Radial Distribution Function for Sticky Hard Rods

This Demonstration shows the exact statistical-mechanical radial distribution function of a one-dimensional system of so-called sticky hard rods (see the Details section). The Demonstration also presents the values of the ratio (where is the inverse temperature, is the pressure, and is the number density), the scaled inverse isothermal compressibility , and the excess internal energy per particle . The sliders let you control the maximum distance in the plot of , the packing fraction, and the stickiness parameter. Zero stickiness corresponds to the case of simple hard rods.


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Assume a one-dimensional fluid of particles interacting with an impenetrable hard core of length plus an attractive square-well potential of depth and width . The sticky-hard-rod system is defined by the limits , with "stickiness" a constant . In the Demonstration the small (but finite) value is assumed.
For the exact solution of the sticky-hard-rod problem, see [1] or [2].
[1] N. A. Seaton and E. D. Glandt, "Monte Carlo Simulation of Adhesive Disks," Journal of Chemical Physics, 84(8), 1986 pp. 4595–4602.
[2] S. B. Yuste and A. Santos, "Radial Distribution Function for Sticky Hard-Core Fluids," Journal of Statistical Physics 72(3–4), 1993 pp. 703–720.
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