Mayer f-function

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The Mayer f-function, or f-bond is defined as (Ref. 1 Chapter 13 Eq. 13.2):

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

where

In other words, the Mayer function is the Boltzmann factor of the interaction potential, minus one.

Diagrammatically the Mayer f-function is written as

Mayer f function.png

Hard sphere model[edit]

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 \sigma is the hard sphere diameter.

References[edit]

  1. Joseph Edward Mayer and Maria Goeppert Mayer "Statistical Mechanics" John Wiley and Sons (1940)
  2. Joseph E. Mayer "Contribution to Statistical Mechanics", Journal of Chemical Physics 10 pp. 629-643 (1942)