Elastic anisotropy effects on the electrical responses of a thin sample of nematic liquid crystal

The electrical responses of a nematic liquid crystal cell are investigated by means of the elastic continuum theory. The nematic medium is considered as a parallel circuit of a resistance and a capacitance and the electric current profile across the sample is determined as a function of the elastic constants. In the reorientation process of the nematic director, the resistance and capacitance of the sample are determined by taking into account the elastic anisotropy. A nonmonotonic profile for the current is observed in which a minimum value of the current may be used to estimate the elastic constants values. This scenario suggests a theoretical method to determine the values of the bulk elastic constants in a single planar aligned cell just by changing the direction of applied electrical field and measuring the resulting electrical current.

Figure 1

Behavior of the tilt angle profile ${\psi }_m\left(t\right)$ vs $t\left(s\right)$, for different values of $\kappa$ and the parameters presented in Table 1. The discontinuity observed occurs at time $t=t_c\approx 0.8592\mathrm{s}$, which coincides with the time that $V\left(t\right)$ reaches $V_c$ for these parameters.

Figure 2

(a) Behavior of the resistance $R\left(t\right)$ vs $t\left(s\right)$, for different values of $\kappa$, and (b) behavior of the capacitance $C\left(t\right)$ vs $t\left(s\right)$, for different values of $\kappa$. The physical parameters are given in Table 1.

Figure 3

Behavior of the intensity of the electric current $I\left(t\right)$ vs $t\left(s\right)$, for different values of $\kappa$ and physical parameters presented in Table 1. The highlighted part shows more clearly the behavior immediately below and above of the Fréedericksz threshold.

Figure 4

Separate profiles of the contributions to electric current from Eq. (11) evidencing (a) the amplitude of the discontinuity, and (b) the concavity observed in Fig. 3. The capacitive part of the electric current coincides with the profile of capacitance due the fact that $dV/dt=1$.

Figure 5

Behavior of the time in which the minimum occurs vs $\kappa$. Physical parameters are given in Table 1.