Difference between revisions of "Gay-Berne model"

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{{Stub-general}}
 
 
The '''Gay-Berne''' model is used extensively in simulations of [[liquid crystals | liquid crystalline]] systems. The Gay-Berne model
 
The '''Gay-Berne''' model is used extensively in simulations of [[liquid crystals | liquid crystalline]] systems. The Gay-Berne model
 
is an anistropic form of the [[Lennard-Jones model | Lennard-Jones 12:6 potential]].
 
is an anistropic form of the [[Lennard-Jones model | Lennard-Jones 12:6 potential]].
 +
<math>U_{ij}^{\mathrm LJ/GB} =
 +
4 \epsilon_0^{\mathrm LJ/GB}
 +
[\epsilon^{\mathrm LJ/GB}]^{\mu}
 +
( {\mathbf {\hat u}}_j , {\mathbf {\hat r}}_{ij} )
 +
\times  \left[ \left(
 +
\frac{\sigma_0^{\mathrm LJ/GB}
 +
}
 +
{
 +
r_{ij} -
 +
\sigma^{\mathrm LJ/GB}
 +
({\mathbf {\hat{u}}}_j, {\mathbf {\hat{r}}}_{ij} )
 +
+ {\sigma_0}^{\mathrm LJ/GB}
 +
}
 +
\right)^{12}
 +
-
 +
\left(
 +
\frac
 +
{
 +
\sigma_0^{\mathrm LJ/GB}
 +
}
 +
{
 +
r_{ij} -
 +
\sigma^{\mathrm LJ/GB}
 +
({\mathbf {\hat{u}}}_j, {\mathbf {\hat{r}}}_{ij} )
 +
+ {\sigma_0}^{\mathrm LJ/GB}
 +
}
 +
\right)^{6}
 +
\right],
 +
</math>
 +
where, in the limit of one of the particles being spherical, gives:
 +
 +
:<math>\sigma^{\mathrm LJ/GB} ({\mathbf {\hat{u}}}_j, {\mathbf {\hat{r}}}_{ij} ) ={\sigma_0}{[1 - \chi \alpha^{-2}
 +
{({\mathbf {\hat{r}}}_{ij} \cdot  {\mathbf {\hat{u}}}_j )}^{2}]}^{-1/2}</math>
 +
 +
and
 +
 +
:<math>\epsilon^{\mathrm LJ/GB}({\mathbf {\hat{u}}}_j, {\mathbf {\hat{r}}}_{ij} ) ={\epsilon_0}{[1 - \chi\prime  \alpha\prime^{-2}
 +
{({\mathbf {\hat{r}}}_{ij} \cdot  {\mathbf {\hat{u}}}_j )}^{2}]}</math>
 +
 +
with
 +
 +
:<math>\frac{\chi}{\alpha^{2}}=\frac{l_{j}^{2}-d_{j}^{2}}{l_{j}^{2}+d_{i}^{2}}</math>
 +
 +
and
 +
 +
:<math>\frac{\chi \prime }{\alpha \prime^{2}}=1- {\left(\frac{\epsilon_{ee}}{\epsilon_{ss}}\right)} ^{\frac{1}{\mu}}.</math>
 +
 
==References==
 
==References==
 
#[http://dx.doi.org/10.1063/1.441483  J. G. Gay and B. J. Berne "Modification of the overlap potential to mimic a linear site–site potential", Journal of Chemical Physics '''74''' pp. 3316-3319  (1981)]
 
#[http://dx.doi.org/10.1063/1.441483  J. G. Gay and B. J. Berne "Modification of the overlap potential to mimic a linear site–site potential", Journal of Chemical Physics '''74''' pp. 3316-3319  (1981)]

Revision as of 12:04, 3 October 2007