To Be or Not To Be Polar: The Ferroelectric and Antiferroelectric Nematic Phases

We report two new series of compounds that show the ferroelectric nematic, NF, phase in which the terminal chain length is varied. The longer the terminal chain, the weaker the dipole–dipole interactions of the molecules are along the director and thus the lower the temperature at which the axially polar NF phase is formed. For homologues of intermediate chain lengths, between the non-polar and ferroelectric nematic phases, a wide temperature range nematic phase emerges with antiferroelectric character. The size of the antiparallel ferroelectric domains critically increases upon transition to the NF phase. In dielectric studies, both collective (“ferroelectric”) and non-collective fluctuations are present, and the “ferroelectric” mode softens weakly at the N–NX phase transition because the polar order in this phase is weak. The transition to the NF phase is characterized by a much stronger lowering of the mode relaxation frequency and an increase in its strength, and a typical critical behavior is observed.

transition because the polar order in this phase is weak.The transition to the NF phase is characterized by a much stronger lowering of the mode relaxation frequency and an increase in its strength, typical critical behavior is observed.
Ferroelectric materials have a spontaneous reversible electric polarization and show piezoelectric and pyroelectric properties ensuring their widespread use in leading-edge electronics such as actuators, sensors and memory elements. 1,2In a liquid crystal, the switching of the electric polarization is coupled with the elastic or optical properties of the material, and this is highly desirable for applications in soft optoelectronic devices. 3Liquid crystalline improper ferroelectric phases have been known for decades; ferroelectric smectic phases have been studied since the 1970s 4 and ferroelectric columnar phases since the 1990s 5 .It has been shown that due to the competing interactions within these phases, their structures are often complex, and only a relatively small number of ferroelectric, antiferroelectric and ferrielectric phases have been found 6 .Furthermore, these phases have found only very limited commercialization in, for example, liquid crystal on silicon (LCoS) displays.Their wider application potential has failed to be realized mainly due to the challenge of producing defect free large area samples.
Recently, a polar nematic phase was discovered 7,8 and later assigned as the ferroelectric nematic phase, NF. 9 This is the least ordered polar liquid crystalline phase.In the conventional nematic phase, N, the rod-like molecules more or less align in a common direction known as the director described by a unit vector, n, whereas their centres of mass are distributed randomly such that the phase has a fluid character.The director possesses inversion symmetry, i.e. n = −n, and so the phase is non-polar.In the NF phase, however, the inversion symmetry is broken, i.e. n ≠ −n, and the phase becomes polar.It appears that this polar NF phase, in contrast to the previously studied smectic and columnar phases, is a proper ferroelectric phase, in which the polar order is induced due to dipole-dipole interactions and the polarization is found along the director. 9The high fluidity of the NF phase combined with its polar properties immediately caught the attention of scientists around the world due not only to its huge application potential but also its fundamental significance as a spontaneously ferroelectric fluid.The NF phase became one of the hottest topics in liquid crystal research.  Owinto the fluid nature of the NF phase, a uniform polarization direction can be obtained in large areas -a key to realizing its application potential. 35However, the question arises whether the competitive interactions that drive the formation of the NF phase can also lead to other complex structures as is the case with the improper ferroelectric liquid crystal phases.
To date there have been some 200 mesogens reported which exhibit the NF phase but in general these materials are designed using three archetypal architectures which appear to have somewhat similar properties despite having differing chemical structures (Fig. 1). 8,11,36These materials all have a large longitudinal dipole moment giving strong dipole-dipole interactions and also possess some degree of lateral bulk thought to inhibit anti-parallel correlations between molecules. 37,38e report here two homologous series based on RM734 36 (Fig. 2), which both have strong longitudinal dipole moments (~11-12D), but in which the lateral methoxy group has been moved from the terminal to the central phenyl ring and a hydrogen ortho to the terminal nitro group is replaced by a fluorine atom.The series differ in the nature of the terminal chain; the nOEC3F series contains an alkyloxy chain and the nEC6F series an alkyl chain.For both series we report the change in behavior on extending the length of the terminal chain.A detailed description of the preparation of both these series, including the structural characterization data for all intermediates and final products, is provided in the Supplementary Information.

