Fréedericksz transition in the director-density coupling theory

We show that the director-density coupling theory gives rise to a singular behavior for the mass density. To overcome this drawback, we propose to supplement the theory with a term that can be derived by regarding liquid crystals as anisotropic Korteweg fluids. We thus show that the static bevahior of the resulting theory predicts a Fréedericksz transition accompanied by a modulation in the mass density.

Figure 1

Cell of thickness $a$ containing nematic liquid crystal connected to a fixed voltage source: (a) homeotropic alignment and (b) planar alignment. On the right, the coordinate system defines the angles $\theta$ for the director.

Figure 2

Maximum angle versus $\sigma /{\sigma }_c$ for $K_1=6.4\times {10}^{-12}\mathrm{N},K_3=10\times {10}^{-12}\mathrm{N},\left|\Delta \varepsilon \right|=1.0$, and ${\varepsilon }_{\parallel }=3.0$. The solid line is obtained from Eq. (39) and the dots are calculated using Eq. (51).

Figure 3

$\theta \left(z\right)$ versus $z/a$ for $K_1=6.4\times {10}^{-12}$ N, $K_3=10\times {10}^{-12}\mathrm{N},\left|\Delta \varepsilon \right|=1.0$, and ${\varepsilon }_{\parallel }=3.0$. The solid line is obtained from Eq. (38) using ${\theta }_m=0.7854$ and $\sigma /{\sigma }_c=1.2602$, and the dots are calculated using Eq. (56).

Figure 4

Plot of $Z$ as a function of $r\equiv K_1^{\prime }/K_1$ for $K_1=6.4\times {10}^{-12}\mathrm{N},K_3=10\times {10}^{-12}\mathrm{N},\left|\Delta \varepsilon \right|=1.0$, and ${\varepsilon }_{\parallel }=3.0$.

Figure 5

Plot of $Z^{\prime }$ as a function of $r^{\prime }\equiv K_3^{\prime }/K_3$ for $K_1=6.4\times {10}^{-12}\mathrm{N},K_3=10\times {10}^{-12}\mathrm{N},\Delta \varepsilon =1.0$, and ${\varepsilon }_{\perp }=4.0$.