The ferroelectric nematic phase: on the role of lateral alkyloxy chains

ABSTRACT The synthesis and characterisation of the 4-({[4’-nitro-(1,1’-biphenyl)−4-yl]oxy}carbonyl)phenyl 2-alkoxy-4-methoxybenzoates are reported: the 1O(m-On)PEPEBNO2 series. These materials include an additional phenyl ring compared to the extensively studied ferroelectric nematogen RM734, added to increase the liquid crystal transition temperatures. All members of the series exhibited both conventional nematic (N) phase and ferroelectric nematic (NF) phases; TNI and TNFN both decrease on increasing n, the length of the lateral alkoxy chain. The properties of this four-ring series are compared with analogous three-ring laterally substituted variants of RM734; the addition of the extra phenyl ring has a significantly more pronounced effect on the value of TNI than on TNFN. The increase in TNI may be attributed to the enhanced structural anisotropy and more favourable intermolecular interactions arising from the insertion of the phenyl ring, whereas the much weaker effect on TNFN may reflect a change in the shape of the molecule. We also report two materials with three-ring structures, the 4’-nitro-(1,1’-biphenyl)-4-yl 2-alkoxy-4-methoxybenzoates: 1O(m-On)PEBNO2 (n = 1 and 2). The removal of the ester linkage between RM734 and 1O(m-O1)PEPNO2 extinguishes the NF phase and this appears to be consistent with a model in which the molecules are described in terms of a longitudinal surface charge density wave. Graphical abstract


Introduction
The least ordered liquid crystal phase, the conventional nematic phase (N), is technologically the most significant, being used extensively in display devices [1].In the N phase, the centres of mass of the rod-like molecules are arranged randomly, but their long axes are pointed along a common direction known as the director, represented by the unit vector n, Figure 1(a).The N phase has inversion symmetry (i.e.n = -n) and is therefore nonpolar.Predictions of a polar nematic phase -one without inversion symmetry (n ≠ -n, Figure 1(b)) -were made first by Max Born in 1916, who suggested that such a polar fluid would exist if its constituent molecules possessed sufficiently large dipole moments that dipoledipole interactions between molecules could overcome thermal fluctuations [2].Experimentally, however, such a phase was only observed over a century later.In 2017, independent and simultaneous reports described two materials -RM734 [3,4] and DIO [5], Figure 2 -that exhibited ferroelectric ordering in a nematic phase at temperatures below the conventional N phase [6].This lower temperature nematic phase, later assigned as the ferroelectric nematic phase (N F ), shows a huge spontaneous polarisation and strong non-linear optical response [6,7].These remarkable properties, coupled with nematic fluidity, are not only of huge fundamental significance but also endow the N F phase with the very real potential to revolutionise liquid crystal-based technologies.
The rational design of materials capable of exhibiting the N F phase requires an understanding of the relevant structure-property relationships and these empirical relationships have still to be established let alone understood.The archetypal ferroelectric nematogens, RM734 and DIO, both have large longitudinal molecular dipole moments and some degree of lateral steric bulk -either a lateral methoxy group or a large degree of fluorination, respectively -features that appear to be pre-requisites for the observation of the N F phase.Relatively subtle structural changes to these molecules have yielded a range of materials that show ferroelectric nematic behaviour [8][9][10][11][12][13][14][15][16][17].Most recently, a supramolecular hydrogen-bonded ferroelectric nematogen has been reported that has a much smaller longitudinal dipole moment than the covalently bonded examples [18].This highlights the pressing need to enhance our understanding of the structural features required to observe the N F phase and this can only be achieved through the synthesis and characterisation of new materials.
We recently reported the effect of lengthening the lateral alkoxy chain in two series of materials based on RM734, 5-m and 6-m, the former is shown in Figure 2 [19].This study revealed that the bulky lateral alkyloxy chain stabilises the N F phase relative to the N phase, and here we seek to exploit this ability of the N F phase to tolerate bulky lateral substituents and report the synthesis and characterisation of the 4-({[4'-nitro-(1,1'-biphenyl)-4-yl]oxy}carbonyl)phenyl 2-alkoxy−4-methoxybenzoates, Figure 3.These materials include an additional phenyl ring compared to RM734 in an attempt to increase the liquid crystal transition temperatures.The materials are referred to by the acronym 1O(m-On)PEPEBNO 2 , where 1O is the terminal methoxy group, P a phenyl ring, E an ester, B a biphenyl moiety and NO 2 the nitro terminal group.The bracketed part denotes the lateral alkyloxy chain, where n is the number of carbon atoms in the chain and m signifies that the lateral group is in the   meta position with respect to the terminal chain.The homologues with n = 1-9 have been studied, and their properties compared to those of the 5-m series.

