Thermotropic reentrant isotropic symmetry and induced smectic antiferroelectricity in the ferroelectric nematic material RM734

Significance

The recent discovery of ferroelectric nematic liquids has provided a pathway into exploration of the ferroelectric nematic realm, a space of exotic soft matter liquid crystal phases and phenomena based on the spontaneous self-organization of polar molecules into liquid phases, where the local polarization density has nearly its maximum possible value. Such a low entropy state in a liquid can be a condition of frustration, subject to instabilities that produce spatial modulation and antiferroelectricity, for example. Here we report an extreme case of such behavior in which, upon cooling, a ferroelectric nematic phase transitions into an optically isotropic, macroscopically nonpolar, transparent liquid phase, stabilized by the appearance of robust, short-range-ordered, apolar nanoscale structuring.

Abstract

We report a transition from the ferroelectric nematic liquid crystal (N_F) phase to a lower-temperature, apolar fluid phase having reentrant isotropic symmetry (I_R), in the liquid crystal compound RM734 doped with small concentrations of the ionic liquids 1-Butyl-3-methylimidazolium hexafluorophosphate (BMIM-PF₆) or 1-Ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMIM-TFSI). Even a trace amount of ionic liquid dopant facilitates the kinetic pathway for the transition from the N_F to the I_R, enabling simple cooling to produce this isotropic fluid phase rather than resulting in immediate crystallization. The I_R was also obtained in the absence of specific ionic liquid doping by appropriate temperature cycling in three distinct, as-synthesized-and-purified batches of RM734, two commercial and one from our laboratory. Ionic liquid doping also stabilizes the smectic Z_A, an additional birefringent antiferroelectric phase having the director parallel to fluid smectic layers, significantly increasing its temperature range between the paraelectric and ferroelectric nematic phases with increasing BMIM concentration.

Proper ferroelectricity in liquids was predicted in the 1910s by Debye (1) and Born (2), who applied the Langevin–Weiss model of ferromagnetism to propose a liquid-state phase change in which the ordering transition is a spontaneous polar orientation of molecular electric dipoles. A century later, in 2017, two groups independently reported, in addition to the typical high-temperature isotropic (I) and nematic (N) phases, novel nematic phases in strongly dipolar molecules, the “splay nematic” in the molecule RM734 (3–5) and a “ferroelectric-like nematic” phase in the molecule DIO (6). These nematic phases were subsequently demonstrated to be ferroelectric in RM734 (7) and in DIO (8, 9), and to be the same phase in these two materials (9). This phase, the ferroelectric nematic (N_F), is a uniaxially symmetric, spatially homogeneous liquid having nearly saturated polar ordering of its longitudinal molecular dipoles (polar order parameter > 0.9) (7, 9). Additional new phases common to these families of molecules motivated the notion of the ferroelectric nematic realm: the antiferroelectric SmZ_A in DIO, RM734, and their mixtures (10–12), exhibiting smectic layers of alternating ferroelectric polarization having the director and polarization parallel to the layer planes; the ferroelectric smectic A (SmA_F), also uniaxial with nearly saturated polarization (13, 14); and a diverse array of more recent discoveries (15).

We report here unexpected phenomenology of RM734, identified by doping it with the ionic liquids (ILs) BMIM-PF₆ (BMIM) or EMIM-TFSI (EMIM). As shown in Fig. 1, upon doping the nominal bulk LC phase sequence of RM734 (12), [I – 188 °C – N – 132.1 °C – SmZ_A – 131 °C – N_F – ≲100 °C – X], is modified to exhibit; i) dramatic stabilization of the SmZ_A phase, its temperature range at the boundary between the N and N_F phases expanding exponentially with increasing IL concentration from the IL-doping-free value of 1.1 °C (16); and ii) a transition from the ferroelectric nematic liquid crystal (N_F) phase to a low-temperature viscoelastic fluid phase with isotropic symmetry (the reentrant isotropic, I_R) in mixtures of the liquid crystal compound RM734 with sub-few-percent concentrations of BMIM or EMIM (16). This work has been confirmed in a more recent preprint (17), and extended by us to DIO (18). The reentrant I_R phase is optically isotropic and therefore apolar with zero electric field applied, and responds only weakly to applied electric field. Even a trace amount of ionic liquid dopant facilitates the kinetic pathway of the transition from N_F to I_R, enabling simple cooling of the N_F to produce the I_R phase rather than resulting in crystallization. At low IL concentration the I_R phase is metastable at room temperature, with ultimate crystallization taking hours to weeks.

Fig. 1.

(A) Structures of the chemical species studied. (B) The phase diagram of RM734 and RM734/BMIM mixtures, including the I_R, a phase which we have identified as being of the ferroelectric nematic realm. The molecule RM734 is mesogenic, exhibiting the following phase sequence on cooling from 200 °C: high-temperature dielectric isotropic (I); paraelectric nematic (N); ferroelectric nematic (N_F); and, depending on the cooling process, crystal (X) or low-temperature, apolar isotropic (I_R). The phase diagram was obtained from SAXS and WAXS experiments and optical microscopy observations of RM734β/BMIM mixtures (see text). Exposing the mixtures to temperatures higher than T ~ 150 °C produces irreversible changes in phase behavior, so the I – N transition temperature in the mixtures was evaluated only approximately. The I_R phase is gel-like and deformable when it first appears on cooling, becoming stiffer and then glassy as T is decreased. The times and temperatures required for crystallization were found to be highly dependent on the ionic liquid concentration c_IL and on sample geometry, with longer times and lower temperatures required at higher dopant concentrations. The mixtures exhibit a lamellar, modulated, antiferroelectric phase (SmZ_A), also observed in a ~1 °C-wide intermediate range between the N and N_F phases in undoped RM734. At sufficiently high BMIM concentrations (shaded region), phase separation of the dopant material is observed.

The development of antiferroelectric SmZ_A or apolar I_R ordering adjacent in temperature to the strongly polar-ordered N_F phase may seem surprising, but the century-long experimental and theoretical study of ferroelectric and ferromagnetic materials with dipolar interactions, both crystals and liquid crystals, shows that ferroelectricity (F) and antiferroelectricity (A) go hand in hand, such that if one is found, the other will be observed in related materials, or even as coexisting phases (19–21). At the root of this behavior are dipole–dipole interactions and their inherent ambivalence: Dipole pairs arranged end-to-end prefer to be oriented parallel, whereas dipole pairs arranged side-by-side prefer to be antiparallel. Pair correlations are substantially end-to-end in the N, N_F, and SmZ_A phases (7), This frustration is a recipe for obtaining reentrant phases in liquid crystals (22–25) and for generating modulated, anisotropic, antiferroelectric phases of the SmZ_A type (10), having layers of uniform P extended along the end-to-end direction and antiferroelectric ordering of adjacent layers. In reentrant nematic phases, uniaxial nematic symmetry reappears in a phase diagram but with different local structural arrangement than the higher temperature nematic. In the present case, the distinctions of short-range structure from the higher temperature ferroelectric nematic are also dramatic, an X-ray structure factor of diffuse scattering indicating that the I_R phase has distinctive short-range positional order, in a phase which the optics show to be structurally isotropic. Here, we probe this reentrance of isotropic symmetry from a highly polar and anisotropic N_F liquid crystal state.