Results and Discussion
We have shown previously that increasing the length of a lateral alkyloxy chain for RM734-type materials destabilizes the ferroelectric properties. 13,23,24,26However the N-NF phase transition temperature decreases less than the Iso-N transition temperature, such that for most homologues in which there is a fluorine atom ortho to the terminal nitro group, a direct Isoferroelectric nematic phase transition is observed.In contrast, here we observed that increasing the length of the terminal alkyl chain only weakly affects the clearing temperatures, whereas the stability of ferroelectric NF phase strongly decreases in favor of the N and intermediate NX phases (Fig. 3).For the nEC6F series, when n = 1 and 2 a direct Iso-NF transition is seen, for n = 3 and 4 the sequence Iso-N-NX-NF is observed, and for homologues n = 5 and 6 an Iso-N-NX phase sequence is found.The longest homologues crystallized close to room temperature, but without first entering the NF phase (Fig. 3).Such phase behavior is expected given that increasing the length of the terminal alkyl chain decreases the dipole-dipole interactions along the director, and thus the tendency to form an axially ferroelectric arrangement of dipole moments diminishes.The stabilization of the NX phase over a broad temperature range for the n = 5 and 6 homologues, offers the possibility for a detailed characterization of this phase.This is particularly important since the structure of NX phase is still under debate.Chen et al suggested that the phase has only shortrange order regarding molecular positions, but shows a regular array of antiferroelectric domains along the direction perpendicular to the director. 39To date, the structure of the NX phase (referred to by Chen et al as SmZA) was confirmed by Xray diffraction studies in only a single compound, namely DIO (Fig. 1).For the studied materials, the N-NX phase transition is weakly first order.It is accompanied by only a small, step-like increase of optical birefringence, of less than 0.001 for 4EC6F (Fig. 4a), and this decreases on increasing the terminal alkyl chain length.Thus, one can assume that the orientational order of the molecules remains similar in the N and Nx phases.
In optical studies performed using planar aligned cells, there is clearly a transition detected at the temperature described by the birefringence measurements.In the N phase there is a uniform texture observed, and on entering the NX phase, the flickering characteristic to non-polar phases ceases and chevron-like defects appear a few degrees below phase transition (Fig. 4).The dielectric studies performed for homologue 4EC6F shows a weak dielectric mode in the N phase (with a relaxation frequency ~10 5 Hz) that continuously slows down but increases in strength through the entire range of the N and NX phases.The N-NX phase transition is marked by only a slight change in the value of the mode strength (Fig. 5a).This mode might be ascribed to the noncollective rotations of molecules with strong dipole moments around their highest inertia axis.Entering the NF phase, there is a dramatic change in the dielectric response and a very strong, low relaxation frequency (~10 3 Hz) mode appears.Furthermore, in optical studies there is also a clear transition observed upon entry to the NF phase with the emergence of a blocky type texture with some focal conic-like defects (Fig. 4). 28In the NX phase under a weak bias electric field, the relaxation mode due to non-collective molecular rotations is quenched and the mode due to the collective ferroelectric fluctuation is excited.Suppressing the noncollective fluctuations by a bias electric field allows us to follow the evolution of the 'ferroelectric' mode (~10 3 Hz) over the whole temperature range (Fig. 5b,c).This mode slightly 'softens' at the N-NX phase transition as the polar order in this phase is weak, but the transition to the NF phase is marked by a much stronger critical lowering of the mode frequency and an increase of its strength.Therefore, typical critical behavior is observed.In order to probe the structure of the NX phase, small angle x-ray diffraction studies (SAXS) were performed.Using a strong synchrotron source, in addition to the diffuse signal due to the short-range positional order of the molecules, which is typical for the nematic phase, there was also a separate sharp, machine resolution limited signal (Fig. 6).This observation proved that there was long range ordering within the phase due to the periodic structure of the antiferroelectric domains.The low intensity of the signal shows that the related electron density modulation is very weak.The signal position depends on the terminal alkyl chain such that higher values of n give shorter periodicities, being, deep within the NX phase, around 75 Å, 50 Å and 40 Å (just 20-10 molecular widths) for 4EC6F, 5EC6F and 6EC6F respectively.It would appear that the size of the domains defining the NX structure can be correlated with the tendency to form the NF phase.The size of the domains increases on approaching the transition to the NF phase, and this tendency is clearly seen for the 4EC6F.However, for 5EC6F a much weaker and non-monotonic temperature dependence is observed.For 6EC6F, which is the homologue with the longest terminal alkyl chain length, the size of the domains monotonically decreases on cooling, suggesting that for this compound the tendency to form the ferroelectric nematic phase is very weak, and therefore does not influence the domain size.
