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

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

for rigid non-spherical particles where $\mathbf {r}$ denotes position and $\Omega$ 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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