WOLFRAM NOTEBOOK

WOLFRAM|DEMONSTRATIONS PROJECT

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

​
interaction potential
square well
square shoulder
square (shoulder) width
0.5
temperature
1
packing fraction
0.3
function
g(r)
S(k)
β P
ρ
u
ex
ϵ
β P
ρ
= 1.149
β
∂P
∂ρ
= 1.422
u
ex
ϵ
= -0.338
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
g(r)
and the structure factor
S(k)
[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
βP/ρ
(where
β=1/kT
is the inverse temperature,
P
is the pressure, and
ρ
is the number density), the scaled inverse isothermal compressibility
β∂P/∂ρ
, and the excess internal energy per particle
u
ex
/ϵ
. Sliders let you control the width of the square well or shoulder, the reduced temperature, and the packing fraction. The quantities
βP/ρ
and
u
ex
/ϵ
are also plotted as functions of the packing fraction.
Wolfram Cloud

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.


I understand and wish to continue anyway »

You are using a browser not supported by the Wolfram Cloud. Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.