Hemmer and Stell model
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The Hemmer and Stell model intermolecular pair 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)} , is given by (Ref. 1 Eq. 2, Ref. 2 Eq. 1-3):
- 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) = \Phi_{12}(r)_{\mathrm {repulsive}} + \Phi_{12}(r)_{\mathrm{attractive}}}
where a short range piece-wise 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 {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.