supramolecular systems.


Introduction
The term "liquid crystal" refers to a large number of states of matter that possess some degree of positional and/or orientational order, which is intermediate between isotropic liquids and crystalline solids. Much has been written about nematic liquid crystals and the twist-bend nematic phase, and so for the sake of brevity a short introduction to the topic suffices. The uniaxial nematic phase is arguably the simplest liquid crystal phase, with the constituent molecules (or particles) being, on average, oriented along a vector termed the director. Nematic liquid crystals are of special interest due to their role in display technology, and the discovery of new nematic ground states such as the twist-bend nematic is met with great enthusiasm. Biaxial nematics, in which the molecules are oriented along two orthogonal directors [1], are known to exist [2], but are outside the scope of this review. Similarly, although beyond the scope of this review, we note that nematic phases are almost exclusively apolar, that is, molecules orient both parallel and antiparallel to the director; very recently, the polar ferroelectric nematic phase has been shown to exist [3][4][5][6][7].
Introduction of chirality to a nematic liquid crystal leads to the formation of a chiral nematic phase, which has a helical superstructure. Dozov and Meyer independently suggested that bent shaped molecules could spontaneously form a heliconical nematic structure that is locally chiral, even when formed of achiral molecules [8]. This is termed the twist-bend nematic (N TB ) phase, and was reported experimentally in a landmark work in 2011 [9]. The N TB phase has been described as the "structural link" between the uniaxial nematic phase and the helical chiral nematic mesophase [10]. A number of techniques have measured [10][11][12][13] (or inferred [14,15]) the repeat length of the N TB phase, with in situ resonant X-ray scattering being particularly noteworthy [16,17], and while the precise pitch length is material dependent, a value of around 10 nm is typical. This being said, other models have been proposed that merit further experimental investigation [18], but were outside the scope of this review.
The average conical angle between the mesogens and the helical axis can be measured by NMR [19] or birefringence [20], or by reconstructing the ODF using order parameter data from, for example, SAXS [21], polarised Raman spectroscopy [22], or NMR [23]. The conical angle of the N TB phase remains below the magic angle and the phase is uniaxial with positive birefringence, confirmed by conoscopic investigation [24]. Calorimetric studies The conical angle of the NTB phase remains below the magic angle and the phas ial with positive birefringence, confirmed by conoscopic investigation [24]. Ca studies show the NTB-N is typically first order, and close to tricritical [9,[25][26][27][28] phase has been shown to be strongly shear thinning; for the material KA(0.2), a nent mixture with a pitch length of 10.5 nm [29,30], it was shown that at low (<1 stress, the viscosity was ~1000× larger than the nematic phase. For the same m high shear stress (>10 Pa), the viscosity of the NTB-phase dropped by two orders tude as the helix underwent shear-induced realignment [31].
As with all mesophases, the formation of the NTB phase in a given mater mately linked to molecular structure, and there has been significant effort in the new materials that exhibit the NTB phase [32]. The molecular structure of liquid c dimers can be subdivided into distinct regions, as outlined in Figure 1B. In th terms, a dimer consists of two rigid mesogenic units joined by a flexible space For a trimer, three mesogenic units are joined in a similar fashion, and so on. the region of 1000, materials are known to exhibit the NTB phase, and so in this r focused on systematic variations to key areas of molecular structure rather than futile attempt to cover all materials.

Materials
The CBnCB family are archetypal NTB materials, and a logical place to beg view. These materials feature two cyanobiphenyl mesogenic units separated b ylene units. As with all LC dimers, the CBnCB family displays a strong odd-ev with the even parity members displaying notably higher clearing points than t odd spacer parity. With the exception of the shortest homologue (CB3CB), all o

Materials
The CBnCB family are archetypal N TB materials, and a logical place to begin our review. These materials feature two cyanobiphenyl mesogenic units separated by n methylene units. As with all LC dimers, the CBnCB family displays a strong odd-even effect, with the even parity members displaying notably higher clearing points than those with odd spacer parity. With the exception of the shortest homologue (CB3CB), all odd parity CBnCBs displayed two nematic phases, the lower temperature nematic phase being identified as the N TB phase (Table 1). Even parity CBnCB materials displayed only a conventional nematic phase. Table 1. Transition temperatures (T A-B , • C) of the CBnCB family of materials [9,23,26,[36][37][38][39][40].

No. Name n TMP TN TB -N TN-Iso
Due to their favourable working temperatures, the properties of the NTB phase of some members of the CBnCB family have been quite well explored. The helix pitch length of CB7CB was measured by freeze-fracture TEM by Chen et al. [11], who found a value of 8.3 nm. Later, Zhu et al. measured the NTB pitch length of CB9CB as a function of temperature by resonant X-ray scattering at the carbon K-edge [16]; the pitch length was largest close to the NTB-N transition (~9.8 nm), and decreased to around 8 nm with decreasing temperature. Yu and Wilson recently reported fully atomistic MD simulations of CB7CB, which yielded an NTB phase with a pitch length of 8.35 nm [41]. The conical tilt-angle within these simulations (~29°) agreed well with the experimental values [11,20].
The orientational order parameters of several members of the CBnCB family have been measured, with results from different methods generally being consistent with one another. For odd parity CBnCBs, the thermal evolution of orientational order within the nematic phase is unremarkable, however, at TN TB -N, there is a decrease in orientational ordering. This decrease results from the molecules tilting away from the helix, which manifests as a reduction in, or even negative value of <P4> [21,42]. This behaviour of the orientational order parameters has also been observed by NMR [43], and is reported to be consistent with the polar twisted nematic (NPT) model of the NTB phase. CB8CB, which has even spacer parity and does not show the NTB phase, displays unusually large nematic order parameters [22], as does CB10CB [43].
We next consider variations in the mesogenic units. Compound 11 belongs to a class of materials known as "PZP" dimers (P = phenyl, Z = carboxylate ester). The synthesis of these materials is trivial; the penultimate step is esterification of bis 1,9-(4-hydroxyphenyl)nonane, permitting the synthesis of a large number of variations in core structure via esterification. In Table 2, we present the transition temperatures of a set of PZP-9-PZP dimers with varying terminal groups. While cyano, isothiocyanato, and alkyl/alkoxy groups are found to support the formation of the NTB phase [44,45], various other polar units (nitro, fluoro, trifluoromethyl, pentafluorosulphanyl) render the resulting materials non-mesogenic [44]. For compound 15, the -NCS unit enables measurement of the NTB pitch length (~9 nm) using resonant X-ray scattering at the carbon K-edge and also the sulphur K-edge [46]. Due to their favourable working temperatures, the properties of the N TB phase of some members of the CBnCB family have been quite well explored. The helix pitch length of CB7CB was measured by freeze-fracture TEM by Chen et al. [11], who found a value of 8.3 nm. Later, Zhu et al. measured the N TB pitch length of CB9CB as a function of temperature by resonant X-ray scattering at the carbon K-edge [16]; the pitch length was largest close to the N TB -N transition (~9.8 nm), and decreased to around 8 nm with decreasing temperature. Yu and Wilson recently reported fully atomistic MD simulations of CB7CB, which yielded an N TB phase with a pitch length of 8.35 nm [41]. The conical tilt-angle within these simulations (~29 • ) agreed well with the experimental values [11,20].
The orientational order parameters of several members of the CBnCB family have been measured, with results from different methods generally being consistent with one another. For odd parity CBnCBs, the thermal evolution of orientational order within the nematic phase is unremarkable, however, at T N TB -N , there is a decrease in orientational ordering. This decrease results from the molecules tilting away from the helix, which manifests as a reduction in, or even negative value of <P4> [21,42]. This behaviour of the orientational order parameters has also been observed by NMR [43], and is reported to be consistent with the polar twisted nematic (N PT ) model of the N TB phase. CB8CB, which has even spacer parity and does not show the N TB phase, displays unusually large nematic order parameters [22], as does CB10CB [43].
We next consider variations in the mesogenic units. Compound 11 belongs to a class of materials known as "PZP" dimers (P = phenyl, Z = carboxylate ester). The synthesis of these materials is trivial; the penultimate step is esterification of bis 1,9-(4-hydroxyphenyl)nonane, permitting the synthesis of a large number of variations in core structure via esterification. In Table 2, we present the transition temperatures of a set of PZP-9-PZP dimers with varying terminal groups. While cyano, isothiocyanato, and alkyl/alkoxy groups are found to support the formation of the N TB phase [44,45], various other polar units (nitro, fluoro, trifluoromethyl, pentafluorosulphanyl) render the resulting materials non-mesogenic [44]. For compound 15, the -NCS unit enables measurement of the N TB pitch length (~9 nm) using resonant X-ray scattering at the carbon K-edge and also the sulphur K-edge [46]. Table 2. Transition temperatures (T A-B , • C) of some symmetric (PZP)-9 materials with varying terminal unit [44,45].  The synthetic flexibility afforded by the PZP dimers makes it possible to prepare dissymmetric materials such as those shown in Table 3 [47,48]. With a single phenyl 4-cyanobenzoate mesogenic unit, it is possible to obtain materials that display the NTB phase, even when the second mesogenic unit incorporates an 'unfavourable' terminal unit (e.g., NO2, SF5, etc.) [47,48]. This approach also lends itself to the synthesis of trimers, tetramers, and so on, as will be discussed later. A general trend in the materials presented in Table 3 is that the addition of additional fluorine atoms ortho to the terminal group leads to depressions in both TN TB -N and TN-Iso, mirroring the behaviour of calamitic materials [49]. One advantage enjoyed by unsymmetrical materials is that their melting points are generally lower than those of the corresponding symmetrical derivatives, which compensates for the more elaborate synthesis required. Table 3. Transition temperatures (TA-B, °C) of some dissymmetric (PZP)-9 materials with varying terminal unit [47,48] The synthetic flexibility afforded by the PZP dimers makes it possible to prepare dissymmetric materials such as those shown in Table 3 [47,48]. With a single phenyl 4-cyanobenzoate mesogenic unit, it is possible to obtain materials that display the N TB phase, even when the second mesogenic unit incorporates an 'unfavourable' terminal unit (e.g., NO 2 , SF 5 , etc.) [47,48]. This approach also lends itself to the synthesis of trimers, tetramers, and so on, as will be discussed later. A general trend in the materials presented in Table 3 is that the addition of additional fluorine atoms ortho to the terminal group leads to depressions in both T N TB -N and T N-Iso , mirroring the behaviour of calamitic materials [49]. One advantage enjoyed by unsymmetrical materials is that their melting points are generally lower than those of the corresponding symmetrical derivatives, which compensates for the more elaborate synthesis required. Table 3. Transition temperatures (T A-B , • C) of some dissymmetric (PZP)-9 materials with varying terminal unit [47,48].  The synthetic flexibility afforded by the PZP dimers makes it possible to prepare dissymmetric materials such as those shown in Table 3 [47,48]. With a single phenyl 4-cyanobenzoate mesogenic unit, it is possible to obtain materials that display the NTB phase, even when the second mesogenic unit incorporates an 'unfavourable' terminal unit (e.g., NO2, SF5, etc.) [47,48]. This approach also lends itself to the synthesis of trimers, tetramers, and so on, as will be discussed later. A general trend in the materials presented in Table 3 is that the addition of additional fluorine atoms ortho to the terminal group leads to depressions in both TN TB -N and TN-Iso, mirroring the behaviour of calamitic materials [49]. One advantage enjoyed by unsymmetrical materials is that their melting points are generally lower than those of the corresponding symmetrical derivatives, which compensates for the more elaborate synthesis required.  The synthetic flexibility afforded by the PZP dimers makes it possible to prepare dissymmetric materials such as those shown in Table 3 [47,48]. With a single phenyl 4-cyanobenzoate mesogenic unit, it is possible to obtain materials that display the NTB phase, even when the second mesogenic unit incorporates an 'unfavourable' terminal unit (e.g., NO2, SF5, etc.) [47,48]. This approach also lends itself to the synthesis of trimers, tetramers, and so on, as will be discussed later. A general trend in the materials presented in Table 3 is that the addition of additional fluorine atoms ortho to the terminal group leads to depressions in both TN TB -N and TN-Iso, mirroring the behaviour of calamitic materials [49]. One advantage enjoyed by unsymmetrical materials is that their melting points are generally lower than those of the corresponding symmetrical derivatives, which compensates for the more elaborate synthesis required.  The synthetic flexibility afforded by the PZP dimers makes it possible to prepare dissymmetric materials such as those shown in Table 3 [47,48]. With a single phenyl 4-cyanobenzoate mesogenic unit, it is possible to obtain materials that display the NTB phase, even when the second mesogenic unit incorporates an 'unfavourable' terminal unit (e.g., NO2, SF5, etc.) [47,48]. This approach also lends itself to the synthesis of trimers, tetramers, and so on, as will be discussed later. A general trend in the materials presented in Table 3 is that the addition of additional fluorine atoms ortho to the terminal group leads to depressions in both TN TB -N and TN-Iso, mirroring the behaviour of calamitic materials [49]. One advantage enjoyed by unsymmetrical materials is that their melting points are generally lower than those of the corresponding symmetrical derivatives, which compensates for the more elaborate synthesis required.  The synthetic flexibility afforded by the PZP dimers makes it possible to prepare dissymmetric materials such as those shown in Table 3 [47,48]. With a single phenyl 4-cyanobenzoate mesogenic unit, it is possible to obtain materials that display the NTB phase, even when the second mesogenic unit incorporates an 'unfavourable' terminal unit (e.g., NO2, SF5, etc.) [47,48]. This approach also lends itself to the synthesis of trimers, tetramers, and so on, as will be discussed later. A general trend in the materials presented in Table 3 is that the addition of additional fluorine atoms ortho to the terminal group leads to depressions in both TN TB -N and TN-Iso, mirroring the behaviour of calamitic materials [49]. One advantage enjoyed by unsymmetrical materials is that their melting points are generally lower than those of the corresponding symmetrical derivatives, which compensates for the more elaborate synthesis required.  The synthetic flexibility afforded by the PZP dimers makes it possible to prepare dissymmetric materials such as those shown in Table 3 [47,48]. With a single phenyl 4-cyanobenzoate mesogenic unit, it is possible to obtain materials that display the NTB phase, even when the second mesogenic unit incorporates an 'unfavourable' terminal unit (e.g., NO2, SF5, etc.) [47,48]. This approach also lends itself to the synthesis of trimers, tetramers, and so on, as will be discussed later. A general trend in the materials presented in Table 3 is that the addition of additional fluorine atoms ortho to the terminal group leads to depressions in both TN TB -N and TN-Iso, mirroring the behaviour of calamitic materials [49]. One advantage enjoyed by unsymmetrical materials is that their melting points are generally lower than those of the corresponding symmetrical derivatives, which compensates for the more elaborate synthesis required.  The synthetic flexibility afforded by the PZP dimers makes it possible to prepare dissymmetric materials such as those shown in Table 3 [47,48]. With a single phenyl 4-cyanobenzoate mesogenic unit, it is possible to obtain materials that display the NTB phase, even when the second mesogenic unit incorporates an 'unfavourable' terminal unit (e.g., NO2, SF5, etc.) [47,48]. This approach also lends itself to the synthesis of trimers, tetramers, and so on, as will be discussed later. A general trend in the materials presented in Table 3 is that the addition of additional fluorine atoms ortho to the terminal group leads to depressions in both TN TB -N and TN-Iso, mirroring the behaviour of calamitic materials [49]. One advantage enjoyed by unsymmetrical materials is that their melting points are generally lower than those of the corresponding symmetrical derivatives, which compensates for the more elaborate synthesis required.  The synthetic flexibility afforded by the PZP dimers makes it possible to prepare dissymmetric materials such as those shown in Table 3 [47,48]. With a single phenyl 4-cyanobenzoate mesogenic unit, it is possible to obtain materials that display the NTB phase, even when the second mesogenic unit incorporates an 'unfavourable' terminal unit (e.g., NO2, SF5, etc.) [47,48]. This approach also lends itself to the synthesis of trimers, tetramers, and so on, as will be discussed later. A general trend in the materials presented in Table 3 is that the addition of additional fluorine atoms ortho to the terminal group leads to depressions in both TN TB -N and TN-Iso, mirroring the behaviour of calamitic materials [49]. One advantage enjoyed by unsymmetrical materials is that their melting points are generally lower than those of the corresponding symmetrical derivatives, which compensates for the more elaborate synthesis required. Table 3. Transition temperatures (TA-B, °C) of some dissymmetric (PZP)-9 materials with varying terminal unit [47,48].

