Rational Design of Rod‐Like Liquid Crystals Exhibiting Two Nematic Phases

Abstract Recently, a polar, rod‐like liquid‐crystalline material was reported to exhibit two distinct nematic mesophases (termed N and NX) separated by a weakly first‐order transition. Herein, we present our initial studies into the structure–property relationships that underpin the occurrence of the lower‐temperature nematic phase, and report several new materials that exhibit this same transformation. We have prepared material with significantly enhanced temperature ranges, allowing us to perform a detailed study of both the upper‐ and lower‐temperature nematic phases by using small‐angle X‐ray scattering. We observed a continuous change in d spacing rather than a sharp change at the phase transition, a result consistent with a transition between two nematic phases, structures of which are presumably degenerate.


Introduction
The nematic liquid-crystalline state-asw as exhibited by lowmolar-mass liquid crystals-is characterised by relatively high fluidity,alack of positional ordering of molecules, but with short-range orientationalo rder.T ransitions from one nematic phase into another are rare, but also highly topicald ue, in part, to the recent discovery of the twist-bend nematic phase. [1][2][3][4][5][6] Severalo ther nematic or nematic-likem esophases are knownt oe xist (chiral nematic (N*), discotic nematic (N D ), [7] re-entrant nematic (N RE ), [8] biaxialn ematic (N B ), [9,10] blue phases (BPI, BPII, BPIII)) or are either predicted to exist or have possibly been discovered (cubaticn ematic (N cub ), [11] splay-bend nematic (N SB ) [12,13] ). Recently,w eh ave reported ap olar liquid-crystalline material( 1,T able 1) that exhibited two distinct nematic mesophases,w ith aw eakf irst-ordert ransition between the two phases. [14] Other examples of nematic-to-nematic transitions have been observed in binary mixtureso fr e-entrant materials, [15] in frustratedc hiral rod-like systems [16] and in main-chain liquid crystal polymers. [17] In terms of response to appliede lectric fields, the two nematic phases are similar, exhibiting a FrØedericksz transition with threshold voltages of approximately 0.3 Va nd approximately 0.45 Vi nt he Na nd N X phases, respectively.C onnoscopyd emonstrates the uppert emperature nematicp haseo f1 to be uniaxial and optically positive;h owever,f ollowingt he N X -N transition, the homeotropic alignment is lost, andaschlierent exture obtained:t herefore, it is unclear if this lower temperature nematic phase is uniaxial or biaxiala t this time. For compound 1,t he N X -N transition occurs at 85.6 8C( determined by DSC);h owever,t his is below the melting point of the material, and the mesophase is therefore metastable;i ft he properties and local structure of the N X phase are to be understood,i ti si mportant that materials with superior working temperaturer anges are developed.
Given that only one materiali sk nownt oe xhibit this nematic-to-nematic transition, as tructure-property relationship is presently absent. Herein, we follow up on our earlierw ork by describing how the occurrence or absence of the N X mesophase exhibitedb yc ompound 1 depends on molecular structure as showni nF igure 1, with the ultimate aim of preparing materials with superior working temperatures to that of the parentc ompound, and whichc ould be subjected to in-depth study across the N X -N phase transition. Table 1. Transition temperatures, associatede nthalpies of transition and dimensionless entropies of transition for compound 1,a sw as determined using DSC at ah eat/cool rate of 10 8Cmin À1 . [14] MP N X -N N-iso

Experimental Section
