Effects of dielectric relaxation on the director dynamics of uniaxial nematic liquid crystals

The dielectric anisotropy of liquid crystals causes director reorientation in an applied electric field and is thus at the heart of electro-optic applications of these materials. The components of the dielectric tensor are frequency dependent. Until recently, this frequency dependence was not accounted for in a description of director dynamics in an electric field. We theoretically derive the reorienting dielectric torque acting on the director, taking into account the entire frequency spectrum of the dielectric tensor. The model allows one to include the effects of multiple relaxations in both parallel and perpendicular components of the dielectric tensor, thus generalizing a recent model [Y. Yin et al., Phys. Rev. Lett. 95, 087801 (2005)] limited by the single-relaxation approach. The model predicts the “dielectric memory effect” (DME)—i.e., dependence of the dielectric torque on both the “present” and “past” values of the electric field and the director. The model describes the experimentally observed director reorientation in the case when the rise time of the applied voltage is smaller than the dielectric relaxation time. In typical materials such as pentylcyanobiphenyl (5CB), in which the dielectric anisotropy is positive at low frequencies, the DME slows down the director reorientation in a sharply rising electric field, as the sharp front is perceived as a high-frequency excitation for which the dielectric anisotropy is small or even of a negative sign. In materials that are dielectrically negative, the DME speeds up the response when a sharp pulse is applied.

Figure 1

Experimental setup for the DME experiment.

Figure 2

Dielectric dispersion curves of 5CB based on the Debye model, Eq. (24), where ${\epsilon }_{l\parallel }=19.0$, ${\epsilon }_{h\parallel }=5.0$, and ${\tau }_{\parallel }=64\mathrm{ns}$; ${\epsilon }_{l\perp }=6.5$, ${\epsilon }_{h\perp }=2.4$, and ${\tau }_{\perp }=3.5\mathrm{ns}$ for $23°\mathrm{C}$ (a) and ${\epsilon }_{l\parallel }=17.5$, ${\epsilon }_{h\parallel }=4.6$, and ${\tau }_{\parallel }=36\mathrm{ns}$; ${\epsilon }_{l\perp }=7$, ${\epsilon }_{h\perp }=2.4$, and ${\tau }_{\perp }=3.5\mathrm{ns}$ for $30°\mathrm{C}$ (b).

Figure 3

Normalized light intensity (a), (b) transmitted by the electrically driven 5CB cell and a pair of crossed polarizers as a function of time at $23°\mathrm{C}$ (a) and $30°\mathrm{C}$ (b). (c) Applied voltage with simulated time dependence (solid curve). The circles are the experimental data; the curves in (a) and (b) represent simulations with different models as indicated by the labels.

Figure 4

Experimental data on dielectric dispersion curves of the mixture with $7.0\mathrm{wt.}\%$ 5CB and $93.0\mathrm{wt.}\%$ MLC2048 for the real components (${\epsilon }_{\parallel }^{\prime }$, ${\epsilon }_{\perp }^{\prime }$) and the imaginary components (${\epsilon }_{\parallel }^{″}$, ${\epsilon }_{\perp }^{″}$) at room temperature $23°\mathrm{C}$. The solid curves are fitted with Eq. (28), where ${\epsilon }_{l\parallel }=10.4$, ${\epsilon }_{m\parallel }=5.3$, ${\epsilon }_{h\parallel }=3.5$, ${\epsilon }_{\perp }=6.4$, ${\tau }_1=6.0\mu \mathrm{s}$, and ${\tau }_2=0.23\mu \mathrm{s}$.

Figure 5

The first and second dielectric relaxation times (a) and dielectric strength (b) of the parallel component ${\epsilon }_{\parallel }$ of $5\mathrm{CB}+\mathrm{MLC}2048$ mixtures versus the weight concentration of 5CB at $23°\mathrm{C}$.

Figure 6

Normalized transmitted light intensity versus time (a) for $7.0\mathrm{wt.}\%$ $5\mathrm{CB}+93.0\mathrm{wt.}\%$ MLC2048 mixture driven by fast-changing rectangular pulse (b). The circles are the experimental data; the curves represent simulations with different models as indicated by the labels.

Figure 7

Dielectric dispersion curves for the real components (${\epsilon }_{\parallel }$, ${\epsilon }_{\perp }$) of the mixture $53.7\mathrm{wt.}\%$ $\mathrm{MLC}7026\text{−}100+46.3\mathrm{wt.}\%$ MLC2048 at $23°\mathrm{C}$. The solid curve is fitted with Eq. (24) where ${\epsilon }_{h\parallel }=3.5$, ${\epsilon }_{l\parallel }=6.0$, and ${\tau }_{\parallel }=2.1\mu \mathrm{s}$.

Figure 8

Normalized transmitted light intensity (a) and voltage (b) versus time for the mixture $53.7\mathrm{wt.}\%$ $\mathrm{MLC}7026\text{−}100+46.3\mathrm{wt.}\%$ MLC2048 driven by a fast-changing rectangular pulse. The circles are the experimental data; the curves represent simulations with different models as indicated by the labels.

Figure 9

Transmitted light intensity versus time (a) for the cell filled with the mixture $53.7\mathrm{wt.}\%$ $\mathrm{MLC}7026\text{−}100+46.3\mathrm{wt.}\%$ MLC2048, driven by ac pulses at the same frequency $10\mathrm{kHz}$ and the same amplitude $40{\mathrm{V}}_{\mathrm{rms}}$ but of different shapes, a rectangular and sinusoidal one (b).

Figure 10

Transmitted light intensity versus time (a) for the cell filled with the mixture $53.7\mathrm{wt.}\%$ $\mathrm{MLC}7026\text{−}100+46.3\mathrm{wt.}\%$ MLC2048, driven by a dc pulse 1 of duration of $150\mu \mathrm{s}$ and amplitude $100\mathrm{V}$ and by a pulse 2 with a total duration $150\mu \mathrm{s}$ and amplitude $\pm 100\mathrm{V}$, with polarity changed once (b).