No. X TMP TN TB -N TN-Iso
Turning now to variations in the linking groups and spacer regions, while the NTB phase is most commonly associated with dimers incorporating a methylene spacer, it is also found in a large number of materials with imine linking units. The imine-linked (3hydroxylphenyl) 4-alkylbenzoate dimers reported by Šepelj et al. (Table 4) showed a delicate balance between columnar, nematic, and NTB mesophases, with the specific phase type being dependent upon both the length of the central spacer as well as the peripheral alkyl chains [50]. Table 4. Transition temperatures (TA-B, °C) of some imine-linked phenyl 4-alkoxybenzoate dimers [51][52][53].

No.
n m TMP TCol-N/Iso  TN TB -N  TN-Iso   30  4  5  106  --102  31  6  5  113  -87  97  32  8  5  103  99  -102  33  10  5  105  111  --34  12  5  107  116  --35  14  5  105  120  --36  4  7  119  --121  37  6  7  98  -93  113  38  8  7  103  --110  39  10  7  97  106  -108  40  12  7  100  112  --41  14  7  99 117 --Analogous in structure to the materials shown in Table 5, Šepelj et al. reported a family of imine linked phenyl 4-alkoxybenzoate dimers. Only one member displayed the twist-bend nematic phase, with m = 7 and n = 4, the majority of the materials displaying a B6 type mesophase. 88 Turning now to variations in the linking groups and spacer regions, while the NTB phase is most commonly associated with dimers incorporating a methylene spacer, it is also found in a large number of materials with imine linking units. The imine-linked (3hydroxylphenyl) 4-alkylbenzoate dimers reported by Šepelj et al. (Table 4) showed a delicate balance between columnar, nematic, and NTB mesophases, with the specific phase type being dependent upon both the length of the central spacer as well as the peripheral alkyl chains [50]. Turning now to variations in the linking groups and spacer regions, while the N TB phase is most commonly associated with dimers incorporating a methylene spacer, it is also found in a large number of materials with imine linking units. The imine-linked (3-hydroxylphenyl) 4-alkylbenzoate dimers reported by Šepelj et al. (Table 4) showed a delicate balance between columnar, nematic, and N TB mesophases, with the specific phase type being dependent upon both the length of the central spacer as well as the peripheral alkyl chains [50]. Turning now to variations in the linking groups and spacer regions, while the NTB phase is most commonly associated with dimers incorporating a methylene spacer, it is also found in a large number of materials with imine linking units. The imine-linked (3hydroxylphenyl) 4-alkylbenzoate dimers reported by Šepelj et al. (Table 4) showed a delicate balance between columnar, nematic, and NTB mesophases, with the specific phase type being dependent upon both the length of the central spacer as well as the peripheral alkyl chains [50]. Analogous in structure to the materials shown in Table 5, Šepelj et al. reported a family of imine linked phenyl 4-alkoxybenzoate dimers. Only one member displayed the twist-bend nematic phase, with m = 7 and n = 4, the majority of the materials displaying a B6 type mesophase.
We now explore the role of the chemical makeup of the central spacer beyond the methylene and imine systems already discussed. Archbold et al. reported a family of cyanobiphenyl dimers that are homologous to CB7CB in structure, having spacers of comparable length (seven methylene or equivalent units) but with different chemical makeup (Table 6) [54]. Materials incorporating two alkyne units were non-mesogenic. The onset temperature of the N TB phase was significantly reduced for the dipropyl ether spacer (55), while the N TB phase was absent for 61, which included a diethylegylcol spacer. The bis imine material 60 exhibited a direct N TB to isotropic transition temperature. Archbold et al. linked the observed transition temperatures to the average bend of the molecule, itself obtained as a probability weighted average of many conformers obtained with the rotational isomeric state (RIS) approximation, with the suggestion that an 'optimal' bend angle exists for the N TB phase, which leads to, inter alia, direct N TB -Iso transitions. This is exemplified by the high thermal stabilities of the N TB phases of the ketone-linked material (CBK-5-KCB) as well as the imine-linked material (CBI-3-ICB). Table 5. Transition temperatures (T A-B , • C) of salicylaldimine dimers with odd spacer parity [50].  We now explore the role of the chemical makeup of the central spacer beyond the methylene and imine systems already discussed. Archbold et al. reported a family of cyanobiphenyl dimers that are homologous to CB7CB in structure, having spacers of comparable length (seven methylene or equivalent units) but with different chemical makeup ( Table 6) [54]. Materials incorporating two alkyne units were non-mesogenic. The onset temperature of the NTB phase was significantly reduced for the dipropyl ether spacer (55), while the NTB phase was absent for 61, which included a diethylegylcol spacer. The bis imine material 60 exhibited a direct NTB to isotropic transition temperature. Archbold et al. linked the observed transition temperatures to the average bend of the molecule, itself obtained as a probability weighted average of many conformers obtained with the rotational isomeric state (RIS) approximation, with the suggestion that an 'optimal' bend angle exists for the NTB phase, which leads to, inter alia, direct NTB-Iso transitions. This is exemplified by the high thermal stabilities of the NTB phases of the ketone-linked material (CBK-5-KCB) as well as the imine-linked material (CBI-3-ICB).  We now explore the role of the chemical makeup of the central spacer beyond the methylene and imine systems already discussed. Archbold et al. reported a family of cyanobiphenyl dimers that are homologous to CB7CB in structure, having spacers of comparable length (seven methylene or equivalent units) but with different chemical makeup ( Table 6) [54]. Materials incorporating two alkyne units were non-mesogenic. The onset temperature of the NTB phase was significantly reduced for the dipropyl ether spacer (55), while the NTB phase was absent for 61, which included a diethylegylcol spacer. The bis imine material 60 exhibited a direct NTB to isotropic transition temperature. Archbold et al. linked the observed transition temperatures to the average bend of the molecule, itself obtained as a probability weighted average of many conformers obtained with the rotational isomeric state (RIS) approximation, with the suggestion that an 'optimal' bend angle exists for the NTB phase, which leads to, inter alia, direct NTB-Iso transitions. This is exemplified by the high thermal stabilities of the NTB phases of the ketone-linked material (CBK-5-KCB) as well as the imine-linked material (CBI-3-ICB). We now explore the role of the chemical makeup of the central spacer beyond the methylene and imine systems already discussed. Archbold et al. reported a family of cyanobiphenyl dimers that are homologous to CB7CB in structure, having spacers of comparable length (seven methylene or equivalent units) but with different chemical makeup ( Table 6) [54]. Materials incorporating two alkyne units were non-mesogenic. The onset temperature of the NTB phase was significantly reduced for the dipropyl ether spacer (55), while the NTB phase was absent for 61, which included a diethylegylcol spacer. The bis imine material 60 exhibited a direct NTB to isotropic transition temperature. Archbold et al. linked the observed transition temperatures to the average bend of the molecule, itself obtained as a probability weighted average of many conformers obtained with the rotational isomeric state (RIS) approximation, with the suggestion that an 'optimal' bend angle exists for the NTB phase, which leads to, inter alia, direct NTB-Iso transitions. This is exemplified by the high thermal stabilities of the NTB phases of the ketone-linked material (CBK-5-KCB) as well as the imine-linked material (CBI-3-ICB). We now explore the role of the chemical makeup of the central spacer beyond the methylene and imine systems already discussed. Archbold et al. reported a family of cyanobiphenyl dimers that are homologous to CB7CB in structure, having spacers of comparable length (seven methylene or equivalent units) but with different chemical makeup ( Table 6) [54]. Materials incorporating two alkyne units were non-mesogenic. The onset temperature of the NTB phase was significantly reduced for the dipropyl ether spacer (55), while the NTB phase was absent for 61, which included a diethylegylcol spacer. The bis imine material 60 exhibited a direct NTB to isotropic transition temperature. Archbold et al. linked the observed transition temperatures to the average bend of the molecule, itself obtained as a probability weighted average of many conformers obtained with the rotational isomeric state (RIS) approximation, with the suggestion that an 'optimal' bend angle exists for the NTB phase, which leads to, inter alia, direct NTB-Iso transitions. This is exemplified by the high thermal stabilities of the NTB phases of the ketone-linked material (CBK-5-KCB) as well as the imine-linked material (CBI-3-ICB). We now explore the role of the chemical makeup of the central spacer beyond the methylene and imine systems already discussed. Archbold et al. reported a family of cyanobiphenyl dimers that are homologous to CB7CB in structure, having spacers of comparable length (seven methylene or equivalent units) but with different chemical makeup ( Table 6) [54]. Materials incorporating two alkyne units were non-mesogenic. The onset temperature of the NTB phase was significantly reduced for the dipropyl ether spacer (55), while the NTB phase was absent for 61, which included a diethylegylcol spacer. The bis imine material 60 exhibited a direct NTB to isotropic transition temperature. Archbold et al. linked the observed transition temperatures to the average bend of the molecule, itself obtained as a probability weighted average of many conformers obtained with the rotational isomeric state (RIS) approximation, with the suggestion that an 'optimal' bend angle exists for the NTB phase, which leads to, inter alia, direct NTB-Iso transitions. This is exemplified by the high thermal stabilities of the NTB phases of the ketone-linked material (CBK-5-KCB) as well as the imine-linked material (CBI-3-ICB). We now explore the role of the chemical makeup of the central spacer beyond the methylene and imine systems already discussed. Archbold et al. reported a family of cyanobiphenyl dimers that are homologous to CB7CB in structure, having spacers of comparable length (seven methylene or equivalent units) but with different chemical makeup ( Table 6) [54]. Materials incorporating two alkyne units were non-mesogenic. The onset temperature of the NTB phase was significantly reduced for the dipropyl ether spacer (55), while the NTB phase was absent for 61, which included a diethylegylcol spacer. The bis imine material 60 exhibited a direct NTB to isotropic transition temperature. Archbold et al. linked the observed transition temperatures to the average bend of the molecule, itself obtained as a probability weighted average of many conformers obtained with the rotational isomeric state (RIS) approximation, with the suggestion that an 'optimal' bend angle exists for the NTB phase, which leads to, inter alia, direct NTB-Iso transitions. This is exemplified by the high thermal stabilities of the NTB phases of the ketone-linked material (CBK-5-KCB) as well as the imine-linked material (CBI-3-ICB). We now explore the role of the chemical makeup of the central spacer beyond the methylene and imine systems already discussed. Archbold et al. reported a family of cyanobiphenyl dimers that are homologous to CB7CB in structure, having spacers of comparable length (seven methylene or equivalent units) but with different chemical makeup (Table 6) [54]. Materials incorporating two alkyne units were non-mesogenic. The onset temperature of the NTB phase was significantly reduced for the dipropyl ether spacer (55), while the NTB phase was absent for 61, which included a diethylegylcol spacer. The bis imine material 60 exhibited a direct NTB to isotropic transition temperature. Archbold et al. linked the observed transition temperatures to the average bend of the molecule, itself obtained as a probability weighted average of many conformers obtained with the rotational isomeric state (RIS) approximation, with the suggestion that an 'optimal' bend angle exists for the NTB phase, which leads to, inter alia, direct NTB-Iso transitions. This is exemplified by the high thermal stabilities of the NTB phases of the ketone-linked material (CBK-5-KCB) as well as the imine-linked material (CBI-3-ICB). We now explore the role of the chemical makeup of the central spacer beyond the methylene and imine systems already discussed. Archbold et al. reported a family of cyanobiphenyl dimers that are homologous to CB7CB in structure, having spacers of comparable length (seven methylene or equivalent units) but with different chemical makeup (Table 6) [54]. Materials incorporating two alkyne units were non-mesogenic. The