Synthesis
The synthetic route used to prepare the 1O(m-On)PEPEBNO 2 series is shown in Scheme 1 and the 1O(m-On)PEBNO 2 series in Scheme 2. A detailed description of the preparation of all intermediates and final homologues along with structural characterisation data is provided in the Supplementary Information.

Optical studies
Phase characterisation was performed using polarised optical microscopy (POM), using an Olympus BH2 polarising light microscope equipped with a Linkam TMS92 hot stage and a Zeiss AxioImager A2m equipped with a Linkam THMS600 hot stage.Planar aligned cells with an ITO conducting layer and a cell thickness of 2.9-3.5 μm were purchased from INSTEC.

Thermal studies
Thermal behaviour of the materials was studied using differential scanning calorimetry (DSC) using a Mettler Toledo DSC1 equipped with a TSO 801RO sample robot and calibrated using indium and zinc standards.Heating and cooling rates were 10°C min −1 in all cases, with a 3-min isotherm between heating and cooling segments.Thermal data were extracted from the second heating trace unless otherwise stated.Samples were run in  duplicate and an average of the two measurements of temperature and entropy change is reported.The thermal stability of 1O(m-O1)PEPEBNO 2 was evaluated using thermogravimetric analysis (TGA) using a Mettler Toledo TGA2 STAR e system equipped with a small furnace (1100°C limit) and a sample robot.

Molecular modelling
The geometric parameters of the 1O(m-On)PEPEBNO 2 series were obtained using quantum mechanical DFT calculations with Gaussian09 software [20].Optimisation of the molecular structures was carried out at the B3LYP/ 6-31 G(d) level of theory.Visualisations of electronic surfaces were generated from the optimised geometries using GaussView5 software and visualisations of the spacefilling models were produced post-optimisation using the QuteMol package [21].

