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Difference between revisions of "Gay-Berne model"

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m (Added a See also section)
m (References: Added a recent publication)
 
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*[http://dx.doi.org/10.1103/PhysRevE.54.559  Douglas J. Cleaver, Christopher M. Care, Michael P. Allen, and Maureen P. Neal "Extension and generalization of the Gay-Berne potential" Physical Review E '''54''' pp. 559-567 (1996)]
 
*[http://dx.doi.org/10.1103/PhysRevE.54.559  Douglas J. Cleaver, Christopher M. Care, Michael P. Allen, and Maureen P. Neal "Extension and generalization of the Gay-Berne potential" Physical Review E '''54''' pp. 559-567 (1996)]
 
*[http://dx.doi.org/10.1016/S0009-2614(98)01090-2 Roberto Berardi, Carlo Fava, Claudio Zannoni "A Gay–Berne potential for dissimilar biaxial particles",  Chemical Physics Letters '''297''' pp. 8-14 (1998)]
 
*[http://dx.doi.org/10.1016/S0009-2614(98)01090-2 Roberto Berardi, Carlo Fava, Claudio Zannoni "A Gay–Berne potential for dissimilar biaxial particles",  Chemical Physics Letters '''297''' pp. 8-14 (1998)]
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*[http://dx.doi.org/10.1080/00268976.2016.1274437 Luis F. Rull and José Manuel Romero-Enrique "Computer simulation study of the nematic-vapour interface in the Gay-Berne model", Molecular Physics '''115''' pp. 1214-1224 (2017)]
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[[category:liquid crystals]]
 
[[category:liquid crystals]]
 
[[category:models]]
 
[[category:models]]

Latest revision as of 15:33, 19 May 2017

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