First-principles experimental demonstration of ferroelectricity in a thermotropic nematic liquid crystal: Polar domains and striking electro-optics

Abstract

We report the experimental determination of the structure and response to applied electric field of the lower-temperature nematic phase of the previously reported calamitic compound 4-[(4-nitrophenoxy)carbonyl]phenyl2,4-dimethoxybenzoate (RM734). We exploit its electro-optics to visualize the appearance, in the absence of applied field, of a permanent electric polarization density, manifested as a spontaneously broken symmetry in distinct domains of opposite polar orientation. Polarization reversal is mediated by field-induced domain wall movement, making this phase ferroelectric, a 3D uniaxial nematic having a spontaneous, reorientable polarization locally parallel to the director. This polarization density saturates at a low temperature value of ∼6 µC/cm², the largest ever measured for a fluid or glassy material. This polarization is comparable to that of solid state ferroelectrics and is close to the average value obtained by assuming perfect, polar alignment of molecular dipoles in the nematic. We find a host of spectacular optical and hydrodynamic effects driven by ultralow applied field (E ∼ 1 V/cm), produced by the coupling of the large polarization to nematic birefringence and flow. Electrostatic self-interaction of the polarization charge renders the transition from the nematic phase mean field-like and weakly first order and controls the director field structure of the ferroelectric phase. Atomistic molecular dynamics simulation reveals short-range polar molecular interactions that favor ferroelectric ordering, including a tendency for head-to-tail association into polar, chain-like assemblies having polar lateral correlations. These results indicate a significant potential for transformative, new nematic physics, chemistry, and applications based on the enhanced understanding, development, and exploitation of molecular electrostatic interaction.

Keywords: ferroelectric; liquid; liquid crystal; nematic; polar.

Fig. 1.

Ferroelectric nematic phase. (A) Structure of RM734 and schematic of molecular alignment in the ferroelectric nematic (N_F) phase. The molecular organization is translationally symmetric in 3D and macroscopically uniaxial, with local mean molecular long axis, n(r), aligned generally along the buffing direction z, and polar, with a local, mean molecular dipole orientation, P(r), along n. H and O are used to represent the methoxy and nitro ends of the molecule, respectively. (B–G) DTLM images showing electro-optic evidence for ferroelectricity in a planar-aligned cell of RM734 in the N_F phase (t = 11 µm thick). In the higher-temperature N phase, P(r) = 0, but when cooled into the N_F phase without an applied field, RM734 spontaneously forms macroscopic domains with P > 0 or P < 0. When slowly cooled below the N_F phase transition at T = 133 °C, the initial texture (B) coarsens into a pattern of domains with distinct boundaries (C). (D–G) T = 120 °C. Starting from D with no field, application of an ultrasmall in-plane test field |E_z| ∼0.5 V/cm along the buffing direction produces reversible reorientation of P without changing its magnitude. (E and F) Application of a negative E_z starts the in-plane reorientation of n(r) about x inside the domains, producing the dark bands there, while (G) positive E_z produces reorientation outside of the domains, proving that these regions are of opposite polarization. The E ∼ 1 V/cm threshold field for this reorientation indicates that n(r) in these domains is coupled to E by a polarization P ∼5 µC/cm², which is comparable to the bulk polarization density measured electronically. The higher applied field in F has moved the boundary of one lenticular domain to increase the area with the field-preferred orientation, effecting a hysteretic reversal of P(r). (Scale bar, 30 µm.)

Fig. 2.

DTLM images showing polar Freedericksz twist transition in ferroelectric domains with opposite polar orientation at T = 120 °C. These domains, grown field-free upon cooling from the N phase to this temperature, have a polarization density P. (A) Field-free initial state showing three domains separated by domain walls, each domain having n(r) along the buffing direction z. (B) Application of an ultra-small, positive test field E_z = 1 V/cm induces a birefringence color change resulting from in-plane reorientation of n(r) in the center domain, leaving the upper and lower domains unchanged. (C) Application of E_z < 0 induces an in-plane reorientation of n(r) in the upper and lower domains. There is little optical change or reorientation in the central domain. If the field is returned to E = 0, the system returns to the starting state (A). These observations demonstrate that the domains are polar and also enable the absolute determination of the direction of P(r): domains that have the orientation preferred by the applied field do not reorient. In this experiment, P(r) and n(r) within the domains rotate about x but the field is not large enough to move the domain walls, which are pinned by the surfaces. The polarization vectors (shaded green) and circular arcs (white) depict the field-induced reorientation of P(r) in the midplane of the cell: P(r) does not reorient at the surfaces in this experiment, remaining parallel to the buffing direction. These field-induced reorientations with P(r) starting nearly antiparallel to E are polar azimuthal Freedericksz transitions. The threshold field, E_P = (π/t)²(K_T/P), estimated using the measured P ∼5 µC/cm² at T =120 °C (Fig. 3), is E_P ∼1 V/cm, comparable to the fields employed here. t = 11 µm. (Scale bar, 30 µm.)