Results

The molecular species studied are shown in Fig. 1A. We carried out SAXS and WAXS experiments, polarized transmission optical microscopy (PTOM), and polarization current measurement of RM734/ionic liquid (IL) mixtures with the ionic liquid dilute, focusing here on RM734/BMIM at weight% ionic liquid concentrations, c_IL, in the range 0% ≤ c_IL ≤ 10%. Unless stated otherwise, these experiments were carried out using a commercial RM734 sample (RM734β) having transition sequence, I – 179 °C – N – 129 °C – SmZ_A – 128 °C –N_F – ≲100 °C – X). Because of the low IL doping concentrations employed, experiments were also carried out on RM734 samples (α,β,γ) of lower (α) and higher (γ) impurity concentration, as noted.

The phase diagram of Fig. 1B, constructed using X-ray and optical observations, summarizes our principal results on RM734β/IL mixtures. We find that the introduction of tiny amounts of ionic liquid can produce stunning changes in the phase behavior in the ferroelectric nematic realm. Even a very low concentration of ionic liquid (c_IL ~ 0.01%) facilitates, upon lowering T below ~70 °C, the appearance of the I_R, the “R” distinguishing this phase from the dielectric high-temperature isotropic phase (I) (Fig. 1B). Remarkably, even with such low concentrations of ionic liquid, the first-order thermotropic transition upon cooling from the N_F phase to the I_R phase fills the entire sample volume with I_R, suggesting that the I_R phase may be intrinsic to the RM734β host, with the ionic liquid dopant serving to create a kinetic pathway for its nucleation.

At the boundary between the N and N_F phases the SmZ_A-like phase, an intermediate phase is observed in undoped RM734 over a ~1.1 °C temperature range (12), with an increasing phase range with increasing c_IL, ultimately supplanting the ferroelectric nematic. This phase i) has the same position in the phase diagram as the SmZ_A phase has in DIO, and in mixtures of DIO with up to 90% RM734 (11); ii) is a spatially modulated antiferroelectric with layers that orient normal to the plates in glass cells; and iii) has the nematic director parallel to the layer planes, to the cell plates, and to the buffing direction, all geometrical characteristics of the SmZ_A, suggesting that this phase is a SmZ_A variant.

The onset of macroscopic phase separation of the ionic liquid component is observed for c_IL ≳ 5% (shaded region in Fig. 1B). Here we focus on the mesophase behavior at the lowest ionic liquid concentrations. For c_IL > 0.1%, the transition to the I_R is thermotropic and occurs at T_IR ~ 67 °C, which temperature has little dependence on c_IL. Remarkably, some manifestation of this transition appears at this same temperature over a wide range of c_IL values, from undoped RM734 to high concentration ionic liquid doping at c_IL ~ 90%, to be discussed in detail elsewhere, indicating that the phase transition to the I_R is largely a transition of RM734, which is aggregating and/or nanophase separating at T_IR.

However, the ordering process at T_IR does not lead to a crystallized state, but a less-ordered gel-like viscoelastic fluid mesophase. Possible local structural themes, such as bicontinuous nanophase segregation, are discussed below. In such structures, RM734 and ionic liquid or other impurities are likely nanophase separated, with the ionic liquid and impurities not having a direct influence on the I_R phase transition temperature. However, the ionic liquid doping has a significant impact on the overall LC/I_R phase behavior, by generating nucleation centers that facilitate the dynamic phase transition process to the I_R, and in the concentration range 0.2% < c_IL < 5%, providing stabilization of the local structure of I_R phase. The gel-like nature of the I_R can be seen on cooling through the transition from N_F to I_R phase, wherein the transition boundary is not smooth liquid–liquid-like but structured. Mechanical deformation of this structure in an I_R droplet produces a reversible elastic response at low shear, and permanent deformation of the droplet at high shear.

X-ray Scattering from RM734/BMIM Mixtures.

Powder-average SAXS and WAXS scans of temperature-controlled samples in 0.7 mm diameter, thin-wall capillaries were obtained upon slow cooling, with results shown in Fig. 2 and SI Appendix, Figs. S1–S10. A selection of scans at temperatures in the N, SmZ_A, N_F, and I_R, phases in the c_IL = 1% mixture, as well as in the X (crystal) phase of undoped RM734, are shown in Fig. 2A. The complete set of X-ray scattering scans during cooling for all of the concentrations studied are available in SI Appendix. The gray- shaded peak at q ~ 0.4 Å⁻¹ is due to a Kapton window in the beam path, which is absent in room temperature scans (Fig. 2B).

Fig. 2.

SAXS and WAXS scans obtained during slow cooling of RM734β/BMIM mixtures. The I_R phase exhibits a diffuse peak at small wave vector (q ~ 0.08 Å⁻¹, SAXS Insets) indicating supermolecular periodicity (d_M ~ 80 Å), and a distinctive pattern of diffuse peaks in the q-range of side-by-side molecular packing but with wave vectors very different from those of the crystal (X) phase. (A) Scans obtained on a c_IL = 1 wt% RM734/ BMIM mixture at selected T values show the observed structure factor I(q) typical of each of the N, SmZ_A, N_F, I_R, and X phases. The complete set of scans vs. T is shown in SI Appendix. The shaded peak at q ~ 0.4 Å⁻¹ is due to a Kapton window in the X-ray beam path. The scans show significant differences between the X-ray structure function of the I_R and those of the X and higher T phases. (B) Scans obtained at T = 25 °C for selected c_IL values show that the structure–function of the I_R phase depends only weakly on BMIM concentration. The SAXS scan baselines are shifted for clarity.