4-Hydroxy-4'-nitrobiphenyl was prepared as was described previously. [18] Chemical reagents were purchased from commercial suppliers (Sigma Aldrich, TCI, Fluorochem and Apollo Scientific) and used without further purification. Solvents were purchased from Fisher Scientific and dried by percolation through activated alumina prior to use. Polarised optical microscopy was performed on a Zeiss Axioskop 40Pol microscope by using aM ettler FP82HT hotstage controlled by aM ettler FP90 central processor.P hotomicrographs were captured via an InfinityX-21 MP digital camera mounted atop the microscope. Differential scanning calorimetry (DSC) was performed on aM ettler DSC822 e calibrated before use against indium and zinc standards under an atmosphere of dry nitrogen, with DSC data then processed in Matlab. Computational chemistry was performed by using Gaussian G09 (Revision E.01) [19] on the York Advanced Research Computing Cluster (YARCC), as was described in the text. Small-angle X-ray diffraction was performed by using aB ruker D8 Discover equipped with at emperature controlled, bored graphite rod furnace, custom built at the University of York. The radiation used was Cu Ka (l = 0.154056 nm) from a1mS microfocus source. Diffraction patterns were recorded on a2 048 2048 pixel Bruker VANTEC 500 area detector set at ad istance of 121 mm from the sample, allowing simultaneous collection of small angle and wide angle scattering data. Samples were filled into 0.9 mm O.D. capillary tubes and aligned with ap air of 1T magnets, with the field direction being perpendicular to the incident X-ray beam. Diffraction patterns were collected as af unction of temperature, and the data was processed by using custom Matlab scripts. Raw data are available upon request from the University of York data catalogue. Full experimental details, including synthetic schemes and chemical characterisation, are given in the Supporting Information.

Results and Discussion
Initially,w ep repared as election of compounds analogous in structure to 1 but with varying terminal chain lengths. Transition temperatures and phase identification were determined with ac ombinationo fp olarised-light opticalm icroscopy (POM),d ifferentials canning calorimetry (DSC) and variable temperature small angle X-ray scattering (VT-SAXS), as summarisedb elow in Ta ble 2.
Increasing the length of the terminal chain from C2 in the parentc ompound led to the loss of the N X phasea long with modest reductions in melting point and clearing point, thereby indicating that the N X phase is preferred when potential nanosegregation is minimised. Thus, shortening the terminal chain to C1 (i.e.,O Me) affords compound 2,a nd relative to the parentc ompound, this structuralc hange gives al arge increase in the onset temperature of the N X phase. Representativep hotomicrographs are shown in Figure 2c-e. The enthalpy associated with the N X -N transition for both 1 and 2 is vanishingly small (0.2 kJ mol À1 for both), and this results in the associated entropy of transition being extremely small forb oth materials (DS Nx-N /R, 0.06 and 0.07 for 1 and 2,r espectively). As was noted by us previously,t he small value of the enthalpy/entropy associated with the N X -N transition is consistentw ith a transition betweent wo phases with the same macroscopic symmetry. [14] Ap hase diagram was constructed between 1 and 2 as shown in Figure 2a.B oth compounds 1 and 2 were found to be miscible at all concentrations with both the N-Iso and N X -N transition temperatures varying approximately linearly with concentration and therefore confirming the N X phase is indeed exhibited by both materials. Given that al inear relationship exists between concentration and T Nx-N ,w ew ere able to obtain "virtual" transition temperatures by extrapolationf or materials that do not exhibit this mesophase or exhibit it at temperatures that are experimentallyi naccessible. We also constructed ap hase diagram between compounds 1 and 3 (Figure 2b), both materials are miscible across all concentrations studied,b ut the N X phase was found to decrease linearly with increasing concentrationo f3,d isappearing at 43 wt %. By using al inear fit, we obtained av irtual (i.e.,e xtrapolated) N X -N transition temperature of approximately 8.5 8C. As was demonstrated by the materials in Table 2, the N X -N transition apparently displays no odd-even effect with regards to the terminal chain length, again confirming that nanosegregation associated with the aromatic to aliphatic proportions strongly influences mesophase formation.  [a] An extrapolated "virtual" transitiont emperaturew as determined by linear fitting of T Nx -N versus concentration ( Figure 2b); however,t he material does not exhibit this phase in its neat state.
