Evolution of a rare sequence of surface transitions with temperature and film thickness

In free-standing smectic films, layers near the surfaces of the film often contain molecules tilted away from the layer normal, while in the bulk of the film the magnitude of the tilt decays exponentially with distance from the surface. We have identified the detailed molecular tilt orientations in the surface layers of films for one antiferroelectric liquid crystal compound. A series of five surface structures exists with different nonplanar tilt arrangements for each structure. The molecular orientations in the surface layers evolve with temperature. The polarization of the film also evolves with temperature, corresponding to the tilt arrangements. Using ellipsometric data, we reconstruct the changes in the magnitude and azimuthal direction of the tilt as functions of temperature. We have also studied films of several different thicknesses. We present a phase diagram for the five surface structures showing the dependence on temperature and film thickness.

Figure 1

Chemical structure of 12OF1M7.

Figure 2

Definition of angles in the film plane 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. $\overrightarrow{c_j}$ is the $\vec{c}$ vector of the $j\text{th}$ layer.

Figure 3

These diagrams represent the five surface structures observed in the bulk $\text{Sm}A$ temperature window. The arrows are the $\vec{c}$ vectors for each layer. Vector lengths and angles are not to scale. The highest temperature surface tilt structure is on the right.

Figure 4

(Color online) (a) $\Psi$ and $\Delta$ vs $\alpha$ for $\text{Sm}S{T}_2$ in a 13 layer film. (b) shows $\Psi$ vs $\Delta$. Crosses (circles) represent data and solid (dashed) lines represent simulation results at $94.77°\text{C}$ $\left(92.54°\text{C}\right)$.

Figure 5

(Color online) (a) $\Psi$ and $\Delta$ vs $\alpha$ for $\text{Sm}S{T}_3$ in a 21 layer film. (b) shows $\Psi$ vs $\Delta$. Crosses (circles) represent data and solid (dashed) lines represent simulation results at $93.64°\text{C}$ $\left(92.66°\text{C}\right)$.

Figure 6

(a) Surface tilt ${\theta }_{surf}$ and (b) tilt correlation length $\xi$ vs temperature. The points were obtained from simulations. Closed (open) symbols represent data from the $\text{Sm}S{T}_2$ $\left(\text{Sm}S{T}_3\right)$ phase. Different symbols correspond to different film thicknesses.

Figure 7

The nonplanar angle ${\phi }_2-{\phi }_1$ vs temperature. The points were obtained from simulations. Closed (open) symbols represent data from the $\text{Sm}S{T}_2$ $\left(\text{Sm}S{T}_3\right)$ phase. Different symbols correspond to different film thicknesses.

Figure 8

Net ferroelectric polarization vs temperature. The points were obtained from simulations. The net ferroelectric polarization is proportional to the sum of the $\vec{c}$ vectors for each layer. Closed (open) symbols represent data from the $\text{Sm}S{T}_2$ $\left(\text{Sm}S{T}_3\right)$ phase. Different symbols correspond to different film thicknesses.

Figure 9

(Color online) Temperature dependence of $\Delta$ and $\Psi$ under two orientations of the electric field for a 13 layer film while cooling at a rate of 20 mK/min. Circles are data obtained at $\alpha =0°$ and triangles are data obtained at $\alpha =90°$. The vertical dashed line marks the temperature at which the film structure rotated by $180°$, as described in the text.

Figure 10

These diagrams show two mechanisms by which the $\text{Sm}S{T}_2$ and $\text{Sm}S{T}_3$ structures can rotate by $180°$. The $\text{Sm}S{T}_2$ structures in (a) and (b) have their polarizations aligned with the electric field when the correlation length is small or large, respectively. The dashed arrows in (a) represent an increase in $\xi$. The $\text{Sm}S{T}_3$ structures in (c) and (d) have their polarizations aligned with the electric field when ${\phi }_2-{\phi }_1>180°$ and ${\phi }_2-{\phi }_1<180°$, respectively. The dashed arrows in (c) represent evolution of ${\phi }_2$.

Figure 11

The critical correlation length at which reorientation occurs for a 13-layer film. The line was obtained by setting Eq. (2) equal to zero and solving numerically. See the text for discussion of the dashed arrow.

Figure 12

Phase diagram for the five surface phases. The error bars represent the range of hysteresis in the transition temperatures during heating and cooling temperature ramps.