Fig. 2A shows three distinct types of I(q) scans, those of i) the higher temperature, anisotropic, N, SmZ_A, and N_F phases; ii) the reentrant I_R; and iii) the low temperature crystal X phase, as follows: i) The N, SmZ_A, and N_F phases each exhibit a broad diffuse WAXS hump at q ~ 1.5 Å⁻¹, which arises from the powder average of the equatorial diffuse peak observed in the WAXS of magnetically aligned N and N_F RM734 samples and reflect side-by-side positional correlation due to steric repulsion of the molecules associated end-to-end (3, 9). Statistical distribution of different local geometries inhomogeneously broadens the hump. ii) The transition to the I_R phase results in significant changes in the scattering, including the appearance of a diffuse peak at small q in the SAXS range (Fig. 2 B, Inset), and the breakup of the broad WAXS peak into several narrower, diffuse peaks, marking the development of specific, longer ranged, side-by-side intermolecular positional correlations in the I_R phase. The apolar nature of the I_R suggests that the molecules are antiparallel in these correlations. The small-angle peak is located at q = q_M(T), where q_M = 0.080 Å⁻¹ at T = 70 °C, increasing to q_M = 0.085 Å⁻¹ at T = 25 °C. This peak position [corresponding to a length (2π/q_M) = d_M ≈ 75 Å] is indicative of three-dimensional (3D) electron density modulation of objects of dimension d_M. These objects, given the isotropy and transparency of the I_R observed optically as discussed below, would be some form of short-ranged apolar assembly of antiparallel molecules with a dimension comparable to d_M. The small angle peak is diffuse, with a half-width at half maximum (HWHM) of δq ~ 0.03 Å⁻¹, or d_M ~ 2/δq, compatible with this picture. The ratio δq/q_M ~ 0.38 is similar to that found in the static structure factor of a condensed hard sphere liquid in 3D, generated by the interference of the scattering from each sphere with that of its shell of nonoverlapping nearest neighbors (26). In the present case the “spheres” would be unit-cell-like dynamic assemblies of many tens to ~ one hundred molecules. The internal structure of these assemblies produces the principal WAXS peaks at q ~ 1.2, 1.7 Å⁻¹, the position and HWHM of which (δq ~ 0.1 Å⁻¹), indicate local order something like molecules surrounded by six colinear neighbors as a basic element. All of these elements are consistent with the observation that the I_R phase is a high-viscosity fluid gel with local short-range order, and disorder on longer length scale. iii) The birefringent crystal (X) phase reappears only several days after returning the mixture to room temperature, generating a characteristic crystal powder pattern of peaks that are considerably sharper than those of the I_R phase. Taking crystallite dimension d_X to be d_X ~ 2/δ_X, and δ_X ~ 0.01 Å⁻¹, crystallite dimensions of d_X ~ 200 Å appear to dominate the crystal scattering.

The X-ray scattering I(q) of the I_R phase at T = 25 °C in a RM734β/BMIM (c_IL = 1%) mixture is compared with that from samples with different ionic liquid concentrations in Fig. 2B. These scans show that the X-ray peak structure in the I_R phase varies only very weakly with concentration for c_IL in the range 0.2% ≤ c_IL ≤ 10%, in both the SAXS and WAXS wave vector regimes. This, and the fact that the I_R phase is observed at very low dopant concentrations, suggests that the causative molecular organization of the I_R phase is intrinsic to the RM734β host.

Optical Textures and Electro-Optics of RM734/BMIM Mixtures.

PTOM observations of the mixtures were made principally in glass cells with spacing t in the range 3.5 µm < t < 20 µm between the glass plates. One plate was coated with a pair of ITO electrodes separated by a 1.04 mm-wide gap that were used to apply in-plane electric fields, E, largely parallel to the sample plane. The cell temperature T was kept below 150 °C both during filling and afterward, as higher temperatures damaged the components, resulting in irreversible changes in phase behavior. The plates were treated with polyimide layers buffed antiparallel along a direction 3° off from the electrode edges. This preparation produces uniform planar alignment of the nematic director n(r), the local mean molecular long axis and the optic axis, parallel to the glass and oriented 3° from normal to the applied electric field. The 3° offset ensures a well-defined initial field-induced reorientation direction of n(r) with field application. Upon cooling into the N_F phase, the n(r)-P(r) couple adopts a π-twisted geometry, a result of the antipolar orientation of the ferroelectric polarization, P(r), on the two surfaces imposed by the buffing (27). Here we describe, by way of example, observations of two mixtures with different dopant concentrations in buffed cells and the behavior of a free drop of one of the mixtures on an untreated glass surface.

Example 1: c_IL = 0.2% mixture in a t = 3.5 µm cell.

Fig. 3 shows a twisted ferroelectric nematic monodomain in a c_IL = 0.2% mixture being slowly cooled through the N_F to I_R phase transition at T ≈ 66 °C. The I_R phase is dark between crossed polarizer and analyzer for all cell orientations, nucleating via a first-order transition as small domains which eventually grow to cover the whole sample. The N_F monodomain structure is largely undisturbed the IR isotropic inclusions, evidence for the screening of bound polarization charge by ions (SI Appendix, Fig. S15). The final I_R state is dark when viewed between crossed polarizer and analyzer (Fig. 3D) but can exhibit a patchy texture of weakly transmitting areas with low remnant birefringence. Estimating this birefringence, which decreases in samples with increasing c_IL and is undetectable when c_IL > 1%, indicates it to be caused by sub-10 nm thick layers on the glass surfaces where there may be induced nematic order.

Fig. 3.

PTOM images of a 3.5 µm thick RM734β/c_IL = 0.2% BMIM mixture between glass plates with antiparallel rubbed alignment layers. (A) In the N_F phase, this surface treatment results in a uniform π-twist of the director from one plate to the other, producing a pink birefringence color between crossed polarizer and analyzer. (B and C) During continuous, slow cooling from the N_F phase, dark domains of the I_R phase begin to appear at temperatures below ~70 °C, eventually covering the entire cell area (D). In such low-concentration mixtures, a thin birefringent layer a few nanometers thick remains on the sample surfaces when the bulk is in the I_R phase. Such a layer is not observed for higher BMIM concentrations (Fig. 4).

“Apolar” reentrant isotropic phase (I _R). In-plane applied electric fields of a few V/mm that are sufficient to reorient the director in the N_F phase to be nearly along the field (22) have no visible effect on the I_R dark domains. Electric field applied normal to the plates in t = 0.8 µm thick sandwich cells can enhance the weak patchy birefringence at high field, but induce no general substantial reorientation of P, i.e., induction of ferroelectric ordering, even at fields as high as 100 V/µm. This behavior differs from that typically considered antiferroelectric in crystals and liquid crystals, in which the ferroelectric ordering can be reintroduced with field applied above a threshold value which can be quite low, especially as in the case here, where there is an adjacent ferroelectric phase (10). However, as discussed in connection with Fig. 2A, the I_R has a distinct local structure which must maintain low or zero local polarization much more aggressively than that in the other phases (N, SmZ_A, N_F).