For 5EC6F resonant soft x-ray scattering studies (RSoXS) were also conducted.The diffraction signal at the resonance condition was sensitive to the orientation of the molecules unlike conventional x-ray diffraction.The RSoXS signal was found at a periodicity double that detected in the SAXS measurements (Fig. 6), and this clearly confirms that structure is related to an antiparallel orientation of molecules in neighboring domains.(blue) measured using X-ray diffraction.In the inset: comparison of the periodicities deduced from non-resonant (XRD) and resonant (RSoXS) studies; (right) the 2D XRD pattern registered for n = 6 in the NX phase, at T = 40 °C.The sharp signal at q = 0.15 Å -1 is due to periodic structure of antiferroelectric domains, while the diffused signal centered at q = 0.26 Å -1 reflects the short-range positional order of molecules along the director of the nematic phase.
For comparison we studied the homologous series nOEC3F, in which the terminal alkyl chain is replaced by an alkyloxy chain.Although in general the stability of the liquid crystalline phases is increased by introducing an oxygen atom between a terminal alkyl chain and the mesogenic unit, the tendency to form the polar NF phase was diminished (Fig. S1).This may be somewhat surprising considering the average overall molecular dipole of the nOEC3F series is 13.0 D compared to 12.0 D for the nEC6F series, (Fig. 7).Apparently, larger longitudinal dipole moments are not exclusively the driving force for the formation of the NF phase.Within the framework of the model of the NF phase proposed by Madhusuhana, the molecules are described by longitudinal surface charge density waves which interact to prevent the formation of antiparallel structures. 40In order to stabilize the ferroelectric nematic phase and promote the parallel alignment of the calamitic molecules, the amplitude of the charge density waves at either end of the molecule should be reduced.We have reported previously that this may be achieved using a fluorine atom at the ortho position to the terminal nitro group rather than a hydrogen atom, in order to reduce the electron density associated with the nitro group. 23,24In this case, however, we are instead changing the electron density associated with the ring to which the terminal alkyl or alkyloxy chain is attached.An alkyloxy chain is a stronger activating functional group when compared to an alkyl chain due to its enhanced electron donating character and this means that there is a greater electron density in the terminal ring of the nOEC3F series compared to the nEC6F series (Fig. 7). 41This increase in electron density will cause the amplitude of the surface charge density wave to increase for the nOEC3F series and, hence the temperatures of the N-NF and N-NX phase transitions show a more pronounced decrease on the elongation of terminal chain for the alkyloxy derivatives when compared to their alkyl counterparts.This decrease may also be attributed, to some extent, to shape effects, given that the alkyloxy chain lies more or less in the plane of the mesogenic unit to which it is attached, whereas the alkyl chain protrudes at an angle, and this will also disrupt the anti-parallel correlations between the molecules (Fig. 7).This weaker tendency to form ferroelectric phases in the nOEC3F series was also confirmed by X-ray diffraction studies performed for the material 3OEC3F.The periodicity of the antiferroelectric domain structure in the NX phase varied from 45 to 42 Å (65 -45 °C), which is less than that found for the alkyl terminated analogue 4EC6F, having the same total length of terminal chain.The dielectric measurements for 3OEC3F revealed two clear relaxation modes in the whole temperature range of the NX and N phases (Fig. S2).As described for 4EC6F, upon the application of a bias electric field in the NX phase, the non-collective, higher frequency mode is quenched and instead the 'ferroelectric mode' is excited.In 3OEC3F, the temperature evolution of this 'ferroelectric mode' under a bias field showed a very weak softening behavior at the N-NX phase transition and this softening was much less pronounced than observed for the analogous compound 4EC6F.Such behavior is consistent with the optical observations, as there was a nearly smooth evolution of optical birefringence across the N-Nx phase transition (Fig. S3), revealing its nearly continuous character and the weak polar ordering in the domains.

