Hemmer and Stell model: Difference between revisions
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The '''Hemmer and Stell model''' [[intermolecular pair potential]], <math>\ | The '''Hemmer and Stell model''' [[intermolecular pair potential]], <math>\Phi_{12}(r)</math>, is given by (Ref. 1 Eq. 2, Ref. 2 Eq. 1-3): | ||
:<math>\ | :<math>\Phi_{12}(r) = \Phi_{12}(r)_{\mathrm {repulsive}} + \Phi_{12}(r)_{\mathrm{attractive}}</math> | ||
where a short range piece-wise potential | where a short range piece-wise potential | ||
:<math> | :<math> | ||
\ | \Phi_{12}(r)_{\mathrm {repulsive}} = \left\{ | ||
\begin{array}{ll} | \begin{array}{ll} | ||
\infty & {\rm if} \; r < d \\ | \infty & {\rm if} \; r < d \\ | ||
| Line 14: | Line 14: | ||
\end{array} \right. | \end{array} \right. | ||
</math> | </math> | ||
where <math>d</math> is the hard core radius, along with a long-range attractive potential; | where <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>, <math>d</math> is the hard core radius, along with a long-range attractive potential; | ||
:<math>\ | :<math>\Phi_{12}(r)_{\mathrm{attractive}} = -a\gamma \exp (-\gamma r)</math> | ||
where <math>a</math> is a positive constant. | where <math>a</math> is a positive constant. | ||
Latest revision as of 15:57, 17 July 2008
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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.