We subjected compound 2 to analysisb yS AXS with the intention of studying the change in scattering as af unction of temperature across both nematic phases.S imilar to compound 1,w eo bserved that the scattering of X-rays by 2 was weak, and thusw er equired relativelyl ong exposure times to obtain good signal-to-noise ratios.D espite the increase in the N X -N transition temperature afforded by compound 2,w eo bserved that the material was still pronetocrystallisation during experimental studies, and so we werel imited to collecting individual SAXS frames at specific temperatures rather than across the entire phase range.
In both the higher-and lower-temperature nematic phases, the observed scattering was broadly similart ot hat reported previously for 1; [14] three diffuse peaks were seen at "small" angles parallel to the external aligningf ield (i.e.,a long the director,F igure 2c). The positions of each of the three peaks were determined by deconvolution (Figure 4), the resultsa re presented in Ta ble 3. Although the d spacing of peak 1( smallest value of Q)i sc omparable,ifnotably larger than, the molecular length of 2 (calculated to be 20.5 at DFT(B3LYP/6-31G(d)) the other two peaks occur at significantly smaller d spacing.
In both the nematic and N X phases,w eo bserved two peaks at "wide" angles (i.e.,p erpendicular to the aligning field and the director,F igure 3d); ab road peak at large values of Q,a nd al ess intense broad peak at small values of Q (Q = 0.3565 À1 , d = 17.7 ). The scattering perpendicular to the aligningf ield is ac onsequence of the average lateral separation of the molecules, given that compound 1 has been demonstrated to form extensive antiparallel pairs, it is unsurprising that the wideangle peak is so broad,b ecause many different forms of pairing are likely to exist (dimer,t rimer,… n-mer). The broad peak can be deconvoluted into two separate peaks ( Figure 4, Q = 1.0018 and 1.2755 À1 ,e qualt od = 6.3 and 4.9 ,r espectively);  4.9 is close to the width of an individual molecule and so we speculate that 6.3 is the width of ap aired species. It is interesting to note that the positiono fe ach individual peak is the same in both the Na nd N X phases;h owever,t heir relative size changes with the intensity of the peak at 6.3 increasing and that of the peak at 4.9 decreasing. If we assume that 4.9 and 6.3 are indeed the widths of an unpaired molecule and a paired species, respectively,t hen this suggests the degree of dimerisation is inverselyp roportionalt ot emperature and therefore higheri nt he N X phase than in the nematic, ar esult consistentw ith measuremento ft he Kirkwood factor of compound 1. [14] Next, we prepared as eries of compounds with varyingl ateral group, allowing us to assess how variations to the steric bulk of the lateral unit impact upon the N X -N transition. We also studied how moving this lateralg roup from the 2-to the 3-position of the left-hand ring (8)i mpacts on mesomorphic behaviour.T he melting properties for these compounds are given in Ta ble 4a long with the parent material( 1)f or comparison.
Materials, in which the lateral group is smaller than methoxy (7, 9 and 10)d on ot exhibit the N X phase, whereas repositioning the methoxy group fromt he 2-position to the 3-position (8)a lso leads to the loss of the N X phase. Increasing the length of the lateral alkyl chain, and hence the bulk volume, leads to ar eduction in clearing points (Figure5)a nd either as mall in-   and associated enthalpies of transition [kJ mol À1 ]f or compounds 7-12,i nt he case of compound 9 (denoted with a hash)t he material begins to decompose before the clearingp oint at 240 8Ci sr eached. An extrapolated "virtual"t ransition temperature was determined by linear fitting of T Nx -N versusc oncentrationf or 7, 9 and 10 (see Figure6); however, these materials did not exhibit the N X phase in their neat state. [b] An extrapolated "virtual" transition temperature was determined by linear fitting of T NX ÀN versus concentrationf or compounds 7, 9 and 10 ( Figure 6);h owever, these materials did not exhibit the N X phase in their neat state. Compounds 7, 9 and 10 do not exhibit the N-N X transition in their neat state, and so virtualt ransition temperatures were obtainedb yc onstructingp hase diagrams between these materials and the standard compound 1.L inear fitting of T Nx-N as af unction of concentrationa ffords the virtualt ransition temperature. Phase diagrams are presented in Figure 6, the virtual T Nx-N values were found to be, respectively, À23.8, 1.8 and 32.7 8Cfor 7, 9 and 10.
