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.

1. 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 (NTB) phase, and was reported experimentally in a landmark work in 2011 [9]. The NTB 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 NTB 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 NTB phase remains below the magic angle and the phase is uniaxial with positive birefringence, confirmed by conoscopic investigation [24]. Calorimetric studies show the NTB-N is typically first order, and close to tricritical [9,25,26,27,28]. The NTB phase has been shown to be strongly shear thinning; for the material KA(0.2), a 6-component mixture with a pitch length of 10.5 nm [29,30], it was shown that at low (<1 Pa) shear stress, the viscosity was ~1000× larger than the nematic phase. For the same material at high shear stress (>10 Pa), the viscosity of the NTB-phase dropped by two orders of magnitude as the helix underwent shear-induced realignment [31].

As with all mesophases, the formation of the NTB phase in a given material is intimately linked to molecular structure, and there has been significant effort in the design of new materials that exhibit the NTB phase [32]. The molecular structure of liquid crystalline dimers can be subdivided into distinct regions, as outlined in Figure 1B. In the simplest terms, a dimer consists of two rigid mesogenic units joined by a flexible spacer [33,34,35]. For a trimer, three mesogenic units are joined in a similar fashion, and so on. Today, in the region of 1000, materials are known to exhibit the NTB phase, and so in this review, we focused on systematic variations to key areas of molecular structure rather than making a futile attempt to cover all materials.

Figure 1

(A) Cartoon depiction of the heliconical director precession in the twist-bend nematic phase; mesogenic units are shown as cylinders, and are coloured according to their position along the helix axis. (B) The general structure of terminally appended liquid crystalline dimers and oligomers, subdivided into regions of interest to this review. For each subdivision example, chemical fragments that have been utilised in NTB materials are given. (C) Schematic depiction of the relationship between dimers, trimers, and tetramers in terms of their subunit composition.

2. Materials

The CBnCB family are archetypal NTB 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 NTB phase (Table 1). Even parity CBnCB materials displayed only a conventional nematic phase.

Table 1

Transition temperatures (TA-B, °C) of the CBnCB family of materials [9,23,26,36,37,38,39,40].

No.	Name	n	TMP	TNTB-N	TN-Iso
1	CB3CB	3	142.1	-	-
2	CB5CB	5	150	92	97
3	CB6CB	6	183	-	230
4	CB7CB	7	102	104.5	116
5	CB8CB	8	175	-	195.9
6	CB9CB	9	83	105.0	119.8
7	CB10CB	10	140	-	174.1
8	CB11CB	11	99.9	108.6	125.5
9	CB12CB	12	139	-	157
10	CB13CB	13	106	105	122

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, 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 [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].

Table 2

Transition temperatures (TA-B, °C) of some symmetric (PZP)-9 materials with varying terminal unit [44,45].

No.	X	TMP	TNTB-N	TN-Iso
11	–CN	157.6	114.5	146.6
12	–NO2	105.4	-	-
13	–F	97.6	-	-
14	–CF3	102.4	-	-
15	–NCS	97.7	103.7	127.4
16	–SF5	123.0	-	-
17	–C5H11	72.8	58.8	66.2
18	–OC5H11	71.8	76.0	86.6

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 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	TNTB-N	TN-Iso
11		157.6	114.5	146.6
19		112.6	95.0	120.7
20		115.4	100.5	124.9
21		92.6	78.8	97.6
22		86.2	78.2	95.9
23		83.2	63.8	79.0
24		93.8	46.0	60.0
25		110.0	69.6	78.3
26		95.6	100.0	123.8
27		102.2	61.2	72.8
28		88.7	80.7	95.1
29		91.9	85.2	110.0

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 (3-hydroxylphenyl) 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	TNTB-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.

Table 5

Transition temperatures (TA-B, °C) of salicylaldimine dimers with odd spacer parity [50].

No.	n	m	TMP	TB6-N/Iso	TNTB-N	TN-Iso
42	4	5	114.0	99.1	-	102.0
43	6	5	123.5	116.9	-	-
44	8	5	94.2	121.0	-	-
45	10	5	88.5	109.5	-	-
46	12	5	96.2	96.1	-	-
47	14	5	101.2	-	-	-
48	4	7	112.2	84.4	96.6	115.0
49	6	7	96.4	114.7	-	-
50	8	7	111.2	119.5	-	-
51	10	7	100.1	110.1	-	-
52	12	7	90.9	99.3	-	-

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).