Conclusion
In conclusion, the results obtained indicate that the NX phase is built from small polar regions, which form a regular antiferroelectric structure.The dielectric response measured indicates that the polar order in these regions is weak, and that the phase transition to the conventional non-polar nematic is very weakly first order.The periodicity of the antiferroelectric domains array in the NX phase increases with increasing ferroelectric interactions in the system, and the closer it is to the transition to the ferroelectric nematic phase, the wider these domains become.The question remains what causes the density modulation responsible for the weak X-ray signal in the NX phase?It is possible that either the domain walls have slightly different densities than the ferroelectric domains, or that the polarization splays or its magnitude is modulated across the domain, leading to slightly different densities at the domain boundaries.

Experimental Reagents
All reagents and solvents that were available commercially were purchased from Sigma Aldrich, Fisher Scientific or Fluorochem and were used without further purification unless otherwise stated.

Thin Layer Chromatography
Reactions were monitored using thin layer chromatography, and the appropriate solvent system, using aluminium-backed plates with a coating of Merck Kieselgel 60 F254 silica which were purchased from Merck KGaA.The spots on the plate were visualised by UV light (254 nm).

Column Chromatography
For normal phase column chromatography, the separations were carried out using silica gel grade 60 Å, 40-63 µm particle size, purchased from Fluorochem and using an appropriate solvent system.

Structure Characterisation
All final products and intermediates that were synthesised were characterised using 1 H NMR, 19 F NMR, 13 C NMR and infrared spectroscopies.The NMR spectra were recorded on a 400 MHz Bruker Avance III HD NMR spectrometer.The infrared spectra were recorded on a Perkin Elmer Spectrum Two FTIR with an ATR diamond cell.

Purity Analysis
In order to determine the purity of the final products, high-resolution mass spectrometry was carried out using a Waters XEVO G2 Q-Tof mass spectrometer by Dr. Morag Douglas at the University of Aberdeen.

Birefringence
The optical retardation was measured with a setup consisting of a photoelastic modulator (PEM-90, Hinds), halogen lamp (Hamamatsu LC8) equipped with a set of narrow bandpass filters as a light source, and a photodiode (FLC Electronics PIN-20).The measured intensity of the transmitted light was de-convoluted with a lock-in amplifier (EG&G 7265) into 1f and 2f components to yield a retardation induced by the sample.Glass cells with thickness 1.6 m and surfactant assuring planar anchoring condition were used.

Dielectric Measurments
The complex dielectric permittivity was measured in 1 Hz -10 MHz frequency (f) range using Solatron 1260 impedance analyzer.Material was placed in glass cells with ITO or Au electrodes (and no polymer alignment layer to avoid influence of high capacitance of thin polymer layer) and thickness ranging from 5 to 10 microns.The relaxation frequency, fr, and dielectric strength of the mode Δε, were evaluated by fitting the complex dielectric permittivity to Cole-Cole formula.

X-ray diffraction studies
Were performed at the Advanced Light Source, Lawrence Berkeley National Laboratory.Diffraction at small angle range were carried out on the SAXS beam line (7.3.3) at the energy of incident beam 10 keV.Samples were prepared in thin-walled glass capillaries or placed on heating plate as droplets.The scattering intensity was recorded using the Pilatus 2M detector, placed at the distance 2575 mm from the sample.The resonant x-ray scattering was performed on the soft x-ray beam line (11.0.1.2).The energy of incident beam was tuned to the K-edge of carbon absorption (283 eV).Samples with thickness lower than 1 μm were placed on a TEM grid.The scattering intensity was recorded using the Princeton PI-MTE CCD detector.

