Second Virial Coefficients for the Lennard-Jones (2n-n) Potential

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The Lennard–Jones interaction potential is defined as
, where
is the minimum,
is the distance at which the potential changes sign, and
is an exponent that defines the shape of the potential. The conventional Lennard–Jones potential uses
. In this Demonstration, you can control the exponent
to plot the second virial coefficient
, relative to the hard-sphere value
, as a function of the reduced temperature
. The value of the Boyle temperature
(at which
) is also calculated. You can control the temperature range
of the plot in units of the Boyle temperature.
Contributed by: Andrés Santos (March 2012)
Open content licensed under CC BY-NC-SA
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The classical second virial coefficient of a gas of particles interacting via a potential is
. In the particular case of the Lennard–Jones
potential
, it is possible to prove that
. Here,
, where
is the second virial coefficient of a gas of hard spheres of diameter
,
is the reduced temperature, and
is a parabolic cylinder function.
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