Hemmer and Stell model
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The Hemmer and Stell model intermolecular pair potential, , is given by (Ref. 1 Eq. 2, Ref. 2 Eq. 1-3):
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \Phi _{12}(r)=\Phi _{12}(r)_{\mathrm {repulsive} }+\Phi _{12}(r)_{\mathrm {attractive} }}
where a short range piece-wise potential
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r := |\mathbf{r}_1 - \mathbf{r}_2|} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d} is the hard core radius, along with a long-range attractive potential;
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi_{12}(r)_{\mathrm{attractive}} = -a\gamma \exp (-\gamma r)}
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} is a positive constant.