| 43 |
|
\begin{figure} |
| 44 |
|
\centering |
| 45 |
|
\includegraphics[width=\linewidth]{smcp.eps} |
| 46 |
< |
\caption[] |
| 47 |
< |
{} |
| 46 |
> |
\caption[SmCP Phase Packing] {Four possible SmCP phase packings that |
| 47 |
> |
are characterized by the relative tilt direction(A and S refer an |
| 48 |
> |
anticlinic tilt or a synclinic ) and the polarization orientation (A |
| 49 |
> |
and F represent antiferroelectric or ferroelectric polar order).} |
| 50 |
|
\label{LCFig:SMCP} |
| 51 |
|
\end{figure} |
| 52 |
|
|
| 183 |
|
\begin{figure} |
| 184 |
|
\centering |
| 185 |
|
\includegraphics[width=\linewidth]{banana.eps} |
| 186 |
< |
\caption[]{} \label{LCFig:BananaMolecule} |
| 186 |
> |
\caption[Schematic representation of a typical banana shaped |
| 187 |
> |
molecule]{Schematic representation of a typical banana shaped |
| 188 |
> |
molecule.} \label{LCFig:BananaMolecule} |
| 189 |
|
\end{figure} |
| 190 |
|
|
| 191 |
|
%\begin{figure} |
| 275 |
|
As a useful set of correlation functions to describe |
| 276 |
|
position-orientation correlation, rotation invariants were first |
| 277 |
|
applied in a spherical symmetric system to study x-ray and light |
| 278 |
< |
scatting\cite{Blum1971}. Latterly, expansion of the orientation pair |
| 278 |
> |
scatting\cite{Blum1972}. Latterly, expansion of the orientation pair |
| 279 |
|
correlation in terms of rotation invariant for molecules of |
| 280 |
|
arbitrary shape was introduce by Stone\cite{Stone1978} and adopted |
| 281 |
< |
by other researchers in liquid crystal studies\cite{Berardi2000}. |
| 281 |
> |
by other researchers in liquid crystal studies\cite{Berardi2003}. |
| 282 |
|
|
| 283 |
|
\begin{eqnarray} |
| 284 |
|
S_{22}^{220} (r) & = & \frac{1}{{4\sqrt 5 }} \left< \delta (r - |