We next explored how the magnitude of the lateral dipole momenti nfluenced the N X -N transition by preparing compounds 13 and 14 (Table 5). Positioning af luorine atom ortho to the nitro group in compound 1 gave 13,w hich compared to the parent material exhibitedasignificant increasei nt he N X -N transition temperature, as well as as ignificantly reduced clearing point. Conversely,i fat erminal nitrile is used in place of the nitro group, the N X phase is suppressed.I na na ttempt to rationalise this, we calculated dipole moments at the B3LYP/ 6-31G(d) level of DFT.T he dipole moment of 13 is, predictably, larger (12.5 Debye) than that of both 1 (11.7 Debye)a nd 14 (11.5 Debye), suggesting that the magnitude of the dipole momentisimportant to the formation of this phase. Phase diagrams were constructed for binary mixtures of compound 1 with 13 and 14 ( Figure 7). Across both phase diagrams, the clearing point was observed to vary linearly with concentration. For mixtures of 1 and 13,t he N X -N transition was found to vary linearly with concentration( T NX-N = 30.393 x + 80.043, R 2 > 0.96), indicating that the lower temperature mesophase    exhibitedb yt hese two materials is the same. However,f or mixtures of 1 and 14,t he N X phase wasn ot observed even at low concentrationso f14 ( % 10 wt %). Studyingc ompounds 1, 13 and 14,i ti st empting to hypothesise about the role of the electric dipole moment: 13 has the largest dipole moment and the highestN X -N transition temperature; 1 has as maller electric dipole moment than 13 and al ower N X -N transition temperature; 14 has as maller dipole momentt han 1 and does not exhibit the N X phase. Althoughasmall sample size, this hints that reducing the magnitude of the molecular electric dipole moment also serves to reduce the thermals tabilityo ft he N X phase. As at est to this hypothesis, we prepared two materials, in one of which ac arboxylate ester was removed (15), and another-in which a single carboxylate ester had itso rientation "reversed" relative to that of the parentc ompound (16). Both structural modifications would be expected to reduce the molecular dipole moment, and we confirmed this with DFT(B3LYP/6-31G(d)) calculated dipole moments. In the case of the modulated twistbend phase, this reversal of carboxylate esters was found to impact on the thermals tability of the TB phase. [21] As will be discussed shortly,w ea lso prepared several materials with larger dipole moments to test this hypothesis.
With regards to the ester unit, its removal (to give the biphenylbenzoate 15)orr eversal (to give the phenyl4-nitrobenzoate 16)r esults in the loss of the N X -N phase transformation and gave materials that are only nematogenic, with both 15 and 16 having ah igherm elting point than the parent 1. Dipole moments were calculated at the B3LYP/6-31G(dp) level to be 10.04 and 8.26 Debye for 15 and 16,r espectively.B oth materialse xhibit an ematic phase;h owever,n either exhibits the N X -N transition. Construction of ap hase diagramb etween 1 and 15 and linear fitting of T Nx-N versus concentration gave the extrapolatedv alue shown in Ta ble 6, with the phase diagram presented in Figure 8.
Most structural modificationst ot he molecular structure of compound 1 were found to suppress the formation of the N X phase, with the exception of reducing the length of the terminal ethoxy chain to methoxy (2)a nd increasingt he dipole momentb yi ncorporating af luoro substituent ortho to the terminal nitro (13). Combining these two features gave 17.C om-pounds 18, 19 and 20 were prepared to furthers tudy how the molecular dipole momenta nd terminal groups influences the nematicand N X phases. Transition temperatures and associated enthalpies of transition are given in Table 7.
