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(r_{12})= \exp\left(-\frac{\Phi_{12}(r)}{k_BT}\right) -1 </math>  
:<math>f_{12}=f({\mathbf r}_{12})= \exp\left(-\frac{\Phi_{12}(r)}{k_BT}\right) -1 </math>  


where
where
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:[[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:

where

Diagrammatically the Mayer f-function is written as

Hard sphere model

For the hard sphere model the Mayer f-function becomes:

where is the hard sphere diameter.

References

  1. Joseph E. Mayer "Contribution to Statistical Mechanics", Journal of Chemical Physics 10 pp. 629-643 (1942)