Gay-Berne model

The Gay-Berne model is used extensively in simulations of liquid crystalline systems. The Gay-Berne model is an anistropic form of the Lennard-Jones 12:6 potential. $U_{ij}^{\mathrm{L}J/GB}=4\underset{0}{\overset{\mathrm{L}J/GB}{ϵ}}[{ϵ}^{\mathrm{L}J/GB}{]}^{\mu }({\hat{u}}_j,{\hat{r}}_{ij})\times [{(\frac{\underset{0}{\overset{\mathrm{L}J/GB}{\sigma }}}{r_{ij}-{\sigma }^{\mathrm{L}J/GB}({\hat{u}}_j,{\hat{r}}_{ij})+{{\sigma }_0}^{\mathrm{L}J/GB}})}^{12}-{(\frac{\underset{0}{\overset{\mathrm{L}J/GB}{\sigma }}}{r_{ij}-{\sigma }^{\mathrm{L}J/GB}({\hat{u}}_j,{\hat{r}}_{ij})+{{\sigma }_0}^{\mathrm{L}J/GB}})}^6],$ where, in the limit of one of the particles being spherical, gives:

${\sigma }^{\mathrm{L}J/GB}({\hat{u}}_j,{\hat{r}}_{ij})={\sigma }_0{[}^1$

and

${ϵ}^{\mathrm{L}J/GB}({\hat{u}}_j,{\hat{r}}_{ij})={ϵ}_0[1-\chi \prime \alpha {\prime }^{-2}{(}^{{\hat{r}}_{ij}}]$

with

$\frac{\chi }{{\alpha }^2}=\frac{l_j^2-d_j^2}{l_j^2+d_i^2}$

and

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

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. 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)
3. Enrique De Miguel "Reexamining the phase diagram of the Gay-Berne fluid", Molecular Physics 100 pp. 2449-2459 (2002)
4. Julian T. Brown, Michael P. Allen, Elvira Martín del Río and Enrique de Miguel "Effects of elongation on the phase behavior of the Gay-Berne fluid", Physical Review E 57 pp. 6685 - 6699 (1998)