Molecular Flexibility and Bend in Semi-Rigid Liquid Crystals: Implications for the Heliconical Nematic Ground State

The N_TB phase phases possess a local helical structure with a pitch length of a few nanometers and is typically exhibited by materials consisting of two rigid mesogenic units linked by a flexible oligomethylene spacer of odd parity, giving a bent shape. We report the synthesis and characterisation of two novel dimeric liquid crystals, and perform a computational study on 10 cyanobiphenyl dimers with varying linking groups, generating a large library of conformers for each compound; this allows us to present molecular bend angles as probability weighted averages of many conformers, rather than use a single conformer. We validate conformer libraries by comparison of interproton distances with those obtained from solution-based 1D ¹H NOESY NMR, finding good agreement between experiment and computational work. Conversely, we find that using any single conformer fails to reproduce experimental interproton distances. We find the use of a single conformer significantly overestimates the molecular bend angle while also ignoring flexibility; in addition, we show that the average bend angle and flexibility are both linked to the relative stability of the N_TB phase.     

Twist-bend nematics,liquid crystal dimers,structure–property relations

ABSTRACT

One of the current challenges in liquid crystal science is to understand the molecular factors leading to the formation of the intriguing twist-bend nematic phase (N_TB) and determine its properties. During our earlier hunt for the N_TB phase created on cooling directly from the isotropic phase and not the nematic phase, we had prepared 30 symmetric liquid crystal dimers. These had odd spacers and methylene links to the two mesogenic groups; desirable but clearly not essential features for the formation of the N_TB. Here, we report the phases that the dimers exhibit and their transition temperatures as functions of both the lengths of the spacer and the terminal chains. In addition we describe the transitional entropies, their optical textures, the X-ray scattering patterns and the ²H NMR spectra employed in characterising the phases. All of which may lead to important properties of the twist-bend nematic phase.     

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

ABSTRACT

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

On the twist-bend nematic phase formed directly from the isotropic phase

The intriguing twist-bend nematic (N_TB) phase is formed, primarily, by liquid crystal dimers having odd spacers. Typically, the phase is preceded by a nematic (N) phase via a weak first-order transition. Our aim is to obtain dimers where the N_TB phase is formed directly from the isotropic (I) phase via a strong first-order phase transition. The analogy between such behaviour and that of the smectic A (SmA)–N–I sequence suggests that this new dimer will require a short spacer. This expectation is consistent with the prediction of a molecular field theory, since the decrease in the spacer length results in an increase in the molecular curvature. A vector of odd dimers based on benzoyloxybenzylidene mesogenic groups with terminal ethoxy groups has been synthesised with spacers composed of odd numbers of methylene groups. Spacers having 5, 7, 9 and 11 methylene groups are found to possess the conventional phase sequence N_TB–N–I; surprisingly, for the propane spacer, the N_TB phase is formed directly from the I phase. The properties of these dimers have been studied with care to ensure that the identification of the N_TB phase is reliable.     

Ether- and Thioether-Linked Naphthalene-Based Liquid-Crystal Dimers: Influence of Chalcogen Linkage and Mesogenic-Arm Symmetry on the Incidence and Stability of the Twist–Bend Nematic Phase

The twist–bend nematic (N_TB) phase with a heliconical nanostructure of the local director generating symmetry breaking by achiral bent-shaped molecules is a hot topic of current liquid-crystal science. As opposed to the most common methylene-linked dimers, this study demonstrates chalcogen ether- and/or thioether-linked 6-(4-cyanophenyl)-2-naphthyl-based liquid-crystal dimers with symmetric and asymmetric π-conjugated mesogenic-arm structures that exhibit the N_TB phase. Although the symmetric bis(ether)-linked dimer exhibits only the conventional nematic (N) phase, the asymmetric bis(ether)-linked dimer can form the N_TB phase. All thioether-linked dimers form the N_TB phase, wherein the dimers with asymmetric arms vitrify in the N_TB phase on cooling to room temperature. The phase transitions are discussed in terms of the chalcogen linkage combination, mesogenic-arm symmetry, and spacer length. It is revealed that thioether-linked dimers based on asymmetric π-conjugated mesogenic arms with terminal cyano groups are highly beneficial for the realization of materials that form a wide range of N_TB phases and glassy N_TB states at room temperature.     

