A Nanohelicoidal Nematic Liquid Crystal Formed by a Non‐Linear Duplexed Hexamer

Abstract The twist‐bend modulated nematic liquid‐crystal phase exhibits formation of a nanometre‐scale helical pitch in a fluid and spontaneous breaking of mirror symmetry, leading to a quasi‐fluid state composed of chiral domains despite being composed of achiral materials. This phase was only observed for materials with two or more mesogenic units, the manner of attachment between which is always linear. Non‐linear oligomers with a H‐shaped hexamesogen are now found to exhibit both nematic and twist‐bend modulated nematic phases. This shatters the assumption that a linear sequence of mesogenic units is a prerequisite for this phase, and points to this state of matter being exhibited by a wider range of self‐assembling structures than was previously envisaged. These results support the double helix model of the TB phase as opposed to the simple heliconical model. This new class of materials could act as low‐molecular‐weight surrogates for cross‐linked liquid‐crystalline elastomers.

The phenomenon of spontaneous breaking of mirror symmetry manifests in aw ide range of scientific disciplines and ongoing problems,from subatomic physics to autocatalysis to biological homochirality. [1] Thet wist-bend modulated nematic phase (TB), predicted by Dozov, [2] possesses ah elical structure with ap itch length of approximately 10 nm; [3] this phase is chiral despite being typically formed by achiral molecules and is the first example of spontaneous symmetry breaking in aliquid system without accompanying positional order.T he TB phase was first identified in liquid-crystalline dimers, [4] and the relationship between molecular structure and the incidence of this phase has been an active area of research, with the majority of explored structural variations presented in Figure 1a. [5] Apart from being found in lowmolecular-weight dimers,the generation of the TB phase has been demonstrated in oligomers [6] and polymers. [7] TheT B phase exhibits af ast (microsecond) electrooptic response [8] and also provides as imple route to materials with defined nanostructures via in situ photopolymerisation, [9] which may find use in photonics. [10] Without exception, all examples of the TB phase are found in materials in which the rigid mesogenic units are mutually attached in al inear manner akin to am ain-chain polymer,t hereby inducing dimers to behave like polymers. We had suggested that the TB phase may have adouble helix structure, [11] and this idea has been revisited in some detail by others recently. [12] Such aphase structure,ifitexists,should be stabilised by duplexed oligomers in which two (or more) linear oligomers are laterally linked (shown in Figure 1d), whereas asingle helix would be destabilised (Figure 1b). We devised the novel trimer D11 3 and related duplexed hexamer D11 3 (2) as atest of this idea.
spectroscopy ( 1 Hand 13 C{ 1 H}) and APCI mass spectrometry, with purity of both the trimer and hexamer assayed by reverse phase HPLC.C omputational chemistry was performed in Gaussian G16; [14] conformer libraries were built via the MODREDUNDANT keyword with geometries and energies extracted via Matlab scripts as described. [15] Selected output files were visualised using Qutemol. [16] Full synthetic and instrumental details are given in the Supporting Information.
Thetrimer D11 3 and the hexamer D11 3 (2) were studied by polarised optical microscopy (POM) differential scanning calorimetry (DSC) and simultaneous small-and wide-angle X-ray scattering (SWAXS) to determine transition temperatures and phase types.T abulated transition temperatures and enthalpies of transition are given in Table 1.
Phase identification was made by ac ombination of microscopy and SWAXS experiments,w hereas transition temperatures and enthalpies were determined from DSC.The nematic phase exhibits ad istinctive schlieren texture (Figure 2a), which transforms into the blocky texture immediately following the TB-N transition (Figure 2b,c) which evolves into the rope-like texture with further cooling (Figure 2d). We confirm these phase assignments for D11 3 (2) by way of miscibility with CB9CB, [3a] ac ontact preparation shows the two materials are be mutually miscible in both mesophases and therefore our assignment of both phases is correct;p hotomicrographs are presented in the Supporting Information, Figure S1. Previous results indicate that lateral groups,b oth polar [5b, 6a] and non-polar, [11] tend to depress the thermal stability of the TB phase;y et dimerisation of the trimer D11 3 into the duplex trimer D11 3 (2) unexpectedly increases the TB-N transition temperature by over 30 8 8C. The enthalpy associated with the TB-N transition in both materials is comparable to prior (linear) oligomeric examples,a nd the transition is first-order. [6] During SWAXS study no scattering is observed from the TB helix during non-resonant SWAXS study (Figure 2f)a sh as been noted previously, [3a] although the lack of Bragg scattering supports our assignment as an ematic-like phase.T he intensity of the wide-angle scattering peak is significantly greater than that at smallangles,indicating both nematic and TB phases lack significant lamellar fluctuations (cybotaxis). Thed -spacing value of the small angle peak is temperature invariant and has av alue of 22.1 ,t his is shorter than the molecular length (see below). Thew ide-angle scattering peak has av alue of 5 ,w hich Scheme 1. Synthesis of D11 3 and D11 3 (2) from i1.  corresponds to the average lateral molecular separation. We do not observe any further scattering from the sample of D11 3 (2) at smaller angles (2q ! 0.78 8, q ! 