Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 PercusYevickRDF

Source Notebook

Evaluate the radial distribution function for a fluid of hard spheres

Contributed by: Andrés Santos

ResourceFunction["PercusYevickRDF"][e,r]

gives the radial distribution function for a fluid of hard spheres at packing fraction e and distance r.

Details

ResourceFunction["PercusYevickRDF"] uses the exact solution of the Percus-Yevick integral equation to evaluate the radial distribution function.
All arguments must be numeric.
The distance r is taken to be in units of the sphere diameter. Only distances up to 5 are supported.

Examples

Basic Examples (2) 

Value at contact:

In[1]:=
ResourceFunction["PercusYevickRDF"][0.3, 1]
Out[1]=

Value at r=1.5:

In[2]:=
ResourceFunction["PercusYevickRDF"][0.3, 1.5]
Out[2]=

Applications (1) 

Plot the radial distribution function:

In[3]:=
Plot[ResourceFunction["PercusYevickRDF"][.5, r], {r, 0, 5}, PlotRange -> All, Frame -> True]
Out[3]=

Publisher

Andres Santos

Version History

  • 1.0.0 – 05 July 2022

Source Metadata

  • Citation:
    • Wertheim, M. S., "Exact Solution of the Percus–Yevick Integral Equation for Hard Spheres." Physical Review Letters, vol. 10, no. 8, 321–323, 1963. DOI: 10.1103/PhysRevLett.10.321.
    • Thiele, E., "Equation of State for Hard Spheres." The Journal of Chemical Physics, vol. 39, no. 2, 474–479, 1963. DOI: 10.1063/1.1734272.

Related Resources

Author Notes

The function does not provide correct results beyond r=5.

License Information