Effect of the linking unit on the twist-bend nematic phase in liquid crystal dimers: a comparative study of two homologous series of methylene- and ether-linked dimers

ABSTRACT

Two series of bimesogens with phenyl benzoate mesogenic units were prepared: one series having a heptamethylene spacer and the other a pentamethylene spacer with two ether-linking groups. These materials were prepared to provide experimental backing to the widely held hypothesis that methylene-linked bimesogens are more likely to exhibit the twist-bend nematic mesophase than their ether-linked counterparts. Several of the methylene-linked materials exhibited nematic and N_TB mesophases, whereas the analogous ether-linked materials gave only nematic phases albeit with significantly higher clearing points. Virtual N–N_TB transition temperatures for both methylene- and ether-linked bimesogens were extrapolated by constructing binary phase diagrams with the well-studied twist-bend material CB9CB. Contrary to our expectations these virtual transition temperatures were in most cases higher for the ether-linked bimesogens than in the analogous methylene compounds, this runs counter to reported theories and hypotheses that the incorporation of ether-linking groups should serve to destabilise the N_TB phase.     

Azobenzene-based liquid crystal dimers and the twist-bend nematic phase

ABSTRACT

The synthesis and characterisation of two new sets of non-symmetric liquid crystal dimers is reported, the 1-(4-substitutedazobenzene-4′-yloxy)-6-(4-cyanobiphenyl-4′-yl)hexanes (CB6OABX) and 1-(4-substitutedazobenzene-4′-yloxy)-6-(4-cyanobiphenyl-4′-yloxy)pentanes (CBO5OABX). The terminal substituents are methyl, methoxy, butyl, butyloxy, nitrile and nitro. All the CB6OABX dimers exhibit twist-bend nematic (N_TB) and nematic (N) phases. The CBO5OABX dimers also all show an N phase but only the butyl and butyloxy homologues exhibit the N_TB phase. The transitional behaviour of the non-symmetric dimers is compared to that of the corresponding symmetric dimers, the 1,5-bis(4-substitutedazobenzene-4′-yloxy)pentanes (XABO5OABX) and either 1,7-bis(4-cyanobiphenyl-4′-yl)heptane or 1,5-bis(4-cyanobiphenyl-4′-yloxy)pentane. The XABO5OABX dimers all show a nematic phase and in addition, the butyl homologue exhibits a smectic A phase. The difference in transitional behaviour between the CB6OABX and CBO5OABX dimers is attributed to the difference in their molecular shapes arising from different bond angles between the para axis of the cyanobiphenyl unit and the first bond in the spacer. Specifically, the all-trans conformation of a CBO5OABX dimer is more linear than that of the corresponding CB6OABX dimer. Differences within each set of dimers are attributed to changes in the average molecular shape and the strength of the mixed mesogen interaction on varying the terminal group. Crystal structures are reported for CB6OABOMe, CBO5OABNO₂ and MeOABO5OABOMe.     

Structure-property relationships in azobenzene-based twist-bend nematogens

ABSTRACT

The synthesis and characterisation of a new set of azobenzene-based non-symmetric liquid crystal dimers, the 1-(4-substitutedazobenzene-4?-yloxy)-6-(4-methoxybiphenyl-4?-yl)hexanes (MeOB6OABX), that exhibit the twist-bend nematic phase, N_TB, is described. The terminal substituents are methyl, methoxy, ethyl, butyl, butoxy, and nitrile. All six dimers exhibit both the N_TB and conventional nematic, N, phases. The identification of the N_TB phase was performed using polarised light microscopy and confirmed for binary mixtures with a standard twist-bend nematogen 1,7-bis-4-(4?-cyanobiphenyl) heptane (CB7CB). The transitional behaviour of the MeOB6OABX dimers is compared with that of the corresponding ether-linked 1-(4-substitutedazobenzene-4?-yloxy)-6-(4-methoxybiphenyl-4?-yloxy)pentanes, MeOBO5OABX, all of which exhibit a conventional nematic phase. In addition, the nitrile-substituted MeOBO5OABCN shows the N_TB phase. The behaviour of these non-symmetric dimers is also compared to that of the corresponding symmetric dimers. Differences in the transitional properties between these sets of new materials are accounted for in terms of not only molecular shape but also other factors including the strength of the mixed mesogen interaction.     

