On the molecular origins of the ferroelectric splay nematic phase

The study addresses why and how ferroelectric (polar) nematic order can arise in bulk molecular liquid crystals and why closely related compounds may or may not exhibit the splay-nematic (Ns) phase. Although ferroic order in dipolar liquids is not fundamentally forbidden, long-range polar order in rod-like nematics has been elusive due to entropic and dipolar interaction constraints that favor antiparallel arrangements. Recent discovery of a ferroelectric splay-nematic phase in RM734 revealed macroscopic polarization and splay elastic softening, but small structural modifications (e.g., replacing terminal nitro with nitrile) suppress the Ns phase. The purpose is to identify the microscopic (molecular-level) mechanism driving the emergence of polar nematic order and the Ns phase by comparing RM734 with its nitrile analogue RM734-CN. The work combines experiments and simulations to test whether polar order is favored by molecular packing (reduced excluded volume) and to establish diagnostics (e.g., X-ray scattering) and computational tools for predicting materials exhibiting polar nematic phases.

Prior theoretical and experimental studies show that disk-like particles can give ferromagnetic nematic order; however, polar nematic phases in thermotropic molecular systems were only recently realized. RM734-like materials (elongated, large longitudinal dipole, slight wedge shape with lateral groups) exhibit a high-temperature apolar nematic (N) and a low-temperature ferroelectric splay-nematic (Ns) phase, with a ferroelectric–ferroelastic transition accompanied by splay elastic softening and micron-scale director modulation. Requirements identified for Ns in RM734 analogues include short terminal chains and a terminal nitro group; replacing nitro with nitrile (RM734-CN) eliminates Ns, and even small admixtures suppress the phase. A DIO compound with related features showed similar low-temperature polar nematic behavior, later confirmed as the same Ns phase. Despite these advances, Ns examples are scarce and typically at high temperature, and the microscopic mechanism remains unclear. Theory (e.g., density functional treatments) suggested that increasing density and conical/wedge molecular geometry can favor polar order and elastic softening, motivating investigation of packing and excluded volume effects.

The authors conducted a combined experimental–computational study comparing RM734 (nitro-terminated) and RM734-CN (nitrile-terminated):

• Broadband dielectric spectroscopy (10^3–1.1×10^8 Hz) on homeotropically aligned samples between gold-plated electrodes, measuring on cooling from isotropic. Spectra were fit with the Havriliak–Negami equation to extract characteristic relaxation processes (frequencies and amplitudes) and to identify molecular (m2, m3) and collective (m1) modes.
• Viscoelastic characterization via dynamic light scattering (DLS) to probe splay fluctuation relaxation rates and intensities (pure splay geometry), combined with Frederiks transition thresholds in planar cells to obtain absolute splay elastic constant K1. From relaxation rates K1/η1, splay viscosities η1 were determined versus temperature.
• X-ray scattering (SAXS/WAXS) on magnetically aligned samples; small-angle intensities were radially integrated; orientational order parameters P2 were extracted from azimuthally integrated WAXS patterns.
• Normalized density change measurements across phases by monitoring meniscus displacement in a sealed rectangular capillary under polarized optical microscopy during controlled cooling.
• Electronic structure (DFT) calculations: M06HF-D3/aug-cc-pVTZ level, fully relaxed dihedral scans, dipole moments and orientations, polarizabilities at 800 nm; RESP charges (for MD) from B3LYP/6-31G(d) optimized geometries.
• Molecular dynamics (MD) simulations: fully atomistic GROMACS using GAFF-LCFF force field with RESP charges. Systems of 680 molecules initialized in polar (all dipoles +x) or apolar (1:1 +x/−x) nematic configurations. After compression to ~1 g cm^-3, 30 ns equilibration, 250 ns production runs with anisotropic barostat at 1 bar, Nosé–Hoover thermostat, PME electrostatics and 1.2 nm cutoffs. Temperatures from 400–600 K were explored by reheating/cooling. Orientational order parameters P2, biaxiality B, polar order P1, polarization P, and director–polarization angle were computed. Cylindrical pair-correlation functions g(r,h) analyzed packing motifs. Simulated SAXS/WAXS patterns and small-angle intensities I(Q) were computed (CRYSOL and custom procedures) and compared to experiments. Additional analogues (RM63, RM500, RM554) were also simulated in polar/apolar nematic configurations to test generality.

