Modified Lennard-Jones model

From SklogWiki
Jump to: navigation, search

The modified Lennard-Jones model is given by (Eq. 2 [1]):


\Phi_{12}(r) = \left\{ 
\begin{array}{ll}
4 \epsilon \left[ \left(\frac{\sigma}{r} \right)^{12}-  \left( \frac{\sigma}{r}\right)^6 \right]  + C_1 &  r \leq  2.3 \sigma \\
C_2 \left(\frac{\sigma}{r} \right)^{12}   + C_3 \left(\frac{\sigma}{r} \right)^{6}  + C_4  \left(\frac{r}{\sigma} \right)^{2}  + C_5 &  2.3 \sigma < r < 2.5 \sigma\\
0 &  2.5 \sigma \leq r
\end{array} \right.

where C_1 = 0.016132 \epsilon, C_2 = 3136.6 \epsilon C_3 = -68.069 \epsilon C_4 = 0.083312 \epsilon and C_5 = 0.74689\epsilon. These parametrs are chosen so that the function \Phi_{12}(r), as well as the first derivative, is continuous both at r = 2.3\sigma and r = 2.5\sigma. These parameters have recently been recalculated with greater precision by Asano and Fuchizaki [2], leading to C_1 = 0.0163169237\epsilon, C_2 = 3136.5686  \epsilon C_3 = -68.069 \epsilon [3], C_4 =  -0.0833111261 \epsilon and C_5 = 0.746882273 \epsilon.

Virial coefficients[edit]

The virial coefficients up to the seventh order have been calculated for the range of temperatures k_BT/\epsilon = 0.3-70 [4]. See also [5].

References[edit]