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

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

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 function and the structure factor [2] for a one-dimensional system of particles interacting via square-well and square-shoulder potentials [3, 4]. We also find 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 . Sliders let you control the width of the square well or shoulder, the reduced temperature, and the packing fraction. The quantities and are also plotted as functions of the packing fraction.

g(r)

S(k)

βP/ρ

β=1/kT

P

ρ

β∂P/∂ρ

u/ϵ

ex

βP/ρ

u/ϵ

ex