Table 6

Transition temperatures (TA-B, °C) of cyanobiphenyl derivatives with varying central spacer composition, equivalent to heptamethylene [54].

No.	Name	χ	TMP	TNTB-N	TN-Iso	Ave. Bend/°
53	CBT3TCB		160.5	-	-	n/r
54	CBT1O1TCB		>225	-	-	n/r
4	CB7CB		104.4	105.5	118.9	103.5
55	CB3O3CB		100.5	46.0	68.0	91.0
56	CBT4OCB		132.8	97.0	145.2	100.5
57	CB6OCB		102.1	110.5	154.2	104.4
58	CBO5OCB		137.9	81.3	189.2	102.9
59	CBK5KCB		158.1	145.1	189.4	108.2
60	CBI3ICB		170.8	114.9	-	115.1
61	CBO2O2OCB		150.5	-	157.8	104.5

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 1H-1H 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 to TN-Iso is achieved by having an average bend angle in excess of 110°.

Table 7

Transition temperatures (TA-B, °C) of cyanobiphenyl derivatives with varying central spacer composition, equivalent to nonamethylene [54,55,56,57,58]. * Glass to NTB transition.

No.	Name	χ	TMP	TNTB-N	TN-Iso	Ave. Bend/°
6	CB9CB		83.3	105.4	121.5	103.1
62	CBI7ICB		140.8	114.7	138.7	111.5
63	CB8KCB		127.8	128.1	153.9	98.5
64	CBT6OCB		137.1	102.0	153.6	98.5
65	CB8OCB		110.6	109.9	153.3	100.7
66	CBS7SCB		15.9 *	88.3	115.2	99.2
67	CBS7OCB		55.0	95.9	146.7	96.8
68	CBSe7SeCB		80.8	43.1	71.9	98.8
69	CBcZ5OCB		95.1	39.8	91.3	93.0
70	CBcO5OCB		122.4	71.3	129.9	96.8
71	CBO7OCB		120.0	-	-	-
72	CBT5CBT		169.1	-	-	-

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 NTB 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 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 8

Transition temperatures (TA-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 NTB transition.

No.	Name	n	X	Y	TMP	TNTB-N	TN-Iso
73	CB4OCB	3	–CH2–	–O–	121	103	143
74	CB4SCB	3	–CH2–	–S–	126.2	70.3	86.8
75	CBO3SCB	3	–O–	–S–	101.1	47	137.5
76	CBS3SCB	3	–S–	–S–	70.1	44.0	83.2
77	CB6OCB	5	–CH2–	–O–	99	109	155
78	CB6SCB	5	–CH2–	–S–	99.0	89.6	113.2
79	CBO5SCB	5	–O–	–S–	59.5	90.1	143.8
80	CBS5SCB	5	–S–	–S–	68.9	78.0	107.8
65	CB8OCB	7	–CH2–	–O–	112	108	154
81	CB8SCB	7	–CH2–	–S–	92.6	93.9	117.8
67	CBO7SCB	7	–O–	–S–	16.0 *	95.9	146.7
66	CBS7SCB	7	–S–	–S–	15.9 *	88.3	115.2
82	CB9OCB	9	–CH2–	–O–	116	107	148
83	CB9SCB	9	–CH2–	–S–	103.4	95.5	119.0
84	CBO9SCB	9	–O–	–S–	98.0	95	143.0
85	CBS9SCB	9	–S–	–S–	100.8	89	116.7

Arakawa et al. subsequently demonstrated cyanobiphenyl dimers with mixed thioether/ketone linking units [65] (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.

Table 9

Transition temperatures (TA-B, °C) of cyanobiphenyl derivatives with mixed ketone/thioether linking units [65].

No.	Name	n	TMP	TNTB-N	TN-Iso
86	CBK3SCB	3	114.6	104.6	132.6
87	CBK5SCB	5	120.9	110.0	152.3
88	CBK7SCB	7	121.8	113.6	152.1
89	CBK9SCB	9	155.8	-	145.0

3. 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.

Table 10

Transition temperatures (TA-B, °C) of unsymmetrical cholesterol containing dimers.

