# Radial Distribution Function for One-Dimensional Square-Well and Square-Shoulder Fluids

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In statistical mechanics, the radial distribution function represents the distribution of interparticle separations [1].

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Contributed by: Andrés Santos (April 2015)

Open content licensed under CC BY-NC-SA

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## Details

In this one-dimensional system, the particles interact with an impenetrable hard core of length plus either an attractive square-well or a repulsive square-shoulder potential of energy and width . This can be represented by a pairwise potential-energy function . The exact solution for the radial distribution function is worked out in references [3] and [4]. As a very rudimentary approximation, . The structure factor is given by .

References

[1] Wikipedia. "Radial Distribution Function." (Apr 10, 2015) en.wikipedia.org/wiki/Radial_distribution_function.

[2] Wikipedia. "Structure Factor." (Apr 10, 2015) en.wikipedia.org/wiki/Structure_factor.

[3] Z. W. Salsburg, R. W. Zwanzig, and J. G. Kirkwood, "Molecular Distribution Functions in a One-Dimensional Fluid," *The Journal of Chemical Physics*, 21(6), 1953 pp. 1098–1107. doi:10.1063/1.1699116.

[4] S. B. Yuste and A. Santos, "A Model for the Structure of Square-Well Fluids," *The Journal of Statistical Physics,* 101(3), 1994 pp. 2355–2364. doi:10.1063/1.467676.

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