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Difference between revisions of "Gay-Berne model"

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*[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/10.1103/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/10.1016/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)]
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*[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)]
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[[category:liquid crystals]]
 
[[category:liquid crystals]]
 
[[category:models]]
 
[[category:models]]

Latest revision as of 16:33, 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.

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

{\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 [2].

Phase diagram[edit]

Main article: Phase diagram of the Gay-Berne model

See also[edit]

References[edit]

  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. Rasmus A. X. Persson "Note: Modification of the Gay-Berne potential for improved accuracy and speed", Journal of Chemical Physics 136 226101 (2012)

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