Molecular modelling
The geometric parameters of the nOEC3F and nEC6F series were calculated with quantum mechanical DFT calculations using Gaussian09 software. 1Optimisation of the molecular structures was carried out at the B3LYP/6-31G(d) level of theory.A frequency check was used to confirm that the minimum energy conformation found was an energetic minimum.Visualisations of electronic surfaces and ball-and-stick models were generated from the optimised geometries using the GaussView 5 software, specifically the electronic surfaces were calculated using the cubegen utility in GaussView.Visualisations of the space-filling models were produced post-optimisation using the QuteMol package. 2

Polarised Optical Microscopy
Optical studies were performed by using a Zeiss Axio Imager A2m polarising light microscope, equipped with a Linkam heating stage or using a Olympus BH2 polarising light microscope equipped with a Linkham TMS 92 hot stage.Samples were prepared in commercial cells (AWAT) of various thickness (1.5 -20 m) with ITO electrodes and planar alignment or in commercial cells purchased from INSTEC with a cell thickness of 2.9 -3.5 m and also planar alignment.The optical microscopic image was analyzed (director field and birefringence) with ABRIO system.

Differential scanning calorimetry
The phase behaviour of the materials was studied by differential scanning calorimetry performed using Mettler Toledo DSC1 or DSC3 differential scanning calorimeters equipped with TSO 801RO sample robots and calibrated using indium and zinc standards.Heating and cooling rates were 10 °C min −1 , with a 3-min isotherm between either heating or cooling, and all samples were measured under a nitrogen atmosphere.The enatiotropic transition temperatures and associated enthalpy changes were extracted from the heating traces wheress the monotropic transition temperatures and associated enthalpy changes were extracted from the cooling traces.

4-Formyl-3-methoxyphenyl 4-alkyloxybenzoates (1)
To a pre-dried flask flushed with argon, 4-alkyloxybenzoic acid of the appropriate chain length (1 eq), 4-hydroxy-2-methoxybenzaldehyde (1.1 eq) and 4-dimethylaminopyridine (0.13 eq) were added.The solids were solubilised with dichloromethane (100 mL) and tetrahydrofuran (20 mL) while being stirred for 10 min before N,N'-dicyclohexylcarbodiimide (1.3 eq) was added to the flask and the reaction was allowed to proceed overnight.The quantities of the reagents used in each reaction are listed in Table S1.The extent of the reaction was monitored by TLC using an appropriate solvent system (RF values quoted in the product data).The precipitate which formed was removed by vacuum filtration and the filtrate collected.The collected solvent was evaporated under vacuum to leave a solid which was recrystallised from hot ethanol (200 mL).

4-((4-Alkyloxybenzoyl)oxy)-2-methoxybenzoic acid (2)
To a pre-dried flask flushed with argon, Compound 1 (1 eq) and resorcinol (1.5 eq) were solubilised in DMSO (100 mL).Sodium chlorite (4 eq) and sodium hydrogen phosphate monohydrate (3.5 eq) were solubilised in water (60 mL) before being slowly poured into the reaction flask and the resultant mixture was stirred at room temperature overnight.The quantities of the reagents used in each reaction are listed in Table S2.The extent of the reaction was monitored by TLC using an appropriate solvent system (RF values quoted in the product data).The reaction mixture was diluted with water (200 mL) and the pH of the mixture was adjusted to 1 using 32% hydrochloric acid (≈ 30 mL).A white solid precipitated after acidification which was collected by vacuum filtration and recrystallised from hot ethanol (250 mL).

3-Fluoro-4-nitrophenyl 2-methoxy-4-((4-alkyloxybenzoyl)oxy)benzoates (3)
To a pre-dried flask flushed with argon, Compound 2 (1 eq), 3-fluoro-4-nitrophenol (1.2 eq), and N,N'-dicyclohexylcarbodiimide (1.5 eq) were added to the flask.The solids were solubilised with dichloromethane (30 mL) and stirred for 30 min before 4dimethylaminopyridine (0.15 eq) was added.The quantities of the reagents used in each reaction are listed in Table S3.The temperature of the reaction mixture was increased to room temperature and the reaction was allowed to proceed overnight.For the reactions with N,N'-dicyclohexylcarbodiimide, the white precipitate which formed was removed by vacuum filtration and the filtrate collected.The solvent was removed under vacuum and the crude product was purified using a silica gel column with an appropriate solvent system (RF values quoted in product data).The eluent fractions of interest were evaporated under vacuum to leave a white solid which was recrystallised from hot ethanol (60 mL).

