Mayer f-function

The Mayer f-function, or f-bond is defined as:

$f_{12}=f({\mathbf {r} }_{12})=\exp \left(-{\frac {\Phi _{12}(r)}{k_{B}T}}\right)-1$

where

• $k_{B}$ is the Boltzmann constant.
• $T$ is the temperature.
• $\Phi _{12}(r)$ 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:

$f_{12}=\left\{{\begin{array}{lll}-1&;&r_{12}\leq \sigma ~~({\rm {overlap}})\\0&;&r_{12}>\sigma ~~({\rm {no~overlap}})\end{array}}\right.$

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.

References

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