Gay-Berne model: Difference between revisions

Revision as of 09:11, 26 September 2008

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_{i j}^{L J / G B} = 4 ϵ_{0}^{L J / G B} [ϵ^{L J / G B}]^{μ} ({\hat{u}}_{j}, {\hat{r}}_{i j}) \times [{(\frac{σ_{0}^{L J / G B}}{r_{i j} - σ^{L J / G B} ({\hat{u}}_{j}, {\hat{r}}_{i j}) + {σ_{0}}^{L J / G B}})}^{12} - {(\frac{σ_{0}^{L J / G B}}{r_{i j} - σ^{L J / G B} ({\hat{u}}_{j}, {\hat{r}}_{i j}) + {σ_{0}}^{L J / G B}})}^{6}],

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

σ^{L J / G B} ({\hat{u}}_{j}, {\hat{r}}_{i j}) = σ_{0} [^{1 - χ α^{- 2} (^{{\hat{r}}_{i j} \cdot {\hat{u}}_{j}) 2}] - 1 / 2}

and

ϵ^{L J / G B} ({\hat{u}}_{j}, {\hat{r}}_{i j}) = ϵ_{0} [1 - χ' α'^{- 2} (^{{\hat{r}}_{i j} \cdot {\hat{u}}_{j}) 2}]

with

\frac{χ}{α^{2}} = \frac{l_{j}^{2} - d_{j}^{2}}{l_{j}^{2} + d_{i}^{2}}

and

\frac{χ'}{α'^{2}} = 1 - {(\frac{ϵ_{e e}}{ϵ_{s s}})}^{\frac{1}{μ}} .

Main article: Phase diagram of the Gay-Berne model

@@ Line 1: / Line 1: @@
-The '''Gay-Berne''' model is used extensively in simulations of [[liquid crystals | liquid crystalline]] systems. The Gay-Berne model
+The '''Gay-Berne model''' (Ref. 1) 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]].
-<math>U_{ij}^{\mathrm LJ/GB} =
+:<math>U_{ij}^{\mathrm LJ/GB} =
 \epsilon_0^{\mathrm LJ/GB}
 [\epsilon^{\mathrm LJ/GB}]^{\mu}
@@ Line 30: / Line 30: @@
 \right],
 </math>
 where, in the limit of one of the particles being spherical, gives: