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|
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A series of molecular dynamics simulations were perform 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 three GB particles |
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which is characterized by $\mu = 1,~ \nu = 2, |
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every banana shaped molecule has been represented by three GB |
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particles which is characterized by $\mu = 1,~ \nu = 2, |
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~\epsilon_{e}/\epsilon_{s} = 1/5$ and $\sigma_{e}/\sigma_{s} = 3$. |
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All of the simulations begin with same equilibrated isotropic |
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configuration where 1024 molecules without dipoles were confined in |
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arbitrary shape was introduce by Stone\cite{Stone1978} and adopted |
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by other researchers in liquid crystal studies\cite{Berardi2000}. |
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|
| 279 |
< |
\begin{equation} |
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S_{22}^{220} (r) = \frac{1}{{4\sqrt 5 }}\left\langle {\delta (r - |
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r_{ij} )((\hat x_i \cdot \hat x_j )^2 - (\hat x_i \cdot \hat y_j |
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< |
)^2 - (\hat y_i \cdot \hat x_j )^2 + (\hat y_i \cdot \hat y_j |
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)^2 ) - 2(\hat x_i \cdot \hat y_j )(\hat y_i \cdot \hat x_j ) - |
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> |
\begin{eqnarray} |
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> |
S_{22}^{220} (r) & = & \frac{1}{{4\sqrt 5 }}\left\langle {\delta (r |
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> |
- r_{ij} )((\hat x_i \cdot \hat x_j )^2 - (\hat x_i \cdot \hat |
| 282 |
> |
y_j )^2 - (\hat y_i \cdot \hat x_j )^2 + (\hat y_i \cdot \hat |
| 283 |
> |
y_j |
| 284 |
> |
)^2 ) \right.\\ |
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& & \left.- 2(\hat x_i \cdot \hat y_j )(\hat y_i \cdot \hat x_j ) - |
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2(\hat x_i \cdot \hat x_j )(\hat y_i \cdot \hat y_j ))} |
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\right\rangle |
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< |
\end{equation} |
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> |
\end{eqnarray} |
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|
| 290 |
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\begin{equation} |
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S_{00}^{221} (r) = - \frac{{\sqrt 3 }}{{\sqrt {10} }}\left\langle |