A Twist‐Bend Nematic (NTB) Phase of Chiral Materials

New chiral dimers consisting of a rod‐like and cholesterol mesogenic units are reported to form a chiral twist‐bend nematic phase (N_TB*) with heliconical structure. The compressibility of the N_TB phase made of bent dimers was found to be as large as in smectic phases, which is consistent with the nanoperiodic structure of the N_TB phase. The atomic force microscopy observations in chiral bent dimers revealed a periodicity of about 50 nm, which is significantly larger than the one reported previously for non‐chiral compounds (ca. 10 nm).     

Geometric aspects influencing N-NTB transition - implication of intramolecular torsion

Herein we report a comprehensive study on novel carbonyl- and ethenyl-linked symmetric dimers that combine synthesis, mesomorphic properties and molecular modelling. The study has been focused on the impact of geometry imposed by the linkage group on the incidence of the twist-bend nematic (N_TB) phase. Comparison of the mesomorphic properties of these two series complemented with computational studies of conformational space around the linkage group points molecular curvature and intramolecular torsion plays important role in the appearance of the N_TB phase and can be regarded as the basic structural requirements for design of new twist-bend nematogen materials.     

Cyanobiphenyl-based liquid crystal dimers and the twist-bend nematic phase

ABSTRACT

The synthesis and characterisation of several members of the 1,ω-bis(4-cyanobiphenyl-4′-yl) alkane (CBnCB) and the 1-(4-cyanobiphenyl-4′-yloxy)-ω-(4-cyanobiphenyl-4′-yl) alkane (CBnOCB) homologous series are reported. The new odd members described CB5CB, CB13CB, CB4OCB, CB8OCB and CB10OCB all exhibit twist-bend nematic and nematic phases. The members of these series already reported in literature, CB7CB, CB9CB, CB11CB and CB6OCB, were also prepared in order to allow for a direct comparison of their transitional properties. The properties of these dimers are also compared to those of the corresponding members of the 1,ω-bis(4-cyanobiphenyl-4,-yloxy) alkanes (CBOnOCB). For any given total spacer length, for odd members of these series, the nematic–isotropic transition temperatures and associated entropy changes are greatest for the CBOnOCB dimer and lowest for the CBnCB dimer. These trends are understood in terms of molecular shape. For short spacer lengths, the twist-bend nematic–nematic transition temperature (T_NTBN) is higher for the CBnOCB series than for the CBnCB series but this is reversed as the spacer length increases. Of the CBOnOCB dimers, a virtual value of T_NTBN was estimated for CBO3OCB and T_NTBN was measured for CBO5OCB. These values are considerably lower than those observed for the corresponding members of the CBnCB or CBnOCB series. The dependence of T_NTBN on molecular structure is discussed not only in terms of the molecular curvature but also in the ability of the molecules to pack efficiently. As the temperature range of the preceding nematic phase increases, so the twist-bend nematic–nematic transition entropy change decreases and the transition approaches second order for the longer spacers. For comparative purposes, the transitional behaviour of the even-membered dimers CB6CB, CB5OCB and CBO4OCB is reported and differences accounted for in terms of molecular shape.     

Apolar Bimesogens and the Incidence of the Twist–Bend Nematic Phase

The nematic twist–bend phase (N_TB) was, until recently, only observed for polar mesogenic dimers, trimers or bent‐core compounds. In this article, we report a comprehensive study on novel apolar materials that also exhibit N_TB phases. The N_TB phase was observed for materials containing phenyl, cyclohexyl or bicyclooctyl rings in their rigid‐core units. However, for materials with long (>C7) terminal chains or mesogenic core units comprising three ring units, the N_TB phase was not observed and instead the materials exhibited smectic phases. One compound was found to exhibit a transition from the N_TB phase to an anticlinic smectic C phase; this is the first example of this polymorphism. Incorporation of lateral substitution with respect to the central core unit led to reductions in transition temperatures; however, the N_TB phase was still found to occur. Conversely, utilising branched terminal groups rendered the materials non‐mesogenic. Overall, it appears that it is the gross molecular topology that drives the incidence of the N_TB phase rather than simple dipolar considerations. Furthermore, dimers lacking any polar groups, which were prepared to test this hypothesis, were found to be non mesogenic, indicating that at the extremes of polarity these effects can dominate over topology.     

