Uhlenbeck-Ford model: Difference between revisions

Revision as of 23:56, 11 October 2017

The Uhlenbeck-Ford model (UFM) was originally proposed by G. Uhlenbeck and G. Ford^[1] 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 $k_{B}$ is 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

↑ [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.]

Related reading

[1] [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.]

[1]

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	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 <math> k_B T </math> 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.		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 <math>k_B T</math> where <math>k_B</math> is the Boltzmman constant and <math>T</math> 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.

Uhlenbeck-Ford model: Difference between revisions

Revision as of 23:56, 11 October 2017

Functional form

References

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