onset temperature of the NTB phase was significantly reduced for the dipropyl ether spacer (55), while the NTB phase was absent for 61, which included a diethylegylcol spacer. The bis imine material 60 exhibited a direct NTB to isotropic transition temperature. Archbold et al. linked the observed transition temperatures to the average bend of the molecule, itself obtained as a probability weighted average of many conformers obtained with the rotational isomeric state (RIS) approximation, with the suggestion that an 'optimal' bend angle exists for the NTB phase, which leads to, inter alia, direct NTB-Iso transitions. This is exemplified by the high thermal stabilities of the NTB phases of the ketone-linked material (CBK-5-KCB) as well as the imine-linked material (CBI-3-ICB). We now explore the role of the chemical makeup of the central spacer beyond the methylene and imine systems already discussed. Archbold et al. reported a family of cyanobiphenyl dimers that are homologous to CB7CB in structure, having spacers of comparable length (seven methylene or equivalent units) but with different chemical makeup (Table 6) [54]. Materials incorporating two alkyne units were non-mesogenic. The onset temperature of the NTB phase was significantly reduced for the dipropyl ether spacer (55), while the NTB phase was absent for 61, which included a diethylegylcol spacer. The bis imine material 60 exhibited a direct NTB to isotropic transition temperature. Archbold et al. linked the observed transition temperatures to the average bend of the molecule, itself obtained as a probability weighted average of many conformers obtained with the rotational isomeric state (RIS) approximation, with the suggestion that an 'optimal' bend angle exists for the NTB phase, which leads to, inter alia, direct NTB-Iso transitions. This is exemplified by the high thermal stabilities of the NTB phases of the ketone-linked material (CBK-5-KCB) as well as the imine-linked material (CBI-3-ICB). We now explore the role of the chemical makeup of the central spacer beyond the methylene and imine systems already discussed. Archbold et al. reported a family of cyanobiphenyl dimers that are homologous to CB7CB in structure, having spacers of comparable length (seven methylene or equivalent units) but with different chemical makeup (Table 6) [54]. Materials incorporating two alkyne units were non-mesogenic. The onset temperature of the NTB phase was significantly reduced for the dipropyl ether spacer (55), while the NTB phase was absent for 61, which included a diethylegylcol spacer. The bis imine material 60 exhibited a direct NTB to isotropic transition temperature. Archbold et al. linked the observed transition temperatures to the average bend of the molecule, itself obtained as a probability weighted average of many conformers obtained with the rotational isomeric state (RIS) approximation, with the suggestion that an 'optimal' bend angle exists for the NTB phase, which leads to, inter alia, direct NTB-Iso transitions. This is exemplified by the high thermal stabilities of the NTB phases of the ketone-linked material (CBK-5-KCB) as well as the imine-linked material (CBI-3-ICB). Refining the earlier approach of Archbold et al., Mandle and Goodby investigated the conformational preference of a series of homologues of CB9CB (Table 7) [55,56]. Again, the rotational isomeric state approximation was used to generate conformational libraries for each material; the average bend angle between the two mesogenic units then being calculated as a probability weighted average. Conformational ensembles were validated by comparison of average inter-proton distances with those obtained from 1 H-1 H NOESY NMR experiments. It is suggested that the stability of the NTB phase is related to the average bend angle, specifically, a high ratio of TN TB -N to TN-Iso is achieved by having an average bend angle in excess of 110°. Refining the earlier approach of Archbold et al., Mandle and Goodby investigated the conformational preference of a series of homologues of CB9CB (Table 7) [55,56]. Again, the rotational isomeric state approximation was used to generate conformational libraries for each material; the average bend angle between the two mesogenic units then being calculated as a probability weighted average. Conformational ensembles were validated by comparison of average inter-proton distances with those obtained from 1 H-1 H NOESY NMR experiments. It is suggested that the stability of the NTB phase is related to the average bend angle, specifically, a high ratio of TN TB -N to TN-Iso is achieved by having an average bend angle in excess of 110°. Refining the earlier approach of Archbold et al., Mandle and Goodby investigated the conformational preference of a series of homologues of CB9CB (Table 7) [55,56]. Again, the rotational isomeric state approximation was used to generate conformational libraries for each material; the average bend angle between the two mesogenic units then being calculated as a probability weighted average. Conformational ensembles were validated by comparison of average inter-proton distances with those obtained from 1 H-1 H NOESY NMR experiments. It is suggested that the stability of the N TB phase is related to the average bend angle, specifically, a high ratio of T N TB -N to T N-Iso is achieved by having an average bend angle in excess of 110 • . Table 7. Transition temperatures (T A-B , • C) of cyanobiphenyl derivatives with varying central spacer composition, equivalent to nonamethylene [54][55][56][57][58]. * Glass to N TB transition. the rotational isomeric state approximation was used to generate conformational libraries for each material; the average bend angle between the two mesogenic units then being calculated as a probability weighted average. Conformational ensembles were validated by comparison of average inter-proton distances with those obtained from 1 H-1 H NOESY NMR experiments. It is suggested that the stability of the NTB phase is related to the average bend angle, specifically, a high ratio of TN TB -N to TN-Iso is achieved by having an average bend angle in excess of 110°. We now consider four families of related cyanobiphenyl dimers with varying linking groups and spacer lengths (Table 8) [59][60][61]. The chemical makeup of each family is evident from their names (e.g., the CBnOCB series feature one methylene and one ether linking unit, the CBnSCB series feature one methylene and one thioether linking unit, and so on). Further examples from each family are to be found in the given references. Generally, the transition temperatures of thioether containing materials are lower than the equivalent CBnOCB material, with the difference being most pronounced for shorter spacer lengths. A simple explanation suffices here, with a deeper understanding needing to draw on other relevant conformational effects. Consider that a methylene unit imparts a tetrahedral bond angle (109.5°), an ether gives an angle of 104.5°, but an arylthioether has a bond angle of ~90°. The influence of thioethers is therefore most pronounced for shorter chain lengths, for each material; the average bend angle between the two mesogenic units then being calculated as a probability weighted average. Conformational ensembles were validated by comparison of average inter-proton distances with those obtained from 1 H-1 H NOESY NMR experiments. It is suggested that the stability of the NTB phase is related to the average bend angle, specifically, a high ratio of TN TB -N to TN-Iso is achieved by having an average bend angle in excess of 110°.
We now consider four families of related cyanobiphenyl dimers with varying linking groups and spacer lengths (Table 8) [59][60][61]. The chemical makeup of each family is evident from their names (e.g., the CBnOCB series feature one methylene and one ether linking unit, the CBnSCB series feature one methylene and one thioether linking unit, and so on). Further examples from each family are to be found in the given references. Generally, the transition temperatures of thioether containing materials are lower than the equivalent CBnOCB material, with the difference being most pronounced for shorter spacer lengths. A simple explanation suffices here, with a deeper understanding needing to draw on other relevant conformational effects. Consider that a methylene unit imparts a tetrahedral bond angle (109.5°), an ether gives an angle of 104.5°, but an arylthioether has a bond angle of ~90°. The influence of thioethers is therefore most pronounced for shorter chain lengths, 83 for each material; the average bend angle between the two mesogenic units then being calculated as a probability weighted average. Conformational ensembles were validated by comparison of average inter-proton distances with those obtained from 1 H-1 H NOESY NMR experiments. It is suggested that the stability of the NTB phase is related to the average bend angle, specifically, a high ratio of TN TB -N to TN-Iso is achieved by having an average bend angle in excess of 110°.
We now consider four families of related cyanobiphenyl dimers with varying linking groups and spacer lengths (Table 8) [59][60][61]. The chemical makeup of each family is evident from their names (e.g., the CBnOCB series feature one methylene and one ether linking unit, the CBnSCB series feature one methylene and one thioether linking unit, and so on). Further examples from each family are to be found in the given references. Generally, the transition temperatures of thioether containing materials are lower than the equivalent CBnOCB material, with the difference being most pronounced for shorter spacer lengths. A simple explanation suffices here, with a deeper understanding needing to draw on other relevant conformational effects. Consider that a methylene unit imparts a tetrahedral bond angle (109.5°), an ether gives an angle of 104.5°, but an arylthioether has a bond angle of ~90°. The influence of thioethers is therefore most pronounced for shorter chain lengths, calculated as a probability weighted average. Conformational ensembles were validated by comparison of average inter-proton distances with those obtained from 1 H-1 H NOESY NMR experiments. It is suggested that the stability of the NTB phase is related to the average bend angle, specifically, a high ratio of TN TB -N to TN-Iso is achieved by having an average bend angle in excess of 110°.
We now consider four families of related cyanobiphenyl dimers with varying linking groups and spacer lengths (Table 8) [59][60][61]. The chemical makeup of each family is evident from their names (e.g., the CBnOCB series feature one methylene and one ether linking unit, the CBnSCB series feature one methylene and one thioether linking unit, and so on). Further examples from each family are to be found in the given references. Generally, the transition temperatures of thioether containing materials are lower than the equivalent CBnOCB material, with the difference being most pronounced for shorter spacer lengths. A simple explanation suffices here, with a deeper understanding needing to draw on other relevant conformational effects. Consider that a methylene unit imparts a tetrahedral bond angle (109.5°), an ether gives an angle of 104.5°, but an arylthioether has a bond angle of ~90°. The influence of thioethers is therefore most pronounced for shorter chain lengths, calculated as a probability weighted average. Conformational ensembles were validated by comparison of average inter-proton distances with those obtained from 1 H-1 H NOESY NMR experiments. It is suggested that the stability of the NTB phase is related to the average bend angle, specifically, a high ratio of TN TB -N to TN-Iso is achieved by having an average bend angle in excess of 110°.
We now consider four families of related cyanobiphenyl dimers with varying linking groups and spacer lengths (Table 8) [59][60][61]. The chemical makeup of each family is evident from their names (e.g., the CBnOCB series feature one methylene and one ether linking unit, the CBnSCB series feature one methylene and one thioether linking unit, and so on). Further examples from each family are to be found in the given references. Generally, the transition temperatures of thioether containing materials are lower than the equivalent CBnOCB material, with the difference being most pronounced for shorter spacer lengths. A simple explanation suffices here, with a deeper understanding needing to draw on other relevant conformational effects. Consider that a methylene unit imparts a tetrahedral bond angle (109.5°), an ether gives an angle of 104.5°, but an arylthioether has a bond angle of ~90°. The influence of thioethers is therefore most pronounced for shorter chain lengths, by comparison of average inter-proton distances with those obtained from 1 H-1 H NOESY NMR experiments. It is suggested that the stability of the NTB phase is related to the average bend angle, specifically, a high ratio of TN TB -N to TN-Iso is achieved by having an average bend angle in excess of 110°.
