Transient, polarity-dependent dielectric response in a twisted nematic liquid crystal under very low frequency excitation

The electric Freedericksz transition is a second-order quadratic effect, which, in a planarly aligned nematic liquid crystal layer, manifests above a threshold field as a homogeneous symmetric distortion with maximum director-tilt in the midplane. We find that, upon excitation by a low frequency $(<0.2\mathrm{Hz})$ square-wave field, the instability becomes spatially and temporally varying. This is demonstrated using calamitic liquid crystals, initially in the 90°-twisted planar configuration. The distortion occurs close to the negative electrode following each polarity switch and, for low-voltage amplitudes, decays completely in time. We use the elastically favorable geometry of Brochard-Leger walls to establish the location of maximum distortion. Thus, at successive polarity changes, the direction of extension of both annular and open walls switches between the alignment directions at the two substrates. For high voltages, this direction is largely along the midplane director, while remaining marginally oscillatory. These results are broadly understood by taking into account the time-varying and inhomogeneous field conditions that prevail soon after the polarity reverses. Polarity dependence of the instability is traced to the formation of intrinsic double layers that lead to an asymmetry in field distribution in the presence of an external bias. Momentary field elevation near the negative electrode following a voltage sign reversal leads to locally enhanced dielectric and gradient flexoelectric torques, which accounts for the surface-like phenomenon observed at low voltages. These spatiotemporal effects, also found earlier for other instabilities, are generic in nature.

Figure 1

Chemical structures of (a) 6OPh8Py and (b) PCH5.

Figure 2

Sample configuration. (a) The molecular alignment is along $x$ at the bottom substrate and along $y$ at the top substrate. The twist may be, while looking along $z$, clockwise (as in the right half) or anticlockwise (as in the left half). Field is taken positive when the top electrode is negative. (b) In the presence of pretilt, depending on the twist-sense, the tilt may persist uniformly across the thickness (as in the left half), or may gradually disappear while approaching the midplane $z=d/2$ from either the bottom substrate at $z=0$ or the top one at $z=d$ (as in the right half).

Figure 3

Variation of cell capacitance with rms voltage at a fixed frequency (50 kHz) and different temperatures for TN 6OPh8Py held in a $5\text{−}\mu \mathrm{m}$ AWAT cell. Insets: (bottom right) Temperature variation of the Freedericksz threshold with $U_{\mathrm{F}}$ and $U_{\mathrm{OF}}$ denoting capacitive and optical thresholds, respectively; (top left) Temperature variation of effective elastic constant $k_{\mathrm{e}}$ from $U_{\mathrm{F}}$. All continuous lines are second-order polynomial fits.

Figure 4

(a) Interferogram depicting the equilibrium elliptical geometry of a collapsing loop wall in a $19.2\text{−}\mu \mathrm{m}$-thick TN layer of 6OPh8Py at $64{}^{\circ }\mathrm{C}$, formed on sudden application of a SQW field (4 V, 10 kHz). The major axis lies very nearly along the diagonal (yellow) line coinciding with the midplane director. Polarizers are along $x$. Mercury green light. $5\mu \mathrm{m}$ each scale div. (b) Director configuration in the sample midplane corresponding to the elliptical wall in (a); the wall is of twist type along the minor axis and splay-bend type along the major axis.

Figure 5

Electro-optic response in a $5\text{−}\mu \mathrm{m}$-thick TN layer of 6OPh8Py at $64{}^{\circ }\mathrm{C}$ driven by a $1\mathrm{mHz}$ sawtooth wave of amplitude $5.7\mathrm{V}$. Parallel polarizers $\mathrm{P}(45)-\mathrm{A}(45)$. Mercury green light.

