Gay-Berne model: Difference between revisions
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The '''Gay-Berne''' | 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 | ||
is an | is an anisotropic form of the [[Lennard-Jones model | Lennard-Jones 12:6 potential]]. | ||
<math>U_{ij}^{\mathrm LJ/GB} = | :<math>U_{ij}^{\mathrm LJ/GB} = | ||
4 \epsilon_0^{\mathrm LJ/GB} | 4 \epsilon_0^{\mathrm LJ/GB} | ||
[\epsilon^{\mathrm LJ/GB}]^{\mu} | [\epsilon^{\mathrm LJ/GB}]^{\mu} | ||
| Line 30: | Line 30: | ||
\right], | \right], | ||
</math> | </math> | ||
where, in the limit of one of the particles being spherical, gives: | where, in the limit of one of the particles being spherical, gives: | ||
| Line 47: | Line 48: | ||
:<math>\frac{\chi \prime }{\alpha \prime^{2}}=1- {\left(\frac{\epsilon_{ee}}{\epsilon_{ss}}\right)} ^{\frac{1}{\mu}}.</math> | :<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== | ==Phase diagram== | ||
:''Main article: [[Phase diagram of the Gay-Berne model]]'' | :''Main article: [[Phase diagram of the Gay-Berne model]]'' | ||
==See also== | |||
*[[Soft-core Gay-Berne model]] | |||
==References== | ==References== | ||
<references/> | |||
'''Related reading''' | |||
*[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)] | |||
*[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/10.1080/00268976.2016.1274437 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]] | ||
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.
![{\displaystyle U_{ij}^{\mathrm {L} J/GB}=4\epsilon _{0}^{\mathrm {L} J/GB}[\epsilon ^{\mathrm {L} J/GB}]^{\mu }({\mathbf {\hat {u}} }_{j},{\mathbf {\hat {r}} }_{ij})\times \left[\left({\frac {\sigma _{0}^{\mathrm {L} J/GB}}{r_{ij}-\sigma ^{\mathrm {L} J/GB}({\mathbf {\hat {u}} }_{j},{\mathbf {\hat {r}} }_{ij})+{\sigma _{0}}^{\mathrm {L} J/GB}}}\right)^{12}-\left({\frac {\sigma _{0}^{\mathrm {L} J/GB}}{r_{ij}-\sigma ^{\mathrm {L} J/GB}({\mathbf {\hat {u}} }_{j},{\mathbf {\hat {r}} }_{ij})+{\sigma _{0}}^{\mathrm {L} J/GB}}}\right)^{6}\right],}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2772fe11a58f7457bf6d9b2d0c7647032a2019b8)
where, in the limit of one of the particles being spherical, gives:
![{\displaystyle \sigma ^{\mathrm {L} J/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}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f559304db8b0a3db5a0c82414e2d4289ea52e01)
and
![{\displaystyle \epsilon ^{\mathrm {L} J/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}]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/278dbbf31474c1792aa835e8e9e9f9a3da8ab095)
with
and
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]
- ↑ 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)
- ↑ Rasmus A. X. Persson "Note: Modification of the Gay-Berne potential for improved accuracy and speed", Journal of Chemical Physics 136 226101 (2012)
Related reading
- R. Berardi, C. Fava and C. Zannoni "A generalized Gay-Berne intermolecular potential for biaxial particles", Chemical Physics Letters 236 pp. 462-468 (1995)
- 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)
- Roberto Berardi, Carlo Fava, Claudio Zannoni "A Gay–Berne potential for dissimilar biaxial particles", Chemical Physics Letters 297 pp. 8-14 (1998)
- 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)