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The '''Mayer ''f''-function''', or ''f-bond'' is defined as (Ref. 1 Chapter 13 Eq. 13.2):
:<math>f_{12}=f({\mathbf r}_{12}) := \exp\left(-\frac{\Phi_{12}(r)}{k_BT}\right) -1 </math>  
<math>f_{ij}=f(r_{ij})= \exp\left(-\frac{u(r)}{k_BT}\right) -1 </math>  
* <math>k_B</math> is the [[Boltzmann constant]].
* <math>k_B</math> is the [[Boltzmann constant]]
* <math>T</math> is the [[temperature]].
* <math>T</math> is the temperature
* <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]].
* <math>u(r)</math> is the potential
In other words, the Mayer function is the [[Boltzmann factor]] of the interaction potential,
minus one.
[[Cluster diagrams | Diagrammatically]] the Mayer ''f''-function is written as
==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.
where <math>\sigma</math> is the hard sphere diameter.
# Joseph Edward Mayer and Maria Goeppert Mayer "Statistical Mechanics" John Wiley and Sons (1940)
#[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]]

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