Fig. 3.

Characteristics of polarization reversal in an applied field. (A) Temperature dependence of the cell current with a 200-Hz square wave generating a field E_p = 95 V/mm applied in-plane to a t = 15-µm-thick cell with 1-cm-wide ITO electrodes spaced by d = 1 mm. In the I and N phases (T ≥ 133 °C), the current is small and capacitive. On cooling into the N_F phase, an additional current contribution appears, the area of which is independent of voltage and is equal to the net polarization reversal charge, Q = 2PA, where A = 15 µm × 1 cm is the effective cross-sectional area of the volume of LC material reoriented by the applied field. In the N_F phase, the polarization reversal current becomes a distinct peak that grows in area on cooling, indicative of an increasing polarization density, and the reorientation takes place more slowly, reflecting the increase of orientational viscosity. The double-headed arrow shows the reversal time at T = 110 °C (dashed drop lines in C). (B) The polarization density P of RM734 measured on cooling (black squares) saturates at P ∼6 µC/cm² at the lowest temperatures. The open circles are values of P of the plupolar nematic calculated from the POL MD simulation of the N_F phase (Fig. 7 and SI Appendix, Sections S9 and S10). In the plupolar nematic, long-wavelength orientation fluctuations are suppressed, giving a P value determined by molecular-scale fluctuations and local packing. RM734 approaches the plupolar condition at low T. The region near the transition has not been studied in detail. (C) Field dependence of the reversal time 𝛥t, taken as the full width at half-height of the polarization or optical reversal pulse following a field step in a 100-Hz, bipolar, square-pulse train of peak amplitude E_p in planar-aligned cells with in-plane electrodes spaced by d = 20 µm, 60 µm, and 1 mm at T = 110 °C. The reversal time scales as 1/E_p as expected for reorientation driven by ferroelectric torques. The dashed lines identify the measurement with E_p = 95 V/mm highlighted in A. The risetime 𝜏 = γ₁/PE is ∼0.1𝛥t, giving a value of γ₁ ∼0.1 Pa-s, comparable to the viscosity of 5CB at T =25 °C.

Fig. 4.

DTLM images of a large, twisted domain with surface polarization pointing to the right, surrounded by a uniform region with surface and bulk polarization pointing to the left, in the direction of an applied field. (A) Twisted domain (magenta) and structural elements P, n, and E. (B) The section drawing shows the two-dimensional structure of the cell in the x, z plane along the top edge of the image: the uniform (U), field-preferred state of the background; the surface orientations reversing at the boundaries of the central domain; P in the twisted–untwisted (TU) state in the center of the domain, with the orientation in the middle of the cell indicated by green vectors, and the intermediate left- and right-handed twisted states T_L and T_R (olive and gold). π surface disclination lines (magenta dots) mediate polarization reorientation at the top (pink line) and bottom (cyan line) cell plates. Where the surface disclination lines overlap, the director is uniformly oriented along y through the thickness of the cell, giving extinction between the crossed polarizers (dark spots circled in A). In the absence of applied field, the left and right surface polarization states are energetically equivalent. (C) The central domain shrinks with increasing E field. The birefringence color changes from green to blue to pink as the rotation of P in the middle of the cell increases. T = 120 °C. t = 11 µm. Silica spheres (orange arrow) for visual size reference in the bottom of C have an apparent diameter of 4 µm (See SI Appendix, Fig. S10). (Scale bars, 35 µm.)

Fig. 5.

Common polarization reversal scenarios in RM734. Field-induced reorientation of P is indicated schematically using white arcs and green vectors. (A) Stripe formation. Applying a 5-Hz triangle-wave electric field with peak amplitudes in the range 0 < E_p < 10 V/cm to a region with an initially uniform in-plane director (panel 1) induces a periodic modulation in the orientation of n(r) and P(r) along z (a director bend wave; panel 2) whenever the field changes sign. As the applied field strength is increased (panels 3 and 4), the stripes form with sharper boundaries and have uniform internal orientation determined by the field strength. The zigzag arrangement of the director in successive stripes ensures that the normal component of P is constant across the stripe boundaries, so that there is no net polarization charge there. (B) Polygonal domains. During field reversal, polarization charge effects alternatively lead to the formation of tile-like domains with uniform n(r). These polygons have sharp domain boundaries that are oriented such that P⋅l, where l is along the boundary, is the same on both sides of the boundary, reducing space charge. The angular jump in n(r) across the boundary highlighted in panel 4 is 90°. (C) Director field reorientation around inclusions. Air bubbles in the cell can be used to track the orientation of n(r) in a reversing field. The director field near the bubble, sketched below each panel, is locally distorted, bending around the inclusion with splay deformations confined to two 180° wedge disclinations (red dots) located at opposite ends of the bubble. The blue color in panels 4 and 5 is indicative of a TU state of the kind shown in Fig. 4, with a surface disclination then moving out from the bubble boundary to give the final, uniform state seen in panel 6. (Scale bars, 40 µm in A, 30 µm in B, and 20 µm in C.)