Compared to the parent material, compound 17 haso nly a modest increasei nt he onset temperature for the N X to nematic phase transition, with significantly reduced isotropisation temperature and ah igherm elting point. As was expected, the cyano-terminated material 18 did not exhibit the N X phase (mirroring the behaviour of 14). Compounds 19 and 20 were prepared to determine if the incidence of the N X phase is specific to nitro-terminated materials, or if it can be formed by compounds with other suitably polar groups. There are several reports of liquid-crystalline materials incorporating the pentafluorosulfanyl (SF 5 )g roup; [18,[22][23][24][25][26] given the large dipole moment, we considered that am aterial analogoust o1/17 but with this terminalg roup in lieu of the nitro group may yield the N X -N polymorphism;h owever,c ompound 21 exhibited only am onotropic nematic phase, but didn ot exhibit aN X -N transition. Because both materials exhibited only an ematic phase, it would appear at presentt hat an itro group is essential, but given the limited set of compounds known to exhibit this phase, it is perhaps too early to draw firm property-struc- Mixturescontaining morethan approximately 10 wt %o f15 recrystallize prior to the N X -N phaset ransition; the error in this extrapolated valuei st herefore higher than for others in this work and is estimated to be AE 7 8C.  No. X= R 1 R 2 Cr N X NIso ture correlations.D ipole moments for each of the materials presented in Table 5w ere calculated at the B3LYP/6-31G(dp) level of DFT:1 1.37 Debye for 2;1 2.14 Debye for 17; 11.13 Debye for 18; 12.00 Debyef or 19;1 2.84 Debye for 20; 10.53 Debye for 21.F or the nitrile-terminated compound 18, the calculated dipole moment is intermediate between the two nitro-terminated materials 2 and 18, both of which exhibited the lower temperature nematic phase. The present results suggest that it is not the magnitude of the dipole moment of an individualm olecule that dictates the incidence of the lower temperature nematic phase,but rather some property inherent to the nitro group, for instance, the extento ft he delocalization of the electrons,a nd hence polarizability,o ver ab roader functional group than nitrile. One of our objectivesw as to obtain materials exhibiting an enantiotropic N X phase, rendering them amenable to further study;h owever,t his was not met. The thermal stability of the N X -N transition is highest when the material features short terminal chains andah ighly polar terminal nitro group;h owever, these conditions also (predictably) lead to high meltingp oints. Using transition temperatures and enthalpy data obtained by DSC, we used the modificationt ot he Schroder van Laar equation reported by Raynes to predict both the composition and transition temperatures of the eutectic blends of an umber of possible binary mixtures. [27] This methodp redicted that the eutectic mixture of 2 and 17 should exhibit an enantiotropic N X transition (N X -N 134.5 8C, with am eltingp oint of 126.0 8C).
The phase diagram of binary mixtures of 2/17 is shown in Figure 9. Althoughi tw as found that the experimentalm elting points were somewhat highert han predicted,t he mixture containing approximately 24 wt %of17 exhibiteda ne nantiotropic N X phase. Given thep ropensity of nitro-terminated materials to form antiparallel pairs, it may be that considering the phase diagram as being "binary", is misleading due to the formation of AA, AB andB Bp airs in addition to the unpaired species (in which A/B = 2/17), and this may be account for the underestimation of the melting point. Because the N X -N and N-iso transition temperatures are simply aw eighted average of the two pure components, we observed predicted valuest ob er easonably close to those determined experimentally.
