Radial Distribution Functions for Nonadditive Hard-Rod Mixtures

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In statistical mechanics, the radial distribution function represents the distribution of interparticle separations [1]. This Demonstration shows the results of exact statistical-mechanical computations of the radial distribution functions for a one-dimensional binary system of particles interacting via hard-rod potentials [2, 3].

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The interactions between two particles of component 1 or two particles of component 2 are characterized by the lengths or , respectively, while the interaction between one particle of each component is characterized by the length . If , the mixture is said to be additive, otherwise, nonadditive. In the latter case, the nonadditivity can be either positive, , or negative, . We also find the values of the ratio and plot them, where , the inverse temperature; is the pressure; and is the number density. Sliders let you control the size and distance ratios and , the concentration (or mole fraction) of component 1, , and the total packing fraction .

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Contributed by: Andrés Santos (June 2015)
Open content licensed under CC BY-NC-SA


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References

[1] Wikipedia. "Radial Distribution Function." (Jun 8, 2015) en.wikipedia.org/wiki/Radial_distribution_function.

[2] 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.

[3] A. Santos, "Exact Bulk Correlation Functions in One-Dimensional Nonadditive Hard-Core Mixtures," Physical Review E, 76(6), 2007 062201. doi:10.1103/PhysRevE.76.062201.



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