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The '''Gay-Berne model''' <ref>[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)]</ref> is used extensively in simulations of [[liquid crystals | liquid crystalline]] systems. The Gay-Berne model
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The '''Gay-Berne''' model is used extensively in simulations of [[liquid crystals | liquid crystalline]] systems.  
is an anisotropic 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>
 
 
 
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 <ref>[http://dx.doi.org/10.1063/1.4729745 Rasmus A. X. Persson "Note: Modification of the Gay-Berne potential for improved accuracy and speed", Journal of Chemical Physics '''136''' 226101 (2012)]</ref>.
 
==Phase diagram==
 
:''Main article: [[Phase diagram of the Gay-Berne model]]''
 
==See also==
 
*[[Soft-core Gay-Berne model]]
 
 
==References==
 
==References==
<references/>
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#[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)]
'''Related reading'''
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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/10.1016/0009-2614(95)00212-M R. Berardi, C. Fava and C. Zannoni "A generalized Gay-Berne intermolecular potential for biaxial particles", Chemical Physics Letters '''236''' pp. 462-468 (1995)]
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#[http://dx.doi.org/10.1080/00268970210121605 Enrique De Miguel "Reexamining the phase diagram of the Gay-Berne fluid", Molecular Physics '''100''' pp. 2449-2459 (2002)]
*[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)]
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#[http://dx.doi.org/10.1103/PhysRevE.57.6685  Julian T. Brown, Michael P. Allen, Elvira Martín del Río and Enrique de Miguel "Effects of elongation on the phase behavior of the Gay-Berne fluid", Physical Review E '''57''' pp. 6685 - 6699 (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)]
 
*[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)]
 
 
 
  
 
[[category:liquid crystals]]
 
[[category:liquid crystals]]
 
[[category:models]]
 
[[category:models]]

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