Facile Synthesis of Liquid Crystal Dimers Bridged with a Phosphonic Group

Liquid crystal (LC) dimers with well-defined composition and structure arouse broad attentions for their exhibiting LC properties beyond conventional low molar mass mesogens and serving as fascinating model compounds for LC polymers. Here in this work, a series of LC dimers bridged with a phosphonic group have been synthesized through a facile free radical mediated addition reaction between hypophosphorous acid and vinyl terminated cyanobiphenyl mesogens with variant length alkyl spacers. In addition, two esterified derivatives and a group of mono-addition homologues with a terminal phosphonic acid group have also been prepared for comparison study. All the newly synthesized compounds exhibit monotropic nematic (N) phase with typical schlieren textures except for the LC dimer with the longest eleven-methylene spacer, which surprisingly shows twist-bend nematic (N_TB) phase directly from the isotropic state upon cooling. Moreover, the thermal transition properties such as the nematic-isotropic transition temperatures and associated entropy changes of the series LC dimers display a modest odd-even effect. Furthermore, both the LC dimers and the mono-addition homologues in N phase are quite easy to achieve homeotropic alignment upon annealing thanks to the supramolecular interactions between the introduced phosphonic acid group and the hydroxylated glass surface. This work thus provides a novel synthesis strategy for a class of LC materials bridged with a phosphonic acid group prone to further functionalization, which may serve as promising vertical alignment agents and pave the way for developing a new kind of functionalized LC materials of N_TB phase.     

Molecular structure and the twist-bend nematic phase: the role of terminal chains

ABSTRACT

The synthesis and characterisation of two homologous series of non-symmetric dimers are reported, the 1-(4-methoxybiphenyl-4?-yl)-6-(4-alkylanilinebenzylidene-4?-oxy)hexanes (MeOB6O.m, m = 1–10) and 1-(4-methoxybiphenyl-4?-yl)-6-(4-alkyloxyanilinebenzylidene-4?-oxy)hexanes (MeOB6O.Om, m = 1–9). All 10 members of the MeOB6O.m series exhibit the conventional nematic phase. At lower temperatures, the members with m = 1–7 formed the twist-bend nematic phase, N_TB, whereas for m = 8–10 smectic behaviour replaced the N_TB phase. All nine members of the MeOB6O.Om series also show the conventional nematic phase and for m = 1–3, a strongly monotropic N_TB phase is also observed. The alkyloxy terminated dimers show the higher values of T_NI and T_{NTB N} . For both series, the values of T_NI and T_{NTB N} show a modest alternation and in the same sense as m is increased. These observations suggest that the spatial uniformity of molecular curvature is important in driving the formation of the N_TB phase. The observation of smectic behaviour is attributed to the molecular inhomogeneity arising from the long terminal alkyl chain driving microphase separation. The transitional behaviour of these series is compared to those of the corresponding cyanobiphenyl-based series and overarching observations discussed.     

Sulfur-linked cyanobiphenyl-based liquid crystal dimers and the twist-bend nematic phase

ABSTRACT

The synthesis and characterisation of two series of cyanobiphenyl-based liquid crystal dimers containing sulfur links between the spacer and mesogenic units, the 4?-[1,ω-alkanediylbis(thio)]bis-[1,1?-biphenyl]-4-carbonitriles (CBSnSCB), and 4?-({ω-[(4?-cyano[1,1?-biphenyl]-4-yl)oxy]alkyl}thio)[1,1?-biphenyl]-4-carbonitriles (CBSnOCB) are described. The odd members of both series show twist-bend nematic and nematic phases, whereas the even members exhibit only the nematic phase. An analogous cyanoterphenyl-based dimer, 3⁴-{6-[(4?-cyano[1,1?-biphenyl]-4-yl)thio]-hexyl}[1¹,2¹:2⁴,3¹-terphenyl]-1⁴-carbonitrile (CT6SCB), is also reported and shows enantiotropic N_TB and N phases. The transitional properties of these dimers are discussed in terms of molecular curvature, flexibility and biaxiality. The same molecular factors also influence the birefringence of nematic phases. Resonant X-ray scattering studies of the twist-bend nematic phase at both the carbon and sulfur absorption edges were performed, which allowed for the determination of critical behaviour of the helical pitch at the transition to the nematic phase, the behaviour was found to be independent of molecular structure. It was also observed that despite the different molecular bending angle and flexibility, in all compounds the helical pitch length far from the N-N_TB transition corresponds to 4 longitudinal molecular distances.     

