Virial coefficient

The Mayer f-function is an auxiliary function that often appears in the series expansion of thermodynamic quantities related to classical many-particle systems.

Definition

Consider a system of classical particles interacting through a pair-wise potential

$V(\mathbf{i},\mathbf{j})$

where the bold labels $\mathbf{i}$ and $\mathbf{j}$ denote the continuous degrees of freedom associated with the particles, e.g.,

$\mathbf{i}={\mathbf{r}}_i$

for spherically symmetric particles and

$\mathbf{i}=({\mathbf{r}}_i,{\mathrm{\Omega }}_i)$

for rigid non-spherical particles where $\mathbf{r}$ denotes position and $\mathrm{\Omega }$ the orientation parametrized e.g. by Euler angles. The Mayer f-function is then defined as

$f(\mathbf{i},\mathbf{j})=e^{-\beta V(\mathbf{i},\mathbf{j})}-1$

where $\beta =(k_{B}T{)}^{-1}$ the inverse absolute temperature in units of (Temperature times the Boltzmann constant $k_B$)^-1 .

See also

• Virial coefficient
• Cluster expansion
• Excluded volume

Notes

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