Figure 6

Transient evolution of Freedericksz' distortion in TN 6OPh8Py at $65.9{}^{\circ }\mathrm{C}$, under excitation by a SQW field with $f=0.1\mathrm{Hz}$ and $U=1.7\mathrm{V}$. The frame rate is $34f$, so that frames captured at successive polarity reversals $({\mathrm{F}}_{18}$ and ${\mathrm{F}}_{35})$ are separated by 16 frames $({\mathrm{F}}_{19}-{\mathrm{F}}_{34})$. Diffuse bottle-green colored walls formed between oppositely tilted regions extend either along $x$, as in ${\mathrm{F}}_{18}$ or along $y$, as in ${\mathrm{F}}_{35}$. The distortion grows and decays over about $1.5\mathrm{s}$, and the sample remains in the undistorted state through the remaining $3.5\mathrm{s}$ of the half period of the SQW, as in ${\mathrm{F}}_{23}-{\mathrm{F}}_{34}$. $\mathrm{P}(45)-\mathrm{A}(135)$. $d=7.67\mu \mathrm{m}$. Each scale div. represents $10\mu \mathrm{m}$.

Figure 7

Polarity-dependent Freedericksz distortion as revealed by the anisotropic geometry of well-developed BL loop-walls evolving transiently at polarity reversals in a $5.25\text{−}\mu \mathrm{m}$-thick TN layer of 6OPh8Py, under a SQW field $(f=50\mathrm{mHz}$; $U=2.6\mathrm{V})$; $f_{\mathrm{r}}=74f$. The textures are of two oppositely twisted regions separated by a disclination line. ${\mathrm{F}}_6$ and ${\mathrm{F}}_{43}$ are the frames captured at successive polarity reversals, showing the loops extending along $y$ and $x$, respectively. They are separated by 36 frames $({\mathrm{F}}_7-{\mathrm{F}}_{42})$ all showing the texture corresponding to the distortion free state. ${\mathrm{F}}_7$ and the insets ${\mathrm{F}}_5,{\mathrm{F}}_{42}$, and ${\mathrm{F}}_{44}$ (of reduced size), exemplify the distortion free state. $\mathrm{P}(85)-\mathrm{A}(90),64{}^{\circ }\mathrm{C}$. Each scale division represents $10\mu \mathrm{m}$ (for insets, $40\mu \mathrm{m})$.

Figure 8

Polarity-dependent transient Freedericksz distortion revealed by the preferential formation of open twist walls in a TN platelet of 6OPh8Py surrounded by the isotropic fluid close to $T_{\mathrm{NI}}$; SQW field $(f=20\mathrm{mHz}$; $U=3.5\mathrm{V})$; $f_{\mathrm{r}}\approx 150f$. ${\mathrm{F}}_{52}$ and ${\mathrm{F}}_{127}$ are the frames captured at successive polarity reversals, showing the walls extending predominantly along $x$ and $y$, respectively, and terminating at the interface. They are separated by 74 frames $({\mathrm{F}}_{53}-{\mathrm{F}}_{126})$ of which the initial few $({\mathrm{F}}_{53}-{\mathrm{F}}_{61})$ show the progressive decay of walls, and the remaining, the texture of the distortion free state as in ${\mathrm{F}}_{51}$. $\mathrm{P}(90)-\mathrm{A}(0),5\mu \mathrm{m}$ each scale div.

Figure 9

Polarity-dependent transient Freedericksz instability observed under SQW excitation $(U=3.1\mathrm{V}$; $f=0.04\mathrm{Hz})$ of nematic domains close to $T_{\mathrm{NI}}$. In ${\mathrm{F}}_{11}$ recorded with polarizers P(60)–A(0) just prior to a polarity switch, the yellow and green islands within the isotropic liquid are oppositely twisted nematic domains free from Freedericksz distortion. In ${\mathrm{F}}_{12}$, recorded soon after the field reversal, the lower two circular domains exhibit predominantly horizontal twist walls in the Freedericksz distorted state, formed close to the bottom substrate; the other domains of opposite twist show a uniform distortion; the distortion in all the domains decays and disappears in time, with frames ${\mathrm{F}}_{16}–{\mathrm{F}}_{50}$ (not included) showing the quiescent texture, just as ${\mathrm{F}}_{11}$. ${\mathrm{F}}_{51}$ gives the texture at the next polarity switch; the twist walls in the lower two drops here are predominantly vertical and formed near the top substrate. $10\mu \mathrm{m}$ each scale div.

Figure 10

Formation of a linear BL wall nearly along the diagonal at higher voltages in a TN domain surrounded by isotropic liquid at a temperature close to $T_{\mathrm{NI}}$. The dashed reference lines are at ${45}^{\circ }$ to $x$. Frames (a) and (b), as also (c) and (d), which are captured just before and after the polarity change, respectively, belong to a time series with $f_{\mathrm{r}}=32f$. P(30)–A(0), $4.4\mathrm{V},50\mathrm{mHz}$. $5\mu \mathrm{m}$ each scale div.