We now consider four families of related cyanobiphenyl dimers with varying linking groups and spacer lengths (Table 8) [59][60][61]. The chemical makeup of each family is evident from their names (e.g., the CBnOCB series feature one methylene and one ether linking unit, the CBnSCB series feature one methylene and one thioether linking unit, and so on). Further examples from each family are to be found in the given references. Generally, the transition temperatures of thioether containing materials are lower than the equivalent CBnOCB material, with the difference being most pronounced for shorter spacer lengths. A simple explanation suffices here, with a deeper understanding needing to draw on other relevant conformational effects. Consider that a methylene unit imparts a tetrahedral bond angle (109.5°), an ether gives an angle of 104.5°, but an arylthioether has a bond angle of ~90°. The influence of thioethers is therefore most pronounced for shorter chain lengths, NMR experiments. It is suggested that the stability of the NTB phase is related to the average bend angle, specifically, a high ratio of TN TB -N to TN-Iso is achieved by having an average bend angle in excess of 110°. We now consider four families of related cyanobiphenyl dimers with varying linking groups and spacer lengths (Table 8) [59][60][61]. The chemical makeup of each family is evident from their names (e.g., the CBnOCB series feature one methylene and one ether linking unit, the CBnSCB series feature one methylene and one thioether linking unit, and so on). Further examples from each family are to be found in the given references. Generally, the transition temperatures of thioether containing materials are lower than the equivalent CBnOCB material, with the difference being most pronounced for shorter spacer lengths. A simple explanation suffices here, with a deeper understanding needing to draw on other relevant conformational effects. Consider that a methylene unit imparts a tetrahedral bond angle (109.5°), an ether gives an angle of 104.5°, but an arylthioether has a bond angle of ~90°. The influence of thioethers is therefore most pronounced for shorter chain lengths, 15 NMR experiments. It is suggested that the stability of the NTB phase is related to the average bend angle, specifically, a high ratio of TN TB -N to TN-Iso is achieved by having an average bend angle in excess of 110°. We now consider four families of related cyanobiphenyl dimers with varying linking groups and spacer lengths (Table 8) [59][60][61]. The chemical makeup of each family is evident from their names (e.g., the CBnOCB series feature one methylene and one ether linking unit, the CBnSCB series feature one methylene and one thioether linking unit, and so on). Further examples from each family are to be found in the given references. Generally, the transition temperatures of thioether containing materials are lower than the equivalent CBnOCB material, with the difference being most pronounced for shorter spacer lengths. A simple explanation suffices here, with a deeper understanding needing to draw on other relevant conformational effects. Consider that a methylene unit imparts a tetrahedral bond angle (109.5°), an ether gives an angle of 104.5°, but an arylthioether has a bond angle of ~90°. The influence of thioethers is therefore most pronounced for shorter chain lengths, 55 age bend angle, specifically, a high ratio of TN TB -N to TN-Iso is achieved by having an average bend angle in excess of 110°. We now consider four families of related cyanobiphenyl dimers with varying linking groups and spacer lengths (Table 8) [59][60][61]. The chemical makeup of each family is evident from their names (e.g., the CBnOCB series feature one methylene and one ether linking unit, the CBnSCB series feature one methylene and one thioether linking unit, and so on). Further examples from each family are to be found in the given references. Generally, the transition temperatures of thioether containing materials are lower than the equivalent CBnOCB material, with the difference being most pronounced for shorter spacer lengths. A simple explanation suffices here, with a deeper understanding needing to draw on other relevant conformational effects. Consider that a methylene unit imparts a tetrahedral bond angle (109.5°), an ether gives an angle of 104.5°, but an arylthioether has a bond angle of ~90°. The influence of thioethers is therefore most pronounced for shorter chain lengths, 80 age bend angle, specifically, a high ratio of TN TB -N to TN-Iso is achieved by having an average bend angle in excess of 110°. We now consider four families of related cyanobiphenyl dimers with varying linking groups and spacer lengths (Table 8) [59][60][61]. The chemical makeup of each family is evident from their names (e.g., the CBnOCB series feature one methylene and one ether linking unit, the CBnSCB series feature one methylene and one thioether linking unit, and so on). Further examples from each family are to be found in the given references. Generally, the transition temperatures of thioether containing materials are lower than the equivalent CBnOCB material, with the difference being most pronounced for shorter spacer lengths. A simple explanation suffices here, with a deeper understanding needing to draw on other relevant conformational effects. Consider that a methylene unit imparts a tetrahedral bond angle (109.5°), an ether gives an angle of 104.5°, but an arylthioether has a bond angle of ~90°. The influence of thioethers is therefore most pronounced for shorter chain lengths, 95 bend angle in excess of 110°. We now consider four families of related cyanobiphenyl dimers with varying linking groups and spacer lengths (Table 8) [59][60][61]. The chemical makeup of each family is evident from their names (e.g., the CBnOCB series feature one methylene and one ether linking unit, the CBnSCB series feature one methylene and one thioether linking unit, and so on). Further examples from each family are to be found in the given references. Generally, the transition temperatures of thioether containing materials are lower than the equivalent CBnOCB material, with the difference being most pronounced for shorter spacer lengths. A simple explanation suffices here, with a deeper understanding needing to draw on other relevant conformational effects. Consider that a methylene unit imparts a tetrahedral bond angle (109.5°), an ether gives an angle of 104.5°, but an arylthioether has a bond angle of ~90°. The influence of thioethers is therefore most pronounced for shorter chain lengths, bend angle in excess of 110°. We now consider four families of related cyanobiphenyl dimers with varying linking groups and spacer lengths (Table 8) [59][60][61]. The chemical makeup of each family is evident from their names (e.g., the CBnOCB series feature one methylene and one ether linking unit, the CBnSCB series feature one methylene and one thioether linking unit, and so on). Further examples from each family are to be found in the given references. Generally, the transition temperatures of thioether containing materials are lower than the equivalent CBnOCB material, with the difference being most pronounced for shorter spacer lengths. A simple explanation suffices here, with a deeper understanding needing to draw on other relevant conformational effects. Consider that a methylene unit imparts a tetrahedral bond angle (109.5°), an ether gives an angle of 104.5°, but an arylthioether has a bond angle of ~90°. The influence of thioethers is therefore most pronounced for shorter chain lengths, We now consider four families of related cyanobiphenyl dimers with varying linking groups and spacer lengths (Table 8) [59][60][61]. The chemical makeup of each family is evident from their names (e.g., the CBnOCB series feature one methylene and one ether linking unit, the CBnSCB series feature one methylene and one thioether linking unit, and so on). Further examples from each family are to be found in the given references. Generally, the transition temperatures of thioether containing materials are lower than the equivalent CBnOCB material, with the difference being most pronounced for shorter spacer lengths. A simple explanation suffices here, with a deeper understanding needing to draw on other relevant conformational effects. Consider that a methylene unit imparts a tetrahedral bond angle (109.5°), an ether gives an angle of 104.5°, but an arylthioether has a bond angle of ~90°. The influence of thioethers is therefore most pronounced for shorter chain lengths, We now consider four families of related cyanobiphenyl dimers with varying linking groups and spacer lengths (Table 8) [59][60][61]. The chemical makeup of each family is evident from their names (e.g., the CBnOCB series feature one methylene and one ether linking unit, the CBnSCB series feature one methylene and one thioether linking unit, and so on). Further examples from each family are to be found in the given references. Generally, the transition temperatures of thioether containing materials are lower than the equivalent CBnOCB material, with the difference being most pronounced for shorter spacer lengths. A simple explanation suffices here, with a deeper understanding needing to draw on other relevant conformational effects. Consider that a methylene unit imparts a tetrahedral bond angle (109.5 • ), an ether gives an angle of 104.5 • , but an arylthioether has a bond angle of~90 • . The influence of thioethers is therefore most pronounced for shorter chain lengths, whereas for longer spacers, they are somewhat offset. The thioether is somewhat unfavourable for the formation of the N TB phase as it tends to depress the average bend angle away from the apparent favoured value of >110 • C. However, for some materials (CBO7SCB, 67, and CBS7SCB, 66) the melting point is suppressed to such a degree that the materials are in the N TB phase at ambient temperature, which is a remarkable achievement that greatly simplifies experimentation. The helical pitch length of several compounds in Table 8 has been reported: CB6OCB~10-15 nm [62], CBS7SCB 8.7 nm, CBO7SCB 18.4 nm, and CBO5SCB 14.8 nm [63]. Linking the N TB pitch length to molecular geometric parameters appears to be a logical future direction. Almost simultaneously with Arakawa et al. [61], the CBSnSCB and CBOnSCB materials were also synthesised and reported independently by Imrie et al. [64]. Imrie et al. also reported the pitch lengths of CBO5SCB (~8.9 nm), CBS7SB (~8.7 nm), and the mixed cyanoterphenyl/cyanobiphenyl material, CT6SCB (~9.7 nm); in all three cases, this corresponded to approximately four end-to-end molecular lengths.
Arakawa et al. subsequently demonstrated cyanobiphenyl dimers with mixed thioether/ketone linking units [65] (Table 9). Earlier, Archbold et al. found that ketonelinking units generated highly stable N TB phases due to their favourable bend angles (Table 6) [54]. Employing mixed ketone and thioether units showed a dramatic increase in the N TB onset temperature when compared to the equivalent materials employing either two thioethers (CBSnSCB), or one thioether and one other linking unit (CBnSCB, CBOnSCB, CBSnSCB). Again, a simple explanation suffices for the sake of this review: the ketone unit has a bond angle of~120 • , which offsets the unfavourable angle imposed by the thioether. Clearly, a detailed DFT study of the conformational landscape of these materials (and in-deed, others) appears warranted, and presents one possible route to further understanding these intriguing materials. Table 8. Transition temperatures (T A-B , • C) of cyanobiphenyl derivatives with methylene, ether, or thioether linking groups and varying spacer length: selected members of the CBnOCB [59,60], CBnSCB [61], CBOnSCB [61], and CBSnSCB [61] series. * Glass to N TB transition. the materials are in the NTB phase at ambient temperature, which is a remarkable achievement that greatly simplifies experimentation. The helical pitch length of several compounds in Table 8 has been reported: CB6OCB ~10-15 nm [62], CBS7SCB 8.7 nm, CBO7SCB 18.4 nm, and CBO5SCB 14.8 nm [63]. Linking the NTB pitch length to molecular geometric parameters appears to be a logical future direction. Almost simultaneously with Arakawa et al. [61], the CBSnSCB and CBOnSCB materials were also synthesised and reported independently by Imrie et al. [64]. Imrie et al. also reported the pitch lengths of CBO5SCB (~8.9 nm), CBS7SB (~8.7 nm), and the mixed cyanoterphenyl/cyanobiphenyl material, CT6SCB (~9.7 nm); in all three cases, this corresponded to approximately four end-to-end molecular lengths.  (Table 9). Earlier, Archbold et al. found that ketone-linking units generated highly stable NTB phases due to their favourable bend angles (Table 6) [54]. Employing mixed ketone and thioether units showed a dramatic increase in the NTB onset temperature when compared to the equivalent materials employing either two thioethers (CBSnSCB), or one thioether and one other linking unit (CBnSCB, CBOnSCB, CBSnSCB). Again, a simple explanation suffices for the sake of this review: the ketone unit has a bond angle of ~120°, which offsets the unfavourable angle imposed by the thioether. Clearly, a detailed DFT study of the conformational landscape of these materials (and indeed, others) appears warranted, and presents one possible route to further understanding these intriguing materials.