Example 2: c_IL = 1% mixture in a t = 3.5 µm cell.

The textures observed while cooling this mixture from the N to the I_R phase, with and without applied electric field as shown in Fig. 4, exhibit the following features:

Fig. 4.

PTOM image of a 3.5 µm thick RM734 sample between glass plates with antiparallel-rubbed alignment layers. This surface treatment produces nearly uniform director alignment in the N and SmZ_A phases, and a director structure that is uniformly π-twisted from one plate to the other (22) in the N_F phase. A pair of rectangular evaporated electrodes on one cell plate are spaced by 1 mm, enabling application of an in-plane electric field E. (A) Effect of applied field in the N, SmZ_A, and N_F phases. (A1 → A2) Paraelectric nematic phase (N): Applied field induces twist of n in the interior of the cell; the twist relaxes away once the field is removed. (A3) Modulated antiferroelectric phase (SmZ_A): Applied field has induced twist of n in the interior of the cell, which does not relax away once the field is removed, evidence that the SmZ_A is structured. (A3 → A4) Modulated antiferroelectric phase (SmZ_A): Following initial alignment of n with a large, in-plane field as indicated, there is little response to fields applied subsequently with strengths comparable to those that readily reorient the N phase, evidence that the SmZ_A is antiferroelectric. (A5 → A6) Ferroelectric nematic phase (N_F): Small applied fields alter the planar twist of n everywhere in the sample; the twist sense may be reversed by changing the sign of the field. (B) Nucleation and growth of the I_R phase. (B1–B3) At low temperatures, the antiferroelectric isotropic (I_R) phase grows into the N_F. At this relatively large ionic liquid concentration, there is no observable remnant birefringence in the I_R phase, even in applied fields of up to 100 V/mm. (B4) The I_R phase, viewed here without an analyzer, is essentially transparent, transmitting 8.5% more light than the surrounding air bubbles. This is consistent with the I_R showing very little scattering and nearly matching the refractive index of the glass plates, while the intensity of light passing through the bubbles is reduced by two Fresnel reflections at the air/glass interfaces.

Paraelectric nematic phase (N). The uniformly aligned N monodomain of Fig. 4A1 has a birefringence color in the first-order blue-to-green Michel-Levy band (retardance ~ 670 nm) (28)], with the larger index for optical polarization along n. Application of an in-plane electric field of the order of 100 V/mm induces a twist Freedericksz transition (7) in the narrow LC isthmus between the two air bubbles (where E is largest), reorienting n(r) in the plane of the cell and reducing the birefringence color to a first-order orange-red (Fig. 4A2). The LC regions at either end of the isthmus are below the Freedericksz threshold field.

Antiferroelectric modulated phase (SmZ _A). Upon cooling into the SmZ_A phase, the smooth N birefringence becomes textured by weak spatial nonuniformity but with the average director still along the buffing (Fig. 4A3 blue areas), forming “bookshelf” lamellar domains in a fashion similar to that observed in the SmZ_A phase (10). Now field-induced reorientation exhibits strong hysteresis, as shown by the yellow area in Fig. 4A3 at zero field, where previous application and removal of a large field reorganized this part of the cell into an array of permanently reoriented domains (Fig. 4A3). Subsequent application of (low) fields with magnitudes comparable to those used to reorient the nematic produce little additional change in the SmZ_A texture (Fig. 4A4), providing evidence that it is antiferroelectric. At lower temperatures in the SmZ_A phase, well-ordered stripe patterns with ~10 µm periodicity are observed (Fig. 5 B and C). These disappear at the transition to the N_F phase.

Fig. 5.

PTOM images of RM734/BMIM (c_IL = 1%) mixtures. (A) Optical appearance of a t ~ 30 µm thick, free drop on an untreated glass substrate obtained on cooling, with and without crossed analyzer. Here the SmZ_A layer spacing, the thickness of its antiferroelectric polar domains, is large compared to that of DIO, starting at d ~ 200 nm at high T and increasing to the micron range with decreasing T. (A1) Disordered nematic texture. (A2 to A3) Red light transmission at high T in the SmZ_A phase, due to scattering of short-wavelength light by layering with spacing comparable to the half-wavelength of blue light in the LC. (A4 to A6) Visible light scattering moving to larger wavelength and smaller scattering angle as SmZ_A layer spacing increases with decreasing T. (A7) Strong scattering makes the sample opaque. (A8) Coarsening of SmZ_A layering/polar domains becomes visible in the microscope. (A9) Disordered ferroelectric nematic texture. (B and C) Layer undulations and modulated textures in the SmZ_A phase between buffed glass plates (antiparallel buffing b) spaced by t = 20 µm. Cooling the sample into the SmZ_A phase and then heating it from the middle of the SmZ_A phase range to near the transition to the N and holding it causes stable patterns of layer undulations and extended stripes to appear. The texture in transmitted light without an analyzer is a mosaic of red-orange and yellow sawtooth-like undulations, suggesting the development of several distinct, coexisting layer spacings which scatter different wavelengths of light, as suggested schematically in the Inset in (B), under the dynamic conditions of forced layer shrinkage. In the chevron model developed to describe layer shrinkage in smectic C cells (25–27), such zig-zag defects mediate the formation of stripes, each of width comparable to the sample thickness, t, which is approximately what is observed here. (C) shows that the zig-zag texture within the stripes can be observed with crossed polarizer and analyzer. The red/green colors of the stripes interchange when the sample is rotated by a few degrees, providing additional visualization of the zig-zag optic-axis orientation.

Ferroelectric nematic phase (N _F). Upon cooling into the N_F phase, the director-polarization field twists spontaneously between the top and bottom glass plates. The resulting texture is a mosaic of Grandjean-like, planar-aligned domains having the polarization parallel to the plates, but with varying magnitude and sign of twist (Fig. 4A5). These twist domains are extremely responsive to applied fields over the entire cell area (Fig. 4A6), even at the left- and right-hand ends of the LC isthmus where the applied field is smallest, of order 1 V/mm. This is typical ferroelectric nematic behavior in an antiparallel-buffed cell.

