Difference between revisions of "Mayer f-function"

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(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...)
 
m (Defined as)
 
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Definition:
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The '''Mayer ''f''-function''', or ''f-bond'' is defined as (Ref. 1 Chapter 13 Eq. 13.2):
  
<math>f_{ij}=f(r_{ij})= \exp\left(-\frac{u(r)}{k_BT}\right) -1 </math>  
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:<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]]
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* <math>k_B</math> is the [[Boltzmann constant]].
* <math>T</math> is the temperature
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* <math>T</math> is the [[temperature]].
* <math>u(r)</math> is the potential
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* <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]].
  
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In other words, the Mayer function is the [[Boltzmann factor]] of the interaction potential,
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minus one.
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[[Cluster diagrams | Diagrammatically]] the Mayer ''f''-function is written as
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:[[Image:Mayer_f_function.png]]
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==Hard sphere model==
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For the [[hard sphere model]]  the Mayer ''f''-function becomes:
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: <math>
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f_{12}= \left\{ \begin{array}{lll}
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-1 & ; & r_{12} \leq  \sigma ~~({\rm  overlap})\\
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0      & ; & r_{12} > \sigma ~~({\rm  no~overlap})\end{array} \right.
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</math>
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where <math>\sigma</math> is the hard sphere diameter.
 
==References==
 
==References==
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# Joseph Edward Mayer and Maria Goeppert Mayer "Statistical Mechanics" John Wiley and Sons (1940)
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#[http://dx.doi.org/10.1063/1.1723631 Joseph E. Mayer "Contribution to Statistical Mechanics", Journal of Chemical Physics '''10''' pp. 629-643 (1942)]
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[[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):

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)