Chiral NTB Materials
The NTB phase has been described as the "structural link" between the conventional nematic phase and the helical chiral nematic (cholesteric) phase [10]. As discussed, the NTB phase has a helical structure and when formed from achiral molecules, there is no preference for left-or right-handed helices. Our focus in this review was on molecular structure and the materials that generate the NTB phase, so our focus was on examples whereby chirality results from the molecular structure of the dimer itself, rather than systems in which chirality is introduced via an additive [66].
Gorecka et al. reported a number of ester-linked unsymmetrical dimers that incorporated cholesterol as a mesogenic unit; these materials are chiral, and thus they are the first reported chiral NTB materials. The length of the central spacer and its parity dictate the balance between exhibiting NTB (odd parity) or SmA (even parity) mesophases in these materials. The mesophase behaviour of these materials is more complex than shown in Table 10, with the materials exhibiting multiple nematic phases and/or blue phases. The NTB pitch length of 90 was measured to be 50 nm by in situ AFM, notably larger than that of CB7CB, but still about a few molecular lengths [24,67]. Later, the helical pitch length of 99 was measured by resonant carbon K-edge X-ray scattering and found to take a value of ~11 nm [68]. The pitch length of the chiral nematic phase was determined to be 224 nm by the same method.

Chiral N TB Materials
The N TB phase has been described as the "structural link" between the conventional nematic phase and the helical chiral nematic (cholesteric) phase [10]. As discussed, the N TB phase has a helical structure and when formed from achiral molecules, there is no preference for left-or right-handed helices. Our focus in this review was on molecular structure and the materials that generate the N TB phase, so our focus was on examples whereby chirality results from the molecular structure of the dimer itself, rather than systems in which chirality is introduced via an additive [66].
Gorecka et al. reported a number of ester-linked unsymmetrical dimers that incorporated cholesterol as a mesogenic unit; these materials are chiral, and thus they are the first reported chiral N TB materials. The length of the central spacer and its parity dictate the balance between exhibiting N TB (odd parity) or SmA (even parity) mesophases in these materials. The mesophase behaviour of these materials is more complex than shown in Table 10, with the materials exhibiting multiple nematic phases and/or blue phases. The N TB pitch length of 90 was measured to be 50 nm by in situ AFM, notably larger than that of CB7CB, but still about a few molecular lengths [24,67]. Later, the helical pitch length of 99 was measured by resonant carbon K-edge X-ray scattering and found to take a value of 11 nm [68]. The pitch length of the chiral nematic phase was determined to be 224 nm by the same method. Gorecka et al. reported a number of ester-linked unsymmetrical dimers that incorporated cholesterol as a mesogenic unit; these materials are chiral, and thus they are the first reported chiral NTB materials. The length of the central spacer and its parity dictate the balance between exhibiting NTB (odd parity) or SmA (even parity) mesophases in these materials. The mesophase behaviour of these materials is more complex than shown in Table 10, with the materials exhibiting multiple nematic phases and/or blue phases. The NTB pitch length of 90 was measured to be 50 nm by in situ AFM, notably larger than that of CB7CB, but still about a few molecular lengths [24,67]. Later, the helical pitch length of 99 was measured by resonant carbon K-edge X-ray scattering and found to take a value of ~11 nm [68]. The pitch length of the chiral nematic phase was determined to be 224 nm by the same method. Gorecka et al. also reported another family of cholesterol containing dimers that exhibited the N TB phase (Table 11), with some members also exhibiting a smectic phase of unknown structure (SmX) [24]. The pitch length of 104 in the N TB phase was measured by the resonant X-ray scattering method, with a temperature dependent value of 13.3-20.3 nm. Conversely, the chiral nematic pitch length for this material was measured by the same technique to be 220 nm [68]. Although not reported upon, the incorporation of an azo unit presumably enables isothermal N TB transitions in these materials (via photoisomerisation), as first reported by Paterson et al. [69]. Gorecka et al. also reported another family of cholesterol containing dimers that exhibited the NTB phase (Table 11), with some members also exhibiting a smectic phase of unknown structure (SmX) [24]. The pitch length of 104 in the NTB phase was measured by the resonant X-ray scattering method, with a temperature dependent value of 13.3-20.3 nm. Conversely, the chiral nematic pitch length for this material was measured by the same technique to be 220 nm [68]. Although not reported upon, the incorporation of an azo unit presumably enables isothermal NTB transitions in these materials (via photoisomerisation), as first reported by Paterson et al. [69]. Mandle and Goodby reported the synthesis of symmetrical LC dimers in which the central spacer is itself chiral (Table 12); starting from (R)-2-methylglutaric acid, four synthetic steps telescoped into two reactions afforded the key (R)-bis-1,5-(4-hydroxyphenyl)-2-methylpentane intermediate, which was elaborated using standard esterification protocols, affording compounds 107-113. The measured helical twisting power of 107 was rather low (0.36 mm −1 wt% −1 ) due to the large degree of conformational freedom experienced by the lateral methyl unit. The NTB phase was only exhibited by materials whose mesogenic units had a large aspect ratio due to the unfavourable conformational effects of the lateral methyl unit within the central spacer. However, this also gave rise to the unusual SmA-NTB transition in compounds 111 and 112, which has previously only been observed for a small handful of materials [70]. Mandle and Goodby reported the synthesis of symmetrical LC dimers in which the central spacer is itself chiral (Table 12); starting from (R)-2-methylglutaric acid, four synthetic steps telescoped into two reactions afforded the key (R)-bis-1,5-(4-hydroxyphenyl)-2methylpentane intermediate, which was elaborated using standard esterification protocols, affording compounds 107-113. The measured helical twisting power of 107 was rather low (0.36 mm −1 wt% −1 ) due to the large degree of conformational freedom experienced by the lateral methyl unit. The N TB phase was only exhibited by materials whose mesogenic units had a large aspect ratio due to the unfavourable conformational effects of the lateral methyl unit within the central spacer. However, this also gave rise to the unusual SmA-N TB transition in compounds 111 and 112, which has previously only been observed for a small handful of materials [70]. central spacer is itself chiral (Table 12); starting from (R)-2-methylglutaric acid, four synthetic steps telescoped into two reactions afforded the key (R)-bis-1,5-(4-hydroxyphenyl)-2-methylpentane intermediate, which was elaborated using standard esterification protocols, affording compounds 107-113. The measured helical twisting power of 107 was rather low (0.36 mm −1 wt% −1 ) due to the large degree of conformational freedom experienced by the lateral methyl unit. The NTB phase was only exhibited by materials whose mesogenic units had a large aspect ratio due to the unfavourable conformational effects of the lateral methyl unit within the central spacer. However, this also gave rise to the unusual SmA-NTB transition in compounds 111 and 112, which has previously only been observed for a small handful of materials [70].  central spacer is itself chiral (Table 12); starting from (R)-2-methylglutaric acid, four synthetic steps telescoped into two reactions afforded the key (R)-bis-1,5-(4-hydroxyphenyl)-2-methylpentane intermediate, which was elaborated using standard esterification protocols, affording compounds 107-113. The measured helical twisting power of 107 was rather low (0.36 mm −1 wt% −1 ) due to the large degree of conformational freedom experienced by the lateral methyl unit. The NTB phase was only exhibited by materials whose mesogenic units had a large aspect ratio due to the unfavourable conformational effects of the lateral methyl unit within the central spacer. However, this also gave rise to the unusual SmA-NTB transition in compounds 111 and 112, which has previously only been observed for a small handful of materials [70]. central spacer is itself chiral (Table 12); starting from (R)-2-methylglutaric acid, four synthetic steps telescoped into two reactions afforded the key (R)-bis-1,5-(4-hydroxyphenyl)-2-methylpentane intermediate, which was elaborated using standard esterification protocols, affording compounds 107-113. The measured helical twisting power of 107 was rather low (0.36 mm −1 wt% −1 ) due to the large degree of conformational freedom experienced by the lateral methyl unit. The NTB phase was only exhibited by materials whose mesogenic units had a large aspect ratio due to the unfavourable conformational effects of the lateral methyl unit within the central spacer. However, this also gave rise to the unusual SmA-NTB transition in compounds 111 and 112, which has previously only been observed for a small handful of materials [70]. thetic steps telescoped into two reactions afforded the key (R)-bis-1,5-(4-hydroxyphenyl)-2-methylpentane intermediate, which was elaborated using standard esterification protocols, affording compounds 107-113. The measured helical twisting power of 107 was rather low (0.36 mm −1 wt% −1 ) due to the large degree of conformational freedom experienced by the lateral methyl unit. The NTB phase was only exhibited by materials whose mesogenic units had a large aspect ratio due to the unfavourable conformational effects of the lateral methyl unit within the central spacer. However, this also gave rise to the unusual SmA-NTB transition in compounds 111 and 112, which has previously only been observed for a small handful of materials [70]. thetic steps telescoped into two reactions afforded the key (R)-bis-1,5-(4-hydroxyphenyl)-2-methylpentane intermediate, which was elaborated using standard esterification protocols, affording compounds 107-113. The measured helical twisting power of 107 was rather low (0.36 mm −1 wt% −1 ) due to the large degree of conformational freedom experienced by the lateral methyl unit. The NTB phase was only exhibited by materials whose mesogenic units had a large aspect ratio due to the unfavourable conformational effects of the lateral methyl unit within the central spacer. However, this also gave rise to the unusual SmA-NTB transition in compounds 111 and 112, which has previously only been observed for a small handful of materials [70]. Walker et al. reported a family of unsymmetrical dimers that are terminated by either butyl, racemic 2-methylbutyl, or (S)-2-methylbutyl chains (Table 13) [71]. The NTB-N transition temperature was marginally higher for chiral materials than the achiral analogues, in agreement with the theoretical predictions [72]. Notably, the NTB phase formed by 119 was found to be miscible with that of the achiral material CB6OCB (77). Walker et al. reported a family of unsymmetrical dimers that are terminated by either butyl, racemic 2-methylbutyl, or (S)-2-methylbutyl chains (Table 13) [71]. The NTB-N transition temperature was marginally higher for chiral materials than the achiral analogues, in agreement with the theoretical predictions [72]. Notably, the NTB phase formed by 119 was found to be miscible with that of the achiral material CB6OCB (77). Walker et al. reported a family of unsymmetrical dimers that are terminated by either butyl, racemic 2-methylbutyl, or (S)-2-methylbutyl chains (Table 13) [71]. The NTB-N transition temperature was marginally higher for chiral materials than the achiral analogues, in agreement with the theoretical predictions [72]. Notably, the NTB phase formed by 119 was found to be miscible with that of the achiral material CB6OCB (77). Walker et al. reported a family of unsymmetrical dimers that are terminated by either butyl, racemic 2-methylbutyl, or (S)-2-methylbutyl chains (Table 13) [71]. The N TB -N transition temperature was marginally higher for chiral materials than the achiral analogues, in agreement with the theoretical predictions [72]. Notably, the N TB phase formed by 119 was found to be miscible with that of the achiral material CB6OCB (77). Table 13. Transition temperatures (T A-B , • C) of unsymmetrical CBnOPZPZP dimers with a terminal butyl, (S)-2-methylbutyl, or rac 2-methylbutyl chain [71].  (Table 13) [71]. The NTB-N transition temperature was marginally higher for chiral materials than the achiral analogues, in agreement with the theoretical predictions [72]. Notably, the NTB phase formed by 119 was found to be miscible with that of the achiral material CB6OCB (77). Walker et al. reported a family of unsymmetrical dimers that are terminated by either butyl, racemic 2-methylbutyl, or (S)-2-methylbutyl chains (Table 13) [71]. The NTB-N transition temperature was marginally higher for chiral materials than the achiral analogues, in agreement with the theoretical predictions [72]. Notably, the NTB phase formed by 119 was found to be miscible with that of the achiral material CB6OCB (77). Walker et al. reported a family of unsymmetrical dimers that are terminated by either butyl, racemic 2-methylbutyl, or (S)-2-methylbutyl chains (Table 13) [71]. The NTB-N transition temperature was marginally higher for chiral materials than the achiral analogues, in agreement with the theoretical predictions [72]. Notably, the NTB phase formed by 119 was found to be miscible with that of the achiral material CB6OCB (77). Walker et al. reported a family of unsymmetrical dimers that are terminated by either butyl, racemic 2-methylbutyl, or (S)-2-methylbutyl chains (Table 13) [71]. The NTB-N transition temperature was marginally higher for chiral materials than the achiral analogues, in agreement with the theoretical predictions [72]. Notably, the NTB phase formed by 119 was found to be miscible with that of the achiral material CB6OCB (77). Walker et al. reported a family of unsymmetrical dimers that are terminated by either butyl, racemic 2-methylbutyl, or (S)-2-methylbutyl chains (Table 13) [71]. The NTB-N transition temperature was marginally higher for chiral materials than the achiral analogues, in agreement with the theoretical predictions [72]. Notably, the NTB phase formed by 119 was found to be miscible with that of the achiral material CB6OCB (77). Table 13. Transition temperatures (TA-B, °C) of unsymmetrical CBnOPZPZP dimers with a terminal butyl, (S)-2-methylbutyl, or rac 2-methylbutyl chain [71]. Walker et al. reported a family of unsymmetrical dimers that are terminated by either butyl, racemic 2-methylbutyl, or (S)-2-methylbutyl chains (Table 13) [71]. The NTB-N transition temperature was marginally higher for chiral materials than the achiral analogues, in agreement with the theoretical predictions [72]. Notably, the NTB phase formed by 119 was found to be miscible with that of the achiral material CB6OCB (77). Walker et al. reported a family of unsymmetrical dimers that are terminated by either butyl, racemic 2-methylbutyl, or (S)-2-methylbutyl chains (Table 13) [71]. The NTB-N transition temperature was marginally higher for chiral materials than the achiral analogues, in agreement with the theoretical predictions [72]. Notably, the NTB phase formed by 119 was found to be miscible with that of the achiral material CB6OCB (77). Walker et al. reported a family of unsymmetrical dimers that are terminated by either butyl, racemic 2-methylbutyl, or (S)-2-methylbutyl chains (Table 13) [71]. The NTB-N transition temperature was marginally higher for chiral materials than the achiral analogues, in agreement with the theoretical predictions [72]. Notably, the NTB phase formed by 119 was found to be miscible with that of the achiral material CB6OCB (77). Walker et al. reported a family of unsymmetrical dimers that are terminated by either butyl, racemic 2-methylbutyl, or (S)-2-methylbutyl chains (Table 13) [71]. The NTB-N transition temperature was marginally higher for chiral materials than the achiral analogues, in agreement with the theoretical predictions [72]. Notably, the NTB phase formed by 119 was found to be miscible with that of the achiral material CB6OCB (77). Walker et al. reported a family of unsymmetrical dimers that are terminated by either butyl, racemic 2-methylbutyl, or (S)-2-methylbutyl chains (Table 13) [71]. The NTB-N transition temperature was marginally higher for chiral materials than the achiral analogues, in agreement with the theoretical predictions [72]. Notably, the NTB phase formed by 119 was found to be miscible with that of the achiral material CB6OCB (77). Walker et al. reported a family of unsymmetrical dimers that are terminated by either butyl, racemic 2-methylbutyl, or (S)-2-methylbutyl chains (Table 13) [71]. The NTB-N transition temperature was marginally higher for chiral materials than the achiral analogues, in agreement with the theoretical predictions [72]. Notably, the NTB phase formed by 119 was found to be miscible with that of the achiral material CB6OCB (77).

