Surface-induced multiple reentrant transitions

We have studied tilted surface layers in the bulk SmA temperature window of one liquid crystal using null transmission ellipsometry. Five distinct nonplanar surface structures were observed. We present analyses of the tilt and azimuthal profiles of the structures and examine the transitions between the structures. The transitions are identified as a double reentrant synclinic-anticlinic-synclinic-anticlinic transition. Meanwhile, the transitions also display reentrant ferroelectric-antiferroelectric-ferroelectric behavior.

Figure 1

Chemical structure of (S)12OF1M7.

Figure 2

Definition of angles used in the text. $\mathbf{k}$ is the projection of the wave vector of the incident light on the film plane. $\mathbf{E}$ is the direction of the applied electric field. ${\mathbf{c}}_j$ is the $c$ director of the $j\mathrm{th}$ layer.

Figure 3

(Color online) Temperature dependence of $\Delta$ and $\Psi$ under two different orientations of $E$ for a 16-layer film. Open (closed) symbols are data obtained while heating (cooling) at a rate of $20\mathrm{mK}∕\min$. The electric field strength was $E=7.14\mathrm{V}∕\mathrm{cm}$. Circles and triangles are data obtained at $\alpha =0°$ and squares and diamonds are data obtained at $\alpha =90°$. Downward arrows mark five transition temperatures. Upward arrows mark the temperatures at which the rotation data in Figs. 4, 5, 6, 7, 8 were obtained.

Figure 4

(Color online) (a) shows dependence of $\Delta$ and $\Psi$ on $\alpha$ at $T=102.60°\mathrm{C}$ $\left({\mathrm{SmST}}_1\right)$. (b) plots $\Psi$ versus $\Delta$. Circles are data and solid lines are simulation results. (c) Shows directions of the components of the polarization for the structure in equilibrium at $\alpha =0°$. The arrows for $P_{\mathrm{FE}}$ and $P_{\mathrm{FL}}$ are drawn using $e_1=e_2$. The same symbols and scales are used in Figs. 5, 6, 7, 8, except where noted. The electric field strength for Figs. 4, 5, 6, 7, 8 was $E=7.14\mathrm{V}∕\mathrm{cm}$.

Figure 5

(Color online) (a) $\Delta$ and $\Psi$ versus $\alpha$ and (b) $\Psi$ versus $\Delta$ at $T=94.42°\mathrm{C}$ $\left({\mathrm{SmST}}_2\right)$. (c) Shows directions of the components of the polarization. $P_{\mathrm{FE}}$ is very small for this structure because the surfaces are nearly antiferroelectric, so a different scale has been used for the diagram. $e_2$ is the same for all diagrams, but $e_1=100e_2$ in this figure, in contrast to Figs. 4 and 6, 7, 8.

Figure 6

(Color online) (a) $\Delta$ and $\Psi$ versus $\alpha$ and (b) $\Psi$ versus $\Delta$ at $T=93.48°\mathrm{C}$ $\left({\mathrm{SmST}}_3\right)$. (c) Shows directions of the components of the polarization. $\Sigma {\mathrm{P}}_{\mathrm{FL}}\left(\mathrm{int}\right)$ represents the net $P_{\mathrm{FL}}$ from the interior layers.

Figure 7

(Color online) (a) $\Delta$ and $\Psi$ versus $\alpha$ and (b) $\Psi$ versus $\Delta$ at $T=92.14°\mathrm{C}$ $\left({\mathrm{SmST}}_4\right)$. (c) Shows directions of the components of the polarization.

Figure 8

(Color online) (a) $\Delta$ and $\Psi$ versus $\alpha$ and (b) $\Psi$ versus $\Delta$ at $T=91.23°\mathrm{C}$ $\left({\mathrm{SmST}}_5\right)$. (c) Shows directions of the components of the polarization.