Fig. 2.

SAXS scattering from the N and SmZ_A phases of DIO. These diffractograms are from a sample in a 1 mm-diameter capillaries in which the director, n, is aligned along the magnetic field B (red), studied on the SMI microbeam line at NSLS II. (A and B) Non-resonant diffractograms obtained on cooling show a diffuse scattering arc at q_z = 0.25Å⁻¹ from head-to-tail stacking of the molecules in the N and SmZ_A phases. In the SmZ_A phase, equatorial Bragg spots appear, indicating the presence of an electron density wave of w_M = 8.8-nm periodicity, with wavevector q_M normal to n. These peaks disappear upon transitioning to the N_F phase (G, SI Appendix, Figs. S4 and S5). (C) The scattering pattern rotates from (A) to (B) because of layer reorientations caused by a small reduction in layer thickness upon cooling in the SmZ_A phase (see text). (D) Line scan through the non-resonant scattering peaks. The central part of the beam is blocked by the beam stop. (E) Since the sample is a powder in orientation about the B field, the observed scattering pattern could be indicative of either lamellar or hexagonal columnar positional ordering. Since non-resonant scattering is sensitive only to electron density, the layers (of thickness w_M) of opposite polarization scatter identically. Layer boundaries (white stripes) have different electron density than the layer centers (gray stripes), making w_M the period observed in nonresonant scattering. However, as shown in (H) and SI Appendix, Fig. S5, carbon-edge resonant scattering exhibits the half-order peak at q_R = q_M/2, showing conclusively that the SmZ_A is lamellar and bilayer with period 2w_M. The DTOM experiments show that it is lamellar and antiferroelectric, with layers of alternating polarization P(y), sketched in (E1) for low polarization (ξ_P > w), and in (E2) for high polarization (ξ_P << w), the case relevant to the SmZ_A (see text). The tilt modulation θ(y) is suppressed at large P by the self-electric field due to the polarization charge, ρ = −∇·P, indicated in red. Other smectic structures (e.g., the SmC, sketched in E3) have spontaneous antiferroelectric polarization in the tilt plane as well as splay modulation SI Appendix, Section 8), but in different geometries. (F) X-ray scattering peaks from various smectics with the director aligned by the magnetic field B. (G–I) Dependence on T of the Bragg peak parameters from data as in SI Appendix, Figs. S4 and S5 [non-resonant peak intensity (I_p), non-resonant peak position (q_M = 2π/w_M), resonant peak position (q_R = 2π/2w_M), and non-resonant half-width at half-maximum (HWHM_M)]. (H) Layers of opposite P have different carbon K-edge resonant scattering cross-sections, and therefore Bragg scatter at the full antiferroelectric period 2w_M. (I) The HWHM_M values of the mid-range peaks (T ~ 75 °C) are SAXS-resolution limited.