Gay-Berne model: Difference between revisions
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The '''Gay-Berne model''' | 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 anistropic form of the [[Lennard-Jones model | Lennard-Jones 12:6 potential]]. | is an anistropic form of the [[Lennard-Jones model | Lennard-Jones 12:6 potential]]. | ||
:<math>U_{ij}^{\mathrm LJ/GB} = | :<math>U_{ij}^{\mathrm LJ/GB} = | ||
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:''Main article: [[Phase diagram of the Gay-Berne model]]'' | :''Main article: [[Phase diagram of the 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)] | |||
[[category:liquid crystals]] | [[category:liquid crystals]] | ||
[[category:models]] | [[category:models]] | ||
Revision as of 12:31, 11 November 2009
The Gay-Berne model [1] is used extensively in simulations of liquid crystalline systems. The Gay-Berne model is an anistropic form of the Lennard-Jones 12:6 potential.
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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:
![{\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
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{\chi}{\alpha^{2}}=\frac{l_{j}^{2}-d_{j}^{2}}{l_{j}^{2}+d_{i}^{2}}}
and
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{\chi \prime }{\alpha \prime^{2}}=1- {\left(\frac{\epsilon_{ee}}{\epsilon_{ss}}\right)} ^{\frac{1}{\mu}}.}
Phase diagram
- Main article: Phase diagram of the Gay-Berne model
References
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)