# Difference between revisions of "Mayer f-function"

Carl McBride (talk | contribs) (New page: Definition: <math>f_{ij}=f(r_{ij})= \exp\left(-\frac{u(r)}{k_BT}\right) -1 </math> where * <math>k_B</math> is the Boltzmann constant * <math>T</math> is the temperature * <math>u(r...) |
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− | + | The '''Mayer ''f''-function''', or ''f-bond'' is defined as (Ref. 1 Chapter 13 Eq. 13.2): | |

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

where | where | ||

− | * <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> | + | * <math>\Phi_{12}(r)</math> is the [[intermolecular pair 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 | ||

+ | |||

+ | :[[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== | ||

+ | # 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]] |

## Latest revision as of 18:50, 20 February 2015

The **Mayer f-function**, or

*f-bond*is defined as (Ref. 1 Chapter 13 Eq. 13.2):

where

- is the Boltzmann constant.
- is the temperature.
- is the intermolecular pair potential.

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

Diagrammatically the Mayer *f*-function is written as

## Hard sphere model[edit]

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

where is the hard sphere diameter.

## References[edit]

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