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| The '''Mayer ''f''-function''', or ''f-bond'' is defined as (Ref. 1 Chapter 13 Eq. 13.2):
| | Definition: |
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| :<math>f_{12}=f({\mathbf r}_{12}) := \exp\left(-\frac{\Phi_{12}(r)}{k_BT}\right) -1 </math>
| | <math>f_{ij}=f(r_{ij})= \exp\left(-\frac{u(r)}{k_BT}\right) -1 </math> |
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| 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>\Phi_{12}(r)</math> is the [[intermolecular pair potential]]. | | * <math>u(r)</math> is the 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.
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| ==References== | | ==References== |
| # 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]] |