• Dielectric spectroscopy: In both materials the isotropic phase shows a broad single relaxation (~40 MHz, Δε_iso ~ 12). In the nematic phase, spectra decompose into three modes: high-frequency m3 (rotation about long axis), and two low-frequency modes m2 (rotation about short axis) and m1 (collective dipolar reorientation). RM734 exhibits strong growth of m1 amplitude (Δε1) and rapid slowing (softening) on cooling toward N–Ns, indicating increasing polar correlations. In RM734-CN, m1 shows weaker, Arrhenius-like behavior throughout N with amplitudes comparable to m2, lacking the divergent trend seen in RM734; m2 amplitudes are comparable between materials, consistent with similar molecular dipoles.
• Viscoelasticity: Splay elastic constant K1 in RM734 softens strongly on approach to N–Ns, while RM734-CN remains nearly constant and unusually low but without pretransitional softening. The splay mode diffusion coefficient K1/η1 and viscosity η1 reflect this: RM734 shows pronounced softening (decrease of K1/η1) and a steep increase in η1 before N–Ns; RM734-CN exhibits slight slowing and Arrhenius-like η1.
• DFT: Global-minimum dipole moments are similar (RM734: 11.4 D; RM734-CN: 11.2 D) with dipole–axis angles ~18.3° and ~20°, respectively. Anisotropic polarizability is larger for RM734-CN, consistent with its higher birefringence, while isotropic polarizabilities are comparable.
• MD orientational order: Both compounds form nematic states at and below ~450 K (P2 ≳ 0.3), isotropic above ~500 K, matching experimental clearing points (RM734 461 K; RM734-CN 473.6 K). Simulated P2 at 400 K are ~0.73–0.76 (overestimated vs WAXS: RM734 0.68; RM734-CN 0.62). Polar simulations yield large P1 (~0.895) and significant polarization P (RM734 0.064 C/m^2; RM734-CN 0.052 C/m^2), while apolar simulations give near-zero P1 and P.
• MD density and packing: At a given temperature, RM734 shows a higher mass density in the polar nematic than in the apolar nematic by ~0.5%, indicating more efficient packing in the polar state; RM734-CN shows no appreciable density difference between polar and apolar simulations. Translational diffusion constants are larger in the polar state for RM734. Experimentally, across the N–Ns transition in RM734, a 0.1–0.2% increase in density relative to N-phase extrapolation was observed, consistent in sign with MD (magnitude smaller due to gradual pretransitional polar order and weakly first-order transition).
• Pair-correlation functions: RM734 (polar) exhibits strong head-to-tail on-axis correlations (h ≈ ±20 Å), consistent with nitro-terminated head/tail pairing; RM734-CN (polar) shows reduced head-to-tail preference and stronger staggered side-by-side off-axis peaks (h ≈ r ≈ 6 Å), indicative of CN–ester-driven lateral interactions. Apolar simulations show mixed head-to-head and side-by-side arrangements in both compounds.
• X-ray scattering: Experimental RM734 displays multiple weak small-angle peaks (001, 002, 003) in N and Ns phases; RM734-CN lacks these additional peaks. Simulated polar nematic states (both compounds) reproduce multiple low-Q peaks, whereas apolar states do not, indicating that these features are signatures of polar nematic order rather than molecular structure alone. Overall weak SAXS intensity indicates weak positional correlations consistent with pair-correlation analyses.
• Generality across analogues: MD simulations on RM554 (exhibits Ns) versus RM63 and RM500 (do not) show that materials with Ns exhibit increased density in polar versus apolar nematic configurations, supporting the hypothesis that enhanced packing (reduced excluded volume) in polar order underlies Ns formation.

The comparative analysis demonstrates that the emergence of ferroelectric polar order and the splay-nematic phase in RM734 is driven by molecular packing: polar alignment of slightly wedge-shaped molecules reduces excluded volume and attractive interaction energy, enabling a denser state than the apolar nematic. This packing advantage is absent in the nitrile analogue RM734-CN, which instead favors staggered side-by-side arrangements due to CN–ester interactions that, together with lateral methoxy groups, increase excluded volume for polar alignment and suppress growth of polar correlations. The distinct viscoelastic behavior—marked K1 softening and viscosity rise in RM734 but not in RM734-CN—links to the development of polar order that destabilizes uniform splay elasticity near N–Ns. Dielectric spectra corroborate this: RM734 shows a dominant, softening collective mode (m1) reflecting cooperative dipole reorientations; RM734-CN shows weaker, Arrhenius-like m1, indicating limited polar correlation growth. Despite similar molecular dipole moments and comparable isotropic polarizabilities, differences in anisotropic polarizability and, more importantly, in positional/orientational correlations lead to divergent macroscopic phases. The work further shows that weak SAXS with multiple low-angle peaks is an indicator of polar nematic order; simulations reproduce these features only in polar configurations, providing a structural fingerprint of polar order in nematics. Together, the results answer the research question by identifying reduced excluded volume via head-to-tail packing as the microscopic driver for polar nematic order and Ns formation, and establish computational and scattering-based diagnostics to predict candidate materials.

This study identifies the molecular origin of the ferroelectric splay-nematic phase: subtle chemical changes that promote head-to-tail packing (e.g., terminal nitro group) enable denser packing under polar order, reducing excluded volume and stabilizing polar nematic states that undergo splay elastic softening and form the Ns phase. Conversely, replacing nitro with nitrile disrupts this packing, favoring side-by-side motifs and suppressing Ns. The authors demonstrate that atomistic MD can distinguish polar vs apolar nematic states through density differences, packing correlations, and simulated SAXS/WAXS, and that multiple weak low-angle peaks in SAXS are a practical marker of polar nematic order. The approach generalizes across analogues (e.g., RM554 vs RM63/RM500), offering a predictive pathway for materials design. Future work should focus on: expanding chemical space to identify room-temperature Ns materials; refining force fields for quantitative property prediction; exploring confinement and ionic effects on domain structures; and coupling MD with high-throughput screening to rationally design wedge-shaped dipolar mesogens with favorable head-to-tail interactions.

• Atomistic MD simulations use nanometer-scale boxes (~10×6×6 nm^3) and cannot capture the micron-scale splay modulation of the Ns phase; only uniform polar/apolar nematic states are simulated.
• Simulated orientational order parameters (P2) are higher than experimental WAXS estimates, consistent with known overestimation in fully atomistic MD; quantitative discrepancies remain.
• The measured experimental density increase across N–Ns (0.1–0.2%) is smaller than the simulated polar–apolar difference (~0.5%), reflecting pretransitional polar order and weakly first-order transitions, as well as methodological differences in measuring/estimating densities.
• The study compares a limited set of analogues; broader chemical diversity and direct measurements of microscopic packing motifs would strengthen generality.
• Temperature ranges for Ns remain high for practical applications; extrapolation to room temperature systems requires further validation.