4-Formyl-3-methoxyphenyl 4-alkylbenzoates (4)
To a pre-dried flask flushed with argon, 4-alkylbenzoic acid of the appropriate chain length (1 eq), 4-hydroxy-2-methoxybenzaldehyde (1.1 eq) and 4-dimethylaminopyridine (0.13 eq) were added.The solids were solubilised with dichloromethane (100 mL) and tetrahydrofuran (20 mL) while being stirred for 10 min before N,N'-dicyclohexylcarbodiimide (1.3 eq) was added to the flask and the reaction was allowed to proceed overnight.The quantities of the reagents used in each reaction are listed in Table S4.The extent of the reaction was monitored by TLC using an appropriate solvent system (RF values quoted in the product data).The precipitate which formed was removed by vacuum filtration and the filtrate collected.The collected solvent was evaporated under vacuum to leave a solid which was recrystallised from hot ethanol (150 mL).

4-((4-Alkylbenzoyl)oxy)-2-methoxybenzoic acid (5)
To a pre-dried flask flushed with argon, Compound 4 (1 eq) and resorcinol (1.5 eq) were solubilised in DMSO (100 mL or 120 mL for n = 3).Sodium chlorite (4 eq) and sodium hydrogen phosphate monohydrate (3.5 eq) were solubilised in water (60 mL or 80 mL for n = 3) before being slowly poured into the reaction flask and the resultant mixture was stirred at room temperature overnight.The quantities of the reagents used in each reaction are listed in Table S5.The extent of the reaction was monitored by TLC using an appropriate solvent system (RF values quoted in the product data).The reaction mixture was diluted with water (200 mL) and the pH of the mixture was adjusted to 1 using 32% hydrochloric acid (≈ 30 mL).A solid precipitated after acidification which was collected by vacuum filtration and recrystallised from hot ethanol (150 mL) or hot ethanol (70 mL) with 40:60 petroleum ether (60 mL) for n = 6.

Figure 2 .
Figure 2. The molecular structures of: (left) the nOEC3F and (right) the nEC6F series where n refers to the number of carbon atoms in the terminal chain.

Figure 3 .
Figure 3. Phase diagram for the nEC6F series of ferroelectric nematogens with molecular structure shown in Fig.2.The conventional non-polar nematic phase is represented by N, the antiferroelectric nematic phase by NX and the polar ferroelectric nematic phase by NF.

Figure 4 .
Figure 4. (a) Optical birefringence (red line) of 4EC6F measured with red light (= 690 nm) across the N-NX phase transition.The black line shows the derivative d(n)/dT, and this clearly shows the transition temperature associated with the NX phase.(b-d) Optical textures of N, Nx and NF phases observed between crossed polarizers in a 1.8-µm-thick cell with planar anchoring, with the chevron defects and focal conic-like defects appearing in the NX and NF phases, respectively.

Figure 5 .
Figure 5.The imaginary part of dielectric susceptibility measured for 4EC6F (n = 4): (a) the temperature and frequency dependence across the N-NX-NF phase sequence, (b) the frequency and bias field dependence in the NX phase (at T = 80 °C); where the high-frequency mode is suppressed and the lower-frequency ferroelectric mode is excited above threshold field of 0.12 V / µm; and (c) a map showing the evolution of the 'ferroelectric' mode vs. temperature and frequency.The measurements were performed under a bias electric field of 0.3 V / µm.

Figure 6 .
Figure 6.(left) Periodicity of the antiferroelectric domain structure in the NX phase (d) vs. temperature for the nEC6F series with n = 4 (red), n = 5 (black) and n = 6

Figure 7 .
Figure 7. Molecular modelling of: (left) 3OEC3F and (right) 4EC6F calculated at the B3LYP/6-31(d) level of theory.The molecules are visualized using: (top) ball and stick models, (middle) electrostatic potential surfaces and (bottom) space-filling models.The arrow indicates the direction of the calculated dipole moment, with the head representing positive charge moving to the base which is negative.

Table S7 .
The phase transition temperatures for the nEC6F series with an alkyl (Cn) terminal chain, the temperatures are given in o C and associated transition enthalpy changes (in parenthesis) in Jg-1