| 78 |
|
liquid crystal phases\cite{Lansac2003}. Other anisotropic models |
| 79 |
|
using Gay-Berne(GB) potential, which produce interactions that favor |
| 80 |
|
local alignment, give the evidence of the novel packing arrangements |
| 81 |
< |
of bent-core molecules\cite{Memmer2002,Orlandi2006}. |
| 81 |
> |
of bent-core molecules\cite{Memmer2002}. |
| 82 |
|
|
| 83 |
|
Experimental studies by Levelut {\it et al.}~\cite{Levelut1981} |
| 84 |
|
revealed that terminal cyano or nitro groups usually induce |
| 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 |
|
|
| 264 |
|
\caption{LIQUID CRYSTAL STRUCTURAL PROPERTIES AS A FUNCTION OF |
| 265 |
|
TEMPERATURE} \label{liquidCrystal:p2} |
| 266 |
|
\begin{center} |
| 267 |
< |
\begin{tabular}{|c|c|c|c|c|c|} |
| 267 |
> |
\begin{tabular}{cccccc} |
| 268 |
|
\hline |
| 269 |
|
Temperature (K) & 420 & 440 & 460 & 480 & 600\\ |
| 270 |
|
\hline |
| 278 |
|
|
| 279 |
|
The molecular organization obtained at temperature $T = 460K$ (below |
| 280 |
|
transition temperature) is shown in Figure~\ref{LCFigure:snapshot}. |
| 281 |
< |
|
| 282 |
< |
It is also important to show the density correlation along the |
| 283 |
< |
director which is given by : |
| 281 |
> |
The diagonal view in Fig~\ref{LCFigure:snapshot}(a) shows the |
| 282 |
> |
stacking of the banana shaped molecules while the side view in n |
| 283 |
> |
Figure~\ref{LCFigure:snapshot}(b) demonstrates formation of a |
| 284 |
> |
chevron structure. The first peak of Radial distribution function |
| 285 |
> |
$g(r)$ in Fig.~\ref{LCFigure:gofrz}(a) shows the minimum distance |
| 286 |
> |
for two in plane banana shaped molecules is 4.9 \AA, while the |
| 287 |
> |
second split peak implies the biaxial packing. It is also important |
| 288 |
> |
to show the density correlation along the director which is given by |
| 289 |
> |
: |
| 290 |
|
\begin{equation} |
| 291 |
< |
g(z) =< \delta (z-z_{ij})>_{ij} / \pi R^{2} \rho |
| 291 |
> |
g(z) =\frac{1}{\pi R^{2} \rho}< \delta (z-z_{ij})>_{ij} |
| 292 |
|
\end{equation}, |
| 293 |
|
where $z_{ij} = r_{ij} \dot Z$ was measured in the director frame |
| 294 |
< |
and $R$ is the radius of the cylindrical sampling region. |
| 294 |
> |
and $R$ is the radius of the cylindrical sampling region. The |
| 295 |
> |
oscillation in density plot along the director in |
| 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. |
| 299 |
> |
|
| 300 |
> |
\subsection{Rotational Invariants} |
| 301 |
> |
|
| 302 |
> |
As a useful set of correlation functions to describe |
| 303 |
> |
position-orientation correlation, rotation invariants were first |
| 304 |
> |
applied in a spherical symmetric system to study x-ray and light |
| 305 |
> |
scatting\cite{Blum1972}. Latterly, expansion of the orientation pair |
| 306 |
> |
correlation in terms of rotation invariant for molecules of |
| 307 |
> |
arbitrary shape was introduce by Stone\cite{Stone1978} and adopted |
| 308 |
> |
by other researchers in liquid crystal studies\cite{Berardi2003}. In |
| 309 |
> |
order to study the correlation between biaxiality and molecular |
| 310 |
> |
separation distance $r$, we calculate a rotational invariant |
| 311 |
> |
function $S_{22}^{220} (r)$, which is given by : |
| 312 |
> |
\begin{eqnarray} |
| 313 |
> |
S_{22}^{220} (r) & = & \frac{1}{{4\sqrt 5 }} \left< \delta (r - |
| 314 |
> |
r_{ij} )((\hat x_i \cdot \hat x_j )^2 - (\hat x_i \cdot \hat y_j |
| 315 |
> |
)^2 - (\hat y_i \cdot \hat x_j )^2 + (\hat y_i \cdot \hat y_j |
| 316 |
> |
)^2 ) \right. \notag \\ |
| 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{figure} |
| 325 |
|
\centering |
| 342 |
|
\label{LCFigure:gofrz} |
| 343 |
|
\end{figure} |
| 344 |
|
|
| 345 |
< |
\subsection{Rotational Invariants} |
| 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 |
|
|
| 312 |
– |
As a useful set of correlation functions to describe |
| 313 |
– |
position-orientation correlation, rotation invariants were first |
| 314 |
– |
applied in a spherical symmetric system to study x-ray and light |
| 315 |
– |
scatting\cite{Blum1972}. Latterly, expansion of the orientation pair |
| 316 |
– |
correlation in terms of rotation invariant for molecules of |
| 317 |
– |
arbitrary shape was introduce by Stone\cite{Stone1978} and adopted |
| 318 |
– |
by other researchers in liquid crystal studies\cite{Berardi2003}. |
| 319 |
– |
|
| 320 |
– |
\begin{eqnarray} |
| 321 |
– |
S_{22}^{220} (r) & = & \frac{1}{{4\sqrt 5 }} \left< \delta (r - |
| 322 |
– |
r_{ij} )((\hat x_i \cdot \hat x_j )^2 - (\hat x_i \cdot \hat y_j |
| 323 |
– |
)^2 - (\hat y_i \cdot \hat x_j )^2 + (\hat y_i \cdot \hat y_j |
| 324 |
– |
)^2 ) \right. \\ |
| 325 |
– |
& & \left. - 2(\hat x_i \cdot \hat y_j )(\hat y_i \cdot \hat x_j ) - |
| 326 |
– |
2(\hat x_i \cdot \hat x_j )(\hat y_i \cdot \hat y_j )) \right> |
| 327 |
– |
\end{eqnarray} |
| 328 |
– |
|
| 329 |
– |
\begin{equation} |
| 330 |
– |
S_{00}^{221} (r) = - \frac{{\sqrt 3 }}{{\sqrt {10} }}\left\langle |
| 331 |
– |
{\delta (r - r_{ij} )((\hat z_i \cdot \hat z_j )(\hat z_i \cdot |
| 332 |
– |
\hat z_j \times \hat r_{ij} ))} \right\rangle |
| 333 |
– |
\end{equation} |
| 334 |
– |
|
| 356 |
|
\section{Conclusion} |
| 357 |
< |
To investigate the molecular organization behavior due to different |
| 358 |
< |
dipolar orientation and position with respect to the center of the |
| 359 |
< |
molecule, |
| 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. 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. |
