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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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| is an anisotropic form of the [[Lennard-Jones model | Lennard-Jones 12:6 potential]].
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| :<math>U_{ij}^{\mathrm LJ/GB} =
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| 4 \epsilon_0^{\mathrm LJ/GB}
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| [\epsilon^{\mathrm LJ/GB}]^{\mu}
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| ( {\mathbf {\hat u}}_j , {\mathbf {\hat r}}_{ij} )
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| \times \left[ \left(
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| \frac{\sigma_0^{\mathrm LJ/GB}
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| }
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| {
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| r_{ij} -
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| \sigma^{\mathrm LJ/GB}
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| ({\mathbf {\hat{u}}}_j, {\mathbf {\hat{r}}}_{ij} )
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| + {\sigma_0}^{\mathrm LJ/GB}
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| }
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| \right)^{12}
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| -
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| \left(
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| \frac
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| {
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| \sigma_0^{\mathrm LJ/GB}
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| }
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| {
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| r_{ij} -
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| \sigma^{\mathrm LJ/GB}
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| ({\mathbf {\hat{u}}}_j, {\mathbf {\hat{r}}}_{ij} )
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| + {\sigma_0}^{\mathrm LJ/GB}
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| }
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| \right)^{6}
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| \right],
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| </math>
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|
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| where, in the limit of one of the particles being spherical, gives:
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|
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| :<math>\sigma^{\mathrm LJ/GB} ({\mathbf {\hat{u}}}_j, {\mathbf {\hat{r}}}_{ij} ) ={\sigma_0}{[1 - \chi \alpha^{-2}
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| {({\mathbf {\hat{r}}}_{ij} \cdot {\mathbf {\hat{u}}}_j )}^{2}]}^{-1/2}</math>
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|
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| and
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|
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| :<math>\epsilon^{\mathrm LJ/GB}({\mathbf {\hat{u}}}_j, {\mathbf {\hat{r}}}_{ij} ) ={\epsilon_0}{[1 - \chi\prime \alpha\prime^{-2}
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| {({\mathbf {\hat{r}}}_{ij} \cdot {\mathbf {\hat{u}}}_j )}^{2}]}</math>
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|
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| with
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|
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| :<math>\frac{\chi}{\alpha^{2}}=\frac{l_{j}^{2}-d_{j}^{2}}{l_{j}^{2}+d_{i}^{2}}</math>
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|
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| and
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|
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| :<math>\frac{\chi \prime }{\alpha \prime^{2}}=1- {\left(\frac{\epsilon_{ee}}{\epsilon_{ss}}\right)} ^{\frac{1}{\mu}}.</math>
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|
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| 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>.
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| ==Phase diagram==
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| :''Main article: [[Phase diagram of the Gay-Berne model]]''
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| ==See also==
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| *[[Soft-core Gay-Berne model]]
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| ==References== | | ==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)] |
| '''Related reading'''
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| *[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/10.1103/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/10.1016/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]] |