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


where
where
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* <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]].
* <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]].


Diagrammatically the Mayer ''f''-function is written as  
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]]
:[[Image:Mayer_f_function.png]]
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where <math>\sigma</math> is the hard sphere diameter.
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)]  
#[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

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]

  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)