Uhlenbeck-Ford model: Difference between revisions

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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 <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. A recent study showed that this model can be used as a reference system for fluid-phase free-energy calculations <ref>[http://dx.doi.org/10.1063/1.4967775  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)]</ref>.   
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. A recent study showed that this model can be used as a reference system for fluid-phase free-energy calculations <ref name="JCP">>[http://dx.doi.org/10.1063/1.4967775  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)]</ref>.   




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== Equation of state ==  
== Equation of state ==  


The UFM's equation of state using virial expansion has recently been studied by Paula Leite, Freitas, Azevedo and de Koning <ref>[http://dx.doi.org/10.1063/1.4967775  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)]</ref>. This equation of state is given by
The UFM's equation of state using virial expansion has recently been studied by Paula Leite, Freitas, Azevedo and de Koning <ref name="JCP"></ref>. This equation of state is given by


:<math>\beta bP = x + \sum_{n=2}^{\infty} \tilde{B}_n \,x^n</math>
:<math>\beta bP = x + \sum_{n=2}^{\infty} \tilde{B}_n \,x^n</math>

Revision as of 00:33, 12 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 where is the Boltzmman constant and 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. A recent study showed that this model can be used as a reference system for fluid-phase free-energy calculations [2].


Functional form

The Uhlenbeck-Ford model is given by :

where

  • is a scaling factor;
  • is the well depth (energy);
  • is the interparticle distance;
  • is a length-scale parameter.

Equation of state

The UFM's equation of state using virial expansion has recently been studied by Paula Leite, Freitas, Azevedo and de Koning [2]. This equation of state is given by

where

  • is a constant;
  • is an adimensional variable;
  • are reduced virial coefficients.

References

  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.]
  2. 2.0 2.1 >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)
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