Polarization Plasticity of Ferroelectric Nematics: a case of Electrostatic Frustration in Simple Planar Electrode Cells

Abstract

Because of their spontaneous bulk polarization, ferroelectric nematic liquid crystals can be easily brought by surface coupling or confinement in a state in which the accumulation of bound charges becomes incompatible with polar order, creating frustration. This condition also occurs in the simplest cells with parallel uncoated metal electrodes where we find that the polarization charge accumulating on the electrodes is proportional to the applied voltage for $ΔV< V_{sat}$, a threshold value independent of cell thickness. We show that below $V_{sat}$, frustration drives the system into a regime of polarization plasticity, in which nematic ordering is preserved and the nematic director remains perpendicular to the electrodes, while instead the polarization is reduced to cancel the internal electric field. In this regime, the kinetics of bound charge reversal becomes independent from $ΔV$. The observations are consistent with a model in which the system splits into antipolar tubular domains of mesoscale diameter extending from electrode to electrode, in which the polarization retains its unconstrained equilibrium value, separated by pure polarization-reversal walls.

Figures (8)

• Figure 1: Charge measurements a) Electrical scheme used for the measurement of the current intensity $\mathit{i}$ following voltage reversal. b) Typical $\mathit{i}(t)$ profile (red line, right-hand axis) recorded when applying a squared wave voltage (black curve, left-hand axis). c) Polarization charge density $\sigma_b$ (generally coinciding with $P$, see text) as a function of the applied voltage $\Delta V$ in bulky cells differing in electrode separation $d$. d) Expansion of the low voltage region of panel c. $V_{sat}$, marking the crossover between Polarization Plasticity (pink shading) and homogeneous $N_F$ polarization (blue shading) is obtained by the intersection of the two linear lines fit at low voltages (0-1V, brown dashed line) and high voltages (10-100V, magenta dashed line).
• Figure 2: Optical characterization of the O3 cell a) Comparison of polarization charge density $\sigma_b$ (generally coinciding with $P$ , see text), SHG intensity $I_{SHG}$, and birefringence $\Delta n$ as a function of $\Delta V$. Each quantity is normalized over their values at $\Delta V=5V$. Color shadings mark the three regimes of voltage described in the text. In pink the polarization plasticity range. b) PTOM images through cross polarizers P and A (white arrows) at different voltages. Black arrow: direction of the applied electric field E. c) Axonometric and lateral view of schematic representations of the polarization arrangement in $N_F$ confined between electrodes with $\Delta V <V_{sat}$ and $\Delta V >V_{sat}$(left and right hand side panel, respectively). Red and blue regions indicate surface of positive and negative bound charge accumulation, respectively. In the left hand side panel we sketch the proposed antipolar tubular domain structure that enables polarization plasticity.
• Figure 3: Kinetics upon voltage reversal a-b) $\mathit{i}(t)$ curves measured in the B4 cell with various voltages. c) Effective resistance $R_{eff}$ determined from the exponential decay time $\tau$ in the bulky cell family, plotted against the shape factor $d/S$. Dashed line: linear fit. d) Discharge time $\tau_c$ (red dots) and optical response time $\tau_T$ (black dots) as a function of $\Delta V$, in the O1 cell. Dashed line: $\Delta V^{-1}$ slope fit to the $\tau_T$ data. e-f) comparison of the current and optical transmission curves normalized to their largest value as a response to voltage reversal with $\Delta V =$ 1V and $\Delta V =$ 20V, respectively.
• Figure 4: Electrostatics and structure in the polarization plasticity state a-b) Thick black line: voltage at equilibrium as a function of the distance from the grounded electrode for $\Delta V< V_{sat}$ (a) $\Delta V \geq V_{sat}$ (b). Colors in (a) indicate the voltage profile across the cell that would be present if $P$ was larger (yellow to red) or smaller (green to blue) than its equilibrium value. c-d) same sketch of the Antipolar Tubular Domain structure as in Fig. 2c. Yellow arrows indicate the motion of the domain walls by which the minority fraction (red) expands to reverse the sign of $P$, as in the transition following voltage reversal.
• Figure S1: SHG measurement setup Schematic representation of the custom SHG intensity measurements setup used in this work.