Bent-Core Systems
Compared to dimers comprising rod-like (calamitic) mesogenic units, there are relatively few examples of bent-core liquid crystals that exhibit the N TB phase. A family of no symmetrical bent-core materials with a central phenyl piperazine group were prepared by Schroder et al. [73] with shorter homologues exhibiting two nematic phases, denoted as N X . Longer chain homologues exhibited the SmC P phase. Later, compound 126 was studied by FFTEM, and the lower temperature nematic was shown to be a N TB phase with a pitch length of 14 nm-larger than CB7CB, but of the order of a few molecular lengths [12]. Based on this, it seems probable that the 'N X ' phase of compounds 124 and 125 is also the N TB phase.
Tamba et al. reported an ether-linked dimer, comprising a bent-core unit as well as a calamitic unit, which exhibited the twist-bend nematic phase as well as an unidentified 'M 2 ' mesophase [74]. Homologues employing other spacer lengths (trimethyleneoxy or hexamethyleneoxy) or a dodecyloxy terminal chain in lieu of the nitrile unit employed in 134 do not exhibit the twist-bend nematic phase. To date, compound 134 (Figure 2), along with those in Table 14, are the only known examples of bent-core materials that exhibit the twist-bend nematic phase, although others have been previously suggested [75].
with those in Table 14, are the only known examples of bent-core materials that exhibit the twist-bend nematic phase, although others have been previously suggested [75]. Table 14. Transition temperatures (TA-B, °C) of N-phenyl piperazine derived bent-core compounds [12,73].

Beyond Dimers: Trimers, Tetramers and Oligomers
Now, our focus shifts beyond covalent dimers to equivalent trimers, tetramers, and so on [76][77][78][79][80][81][82][83][84][85]. We will focus first on materials of special note before considering the behaviour of families of materials. CB6OBA, a hydrogen bonded LC-trimer, was the first oligomeric material shown to exhibit the NTB phase (Table 15) [86]. The hexamethyleneoxy spacer of CB6OBA imparts a gross bent shape to the hydrogen bonded dimer, permitting the formation of the NTB phase, which is absent for the even parity homologue, CB5OBA. The terminal carboxylic acid group contains a hydrogen bond donor and acceptor, thus, both open and closed forms can be observed [87,88].  Table 14. Transition temperatures (T A-B , • C) of N-phenyl piperazine derived bent-core compounds [12,73]. Tamba et al. reported an ether-linked dimer, comprising a bent-core unit as well as a calamitic unit, which exhibited the twist-bend nematic phase as well as an unidentified 'M2' mesophase [74]. Homologues employing other spacer lengths (trimethyleneoxy or hexamethyleneoxy) or a dodecyloxy terminal chain in lieu of the nitrile unit employed in 134 do not exhibit the twist-bend nematic phase. To date, compound 134 (Figure 2), along with those in Table 14, are the only known examples of bent-core materials that exhibit the twist-bend nematic phase, although others have been previously suggested [75]. Table 14. Transition temperatures (TA-B, °C) of N-phenyl piperazine derived bent-core compounds [12,73].

