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

Abstract

Numerous measurements of the dielectric constant ɛ of the recently discovered ferroelectric nematic (N_{F}) liquid crystal (LC) phase report extraordinarily large values of ɛ′ (up to ∼30 000) in the N_{F} phase. We show that what is in fact being measured in such experiments is the high capacitance of the nonferroelectric, interfacial, insulating layers of nanoscale thickness that bound the N_{F} material in typical cells. Polarization reorientation as a linear response to AC electric field drive renders the N_{F} layer effectively electrically conductive, exhibiting low resistance that enables the charging of the interfacial capacitors. We analyze the commonly employed parallel-plate cell filled with N_{F} material of high polarization P, oriented parallel to the plates at zero applied voltage. Minimization of the dominant electrostatic energy renders P spatially uniform and orients the polarization 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 act as reversible energy storage reservoirs, lowering the restoring force (mass) of the PCG mode and producing strong reactive dielectric behavior. Analysis of data from a variety of experiments on ferroelectric LCs (chiral smectics C, bent-core smectics, and the N_{F} phase) supports the PCG model, showing 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 ɛ′ values of the LC by many orders of magnitude.