Gay-Berne model

The Gay-Berne model (Ref. 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.

$U_{ij}^{\mathrm {L} J/GB}=4\epsilon _{0}^{\mathrm {L} J/GB}[\epsilon ^{\mathrm {L} J/GB}]^{\mu }({\mathbf {\hat {u}} }_{j},{\mathbf {\hat {r}} }_{ij})\times \left[\left({\frac {\sigma _{0}^{\mathrm {L} J/GB}}{r_{ij}-\sigma ^{\mathrm {L} J/GB}({\mathbf {\hat {u}} }_{j},{\mathbf {\hat {r}} }_{ij})+{\sigma _{0}}^{\mathrm {L} J/GB}}}\right)^{12}-\left({\frac {\sigma _{0}^{\mathrm {L} J/GB}}{r_{ij}-\sigma ^{\mathrm {L} J/GB}({\mathbf {\hat {u}} }_{j},{\mathbf {\hat {r}} }_{ij})+{\sigma _{0}}^{\mathrm {L} J/GB}}}\right)^{6}\right],$

where, in the limit of one of the particles being spherical, gives:

$\sigma ^{\mathrm {L} J/GB}({\mathbf {\hat {u}} }_{j},{\mathbf {\hat {r}} }_{ij})={\sigma _{0}}{[1-\chi \alpha ^{-2}{({\mathbf {\hat {r}} }_{ij}\cdot {\mathbf {\hat {u}} }_{j})}^{2}]}^{-1/2}$

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

${\frac {\chi \prime }{\alpha \prime ^{2}}}=1-{\left({\frac {\epsilon _{ee}}{\epsilon _{ss}}}\right)}^{\frac {1}{\mu }}.$

Phase diagram

Main article: Phase diagram of the Gay-Berne model

References

1. 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)
2. R. Berardi, C. Fava and C. Zannoni "A generalized Gay-Berne intermolecular potential for biaxial particles", Chemical Physics Letters 236 pp. 462-468 (1995)
3. 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)
4. Roberto Berardi, Carlo Fava, Claudio Zannoni "A Gay–Berne potential for dissimilar biaxial particles", Chemical Physics Letters 297 pp. 8-14 (1998)