Beyond Dimers: Trimers, Tetramers and Oligomers
Now, our focus shifts beyond covalent dimers to equivalent trimers, tetramers, and so on [76][77][78][79][80][81][82][83][84][85]. We will focus first on materials of special note before considering the behaviour of families of materials. CB6OBA, a hydrogen bonded LC-trimer, was the first oligomeric material shown to exhibit the N TB phase (Table 15) [86]. The hexamethyleneoxy spacer of CB6OBA imparts a gross bent shape to the hydrogen bonded dimer, permitting the formation of the N TB phase, which is absent for the even parity homologue, CB5OBA. The terminal carboxylic acid group contains a hydrogen bond donor and acceptor, thus, both open and closed forms can be observed [87,88]. Table 15. Transition temperatures (T A-B , • C) of the hydrogen-bonded trimers CB5OCB (linear) and CB6OBA (bent) [86].  Wang et al. reported a symmetrical trimer that features two cyanobiphenyl units appended to a bent-core [13]; curiously, spacers in this system have even parity, with the requisite bent shape resulting from the 1,3-disubstituted phenyl ring employed within the bent-core unit. The pitch length of the NTB phase of 137 (Figure 3) was measured to be 19 nm using the FFTEM method, which was roughly four molecular lengths. X-ray scattering showed that the nematic phase is intercalated, with the d-spacing of the diffuse small angle peak being at ~1/3 of the molecular length. The orientational order parameters <P2> and <P4> were measured by X-ray scattering, both being found to decrease on entering the NTB phase. Replacement of a single cyanobiphenyl with a decyloxy chain was shown to eliminate the NTB phase [89]. In 2016, Mandle and Goodby reported a methylene linked tetramer comprising phenyl benzoate mesogenic units ( Figure 4) [47,90]. The heliconical tilt angle of the NTB phase of 138 was estimated via the X-ray scattering method, and was found to be comparable to the parent dimer, compound 11 (Table 2) [42]. The synthetic strategy used to prepare this tetramer was further refined to deliver a twist-bend nematic hexamer, with six mesogenic units connected in a linear manner.  So far, all of the materials encountered have had a linear sequence of mesogenic units. The hexamer 139 features two trimers appended via a central heptamethylenedioxy spacer ( Figure 5) [91]. The individual trimers are themselves mesogenic and display the NTB phase; however, the NTB-N transition occurs at a significantly higher temperature in the duplexed hexamer [91]. Wang et al. reported a symmetrical trimer that features two cyanobiphenyl units appended to a bent-core [13]; curiously, spacers in this system have even parity, with the requisite bent shape resulting from the 1,3-disubstituted phenyl ring employed within the bent-core unit. The pitch length of the N TB phase of 137 ( Figure 3) was measured to be 19 nm using the FFTEM method, which was roughly four molecular lengths. X-ray scattering showed that the nematic phase is intercalated, with the d-spacing of the diffuse small angle peak being at~1/3 of the molecular length. The orientational order parameters <P2> and <P4> were measured by X-ray scattering, both being found to decrease on entering the N TB phase. Replacement of a single cyanobiphenyl with a decyloxy chain was shown to eliminate the N TB phase [89].   [13]; curiously, spacers in this system have even parity, with the requisite bent shape resulting from the 1,3-disubstituted phenyl ring employed within the bent-core unit. The pitch length of the NTB phase of 137 ( Figure 3) was measured to be 19 nm using the FFTEM method, which was roughly four molecular lengths. X-ray scattering showed that the nematic phase is intercalated, with the d-spacing of the diffuse small angle peak being at ~1/3 of the molecular length. The orientational order parameters <P2> and <P4> were measured by X-ray scattering, both being found to decrease on entering the NTB phase. Replacement of a single cyanobiphenyl with a decyloxy chain was shown to eliminate the NTB phase [89]. In 2016, Mandle and Goodby reported a methylene linked tetramer comprising phenyl benzoate mesogenic units ( Figure 4) [47,90]. The heliconical tilt angle of the NTB phase of 138 was estimated via the X-ray scattering method, and was found to be comparable to the parent dimer, compound 11 (Table 2) [42]. The synthetic strategy used to prepare this tetramer was further refined to deliver a twist-bend nematic hexamer, with six mesogenic units connected in a linear manner.  So far, all of the materials encountered have had a linear sequence of mesogenic units. The hexamer 139 features two trimers appended via a central heptamethylenedioxy spacer ( Figure 5) [91]. The individual trimers are themselves mesogenic and display the NTB phase; however, the NTB-N transition occurs at a significantly higher temperature in the duplexed hexamer [91]. In 2016, Mandle and Goodby reported a methylene linked tetramer comprising phenyl benzoate mesogenic units ( Figure 4) [47,90]. The heliconical tilt angle of the N TB phase of 138 was estimated via the X-ray scattering method, and was found to be comparable to the parent dimer, compound 11 (Table 2) [42]. The synthetic strategy used to prepare this tetramer was further refined to deliver a twist-bend nematic hexamer, with six mesogenic units connected in a linear manner.  Wang et al. reported a symmetrical trimer that features two cyanobiphenyl units appended to a bent-core [13]; curiously, spacers in this system have even parity, with the requisite bent shape resulting from the 1,3-disubstituted phenyl ring employed within the bent-core unit. The pitch length of the NTB phase of 137 ( Figure 3) was measured to be 19 nm using the FFTEM method, which was roughly four molecular lengths. X-ray scattering showed that the nematic phase is intercalated, with the d-spacing of the diffuse small angle peak being at ~1/3 of the molecular length. The orientational order parameters <P2> and <P4> were measured by X-ray scattering, both being found to decrease on entering the NTB phase. Replacement of a single cyanobiphenyl with a decyloxy chain was shown to eliminate the NTB phase [89].
In 2016, Mandle and Goodby reported a methylene linked tetramer comprising phenyl benzoate mesogenic units ( Figure 4) [47,90]. The heliconical tilt angle of the NTB phase of 138 was estimated via the X-ray scattering method, and was found to be comparable to the parent dimer, compound 11 (Table 2) [42]. The synthetic strategy used to prepare this tetramer was further refined to deliver a twist-bend nematic hexamer, with six mesogenic units connected in a linear manner.   Figure 5) [91]. The individual trimers are themselves mesogenic and display the NTB phase; however, the NTB-N transition occurs at a significantly higher temperature in the duplexed hexamer [91]. So far, all of the materials encountered have had a linear sequence of mesogenic units. The hexamer 139 features two trimers appended via a central heptamethylenedioxy spacer ( Figure 5) [91]. The individual trimers are themselves mesogenic and display the N TB phase; however, the N TB -N transition occurs at a significantly higher temperature in the duplexed hexamer [91]. Jákli et al. reported a homologous family of 2′,3′-difluoroterphenyls [92], from the simple monomer (n = 0, 140, Table 16) to the homologous tetramer 143. Some homologous dimers, with varying terminal/spacer chain length, have also been reported [93][94][95], and a wealth of investigations have been performed on this family of materials [96][97][98].
The monomeric material displays only a nematic phase whereas those with two or more mesogenic units display nematic and NTB phases, with the transition temperature increasing as the number of mesogenic units is increased. So far, we have considered oddeven effects as being restricted to those resulting from the parity of the central spacer. However, for the 'DTC5-C9' family, Jákli et al. showed remarkable odd-even effects in birefringence, bend elastic constants, and X-ray scattering, which resulted from the number of mesogenic units [92].  Table 18) [100] linking groups, but with varying spacer lengths. For a given chain length, the former family exhibited higher transition temperatures than the latter. In both families, materials of even parity displayed nematic and smectic A phases, whereas those of odd parity showed nematic and NTB phases.  Jákli et al. reported a homologous family of 2 ,3 -difluoroterphenyls [92], from the simple monomer (n = 0, 140, Table 16) to the homologous tetramer 143. Some homologous dimers, with varying terminal/spacer chain length, have also been reported [93][94][95], and a wealth of investigations have been performed on this family of materials [96][97][98]. Table 16. Transition temperatures (T A-B , • C) of compounds 140-143, the 'DTC5-C9' family [92]. Jákli et al. reported a homologous family of 2′,3′-difluoroterphenyls [92], from the simple monomer (n = 0, 140, Table 16) to the homologous tetramer 143. Some homologous dimers, with varying terminal/spacer chain length, have also been reported [93][94][95], and a wealth of investigations have been performed on this family of materials [96][97][98].
The monomeric material displays only a nematic phase whereas those with two or more mesogenic units display nematic and NTB phases, with the transition temperature increasing as the number of mesogenic units is increased. So far, we have considered oddeven effects as being restricted to those resulting from the parity of the central spacer. However, for the 'DTC5-C9' family, Jákli et al. showed remarkable odd-even effects in birefringence, bend elastic constants, and X-ray scattering, which resulted from the number of mesogenic units [92].  Table 18) [100] linking groups, but with varying spacer lengths. For a given chain length, the former family exhibited higher transition temperatures than the latter. In both families, materials of even parity displayed nematic and smectic A phases, whereas those of odd parity showed nematic and NTB phases. The monomeric material displays only a nematic phase whereas those with two or more mesogenic units display nematic and N TB phases, with the transition temperature increasing as the number of mesogenic units is increased. So far, we have considered odd-even effects as being restricted to those resulting from the parity of the central spacer. However, for the 'DTC5-C9' family, Jákli et al. showed remarkable odd-even effects in birefringence, bend elastic constants, and X-ray scattering, which resulted from the number of mesogenic units [92].
Arakawa et al. reported two families of symmetrical liquid crystalline trimers featuring ether (CBOnOBOnOCB , Table 17) [99] and mixed ether/thioether (CBSnOBOnSCB ,  Table 18) [100] linking groups, but with varying spacer lengths. For a given chain length, the former family exhibited higher transition temperatures than the latter. In both families, materials of even parity displayed nematic and smectic A phases, whereas those of odd parity showed nematic and N TB phases.
Al-Janabi and Mandle reported a set of liquid crystalline trimers that incorporated various saturated hydrocarbon rings, isosteric with 1,4-disubstituted benzene (Table 19) [101]. Only the 2,6-cuneane material did not exhibit the N TB phase, and this was attributed to the unfavourable bend angles imposed by this non-linear motif. For the materials that exhibited the N TB phase (X = 1,4-benzene, 1,4-cyclohexane, and 1,4-cubane), the heliconical tilt angle was found to be effectively independent of the chemical makeup of the central ring.  Table 18) [100] linking groups, but with varying spacer lengths. For a given chain length, the former family exhibited higher transition temperatures than the latter. In both families, materials of even parity displayed nematic and smectic A phases, whereas those of odd parity showed nematic and NTB phases. Al-Janabi and Mandle reported a set of liquid crystalline trimers that incorporated various saturated hydrocarbon rings, isosteric with 1,4-disubstituted benzene (Table 19) [101]. Only the 2,6-cuneane material did not exhibit the NTB phase, and this was attributed to the unfavourable bend angles imposed by this non-linear motif. For the materials that exhibited the NTB phase (X = 1,4-benzene, 1,4-cyclohexane, and 1,4-cubane), the heliconical tilt angle was found to be effectively independent of the chemical makeup of the central ring. The relationship between the stability of the NTB phase and oligomer shape was studied in detail for a family of cyanobiphenyl/benzylideneaniline oligomers ( Al-Janabi and Mandle reported a set of liquid crystalline trimers that incorporated various saturated hydrocarbon rings, isosteric with 1,4-disubstituted benzene (Table 19) [101]. Only the 2,6-cuneane material did not exhibit the NTB phase, and this was attributed to the unfavourable bend angles imposed by this non-linear motif. For the materials that exhibited the NTB phase (X = 1,4-benzene, 1,4-cyclohexane, and 1,4-cubane), the heliconical tilt angle was found to be effectively independent of the chemical makeup of the central ring. The relationship between the stability of the NTB phase and oligomer shape was studied in detail for a family of cyanobiphenyl/benzylideneaniline oligomers (Table 20) [102]. Due to the explored variations in the composition and parity of the spacer units, neighbouring mesogenic units within this family can have both 'bent' or 'linear' configurations. While all materials exhibit the NTB phase, the heliconical pitch length has a strong dependence on the gross molecular shape; the all bent material 166 has three odd-parity spacers and a pitch of 7 nm, the bent-linear-bent tetramer 170 has a pitch of 12 nm, and the linearbent-linear tetramer 172 has a pitch length of ~17 nm. Al-Janabi and Mandle reported a set of liquid crystalline trimers that incorporated various saturated hydrocarbon rings, isosteric with 1,4-disubstituted benzene (Table 19) [101]. Only the 2,6-cuneane material did not exhibit the NTB phase, and this was attributed to the unfavourable bend angles imposed by this non-linear motif. For the materials that exhibited the NTB phase (X = 1,4-benzene, 1,4-cyclohexane, and 1,4-cubane), the heliconical tilt angle was found to be effectively independent of the chemical makeup of the central ring. The relationship between the stability of the NTB phase and oligomer shape was studied in detail for a family of cyanobiphenyl/benzylideneaniline oligomers (Table 20) [102]. Due to the explored variations in the composition and parity of the spacer units, neighbouring mesogenic units within this family can have both 'bent' or 'linear' configurations. While all materials exhibit the NTB phase, the heliconical pitch length has a strong dependence on the gross molecular shape; the all bent material 166 has three odd-parity spacers and a pitch of 7 nm, the bent-linear-bent tetramer 170 has a pitch of 12 nm, and the linearbent-linear tetramer 172 has a pitch length of ~17 nm. Al-Janabi and Mandle reported a set of liquid crystalline trimers that incorporated various saturated hydrocarbon rings, isosteric with 1,4-disubstituted benzene (Table 19) [101]. Only the 2,6-cuneane material did not exhibit the NTB phase, and this was attributed to the unfavourable bend angles imposed by this non-linear motif. For the materials that exhibited the NTB phase (X = 1,4-benzene, 1,4-cyclohexane, and 1,4-cubane), the heliconical tilt angle was found to be effectively independent of the chemical makeup of the central ring. The relationship between the stability of the NTB phase and oligomer shape was studied in detail for a family of cyanobiphenyl/benzylideneaniline oligomers (Table 20) [102]. Due to the explored variations in the composition and parity of the spacer units, neighbouring mesogenic units within this family can have both 'bent' or 'linear' configurations. While all materials exhibit the NTB phase, the heliconical pitch length has a strong dependence on the gross molecular shape; the all bent material 166 has three odd-parity spacers and a pitch of 7 nm, the bent-linear-bent tetramer 170 has a pitch of 12 nm, and the linearbent-linear tetramer 172 has a pitch length of ~17 nm. Al-Janabi and Mandle reported a set of liquid crystalline trimers that incorporated various saturated hydrocarbon rings, isosteric with 1,4-disubstituted benzene (Table 19) [101]. Only the 2,6-cuneane material did not exhibit the NTB phase, and this was attributed to the unfavourable bend angles imposed by this non-linear motif. For the materials that exhibited the NTB phase (X = 1,4-benzene, 1,4-cyclohexane, and 1,4-cubane), the heliconical tilt angle was found to be effectively independent of the chemical makeup of the central ring. The relationship between the stability of the NTB phase and oligomer shape was studied in detail for a family of cyanobiphenyl/benzylideneaniline oligomers (Table 20) [102]. Due to the explored variations in the composition and parity of the spacer units, neighbouring mesogenic units within this family can have both 'bent' or 'linear' configurations. While all materials exhibit the NTB phase, the heliconical pitch length has a strong dependence on the gross molecular shape; the all bent material 166 has three odd-parity spacers and a pitch of 7 nm, the bent-linear-bent tetramer 170 has a pitch of 12 nm, and the linearbent-linear tetramer 172 has a pitch length of ~17 nm. Al-Janabi and Mandle reported a set of liquid crystalline trimers that incorporated various saturated hydrocarbon rings, isosteric with 1,4-disubstituted benzene (Table 19) [101]. Only the 2,6-cuneane material did not exhibit the NTB phase, and this was attributed to the unfavourable bend angles imposed by this non-linear motif. For the materials that exhibited the NTB phase (X = 1,4-benzene, 1,4-cyclohexane, and 1,4-cubane), the heliconical tilt angle was found to be effectively independent of the chemical makeup of the central ring. The relationship between the stability of the NTB phase and oligomer shape was studied in detail for a family of cyanobiphenyl/benzylideneaniline oligomers (Table 20) [102]. Due to the explored variations in the composition and parity of the spacer units, neighbouring mesogenic units within this family can have both 'bent' or 'linear' configurations. While all materials exhibit the NTB phase, the heliconical pitch length has a strong dependence on the gross molecular shape; the all bent material 166 has three odd-parity spacers and a pitch of 7 nm, the bent-linear-bent tetramer 170 has a pitch of 12 nm, and the linearbent-linear tetramer 172 has a pitch length of ~17 nm.

