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 |
|
|
297 |
|
structure, and the peak at 27 \AA is attribute to the defect in the |
298 |
|
system. |
299 |
|
|
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} |
308 |
– |
|
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 |
> |
lack of detail in. |