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\section{Results and Discussion} |
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|
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< |
A series of molecular dynamics simulations were perform to study the |
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A series of molecular dynamics simulations were performed to study the |
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phase behavior of banana shaped liquid crystals. In each simulation, |
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every banana shaped molecule has been represented by three GB |
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particles which is characterized by $\mu = 1,~ \nu = 2, |
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%where $X$, $Y$ and $Z$ are axis of the director frame. |
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The unit vector for the banana shaped molecule was defined by the |
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principle aixs of its middle GB particle. The $P_2$ order parameters |
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for the bent-core liquid crystal at different temperature is |
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for the bent-core liquid crystal at different temperature are |
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summarized in Table~\ref{liquidCrystal:p2} which identifies a phase |
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transition temperature range. |
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|
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The molecular organization obtained at temperature $T = 460K$ (below |
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transition temperature) is shown in Figure~\ref{LCFigure:snapshot}. |
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The diagonal view in Fig~\ref{LCFigure:snapshot}(a) shows the |
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stacking of the banana shaped molecules while the side view in n |
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stacking of the banana shaped molecules while the side view in |
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Figure~\ref{LCFigure:snapshot}(b) demonstrates formation of a |
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chevron structure. The first peak of the radial distribution |
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function $g(r)$ in Fig.~\ref{LCFigure:gofrz}(a) shows that the |
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also important to show the density correlation along the director |
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which is given by : |
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\begin{equation} |
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g(z) =\frac{1}{\pi R^{2} \rho}< \delta (z-z_{ij})>_{ij} |
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\end{equation}, |
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> |
g(z) =\frac{1}{\pi R^{2} \rho}< \delta (z-z_{ij})>_{ij}, |
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\end{equation} |
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where $ z_{ij} = r_{ij} \cdot \hat Z $ was measured in the |
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director frame and $R$ is the radius of the cylindrical sampling |
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region. The oscillation in density plot along the director in |
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Fig.~\ref{LCFigure:gofrz}(b) implies the existence of the layered |
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structure, and the peak at 27 \AA is attributed to a defect in the |
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structure, and the peak at 27 $\rm{\AA}$ is attributed to a defect in the |
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system. |
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|
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\subsection{Rotational Invariants} |