Fig. 6.

Field-induced flow in the ferroelectric nematic phase. (A) DTLM image of a t = 10-µm-thick, planar-aligned cell of RM734 between untreated glass plates, in the N_F phase at T = 120 °C. The black bars at the bottom are two evaporated gold electrodes on one of the plates, separated by a d = 60 µm gap. The electrodes are outlined in white for clarity. Only the upper edges of the electrodes and the adjacent part of the cell are shown. A square-wave voltage with V_p = 3 V, 0.1 Hz, is applied to the electrodes, producing an electric field in the plane of the cell. This field drives a pattern of defect motion and fluid flow over the entire field of view, with the defect velocity v(r) (white arrows) parallel to the applied field, E(r) (green), which is tangent to half-circles centered on the electrode gap (SI Appendix, Fig. S12). Where the defects are dense, their motion transports the surrounding fluid. When the field is applied, the entire region shown here moves along the field lines. This image, captured during field reversal, shows a periodic array of bend domain walls normal to the director (yellow) and the applied field, as in Fig. 5A, in this case along radial lines. (B) Typical defect in the texture moving along the applied field direction (down in Left and up in Right), in the location circled in A. (C) Temperature dependence of the magnitude of the initial defect velocity along the white dashed track in A following a field reversal. There is no flow in the N phase but on cooling into the N_F phase, the velocity increases rapidly with increasing P before decreasing again at lower T because of the increasing viscosity. A similar dependence on T is observed whether heating or cooling. (Scale bars, 1 mm in A and 100 µm in B.)

Fig. 7.

Results of atomistic molecular dynamic simulations probing molecular-scale organization leading to polar order. (A) RM734, showing its geometrical long axis vector u, terminating at the nitro- (O) and methoxy (H) molecular ends. A nanoscale volume containing 384 molecules is equilibrated into two distinct LC states: a POLAR system with all polar molecular long axes, u, along +z and a NONPOLAR system with half along +z and half along −z. Equilibration of the molecular conformation and packing is readily achieved, but end-to-end flips are rare, so the simulated states remain in the polar or nonpolar limit of equilibrated nematic order. (B–E) Molecular positional/orientational pair correlation functions: conditional probabilities of molecular centers (magenta), about centers fixed at the origin (white dots). (B, F, and G) The POL simulation shows directly the dominant pair correlations adopted by molecules that are polar ordered, in the form of conditional probability densities, g(ρ,z), of molecular centers (magenta fill) around a molecule with its center (white dots) at the origin and long axis u along z. The g(ρ,z) are 𝜑-averaged to be uniaxially symmetric, reflecting the uniaxial symmetry of the N and N_F phases. They exhibit a molecule-shaped, low-density region [g(ρ,z) ∼0] around the origin resulting from the steric overlap exclusion of the molecules; an asymptotic constant value at large ρ giving the normalized average density [g(ρ,z) = 1]; and distinct peaks indicating preferred modes of molecular packing. This analysis reveals two principal preferred packing modes in the POL system: (B and F) polar head-to-tail association stabilized by the attraction of the terminal nitro and methoxy groups and (B and G) polar side-by-side association governed by group charges along the molecule, nitro-lateral methoxy attraction, and steric interactions of the lateral methoxys. (D and E) The NONPOL system exhibits distinct correlation functions for antiparallel and parallel molecular pairs, g_NP^anti(ρ,z) and g_NP^par(ρ,z). (E, H, and I) The preferred antiparallel packing gives strong side-by-side correlations, governed by group charges along the molecule, and (E, J, and K) weaker antipolar nitro–nitro end-to-end association. (D, F, and G) The parallel correlations in the NONPOL system are the most relevant to the stability of polar order in the N_F phase as they are determined by the inherent tendency of the molecular interactions for polar ordering in the presence of enforced polar disorder. Comparison of B and D shows identical preferred modes of parallel association in the two systems, with the POL system correlations being even stronger in the NONPOL system. This is clear evidence that the polar packing motifs giving the correlation functions (B) and (D), exemplified by the sample POL MD configurations (F) and (G), stabilize the polar order of the ferroelectric nematic phase.