Gay-Berne model

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The Gay-Berne model [1] is used extensively in simulations of liquid crystalline systems. The Gay-Berne model is an anisotropic form of the Lennard-Jones 12:6 potential.

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],

where, in the limit of one of the particles being spherical, gives:

\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}

and

\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}]}

with

\frac{\chi}{\alpha^{2}}=\frac{l_{j}^{2}-d_{j}^{2}}{l_{j}^{2}+d_{i}^{2}}

and

\frac{\chi \prime }{\alpha \prime^{2}}=1- {\left(\frac{\epsilon_{ee}}{\epsilon_{ss}}\right)} ^{\frac{1}{\mu}}.

A modification of the Gay-Berne potential has recently been proposed that is said to result in a 10-20% improvement in computational speed, as well as accuracy [2].

Phase diagram[edit]

Main article: Phase diagram of the Gay-Berne model

See also[edit]

References[edit]

Related reading