Reentrant isotropic phase (I _R). The N_F to I_R phase transition is similar in appearance to that observed in the c_IL = 0.2% cell described above, also being first-order and with cells exhibiting heterogeneous nucleation of the I_R phase, which then grow as isolated isotropic domains (Fig. 4B1). With a cooling rate of −2 °C/min, these isotropic regions grow with time to cover the entire filled area of the cell in a few minutes, and are noticeably darker than in the c_IL = 0.2% cell, having a degree of extinction comparable to that of the optically isotropic air bubbles, i.e., the I_R regions have no detectable remnant birefringence. Fig. 4B4 shows an image of the cell in transmission with the analyzer removed. The average brightness of the I_R region is found to be 1.085 times that of the air bubbles. Given that the Fresnel reflections at the air/glass interfaces in the bubble area reduce the transmissivity of these regions by around 8%, this confirms that the intrinsic transmissivity of the I_R phase is close to 1, i.e., that the I_R is not strongly scattering.

Example 3: t ~ 30 µm thick free drop c_IL = 1% mixture on an untreated glass substrate.

A thick film enables the study of the light scattering characteristics of the SmZ_A phase. Fig. 5A shows a thick free drop on untreated glass plates being cooled through the N–SmZ_A and SmZ_A–N_F transitions viewed in transmission, with polarizer and analyzer as indicated. The N and N_F phases (seen in Fig. 5 A1, A8, and A9 respectively) have defected textures but are only weakly scattering. The SmZ_A phase (seen in Fig. 5 A2–A8), on the other hand, is initially strongly iridescent, scattering blue light which illuminates the cell and leaves the transmitted light primarily red, like the setting sun. This scattering appears when an internal modulated structure develops having a periodicity comparable to the wavelength of blue light but which is shifting to longer wavelengths upon cooling toward the N_F, eventually passing through the visible range to the infrared (Fig. 5A4). Thus the modulation period w_SmZ(T) must increase upon cooling, shifting the scattered color toward longer wavelengths and the scattering angles toward smaller values. This concentrates the red scattering toward the forward direction, into the collection aperture of the microscope, as in Fig. 5 A5 and A6. The increasing scale of the modulation period leads to an increase in the absolute scattering cross-section, to such an extent that at sufficiently low temperature, the sample becomes opaque (Fig. 5A7). At the transition to the N_F, the sample becomes transparent again, as the scattering structure of the SmZ_A phase transforms to the macroscopically defected texture of the N_F by means of a first-order phase transition. At this transition, the modulation period grows to be much longer than visible wavelengths, the scattering regime is exited, and the visible transmission observed is the result of adiabatic propagation through a smoothly distorted medium in the N_F phase (Fig. 5 A8 and A9).

Example 4: c_IL = 1% mixture in an antiparallel-buffed t = 20 µm cell.

These observations suggest that the SmZ_A modulation period increases on cooling but provide no information on the nature of the modulated structure. However, the texture shown in Fig. 5B, with the mixture in a t = 20 µm thick glass cell, provides strong evidence that the modulation is lamellar, with layers normal to the plates and on average aligned parallel to the buffing direction, b, like those of the SmZ_A phase in DIO and its mixtures in similar cells (10). This evidence is based on the behavior of thermotropic smectic lamellar phases which also have a modulation periodicity (smectic layer spacing) that is strongly temperature-dependent, such as the smectic C. When such lamellar phases are confined between flat plates with the layers normal to the plates (bookshelf alignment), it has been found that when the sample temperature is changed in such a way that the layers shrink (heating the SmZ_A, in the present case), the layers will buckle in an effort to maintain the bookshelf pitch along the average layer normal direction (29), resulting in chevron layer structures (30) and, on a larger scale, zig-zag walls (31). The chevron texture relevant here is the case where the zig-zag walls run exactly normal to the layers (32), as in Fig. 5 B and C, generating horizontal stripes of width comparable to the sample thickness t. in which locally parallel layers are deformed into zig-zag patterns. In the present case, upon heating the SmZ_A from the middle of its phase range to near the transition to the N, such undulations and long-range stripe patterns appear. The view in transmitted light without an analyzer (Fig. 5B) shows a texture of sharp undulations, the variations in color across the field of view suggesting the coexistence of several distinct layer spacings, as sketched in the inset. According to the model of ref. 27, each such in-plane undulation of the layers generates a pair of stripes, each of width equal to t, which is approximately what is observed here. The stripes appear alternately red (zig)/green (zag) when viewed between crossed polarizer and analyzer (Fig. 5C). A small rotation of the sample causes the “zig” stripe color to interchange with that of the “zag” stripes, providing additional visualization of the optic-axis orientation.

Observation of the I_R phase in undoped RM734.

The observation that even very small concentrations of ionic liquid in RM734 suffice to facilitate the transition into the I_R phase made us generally curious about the role of sample purity in determining the phase behavior of RM734. Indeed, the lack of substantial dependence of the X-ray diffraction on dopant concentration in Fig. 2 strongly suggested that the I_R structure could be a property of the RM734 host, and that undoped RM734 could, in principle, also exhibit the I_R phase. The transition into I_R phase takes place via a strong first-order phase transition bringing to mind that found in metal alloys, where there is a strong dependence on nucleation conditions, kinetics, intrinsic impurities, and temperature history (33).

We therefore carried out experiments on three distinct batches of RM734 having different impurity concentrations, and likely types: RM734α, synthesized in our laboratory according to the scheme in Materials and Methods, having a nematic (N) to ferroelectric nematic (N_F) transition temperature T_N-NF = 133 °C, the temperature reported by Mandle et al. (3); and two commercial samples, RM734β with T_N-NF = 128 °C; and RM734γ with T_N-NF = 124 °C. These transition temperatures suggest increasing impurity content in the α → β → γ sequence. Typical impurity concentrations giving comparable temperature shifts in nematic LC phase transitions are in the few % range, which can be comparable to c_IL. In undoped samples, impurities tend to suppress crystallization and promote the nucleation of the I_R phase, but with doping, even at the c_IL = 0.2% level, the enhanced promotion provided by the IL becomes dominant. Unless otherwise stated, all of the mixture data shown here and in SI Appendix were obtained using the RM734β sample.

We carried out experiments on all three batches in which we varied the temperature vs. time cooling profiles. Thermal treatments were found for each host which did not result in crystallization on cooling, eventually to T = 25 °C, and instead produced the I_R phase. Nucleation of I_R domains proceeds once the condition T < T_IR is reached, but the increase in viscosity associated with the gel-like nature of the I_R dramatically slows the growth of the phase on further cooling, similar to what is observed in the N_F phase (7, 9). A general method for obtaining the I_R is to reduce the temperature quickly to T ~ 40 °C, where the I_R is nucleated and crystals may be nucleated, but both grow very slowly, and then to heat quickly back up to a few degrees below T_IR, where the I_R domains grow much faster than crystals. In absence of IL doping, crystallization was easier to avoid with increasing impurity concentration, RM734γ being the least likely to crystallize. Samples of all three batches of RM734 did eventually crystallize but this process took days or weeks at room temperature. The WAXS scans of the I_R phase so obtained in the three host batches at T = 25 °C are shown in Fig. 6, along with the RM734β/c_IL = 1% BMIM mixture scan. The scans show only minor differences, supporting the notion that the I_R phase is a property of RM734.

