Gay-Berne model

The Gay-Berne model is used extensively in simulations of liquid crystalline systems. The Gay-Berne model is an anisotropic 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

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

with

${\frac {\chi }{\alpha ^{2}}}={\frac {l_{j}^{2}-d_{j}^{2}}{l_{j}^{2}+d_{i}^{2}}}$

and

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\frac {\chi \prime }{\alpha \prime ^{2}}}=1-{\left({\frac {\epsilon _{ee}}{\epsilon _{ss}}}\right)}^{\frac {1}{\mu }}.}

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 .

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)