--- trunk/tengDissertation/LiquidCrystal.tex	2006/06/27 01:33:33	2892
+++ trunk/tengDissertation/LiquidCrystal.tex	2006/06/27 03:06:49	2896
@@ -218,7 +218,8 @@ temperature and pressure.
 a $160\times 160 \times 120$ box. After the dipolar interactions are
 switched on, 2~ns NPTi cooling run with themostat of 2~ps and
 barostat of 50~ps were used to equilibrate the system to desired
-temperature and pressure.
+temperature and pressure. NPTi Production runs last for 40~ns with
+time step of 20~fs.
 
 \subsection{Order Parameters}
 
@@ -295,28 +296,7 @@ system.
 Fig.~\ref{LCFigure:gofrz}(b) implies the existence of the layered
 structure, and the peak at 27 \AA is attribute to the defect in the
 system.
-
-\begin{figure}
-\centering
-\includegraphics[width=4.5in]{snapshot.eps}
-\caption[Snapshot of the molecular organization in the layered phase
-formed at temperature T = 460K and pressure P = 1 atm]{Snapshot of
-the molecular organization in the layered phase formed at
-temperature T = 460K and pressure P = 1 atm. (a) diagonal view; (b)
-side view.} \label{LCFigure:snapshot}
-\end{figure}
 
-\begin{figure}
-\centering
-\includegraphics[width=\linewidth]{gofr_gofz.eps}
-\caption[Correlation Functions of a Bent-core Liquid Crystal System
-at Temperature T = 460K and Pressure P = 10 atm]{Correlation
-Functions of a Bent-core Liquid Crystal System at Temperature T =
-460K and Pressure P = 10 atm. (a) radial correlation function
-$g(r)$; and (b) density along the director $g(z)$.}
-\label{LCFigure:gofrz}
-\end{figure}
-
 \subsection{Rotational Invariants}
 
 As a useful set of correlation functions to describe
@@ -337,15 +317,54 @@ r_{ij} )((\hat x_i  \cdot \hat x_j )^2  - (\hat x_i  \
  & & \left. - 2(\hat x_i  \cdot \hat y_j )(\hat y_i \cdot \hat x_j ) -
 2(\hat x_i  \cdot \hat x_j )(\hat y_i  \cdot \hat y_j )) \right>.
 \end{eqnarray}
+The long range behavior of second rank orientational correlation
+$S_{22}^{220} (r)$ in Fig~\ref{LCFigure:S22220} also confirm the
+biaxiality of the system.
 
-%\begin{equation}
-%S_{00}^{221} (r) =  - \frac{{\sqrt 3 }}{{\sqrt {10} }}\left\langle
-%{\delta (r - r_{ij} )((\hat z_i  \cdot \hat z_j )(\hat z_i  \cdot
-%\hat z_j  \times \hat r_{ij} ))} \right\rangle
-%\end{equation}
+\begin{figure}
+\centering
+\includegraphics[width=4.5in]{snapshot.eps}
+\caption[Snapshot of the molecular organization in the layered phase
+formed at temperature T = 460K and pressure P = 1 atm]{Snapshot of
+the molecular organization in the layered phase formed at
+temperature T = 460K and pressure P = 1 atm. (a) diagonal view; (b)
+side view.} \label{LCFigure:snapshot}
+\end{figure}
 
+\begin{figure}
+\centering
+\includegraphics[width=\linewidth]{gofr_gofz.eps}
+\caption[Correlation Functions of a Bent-core Liquid Crystal System
+at Temperature T = 460K and Pressure P = 10 atm]{Correlation
+Functions of a Bent-core Liquid Crystal System at Temperature T =
+460K and Pressure P = 10 atm. (a) radial correlation function
+$g(r)$; and (b) density along the director $g(z)$.}
+\label{LCFigure:gofrz}
+\end{figure}
+
+\begin{figure}
+\centering
+\includegraphics[width=\linewidth]{s22_220.eps}
+\caption[Average orientational correlation Correlation Functions of
+a Bent-core Liquid Crystal System at Temperature T = 460K and
+Pressure P = 10 atm]{Correlation Functions of a Bent-core Liquid
+Crystal System at Temperature T = 460K and Pressure P = 10 atm. (a)
+radial correlation function $g(r)$; and (b) density along the
+director $g(z)$.} \label{LCFigure:S22220}
+\end{figure}
+
 \section{Conclusion}
 
 We have presented a simple dipolar three-site GB model for banana
 shaped molecules which are capable of forming smectic phases from
-isotropic configuration.
+isotropic configuration. Various order parameters and correlation
+functions were used to characterized the structural properties of
+these smectic phase. However, the forming layered structure still
+had some defects because of the mismatching between the layer
+structure spacing and the shape of simulation box. This mismatching
+can be broken by using NPTf integrator in further simulations. The
+role of terminal chain in controlling transition temperatures and
+the type of mesophase formed have been studied
+extensively\cite{Pelzl1999}. The the lack of flexibility in our
+model due to the missing terminal chains could explained the fact
+that we did not find evidence of chirality.