Electric field-induced interfacial instability in a ferroelectric nematic liquid crystal

Abstract

Studies of sessile droplets and fluid bridges of a ferroelectric nematic liquid crystal in externally applied electric fields are presented. It is found that above a threshold, the interface of the fluid with air undergoes a fingering instability or ramification, resembling to Rayleigh-type instability observed in charged droplets in electric fields or circular drop-type instabilities observed in ferromagnetic liquids in magnetic field. The frequency dependence of the threshold voltage was determined in various geometries. The nematic director and ferroelectric polarization direction was found to point along the tip of the fingers that appear to repel each other, indicating that the ferroelectric polarization is essentially parallel to the director. The results are interpreted in connection to the Rayleigh and circular drop-type instabilities.

Figure 1

A ferroelectric nematic sessile droplet in electric fields along the normal direction of the base plate. (a) Illustration of the G1 geometry with approximate electric field (green lines) and coordinate system. (b–d) Polarizing optical microscopy images of a ferroelectric nematic sessile droplet between crossed polarizers (yellow arrows) and a full-wave plate (λ = 546 nm—blue arrow) at 210 V, 220 V and 300 V, respectively. The cell gap was L = 150 µm.

Figure 2

A ferroelectric nematic fluid bridge in electric field along the normal direction of the base plate. (a) Illustration of the G2 geometry. (b) Top view of a fluid bridge at zero voltage (558 µm diameter, 74 µm thickness) and (c) at f = 800 Hz, 52 V AC voltage. (d) Transformed view of the perimeter of the bridge exhibiting the instability. Darker (lighter) pattern shows the instability at the top (bottom) glass. (e) Side view of the bridge clearly indicates that the instability forms in the vicinity of the electrodes. The schematic illustration describes the experiment for side-view imaging using a long-range microscope.

Figure 3

Schematics of the in-plane (G3) electrode geometry and micrographs of the ferroelectric nematic droplet on interdigitated electrodes. (a) Illustration of the interdigitated electrodes with the coordinate system. Side view ($x-z$ plane) of the electrodes with fringing field (b) and the sessile droplet (c). Reflection microscopy image ($x-y$ plane) of the droplet at 0 V (d) and 75 V (e) applied voltage at f = 10 kHz. Brighter stripes correspond to the electrode areas; the electrode distance was 10 µm. (f) Side view of the geometry with a single thin pair of electrodes with a larger gap (180 µm) between them. (g) The corresponding polarizing microscope image, showing that the fluid fingers spread above the electrodes, where the fringing field is perpendicular to the substrate.

Figure 4

(a) Temperature dependence of the threshold voltage measured at f = 1 kHz in the fluid bridge geometry (G2) with cell thickness L = 74 µm. (a-inset) The roughness of the contact line (Ro_cl) of the fluid bridge at one substrate as function of applied voltage at T = 400.15 K (127 °C) ($T-T_{N{N}_F}\approx -5$ K) and f = 1 kHz. (b) Threshold voltage $U_{\mathit{th}}$ of the interfacial instability as function of frequency at T = 400.15 K (127 °C). The threshold voltage of the interfacial instability measured on substrates with interdigitated surface electrodes (G3 geometry, electrode distance: 10 µm) (c) as a function of temperature at f = 1 kHz and (d) as a function of frequency at T = 400.15 K (127 °C). (c-inset) The normalized circumference S/S₀ of a 125 µm diameter droplet as a function of temperature with a constant applied voltage (U = 75 V, f = 10 kHz).

Figure 5

Geometry of the wide in-plane electrodes (a). Polarizing optical microscopy images of ferroelectric nematic droplets on surface electrode pairs (with 180 µm distance) at 0 V (b), at 90 V (c) and at 120 V (d) with f = 500 Hz sinusoidal driving. (e) A series of neighboring droplets showing the instability and interaction. (f) A magnified area near two branches showing that their tips are arranged to avoid contact between neighbor tips.

Figure 6

Properties of the tips of the side branches of the ferroelectric nematic liquid crystal sessile droplet above the electrically induced fingering instability. (a) Polarimetric microscopy image of the branched ferroelectric fluid interface on wide surface electrode pairs. Green rods indicate the effective orientation of the director. (b) Surface topography of the branched structure measured by interferometric profilometry. (c) Cross-section of one branch indicated by a dotted gray line. (d) Scanning electron microscopy image of the quenched ferroelectric nematic fluid exhibiting the electric field-induced interfacial instability.