0.5 À1 , d 125 ); this excludes the possibility of lamellar twist-bend phases with large layer spacings [17] and hypothetical splay-bend modulated nematic phases which should exhibit Bragg scattering at Q = 2p P SB ,where P SB is the splay bend modulation period. [3a] To rationalise SWAXS data we first obtained an optimised, fully extended all-trans structure of D11 3 (2) a at the B3LYP/6-31G(d) level of DFT (Figure 3b). Them olecular length of this conformer is 62 ;taken in conjunction with the d-spacing of the small angle peak in SWAXS experiments (22.1 )t his indicates the nematic and TB phases are both extensively intercalated, with no segregation of the different mesogenic units into layers (or pseudo layers) which would lead to Bragg (or quasi Bragg) scattering. Thes ingle broad SWAXS peak at small angles is most likely the centre-tocentre separation between mesogenic units; [7] although we do not observe differing scattering peaks for terminally (ca. 24 )a nd laterally (18 )a ppended segments of the molecule.This result is consistent with prior studies on TB forming oligomers,w hich exhibit small angle scattering at 1/n times the molecular length, [6b,c] where ni st he generation of oligomer (n = 3, trimer, n = 4t etramer, and so on) Asingle geometry neglects the flexibility of this molecule; assuming threefold rotation about each dihedral in the spacer gives an imposing number of conformers (4*(3 13)*3 9), which is too expensive to study computationally.W et herefore subdivided D11 3 (2) into two fragments,shown in Figure 3c,d. On each fragment we performed fully relaxed scans at the B3LYP/6-31G(d) level of DFT,allowing each flexible bond to adopt either trans or gauche states,g iving al ibrary of conformers.C learly this method ignores intermolecular interactions which could be important in the condensed LC phase,b ut it provides au seful approximation in this instance.For each conformer we calculate the angle between the two mesogenic units in question and aB oltzmann probability allowing us to present the probability weighted angles given in Figure 3. Within each linear segment the probability of agiven bend angle is skewed towards being bent owing to the odd parity of the spacer (Figure 3e). Them ajor distribution of bend angles is approximately Gaussian, centred at 1088 8 with aFWHM of about 258 8.M inor populations of linear (bend > 1508 8)a nd hairpin (bend < 308 8) conformers exist. Ab road range of angles are adopted between the two central terphenyl mesogenic units (Figure 3f); provided these two units are aw ay off perpendicular (< 758 8) the formation of adouble helical structure is favourable,a nd we note that there is adecrease in the probability of bend angles over about approximately 608 8.I ft he two central units are (close to) perpendicular then the resulting gross molecular shape would be globular,w ith the outer nitriles forming the apex of at etrahedron, rather than adouble helix. Presently it is not clear how flexibility (or lack thereof) of this part of the molecule impacts upon TB phase formation.
This conformational study indicates that D11 3 (2) is likely to adopt aw ide range of conformations,with many of these will being helical or double-helical structures.I fw ec onsider now the parent trimer D11 3 ,t he conformational landscape of this material is effectively defined by the biphenyl-terphenyl bend indicated in Figure 3d.T he formation of ad ouble helix structure by D11 3 relies on non-covalent interactions whereas D11 3 (2) forms this structure to covalent bonding of two trimers.T he observed enhancement in the thermal stability of the TB phase in D11 3 (2) relative to D11 3 suggests the double helix structure not only warrants further experimental study,b ut also suggests that entirely new classes of materials could exhibit this state of matter.W ea lso note the possibility of incorporating stimuli-or chemo-responsive groups (such as azo, [18] crown ether) into the lateral spacer to give functional, tuneable,orswitchable twist-bend materials.Just as linear LC Figure 3. a) Proposed double-helical structure of the TB phase formed by duplexed hexamers. b) Geometry of D11 3 (2) optimised at the B3LYP/6-31G(d) level of DFT;the dihedrals c 1-13 and c 14-23 were used to build conformerl ibraries of the fragments shown in (c) and (d) at using fully relaxed scans at the B3LYP/6-31G(d) level of DFT.e),f)Plots of the probability of agiven interaromatic bend angle from e) fragment cand f) fragment d. The solid line in (e) is aGaussian fit to the major peak.
dimers and oligomers are considered as good model systems for main-chain LC polymers, [19] we consider that the nematic phases of materials such as D11 3 (2) could be considered as low-molecular-weight surrogates for crosslinked nematic LC elastomers,w hich have attracted attention as actuators, sensors,a nd artificial muscle. [20] Furthermore,t he double twisted structure could form ac able-or rope-like arrangement, leading to entirely new forms of matter.
We observe ar emarkable stabilisation of the nanohelical TB phase by covalently bonding two trimers together, affording ad uplexed hexamer. Previous studies show that lateral substitution at the mesogenic units leads to diminished TB phase stability;however,inthe present case the linking of two trimers together actually affords an increase.Rather than forming as ingle helix the duplexed hexamer is conformationally biased towards double helix formation, and computational studies on the conformational landscape support this idea. We consider that the present results support the double helix model of the TB phase which we had previously proposed, [11] and has been revisited in more detail by others recently. [12] There is an eed for development of theoretical models of this phase that account for such ahelical structure. Theo bservation of the TB phase in an on-linear oligomer prompts ar e-evaluation of previously held beliefs about the type of molecular structure required to exhibit this nanohelical phase of matter.