Uhlenbeck-Ford model

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

• [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.]
• 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)