Hemmer and Stell model

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The Hemmer and Stell model intermolecular pair potential, \Phi_{12}(r), is given by (Ref. 1 Eq. 2, Ref. 2 Eq. 1-3):

\Phi_{12}(r) = \Phi_{12}(r)_{\mathrm {repulsive}} + \Phi_{12}(r)_{\mathrm{attractive}}

where a short range piece-wise potential


\Phi_{12}(r)_{\mathrm {repulsive}} = \left\{ 
\begin{array}{ll}
\infty & {\rm if} \; r < d \\
V_0 \left( \frac{1- (r-d)}{\lambda d} \right)& {\rm if} \; d < r < d(1+ \lambda) \\

0 &  {\rm if} \; d( 1+ \lambda) < r 
\end{array} \right.

where r := |\mathbf{r}_1 - \mathbf{r}_2|, d is the hard core radius, along with a long-range attractive potential;

\Phi_{12}(r)_{\mathrm{attractive}} = -a\gamma \exp (-\gamma r)

where a is a positive constant.

References[edit]

  1. P. C. Hemmer and G. Stell "Fluids with Several Phase Transitions", Physical Review Letters 24 pp. 1284 - 1287 (1970)
  2. G. Stell and P. C. Hemmer, "Phase Transitions Due to Softness of the Potential Core", Journal of Chemical Physics' 56, pp. 4274-4286 (1972)