Nematic twist-bend phase under external constraints

ABSTRACT

The recently discovered twist-bend nematic phase, N_TB, has short-pitched heliconical structure with doubly degenerate handedness. In contrast to the classic nematic, in the N_TB phase the director is spontaneously distorted, resulting in unusual elastic properties. The response of the N_TB phase to external stimuli, like chiral doping or applied fields might provide further information about its structure and can find utilisation in practical applications. Here, the N_TB behaviour is theoretically investigated under chiral doping and strong electric fields. We show that the chiral doping removes the N_TB degeneration and modifies the conical tilt angle, leaving the pitch unchanged. Thus, the N_TB helical twisting power is very high and strongly non-linear. Under electric field, we consider separately the ferroelectric, flexoelectric and dielectric couplings. We show that the experiments reported so far disagree with the ferroelectric behaviour, indicating that the N_TB phase is not spontaneously polarised. On the contrary, the observed polar effects fit well with the flexoelectric coupling, confirming the degenerated heliconical structure of the phase. Under very strong fields, we predict a second-order twist-bend nematic – nematic phase transition due to the dielectric torque on the director.     

Developments in liquid-crystalline dimers and oligomers

ABSTRACT

Liquid-crystalline dimers and bimesogens have attracted much attention due to their propensity to exhibit the spontaneously chiral twist-bend mesophase (N_TB), most often by dimers with methylene spacers. Despite their relative ease of synthesis, the number of ether-linked twist-bend materials significantly lags behind those of methylene-linked compounds. In this work, we have prepared and studied a range of ether-linked bimesogens homologous in structure to the FFO9OCB; as with methylene-linked systems, it appears that it is molecular topology and the gross molecular shape that are the primary drivers for the formation of this phase of matter. Dimers and bimesogens are well studied within the context of the twist-bend phase; however, present understanding of this mesophase in oligomeric systems lags far behind. We report our recent efforts to prepare further examples of oligomeric twist-bend nematogens, including further examples of our ‘n+1’ methodology, which may allow the synthesis of high-purity, monodisperse materials of any given length to be prepared. We have observed that there is a tendency for these materials to exhibit highly ordered soft-crystalline mesophases as opposed to the twist-bend phase.     

Twist bend nematic liquid crystals prepared by one-step condensation of 4-(4-Pentylcyclohexyl) benzoic acid and alkyl diol

Twist bend nematic (N_TB)-forming 9OCCHP5 and 11OCCHP5 dimers were synthesised by one-step condensation of 4-(4-pentylcyclohexyl) benzoic acid and alkyl diol with yields as high as 80%. Although each dimer formed the N_TB phase only during the cooling process in a narrow temperature width as large as 4°C, their equiweight mixture formed an N_TB phase during both the heating and cooling processes, displaying elliptical polygonal domains and rope-like optical texture. The N_TB temperature range became wider by 29–38°C and reduced the orientational order parameter significantly from 0.39 to 0.29 with decreasing temperature.     

The oblique chiral nematic phase in calamitic bimesogens

ABSTRACT

The discovery of the oblique chiral (or, the twist-bend, N_TB) nematic phase predicted for bent-core mesogens has engendered much interest due to its unique structure and physical properties, and the possibility of use in the next generation of fast electro-optic technology. Bimesogenic calamitic as well as bent-core mesogens are found to form the N_TB phase. Here, we report direct measurements of the temperature dependence of the conical tilt and the evidence of volcano-like orientational distribution of molecules in the N_TB phase. Optical and x-ray scattering investigations of two single-component calamitic bimesogens and their mixtures show that, while the Maier–Saupe orientational distribution function (ODF) is valid for the higher temperature nematic phase, a generalised expansion in terms of even Legendre functions is needed for the N_TB phase. Temperature dependence of the ODFs and the order parameters 〈P₂(cosβ)〉, 〈P₄(cosβ)〉, and 〈P₆(cosβ)〉 has been measured in both phases. The parameters 〈P₂(cosβ)〉 and 〈P₄(cosβ)〉 increase/decrease in the N/N_TB phase with decreasing temperature, while 〈P₆(cosβ)〉 remains vanishingly small for all samples. The value of 〈P₄(cosβ)〉 becomes negative in the N_TB phase confirming a conical distribution of molecules as they follow a helical trajectory keeping the local director tilted at an angle α wrt the macroscopic director. The heliconical tilt calculated from ODFs, exhibits a power law behaviour with temperature, vanishing at the transition to the N phase.