Difference between revisions of "Mayer f-function"

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The '''Mayer ''f''-function''', or ''f-bond'' is defined as:
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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_{12}=f({\mathbf r}_{12}) := \exp\left(-\frac{\Phi_{12}(r)}{k_BT}\right) -1 </math>  
  
 
where
 
where
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* <math>T</math> is the [[temperature]].
 
* <math>T</math> is the [[temperature]].
 
* <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]].
 
* <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  
 
[[Cluster diagrams | Diagrammatically]] the Mayer ''f''-function is written as  

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):

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)