Results & discussion
The transitional properties of the 1O(m-On)PEPEBNO 2 series are listed in Table 1, and the dependence of the transition temperatures on the length of the lateral chain is shown in Figure 5.All the reported members of the series show N F and N phases; the N phase is enantiotropic for n = 1-7 and monotopic for n = 8 and 9.The homologue with n = 1 decomposes prior to clearing (seen in DSC and TGA traces, shown in Figure S1 and S2, respectively) and thus the value of T NI reported for this is a low estimate.The ferroelectric nematic phase is strongly monotropic for all homologues i.e.T NFN falls far below the melting point such that crystallisation precludes the observation of the transition using DSC (see Figure S3 for an example) and instead is only observed by extensive supercooling when viewed through a polarised optical microscope.
The N and N F phases were assigned based on optical textures observed using POM.Specifically, N phases were assigned by observing either a characteristic schlieren texture containing two-and four-point brush defects, which flashed when subjected to mechanical stress, or a uniform texture when viewed between untreated glass slides and in planar aligned cells, respectively.A representative texture is given in Figure 6(a).The scaled entropy changes associated with the nematic-isotropic transition are consistent with this assignment.The value of ΔS NI /R decreases on increasing n and this may reflect the increasing biaxiality of the compounds as the length of the lateral chain is extended [22,23].
Cooling the N phase saw a striking change in birefringence and the emergence of domain boundaries, see Figure 6(b).The orientation of the director differs between the domains and thus has different polarisations.The formation of these domains is thought to be driven by director splay deformations and is required to connect the opposite polarisation vectors on the lower and upper cell surfaces [8].This texture has been termed a 'banded' texture and is thought to be characteristic of the N F phase [11,19].The highly monotropic nature of the N F phase precluded its study using dielectric spectroscopy or second harmonic generation measurements, normally used to confirm the assignment of the N F phase, due to rapid crystallisation of the sample nearly simultaneous with the N F -N transition.To confirm our phase assignments, we have instead constructed binaryphase diagrams using mixtures of the well-characterised ferroelectric nematogen RM734 with two of our materials, homologues n = 4 and n = 7, and these are shown in Figure 7. Complete miscibility between the two components was observed over the whole composition range, confirming the N and N F assignments.The textures observed were the same as those shown in Figure 6.The values of T NI increased as the concentration of RM734 decreased in both phase diagrams, whereas the values of T NFN showed a linear decrease on decreasing the concentration of RM734 in the mixtures.The virtual values of T NFN estimated from the phase diagrams for n = 4 and n = 7 were in excellent agreement with the temperatures found for the pure compounds using POM, providing further confirmation of these phase assignments.
The dependence of transition temperatures on the length of the lateral chain, n, for the 1O(m-On)PEPEBNO 2 series is shown in Figure 5.The shortest homologue, n = 1, has the highest value of T NI (although as noted in Table 1, this is accompanied by decomposition), and on increasing n, there is an initial sharp drop in T NI which lessens at values of n ≥ 3 to a more gradual decrease.T NFN also decreases on increasing n; however, the values appear to reach to a limiting value in homologues with n ≥ 6.The melting points do not appear to show a regular dependence on varying n.
The transition temperatures of the 1O(m-On)PEPEBNO 2 series are compared with those of the structurally similar 5-m series, Table S1, in Figure 8 [9,19].We note that 5-1 is the extensively studied RM734, Figure 2. The replacement of the nitrophenyl group in 5-m by a nitrobiphenyl moiety in the 1O(m-On)PEPEBNO 2 series has a substantial impact on T NI which increases, on average, by 155°C.This increase may be attributed to the enhanced intermolecular interactions between the mesogenic units, in addition to the greater shape anisotropy endowed by the additional phenyl ring, Figure 9.The values of T NI for both series decrease as the length of the lateral alkyloxy-chain increases and appears to converge towards or reach a limiting value.Similar behaviour was first reported for low molar mass mesogens containing a lateral alkyl chain by Weissflog and Demus [24,25] and was thought to imply that the lateral alkyl chain adopts conformations in which it lies parallel to the molecular axis, although such an assumption is not required to account for this behaviour [26].
The values of T NFN for the 1O(m-On)PEPEBNO 2 and 5-m series are more similar and on average 24°C higher for the 1O(m-On)PEPEBNO 2 series than for the  corresponding member of the 5-m series.Their dependence on the length of the lateral chain is very similar but weaker than that seen for T NI .This may reflect that increasing the chain length inhibits the anti-parallel associations between the molecules and offsets the dilution factor associated with increasing the volume fraction of chains.
The question is how to account for this increase in the values of T NFN on the insertion of the phenyl ring?We saw earlier that the longitudinal molecular dipole moment is thought to be important in driving the formation of the N F phase, but this is just 0.31 D higher for 1O(m-O1)PEPEBNO 2 than for 5-1 (RM734) -the dipole moments being 11.71 D and 11.40 D, respectively -and this would appear too modest an increase to account for the change in transition temperatures.The enhanced structural anisotropy resulting from the insertion of the phenyl ring changes the molecular shape of 1O(m-O1)PEPEBNO 2 and should not be thought of as simply increasing the length-to-breadth ratio compared to that of 5-1.It may be that the increase in T NFN reflects this change in shape.Alternatively, Madhusudana has proposed a model in which the rodlike molecules in the N F phase may be described as possessing longitudinal surface charge density waves and the interaction between these drives the formation of the N F phase [27].Within the framework of the model, the rod-like molecules are represented by regions of alternating positive and negative charges dictated by the electron-withdrawing or donating nature of the functional groups substituted onto the aromatic rings.One terminus of the rod is positively charged and the other negatively, giving a net longitudinal dipole moment.If these rods exist in close proximity, then the neighbouring molecules are sensitive to each other's charge distribution and preferentially pack in a parallel manner.Reducing the amplitude of the charge density wave at either end of the molecule enhances the parallel alignment of the molecules.The addition of the phenyl unit presumably reduces this amplitude at the molecular terminus by spreading the charge distribution and hence increases T NFN , see Figure 9. Indeed, we have previously suggested that this may also explain the enhanced stability of ferroelectric nematogens with additional fluorination in the terminal nitrophenyl ring [19,28].The stability of the N F phase therefore appears to be dictated by a combination of shape anisotropy and electronic effects.We should note that although the values for T NFN are higher for the 1O(m-On)PEPEBNO 2 series than for the 5-m series, the T NFN /T NI ratio is lower, for example, for 1O(m-O9)PEPEBNO 2 , the ratio is 0.744 and considerably lower than the value of 0.978 for 5-9.This reflects the greater role played by structural anisotropy in determining T NI compared to T NFN .
Transitional data for the homologues of the 1O(m-On)PEBNO 2 series (n = 1-2) are listed in Table 2.The conventional nematic phase is again assigned by the observation of a characteristic schlieren texture, Figure 10.An N F phase was not observed for either compound.The N phase may be supercooled in isolated  droplets to around room temperature, indicating a reduction in T NFN by over 100°C when compared to the corresponding 5-m homologues.
The value of T NI for 1O(m-O1)PEBNO 2 is lower than that for 5-1 by 27°C, but that of 1O(m-O2)PEBNO 2 is the same as that for 5-2.This reflects the shape of the T NI line on increasing the length of the lateral chain, and as we have seen, as the interaction strength parameter between the mesogenic units decreases, the dependence of T NI becomes weaker.This is also evident if we compare the values of T NI of 1O(m-On)PEBNO 2 and 1O(m-On)PEPEBNO 2 .For n = 1, the reduction in T NI is almost 200°C and this uses the lower limit of T NI which as we have seen is accompanied by decomposition.This reduction falls to 160°C when comparing the values of T NI for n = 2.
It is clear that T NFN is more sensitive to the removal of the ester linkage when comparing the behaviour of 1O(m-On)PEPNO 2 and corresponding members of the 5-m series, and this is in accord with earlier observations made by Mandle et al. [3].For n = 1, the reduction in the molecular dipole moment is 1.66 D which may, at least in part, account for the reduction in T NFN .Within the framework of the model proposed by Madhusudana [27], the removal of the ester linkage markedly changes the longitudinal surface charge density wave.The ester group may be thought of as an insulating fragment and divides the molecules into distinct electronic regions, see Figure 9. Without the ester link, the electron density is more evenly distributed, resulting in the observed decrease in the stability of the N F phase.