Fig. 6.

Scans showing the SAXS/WAXS X-ray structure functions I(q) of the low-temperature isotropic (I_R) phase at T = 25 °C in three undoped RM734 samples, along with the T = 25 °C scan of the RM734β sample doped with c_IL = 1 wt% BMIM. The intensities are scaled such that the heights of the q = 1.7 Å⁻¹ peaks match. The RM734α scan includes a Kapton peak at q = 0.4 Å⁻¹ which is absent in the other measurements. The scattering patterns of all four samples are similar, implying that the three undoped samples of RM734 have I_R phase structures very similar to that of the doped liquid crystal.

Comparison of Doping with BMIM and EMIM.

Figs. 2B and 6 show that the SAXS/WAXS X-ray structure factors of the I_R phase do not depend strongly on IL concentration Fig. 7 compares SAXS/WAXS scans at T = 25 °C of RM734 samples mixed respectively with c_IL = 5% BMIM and c_IL = 5% EMIM. These have similar 1-methyl-3-alkylimidazolium cations but quite different anions. The scans exhibit almost identical peak structures, providing further evidence that the I_R phase is inherently a property of the host molecule. This result is consistent with the observed phase behavior and microscopic textures of the two mixtures, with EMIM and BMIM doping producing essentially the same phenomenology in RM734 (34, 35).

Fig. 7.

X-ray scattering from RM734 doped with two different ionic liquids. These scans show the SAXS/WAXS X-ray structure functions at T = 25 °C of the I_R phase of RM734β samples doped respectively with c_IL = 5 wt% BMIM and c_IL = 5 wt% EMIM, scaled such that the q = 1.7 Å⁻¹ peaks have the same height. The two samples produce very similar scattering, indicating that BMIM and EMIM, which differ significantly in anion structure, facilitate formation of I_R phases with very similar structure in RM734.

Discussion

Reentrant Isotropy.

The identification of the I_R phase adds an exciting dimension to the ferroelectric nematic realm. The N_F phase, with its saturated nematic order, and nearly perfect polar order even at elevated temperature, can be considered to be perhaps the most-ordered nematic phase. While the N, SmZ_A, and N_F phases combine long-range orientational order with short-range positional disorder, the I_R phase lacks long-range orientational order but has exceptionally robust, short-range molecular positional correlations (Fig. 2A). The thermodynamic availability of the I_R upon cooling points to internal energetic frustration in the N_F as the principal driving force for this transition. This makes the N_F– I_R phase transition a cousin of the nematic-to-helical antiferroelectric twist-bend (N–TB_A) transition, wherein a large internal energy cost in the packing of bent molecules in the N phase is traded for a more compact, short-range “brickwork” packing motif in the TB_A that has lower internal energy, a motif that stabilizes a different (helical) form of long-range ordering (36–38). In the N_F– I_R case, the change in the structure factor I(q) upon passing from the N_F to the I_R is dramatic, as seen in Fig. 2A, with the I_R showing much more distinct, but not crystalline, diffuse peaks in the range (1 Å⁻¹ ≲ q ≲ 2 Å⁻¹). Well-defined, diffuse peaks in this q-range are familiar in phases of rod-shaped or bent-core mesogens, where they arise from the side-by-side packing of molecules in smectic layers on short-range hexagonal (39) or herringbone lattices (40, 41). In the present case, a related energetically preferred local packing generates local correlations which stabilize long-range isotropy.

Thermotropic liquid crystal reentrant isotropy was first reported by Luzatti and Spegt in the cubic Ia3d gyroid phase of strontium alkanoates (42, 43), a phase structure which was also found in the phenyl carboxylate dimers NO₂-n-BCA upon cooling from a smectic C (44–46), and has been observed since then in numerous other systems (47–50). The local gyroid structure is an assembly of molecules into extended supermolecular linear aggregates which form three interlinked sets of spring-like helices, one set running along each of the Cartesian coordinate directions to generate a lattice of cubic symmetry made up of mesoscopic unit cells containing hundreds to thousands of molecules (35–43). Their cubic symmetry renders such phases optically isotropic. The gyroid helices are chiral, which opens the possibility of isotropic phases having macroscopic chirality and consequent optical activity, even if the constituent molecules are achiral. Achiral molecules can also give rise to achiral isotropic phases if helical segments are found in mirror-symmetric pairs, as in the Ia3d.

Another specific example, which may be of particular relevance to the I_R phase in RM734, is the fluid isotropic cubic phase obtained upon cooling the smectic C in the 1,2-bis( 4’n-alkoxybenzoyl) hydrazine (BABH-n) homologous series, also Ia3d (51–59). In this system, at low temperatures the intermolecular hydrogen-bonding between side-by-side, rod-shaped cores enhances the hourglass shape of the molecules (thin cores with fat tails), and thereby the tendency for local twist, stabilizing a cubic phase having equivalent helical networks of opposite chirality (60). Heating increases the side-by-side entropic repulsion of the flexible tails, breaking the intermolecular hydrogen bonds and producing a smectic C phase. Such effects of tail entropy can be enhanced by the use of multitail (phasmidic) molecules, making induction of local twist an effective method for obtaining cubic phases (41, 42, 61).

Extensive X-ray scattering on powder samples has been carried out on such cubic soft crystal systems in the low-Miller index range of their cubic lattice reciprocal spaces, generally with scattering vectors in the SAXS regime (q ≲ 0.4 Å^-1). In many such cases, sets of scattering peaks can be indexed, and in some cases, the peak intensities have been used to calculate unit cell electron density. The observed peak widths appear to be broader than the resolution limits, indicating that crystallite sizes, deduced from the inverse X-ray peak widths, are limited by lattice defects. However, optical observations show the growth of millimeter-dimension, cubic single crystals in some systems (41), providing direct evidence for long-range cubic crystal order.

