| 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 |
|
|
| 187 |
– |
%\begin{figure} |
| 188 |
– |
%\centering |
| 189 |
– |
%\includegraphics[width=\linewidth]{bananGB.eps} |
| 190 |
– |
%\caption[]{} \label{LCFigure:BananaGB} |
| 191 |
– |
%\end{figure} |
| 192 |
– |
|
| 191 |
|
\begin{figure} |
| 192 |
|
\centering |
| 193 |
|
\includegraphics[width=\linewidth]{gb_scheme.eps} |
| 194 |
< |
\caption[]{Schematic diagram showing definitions of the orientation |
| 195 |
< |
vectors for a pair of Gay-Berne molecules} |
| 196 |
< |
\label{LCFigure:GBScheme} |
| 194 |
> |
\caption[Schematic diagram showing definitions of the orientation |
| 195 |
> |
vectors for a pair of Gay-Berne molecules]{Schematic diagram showing |
| 196 |
> |
definitions of the orientation vectors for a pair of Gay-Berne |
| 197 |
> |
molecules} \label{LCFigure:GBScheme} |
| 198 |
|
\end{figure} |
| 199 |
|
|
| 200 |
|
To account for the permanent dipolar interactions, there should be |
| 270 |
|
As a useful set of correlation functions to describe |
| 271 |
|
position-orientation correlation, rotation invariants were first |
| 272 |
|
applied in a spherical symmetric system to study x-ray and light |
| 273 |
< |
scatting\cite{Blum1971}. Latterly, expansion of the orientation pair |
| 273 |
> |
scatting\cite{Blum1972}. Latterly, expansion of the orientation pair |
| 274 |
|
correlation in terms of rotation invariant for molecules of |
| 275 |
|
arbitrary shape was introduce by Stone\cite{Stone1978} and adopted |
| 276 |
< |
by other researchers in liquid crystal studies\cite{Berardi2000}. |
| 276 |
> |
by other researchers in liquid crystal studies\cite{Berardi2003}. |
| 277 |
|
|
| 278 |
|
\begin{eqnarray} |
| 279 |
|
S_{22}^{220} (r) & = & \frac{1}{{4\sqrt 5 }} \left< \delta (r - |
| 291 |
|
\end{equation} |
| 292 |
|
|
| 293 |
|
\section{Results and Conclusion} |
| 295 |
– |
\label{sec:results and conclusion} |
| 296 |
– |
|
| 294 |
|
To investigate the molecular organization behavior due to different |
| 295 |
|
dipolar orientation and position with respect to the center of the |
| 296 |
|
molecule, |