No.	n	m	TMP	TSmA-N*	TNTB-N*	TN*-Iso
90	3	1	112.3	-	55.1	67.7
91	4	1	127.9	146.9	-	191.8
92	5	1	92.5	-	67.9	102.3
93	6	1	152.3	120.0	-	158.4
94	7	1	83.0	-	75.7	110.8
95	9	1	81.2	-	75.7	113.6
96	10	1	82.7	-	-	137.5
97	15	1	62.9	-	63.2	107.9
98	5	2	74.0	-	60.6	93.6
99	5	3	77.5	-	62.2	98.8
100	5	4	44.2	71.9	-	99.3

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].

Table 11

Transition temperatures (TA-B, °C) of unsymmetrical dimers comprising cholesterol and azobenzene units.

No.	n	R	TMP	TSmX-N*	TNTB-N*	TN*-Iso
101	5	–CH3	83.4	-	67.1	105.5
102	5	–OCH3	84.3	-	80.8)	124.9
103	5	–OC2H5	107.0	97.6	-	134.4
104	7	–CH3	63.9	-	74.0	111.5
105	9	–CH3	69.6	-	75.8	113.6
106	15	–CH3	60.5	60.3	-	100.3

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].

Table 12

Transition temperatures (TA-B, °C) of symmetrical dimers containing an (R)-2-methylpentamethylene spacer.

No.	R	TMP	TSmA-NTB*	TNTB-N*	TN*-Iso
107		134.1	-	-	71.1
108		61.6	-	-	-
109		69.1	-	-	-
110		66.6	-	-	233.6
111		117.1	110.8	123.5	219.8
112		119.3	161.0	167.2	236.4
113		123.3	-	-	237.4

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].

No	n	m	TMP/°C	TSmA-NTB*	TNTB-N*	TN*-Iso
114	4		154	-	-	249
115	6		154	-	96	248
116	8		144	-	93	241
117	10		135	-	89	231
118	4		162	-	-	209
119	6		153	-	89	214
120	8		132	-	93	212
121	10		131	88	-	203
122	6		153	-	85	214
123	8		131	-	92	207

4. 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 NTB 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 NX. Longer chain homologues exhibited the SmCP phase. Later, compound 126 was studied by FFTEM, and the lower temperature nematic was shown to be a NTB 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 ‘NX’ phase of compounds 124 and 125 is also the NTB 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 ‘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].

Figure 2

Chemical structure and transition temperatures (°C) of the hybrid bent-core/calamitic dimer reported by Tamba et al. [74]. Phase transitions are presented in parenthesis are monotropic.

Table 14

Transition temperatures (TA-B, °C) of N-phenyl piperazine derived bent-core compounds [12,73].

No.	n	TMP	TSmCP-N/Iso	TColX-N	TNTB-N	TN-Iso
124	4	201	-	-	193	212
125	5	187	-	-	172	192
126	6	176	-	157	169	188
127	7	169	-	-	-	186
128	8	177	180	-	-	180.5
129	9	167	185	-	-	-
130	10	162	191	-	-	-
131	11	161	194	-	-	-
132	12	165	201	-	-	-
133	16	142	193	-	-	-

5. 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 15

Transition temperatures (TA-B, °C) of the hydrogen-bonded trimers CB5OCB (linear) and CB6OBA (bent) [86].

No.	Name	n	TMP	TNTB-N	TN-Iso
135	CB5OBA	5	196	-	209
136	CB6OCB	6	160	159	197

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 and 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].

Figure 3

Chemical structure and transition temperatures (°C) of the hybrid bent-core/calamitic trimer (137) reported by Wang et al. [13]. The melting point was not reported.

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 4

Chemical structure and transition temperatures (°C) of the linear tetramer reported by Mandle and Goodby.

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].

Figure 5

Chemical structure and transition temperatures (°C) of the non-linear hexamer reported by Mandle and Goodby.

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 (TA-B, °C) of compounds 140–143, the ‘DTC5-C9’ family [92].

No.	n	TMP	TSmX-N	TNTB-N	TN-Iso
140	0	34	-	-	116.5
141	1	77	85	124	162
142	2	127	-	145	192
143	3	142	-	168	205

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 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 NTB phases.

Table 17

Transition temperatures (TA-B, °C) of ether-linked trimers 144–151 [99].