Conclusion
The addition of the phenyl ring to 5-1 (RM734) clearly has a significantly more pronounced effect on the value of T NI than on T NFN.The increase in T NI of at least 172°C is wholly expected and may be attributed to the enhanced structural anisotropy and more favourable intermolecular interactions arising from the insertion of the phenyl ring.The much weaker effect on T NFN , an increase of just 10°C, may reflect a change in the shape of the molecule and this now requires further study.In addition, this increase is in accord with the prediction of a molecular model that describes the molecules in the ferroelectric nematic phase as having a longitudinal surface charge density wave, and the phenyl serves to reduce this at the molecule terminus.The behaviour of T NI and T NFN on increasing the length of the alkyloxy chain in the 1O(m-On)PEPEBNO 2 and 5-m series is essentially the same and is more pronounced for T NI than for T NFN .The dependence of T NI may be accounted for in terms of structural anisotropy, whereas the weaker effect on T NFN may be associated with the lateral chain inhibiting anti-parallel associations of the molecules.We also note, however, that these data may suggest that the stability of the N F phase is linked to the molecular shape as suggested by computer simulation studies [29].The removal of the ester linkage between the 5-m and 1O(m-On)PEPNO 2 series has a pronounced effect on the stability of the N F phase, and this appears to be consistent with the model proposed by Madhusudana [27].We clearly have a great deal more to learn about the subtle relationship between molecular structure and the ferroelectric nematic phase.

Figure 5 .
Figure 5. Dependence of the transition temperatures on the number of carbon atoms in the lateral alkyloxy chain, n, for the 1O(m-On)PEPEBNO 2 series.Values of T NI are represented by triangles, T NFN by squares and the melting points by the dashed line.

Figure 6 .
Figure 6.(Colour online) Textures of 1O(m-O3)PEPEBNO 2 in (a) the N phase at 116°C and (b) in the N F phase at 94°C in a planar aligned cell.

Figure 7 .
Figure 7. Phase diagrams constructed using binary mixtures of 1O(m-O4)PEPEBNO 2 (left) and 1O(m-O7)PEPEBNO 2 (right) with the archetypal ferroelectric nematogen RM734.Values of T NI are represented by triangles, T NFN by squares and the melting point by the dashed line.

Figure 8 .
Figure 8. Dependence of the transition temperatures on the number of carbon atoms in the lateral alkyloxy chain, n, for the 1O(m-On)PEPEBNO 2 series (filled symbols) and 5-m series (open symbols).Values of T NI are represented by triangles and T NFN by squares.

Table 1 .
Transition temperatures and associated scaled entropy changes for the 1O(m-On)PEPEBNO 2 series.
a sample decomposes prior to clearing, temperature obtained using TGA.() denotes a monotropic transition.

Table 2 .
Transition temperatures and associated scaled entropy changes for the 1O(m-On)PEBNO 2 series.
*denotes temperature obtained from DSC cooling trace.