| 218 |
|
a $160\times 160 \times 120$ box. After the dipolar interactions are |
| 219 |
|
switched on, 2~ns NPTi cooling run with themostat of 2~ps and |
| 220 |
|
barostat of 50~ps were used to equilibrate the system to desired |
| 221 |
< |
temperature and pressure. |
| 221 |
> |
temperature and pressure. NPTi Production runs last for 40~ns with |
| 222 |
> |
time step of 20~fs. |
| 223 |
|
|
| 224 |
|
\subsection{Order Parameters} |
| 225 |
|
|
| 296 |
|
Fig.~\ref{LCFigure:gofrz}(b) implies the existence of the layered |
| 297 |
|
structure, and the peak at 27 \AA is attribute to the defect in the |
| 298 |
|
system. |
| 298 |
– |
|
| 299 |
– |
\begin{figure} |
| 300 |
– |
\centering |
| 301 |
– |
\includegraphics[width=4.5in]{snapshot.eps} |
| 302 |
– |
\caption[Snapshot of the molecular organization in the layered phase |
| 303 |
– |
formed at temperature T = 460K and pressure P = 1 atm]{Snapshot of |
| 304 |
– |
the molecular organization in the layered phase formed at |
| 305 |
– |
temperature T = 460K and pressure P = 1 atm. (a) diagonal view; (b) |
| 306 |
– |
side view.} \label{LCFigure:snapshot} |
| 307 |
– |
\end{figure} |
| 299 |
|
|
| 309 |
– |
\begin{figure} |
| 310 |
– |
\centering |
| 311 |
– |
\includegraphics[width=\linewidth]{gofr_gofz.eps} |
| 312 |
– |
\caption[Correlation Functions of a Bent-core Liquid Crystal System |
| 313 |
– |
at Temperature T = 460K and Pressure P = 10 atm]{Correlation |
| 314 |
– |
Functions of a Bent-core Liquid Crystal System at Temperature T = |
| 315 |
– |
460K and Pressure P = 10 atm. (a) radial correlation function |
| 316 |
– |
$g(r)$; and (b) density along the director $g(z)$.} |
| 317 |
– |
\label{LCFigure:gofrz} |
| 318 |
– |
\end{figure} |
| 319 |
– |
|
| 300 |
|
\subsection{Rotational Invariants} |
| 301 |
|
|
| 302 |
|
As a useful set of correlation functions to describe |
| 317 |
|
& & \left. - 2(\hat x_i \cdot \hat y_j )(\hat y_i \cdot \hat x_j ) - |
| 318 |
|
2(\hat x_i \cdot \hat x_j )(\hat y_i \cdot \hat y_j )) \right>. |
| 319 |
|
\end{eqnarray} |
| 320 |
+ |
The long range behavior of second rank orientational correlation |
| 321 |
+ |
$S_{22}^{220} (r)$ in Fig~\ref{LCFigure:S22220} also confirm the |
| 322 |
+ |
biaxiality of the system. |
| 323 |
|
|
| 324 |
< |
%\begin{equation} |
| 325 |
< |
%S_{00}^{221} (r) = - \frac{{\sqrt 3 }}{{\sqrt {10} }}\left\langle |
| 326 |
< |
%{\delta (r - r_{ij} )((\hat z_i \cdot \hat z_j )(\hat z_i \cdot |
| 327 |
< |
%\hat z_j \times \hat r_{ij} ))} \right\rangle |
| 328 |
< |
%\end{equation} |
| 324 |
> |
\begin{figure} |
| 325 |
> |
\centering |
| 326 |
> |
\includegraphics[width=4.5in]{snapshot.eps} |
| 327 |
> |
\caption[Snapshot of the molecular organization in the layered phase |
| 328 |
> |
formed at temperature T = 460K and pressure P = 1 atm]{Snapshot of |
| 329 |
> |
the molecular organization in the layered phase formed at |
| 330 |
> |
temperature T = 460K and pressure P = 1 atm. (a) diagonal view; (b) |
| 331 |
> |
side view.} \label{LCFigure:snapshot} |
| 332 |
> |
\end{figure} |
| 333 |
|
|
| 334 |
+ |
\begin{figure} |
| 335 |
+ |
\centering |
| 336 |
+ |
\includegraphics[width=\linewidth]{gofr_gofz.eps} |
| 337 |
+ |
\caption[Correlation Functions of a Bent-core Liquid Crystal System |
| 338 |
+ |
at Temperature T = 460K and Pressure P = 10 atm]{Correlation |
| 339 |
+ |
Functions of a Bent-core Liquid Crystal System at Temperature T = |
| 340 |
+ |
460K and Pressure P = 10 atm. (a) radial correlation function |
| 341 |
+ |
$g(r)$; and (b) density along the director $g(z)$.} |
| 342 |
+ |
\label{LCFigure:gofrz} |
| 343 |
+ |
\end{figure} |
| 344 |
+ |
|
| 345 |
+ |
\begin{figure} |
| 346 |
+ |
\centering |
| 347 |
+ |
\includegraphics[width=\linewidth]{s22_220.eps} |
| 348 |
+ |
\caption[Average orientational correlation Correlation Functions of |
| 349 |
+ |
a Bent-core Liquid Crystal System at Temperature T = 460K and |
| 350 |
+ |
Pressure P = 10 atm]{Correlation Functions of a Bent-core Liquid |
| 351 |
+ |
Crystal System at Temperature T = 460K and Pressure P = 10 atm. (a) |
| 352 |
+ |
radial correlation function $g(r)$; and (b) density along the |
| 353 |
+ |
director $g(z)$.} \label{LCFigure:S22220} |
| 354 |
+ |
\end{figure} |
| 355 |
+ |
|
| 356 |
|
\section{Conclusion} |
| 357 |
|
|
| 358 |
|
We have presented a simple dipolar three-site GB model for banana |
| 359 |
|
shaped molecules which are capable of forming smectic phases from |
| 360 |
< |
isotropic configuration. |
| 360 |
> |
isotropic configuration. Various order parameters and correlation |
| 361 |
> |
functions were used to characterized the structural properties of |
| 362 |
> |
these smectic phase. However, the forming layered structure still |
| 363 |
> |
had some defects because of the mismatching between the layer |
| 364 |
> |
structure spacing and the shape of simulation box. This mismatching |
| 365 |
> |
can be broken by using NPTf integrator in further simulations. The |
| 366 |
> |
role of terminal chain in controlling transition temperatures and |
| 367 |
> |
the type of mesophase formed have been studied |
| 368 |
> |
extensively\cite{Pelzl1999}. The the lack of flexibility in our |
| 369 |
> |
model due to the missing terminal chains could explained the fact |
| 370 |
> |
that we did not find evidence of chirality. |
