M-6-8 potential function: Difference between revisions
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The '''m-6-8 potential function''' <ref>[http://dx.doi.org/10.1063/1.1674009 Max Klein and H. J. M. Hanley "m–6–8 Potential Function", Journal of Chemical Physics '''53''' pp. 4722-4723 (1970)]</ref> is given by (Eq. 1) | The '''m-6-8 potential function''' <ref>[http://dx.doi.org/10.1063/1.1674009 Max Klein and H. J. M. Hanley "m–6–8 Potential Function", Journal of Chemical Physics '''53''' pp. 4722-4723 (1970)]</ref> is given by (Eq. 1) | ||
Latest revision as of 10:06, 14 May 2015
The m-6-8 potential function [1] is given by (Eq. 1)
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \Phi _{12}(r)={\frac {A}{r^{m}}}-{\frac {C_{6}}{r^{6}}}-{\frac {C_{8}}{r^{8}}}}
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|} and 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 the intermolecular pair potential between two particles or sites. 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 the coefficient corresponding to the repulsive term, and 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 C_6} and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle C_{8}} are the coefficients corresponding to the attractive inverse sixth and eighth powers respectively.
This expression can be rewritten in the reduced form (Eq. 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 \Phi^*_{12}(r^*) = \left[ \frac{1}{m-6} \right] \left[ 6+2\gamma \right] \left( \frac{1}{r^*} \right)^m - \left[ \frac{1}{m-6} \right] \left[ m-\gamma(m-8)\right]\left( \frac{1}{r^*} \right)^6 - \frac{\gamma}{r^{*8}} }
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 \Phi^* = \Phi/\epsilon} , 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^* = r/r_m} and 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 \gamma = C_8/r_m^8} . 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 \epsilon} is the "well" depth, and 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_m} is the intermolecular separation at the maximum well depth.
References[edit]
- Related reading