In contrast, the SAXS scattering from the I_R phase in the selection of RM734 samples, mixtures, and temperatures studied here, exhibits a single peak at scattering vectors in the range 0.07 Å⁻¹ ≲ q_M(T) ≲ 0.1 Å⁻¹, with a HWHM δq ~ 0.03 Å⁻¹ that is two orders of magnitude broader than the diffractometer resolution. Thus, this RM734 SAXS scattering peak is diffuse, indicating short-range positional correlations which, given this q_M(T) range, have a length scale comparable to the unit cell sizes in the cubic systems cited above but without long-range cubic crystalline order. This situation is a good description of the “sponge phases” of lyotropic amphiphiles (62), and bent-core smectics (63), and of the Cubic*(Ia3d) – Iso₁* – Iso₂ phase sequences with increasing T observed by Tschierske et al. in a family of achiral polycantenar mesogens, which exhibit Ia3d cubic phases with macroscopic spontaneous chirality (64, 65). The Iso₁* phase has a diffuse scattering peak at q-values where the cubic phase of this family has Bragg reflections, indicating short-range, cubic positional correlations in the Iso₁*. Remarkably, such correlations can maintain the macroscopic chirality of the cubic lattices, the Iso₁* exhibiting conglomerate domains of opposite optical rotation, indicating that they preserve and transmit their local chiral structure to their neighbors (57, 58) even in the absence of a long-range lattice, as has also been found in bent-cores (56). The I_R phase of RM734 may be an achiral example of such behavior, exhibiting similar cubic correlations, suggesting that a related, lower-temperature phase with long-range, cubic structure may exist.

While the SAXS data on cubic phases are extensive, there have been very few systematic studies of reentrant isotropics in the WAXS range (q > 0.5 Å⁻¹), where larger scattering vectors can probe the details of molecular side-by-side packing, of relevance in our system. High-temperature phases such as the spontaneously chiral cubics have a broad, diffuse WAXS reflection (57), similar to that of the high-temperature N and N_F phases of RM734.

However, we have found several experimental systems which exhibit low-temperature, isotropic polymorphism and have distinct, diffuse WAXS peaks very similar to those of the I_R phase, as shown in SI Appendix, Fig. S14. The first is the 50 wt% mixture of the rod-shaped mesogen 8CB with the material W624 (compound 2b in ref. 66), where a thermotropic smectic C-to-isotropic* dimorphism was observed (67). X-ray scattering and extensive freeze-fracture transmission electron microscopy visualization of the local structure in the spontaneously chiral Isotropic* (dark conglomerate) phase showed it to be locally lamellar with strong side-by-side molecular positional correlations and a strong tendency for local saddle-splay layer curvature, the latter driving the assembly of a disordered network of gyroid-like, branched arrays of filaments of nested cylindrical layers (59), a form of sponge phase (55). A similar low-T isotropic phase was also found in neat samples of the bent-core molecule 12-OPIMB (60). These phases feature director splay and saddle splay everywhere, which might serve to stabilize such a phase in the ferroelectric nematic realm (68). However, while these isotropics produce WAXS peaks similar to those of the I_R, their small-q scattering is quite different from that of the I_R, their local nested-cylinder layer structure producing a sequence of smectic-like diffuse peaks in a 1:2:3 lamellar harmonic sequence (59), which is not observed in the RM734 I_R. A quite different low-T isotropic system having X-ray structure more like the I_R of RM734 is described in ref. 69, which reports a small azo-based molecule (W470), which forms side-by-side linear aggregates and gels when diluted with solvent. However, the structure of the reentrant isotropic phase of W470 has not been established.

The soft cubic phases discussed above are based on nanosegregation, which in the gyroid case involves the formation of filamentous networks. Other nanosegregation motifs which may be relevant to understanding the I_R phase are the formation of localized aggregates, such as micelles or localized topological singularities, which then self-assemble into higher-symmetry arrays (35). Experimental demonstrations include crystals of complex defects such as skyrmions (70) and knots (71), block-copolymers (72), and hybrid thermotropic 3D variations, the so-called “transparent nematic” in which dispersed didodecylammonium bromide micelles serve as the cores of fluid hedgehog defects in a rod-shaped mesogenic nematic (73, 74). Periodic arrays of nematic topological defects have been shown theoretically to form stable, space-filling crystal structures (61, 75–78).

SmZ_A Phase.

While the I_R phase shows distinctive microscopic textures and characteristic X-ray scattering features, the WAXS powder structure function of the SmZ_A phase is very similar to those of the N and N_F phases, which bound it in the phase diagram, so that the SmZ_A is difficult to distinguish by X-ray scattering. The SmZ_A phase is observable in the microscope at higher ionic dopant concentration (for example, for c_IL ≥ 0.2%, as in Fig. 5) but is not unambiguously distinguishable optically from pretransition behavior at smaller concentrations or in undoped RM734.

However, the intermediate SmZ_A phase range can be found by precision adiabatic calorimetry by showing the N – SmZ_A and SmZ_A – N_F transitions clearly, at temperatures T_NZ and T_ZF, respectively (11, 12). In RM734/DIO mixtures, with 88% RM734, the SmZ_A range is found to be T_NZ − T_ZF ~2 °C (11), and the SmZ_A nature of this intermediate phase confirmed by continuity of the textures from the higher DIO concentrations where the SmZ_A range is broader. In the absence of DIO doping, the SmZ_A range is found to be T_NZ − T_ZF ~1 °C for RM734 samples of varying nonionic impurity, having T_ZF in the range 132° < T_ZF < 124 °C (12). Thus, with IL doping, due to the low concentrations involved, there is concern about the role of impurities on the SmZ_A phase behavior. Ref. 12 provides information on this issue by reporting T_ZF − T_NZ in RM734 samples with no IL but varying degrees of impurity due to synthetic byproducts and/or thermal degradation. The results show that while the center temperature of the SmZ_A phase range T_NZ = (T_NZ+ T_ZF)/2 can be depressed by impurities by ~8 °C from T = 132 °C, its maximum (highest purity) value among the available samples, the width of the SmZ_A phase range remains nearly constant at ΔT ~ 1.1 °C. On the other hand, according to Fig. 1, the SmZ_A range increases dramatically with IL dopant concentration, indicating a distinct difference between the effect of synthetic and degradation impurities vs. that of ionic impurities. If this is a proper distinction then the SmZ_A phase in RM734 could possibly be a result of some remnant ionic contamination in the as-prepared RM734 samples. In any case, given the very low ion-doping concentration levels involved, sorting out the SmZ_A and I_R phase behavior in “pure” and doped RM734, will require much cleaner RM734 samples than are currently available.