Figure 11

Nematic platelets formed in the isotropic phase of PCH5 at $T_{\mathrm{NI}}$, and in the Freedericksz deformed state. $U=0.6\mathrm{V},f=25\mathrm{mHz}$. Snapshot after the field polarity switch from (a) positive to negative and (b) negative to positive. Rubbing lines within the nematic domains, along $x$ in (a) and $y$ in (b), are rendered visible by the distortion localized near the cathode. P(45)–A(45).

Figure 12

Transient distortion of director distribution following polarity reversals, as observed in a $5\text{−}\mu \mathrm{m}$ TN layer of 6OPh8Py at $U=0.8\mathrm{V}$ and $f=0.1\mathrm{Hz}$. $R_{\mathrm{o}}$ denotes the optical response. Parallel polarizers P(45)–A(45). Mercury green light; $64{}^{\circ }\mathrm{C}$.

Figure 13

Transient distortion of director field following polarity reversals, as observed in a $5\mu \mathrm{m}$ TN layer of 6OPh8Py at $U=2.6\mathrm{V}$ and $f=10\mathrm{mHz}$. $R_{\mathrm{o}}$ denotes the optical response. Parallel polarizers P(0)–A(0). Mercury green light; $64{}^{\circ }\mathrm{C}$.

Figure 14

Effect of applied voltage, at constant frequency $(=10\mathrm{mHz})$, on the transient switching profile, observed with a $5\text{−}\mu \mathrm{m}$-thick layer of 6OPh8Py held between parallel polarizers P(45)–A(45). Mercury green light. The polarity reversal time is set as 0 s. (a) Low-voltage regime. (b) High-voltage regime; $64{}^{\circ }\mathrm{C}$.

Figure 15

Voltage dependence of time $t_{1\mathrm{m}}$ for the occurrence of the first minimum of optical transmission after a polarity switch over in a $5\text{−}\mu \mathrm{m}$-thick, ${90}^{\circ }$-twisted layer of 6OPh8Py at $64{}^{\circ }\mathrm{C}$, held between parallel polarizers P(45)–A(45). The ascending (blue) curve is an exponential fit for the regime in which only a single intensity minimum occurs. The descending (red) curve, which is also exponential, covers the regime wherein the switching profile consists of a maximum between two minima. Inset: Voltage dependence of $t_{2\mathrm{m}}$, the time of occurrence of the second minimum of transmission after a polarity switch over.

Figure 16

Electro-optic response as a function of reduced time at various frequencies and constant voltage for a $5\text{−}\mu \mathrm{m}$-thick TN layer of 6OPh8Py at $64{}^{\circ }\mathrm{C}$ and between diagonally parallel polarizers. The dotted line marks the switching time $t=0$.

Figure 17

Effect of temperature on the transient switching profile at constant voltage [(a) $3.0\mathrm{V}$; (b) $4.5\mathrm{V}]$ and frequency [(a, b) $0.02\mathrm{Hz}]$ of the driving SQW field, as observed with a $5\text{−}\mu \mathrm{m}$-thick TN 6OPh8Py layer between diagonally parallel polarizers, P(45)–A(45), under illumination with mercury green light.

Figure 18

Temperature dependence of the time $t_{1\mathrm{m}}$ at which the first minimum of transmission is observed in a $5\text{−}\mu \mathrm{m}$-thick TN sample of 6OPh8Py. Inset: Time of occurrence of the second minimum, $t_{2\mathrm{m}}$, as a function of $\mathrm{\Theta }$. The continuous lines are exponential fits. Data are from Fig. 17.

Figure 19

Schematic of: (Left) intrinsic double layers, and (Right) electric displacement profiles in the absence of bias (dotted line), soon after applying bias (dashed line) and after ion redistribution under bias (continuous line). $\pm \mathrm{\Sigma }=\pm q{\sigma }^{-}$ denotes the adsorbed charge density and $D_{\mathrm{e}}$ the displacement along $z$, induced by the voltage $U$.