| 69 |
|
where $r_{ij}$ is the vector between molecule $i$ and molecule $j$, |
| 70 |
|
$\Omega _i$ and $\Omega _j$ are the orientational degrees of freedom |
| 71 |
|
for molecule $i$ and molecule $j$ respectively. |
| 72 |
< |
\[ |
| 73 |
< |
V_{LJ} (r_{ij} ) = 4\varepsilon _{ij} \left[ {\left( {\frac{{\sigma |
| 74 |
< |
_{ij} }}{{r_{ij} }}} \right)^{12} - \left( {\frac{{\sigma _{ij} |
| 75 |
< |
}}{{r_{ij} }}} \right)^6 } \right] |
| 76 |
< |
\] |
| 77 |
< |
\[ |
| 78 |
< |
V_{dp} (r_{ij} ,\Omega _i ,\Omega _j ) = \frac{1}{{4\pi \varepsilon |
| 79 |
< |
_0 }}\left[ {\frac{{\mu _i \cdot \mu _j }}{{r_{ij}^3 }} - |
| 80 |
< |
\frac{{3\left( {\mu _i \cdot r_{ij} } \right)\left( {\mu _i \cdot |
| 81 |
< |
r_{ij} } \right)}}{{r_{ij}^5 }}} \right] |
| 82 |
< |
\] |
| 83 |
< |
\[ |
| 84 |
< |
V_{sticky} (r_{ij} ,\Omega _i ,\Omega _j ) = v_0 [s(r_{ij} )w(r_{ij} |
| 85 |
< |
,\Omega _i ,\Omega _j ) + s'(r_{ij} )w'(r_{ij} ,\Omega _i ,\Omega _j |
| 86 |
< |
)] |
| 87 |
< |
\] |
| 72 |
> |
\begin{eqnarray*} |
| 73 |
> |
V_{LJ} (r_{ij} ) &= &4\varepsilon _{ij} \left[ {\left( |
| 74 |
> |
{\frac{{\sigma _{ij} }}{{r_{ij} }}} \right)^{12} - \left( |
| 75 |
> |
{\frac{{\sigma _{ij} |
| 76 |
> |
}}{{r_{ij} }}} \right)^6 } \right], \\ |
| 77 |
> |
V_{dp} (r_{ij} ,\Omega _i ,\Omega _j ) &= & |
| 78 |
> |
\frac{|\mu_i||\mu_j|}{4\pi\epsilon_{0}r_{ij}^{3}} \biggl[ |
| 79 |
> |
\hat{u}_{i} \cdot \hat{u}_{j} - 3(\hat{u}_i \cdot \hat{\mathbf{r}}_{ij}) % |
| 80 |
> |
(\hat{u}_j \cdot \hat{\mathbf{r}}_{ij}) \biggr],\\ |
| 81 |
> |
V_{sticky} (r_{ij} ,\Omega _i ,\Omega _j ) &=& v_0 [s(r_{ij} |
| 82 |
> |
)w(r_{ij} ,\Omega _i ,\Omega _j ) + s'(r_{ij} )w'(r_{ij} ,\Omega _i |
| 83 |
> |
,\Omega _j )].\\ |
| 84 |
> |
\end{eqnarray*} |
| 85 |
|
where $v_0$ is a strength parameter, $s$ and $s'$ are cubic |
| 86 |
< |
switching functions, while $w$ and $w'$ are responsible for the |
| 86 |
> |
switching functions, while $w$ and $w'$ are responsible for the |
| 87 |
|
tetrahedral potential and the short-range correction to the dipolar |
| 88 |
|
interaction respectively. |
| 89 |
|
\[ |