Our observations in the SmZ_A region of Fig. 1B (16) can be summarized as follows: i) the SmZ_A phase temperature range grows exponentially with the ionic liquid concentration, which stabilizes it as an equilibrium phase of the mixtures, intermediate between the N and (N_F or I_R) phases; ii) the SmZ_A phase has a periodic modulation of fluid smectic-like layers; iii) the SmZ_A phase is antiferroelectric; iv) Cooling of the SmZ_A phase produces dramatic layer expansion, which, upon subsequent heating, leads to layer shrinkage, which drives undulations and a chevron layer texture (27). As in DIO, this highly directional texture not only provides direct evidence of smectic layering but also reveals the orientation of the layer normal in 3D. These similarities lead us to identify this modulated phase as a SmZ_A variant having a layer spacing that grows monotonically over the range ~0.2 µm < d < ~100 micron range with decreasing temperature. v) in cells with rubbed alignment surfaces, the SmZ_A phase forms “bookshelf” lamellar domains with the director along the rubbing and the layers normal to the cell plates, as shown in Fig. 5 B and C, in a fashion identical to that of the SmZ_A in DIO (10).

A recently reported Landau model of the SmZ_A under conditions of ionic liquid doping, incorporating Debye screening of polarization-associated electrostatic fields in the fluid by free ions, provides a good qualitative description of features (i– iv) above (17). In this model N_F stripes or columns, having a native flexoelectric tendency for splay, form periodic arrays in one or two dimensions, respectively, where neighbors have antiparallel polarization direction and are separated by polarization reversal walls. These walls have net charge which is compensated by ∇·P space charge in the splayed regions. The phase behavior is controlled by the temperature-dependent coefficient of the P² term in the Landau model, which results in growth of the local polarization magnitude and dramatic growth of the modulation period as temperature is decreased in the SmZ_A. These electrostatic effects are reduced with increasing ionic liquid concentration by Debye screening, limiting the growth of the modulation period and producing a dramatic increase of the SmZ_A phase range.

Nucleation of Reentrant Isotropic Domains.

The examples of complex phases having isotropic symmetry above recount various arrangements of rod-shaped molecules can make isotropic phases by appropriate short-range nanoscale organization, a likely element in the stabilization of the I_R phase. Essentially any of these arrangement can be made from antiparallel molecular pairs to produce apolar short-range ordered structures. Our data show that, while IL doping does not substantially alter the structure of the I_R phase, it appears that very low concentrations facilitate nucleation of domains of the I_R in the N_F, evidence for an N_F – I_R first-order phase transition. The classical nucleation model of this (79) would consider the free energy cost ΔG(R, T) = V(R)[Δg(T) + U_P]+ A(R)σ of formation spherical nucleated drop of radius R of I_R in an aligned N_F, where V(R) and A(R) are the drop volume and area, respectively. Here Δg(T) = g_NF – g_IR, the bulk free energy density difference between the two phases, which must be negative, and U_P ~ P²/6ε (80) is the positive excess electrostatic energy density due to the separation of polarization surface charge across the drop, assuming that the drop is isotropic and polarization-free, and the N_F host is a uniformly oriented domain. This polarization contribution reduces |Δg(T)|, increasing the size of the critical diameter R_c = 2σ/|Δg(T) + U_P| needed for a drop to grow rather than shrink in diameter, and increasing the (barrier) energy ΔG* = 16πσ³/3 | Δg(T) + U_P|² needed by a drop to get to R_c (79), both trends making nucleation less probable. However, The N_F polarization field around an isotropic inclusion in a fluid N_F can spontaneously rearrange to substantially reduce U_P, leaving characteristic structural features in the bulk N_F, as discussed in SI Appendix, Fig. S15 A–C. These deformations require a reduced but nonzero remnant electrostatic/elastic contribution to U_P, and therefore some electrostatic contribution to the barrier for nucleation of the I_R phase. However, SI Appendix, Fig. S15 D and E show that experimentally such deformations are absent in N_F textures in IL-doped RM734 and DIO (18) which have reentrant isotropic domains growing as isotropic inclusions in comparatively undisturbed N_F. This indicates that introducing ionic liquid has reduced U_P to a condition similar to that of nucleation and growth in first-order LC phase transitions where there are no electrostatic effects, as typified by the isotropic droplets growing into the nematic phase of E7 upon heating, illustrated in SI Appendix, Fig. S15F (81). A straightforward explanation of this behavior is screening of electrostatic fields by the IL solute ions, as in the interpretation noted in the previous paragraph of SmZ_A behavior. From the estimates of Debye screening lengths λ_D in ref. 17, e.g., λ_D = 4.1 nm at c_IL = 0.2% assuming complete dissociation of the ions, screening would start reducing nucleation barriers at R_c ~ 2 nm, i.e., near the beginning of nucleation since the short-range structure of the I_R must be at least this scale. SI Appendix, Fig. S15G shows that, in contrast with IL-doped RM734, I_R domain growth in undoped RM734 generates electrostatic deformation in the N_F. This is consistent with the observation that nucleation is more difficult without IL doping, requiring deeper supercooling.

Summary.

Refs. 3–8 opened the pathway leading to the identification of ferroelectric nematic phases in the materials RM734 and DIO, which are longitudinally polar molecular rods with quite different chemical structure. Subsequent work created the ferroelectric nematic realm: i) by showing that these two ferroelectric nematics were actually the same phase (9); ii) by introducing several entirely new phases in these and related materials based on their ability to achieve strong local polar order (10–13); and iii) by further stimulating a now growing family of new materials exhibiting these phases as well as additional ones, and featuring a diverse array of new behaviors.

However, at the heart of ferroelectric nematic research activity lies the following basic, unanswered question: “What sets N_F-forming molecules apart from the countless others (~100,000?) in the liquid crystal literature which have very similar structure and polarity but do not make N_F phases?” It seemed likely from the beginning that some specific unappreciated nanoscale motif of molecular association that enables strong spontaneous polar ordering had been engaged in the N_F. The identification of reentrant isotropic phases in RM734 and DIO provides further evidence for the existence of such a mechanism, simply by showing that it has another job to do. Notwithstanding the few examples summarized above, reentrant isotropy is a quite rare phenomenon in liquid crystal phase behavior, so to find it in both RM734 and DIO, with similarities of local structure, in spite of the significant chemical differences between the two molecules, is likely not to be just coincidence. The local motif must enable both the N_F and the I_R.

Materials and Methods

The mixtures studies were studied using standard liquid crystal phase analysis techniques previously described (7, 9, 10, 13), including PTOM observation of LC textures and their response to electric field, X-ray scattering (SAXS and WAXS), and techniques for measuring polarization and determining electro-optic response. Materials and methods are detailed in SI Appendix.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

SAXS, WAXS, and PTOM data have been deposited in Open Science Framework (DOI: 10.17605/OSF.IO/PNGVE) (82).