Ferroelectric Nematic-Isotropic Liquid Critical End Point

A critical end point above which an isotropic phase continuously evolves into a polar (ferroelectric) nematic phase with an increasing electric field is found in a ferroelectric nematic liquid crystalline material. The critical end point is approximately 30 K above the zero-field transition temperature from the isotropic to nematic phase and at an electric field of the order of $10\mathrm{V}/\mathrm{\mu }\mathrm{m}$. Such systems are interesting from the application point of view because a strong birefringence can be induced in a broad temperature range in an optically isotropic phase.

Figure 1

(a) A single repolarization current peak recorded as a function of time ($t$) in the $N_F$ phase and (b) a double current peak recorded in the isotropic liquid, under application of a triangular voltage (black line, right scales). (c) The light transmission ($T$) through a sample placed between crossed polarizers, taken in the temperature range of the isotropic phase. The sample was tilted with respect to the beam propagation direction by $\sim 20°$. The data presented in (b) and (c) were taken simultaneously, at a temperature 20 K above the $N$-Iso phase transition. Note that the threshold electric field inducing a nonzero light transmission coincides with the field at which the current peak is registered.

Figure 2

The optical retardation (black, open symbols) and SGH signal intensity (green, solid symbols) measured at several temperatures above ${\mathrm{T}}_1$, the $N$-Iso phase transition as a function of a dc electric field applied to the sample. The critical isotherm for retardation is marked in red. A dashed curve represents a bimodal line.

Figure 3

Temperature ($T$)-threshold field ($E_{\mathrm{th}}$) phase diagram for the $N_F$ and Iso phases. The critical end point (CEP) is located approximately 30 K above the zero-field transition temperature and at critical electric field $\sim 15\mathrm{V}/\text{micron}$.

Figure 4

The order parameter $S$ vs electric field $E$ obtained from Eq. (3) at few degrees above $T_0$. For the chosen set of parameters, the stability limit of the $N$ phase is at $T_1=T_0+1.67\mathrm{K}$ and the critical temperature for the Iso-$N_F$ transition at $T_c=T_0+19.3\mathrm{K}$. At $T=T_0+2\mathrm{K}$ the electric field induces a transition from the Iso to the $N$ phase and at a sufficiently high field to the $N_F$ phase. At higher temperatures, a direct Iso-$N_F$ phase transition is induced by the electric field, with a diminishing hysteresis as $T_c$ is approached; the critical isotherm is marked in red. Above $T_c$ a continuous evolution of the order parameter is observed under the electric field.

Figure 5

A theoretical $E$ vs $T$ phase diagram showing the stability limits of the Iso (red area), $N$ (green area), and $N_F$ (black area) phases. In the areas marked with two colors, coexistence of two phases is possible due to the presence of two minima in the free energy $G$ vs $S$ dependence under electric field. The black dot shows the critical end point for the induced Iso-$N_F$ phase transition.