Dielectric spectroscopy of ferroelectric nematic liquid crystals: Measuring the capacitance of insulating interfacial layers

Numerous measurements of the dielectric constant $\epsilon$ of the recently discovered ferroelectric nematic ($N_F$) liquid crystal (LC) phase report extraordinarily large values of $\epsilon^\prime$ (up to ~30,000). We show that what is in fact being measured in such experiments is the high capacitance of the non-ferroelectric, interfacial, insulating layers of nanoscale thickness that bound the $N_F$ material in typical cells. We analyze a parallel-plate cell filled with $N_F$ material of high-polarization $\mathbf{P}$, oriented parallel to the plates at zero applied voltage. Minimization of the dominant electrostatic energy renders $\mathbf{P}$ spatially uniform and orients it to make the electric field in the $N_F$ as small as possible, a condition under which the voltage applied to the cell appears almost entirely across the high-capacity interfacial layers. This coupling of orientation and charge creates a combined polarization-external capacitance (PCG) Goldstone reorientation mode requiring applied voltages orders of magnitude smaller than that of the $N_F$ layer alone to effectively transport charge across the $N_F$ layer. The $N_F$ layer acts as a low-value resistor and the interfacial capacitors as reversible energy storage reservoirs, lowering the restoring force (mass) of the PCG mode and producing strong reactive dielectric behavior. Analysis of data from several experiments on ferroelectric liquid crystals (chiral smectics C, bent-core smectics, and the $N_F$ phase supports the PCG model, showing deriving that deriving dielectric constants from electrical impedance measurements of high-polarization ferroelectric LCs, without properly accounting for the self-screening effects of polarization charge and the capacitive contributions of interfacial layers, can result in overestimation of the $\epsilon^\prime$ values of the LC by many orders of magnitude.Comment: 26 pages of text, 10 figures, 49 references (40 pages total

Topological defect coarsening in quenched smectic-C films analyzed using artificial neural networks

Mechanically quenching a thin film of smectic-C liquid crystal results in the formation of a dense array of thousands of topological defects in the director field. The subsequent rapid coarsening of the film texture by the mutual annihilation of defects of opposite sign has been captured using high-speed, polarized light video microscopy. The temporal evolution of the texture has been characterized using an object-detection convolutional neural network to determine the defect locations, and a binary classification network customized to evaluate the brush orientation dynamics around the defects in order to determine their topological signs. At early times following the quench, inherent limits on the spatial resolution result in undercounting of the defects and deviations from expected behavior. At intermediate to late times, the observed annihilation dynamics scale in agreement with theoretical predictions and simulations of the $2$D XY model.Comment: 11 pages, 10 figure

Scanned conical illumination as a probe of electro-optic retro-reflection

We describe a prototype element for use in probing electro-optic retro-reflection in sensor applications, illuminating a planar-aligned nematic liquid crystal electro-optic cell with convergent light having a single, tunable angle of incidence (tunable conical illumination). This illumination is generated using a 100X, high numerical aperture, long working-distance microscope objective under conditions of extreme spherical aberration. The electro-optic effect observed is multiple-beam optical interference between polarized reflections from the two bounding plates of the cell, rendered tunable with voltage-controlled refractive index changes induced by molecular reorientation of the liquid crystal. Characterization of the reflectivity vs. angle of incidence and applied voltage enables identification of conditions of high-contrast, low power, electro-optic reflectivity control applicable to fiber optics.</p