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

General

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The Lennard–Jones

(2n-n)

interaction potential is defined as

ϕ(r)=4ϵ

2n

σ

r

-

n

σ

r



, where

-ϵ

is the minimum,

σ

is the distance at which the potential changes sign, and

n

is an exponent that defines the shape of the potential. The conventional Lennard–Jones potential uses

n=6

. In this Demonstration, you can control the exponent

n

to plot the second virial coefficient

B

2

(T)

, relative to the hard-sphere value

HS

B

2

=

2

3

π

3

σ

, as a function of the reduced temperature

k

B

T/ϵ

. The value of the Boyle temperature

T

Boyle

(at which

B

2

=0

) is also calculated. You can control the temperature range

T

max

of the plot in units of the Boyle temperature.