Mayer f-function: Difference between revisions
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The '''Mayer ''f''-function''', or ''f-bond'' is defined as: | The '''Mayer ''f''-function''', or ''f-bond'' is defined as: | ||
:<math>f_{12}=f( | :<math>f_{12}=f({\mathbf r}_{12})= \exp\left(-\frac{\Phi_{12}(r)}{k_BT}\right) -1 </math> | ||
where | where | ||
| Line 11: | Line 11: | ||
:[[Image:Mayer_f_function.png]] | :[[Image:Mayer_f_function.png]] | ||
==Hard sphere model== | |||
For the [[hard sphere model]] the Mayer ''f''-function becomes: | |||
: <math> | |||
f_{12}= \left\{ \begin{array}{lll} | |||
-1 & ; & r_{12} \leq \sigma ~~({\rm overlap})\\ | |||
0 & ; & r_{12} > \sigma ~~({\rm no~overlap})\end{array} \right. | |||
</math> | |||
where <math>\sigma</math> is the hard sphere diameter. | |||
==References== | ==References== | ||
#[http://dx.doi.org/10.1063/1.1723631 Joseph E. Mayer "Contribution to Statistical Mechanics", Journal of Chemical Physics '''10''' pp. 629-643 (1942)] | #[http://dx.doi.org/10.1063/1.1723631 Joseph E. Mayer "Contribution to Statistical Mechanics", Journal of Chemical Physics '''10''' pp. 629-643 (1942)] | ||
[[Category: Statistical mechanics]] | [[Category: Statistical mechanics]] | ||
[[Category: Integral equations]] | [[Category: Integral equations]] | ||
Revision as of 11:29, 13 July 2007
The Mayer f-function, or f-bond is defined as:
- 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 f_{12}=f({\mathbf r}_{12})= \exp\left(-\frac{\Phi_{12}(r)}{k_BT}\right) -1 }
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 k_B} is the Boltzmann constant.
- 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 T} is the temperature.
- 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.
Diagrammatically the Mayer f-function is written as
Hard sphere model
For the hard sphere model the Mayer f-function becomes:
- 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 f_{12}= \left\{ \begin{array}{lll} -1 & ; & r_{12} \leq \sigma ~~({\rm overlap})\\ 0 & ; & r_{12} > \sigma ~~({\rm no~overlap})\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 \sigma} is the hard sphere diameter.