No.	n	TMP	TSmA-N	TNTB-N	TN-Iso
144	4	230.1	197	-	297.4
145	5	176.6	-	122	215.4
146	6	217.4	192	-	257.8
147	7	162.9	-	132	207.2
148	8	201.0	175	-	231.9
149	9	155.0	-	135	195.8
150	10	198.0	150	-	210.8
151	11	147.4	-	130.5	185.9

Table 18

Transition temperatures (TA-B, °C) of mixed ether/thioether linked timers 152–160 [100].

No.	n	TMP	TSmA-N	TNTB-N	TN-Iso
152	3	186.4	-	-	142.0
153	4	235.3	-	-	253.2
154	5	171.8	-	117	154.2
155	6	219.0	180	-	217.4
156	7	149.4	-	126	162.4
157	8	195.6	167	-	198.8
158	9	131.3	-	122.7	158.8
159	10	184.8	146	-	176.2
160	11	135.4	-	121	154.4

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.

Table 19

Transition temperatures (TA-B, °C) of compounds 161–164; # sample decomposes at and above 230 °C [101].

No.	X	TMP	TNTB-N	TN-Iso
161		178.8	166.2	304.6
162		169.3	159.8	285.5
163		174.4	163.9	>230 #
164		162.2	-	>230 #

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 linear-bent-linear tetramer 172 has a pitch length of ~17 nm.

Table 20

Transition temperatures (TA-B, °C) of compounds 77, 165–172. Link Seq. refers to the shape (B = bent, L = linear) shape of the all trans conformation of the linkage units [102].

No.	n	χ	p	q	TMP	TNTB-N	TN-Iso	Link Seq.
77	6	-	0	0	99	109	155	B
165	6	-	1	0	153	142	185	BB
166	6	–(CH2)7–	1	1	140	159	180	BBB
167	6	–(CH2)6O–	1	1	151	158	195	BBB
168	6	–O(CH2)5O–	1	1	156	162	215	BBB
169	6	–O(CH2)6O–	1	1	166	166	235	BLB
170	6	–(CH2)8–	1	1	131	152	212	BLB
171	7	–(CH2)7–	1	1	145	132	225	LBL
172	O6	–(CH2)7–	1	1	131	143	242	LBL

6. 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.

Table 21

Transition temperatures (TA-B, °C) of compound 173 and complexes 174 and 175 [103].

No.	X	TMP	TSmX	TSmA-NTB	TNTB-N	TN-Iso
173	none	142.8	-	-	-	-
174		121.9	86.2	-	109.4	166.4
175		112.0	85.5	93.5	98.0	157.7

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.

Table 22

Transition temperatures (TA-B, °C) of complexes 176 and 177 [105].

No.	X	TMP/°C	TNTB-N/°C	TN-Iso/°C
176		107	95	167
177		103	88	145

Walker et al. subsequently demonstrated the CB6OCB:nOS series of materials, utilising the benzoic acid/stilbazole system [106]. A weak odd–even effect was seen for both the NTB–N and N–Iso transition temperatures. Homologues with longer terminal chain length (n ≥ 4) also exhibited smectic C phases. For homologues with longer chains still (n ≥ 8, not shown in Table 23), the NTB phase was absent, instead, the materials showed SmA and SmAB phases [106].

Table 23

Transition temperatures (TA-B, °C) of complexes 178–184 [106].

No.	n	TMP	TSmC-NTB	TNTB-N	TN-Iso
178	1	130	-	110	182
179	2	119	-	115	190
180	3	109	-	108	173
181	4	108	86	113	180
182	5	121	92	107	165
183	6	105	96	106	158
184	7	100	100	104	155

In the same paper, further elaboration of the cyanobiphenyl/stilbazole system to unsymmetrical supramolecular trimers comprising CB6OBA and a stilbazole dimer was reported (Table 24). Although the two materials differed in their melting point, the NTB–N and N–Iso transitions were only slightly different. We note that, although examples are presently limited to hydrogen bonded systems, there is no obvious reason why other types of non-covalent interactions could not be employed in the design of NTB materials (e.g., halogen bonds [107]), and presents a logical avenue for future research.

Table 24

Transition temperatures (TA-B, °C) of complexes 185 and 186 [106].

No.	X	TMP	TNTB-N	TN-Iso
185	-CN	127	143	186
186	-OCH3	140	142	184

7. Summary and Outlook

The decade since the experimental discovery of the NTB 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 NTB 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.