->230 #
The relationship between the stability of the N TB phase and oligomer shape was studied in detail for a family of cyanobiphenyl/benzylideneaniline oligomers (Table 20) [102]. Due to the explored variations in the composition and parity of the spacer units, neighbouring mesogenic units within this family can have both 'bent' or 'linear' configurations. While all materials exhibit the N TB phase, the heliconical pitch length has a strong dependence on the gross molecular shape; the all bent material 166 has three odd-parity spacers and a pitch of 7 nm, the bent-linear-bent tetramer 170 has a pitch of 12 nm, and the linear-bent-linear tetramer 172 has a pitch length of~17 nm.

Supramolecular NTB Materials
We now consider supramolecular LC dimers that result from non-covalent bonds, both achiral and chiral, which exhibit the NTB phase. The hydrogen bonded-LC trimer CB6OBA was the first reported supramolecular NTB material, however, as the complex incorporates two identical molecules, there is no scope for tunability of structure. Walker et al. demonstrated a remarkable pair of supramolecular LC dimers that incorporates dissimilar hydrogen bond acceptors and donors. The parent 4-methoxybiphenyl/stilbazole dimer (173) is non-mesogenic; complexation with either 4-butoxy-or 4-pentyloxybenzoic acid affords the isolable supramolecular complexes shown in Table 21, both of which exhibit the NTB phase [103]. While many materials are known to exhibit transitions from the NTB phase to tilted (SmC, vide infra) or heliconical (SmCTB) [104] phases, complex 175 is unusual in that it exhibits a transition from the NTB phase to an orthogonal smectic A phase, as do compounds 111 and 112. This design strategy was also used to deliver chiral supramolecular NTB materials by use of the cyanobiphenyl/stilbazole system with an appropriate chiral benzoic acid [105]. The transition temperatures for this chiral supramolecular complex are somewhat lower than those of the linear analogue (shown in Table 22), and this depression of transition temperatures by branched alkyl chains is a general phenomenon in LC dimers. Resonant soft X-ray scattering at the carbon K-edge was used to measure the pitch length of 176, which was found to take a temperature dependent value of 8.1-8.4 nm, or around two complex lengths.

Supramolecular N TB Materials
We now consider supramolecular LC dimers that result from non-covalent bonds, both achiral and chiral, which exhibit the N TB phase. The hydrogen bonded-LC trimer CB6OBA was the first reported supramolecular N TB material, however, as the complex incorporates two identical molecules, there is no scope for tunability of structure. Walker et al. demonstrated a remarkable pair of supramolecular LC dimers that incorporates dissimilar hydrogen bond acceptors and donors. The parent 4-methoxybiphenyl/stilbazole dimer (173) is non-mesogenic; complexation with either 4-butoxy-or 4-pentyloxybenzoic acid affords the isolable supramolecular complexes shown in Table 21, both of which exhibit the N TB phase [103]. While many materials are known to exhibit transitions from the N TB phase to tilted (SmC, vide infra) or heliconical (SmC TB ) [104] phases, complex 175 is unusual in that it exhibits a transition from the N TB phase to an orthogonal smectic A phase, as do compounds 111 and 112.

Supramolecular NTB Materials
We now consider supramolecular LC dimers that result from non-covalent bonds, both achiral and chiral, which exhibit the NTB phase. The hydrogen bonded-LC trimer CB6OBA was the first reported supramolecular NTB material, however, as the complex incorporates two identical molecules, there is no scope for tunability of structure. Walker et al. demonstrated a remarkable pair of supramolecular LC dimers that incorporates dissimilar hydrogen bond acceptors and donors. The parent 4-methoxybiphenyl/stilbazole dimer (173) is non-mesogenic; complexation with either 4-butoxy-or 4-pentyloxybenzoic acid affords the isolable supramolecular complexes shown in Table 21, both of which exhibit the NTB phase [103]. While many materials are known to exhibit transitions from the NTB phase to tilted (SmC, vide infra) or heliconical (SmCTB) [104] phases, complex 175 is unusual in that it exhibits a transition from the NTB phase to an orthogonal smectic A phase, as do compounds 111 and 112. This design strategy was also used to deliver chiral supramolecular NTB materials by use of the cyanobiphenyl/stilbazole system with an appropriate chiral benzoic acid [105]. The transition temperatures for this chiral supramolecular complex are somewhat lower than those of the linear analogue (shown in Table 22), and this depression of transition temperatures by branched alkyl chains is a general phenomenon in LC dimers. Resonant soft X-ray scattering at the carbon K-edge was used to measure the pitch length of 176, which was found to take a temperature dependent value of 8.1-8.4 nm, or around two complex lengths.

Supramolecular NTB Materials
We now consider supramolecular LC dimers that result from non-covalent bonds, both achiral and chiral, which exhibit the NTB phase. The hydrogen bonded-LC trimer CB6OBA was the first reported supramolecular NTB material, however, as the complex incorporates two identical molecules, there is no scope for tunability of structure. Walker et al. demonstrated a remarkable pair of supramolecular LC dimers that incorporates dissimilar hydrogen bond acceptors and donors. The parent 4-methoxybiphenyl/stilbazole dimer (173) is non-mesogenic; complexation with either 4-butoxy-or 4-pentyloxybenzoic acid affords the isolable supramolecular complexes shown in Table 21, both of which exhibit the NTB phase [103]. While many materials are known to exhibit transitions from the NTB phase to tilted (SmC, vide infra) or heliconical (SmCTB) [104] phases, complex 175 is unusual in that it exhibits a transition from the NTB phase to an orthogonal smectic A phase, as do compounds 111 and 112. This design strategy was also used to deliver chiral supramolecular NTB materials by use of the cyanobiphenyl/stilbazole system with an appropriate chiral benzoic acid [105]. The transition temperatures for this chiral supramolecular complex are somewhat lower than those of the linear analogue (shown in Table 22), and this depression of transition temperatures by branched alkyl chains is a general phenomenon in LC dimers. Resonant soft X-ray scattering at the carbon K-edge was used to measure the pitch length of 176, which was found to take a temperature dependent value of 8.1-8.4 nm, or around two complex lengths.

Supramolecular NTB Materials
We now consider supramolecular LC dimers that result from non-covalent bonds, both achiral and chiral, which exhibit the NTB phase. The hydrogen bonded-LC trimer CB6OBA was the first reported supramolecular NTB material, however, as the complex incorporates two identical molecules, there is no scope for tunability of structure. Walker et al. demonstrated a remarkable pair of supramolecular LC dimers that incorporates dissimilar hydrogen bond acceptors and donors. The parent 4-methoxybiphenyl/stilbazole dimer (173) is non-mesogenic; complexation with either 4-butoxy-or 4-pentyloxybenzoic acid affords the isolable supramolecular complexes shown in Table 21, both of which exhibit the NTB phase [103]. While many materials are known to exhibit transitions from the NTB phase to tilted (SmC, vide infra) or heliconical (SmCTB) [104] phases, complex 175 is unusual in that it exhibits a transition from the NTB phase to an orthogonal smectic A phase, as do compounds 111 and 112. This design strategy was also used to deliver chiral supramolecular NTB materials by use of the cyanobiphenyl/stilbazole system with an appropriate chiral benzoic acid [105]. The transition temperatures for this chiral supramolecular complex are somewhat lower than those of the linear analogue (shown in Table 22), and this depression of transition temperatures by branched alkyl chains is a general phenomenon in LC dimers. Resonant soft X-ray scattering at the carbon K-edge was used to measure the pitch length of 176, which was found to take a temperature dependent value of 8.1-8.4 nm, or around two complex lengths. This design strategy was also used to deliver chiral supramolecular N TB materials by use of the cyanobiphenyl/stilbazole system with an appropriate chiral benzoic acid [105]. The transition temperatures for this chiral supramolecular complex are somewhat lower than those of the linear analogue (shown in Table 22), and this depression of transition temperatures by branched alkyl chains is a general phenomenon in LC dimers. Resonant soft X-ray scattering at the carbon K-edge was used to measure the pitch length of 176,

Summary and Outlook
The decade since the experimental discovery of the N TB phase by Cestari et al. has seen a resurgence of interest in liquid crystalline dimers and oligomers. Recently, there has been a notable move from symmetrical methylene-linked dimers to more complex forms: chiral systems, photoresponsive dimers, supermolecular materials, higher and non-linear oligomers, and polymers. The recent development of room temperature materials greatly facilitates the exploration of the rich physics of these systems.
General design principles for N TB materials are always evolving; with the ability to tune molecular bend/shape through synthetic chemistry, the ability to prepare oligomers, and supramolecular systems, it is possible to obtain twist-bend nematic materials through rational design rather than through ad hoc experimentation. This being said, the majority of twist-bend nematic materials follow the tried-and-tested formula of end-to-end appended mesogenic units, with only a handful of bent-core materials and a single non-linear oligomer falling outside of this description. It is interesting to speculate as to whether more unconventional molecular geometries (e.g., lambda shaped trimers, mixed rod-disk architectures) are capable of supporting twist-bend nematic order.
Different materials display rather different helix pitches that themselves evolve differently over temperature; an understanding of this from a molecular perspective is currently elusive, but appears a reasonable proposition for future work. The potential for incorporating stimuli responsive groups, coupled with the remarkable physical properties of this phase of matter, suggests that interest in this area will continue for some time.

Conflicts of Interest:
The author declares no conflict of interest.