Uhlenbeck-Ford model

The Uhlenbeck-Ford model (UFM) was originally proposed by G. Uhlenbeck and G. Ford <ref>[G. Uhlenbeck and G. Ford, in Studies in Statistical Mechanics— The Theory of Linear Graphs with Application to the Theory of the Virial Development of the Properties of Gases, edited by G. E. Uhlenbeck and J. de Boer (North-Holland, Amsterdam, 1962), Vol. 2.] <\ref> for the theoretical study of imperfect gases. This model is characterized by an ultrasoft, purely repulsive pairwise interaction potential that diverges logarithmically at the origin and features an energy scale that coincides with the thermal energy unit $k_{B}T$ where k Bis the Boltzmman constant and T the absolute temperature. The particular functional form of the potential permits, in principle, that the virial coeffcients and, therefore, the equation of state and excess free energies for the fluid phase be evaluated analytically.

Functional form

The Uhlenbeck-Ford model is given by :

$U_{UF}(r)=-{\frac {p}{\beta }}\ln \left(1-e^{-(r/\sigma )^{2}}\right)$

where

• $p>0$ is a scaling factor;
• $\beta \equiv (k_{B}T)^{-1}$ is the well depth (energy);
• $r\equiv |\mathbf {r} _{1}-\mathbf {r} _{2}|$ is the interparticle distance;
• $\sigma$ is a length-scale parameter.

References

Related reading

• R. Paula Leite, R. Freitas, R. Azevedo and M. de Koning "The Uhlenbeck-Ford model: Exact virial coefficients and application as a reference system in fluid-phase free-energy calculations", Journal of Chemical Physics 145, 194101 (2016)
• R. Paula Leite, R. Freitas, R. Azevedo and M. de Koning "Supplemental Material: The Uhlenbeck-Ford model: Exact virial coefficients and application as a reference system in fluid-phase free-energy calculations", Journal of Chemical Physics 145, 194101 (2016)
• R. Paula Leite, P. A. Santos-Flórez and M. de Koning "Uhlenbeck-Ford model: Phase diagram and corresponding-states analysis", Physical Review E 96, 032115 (2017)