Similar to initial study,w ep erformeds malla ngle X-ray scattering as af unction of temperature (3 8Cs teps), and by using the radial averaging procedure outlined in Figure 3, we separately obtained scattered intensity parallela nd perpendicular to the director.S cattering data for the eutectic blend of 2/17 is presented as heatmap plots in Figure 10 for whichthe material was studied across ar ange of temperatures in 3 8Cs teps from the isotropic liquid (186 8C) deep into the N X phase (91 8C). The temperatures at which phase transitions occurred are marked on the heatmap plots with dashed lines;u pon cooling from the isotropic liquid into the nematic phase, there is as ignificant change in the scattering pattern;h owever,a tt he N X -N transition, there is little if any change. However,t here is ac ontinual reductioni nt he intensity of the small-angle peaks as a functionoft emperature. The relatively weak scattering at small anglesi ndicates that there is no build-up of pretransitional cybotactic smecticd omains within either the nematic or N X phases. [28,29] Thus, the nematic-to-nematic transition described herein is presumably distinct from those observed in reentrant systems, such as those described in reference [15].F itting the scattered intensity at each temperature allowed us to obtain the position of both small-and wide-angle peaks. Thereisl ittle change in peak positions at small angles (i.e.,p arallel to the director;F igure 10 c) upon cooling from the upper temperature nematici nto the lower temperature "N X ". At wide angles (i.e., perpendicular to the director), the two peaks overlaps ignificantly,a nd although the deconvolutedp eaks do not shift in position (Figure 10 d), we observed that the intensity of peak #1 (Q % 1.1 À1 , d % 5.7 )i ncreased relative to that of peak #2 (Q % 1.3 À1 , d % 4.8 ), leading to at emperature-dependent reductioni nt he Q value of the concurrent peak. Assuming that the earlier hypothesis that peak #2 is the width of asingle molecule, and that peak #1 is the intermolecular spacingo fa dimer pair then the this change in intensity can be understood as being ac onsequence of the increase in pairing of molecules as af unctiono ft emperature. This interpretationo ft he SAXS data is consistentw ith the measurement of the Kirkwood factor of compound 1.
In our initial study on 1,w en oted that the N X -N transition could either occur as ac onsequence of ac ontinual change in the concentration of dimers to unpaired molecules, or alternatively at the transition, there may be ad iscontinuousc hange in this concentration. The present SAXS data supports the former;t he degree of pairing increases continually with reducing temperature, at some critical concentration the degree of pairingi ss ufficient to lead to the N X phase, and af irst-order phase transition occurs. In this sense, the formation of the N X phase proceeds via acomparable mechanism to that described by Cladis for the reentrant nOCB materials (i.e.,4 -alkoxy-4'-cyanobiphenyl, where n is the number of methylene units), althought here is no intervening smectic mesophase in the present case. To date, we have only observed the N X phase in nitro terminated materials, presumablys ome property of the nitro group leads to as pecific pairing, which is crucial to the incidence of this phase.

Conclusions
Compound 1 was previously demonstrated to exhibit two nematicm esophases (N X and N) separated by af irst-order phase transition of small enthalpy;h owever,b ecause the N X -N transition is monotropic-occurring approximately 50 8Cb elow the meltingp oint-detaileds tudy is complicatedb yc rystallisation of the sample. Herein, we have investigated the molecular features that give rise to this phase sequence with av iew to producing materials with superior workingt emperatures to compound 1.
By using the onset temperature of the N X -N phase as am easure of the thermal stability of the lower temperaturen ematic, we found the following property-structurec orrelations:)N X mesophase is promoted by as hort terminal chain (ethoxy or preferably methoxy);2 )terminal nitro group is essential; 3) thermal stabilityc an be increased by positioning additional fluoro groupst oe nhancet he molecular dipole moment; 4) use of otherterminal polar groups (nitrile, pentafluorosulfanyl) or removal/reversal of carboxylate esters (which reduce the dipole moment) is detrimental to N X phase formation;a nd v) lateral "bulky"g roup is required for am aterial to exhibit the N X phase.
By using each of these correlations, we prepared am aterial designed to exhibit ah igh N X -N onset temperature (17), and althoughw eo bserved significantly enhancedt hermal stability of the N X phase relative to that of parent compound (1), the materiala lso exhibited ah igh melting point,w hich is perhaps unsurprising given the large dipole moment and short terminal chains. However,b inary mixtures of 17 with 2 gave an eutectic mixturet hat exhibits an enantiotropic N X phase. Studies of this materialb yX -ray scattering confirmed the identity of both mesophases,a nd allowed us to present SAXS and WAXS data across the entire temperature range, and results suggests a continuous change in the degree of pairing rather than aj ump at the N X -N phase transition.